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| author | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
|---|---|---|
| committer | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
| commit | e1d39294aee16fa6db9ba079b14442358217db71 (patch) | |
| tree | 30e5aa04c1f6596991fda5334f63dfb9b8027849 /TESTING/MATGEN | |
| parent | 5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff) | |
Integrating Doxygen in comments
Diffstat (limited to 'TESTING/MATGEN')
74 files changed, 14958 insertions, 9080 deletions
diff --git a/TESTING/MATGEN/clagge.f b/TESTING/MATGEN/clagge.f index 7ba73df8..36222571 100644 --- a/TESTING/MATGEN/clagge.f +++ b/TESTING/MATGEN/clagge.f @@ -1,63 +1,134 @@ - SUBROUTINE CLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) -* -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER INFO, KL, KU, LDA, M, N -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) - REAL D( * ) - COMPLEX A( LDA, * ), WORK( * ) -* .. -* +*> \brief \b CLAGGE +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, KL, KU, LDA, M, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* REAL D( * ) +* COMPLEX A( LDA, * ), WORK( * ) +* .. +* * Purpose * ======= * -* CLAGGE generates a complex general m by n matrix A, by pre- and post- -* multiplying a real diagonal matrix D with random unitary matrices: -* A = U*D*V. The lower and upper bandwidths may then be reduced to -* kl and ku by additional unitary transformations. +*>\details \b Purpose: +*>\verbatim +*> +*> CLAGGE generates a complex general m by n matrix A, by pre- and post- +*> multiplying a real diagonal matrix D with random unitary matrices: +*> A = U*D*V. The lower and upper bandwidths may then be reduced to +*> kl and ku by additional unitary transformations. +*> +*>\endverbatim * * Arguments * ========= * -* M (input) INTEGER -* The number of rows of the matrix A. M >= 0. -* -* N (input) INTEGER -* The number of columns of the matrix A. N >= 0. -* -* KL (input) INTEGER -* The number of nonzero subdiagonals within the band of A. -* 0 <= KL <= M-1. -* -* KU (input) INTEGER -* The number of nonzero superdiagonals within the band of A. -* 0 <= KU <= N-1. +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> The number of nonzero subdiagonals within the band of A. +*> 0 <= KL <= M-1. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> The number of nonzero superdiagonals within the band of A. +*> 0 <= KU <= N-1. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is REAL array, dimension (min(M,N)) +*> The diagonal elements of the diagonal matrix D. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is COMPLEX array, dimension (LDA,N) +*> The generated m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= M. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX array, dimension (M+N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= * -* D (input) REAL array, dimension (min(M,N)) -* The diagonal elements of the diagonal matrix D. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (output) COMPLEX array, dimension (LDA,N) -* The generated m by n matrix A. +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= M. +*> \ingroup complex_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. +* ===================================================================== + SUBROUTINE CLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) * -* WORK (workspace) COMPLEX array, dimension (M+N) +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value +* .. Scalar Arguments .. + INTEGER INFO, KL, KU, LDA, M, N +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) + REAL D( * ) + COMPLEX A( LDA, * ), WORK( * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/claghe.f b/TESTING/MATGEN/claghe.f index f9e4a03d..6cee2d60 100644 --- a/TESTING/MATGEN/claghe.f +++ b/TESTING/MATGEN/claghe.f @@ -1,57 +1,122 @@ - SUBROUTINE CLAGHE( N, K, D, A, LDA, ISEED, WORK, INFO ) -* -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, N -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) - REAL D( * ) - COMPLEX A( LDA, * ), WORK( * ) -* .. -* +*> \brief \b CLAGHE +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CLAGHE( N, K, D, A, LDA, ISEED, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, K, LDA, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* REAL D( * ) +* COMPLEX A( LDA, * ), WORK( * ) +* .. +* * Purpose * ======= * -* CLAGHE generates a complex hermitian matrix A, by pre- and post- -* multiplying a real diagonal matrix D with a random unitary matrix: -* A = U*D*U'. The semi-bandwidth may then be reduced to k by additional -* unitary transformations. +*>\details \b Purpose: +*>\verbatim +*> +*> CLAGHE generates a complex hermitian matrix A, by pre- and post- +*> multiplying a real diagonal matrix D with a random unitary matrix: +*> A = U*D*U'. The semi-bandwidth may then be reduced to k by additional +*> unitary transformations. +*> +*>\endverbatim * * Arguments * ========= * -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* K (input) INTEGER -* The number of nonzero subdiagonals within the band of A. -* 0 <= K <= N-1. +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The number of nonzero subdiagonals within the band of A. +*> 0 <= K <= N-1. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is REAL array, dimension (N) +*> The diagonal elements of the diagonal matrix D. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is COMPLEX array, dimension (LDA,N) +*> The generated n by n hermitian matrix A (the full matrix is +*> stored). +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= N. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX array, dimension (2*N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= * -* D (input) REAL array, dimension (N) -* The diagonal elements of the diagonal matrix D. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (output) COMPLEX array, dimension (LDA,N) -* The generated n by n hermitian matrix A (the full matrix is -* stored). +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= N. +*> \ingroup complex_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. +* ===================================================================== + SUBROUTINE CLAGHE( N, K, D, A, LDA, ISEED, WORK, INFO ) * -* WORK (workspace) COMPLEX array, dimension (2*N) +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value +* .. Scalar Arguments .. + INTEGER INFO, K, LDA, N +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) + REAL D( * ) + COMPLEX A( LDA, * ), WORK( * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/clagsy.f b/TESTING/MATGEN/clagsy.f index 8b356c94..afa1d80c 100644 --- a/TESTING/MATGEN/clagsy.f +++ b/TESTING/MATGEN/clagsy.f @@ -1,57 +1,122 @@ - SUBROUTINE CLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO ) -* -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, N -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) - REAL D( * ) - COMPLEX A( LDA, * ), WORK( * ) -* .. -* +*> \brief \b CLAGSY +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, K, LDA, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* REAL D( * ) +* COMPLEX A( LDA, * ), WORK( * ) +* .. +* * Purpose * ======= * -* CLAGSY generates a complex symmetric matrix A, by pre- and post- -* multiplying a real diagonal matrix D with a random unitary matrix: -* A = U*D*U**T. The semi-bandwidth may then be reduced to k by -* additional unitary transformations. +*>\details \b Purpose: +*>\verbatim +*> +*> CLAGSY generates a complex symmetric matrix A, by pre- and post- +*> multiplying a real diagonal matrix D with a random unitary matrix: +*> A = U*D*U**T. The semi-bandwidth may then be reduced to k by +*> additional unitary transformations. +*> +*>\endverbatim * * Arguments * ========= * -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* K (input) INTEGER -* The number of nonzero subdiagonals within the band of A. -* 0 <= K <= N-1. +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The number of nonzero subdiagonals within the band of A. +*> 0 <= K <= N-1. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is REAL array, dimension (N) +*> The diagonal elements of the diagonal matrix D. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is COMPLEX array, dimension (LDA,N) +*> The generated n by n symmetric matrix A (the full matrix is +*> stored). +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= N. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX array, dimension (2*N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= * -* D (input) REAL array, dimension (N) -* The diagonal elements of the diagonal matrix D. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (output) COMPLEX array, dimension (LDA,N) -* The generated n by n symmetric matrix A (the full matrix is -* stored). +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= N. +*> \ingroup complex_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. +* ===================================================================== + SUBROUTINE CLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO ) * -* WORK (workspace) COMPLEX array, dimension (2*N) +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value +* .. Scalar Arguments .. + INTEGER INFO, K, LDA, N +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) + REAL D( * ) + COMPLEX A( LDA, * ), WORK( * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/clahilb.f b/TESTING/MATGEN/clahilb.f index 174fd513..4c04f0a9 100644 --- a/TESTING/MATGEN/clahilb.f +++ b/TESTING/MATGEN/clahilb.f @@ -1,104 +1,167 @@ +*> \brief \b CLAHILB +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CLAHILB( N, NRHS, A, LDA, X, LDX, B, LDB, WORK, +* INFO, PATH) +* +* .. Scalar Arguments .. +* INTEGER N, NRHS, LDA, LDX, LDB, INFO +* .. Array Arguments .. +* REAL WORK(N) +* COMPLEX A(LDA,N), X(LDX, NRHS), B(LDB, NRHS) +* CHARACTER*3 PATH +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> CLAHILB generates an N by N scaled Hilbert matrix in A along with +*> NRHS right-hand sides in B and solutions in X such that A*X=B. +*> +*> The Hilbert matrix is scaled by M = LCM(1, 2, ..., 2*N-1) so that all +*> entries are integers. The right-hand sides are the first NRHS +*> columns of M * the identity matrix, and the solutions are the +*> first NRHS columns of the inverse Hilbert matrix. +*> +*> The condition number of the Hilbert matrix grows exponentially with +*> its size, roughly as O(e ** (3.5*N)). Additionally, the inverse +*> Hilbert matrices beyond a relatively small dimension cannot be +*> generated exactly without extra precision. Precision is exhausted +*> when the largest entry in the inverse Hilbert matrix is greater than +*> 2 to the power of the number of bits in the fraction of the data type +*> used plus one, which is 24 for single precision. +*> +*> In single, the generated solution is exact for N <= 6 and has +*> small componentwise error for 7 <= N <= 11. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The dimension of the matrix A. +*> \endverbatim +*> +*> \param[in] NRHS +*> \verbatim +*> NRHS is INTEGER +*> The requested number of right-hand sides. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is COMPLEX array, dimension (LDA, N) +*> The generated scaled Hilbert matrix. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= N. +*> \endverbatim +*> +*> \param[out] X +*> \verbatim +*> X is COMPLEX array, dimension (LDX, NRHS) +*> The generated exact solutions. Currently, the first NRHS +*> columns of the inverse Hilbert matrix. +*> \endverbatim +*> +*> \param[in] LDX +*> \verbatim +*> LDX is INTEGER +*> The leading dimension of the array X. LDX >= N. +*> \endverbatim +*> +*> \param[out] B +*> \verbatim +*> B is REAL array, dimension (LDB, NRHS) +*> The generated right-hand sides. Currently, the first NRHS +*> columns of LCM(1, 2, ..., 2*N-1) * the identity matrix. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of the array B. LDB >= N. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is REAL array, dimension (N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> = 1: N is too large; the data is still generated but may not +*> be not exact. +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_matgen +* +* ===================================================================== SUBROUTINE CLAHILB( N, NRHS, A, LDA, X, LDX, B, LDB, WORK, $ INFO, PATH) -! -! -- LAPACK auxiliary test routine (version 3.2.2) -- -! Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., -! Courant Institute, Argonne National Lab, and Rice University -* June 2010 -! -! David Vu <dtv@cs.berkeley.edu> -! Yozo Hida <yozo@cs.berkeley.edu> -! Jason Riedy <ejr@cs.berkeley.edu> -! D. Halligan <dhalligan@berkeley.edu> -! - IMPLICIT NONE -! .. Scalar Arguments .. +* +* -- LAPACK auxiliary routine (version 3.2.2) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. INTEGER N, NRHS, LDA, LDX, LDB, INFO -! .. Array Arguments .. +* .. Array Arguments .. REAL WORK(N) COMPLEX A(LDA,N), X(LDX, NRHS), B(LDB, NRHS) CHARACTER*3 PATH -! .. -! -! Purpose -! ======= -! -! CLAHILB generates an N by N scaled Hilbert matrix in A along with -! NRHS right-hand sides in B and solutions in X such that A*X=B. -! -! The Hilbert matrix is scaled by M = LCM(1, 2, ..., 2*N-1) so that all -! entries are integers. The right-hand sides are the first NRHS -! columns of M * the identity matrix, and the solutions are the -! first NRHS columns of the inverse Hilbert matrix. -! -! The condition number of the Hilbert matrix grows exponentially with -! its size, roughly as O(e ** (3.5*N)). Additionally, the inverse -! Hilbert matrices beyond a relatively small dimension cannot be -! generated exactly without extra precision. Precision is exhausted -! when the largest entry in the inverse Hilbert matrix is greater than -! 2 to the power of the number of bits in the fraction of the data type -! used plus one, which is 24 for single precision. -! -! In single, the generated solution is exact for N <= 6 and has -! small componentwise error for 7 <= N <= 11. -! -! Arguments -! ========= -! -! N (input) INTEGER -! The dimension of the matrix A. -! -! NRHS (input) INTEGER -! The requested number of right-hand sides. -! -! A (output) COMPLEX array, dimension (LDA, N) -! The generated scaled Hilbert matrix. -! -! LDA (input) INTEGER -! The leading dimension of the array A. LDA >= N. -! -! X (output) COMPLEX array, dimension (LDX, NRHS) -! The generated exact solutions. Currently, the first NRHS -! columns of the inverse Hilbert matrix. -! -! LDX (input) INTEGER -! The leading dimension of the array X. LDX >= N. -! -! B (output) REAL array, dimension (LDB, NRHS) -! The generated right-hand sides. Currently, the first NRHS -! columns of LCM(1, 2, ..., 2*N-1) * the identity matrix. -! -! LDB (input) INTEGER -! The leading dimension of the array B. LDB >= N. -! -! WORK (workspace) REAL array, dimension (N) -! -! -! INFO (output) INTEGER -! = 0: successful exit -! = 1: N is too large; the data is still generated but may not -! be not exact. -! < 0: if INFO = -i, the i-th argument had an illegal value -! -! ===================================================================== +* .. +* +* ===================================================================== -! .. Local Scalars .. +* .. Local Scalars .. INTEGER TM, TI, R INTEGER M INTEGER I, J COMPLEX TMP CHARACTER*2 C2 -! .. Parameters .. -! NMAX_EXACT the largest dimension where the generated data is -! exact. -! NMAX_APPROX the largest dimension where the generated data has -! a small componentwise relative error. -! ??? complex uses how many bits ??? +* .. Parameters .. +* NMAX_EXACT the largest dimension where the generated data is +* exact. +* NMAX_APPROX the largest dimension where the generated data has +* a small componentwise relative error. +* ??? complex uses how many bits ??? INTEGER NMAX_EXACT, NMAX_APPROX, SIZE_D PARAMETER (NMAX_EXACT = 6, NMAX_APPROX = 11, SIZE_D = 8) -! d's are generated from random permuation of those eight elements. +* d's are generated from random permuation of those eight elements. COMPLEX D1(8), D2(8), INVD1(8), INVD2(8) DATA D1 /(-1,0),(0,1),(-1,-1),(0,-1),(1,0),(-1,1),(1,1),(1,-1)/ DATA D2 /(-1,0),(0,-1),(-1,1),(0,1),(1,0),(-1,-1),(1,-1),(1,1)/ @@ -108,17 +171,17 @@ DATA INVD2 /(-1,0),(0,1),(-.5,-.5),(0,-1),(1,0), $ (-.5,.5),(.5,.5),(.5,-.5)/ -! .. -! .. External Functions +* .. +* .. External Functions EXTERNAL CLASET, LSAMEN INTRINSIC REAL LOGICAL LSAMEN -! .. -! .. Executable Statements .. +* .. +* .. Executable Statements .. C2 = PATH( 2: 3 ) -! -! Test the input arguments -! +* +* Test the input arguments +* INFO = 0 IF (N .LT. 0 .OR. N .GT. NMAX_APPROX) THEN INFO = -1 @@ -139,8 +202,8 @@ INFO = 1 END IF -! Compute M = the LCM of the integers [1, 2*N-1]. The largest -! reasonable N is small enough that integers suffice (up to N = 11). +* Compute M = the LCM of the integers [1, 2*N-1]. The largest +* reasonable N is small enough that integers suffice (up to N = 11). M = 1 DO I = 2, (2*N-1) TM = M @@ -154,9 +217,9 @@ M = (M / TI) * I END DO -! Generate the scaled Hilbert matrix in A -! If we are testing SY routines, take -! D1_i = D2_i, else, D1_i = D2_i* +* Generate the scaled Hilbert matrix in A +* If we are testing SY routines, take +* D1_i = D2_i, else, D1_i = D2_i* IF ( LSAMEN( 2, C2, 'SY' ) ) THEN DO J = 1, N DO I = 1, N @@ -173,22 +236,22 @@ END DO END IF -! Generate matrix B as simply the first NRHS columns of M * the -! identity. +* Generate matrix B as simply the first NRHS columns of M * the +* identity. TMP = REAL(M) CALL CLASET('Full', N, NRHS, (0.0,0.0), TMP, B, LDB) -! Generate the true solutions in X. Because B = the first NRHS -! columns of M*I, the true solutions are just the first NRHS columns -! of the inverse Hilbert matrix. +* Generate the true solutions in X. Because B = the first NRHS +* columns of M*I, the true solutions are just the first NRHS columns +* of the inverse Hilbert matrix. WORK(1) = N DO J = 2, N WORK(J) = ( ( (WORK(J-1)/(J-1)) * (J-1 - N) ) /(J-1) ) $ * (N +J -1) END DO -! If we are testing SY routines, -! take D1_i = D2_i, else, D1_i = D2_i* +* If we are testing SY routines, +* take D1_i = D2_i, else, D1_i = D2_i* IF ( LSAMEN( 2, C2, 'SY' ) ) THEN DO J = 1, NRHS DO I = 1, N diff --git a/TESTING/MATGEN/clakf2.f b/TESTING/MATGEN/clakf2.f index 6f401b04..09553ecb 100644 --- a/TESTING/MATGEN/clakf2.f +++ b/TESTING/MATGEN/clakf2.f @@ -1,54 +1,125 @@ - SUBROUTINE CLAKF2( M, N, A, LDA, B, D, E, Z, LDZ ) -* -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER LDA, LDZ, M, N -* .. -* .. Array Arguments .. - COMPLEX A( LDA, * ), B( LDA, * ), D( LDA, * ), - $ E( LDA, * ), Z( LDZ, * ) -* .. -* +*> \brief \b CLAKF2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CLAKF2( M, N, A, LDA, B, D, E, Z, LDZ ) +* +* .. Scalar Arguments .. +* INTEGER LDA, LDZ, M, N +* .. +* .. Array Arguments .. +* COMPLEX A( LDA, * ), B( LDA, * ), D( LDA, * ), +* $ E( LDA, * ), Z( LDZ, * ) +* .. +* * Purpose * ======= * -* Form the 2*M*N by 2*M*N matrix -* -* Z = [ kron(In, A) -kron(B', Im) ] -* [ kron(In, D) -kron(E', Im) ], -* -* where In is the identity matrix of size n and X' is the transpose -* of X. kron(X, Y) is the Kronecker product between the matrices X -* and Y. +*>\details \b Purpose: +*>\verbatim +*> +*> Form the 2*M*N by 2*M*N matrix +*> +*> Z = [ kron(In, A) -kron(B', Im) ] +*> [ kron(In, D) -kron(E', Im) ], +*> +*> where In is the identity matrix of size n and X' is the transpose +*> of X. kron(X, Y) is the Kronecker product between the matrices X +*> and Y. +*> +*>\endverbatim * * Arguments * ========= * -* M (input) INTEGER -* Size of matrix, must be >= 1. +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Size of matrix, must be >= 1. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Size of matrix, must be >= 1. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX, dimension ( LDA, M ) +*> The matrix A in the output matrix Z. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of A, B, D, and E. ( LDA >= M+N ) +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is COMPLEX, dimension ( LDA, N ) +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is COMPLEX, dimension ( LDA, M ) +*> \endverbatim +*> +*> \param[in] E +*> \verbatim +*> E is COMPLEX, dimension ( LDA, N ) +*> \endverbatim +*> \verbatim +*> The matrices used in forming the output matrix Z. +*> \endverbatim +*> +*> \param[out] Z +*> \verbatim +*> Z is COMPLEX, dimension ( LDZ, 2*M*N ) +*> The resultant Kronecker M*N*2 by M*N*2 matrix (see above.) +*> \endverbatim +*> +*> \param[in] LDZ +*> \verbatim +*> LDZ is INTEGER +*> The leading dimension of Z. ( LDZ >= 2*M*N ) +*> \endverbatim +*> +* +* Authors +* ======= * -* N (input) INTEGER -* Size of matrix, must be >= 1. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (input) COMPLEX, dimension ( LDA, M ) -* The matrix A in the output matrix Z. +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of A, B, D, and E. ( LDA >= M+N ) +*> \ingroup complex_matgen * -* B (input) COMPLEX, dimension ( LDA, N ) -* D (input) COMPLEX, dimension ( LDA, M ) -* E (input) COMPLEX, dimension ( LDA, N ) -* The matrices used in forming the output matrix Z. +* ===================================================================== + SUBROUTINE CLAKF2( M, N, A, LDA, B, D, E, Z, LDZ ) * -* Z (output) COMPLEX, dimension ( LDZ, 2*M*N ) -* The resultant Kronecker M*N*2 by M*N*2 matrix (see above.) +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* LDZ (input) INTEGER -* The leading dimension of Z. ( LDZ >= 2*M*N ) +* .. Scalar Arguments .. + INTEGER LDA, LDZ, M, N +* .. +* .. Array Arguments .. + COMPLEX A( LDA, * ), B( LDA, * ), D( LDA, * ), + $ E( LDA, * ), Z( LDZ, * ) +* .. * * ==================================================================== * diff --git a/TESTING/MATGEN/clarge.f b/TESTING/MATGEN/clarge.f index f44a64c8..93b9ee8a 100644 --- a/TESTING/MATGEN/clarge.f +++ b/TESTING/MATGEN/clarge.f @@ -1,48 +1,106 @@ - SUBROUTINE CLARGE( N, A, LDA, ISEED, WORK, INFO ) -* -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) - COMPLEX A( LDA, * ), WORK( * ) -* .. -* +*> \brief \b CLARGE +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CLARGE( N, A, LDA, ISEED, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* COMPLEX A( LDA, * ), WORK( * ) +* .. +* * Purpose * ======= * -* CLARGE pre- and post-multiplies a complex general n by n matrix A -* with a random unitary matrix: A = U*D*U'. +*>\details \b Purpose: +*>\verbatim +*> +*> CLARGE pre- and post-multiplies a complex general n by n matrix A +*> with a random unitary matrix: A = U*D*U'. +*> +*>\endverbatim * * Arguments * ========= * -* N (input) INTEGER -* The order of the matrix A. N >= 0. +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX array, dimension (LDA,N) +*> On entry, the original n by n matrix A. +*> On exit, A is overwritten by U*A*U' for some random +*> unitary matrix U. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= N. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX array, dimension (2*N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (input/output) COMPLEX array, dimension (LDA,N) -* On entry, the original n by n matrix A. -* On exit, A is overwritten by U*A*U' for some random -* unitary matrix U. +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= N. +*> \ingroup complex_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. +* ===================================================================== + SUBROUTINE CLARGE( N, A, LDA, ISEED, WORK, INFO ) * -* WORK (workspace) COMPLEX array, dimension (2*N) +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value +* .. Scalar Arguments .. + INTEGER INFO, LDA, N +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) + COMPLEX A( LDA, * ), WORK( * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/clarnd.f b/TESTING/MATGEN/clarnd.f index ac8117ba..46fa07ac 100644 --- a/TESTING/MATGEN/clarnd.f +++ b/TESTING/MATGEN/clarnd.f @@ -1,45 +1,95 @@ - COMPLEX FUNCTION CLARND( IDIST, ISEED ) +*> \brief \b CLARND * -* -- LAPACK auxiliary routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 +* =========== DOCUMENTATION =========== * -* .. Scalar Arguments .. - INTEGER IDIST -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) -* .. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* COMPLEX FUNCTION CLARND( IDIST, ISEED ) +* +* .. Scalar Arguments .. +* INTEGER IDIST +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* .. +* * Purpose * ======= * -* CLARND returns a random complex number from a uniform or normal -* distribution. +*>\details \b Purpose: +*>\verbatim +*> +*> CLARND returns a random complex number from a uniform or normal +*> distribution. +*> +*>\endverbatim * * Arguments * ========= * -* IDIST (input) INTEGER -* Specifies the distribution of the random numbers: -* = 1: real and imaginary parts each uniform (0,1) -* = 2: real and imaginary parts each uniform (-1,1) -* = 3: real and imaginary parts each normal (0,1) -* = 4: uniformly distributed on the disc abs(z) <= 1 -* = 5: uniformly distributed on the circle abs(z) = 1 +*> \param[in] IDIST +*> \verbatim +*> IDIST is INTEGER +*> Specifies the distribution of the random numbers: +*> = 1: real and imaginary parts each uniform (0,1) +*> = 2: real and imaginary parts each uniform (-1,1) +*> = 3: real and imaginary parts each normal (0,1) +*> = 4: uniformly distributed on the disc abs(z) <= 1 +*> = 5: uniformly distributed on the circle abs(z) = 1 +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> This routine calls the auxiliary routine SLARAN to generate a random +*> real number from a uniform (0,1) distribution. The Box-Muller method +*> is used to transform numbers from a uniform to a normal distribution. +*> +*> \endverbatim +*> +* ===================================================================== + COMPLEX FUNCTION CLARND( IDIST, ISEED ) * -* This routine calls the auxiliary routine SLARAN to generate a random -* real number from a uniform (0,1) distribution. The Box-Muller method -* is used to transform numbers from a uniform to a normal distribution. +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER IDIST +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/claror.f b/TESTING/MATGEN/claror.f index d1d04d26..495976db 100644 --- a/TESTING/MATGEN/claror.f +++ b/TESTING/MATGEN/claror.f @@ -1,8 +1,172 @@ +*> \brief \b CLAROR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CLAROR( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER INIT, SIDE +* INTEGER INFO, LDA, M, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* COMPLEX A( LDA, * ), X( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> CLAROR pre- or post-multiplies an M by N matrix A by a random +*> unitary matrix U, overwriting A. A may optionally be +*> initialized to the identity matrix before multiplying by U. +*> U is generated using the method of G.W. Stewart +*> ( SIAM J. Numer. Anal. 17, 1980, pp. 403-409 ). +*> (BLAS-2 version) +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> SIDE specifies whether A is multiplied on the left or right +*> by U. +*> SIDE = 'L' Multiply A on the left (premultiply) by U +*> SIDE = 'R' Multiply A on the right (postmultiply) by UC> SIDE = 'C' Multiply A on the left by U and the right by UC> SIDE = 'T' Multiply A on the left by U and the right by U' +*> Not modified. +*> \endverbatim +*> +*> \param[in] INIT +*> \verbatim +*> INIT is CHARACTER*1 +*> INIT specifies whether or not A should be initialized to +*> the identity matrix. +*> INIT = 'I' Initialize A to (a section of) the +*> identity matrix before applying U. +*> INIT = 'N' No initialization. Apply U to the +*> input matrix A. +*> \endverbatim +*> \verbatim +*> INIT = 'I' may be used to generate square (i.e., unitary) +*> or rectangular orthogonal matrices (orthogonality being +*> in the sense of CDOTC): +*> \endverbatim +*> \verbatim +*> For square matrices, M=N, and SIDE many be either 'L' or +*> 'R'; the rows will be orthogonal to each other, as will the +*> columns. +*> For rectangular matrices where M < N, SIDE = 'R' will +*> produce a dense matrix whose rows will be orthogonal and +*> whose columns will not, while SIDE = 'L' will produce a +*> matrix whose rows will be orthogonal, and whose first M +*> columns will be orthogonal, the remaining columns being +*> zero. +*> For matrices where M > N, just use the previous +*> explaination, interchanging 'L' and 'R' and "rows" and +*> "columns". +*> \endverbatim +*> \verbatim +*> Not modified. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Number of rows of A. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of columns of A. Not modified. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX array, dimension ( LDA, N ) +*> Input and output array. Overwritten by U A ( if SIDE = 'L' ) +*> or by A U ( if SIDE = 'R' ) +*> or by U A U* ( if SIDE = 'C') +*> or by U A U' ( if SIDE = 'T') on exit. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> Leading dimension of A. Must be at least MAX ( 1, M ). +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. The array elements should be between 0 and 4095; +*> if not they will be reduced mod 4096. Also, ISEED(4) must +*> be odd. The random number generator uses a linear +*> congruential sequence limited to small integers, and so +*> should produce machine independent random numbers. The +*> values of ISEED are changed on exit, and can be used in the +*> next call to CLAROR to continue the same random number +*> sequence. +*> Modified. +*> \endverbatim +*> +*> \param[out] X +*> \verbatim +*> X is COMPLEX array, dimension ( 3*MAX( M, N ) ) +*> Workspace. Of length: +*> 2*M + N if SIDE = 'L', +*> 2*N + M if SIDE = 'R', +*> 3*N if SIDE = 'C' or 'T'. +*> Modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> An error flag. It is set to: +*> 0 if no error. +*> 1 if CLARND returned a bad random number (installation +*> problem) +*> -1 if SIDE is not L, R, C, or T. +*> -3 if M is negative. +*> -4 if N is negative or if SIDE is C or T and N is not equal +*> to M. +*> -6 if LDA is less than M. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_matgen +* +* ===================================================================== SUBROUTINE CLAROR( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER INIT, SIDE @@ -13,101 +177,6 @@ COMPLEX A( LDA, * ), X( * ) * .. * -* Purpose -* ======= -* -* CLAROR pre- or post-multiplies an M by N matrix A by a random -* unitary matrix U, overwriting A. A may optionally be -* initialized to the identity matrix before multiplying by U. -* U is generated using the method of G.W. Stewart -* ( SIAM J. Numer. Anal. 17, 1980, pp. 403-409 ). -* (BLAS-2 version) -* -* Arguments -* ========= -* -* SIDE (input) CHARACTER*1 -* SIDE specifies whether A is multiplied on the left or right -* by U. -* SIDE = 'L' Multiply A on the left (premultiply) by U -* SIDE = 'R' Multiply A on the right (postmultiply) by U* -* SIDE = 'C' Multiply A on the left by U and the right by U* -* SIDE = 'T' Multiply A on the left by U and the right by U' -* Not modified. -* -* INIT (input) CHARACTER*1 -* INIT specifies whether or not A should be initialized to -* the identity matrix. -* INIT = 'I' Initialize A to (a section of) the -* identity matrix before applying U. -* INIT = 'N' No initialization. Apply U to the -* input matrix A. -* -* INIT = 'I' may be used to generate square (i.e., unitary) -* or rectangular orthogonal matrices (orthogonality being -* in the sense of CDOTC): -* -* For square matrices, M=N, and SIDE many be either 'L' or -* 'R'; the rows will be orthogonal to each other, as will the -* columns. -* For rectangular matrices where M < N, SIDE = 'R' will -* produce a dense matrix whose rows will be orthogonal and -* whose columns will not, while SIDE = 'L' will produce a -* matrix whose rows will be orthogonal, and whose first M -* columns will be orthogonal, the remaining columns being -* zero. -* For matrices where M > N, just use the previous -* explaination, interchanging 'L' and 'R' and "rows" and -* "columns". -* -* Not modified. -* -* M (input) INTEGER -* Number of rows of A. Not modified. -* -* N (input) INTEGER -* Number of columns of A. Not modified. -* -* A (input/output) COMPLEX array, dimension ( LDA, N ) -* Input and output array. Overwritten by U A ( if SIDE = 'L' ) -* or by A U ( if SIDE = 'R' ) -* or by U A U* ( if SIDE = 'C') -* or by U A U' ( if SIDE = 'T') on exit. -* -* LDA (input) INTEGER -* Leading dimension of A. Must be at least MAX ( 1, M ). -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. The array elements should be between 0 and 4095; -* if not they will be reduced mod 4096. Also, ISEED(4) must -* be odd. The random number generator uses a linear -* congruential sequence limited to small integers, and so -* should produce machine independent random numbers. The -* values of ISEED are changed on exit, and can be used in the -* next call to CLAROR to continue the same random number -* sequence. -* Modified. -* -* X (workspace) COMPLEX array, dimension ( 3*MAX( M, N ) ) -* Workspace. Of length: -* 2*M + N if SIDE = 'L', -* 2*N + M if SIDE = 'R', -* 3*N if SIDE = 'C' or 'T'. -* Modified. -* -* INFO (output) INTEGER -* An error flag. It is set to: -* 0 if no error. -* 1 if CLARND returned a bad random number (installation -* problem) -* -1 if SIDE is not L, R, C, or T. -* -3 if M is negative. -* -4 if N is negative or if SIDE is C or T and N is not equal -* to M. -* -6 if LDA is less than M. -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/clarot.f b/TESTING/MATGEN/clarot.f index f73d10b4..0060bf6c 100644 --- a/TESTING/MATGEN/clarot.f +++ b/TESTING/MATGEN/clarot.f @@ -1,9 +1,248 @@ +*> \brief \b CLAROT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT, +* XRIGHT ) +* +* .. Scalar Arguments .. +* LOGICAL LLEFT, LRIGHT, LROWS +* INTEGER LDA, NL +* COMPLEX C, S, XLEFT, XRIGHT +* .. +* .. Array Arguments .. +* COMPLEX A( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> CLAROT applies a (Givens) rotation to two adjacent rows or +*> columns, where one element of the first and/or last column/row +*> for use on matrices stored in some format other than GE, so +*> that elements of the matrix may be used or modified for which +*> no array element is provided. +*> +*> One example is a symmetric matrix in SB format (bandwidth=4), for +*> which UPLO='L': Two adjacent rows will have the format: +*> +*> row j: C> C> C> C> C> . . . . +*> row j+1: C> C> C> C> C> . . . . +*> +*> '*' indicates elements for which storage is provided, +*> '.' indicates elements for which no storage is provided, but +*> are not necessarily zero; their values are determined by +*> symmetry. ' ' indicates elements which are necessarily zero, +*> and have no storage provided. +*> +*> Those columns which have two '*'s can be handled by SROT. +*> Those columns which have no '*'s can be ignored, since as long +*> as the Givens rotations are carefully applied to preserve +*> symmetry, their values are determined. +*> Those columns which have one '*' have to be handled separately, +*> by using separate variables "p" and "q": +*> +*> row j: C> C> C> C> C> p . . . +*> row j+1: q C> C> C> C> C> . . . . +*> +*> The element p would have to be set correctly, then that column +*> is rotated, setting p to its new value. The next call to +*> CLAROT would rotate columns j and j+1, using p, and restore +*> symmetry. The element q would start out being zero, and be +*> made non-zero by the rotation. Later, rotations would presumably +*> be chosen to zero q out. +*> +*> Typical Calling Sequences: rotating the i-th and (i+1)-st rows. +*> ------- ------- --------- +*> +*> General dense matrix: +*> +*> CALL CLAROT(.TRUE.,.FALSE.,.FALSE., N, C,S, +*> A(i,1),LDA, DUMMY, DUMMY) +*> +*> General banded matrix in GB format: +*> +*> j = MAX(1, i-KL ) +*> NL = MIN( N, i+KU+1 ) + 1-j +*> CALL CLAROT( .TRUE., i-KL.GE.1, i+KU.LT.N, NL, C,S, +*> A(KU+i+1-j,j),LDA-1, XLEFT, XRIGHT ) +*> +*> [ note that i+1-j is just MIN(i,KL+1) ] +*> +*> Symmetric banded matrix in SY format, bandwidth K, +*> lower triangle only: +*> +*> j = MAX(1, i-K ) +*> NL = MIN( K+1, i ) + 1 +*> CALL CLAROT( .TRUE., i-K.GE.1, .TRUE., NL, C,S, +*> A(i,j), LDA, XLEFT, XRIGHT ) +*> +*> Same, but upper triangle only: +*> +*> NL = MIN( K+1, N-i ) + 1 +*> CALL CLAROT( .TRUE., .TRUE., i+K.LT.N, NL, C,S, +*> A(i,i), LDA, XLEFT, XRIGHT ) +*> +*> Symmetric banded matrix in SB format, bandwidth K, +*> lower triangle only: +*> +*> [ same as for SY, except:] +*> . . . . +*> A(i+1-j,j), LDA-1, XLEFT, XRIGHT ) +*> +*> [ note that i+1-j is just MIN(i,K+1) ] +*> +*> Same, but upper triangle only: +*> . . . +*> A(K+1,i), LDA-1, XLEFT, XRIGHT ) +*> +*> Rotating columns is just the transpose of rotating rows, except +*> for GB and SB: (rotating columns i and i+1) +*> +*> GB: +*> j = MAX(1, i-KU ) +*> NL = MIN( N, i+KL+1 ) + 1-j +*> CALL CLAROT( .TRUE., i-KU.GE.1, i+KL.LT.N, NL, C,S, +*> A(KU+j+1-i,i),LDA-1, XTOP, XBOTTM ) +*> +*> [note that KU+j+1-i is just MAX(1,KU+2-i)] +*> +*> SB: (upper triangle) +*> +*> . . . . . . +*> A(K+j+1-i,i),LDA-1, XTOP, XBOTTM ) +*> +*> SB: (lower triangle) +*> +*> . . . . . . +*> A(1,i),LDA-1, XTOP, XBOTTM ) +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \verbatim +*> LROWS - LOGICAL +*> If .TRUE., then CLAROT will rotate two rows. If .FALSE., +*> then it will rotate two columns. +*> Not modified. +*> \endverbatim +*> \verbatim +*> LLEFT - LOGICAL +*> If .TRUE., then XLEFT will be used instead of the +*> corresponding element of A for the first element in the +*> second row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) +*> If .FALSE., then the corresponding element of A will be +*> used. +*> Not modified. +*> \endverbatim +*> \verbatim +*> LRIGHT - LOGICAL +*> If .TRUE., then XRIGHT will be used instead of the +*> corresponding element of A for the last element in the +*> first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If +*> .FALSE., then the corresponding element of A will be used. +*> Not modified. +*> \endverbatim +*> \verbatim +*> NL - INTEGER +*> The length of the rows (if LROWS=.TRUE.) or columns (if +*> LROWS=.FALSE.) to be rotated. If XLEFT and/or XRIGHT are +*> used, the columns/rows they are in should be included in +*> NL, e.g., if LLEFT = LRIGHT = .TRUE., then NL must be at +*> least 2. The number of rows/columns to be rotated +*> exclusive of those involving XLEFT and/or XRIGHT may +*> not be negative, i.e., NL minus how many of LLEFT and +*> LRIGHT are .TRUE. must be at least zero; if not, XERBLA +*> will be called. +*> Not modified. +*> \endverbatim +*> \verbatim +*> C, S - COMPLEX +*> Specify the Givens rotation to be applied. If LROWS is +*> true, then the matrix ( c s ) +*> ( _ _ ) +*> (-s c ) is applied from the left; +*> if false, then the transpose (not conjugated) thereof is +*> applied from the right. Note that in contrast to the +*> output of CROTG or to most versions of CROT, both C and S +*> are complex. For a Givens rotation, |C|**2 + |S|**2 should +*> be 1, but this is not checked. +*> Not modified. +*> \endverbatim +*> \verbatim +*> A - COMPLEX array. +*> The array containing the rows/columns to be rotated. The +*> first element of A should be the upper left element to +*> be rotated. +*> Read and modified. +*> \endverbatim +*> \verbatim +*> LDA - INTEGER +*> The "effective" leading dimension of A. If A contains +*> a matrix stored in GE, HE, or SY format, then this is just +*> the leading dimension of A as dimensioned in the calling +*> routine. If A contains a matrix stored in band (GB, HB, or +*> SB) format, then this should be *one less* than the leading +*> dimension used in the calling routine. Thus, if A were +*> dimensioned A(LDA,*) in CLAROT, then A(1,j) would be the +*> j-th element in the first of the two rows to be rotated, +*> and A(2,j) would be the j-th in the second, regardless of +*> how the array may be stored in the calling routine. [A +*> cannot, however, actually be dimensioned thus, since for +*> band format, the row number may exceed LDA, which is not +*> legal FORTRAN.] +*> If LROWS=.TRUE., then LDA must be at least 1, otherwise +*> it must be at least NL minus the number of .TRUE. values +*> in XLEFT and XRIGHT. +*> Not modified. +*> \endverbatim +*> \verbatim +*> XLEFT - COMPLEX +*> If LLEFT is .TRUE., then XLEFT will be used and modified +*> instead of A(2,1) (if LROWS=.TRUE.) or A(1,2) +*> (if LROWS=.FALSE.). +*> Read and modified. +*> \endverbatim +*> \verbatim +*> XRIGHT - COMPLEX +*> If LRIGHT is .TRUE., then XRIGHT will be used and modified +*> instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1) +*> (if LROWS=.FALSE.). +*> Read and modified. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_matgen +* +* ===================================================================== SUBROUTINE CLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT, $ XRIGHT ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. LOGICAL LLEFT, LRIGHT, LROWS @@ -14,193 +253,6 @@ COMPLEX A( * ) * .. * -* Purpose -* ======= -* -* CLAROT applies a (Givens) rotation to two adjacent rows or -* columns, where one element of the first and/or last column/row -* for use on matrices stored in some format other than GE, so -* that elements of the matrix may be used or modified for which -* no array element is provided. -* -* One example is a symmetric matrix in SB format (bandwidth=4), for -* which UPLO='L': Two adjacent rows will have the format: -* -* row j: * * * * * . . . . -* row j+1: * * * * * . . . . -* -* '*' indicates elements for which storage is provided, -* '.' indicates elements for which no storage is provided, but -* are not necessarily zero; their values are determined by -* symmetry. ' ' indicates elements which are necessarily zero, -* and have no storage provided. -* -* Those columns which have two '*'s can be handled by SROT. -* Those columns which have no '*'s can be ignored, since as long -* as the Givens rotations are carefully applied to preserve -* symmetry, their values are determined. -* Those columns which have one '*' have to be handled separately, -* by using separate variables "p" and "q": -* -* row j: * * * * * p . . . -* row j+1: q * * * * * . . . . -* -* The element p would have to be set correctly, then that column -* is rotated, setting p to its new value. The next call to -* CLAROT would rotate columns j and j+1, using p, and restore -* symmetry. The element q would start out being zero, and be -* made non-zero by the rotation. Later, rotations would presumably -* be chosen to zero q out. -* -* Typical Calling Sequences: rotating the i-th and (i+1)-st rows. -* ------- ------- --------- -* -* General dense matrix: -* -* CALL CLAROT(.TRUE.,.FALSE.,.FALSE., N, C,S, -* A(i,1),LDA, DUMMY, DUMMY) -* -* General banded matrix in GB format: -* -* j = MAX(1, i-KL ) -* NL = MIN( N, i+KU+1 ) + 1-j -* CALL CLAROT( .TRUE., i-KL.GE.1, i+KU.LT.N, NL, C,S, -* A(KU+i+1-j,j),LDA-1, XLEFT, XRIGHT ) -* -* [ note that i+1-j is just MIN(i,KL+1) ] -* -* Symmetric banded matrix in SY format, bandwidth K, -* lower triangle only: -* -* j = MAX(1, i-K ) -* NL = MIN( K+1, i ) + 1 -* CALL CLAROT( .TRUE., i-K.GE.1, .TRUE., NL, C,S, -* A(i,j), LDA, XLEFT, XRIGHT ) -* -* Same, but upper triangle only: -* -* NL = MIN( K+1, N-i ) + 1 -* CALL CLAROT( .TRUE., .TRUE., i+K.LT.N, NL, C,S, -* A(i,i), LDA, XLEFT, XRIGHT ) -* -* Symmetric banded matrix in SB format, bandwidth K, -* lower triangle only: -* -* [ same as for SY, except:] -* . . . . -* A(i+1-j,j), LDA-1, XLEFT, XRIGHT ) -* -* [ note that i+1-j is just MIN(i,K+1) ] -* -* Same, but upper triangle only: -* . . . -* A(K+1,i), LDA-1, XLEFT, XRIGHT ) -* -* Rotating columns is just the transpose of rotating rows, except -* for GB and SB: (rotating columns i and i+1) -* -* GB: -* j = MAX(1, i-KU ) -* NL = MIN( N, i+KL+1 ) + 1-j -* CALL CLAROT( .TRUE., i-KU.GE.1, i+KL.LT.N, NL, C,S, -* A(KU+j+1-i,i),LDA-1, XTOP, XBOTTM ) -* -* [note that KU+j+1-i is just MAX(1,KU+2-i)] -* -* SB: (upper triangle) -* -* . . . . . . -* A(K+j+1-i,i),LDA-1, XTOP, XBOTTM ) -* -* SB: (lower triangle) -* -* . . . . . . -* A(1,i),LDA-1, XTOP, XBOTTM ) -* -* Arguments -* ========= -* -* LROWS - LOGICAL -* If .TRUE., then CLAROT will rotate two rows. If .FALSE., -* then it will rotate two columns. -* Not modified. -* -* LLEFT - LOGICAL -* If .TRUE., then XLEFT will be used instead of the -* corresponding element of A for the first element in the -* second row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) -* If .FALSE., then the corresponding element of A will be -* used. -* Not modified. -* -* LRIGHT - LOGICAL -* If .TRUE., then XRIGHT will be used instead of the -* corresponding element of A for the last element in the -* first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If -* .FALSE., then the corresponding element of A will be used. -* Not modified. -* -* NL - INTEGER -* The length of the rows (if LROWS=.TRUE.) or columns (if -* LROWS=.FALSE.) to be rotated. If XLEFT and/or XRIGHT are -* used, the columns/rows they are in should be included in -* NL, e.g., if LLEFT = LRIGHT = .TRUE., then NL must be at -* least 2. The number of rows/columns to be rotated -* exclusive of those involving XLEFT and/or XRIGHT may -* not be negative, i.e., NL minus how many of LLEFT and -* LRIGHT are .TRUE. must be at least zero; if not, XERBLA -* will be called. -* Not modified. -* -* C, S - COMPLEX -* Specify the Givens rotation to be applied. If LROWS is -* true, then the matrix ( c s ) -* ( _ _ ) -* (-s c ) is applied from the left; -* if false, then the transpose (not conjugated) thereof is -* applied from the right. Note that in contrast to the -* output of CROTG or to most versions of CROT, both C and S -* are complex. For a Givens rotation, |C|**2 + |S|**2 should -* be 1, but this is not checked. -* Not modified. -* -* A - COMPLEX array. -* The array containing the rows/columns to be rotated. The -* first element of A should be the upper left element to -* be rotated. -* Read and modified. -* -* LDA - INTEGER -* The "effective" leading dimension of A. If A contains -* a matrix stored in GE, HE, or SY format, then this is just -* the leading dimension of A as dimensioned in the calling -* routine. If A contains a matrix stored in band (GB, HB, or -* SB) format, then this should be *one less* than the leading -* dimension used in the calling routine. Thus, if A were -* dimensioned A(LDA,*) in CLAROT, then A(1,j) would be the -* j-th element in the first of the two rows to be rotated, -* and A(2,j) would be the j-th in the second, regardless of -* how the array may be stored in the calling routine. [A -* cannot, however, actually be dimensioned thus, since for -* band format, the row number may exceed LDA, which is not -* legal FORTRAN.] -* If LROWS=.TRUE., then LDA must be at least 1, otherwise -* it must be at least NL minus the number of .TRUE. values -* in XLEFT and XRIGHT. -* Not modified. -* -* XLEFT - COMPLEX -* If LLEFT is .TRUE., then XLEFT will be used and modified -* instead of A(2,1) (if LROWS=.TRUE.) or A(1,2) -* (if LROWS=.FALSE.). -* Read and modified. -* -* XRIGHT - COMPLEX -* If LRIGHT is .TRUE., then XRIGHT will be used and modified -* instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1) -* (if LROWS=.FALSE.). -* Read and modified. -* * ===================================================================== * * .. Local Scalars .. diff --git a/TESTING/MATGEN/clatm1.f b/TESTING/MATGEN/clatm1.f index 6d5bc37c..86ea9370 100644 --- a/TESTING/MATGEN/clatm1.f +++ b/TESTING/MATGEN/clatm1.f @@ -1,8 +1,148 @@ +*> \brief \b CLATM1 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO ) +* +* .. Scalar Arguments .. +* INTEGER IDIST, INFO, IRSIGN, MODE, N +* REAL COND +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* COMPLEX D( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> CLATM1 computes the entries of D(1..N) as specified by +*> MODE, COND and IRSIGN. IDIST and ISEED determine the generation +*> of random numbers. CLATM1 is called by CLATMR to generate +*> random test matrices for LAPACK programs. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry describes how D is to be computed: +*> MODE = 0 means do not change D. +*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND +*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is REAL +*> On entry, used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] IRSIGN +*> \verbatim +*> IRSIGN is INTEGER +*> On entry, if MODE neither -6, 0 nor 6, determines sign of +*> entries of D +*> 0 => leave entries of D unchanged +*> 1 => multiply each entry of D by random complex number +*> uniformly distributed with absolute value 1 +*> \endverbatim +*> +*> \param[in] IDIST +*> \verbatim +*> IDIST is CHARACTER*1 +*> On entry, IDIST specifies the type of distribution to be +*> used to generate a random matrix . +*> 1 => real and imaginary parts each UNIFORM( 0, 1 ) +*> 2 => real and imaginary parts each UNIFORM( -1, 1 ) +*> 3 => real and imaginary parts each NORMAL( 0, 1 ) +*> 4 => complex number uniform in DISK( 0, 1 ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. The random number generator uses a +*> linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to CLATM1 +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is COMPLEX array, dimension ( MIN( M , N ) ) +*> Array to be computed according to MODE, COND and IRSIGN. +*> May be changed on exit if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of entries of D. Not modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> 0 => normal termination +*> -1 => if MODE not in range -6 to 6 +*> -2 => if MODE neither -6, 0 nor 6, and +*> IRSIGN neither 0 nor 1 +*> -3 => if MODE neither -6, 0 nor 6 and COND less than 1 +*> -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 4 +*> -7 => if N negative +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_matgen +* +* ===================================================================== SUBROUTINE CLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. INTEGER IDIST, INFO, IRSIGN, MODE, N @@ -13,81 +153,6 @@ COMPLEX D( * ) * .. * -* Purpose -* ======= -* -* CLATM1 computes the entries of D(1..N) as specified by -* MODE, COND and IRSIGN. IDIST and ISEED determine the generation -* of random numbers. CLATM1 is called by CLATMR to generate -* random test matrices for LAPACK programs. -* -* Arguments -* ========= -* -* MODE (input) INTEGER -* On entry describes how D is to be computed: -* MODE = 0 means do not change D. -* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND -* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* Not modified. -* -* COND (input) REAL -* On entry, used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* IRSIGN (input) INTEGER -* On entry, if MODE neither -6, 0 nor 6, determines sign of -* entries of D -* 0 => leave entries of D unchanged -* 1 => multiply each entry of D by random complex number -* uniformly distributed with absolute value 1 -* -* IDIST (input) CHARACTER*1 -* On entry, IDIST specifies the type of distribution to be -* used to generate a random matrix . -* 1 => real and imaginary parts each UNIFORM( 0, 1 ) -* 2 => real and imaginary parts each UNIFORM( -1, 1 ) -* 3 => real and imaginary parts each NORMAL( 0, 1 ) -* 4 => complex number uniform in DISK( 0, 1 ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. The random number generator uses a -* linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to CLATM1 -* to continue the same random number sequence. -* Changed on exit. -* -* D (input/output) COMPLEX array, dimension ( MIN( M , N ) ) -* Array to be computed according to MODE, COND and IRSIGN. -* May be changed on exit if MODE is nonzero. -* -* N (input) INTEGER -* Number of entries of D. Not modified. -* -* INFO (output) INTEGER -* 0 => normal termination -* -1 => if MODE not in range -6 to 6 -* -2 => if MODE neither -6, 0 nor 6, and -* IRSIGN neither 0 nor 1 -* -3 => if MODE neither -6, 0 nor 6 and COND less than 1 -* -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 4 -* -7 => if N negative -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/clatm2.f b/TESTING/MATGEN/clatm2.f index 310a55bc..76e053bf 100644 --- a/TESTING/MATGEN/clatm2.f +++ b/TESTING/MATGEN/clatm2.f @@ -1,9 +1,223 @@ +*> \brief \b CLATM2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* COMPLEX FUNCTION CLATM2( M, N, I, J, KL, KU, IDIST, ISEED, D, +* IGRADE, DL, DR, IPVTNG, IWORK, SPARSE ) +* +* .. Scalar Arguments .. +* +* INTEGER I, IDIST, IGRADE, IPVTNG, J, KL, KU, M, N +* REAL SPARSE +* .. +* +* .. Array Arguments .. +* +* INTEGER ISEED( 4 ), IWORK( * ) +* COMPLEX D( * ), DL( * ), DR( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> CLATM2 returns the (I,J) entry of a random matrix of dimension +*> (M, N) described by the other paramters. It is called by the +*> CLATMR routine in order to build random test matrices. No error +*> checking on parameters is done, because this routine is called in +*> a tight loop by CLATMR which has already checked the parameters. +*> +*> Use of CLATM2 differs from CLATM3 in the order in which the random +*> number generator is called to fill in random matrix entries. +*> With CLATM2, the generator is called to fill in the pivoted matrix +*> columnwise. With CLATM3, the generator is called to fill in the +*> matrix columnwise, after which it is pivoted. Thus, CLATM3 can +*> be used to construct random matrices which differ only in their +*> order of rows and/or columns. CLATM2 is used to construct band +*> matrices while avoiding calling the random number generator for +*> entries outside the band (and therefore generating random numbers +*> +*> The matrix whose (I,J) entry is returned is constructed as +*> follows (this routine only computes one entry): +*> +*> If I is outside (1..M) or J is outside (1..N), return zero +*> (this is convenient for generating matrices in band format). +*> +*> Generate a matrix A with random entries of distribution IDIST. +*> +*> Set the diagonal to D. +*> +*> Grade the matrix, if desired, from the left (by DL) and/or +*> from the right (by DR or DL) as specified by IGRADE. +*> +*> Permute, if desired, the rows and/or columns as specified by +*> IPVTNG and IWORK. +*> +*> Band the matrix to have lower bandwidth KL and upper +*> bandwidth KU. +*> +*> Set random entries to zero as specified by SPARSE. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Number of rows of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of columns of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] I +*> \verbatim +*> I is INTEGER +*> Row of entry to be returned. Not modified. +*> \endverbatim +*> +*> \param[in] J +*> \verbatim +*> J is INTEGER +*> Column of entry to be returned. Not modified. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> Lower bandwidth. Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> Upper bandwidth. Not modified. +*> \endverbatim +*> +*> \param[in] IDIST +*> \verbatim +*> IDIST is INTEGER +*> On entry, IDIST specifies the type of distribution to be +*> used to generate a random matrix . +*> 1 => real and imaginary parts each UNIFORM( 0, 1 ) +*> 2 => real and imaginary parts each UNIFORM( -1, 1 ) +*> 3 => real and imaginary parts each NORMAL( 0, 1 ) +*> 4 => complex number uniform in DISK( 0 , 1 ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array of dimension ( 4 ) +*> Seed for random number generator. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is COMPLEX array of dimension ( MIN( I , J ) ) +*> Diagonal entries of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] IGRADE +*> \verbatim +*> IGRADE is INTEGER +*> Specifies grading of matrix as follows: +*> 0 => no grading +*> 1 => matrix premultiplied by diag( DL ) +*> 2 => matrix postmultiplied by diag( DR ) +*> 3 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DR ) +*> 4 => matrix premultiplied by diag( DL ) and +*> postmultiplied by inv( diag( DL ) ) +*> 5 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( CONJG(DL) ) +*> 6 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DL ) +*> Not modified. +*> \endverbatim +*> +*> \param[in] DL +*> \verbatim +*> DL is COMPLEX array ( I or J, as appropriate ) +*> Left scale factors for grading matrix. Not modified. +*> \endverbatim +*> +*> \param[in] DR +*> \verbatim +*> DR is COMPLEX array ( I or J, as appropriate ) +*> Right scale factors for grading matrix. Not modified. +*> \endverbatim +*> +*> \param[in] IPVTNG +*> \verbatim +*> IPVTNG is INTEGER +*> On entry specifies pivoting permutations as follows: +*> 0 => none. +*> 1 => row pivoting. +*> 2 => column pivoting. +*> 3 => full pivoting, i.e., on both sides. +*> Not modified. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array ( I or J, as appropriate ) +*> This array specifies the permutation used. The +*> row (or column) in position K was originally in +*> position IWORK( K ). +*> This differs from IWORK for CLATM3. Not modified. +*> \endverbatim +*> +*> \param[in] SPARSE +*> \verbatim +*> SPARSE is REAL +*> Value between 0. and 1. +*> On entry specifies the sparsity of the matrix +*> if sparse matix is to be generated. +*> SPARSE should lie between 0 and 1. +*> A uniform ( 0, 1 ) random number x is generated and +*> compared to SPARSE; if x is larger the matrix entry +*> is unchanged and if x is smaller the entry is set +*> to zero. Thus on the average a fraction SPARSE of the +*> entries will be set to zero. +*> Not modified. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_matgen +* +* ===================================================================== COMPLEX FUNCTION CLATM2( M, N, I, J, KL, KU, IDIST, ISEED, D, $ IGRADE, DL, DR, IPVTNG, IWORK, SPARSE ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. * @@ -17,130 +231,6 @@ COMPLEX D( * ), DL( * ), DR( * ) * .. * -* Purpose -* ======= -* -* CLATM2 returns the (I,J) entry of a random matrix of dimension -* (M, N) described by the other paramters. It is called by the -* CLATMR routine in order to build random test matrices. No error -* checking on parameters is done, because this routine is called in -* a tight loop by CLATMR which has already checked the parameters. -* -* Use of CLATM2 differs from CLATM3 in the order in which the random -* number generator is called to fill in random matrix entries. -* With CLATM2, the generator is called to fill in the pivoted matrix -* columnwise. With CLATM3, the generator is called to fill in the -* matrix columnwise, after which it is pivoted. Thus, CLATM3 can -* be used to construct random matrices which differ only in their -* order of rows and/or columns. CLATM2 is used to construct band -* matrices while avoiding calling the random number generator for -* entries outside the band (and therefore generating random numbers -* -* The matrix whose (I,J) entry is returned is constructed as -* follows (this routine only computes one entry): -* -* If I is outside (1..M) or J is outside (1..N), return zero -* (this is convenient for generating matrices in band format). -* -* Generate a matrix A with random entries of distribution IDIST. -* -* Set the diagonal to D. -* -* Grade the matrix, if desired, from the left (by DL) and/or -* from the right (by DR or DL) as specified by IGRADE. -* -* Permute, if desired, the rows and/or columns as specified by -* IPVTNG and IWORK. -* -* Band the matrix to have lower bandwidth KL and upper -* bandwidth KU. -* -* Set random entries to zero as specified by SPARSE. -* -* Arguments -* ========= -* -* M (input) INTEGER -* Number of rows of matrix. Not modified. -* -* N (input) INTEGER -* Number of columns of matrix. Not modified. -* -* I (input) INTEGER -* Row of entry to be returned. Not modified. -* -* J (input) INTEGER -* Column of entry to be returned. Not modified. -* -* KL (input) INTEGER -* Lower bandwidth. Not modified. -* -* KU (input) INTEGER -* Upper bandwidth. Not modified. -* -* IDIST (input) INTEGER -* On entry, IDIST specifies the type of distribution to be -* used to generate a random matrix . -* 1 => real and imaginary parts each UNIFORM( 0, 1 ) -* 2 => real and imaginary parts each UNIFORM( -1, 1 ) -* 3 => real and imaginary parts each NORMAL( 0, 1 ) -* 4 => complex number uniform in DISK( 0 , 1 ) -* Not modified. -* -* ISEED (input/output) INTEGER array of dimension ( 4 ) -* Seed for random number generator. -* Changed on exit. -* -* D (input) COMPLEX array of dimension ( MIN( I , J ) ) -* Diagonal entries of matrix. Not modified. -* -* IGRADE (input) INTEGER -* Specifies grading of matrix as follows: -* 0 => no grading -* 1 => matrix premultiplied by diag( DL ) -* 2 => matrix postmultiplied by diag( DR ) -* 3 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DR ) -* 4 => matrix premultiplied by diag( DL ) and -* postmultiplied by inv( diag( DL ) ) -* 5 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( CONJG(DL) ) -* 6 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DL ) -* Not modified. -* -* DL (input) COMPLEX array ( I or J, as appropriate ) -* Left scale factors for grading matrix. Not modified. -* -* DR (input) COMPLEX array ( I or J, as appropriate ) -* Right scale factors for grading matrix. Not modified. -* -* IPVTNG (input) INTEGER -* On entry specifies pivoting permutations as follows: -* 0 => none. -* 1 => row pivoting. -* 2 => column pivoting. -* 3 => full pivoting, i.e., on both sides. -* Not modified. -* -* IWORK (workspace) INTEGER array ( I or J, as appropriate ) -* This array specifies the permutation used. The -* row (or column) in position K was originally in -* position IWORK( K ). -* This differs from IWORK for CLATM3. Not modified. -* -* SPARSE (input) REAL -* Value between 0. and 1. -* On entry specifies the sparsity of the matrix -* if sparse matix is to be generated. -* SPARSE should lie between 0 and 1. -* A uniform ( 0, 1 ) random number x is generated and -* compared to SPARSE; if x is larger the matrix entry -* is unchanged and if x is smaller the entry is set -* to zero. Thus on the average a fraction SPARSE of the -* entries will be set to zero. -* Not modified. -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/clatm3.f b/TESTING/MATGEN/clatm3.f index c0354411..f2d9782a 100644 --- a/TESTING/MATGEN/clatm3.f +++ b/TESTING/MATGEN/clatm3.f @@ -1,10 +1,240 @@ +*> \brief \b CLATM3 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* COMPLEX FUNCTION CLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST, +* ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, +* SPARSE ) +* +* .. Scalar Arguments .. +* +* INTEGER I, IDIST, IGRADE, IPVTNG, ISUB, J, JSUB, KL, +* $ KU, M, N +* REAL SPARSE +* .. +* +* .. Array Arguments .. +* +* INTEGER ISEED( 4 ), IWORK( * ) +* COMPLEX D( * ), DL( * ), DR( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> CLATM3 returns the (ISUB,JSUB) entry of a random matrix of +*> dimension (M, N) described by the other paramters. (ISUB,JSUB) +*> is the final position of the (I,J) entry after pivoting +*> according to IPVTNG and IWORK. CLATM3 is called by the +*> CLATMR routine in order to build random test matrices. No error +*> checking on parameters is done, because this routine is called in +*> a tight loop by CLATMR which has already checked the parameters. +*> +*> Use of CLATM3 differs from CLATM2 in the order in which the random +*> number generator is called to fill in random matrix entries. +*> With CLATM2, the generator is called to fill in the pivoted matrix +*> columnwise. With CLATM3, the generator is called to fill in the +*> matrix columnwise, after which it is pivoted. Thus, CLATM3 can +*> be used to construct random matrices which differ only in their +*> order of rows and/or columns. CLATM2 is used to construct band +*> matrices while avoiding calling the random number generator for +*> entries outside the band (and therefore generating random numbers +*> in different orders for different pivot orders). +*> +*> The matrix whose (ISUB,JSUB) entry is returned is constructed as +*> follows (this routine only computes one entry): +*> +*> If ISUB is outside (1..M) or JSUB is outside (1..N), return zero +*> (this is convenient for generating matrices in band format). +*> +*> Generate a matrix A with random entries of distribution IDIST. +*> +*> Set the diagonal to D. +*> +*> Grade the matrix, if desired, from the left (by DL) and/or +*> from the right (by DR or DL) as specified by IGRADE. +*> +*> Permute, if desired, the rows and/or columns as specified by +*> IPVTNG and IWORK. +*> +*> Band the matrix to have lower bandwidth KL and upper +*> bandwidth KU. +*> +*> Set random entries to zero as specified by SPARSE. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Number of rows of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of columns of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] I +*> \verbatim +*> I is INTEGER +*> Row of unpivoted entry to be returned. Not modified. +*> \endverbatim +*> +*> \param[in] J +*> \verbatim +*> J is INTEGER +*> Column of unpivoted entry to be returned. Not modified. +*> \endverbatim +*> +*> \param[in,out] ISUB +*> \verbatim +*> ISUB is INTEGER +*> Row of pivoted entry to be returned. Changed on exit. +*> \endverbatim +*> +*> \param[in,out] JSUB +*> \verbatim +*> JSUB is INTEGER +*> Column of pivoted entry to be returned. Changed on exit. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> Lower bandwidth. Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> Upper bandwidth. Not modified. +*> \endverbatim +*> +*> \param[in] IDIST +*> \verbatim +*> IDIST is INTEGER +*> On entry, IDIST specifies the type of distribution to be +*> used to generate a random matrix . +*> 1 => real and imaginary parts each UNIFORM( 0, 1 ) +*> 2 => real and imaginary parts each UNIFORM( -1, 1 ) +*> 3 => real and imaginary parts each NORMAL( 0, 1 ) +*> 4 => complex number uniform in DISK( 0 , 1 ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array of dimension ( 4 ) +*> Seed for random number generator. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is COMPLEX array of dimension ( MIN( I , J ) ) +*> Diagonal entries of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] IGRADE +*> \verbatim +*> IGRADE is INTEGER +*> Specifies grading of matrix as follows: +*> 0 => no grading +*> 1 => matrix premultiplied by diag( DL ) +*> 2 => matrix postmultiplied by diag( DR ) +*> 3 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DR ) +*> 4 => matrix premultiplied by diag( DL ) and +*> postmultiplied by inv( diag( DL ) ) +*> 5 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( CONJG(DL) ) +*> 6 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DL ) +*> Not modified. +*> \endverbatim +*> +*> \param[in] DL +*> \verbatim +*> DL is COMPLEX array ( I or J, as appropriate ) +*> Left scale factors for grading matrix. Not modified. +*> \endverbatim +*> +*> \param[in] DR +*> \verbatim +*> DR is COMPLEX array ( I or J, as appropriate ) +*> Right scale factors for grading matrix. Not modified. +*> \endverbatim +*> +*> \param[in] IPVTNG +*> \verbatim +*> IPVTNG is INTEGER +*> On entry specifies pivoting permutations as follows: +*> 0 => none. +*> 1 => row pivoting. +*> 2 => column pivoting. +*> 3 => full pivoting, i.e., on both sides. +*> Not modified. +*> \endverbatim +*> +*> \param[in] IWORK +*> \verbatim +*> IWORK is INTEGER array ( I or J, as appropriate ) +*> This array specifies the permutation used. The +*> row (or column) originally in position K is in +*> position IWORK( K ) after pivoting. +*> This differs from IWORK for CLATM2. Not modified. +*> \endverbatim +*> +*> \param[in] SPARSE +*> \verbatim +*> SPARSE is REAL between 0. and 1. +*> On entry specifies the sparsity of the matrix +*> if sparse matix is to be generated. +*> SPARSE should lie between 0 and 1. +*> A uniform ( 0, 1 ) random number x is generated and +*> compared to SPARSE; if x is larger the matrix entry +*> is unchanged and if x is smaller the entry is set +*> to zero. Thus on the average a fraction SPARSE of the +*> entries will be set to zero. +*> Not modified. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_matgen +* +* ===================================================================== COMPLEX FUNCTION CLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST, $ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, $ SPARSE ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. * @@ -19,138 +249,6 @@ COMPLEX D( * ), DL( * ), DR( * ) * .. * -* Purpose -* ======= -* -* CLATM3 returns the (ISUB,JSUB) entry of a random matrix of -* dimension (M, N) described by the other paramters. (ISUB,JSUB) -* is the final position of the (I,J) entry after pivoting -* according to IPVTNG and IWORK. CLATM3 is called by the -* CLATMR routine in order to build random test matrices. No error -* checking on parameters is done, because this routine is called in -* a tight loop by CLATMR which has already checked the parameters. -* -* Use of CLATM3 differs from CLATM2 in the order in which the random -* number generator is called to fill in random matrix entries. -* With CLATM2, the generator is called to fill in the pivoted matrix -* columnwise. With CLATM3, the generator is called to fill in the -* matrix columnwise, after which it is pivoted. Thus, CLATM3 can -* be used to construct random matrices which differ only in their -* order of rows and/or columns. CLATM2 is used to construct band -* matrices while avoiding calling the random number generator for -* entries outside the band (and therefore generating random numbers -* in different orders for different pivot orders). -* -* The matrix whose (ISUB,JSUB) entry is returned is constructed as -* follows (this routine only computes one entry): -* -* If ISUB is outside (1..M) or JSUB is outside (1..N), return zero -* (this is convenient for generating matrices in band format). -* -* Generate a matrix A with random entries of distribution IDIST. -* -* Set the diagonal to D. -* -* Grade the matrix, if desired, from the left (by DL) and/or -* from the right (by DR or DL) as specified by IGRADE. -* -* Permute, if desired, the rows and/or columns as specified by -* IPVTNG and IWORK. -* -* Band the matrix to have lower bandwidth KL and upper -* bandwidth KU. -* -* Set random entries to zero as specified by SPARSE. -* -* Arguments -* ========= -* -* M (input) INTEGER -* Number of rows of matrix. Not modified. -* -* N (input) INTEGER -* Number of columns of matrix. Not modified. -* -* I (input) INTEGER -* Row of unpivoted entry to be returned. Not modified. -* -* J (input) INTEGER -* Column of unpivoted entry to be returned. Not modified. -* -* ISUB (input/output) INTEGER -* Row of pivoted entry to be returned. Changed on exit. -* -* JSUB (input/output) INTEGER -* Column of pivoted entry to be returned. Changed on exit. -* -* KL (input) INTEGER -* Lower bandwidth. Not modified. -* -* KU (input) INTEGER -* Upper bandwidth. Not modified. -* -* IDIST (input) INTEGER -* On entry, IDIST specifies the type of distribution to be -* used to generate a random matrix . -* 1 => real and imaginary parts each UNIFORM( 0, 1 ) -* 2 => real and imaginary parts each UNIFORM( -1, 1 ) -* 3 => real and imaginary parts each NORMAL( 0, 1 ) -* 4 => complex number uniform in DISK( 0 , 1 ) -* Not modified. -* -* ISEED (input/output) INTEGER array of dimension ( 4 ) -* Seed for random number generator. -* Changed on exit. -* -* D (input) COMPLEX array of dimension ( MIN( I , J ) ) -* Diagonal entries of matrix. Not modified. -* -* IGRADE (input) INTEGER -* Specifies grading of matrix as follows: -* 0 => no grading -* 1 => matrix premultiplied by diag( DL ) -* 2 => matrix postmultiplied by diag( DR ) -* 3 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DR ) -* 4 => matrix premultiplied by diag( DL ) and -* postmultiplied by inv( diag( DL ) ) -* 5 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( CONJG(DL) ) -* 6 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DL ) -* Not modified. -* -* DL (input) COMPLEX array ( I or J, as appropriate ) -* Left scale factors for grading matrix. Not modified. -* -* DR (input) COMPLEX array ( I or J, as appropriate ) -* Right scale factors for grading matrix. Not modified. -* -* IPVTNG (input) INTEGER -* On entry specifies pivoting permutations as follows: -* 0 => none. -* 1 => row pivoting. -* 2 => column pivoting. -* 3 => full pivoting, i.e., on both sides. -* Not modified. -* -* IWORK (input) INTEGER array ( I or J, as appropriate ) -* This array specifies the permutation used. The -* row (or column) originally in position K is in -* position IWORK( K ) after pivoting. -* This differs from IWORK for CLATM2. Not modified. -* -* SPARSE (input) REAL between 0. and 1. -* On entry specifies the sparsity of the matrix -* if sparse matix is to be generated. -* SPARSE should lie between 0 and 1. -* A uniform ( 0, 1 ) random number x is generated and -* compared to SPARSE; if x is larger the matrix entry -* is unchanged and if x is smaller the entry is set -* to zero. Thus on the average a fraction SPARSE of the -* entries will be set to zero. -* Not modified. -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/clatm5.f b/TESTING/MATGEN/clatm5.f index 8fcc6006..b49e5c91 100644 --- a/TESTING/MATGEN/clatm5.f +++ b/TESTING/MATGEN/clatm5.f @@ -1,177 +1,292 @@ - SUBROUTINE CLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD, - $ E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA, - $ QBLCKB ) -* -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N, - $ PRTYPE, QBLCKA, QBLCKB - REAL ALPHA -* .. -* .. Array Arguments .. - COMPLEX A( LDA, * ), B( LDB, * ), C( LDC, * ), - $ D( LDD, * ), E( LDE, * ), F( LDF, * ), - $ L( LDL, * ), R( LDR, * ) -* .. -* +*> \brief \b CLATM5 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD, +* E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA, +* QBLCKB ) +* +* .. Scalar Arguments .. +* INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N, +* $ PRTYPE, QBLCKA, QBLCKB +* REAL ALPHA +* .. +* .. Array Arguments .. +* COMPLEX A( LDA, * ), B( LDB, * ), C( LDC, * ), +* $ D( LDD, * ), E( LDE, * ), F( LDF, * ), +* $ L( LDL, * ), R( LDR, * ) +* .. +* * Purpose * ======= * -* CLATM5 generates matrices involved in the Generalized Sylvester -* equation: -* -* A * R - L * B = C -* D * R - L * E = F -* -* They also satisfy (the diagonalization condition) -* -* [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] ) -* [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] ) -* +*>\details \b Purpose: +*>\verbatim +*> +*> CLATM5 generates matrices involved in the Generalized Sylvester +*> equation: +*> +*> A * R - L * B = C +*> D * R - L * E = F +*> +*> They also satisfy (the diagonalization condition) +*> +*> [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] ) +*> [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] ) +*> +*> +*>\endverbatim * * Arguments * ========= * -* PRTYPE (input) INTEGER -* "Points" to a certian type of the matrices to generate -* (see futher details). -* -* M (input) INTEGER -* Specifies the order of A and D and the number of rows in -* C, F, R and L. -* -* N (input) INTEGER -* Specifies the order of B and E and the number of columns in -* C, F, R and L. -* -* A (output) COMPLEX array, dimension (LDA, M). -* On exit A M-by-M is initialized according to PRTYPE. -* -* LDA (input) INTEGER -* The leading dimension of A. -* -* B (output) COMPLEX array, dimension (LDB, N). -* On exit B N-by-N is initialized according to PRTYPE. -* -* LDB (input) INTEGER -* The leading dimension of B. -* -* C (output) COMPLEX array, dimension (LDC, N). -* On exit C M-by-N is initialized according to PRTYPE. -* -* LDC (input) INTEGER -* The leading dimension of C. -* -* D (output) COMPLEX array, dimension (LDD, M). -* On exit D M-by-M is initialized according to PRTYPE. -* -* LDD (input) INTEGER -* The leading dimension of D. -* -* E (output) COMPLEX array, dimension (LDE, N). -* On exit E N-by-N is initialized according to PRTYPE. -* -* LDE (input) INTEGER -* The leading dimension of E. -* -* F (output) COMPLEX array, dimension (LDF, N). -* On exit F M-by-N is initialized according to PRTYPE. -* -* LDF (input) INTEGER -* The leading dimension of F. -* -* R (output) COMPLEX array, dimension (LDR, N). -* On exit R M-by-N is initialized according to PRTYPE. -* -* LDR (input) INTEGER -* The leading dimension of R. -* -* L (output) COMPLEX array, dimension (LDL, N). -* On exit L M-by-N is initialized according to PRTYPE. -* -* LDL (input) INTEGER -* The leading dimension of L. +*> \param[in] PRTYPE +*> \verbatim +*> PRTYPE is INTEGER +*> "Points" to a certian type of the matrices to generate +*> (see futher details). +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Specifies the order of A and D and the number of rows in +*> C, F, R and L. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Specifies the order of B and E and the number of columns in +*> C, F, R and L. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is COMPLEX array, dimension (LDA, M). +*> On exit A M-by-M is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of A. +*> \endverbatim +*> +*> \param[out] B +*> \verbatim +*> B is COMPLEX array, dimension (LDB, N). +*> On exit B N-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of B. +*> \endverbatim +*> +*> \param[out] C +*> \verbatim +*> C is COMPLEX array, dimension (LDC, N). +*> On exit C M-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> The leading dimension of C. +*> \endverbatim +*> +*> \param[out] D +*> \verbatim +*> D is COMPLEX array, dimension (LDD, M). +*> On exit D M-by-M is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDD +*> \verbatim +*> LDD is INTEGER +*> The leading dimension of D. +*> \endverbatim +*> +*> \param[out] E +*> \verbatim +*> E is COMPLEX array, dimension (LDE, N). +*> On exit E N-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDE +*> \verbatim +*> LDE is INTEGER +*> The leading dimension of E. +*> \endverbatim +*> +*> \param[out] F +*> \verbatim +*> F is COMPLEX array, dimension (LDF, N). +*> On exit F M-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDF +*> \verbatim +*> LDF is INTEGER +*> The leading dimension of F. +*> \endverbatim +*> +*> \param[out] R +*> \verbatim +*> R is COMPLEX array, dimension (LDR, N). +*> On exit R M-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDR +*> \verbatim +*> LDR is INTEGER +*> The leading dimension of R. +*> \endverbatim +*> +*> \param[out] L +*> \verbatim +*> L is COMPLEX array, dimension (LDL, N). +*> On exit L M-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDL +*> \verbatim +*> LDL is INTEGER +*> The leading dimension of L. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> Parameter used in generating PRTYPE = 1 and 5 matrices. +*> \endverbatim +*> +*> \param[in] QBLCKA +*> \verbatim +*> QBLCKA is INTEGER +*> When PRTYPE = 3, specifies the distance between 2-by-2 +*> blocks on the diagonal in A. Otherwise, QBLCKA is not +*> referenced. QBLCKA > 1. +*> \endverbatim +*> +*> \param[in] QBLCKB +*> \verbatim +*> QBLCKB is INTEGER +*> When PRTYPE = 3, specifies the distance between 2-by-2 +*> blocks on the diagonal in B. Otherwise, QBLCKB is not +*> referenced. QBLCKB > 1. +*> \endverbatim +*> +* +* Authors +* ======= * -* ALPHA (input) REAL -* Parameter used in generating PRTYPE = 1 and 5 matrices. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* QBLCKA (input) INTEGER -* When PRTYPE = 3, specifies the distance between 2-by-2 -* blocks on the diagonal in A. Otherwise, QBLCKA is not -* referenced. QBLCKA > 1. +*> \date November 2011 * -* QBLCKB (input) INTEGER -* When PRTYPE = 3, specifies the distance between 2-by-2 -* blocks on the diagonal in B. Otherwise, QBLCKB is not -* referenced. QBLCKB > 1. +*> \ingroup complex_matgen * * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices +*> +*> A : if (i == j) then A(i, j) = 1.0 +*> if (j == i + 1) then A(i, j) = -1.0 +*> else A(i, j) = 0.0, i, j = 1...M +*> +*> B : if (i == j) then B(i, j) = 1.0 - ALPHA +*> if (j == i + 1) then B(i, j) = 1.0 +*> else B(i, j) = 0.0, i, j = 1...N +*> +*> D : if (i == j) then D(i, j) = 1.0 +*> else D(i, j) = 0.0, i, j = 1...M +*> +*> E : if (i == j) then E(i, j) = 1.0 +*> else E(i, j) = 0.0, i, j = 1...N +*> +*> L = R are chosen from [-10...10], +*> which specifies the right hand sides (C, F). +*> +*> PRTYPE = 2 or 3: Triangular and/or quasi- triangular. +*> +*> A : if (i <= j) then A(i, j) = [-1...1] +*> else A(i, j) = 0.0, i, j = 1...M +*> +*> if (PRTYPE = 3) then +*> A(k + 1, k + 1) = A(k, k) +*> A(k + 1, k) = [-1...1] +*> sign(A(k, k + 1) = -(sin(A(k + 1, k)) +*> k = 1, M - 1, QBLCKA +*> +*> B : if (i <= j) then B(i, j) = [-1...1] +*> else B(i, j) = 0.0, i, j = 1...N +*> +*> if (PRTYPE = 3) then +*> B(k + 1, k + 1) = B(k, k) +*> B(k + 1, k) = [-1...1] +*> sign(B(k, k + 1) = -(sign(B(k + 1, k)) +*> k = 1, N - 1, QBLCKB +*> +*> D : if (i <= j) then D(i, j) = [-1...1]. +*> else D(i, j) = 0.0, i, j = 1...M +*> +*> +*> E : if (i <= j) then D(i, j) = [-1...1] +*> else E(i, j) = 0.0, i, j = 1...N +*> +*> L, R are chosen from [-10...10], +*> which specifies the right hand sides (C, F). +*> +*> PRTYPE = 4 Full +*> A(i, j) = [-10...10] +*> D(i, j) = [-1...1] i,j = 1...M +*> B(i, j) = [-10...10] +*> E(i, j) = [-1...1] i,j = 1...N +*> R(i, j) = [-10...10] +*> L(i, j) = [-1...1] i = 1..M ,j = 1...N +*> +*> L, R specifies the right hand sides (C, F). +*> +*> PRTYPE = 5 special case common and/or close eigs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD, + $ E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA, + $ QBLCKB ) * -* PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices -* -* A : if (i == j) then A(i, j) = 1.0 -* if (j == i + 1) then A(i, j) = -1.0 -* else A(i, j) = 0.0, i, j = 1...M -* -* B : if (i == j) then B(i, j) = 1.0 - ALPHA -* if (j == i + 1) then B(i, j) = 1.0 -* else B(i, j) = 0.0, i, j = 1...N -* -* D : if (i == j) then D(i, j) = 1.0 -* else D(i, j) = 0.0, i, j = 1...M -* -* E : if (i == j) then E(i, j) = 1.0 -* else E(i, j) = 0.0, i, j = 1...N -* -* L = R are chosen from [-10...10], -* which specifies the right hand sides (C, F). -* -* PRTYPE = 2 or 3: Triangular and/or quasi- triangular. -* -* A : if (i <= j) then A(i, j) = [-1...1] -* else A(i, j) = 0.0, i, j = 1...M -* -* if (PRTYPE = 3) then -* A(k + 1, k + 1) = A(k, k) -* A(k + 1, k) = [-1...1] -* sign(A(k, k + 1) = -(sin(A(k + 1, k)) -* k = 1, M - 1, QBLCKA -* -* B : if (i <= j) then B(i, j) = [-1...1] -* else B(i, j) = 0.0, i, j = 1...N -* -* if (PRTYPE = 3) then -* B(k + 1, k + 1) = B(k, k) -* B(k + 1, k) = [-1...1] -* sign(B(k, k + 1) = -(sign(B(k + 1, k)) -* k = 1, N - 1, QBLCKB -* -* D : if (i <= j) then D(i, j) = [-1...1]. -* else D(i, j) = 0.0, i, j = 1...M -* -* -* E : if (i <= j) then D(i, j) = [-1...1] -* else E(i, j) = 0.0, i, j = 1...N -* -* L, R are chosen from [-10...10], -* which specifies the right hand sides (C, F). -* -* PRTYPE = 4 Full -* A(i, j) = [-10...10] -* D(i, j) = [-1...1] i,j = 1...M -* B(i, j) = [-10...10] -* E(i, j) = [-1...1] i,j = 1...N -* R(i, j) = [-10...10] -* L(i, j) = [-1...1] i = 1..M ,j = 1...N -* -* L, R specifies the right hand sides (C, F). +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* PRTYPE = 5 special case common and/or close eigs. +* .. Scalar Arguments .. + INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N, + $ PRTYPE, QBLCKA, QBLCKB + REAL ALPHA +* .. +* .. Array Arguments .. + COMPLEX A( LDA, * ), B( LDB, * ), C( LDC, * ), + $ D( LDD, * ), E( LDE, * ), F( LDF, * ), + $ L( LDL, * ), R( LDR, * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/clatm6.f b/TESTING/MATGEN/clatm6.f index 5780b607..72ba4e22 100644 --- a/TESTING/MATGEN/clatm6.f +++ b/TESTING/MATGEN/clatm6.f @@ -1,106 +1,196 @@ - SUBROUTINE CLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA, - $ BETA, WX, WY, S, DIF ) -* -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 -* -* .. Scalar Arguments .. - INTEGER LDA, LDX, LDY, N, TYPE - COMPLEX ALPHA, BETA, WX, WY -* .. -* .. Array Arguments .. - REAL DIF( * ), S( * ) - COMPLEX A( LDA, * ), B( LDA, * ), X( LDX, * ), - $ Y( LDY, * ) -* .. -* +*> \brief \b CLATM6 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA, +* BETA, WX, WY, S, DIF ) +* +* .. Scalar Arguments .. +* INTEGER LDA, LDX, LDY, N, TYPE +* COMPLEX ALPHA, BETA, WX, WY +* .. +* .. Array Arguments .. +* REAL DIF( * ), S( * ) +* COMPLEX A( LDA, * ), B( LDA, * ), X( LDX, * ), +* $ Y( LDY, * ) +* .. +* * Purpose * ======= * -* CLATM6 generates test matrices for the generalized eigenvalue -* problem, their corresponding right and left eigenvector matrices, -* and also reciprocal condition numbers for all eigenvalues and -* the reciprocal condition numbers of eigenvectors corresponding to -* the 1th and 5th eigenvalues. -* -* Test Matrices -* ============= -* -* Two kinds of test matrix pairs -* (A, B) = inverse(YH) * (Da, Db) * inverse(X) -* are used in the tests: -* -* Type 1: -* Da = 1+a 0 0 0 0 Db = 1 0 0 0 0 -* 0 2+a 0 0 0 0 1 0 0 0 -* 0 0 3+a 0 0 0 0 1 0 0 -* 0 0 0 4+a 0 0 0 0 1 0 -* 0 0 0 0 5+a , 0 0 0 0 1 -* and Type 2: -* Da = 1+i 0 0 0 0 Db = 1 0 0 0 0 -* 0 1-i 0 0 0 0 1 0 0 0 -* 0 0 1 0 0 0 0 1 0 0 -* 0 0 0 (1+a)+(1+b)i 0 0 0 0 1 0 -* 0 0 0 0 (1+a)-(1+b)i, 0 0 0 0 1 . -* -* In both cases the same inverse(YH) and inverse(X) are used to compute -* (A, B), giving the exact eigenvectors to (A,B) as (YH, X): -* -* YH: = 1 0 -y y -y X = 1 0 -x -x x -* 0 1 -y y -y 0 1 x -x -x -* 0 0 1 0 0 0 0 1 0 0 -* 0 0 0 1 0 0 0 0 1 0 -* 0 0 0 0 1, 0 0 0 0 1 , where -* -* a, b, x and y will have all values independently of each other. +*>\details \b Purpose: +*>\verbatim +*> +*> CLATM6 generates test matrices for the generalized eigenvalue +*> problem, their corresponding right and left eigenvector matrices, +*> and also reciprocal condition numbers for all eigenvalues and +*> the reciprocal condition numbers of eigenvectors corresponding to +*> the 1th and 5th eigenvalues. +*> +*> Test Matrices +*> ============= +*> +*> Two kinds of test matrix pairs +*> (A, B) = inverse(YH) * (Da, Db) * inverse(X) +*> are used in the tests: +*> +*> Type 1: +*> Da = 1+a 0 0 0 0 Db = 1 0 0 0 0 +*> 0 2+a 0 0 0 0 1 0 0 0 +*> 0 0 3+a 0 0 0 0 1 0 0 +*> 0 0 0 4+a 0 0 0 0 1 0 +*> 0 0 0 0 5+a , 0 0 0 0 1 +*> and Type 2: +*> Da = 1+i 0 0 0 0 Db = 1 0 0 0 0 +*> 0 1-i 0 0 0 0 1 0 0 0 +*> 0 0 1 0 0 0 0 1 0 0 +*> 0 0 0 (1+a)+(1+b)i 0 0 0 0 1 0 +*> 0 0 0 0 (1+a)-(1+b)i, 0 0 0 0 1 . +*> +*> In both cases the same inverse(YH) and inverse(X) are used to compute +*> (A, B), giving the exact eigenvectors to (A,B) as (YH, X): +*> +*> YH: = 1 0 -y y -y X = 1 0 -x -x x +*> 0 1 -y y -y 0 1 x -x -x +*> 0 0 1 0 0 0 0 1 0 0 +*> 0 0 0 1 0 0 0 0 1 0 +*> 0 0 0 0 1, 0 0 0 0 1 , where +*> +*> a, b, x and y will have all values independently of each other. +*> +*>\endverbatim * * Arguments * ========= * -* TYPE (input) INTEGER -* Specifies the problem type (see futher details). -* -* N (input) INTEGER -* Size of the matrices A and B. -* -* A (output) COMPLEX array, dimension (LDA, N). -* On exit A N-by-N is initialized according to TYPE. -* -* LDA (input) INTEGER -* The leading dimension of A and of B. -* -* B (output) COMPLEX array, dimension (LDA, N). -* On exit B N-by-N is initialized according to TYPE. -* -* X (output) COMPLEX array, dimension (LDX, N). -* On exit X is the N-by-N matrix of right eigenvectors. -* -* LDX (input) INTEGER -* The leading dimension of X. -* -* Y (output) COMPLEX array, dimension (LDY, N). -* On exit Y is the N-by-N matrix of left eigenvectors. -* -* LDY (input) INTEGER -* The leading dimension of Y. +*> \param[in] TYPE +*> \verbatim +*> TYPE is INTEGER +*> Specifies the problem type (see futher details). +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Size of the matrices A and B. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is COMPLEX array, dimension (LDA, N). +*> On exit A N-by-N is initialized according to TYPE. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of A and of B. +*> \endverbatim +*> +*> \param[out] B +*> \verbatim +*> B is COMPLEX array, dimension (LDA, N). +*> On exit B N-by-N is initialized according to TYPE. +*> \endverbatim +*> +*> \param[out] X +*> \verbatim +*> X is COMPLEX array, dimension (LDX, N). +*> On exit X is the N-by-N matrix of right eigenvectors. +*> \endverbatim +*> +*> \param[in] LDX +*> \verbatim +*> LDX is INTEGER +*> The leading dimension of X. +*> \endverbatim +*> +*> \param[out] Y +*> \verbatim +*> Y is COMPLEX array, dimension (LDY, N). +*> On exit Y is the N-by-N matrix of left eigenvectors. +*> \endverbatim +*> +*> \param[in] LDY +*> \verbatim +*> LDY is INTEGER +*> The leading dimension of Y. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX +*> \endverbatim +*> \verbatim +*> Weighting constants for matrix A. +*> \endverbatim +*> +*> \param[in] WX +*> \verbatim +*> WX is COMPLEX +*> Constant for right eigenvector matrix. +*> \endverbatim +*> +*> \param[in] WY +*> \verbatim +*> WY is COMPLEX +*> Constant for left eigenvector matrix. +*> \endverbatim +*> +*> \param[out] S +*> \verbatim +*> S is REAL array, dimension (N) +*> S(i) is the reciprocal condition number for eigenvalue i. +*> \endverbatim +*> +*> \param[out] DIF +*> \verbatim +*> DIF is REAL array, dimension (N) +*> DIF(i) is the reciprocal condition number for eigenvector i. +*> \endverbatim +*> +* +* Authors +* ======= * -* ALPHA (input) COMPLEX +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* BETA (input) COMPLEX -* Weighting constants for matrix A. +*> \date November 2011 * -* WX (input) COMPLEX -* Constant for right eigenvector matrix. +*> \ingroup complex_matgen * -* WY (input) COMPLEX -* Constant for left eigenvector matrix. +* ===================================================================== + SUBROUTINE CLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA, + $ BETA, WX, WY, S, DIF ) * -* S (output) REAL array, dimension (N) -* S(i) is the reciprocal condition number for eigenvalue i. +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* DIF (output) REAL array, dimension (N) -* DIF(i) is the reciprocal condition number for eigenvector i. +* .. Scalar Arguments .. + INTEGER LDA, LDX, LDY, N, TYPE + COMPLEX ALPHA, BETA, WX, WY +* .. +* .. Array Arguments .. + REAL DIF( * ), S( * ) + COMPLEX A( LDA, * ), B( LDA, * ), X( LDX, * ), + $ Y( LDY, * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/clatme.f b/TESTING/MATGEN/clatme.f index ae14e829..b2499c76 100644 --- a/TESTING/MATGEN/clatme.f +++ b/TESTING/MATGEN/clatme.f @@ -1,12 +1,312 @@ +*> \brief \b CLATME +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CLATME( N, DIST, ISEED, D, MODE, COND, DMAX, +* RSIGN, +* UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, +* A, +* LDA, WORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER DIST, RSIGN, SIM, UPPER +* INTEGER INFO, KL, KU, LDA, MODE, MODES, N +* REAL ANORM, COND, CONDS +* COMPLEX DMAX +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* REAL DS( * ) +* COMPLEX A( LDA, * ), D( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> CLATME generates random non-symmetric square matrices with +*> specified eigenvalues for testing LAPACK programs. +*> +*> CLATME operates by applying the following sequence of +*> operations: +*> +*> 1. Set the diagonal to D, where D may be input or +*> computed according to MODE, COND, DMAX, and RSIGN +*> as described below. +*> +*> 2. If UPPER='T', the upper triangle of A is set to random values +*> out of distribution DIST. +*> +*> 3. If SIM='T', A is multiplied on the left by a random matrix +*> X, whose singular values are specified by DS, MODES, and +*> CONDS, and on the right by X inverse. +*> +*> 4. If KL < N-1, the lower bandwidth is reduced to KL using +*> Householder transformations. If KU < N-1, the upper +*> bandwidth is reduced to KU. +*> +*> 5. If ANORM is not negative, the matrix is scaled to have +*> maximum-element-norm ANORM. +*> +*> (Note: since the matrix cannot be reduced beyond Hessenberg form, +*> no packing options are available.) +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns (or rows) of A. Not modified. +*> \endverbatim +*> +*> \param[in] DIST +*> \verbatim +*> DIST is CHARACTER*1 +*> On entry, DIST specifies the type of distribution to be used +*> to generate the random eigen-/singular values, and on the +*> upper triangle (see UPPER). +*> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) +*> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) +*> 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) +*> 'D' => uniform on the complex disc |z| < 1. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. They should lie between 0 and 4095 inclusive, +*> and ISEED(4) should be odd. The random number generator +*> uses a linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to CLATME +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is COMPLEX array, dimension ( N ) +*> This array is used to specify the eigenvalues of A. If +*> MODE=0, then D is assumed to contain the eigenvalues +*> otherwise they will be computed according to MODE, COND, +*> DMAX, and RSIGN and placed in D. +*> Modified if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry this describes how the eigenvalues are to +*> be specified: +*> MODE = 0 means use D as input +*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND +*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is between 1 and 4, D has entries ranging +*> from 1 to 1/COND, if between -1 and -4, D has entries +*> ranging from 1/COND to 1, +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is REAL +*> On entry, this is used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] DMAX +*> \verbatim +*> DMAX is COMPLEX +*> If MODE is neither -6, 0 nor 6, the contents of D, as +*> computed according to MODE and COND, will be scaled by +*> DMAX / max(abs(D(i))). Note that DMAX need not be +*> positive or real: if DMAX is negative or complex (or zero), +*> D will be scaled by a negative or complex number (or zero). +*> If RSIGN='F' then the largest (absolute) eigenvalue will be +*> equal to DMAX. +*> Not modified. +*> \endverbatim +*> +*> \param[in] RSIGN +*> \verbatim +*> RSIGN is CHARACTER*1 +*> If MODE is not 0, 6, or -6, and RSIGN='T', then the +*> elements of D, as computed according to MODE and COND, will +*> be multiplied by a random complex number from the unit +*> circle |z| = 1. If RSIGN='F', they will not be. RSIGN may +*> only have the values 'T' or 'F'. +*> Not modified. +*> \endverbatim +*> +*> \param[in] UPPER +*> \verbatim +*> UPPER is CHARACTER*1 +*> If UPPER='T', then the elements of A above the diagonal +*> will be set to random numbers out of DIST. If UPPER='F', +*> they will not. UPPER may only have the values 'T' or 'F'. +*> Not modified. +*> \endverbatim +*> +*> \param[in] SIM +*> \verbatim +*> SIM is CHARACTER*1 +*> If SIM='T', then A will be operated on by a "similarity +*> transform", i.e., multiplied on the left by a matrix X and +*> on the right by X inverse. X = U S V, where U and V are +*> random unitary matrices and S is a (diagonal) matrix of +*> singular values specified by DS, MODES, and CONDS. If +*> SIM='F', then A will not be transformed. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] DS +*> \verbatim +*> DS is REAL array, dimension ( N ) +*> This array is used to specify the singular values of X, +*> in the same way that D specifies the eigenvalues of A. +*> If MODE=0, the DS contains the singular values, which +*> may not be zero. +*> Modified if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODES +*> \verbatim +*> MODES is INTEGER +*> \endverbatim +*> +*> \param[in] CONDS +*> \verbatim +*> CONDS is REAL +*> Similar to MODE and COND, but for specifying the diagonal +*> of S. MODES=-6 and +6 are not allowed (since they would +*> result in randomly ill-conditioned eigenvalues.) +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> This specifies the lower bandwidth of the matrix. KL=1 +*> specifies upper Hessenberg form. If KL is at least N-1, +*> then A will have full lower bandwidth. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> This specifies the upper bandwidth of the matrix. KU=1 +*> specifies lower Hessenberg form. If KU is at least N-1, +*> then A will have full upper bandwidth; if KU and KL +*> are both at least N-1, then A will be dense. Only one of +*> KU and KL may be less than N-1. +*> Not modified. +*> \endverbatim +*> +*> \param[in] ANORM +*> \verbatim +*> ANORM is REAL +*> If ANORM is not negative, then A will be scaled by a non- +*> negative real number to make the maximum-element-norm of A +*> to be ANORM. +*> Not modified. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is COMPLEX array, dimension ( LDA, N ) +*> On exit A is the desired test matrix. +*> Modified. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> LDA specifies the first dimension of A as declared in the +*> calling program. LDA must be at least M. +*> Not modified. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX array, dimension ( 3*N ) +*> Workspace. +*> Modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error code. On exit, INFO will be set to one of the +*> following values: +*> 0 => normal return +*> -1 => N negative +*> -2 => DIST illegal string +*> -5 => MODE not in range -6 to 6 +*> -6 => COND less than 1.0, and MODE neither -6, 0 nor 6 +*> -9 => RSIGN is not 'T' or 'F' +*> -10 => UPPER is not 'T' or 'F' +*> -11 => SIM is not 'T' or 'F' +*> -12 => MODES=0 and DS has a zero singular value. +*> -13 => MODES is not in the range -5 to 5. +*> -14 => MODES is nonzero and CONDS is less than 1. +*> -15 => KL is less than 1. +*> -16 => KU is less than 1, or KL and KU are both less than +*> N-1. +*> -19 => LDA is less than M. +*> 1 => Error return from CLATM1 (computing D) +*> 2 => Cannot scale to DMAX (max. eigenvalue is 0) +*> 3 => Error return from SLATM1 (computing DS) +*> 4 => Error return from CLARGE +*> 5 => Zero singular value from SLATM1. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_matgen +* +* ===================================================================== SUBROUTINE CLATME( N, DIST, ISEED, D, MODE, COND, DMAX, $ RSIGN, $ UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, $ A, $ LDA, WORK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER DIST, RSIGN, SIM, UPPER @@ -20,198 +320,6 @@ COMPLEX A( LDA, * ), D( * ), WORK( * ) * .. * -* Purpose -* ======= -* -* CLATME generates random non-symmetric square matrices with -* specified eigenvalues for testing LAPACK programs. -* -* CLATME operates by applying the following sequence of -* operations: -* -* 1. Set the diagonal to D, where D may be input or -* computed according to MODE, COND, DMAX, and RSIGN -* as described below. -* -* 2. If UPPER='T', the upper triangle of A is set to random values -* out of distribution DIST. -* -* 3. If SIM='T', A is multiplied on the left by a random matrix -* X, whose singular values are specified by DS, MODES, and -* CONDS, and on the right by X inverse. -* -* 4. If KL < N-1, the lower bandwidth is reduced to KL using -* Householder transformations. If KU < N-1, the upper -* bandwidth is reduced to KU. -* -* 5. If ANORM is not negative, the matrix is scaled to have -* maximum-element-norm ANORM. -* -* (Note: since the matrix cannot be reduced beyond Hessenberg form, -* no packing options are available.) -* -* Arguments -* ========= -* -* N (input) INTEGER -* The number of columns (or rows) of A. Not modified. -* -* DIST (input) CHARACTER*1 -* On entry, DIST specifies the type of distribution to be used -* to generate the random eigen-/singular values, and on the -* upper triangle (see UPPER). -* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) -* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) -* 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) -* 'D' => uniform on the complex disc |z| < 1. -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. They should lie between 0 and 4095 inclusive, -* and ISEED(4) should be odd. The random number generator -* uses a linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to CLATME -* to continue the same random number sequence. -* Changed on exit. -* -* D (input/output) COMPLEX array, dimension ( N ) -* This array is used to specify the eigenvalues of A. If -* MODE=0, then D is assumed to contain the eigenvalues -* otherwise they will be computed according to MODE, COND, -* DMAX, and RSIGN and placed in D. -* Modified if MODE is nonzero. -* -* MODE (input) INTEGER -* On entry this describes how the eigenvalues are to -* be specified: -* MODE = 0 means use D as input -* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND -* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is between 1 and 4, D has entries ranging -* from 1 to 1/COND, if between -1 and -4, D has entries -* ranging from 1/COND to 1, -* Not modified. -* -* COND (input) REAL -* On entry, this is used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* DMAX (input) COMPLEX -* If MODE is neither -6, 0 nor 6, the contents of D, as -* computed according to MODE and COND, will be scaled by -* DMAX / max(abs(D(i))). Note that DMAX need not be -* positive or real: if DMAX is negative or complex (or zero), -* D will be scaled by a negative or complex number (or zero). -* If RSIGN='F' then the largest (absolute) eigenvalue will be -* equal to DMAX. -* Not modified. -* -* RSIGN (input) CHARACTER*1 -* If MODE is not 0, 6, or -6, and RSIGN='T', then the -* elements of D, as computed according to MODE and COND, will -* be multiplied by a random complex number from the unit -* circle |z| = 1. If RSIGN='F', they will not be. RSIGN may -* only have the values 'T' or 'F'. -* Not modified. -* -* UPPER (input) CHARACTER*1 -* If UPPER='T', then the elements of A above the diagonal -* will be set to random numbers out of DIST. If UPPER='F', -* they will not. UPPER may only have the values 'T' or 'F'. -* Not modified. -* -* SIM (input) CHARACTER*1 -* If SIM='T', then A will be operated on by a "similarity -* transform", i.e., multiplied on the left by a matrix X and -* on the right by X inverse. X = U S V, where U and V are -* random unitary matrices and S is a (diagonal) matrix of -* singular values specified by DS, MODES, and CONDS. If -* SIM='F', then A will not be transformed. -* Not modified. -* -* DS (input/output) REAL array, dimension ( N ) -* This array is used to specify the singular values of X, -* in the same way that D specifies the eigenvalues of A. -* If MODE=0, the DS contains the singular values, which -* may not be zero. -* Modified if MODE is nonzero. -* -* MODES (input) INTEGER -* -* CONDS (input) REAL -* Similar to MODE and COND, but for specifying the diagonal -* of S. MODES=-6 and +6 are not allowed (since they would -* result in randomly ill-conditioned eigenvalues.) -* -* KL (input) INTEGER -* This specifies the lower bandwidth of the matrix. KL=1 -* specifies upper Hessenberg form. If KL is at least N-1, -* then A will have full lower bandwidth. -* Not modified. -* -* KU (input) INTEGER -* This specifies the upper bandwidth of the matrix. KU=1 -* specifies lower Hessenberg form. If KU is at least N-1, -* then A will have full upper bandwidth; if KU and KL -* are both at least N-1, then A will be dense. Only one of -* KU and KL may be less than N-1. -* Not modified. -* -* ANORM (input) REAL -* If ANORM is not negative, then A will be scaled by a non- -* negative real number to make the maximum-element-norm of A -* to be ANORM. -* Not modified. -* -* A (output) COMPLEX array, dimension ( LDA, N ) -* On exit A is the desired test matrix. -* Modified. -* -* LDA (input) INTEGER -* LDA specifies the first dimension of A as declared in the -* calling program. LDA must be at least M. -* Not modified. -* -* WORK (workspace) COMPLEX array, dimension ( 3*N ) -* Workspace. -* Modified. -* -* INFO (output) INTEGER -* Error code. On exit, INFO will be set to one of the -* following values: -* 0 => normal return -* -1 => N negative -* -2 => DIST illegal string -* -5 => MODE not in range -6 to 6 -* -6 => COND less than 1.0, and MODE neither -6, 0 nor 6 -* -9 => RSIGN is not 'T' or 'F' -* -10 => UPPER is not 'T' or 'F' -* -11 => SIM is not 'T' or 'F' -* -12 => MODES=0 and DS has a zero singular value. -* -13 => MODES is not in the range -5 to 5. -* -14 => MODES is nonzero and CONDS is less than 1. -* -15 => KL is less than 1. -* -16 => KU is less than 1, or KL and KU are both less than -* N-1. -* -19 => LDA is less than M. -* 1 => Error return from CLATM1 (computing D) -* 2 => Cannot scale to DMAX (max. eigenvalue is 0) -* 3 => Error return from SLATM1 (computing DS) -* 4 => Error return from CLARGE -* 5 => Zero singular value from SLATM1. -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/clatmr.f b/TESTING/MATGEN/clatmr.f index 6ebeb7f2..70e8bcb3 100644 --- a/TESTING/MATGEN/clatmr.f +++ b/TESTING/MATGEN/clatmr.f @@ -1,11 +1,504 @@ +*> \brief \b CLATMR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CLATMR( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, +* RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, +* CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, +* PACK, A, LDA, IWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER DIST, GRADE, PACK, PIVTNG, RSIGN, SYM +* INTEGER INFO, KL, KU, LDA, M, MODE, MODEL, MODER, N +* REAL ANORM, COND, CONDL, CONDR, SPARSE +* COMPLEX DMAX +* .. +* .. Array Arguments .. +* INTEGER IPIVOT( * ), ISEED( 4 ), IWORK( * ) +* COMPLEX A( LDA, * ), D( * ), DL( * ), DR( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> CLATMR generates random matrices of various types for testing +*> LAPACK programs. +*> +*> CLATMR operates by applying the following sequence of +*> operations: +*> +*> Generate a matrix A with random entries of distribution DIST +*> which is symmetric if SYM='S', Hermitian if SYM='H', and +*> nonsymmetric if SYM='N'. +*> +*> Set the diagonal to D, where D may be input or +*> computed according to MODE, COND, DMAX and RSIGN +*> as described below. +*> +*> Grade the matrix, if desired, from the left and/or right +*> as specified by GRADE. The inputs DL, MODEL, CONDL, DR, +*> MODER and CONDR also determine the grading as described +*> below. +*> +*> Permute, if desired, the rows and/or columns as specified by +*> PIVTNG and IPIVOT. +*> +*> Set random entries to zero, if desired, to get a random sparse +*> matrix as specified by SPARSE. +*> +*> Make A a band matrix, if desired, by zeroing out the matrix +*> outside a band of lower bandwidth KL and upper bandwidth KU. +*> +*> Scale A, if desired, to have maximum entry ANORM. +*> +*> Pack the matrix if desired. Options specified by PACK are: +*> no packing +*> zero out upper half (if symmetric or Hermitian) +*> zero out lower half (if symmetric or Hermitian) +*> store the upper half columnwise (if symmetric or Hermitian +*> or square upper triangular) +*> store the lower half columnwise (if symmetric or Hermitian +*> or square lower triangular) +*> same as upper half rowwise if symmetric +*> same as conjugate upper half rowwise if Hermitian +*> store the lower triangle in banded format +*> (if symmetric or Hermitian) +*> store the upper triangle in banded format +*> (if symmetric or Hermitian) +*> store the entire matrix in banded format +*> +*> Note: If two calls to CLATMR differ only in the PACK parameter, +*> they will generate mathematically equivalent matrices. +*> +*> If two calls to CLATMR both have full bandwidth (KL = M-1 +*> and KU = N-1), and differ only in the PIVTNG and PACK +*> parameters, then the matrices generated will differ only +*> in the order of the rows and/or columns, and otherwise +*> contain the same data. This consistency cannot be and +*> is not maintained with less than full bandwidth. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Number of rows of A. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of columns of A. Not modified. +*> \endverbatim +*> +*> \param[in] DIST +*> \verbatim +*> DIST is CHARACTER*1 +*> On entry, DIST specifies the type of distribution to be used +*> to generate a random matrix . +*> 'U' => real and imaginary parts are independent +*> UNIFORM( 0, 1 ) ( 'U' for uniform ) +*> 'S' => real and imaginary parts are independent +*> UNIFORM( -1, 1 ) ( 'S' for symmetric ) +*> 'N' => real and imaginary parts are independent +*> NORMAL( 0, 1 ) ( 'N' for normal ) +*> 'D' => uniform on interior of unit disk ( 'D' for disk ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry ISEED specifies the seed of the random number +*> generator. They should lie between 0 and 4095 inclusive, +*> and ISEED(4) should be odd. The random number generator +*> uses a linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to CLATMR +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] SYM +*> \verbatim +*> SYM is CHARACTER*1 +*> If SYM='S', generated matrix is symmetric. +*> If SYM='H', generated matrix is Hermitian. +*> If SYM='N', generated matrix is nonsymmetric. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is COMPLEX array, dimension (min(M,N)) +*> On entry this array specifies the diagonal entries +*> of the diagonal of A. D may either be specified +*> on entry, or set according to MODE and COND as described +*> below. If the matrix is Hermitian, the real part of D +*> will be taken. May be changed on exit if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry describes how D is to be used: +*> MODE = 0 means use D as input +*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND +*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is REAL +*> On entry, used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] DMAX +*> \verbatim +*> DMAX is COMPLEX +*> If MODE neither -6, 0 nor 6, the diagonal is scaled by +*> DMAX / max(abs(D(i))), so that maximum absolute entry +*> of diagonal is abs(DMAX). If DMAX is complex (or zero), +*> diagonal will be scaled by a complex number (or zero). +*> \endverbatim +*> +*> \param[in] RSIGN +*> \verbatim +*> RSIGN is CHARACTER*1 +*> If MODE neither -6, 0 nor 6, specifies sign of diagonal +*> as follows: +*> 'T' => diagonal entries are multiplied by a random complex +*> number uniformly distributed with absolute value 1 +*> 'F' => diagonal unchanged +*> Not modified. +*> \endverbatim +*> +*> \param[in] GRADE +*> \verbatim +*> GRADE is CHARACTER*1 +*> Specifies grading of matrix as follows: +*> 'N' => no grading +*> 'L' => matrix premultiplied by diag( DL ) +*> (only if matrix nonsymmetric) +*> 'R' => matrix postmultiplied by diag( DR ) +*> (only if matrix nonsymmetric) +*> 'B' => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DR ) +*> (only if matrix nonsymmetric) +*> 'H' => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( CONJG(DL) ) +*> (only if matrix Hermitian or nonsymmetric) +*> 'S' => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DL ) +*> (only if matrix symmetric or nonsymmetric) +*> 'E' => matrix premultiplied by diag( DL ) and +*> postmultiplied by inv( diag( DL ) ) +*> ( 'S' for similarity ) +*> (only if matrix nonsymmetric) +*> Note: if GRADE='S', then M must equal N. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] DL +*> \verbatim +*> DL is COMPLEX array, dimension (M) +*> If MODEL=0, then on entry this array specifies the diagonal +*> entries of a diagonal matrix used as described under GRADE +*> above. If MODEL is not zero, then DL will be set according +*> to MODEL and CONDL, analogous to the way D is set according +*> to MODE and COND (except there is no DMAX parameter for DL). +*> If GRADE='E', then DL cannot have zero entries. +*> Not referenced if GRADE = 'N' or 'R'. Changed on exit. +*> \endverbatim +*> +*> \param[in] MODEL +*> \verbatim +*> MODEL is INTEGER +*> This specifies how the diagonal array DL is to be computed, +*> just as MODE specifies how D is to be computed. +*> Not modified. +*> \endverbatim +*> +*> \param[in] CONDL +*> \verbatim +*> CONDL is REAL +*> When MODEL is not zero, this specifies the condition number +*> of the computed DL. Not modified. +*> \endverbatim +*> +*> \param[in,out] DR +*> \verbatim +*> DR is COMPLEX array, dimension (N) +*> If MODER=0, then on entry this array specifies the diagonal +*> entries of a diagonal matrix used as described under GRADE +*> above. If MODER is not zero, then DR will be set according +*> to MODER and CONDR, analogous to the way D is set according +*> to MODE and COND (except there is no DMAX parameter for DR). +*> Not referenced if GRADE = 'N', 'L', 'H' or 'S'. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] MODER +*> \verbatim +*> MODER is INTEGER +*> This specifies how the diagonal array DR is to be computed, +*> just as MODE specifies how D is to be computed. +*> Not modified. +*> \endverbatim +*> +*> \param[in] CONDR +*> \verbatim +*> CONDR is REAL +*> When MODER is not zero, this specifies the condition number +*> of the computed DR. Not modified. +*> \endverbatim +*> +*> \param[in] PIVTNG +*> \verbatim +*> PIVTNG is CHARACTER*1 +*> On entry specifies pivoting permutations as follows: +*> 'N' or ' ' => none. +*> 'L' => left or row pivoting (matrix must be nonsymmetric). +*> 'R' => right or column pivoting (matrix must be +*> nonsymmetric). +*> 'B' or 'F' => both or full pivoting, i.e., on both sides. +*> In this case, M must equal N +*> \endverbatim +*> \verbatim +*> If two calls to CLATMR both have full bandwidth (KL = M-1 +*> and KU = N-1), and differ only in the PIVTNG and PACK +*> parameters, then the matrices generated will differ only +*> in the order of the rows and/or columns, and otherwise +*> contain the same data. This consistency cannot be +*> maintained with less than full bandwidth. +*> \endverbatim +*> +*> \param[in] IPIVOT +*> \verbatim +*> IPIVOT is INTEGER array, dimension (N or M) +*> This array specifies the permutation used. After the +*> basic matrix is generated, the rows, columns, or both +*> are permuted. If, say, row pivoting is selected, CLATMR +*> starts with the *last* row and interchanges the M-th and +*> IPIVOT(M)-th rows, then moves to the next-to-last row, +*> interchanging the (M-1)-th and the IPIVOT(M-1)-th rows, +*> and so on. In terms of "2-cycles", the permutation is +*> (1 IPIVOT(1)) (2 IPIVOT(2)) ... (M IPIVOT(M)) +*> where the rightmost cycle is applied first. This is the +*> *inverse* of the effect of pivoting in LINPACK. The idea +*> is that factoring (with pivoting) an identity matrix +*> which has been inverse-pivoted in this way should +*> result in a pivot vector identical to IPIVOT. +*> Not referenced if PIVTNG = 'N'. Not modified. +*> \endverbatim +*> +*> \param[in] SPARSE +*> \verbatim +*> SPARSE is REAL +*> On entry specifies the sparsity of the matrix if a sparse +*> matrix is to be generated. SPARSE should lie between +*> 0 and 1. To generate a sparse matrix, for each matrix entry +*> a uniform ( 0, 1 ) random number x is generated and +*> compared to SPARSE; if x is larger the matrix entry +*> is unchanged and if x is smaller the entry is set +*> to zero. Thus on the average a fraction SPARSE of the +*> entries will be set to zero. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> On entry specifies the lower bandwidth of the matrix. For +*> example, KL=0 implies upper triangular, KL=1 implies upper +*> Hessenberg, and KL at least M-1 implies the matrix is not +*> banded. Must equal KU if matrix is symmetric or Hermitian. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> On entry specifies the upper bandwidth of the matrix. For +*> example, KU=0 implies lower triangular, KU=1 implies lower +*> Hessenberg, and KU at least N-1 implies the matrix is not +*> banded. Must equal KL if matrix is symmetric or Hermitian. +*> Not modified. +*> \endverbatim +*> +*> \param[in] ANORM +*> \verbatim +*> ANORM is REAL +*> On entry specifies maximum entry of output matrix +*> (output matrix will by multiplied by a constant so that +*> its largest absolute entry equal ANORM) +*> if ANORM is nonnegative. If ANORM is negative no scaling +*> is done. Not modified. +*> \endverbatim +*> +*> \param[in] PACK +*> \verbatim +*> PACK is CHARACTER*1 +*> On entry specifies packing of matrix as follows: +*> 'N' => no packing +*> 'U' => zero out all subdiagonal entries +*> (if symmetric or Hermitian) +*> 'L' => zero out all superdiagonal entries +*> (if symmetric or Hermitian) +*> 'C' => store the upper triangle columnwise +*> (only if matrix symmetric or Hermitian or +*> square upper triangular) +*> 'R' => store the lower triangle columnwise +*> (only if matrix symmetric or Hermitian or +*> square lower triangular) +*> (same as upper half rowwise if symmetric) +*> (same as conjugate upper half rowwise if Hermitian) +*> 'B' => store the lower triangle in band storage scheme +*> (only if matrix symmetric or Hermitian) +*> 'Q' => store the upper triangle in band storage scheme +*> (only if matrix symmetric or Hermitian) +*> 'Z' => store the entire matrix in band storage scheme +*> (pivoting can be provided for by using this +*> option to store A in the trailing rows of +*> the allocated storage) +*> \endverbatim +*> \verbatim +*> Using these options, the various LAPACK packed and banded +*> storage schemes can be obtained: +*> GB - use 'Z' +*> PB, HB or TB - use 'B' or 'Q' +*> PP, HP or TP - use 'C' or 'R' +*> \endverbatim +*> \verbatim +*> If two calls to CLATMR differ only in the PACK parameter, +*> they will generate mathematically equivalent matrices. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX array, dimension (LDA,N) +*> On exit A is the desired test matrix. Only those +*> entries of A which are significant on output +*> will be referenced (even if A is in packed or band +*> storage format). The 'unoccupied corners' of A in +*> band format will be zeroed out. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> on entry LDA specifies the first dimension of A as +*> declared in the calling program. +*> If PACK='N', 'U' or 'L', LDA must be at least max ( 1, M ). +*> If PACK='C' or 'R', LDA must be at least 1. +*> If PACK='B', or 'Q', LDA must be MIN ( KU+1, N ) +*> If PACK='Z', LDA must be at least KUU+KLL+1, where +*> KUU = MIN ( KU, N-1 ) and KLL = MIN ( KL, N-1 ) +*> Not modified. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (N or M) +*> Workspace. Not referenced if PIVTNG = 'N'. Changed on exit. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error parameter on exit: +*> 0 => normal return +*> -1 => M negative or unequal to N and SYM='S' or 'H' +*> -2 => N negative +*> -3 => DIST illegal string +*> -5 => SYM illegal string +*> -7 => MODE not in range -6 to 6 +*> -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 +*> -10 => MODE neither -6, 0 nor 6 and RSIGN illegal string +*> -11 => GRADE illegal string, or GRADE='E' and +*> M not equal to N, or GRADE='L', 'R', 'B', 'S' or 'E' +*> and SYM = 'H', or GRADE='L', 'R', 'B', 'H' or 'E' +*> and SYM = 'S' +*> -12 => GRADE = 'E' and DL contains zero +*> -13 => MODEL not in range -6 to 6 and GRADE= 'L', 'B', 'H', +*> 'S' or 'E' +*> -14 => CONDL less than 1.0, GRADE='L', 'B', 'H', 'S' or 'E', +*> and MODEL neither -6, 0 nor 6 +*> -16 => MODER not in range -6 to 6 and GRADE= 'R' or 'B' +*> -17 => CONDR less than 1.0, GRADE='R' or 'B', and +*> MODER neither -6, 0 nor 6 +*> -18 => PIVTNG illegal string, or PIVTNG='B' or 'F' and +*> M not equal to N, or PIVTNG='L' or 'R' and SYM='S' +*> or 'H' +*> -19 => IPIVOT contains out of range number and +*> PIVTNG not equal to 'N' +*> -20 => KL negative +*> -21 => KU negative, or SYM='S' or 'H' and KU not equal to KL +*> -22 => SPARSE not in range 0. to 1. +*> -24 => PACK illegal string, or PACK='U', 'L', 'B' or 'Q' +*> and SYM='N', or PACK='C' and SYM='N' and either KL +*> not equal to 0 or N not equal to M, or PACK='R' and +*> SYM='N', and either KU not equal to 0 or N not equal +*> to M +*> -26 => LDA too small +*> 1 => Error return from CLATM1 (computing D) +*> 2 => Cannot scale diagonal to DMAX (max. entry is 0) +*> 3 => Error return from CLATM1 (computing DL) +*> 4 => Error return from CLATM1 (computing DR) +*> 5 => ANORM is positive, but matrix constructed prior to +*> attempting to scale it to have norm ANORM, is zero +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_matgen +* +* ===================================================================== SUBROUTINE CLATMR( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, $ RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, $ CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, $ PACK, A, LDA, IWORK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER DIST, GRADE, PACK, PIVTNG, RSIGN, SYM @@ -18,366 +511,6 @@ COMPLEX A( LDA, * ), D( * ), DL( * ), DR( * ) * .. * -* Purpose -* ======= -* -* CLATMR generates random matrices of various types for testing -* LAPACK programs. -* -* CLATMR operates by applying the following sequence of -* operations: -* -* Generate a matrix A with random entries of distribution DIST -* which is symmetric if SYM='S', Hermitian if SYM='H', and -* nonsymmetric if SYM='N'. -* -* Set the diagonal to D, where D may be input or -* computed according to MODE, COND, DMAX and RSIGN -* as described below. -* -* Grade the matrix, if desired, from the left and/or right -* as specified by GRADE. The inputs DL, MODEL, CONDL, DR, -* MODER and CONDR also determine the grading as described -* below. -* -* Permute, if desired, the rows and/or columns as specified by -* PIVTNG and IPIVOT. -* -* Set random entries to zero, if desired, to get a random sparse -* matrix as specified by SPARSE. -* -* Make A a band matrix, if desired, by zeroing out the matrix -* outside a band of lower bandwidth KL and upper bandwidth KU. -* -* Scale A, if desired, to have maximum entry ANORM. -* -* Pack the matrix if desired. Options specified by PACK are: -* no packing -* zero out upper half (if symmetric or Hermitian) -* zero out lower half (if symmetric or Hermitian) -* store the upper half columnwise (if symmetric or Hermitian -* or square upper triangular) -* store the lower half columnwise (if symmetric or Hermitian -* or square lower triangular) -* same as upper half rowwise if symmetric -* same as conjugate upper half rowwise if Hermitian -* store the lower triangle in banded format -* (if symmetric or Hermitian) -* store the upper triangle in banded format -* (if symmetric or Hermitian) -* store the entire matrix in banded format -* -* Note: If two calls to CLATMR differ only in the PACK parameter, -* they will generate mathematically equivalent matrices. -* -* If two calls to CLATMR both have full bandwidth (KL = M-1 -* and KU = N-1), and differ only in the PIVTNG and PACK -* parameters, then the matrices generated will differ only -* in the order of the rows and/or columns, and otherwise -* contain the same data. This consistency cannot be and -* is not maintained with less than full bandwidth. -* -* Arguments -* ========= -* -* M (input) INTEGER -* Number of rows of A. Not modified. -* -* N (input) INTEGER -* Number of columns of A. Not modified. -* -* DIST (input) CHARACTER*1 -* On entry, DIST specifies the type of distribution to be used -* to generate a random matrix . -* 'U' => real and imaginary parts are independent -* UNIFORM( 0, 1 ) ( 'U' for uniform ) -* 'S' => real and imaginary parts are independent -* UNIFORM( -1, 1 ) ( 'S' for symmetric ) -* 'N' => real and imaginary parts are independent -* NORMAL( 0, 1 ) ( 'N' for normal ) -* 'D' => uniform on interior of unit disk ( 'D' for disk ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension (4) -* On entry ISEED specifies the seed of the random number -* generator. They should lie between 0 and 4095 inclusive, -* and ISEED(4) should be odd. The random number generator -* uses a linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to CLATMR -* to continue the same random number sequence. -* Changed on exit. -* -* SYM (input) CHARACTER*1 -* If SYM='S', generated matrix is symmetric. -* If SYM='H', generated matrix is Hermitian. -* If SYM='N', generated matrix is nonsymmetric. -* Not modified. -* -* D (input/output) COMPLEX array, dimension (min(M,N)) -* On entry this array specifies the diagonal entries -* of the diagonal of A. D may either be specified -* on entry, or set according to MODE and COND as described -* below. If the matrix is Hermitian, the real part of D -* will be taken. May be changed on exit if MODE is nonzero. -* -* MODE (input) INTEGER -* On entry describes how D is to be used: -* MODE = 0 means use D as input -* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND -* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* Not modified. -* -* COND (input) REAL -* On entry, used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* DMAX (input) COMPLEX -* If MODE neither -6, 0 nor 6, the diagonal is scaled by -* DMAX / max(abs(D(i))), so that maximum absolute entry -* of diagonal is abs(DMAX). If DMAX is complex (or zero), -* diagonal will be scaled by a complex number (or zero). -* -* RSIGN (input) CHARACTER*1 -* If MODE neither -6, 0 nor 6, specifies sign of diagonal -* as follows: -* 'T' => diagonal entries are multiplied by a random complex -* number uniformly distributed with absolute value 1 -* 'F' => diagonal unchanged -* Not modified. -* -* GRADE (input) CHARACTER*1 -* Specifies grading of matrix as follows: -* 'N' => no grading -* 'L' => matrix premultiplied by diag( DL ) -* (only if matrix nonsymmetric) -* 'R' => matrix postmultiplied by diag( DR ) -* (only if matrix nonsymmetric) -* 'B' => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DR ) -* (only if matrix nonsymmetric) -* 'H' => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( CONJG(DL) ) -* (only if matrix Hermitian or nonsymmetric) -* 'S' => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DL ) -* (only if matrix symmetric or nonsymmetric) -* 'E' => matrix premultiplied by diag( DL ) and -* postmultiplied by inv( diag( DL ) ) -* ( 'S' for similarity ) -* (only if matrix nonsymmetric) -* Note: if GRADE='S', then M must equal N. -* Not modified. -* -* DL (input/output) COMPLEX array, dimension (M) -* If MODEL=0, then on entry this array specifies the diagonal -* entries of a diagonal matrix used as described under GRADE -* above. If MODEL is not zero, then DL will be set according -* to MODEL and CONDL, analogous to the way D is set according -* to MODE and COND (except there is no DMAX parameter for DL). -* If GRADE='E', then DL cannot have zero entries. -* Not referenced if GRADE = 'N' or 'R'. Changed on exit. -* -* MODEL (input) INTEGER -* This specifies how the diagonal array DL is to be computed, -* just as MODE specifies how D is to be computed. -* Not modified. -* -* CONDL (input) REAL -* When MODEL is not zero, this specifies the condition number -* of the computed DL. Not modified. -* -* DR (input/output) COMPLEX array, dimension (N) -* If MODER=0, then on entry this array specifies the diagonal -* entries of a diagonal matrix used as described under GRADE -* above. If MODER is not zero, then DR will be set according -* to MODER and CONDR, analogous to the way D is set according -* to MODE and COND (except there is no DMAX parameter for DR). -* Not referenced if GRADE = 'N', 'L', 'H' or 'S'. -* Changed on exit. -* -* MODER (input) INTEGER -* This specifies how the diagonal array DR is to be computed, -* just as MODE specifies how D is to be computed. -* Not modified. -* -* CONDR (input) REAL -* When MODER is not zero, this specifies the condition number -* of the computed DR. Not modified. -* -* PIVTNG (input) CHARACTER*1 -* On entry specifies pivoting permutations as follows: -* 'N' or ' ' => none. -* 'L' => left or row pivoting (matrix must be nonsymmetric). -* 'R' => right or column pivoting (matrix must be -* nonsymmetric). -* 'B' or 'F' => both or full pivoting, i.e., on both sides. -* In this case, M must equal N -* -* If two calls to CLATMR both have full bandwidth (KL = M-1 -* and KU = N-1), and differ only in the PIVTNG and PACK -* parameters, then the matrices generated will differ only -* in the order of the rows and/or columns, and otherwise -* contain the same data. This consistency cannot be -* maintained with less than full bandwidth. -* -* IPIVOT (input) INTEGER array, dimension (N or M) -* This array specifies the permutation used. After the -* basic matrix is generated, the rows, columns, or both -* are permuted. If, say, row pivoting is selected, CLATMR -* starts with the *last* row and interchanges the M-th and -* IPIVOT(M)-th rows, then moves to the next-to-last row, -* interchanging the (M-1)-th and the IPIVOT(M-1)-th rows, -* and so on. In terms of "2-cycles", the permutation is -* (1 IPIVOT(1)) (2 IPIVOT(2)) ... (M IPIVOT(M)) -* where the rightmost cycle is applied first. This is the -* *inverse* of the effect of pivoting in LINPACK. The idea -* is that factoring (with pivoting) an identity matrix -* which has been inverse-pivoted in this way should -* result in a pivot vector identical to IPIVOT. -* Not referenced if PIVTNG = 'N'. Not modified. -* -* SPARSE (input) REAL -* On entry specifies the sparsity of the matrix if a sparse -* matrix is to be generated. SPARSE should lie between -* 0 and 1. To generate a sparse matrix, for each matrix entry -* a uniform ( 0, 1 ) random number x is generated and -* compared to SPARSE; if x is larger the matrix entry -* is unchanged and if x is smaller the entry is set -* to zero. Thus on the average a fraction SPARSE of the -* entries will be set to zero. -* Not modified. -* -* KL (input) INTEGER -* On entry specifies the lower bandwidth of the matrix. For -* example, KL=0 implies upper triangular, KL=1 implies upper -* Hessenberg, and KL at least M-1 implies the matrix is not -* banded. Must equal KU if matrix is symmetric or Hermitian. -* Not modified. -* -* KU (input) INTEGER -* On entry specifies the upper bandwidth of the matrix. For -* example, KU=0 implies lower triangular, KU=1 implies lower -* Hessenberg, and KU at least N-1 implies the matrix is not -* banded. Must equal KL if matrix is symmetric or Hermitian. -* Not modified. -* -* ANORM (input) REAL -* On entry specifies maximum entry of output matrix -* (output matrix will by multiplied by a constant so that -* its largest absolute entry equal ANORM) -* if ANORM is nonnegative. If ANORM is negative no scaling -* is done. Not modified. -* -* PACK (input) CHARACTER*1 -* On entry specifies packing of matrix as follows: -* 'N' => no packing -* 'U' => zero out all subdiagonal entries -* (if symmetric or Hermitian) -* 'L' => zero out all superdiagonal entries -* (if symmetric or Hermitian) -* 'C' => store the upper triangle columnwise -* (only if matrix symmetric or Hermitian or -* square upper triangular) -* 'R' => store the lower triangle columnwise -* (only if matrix symmetric or Hermitian or -* square lower triangular) -* (same as upper half rowwise if symmetric) -* (same as conjugate upper half rowwise if Hermitian) -* 'B' => store the lower triangle in band storage scheme -* (only if matrix symmetric or Hermitian) -* 'Q' => store the upper triangle in band storage scheme -* (only if matrix symmetric or Hermitian) -* 'Z' => store the entire matrix in band storage scheme -* (pivoting can be provided for by using this -* option to store A in the trailing rows of -* the allocated storage) -* -* Using these options, the various LAPACK packed and banded -* storage schemes can be obtained: -* GB - use 'Z' -* PB, HB or TB - use 'B' or 'Q' -* PP, HP or TP - use 'C' or 'R' -* -* If two calls to CLATMR differ only in the PACK parameter, -* they will generate mathematically equivalent matrices. -* Not modified. -* -* A (input/output) COMPLEX array, dimension (LDA,N) -* On exit A is the desired test matrix. Only those -* entries of A which are significant on output -* will be referenced (even if A is in packed or band -* storage format). The 'unoccupied corners' of A in -* band format will be zeroed out. -* -* LDA (input) INTEGER -* on entry LDA specifies the first dimension of A as -* declared in the calling program. -* If PACK='N', 'U' or 'L', LDA must be at least max ( 1, M ). -* If PACK='C' or 'R', LDA must be at least 1. -* If PACK='B', or 'Q', LDA must be MIN ( KU+1, N ) -* If PACK='Z', LDA must be at least KUU+KLL+1, where -* KUU = MIN ( KU, N-1 ) and KLL = MIN ( KL, N-1 ) -* Not modified. -* -* IWORK (workspace) INTEGER array, dimension (N or M) -* Workspace. Not referenced if PIVTNG = 'N'. Changed on exit. -* -* INFO (output) INTEGER -* Error parameter on exit: -* 0 => normal return -* -1 => M negative or unequal to N and SYM='S' or 'H' -* -2 => N negative -* -3 => DIST illegal string -* -5 => SYM illegal string -* -7 => MODE not in range -6 to 6 -* -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 -* -10 => MODE neither -6, 0 nor 6 and RSIGN illegal string -* -11 => GRADE illegal string, or GRADE='E' and -* M not equal to N, or GRADE='L', 'R', 'B', 'S' or 'E' -* and SYM = 'H', or GRADE='L', 'R', 'B', 'H' or 'E' -* and SYM = 'S' -* -12 => GRADE = 'E' and DL contains zero -* -13 => MODEL not in range -6 to 6 and GRADE= 'L', 'B', 'H', -* 'S' or 'E' -* -14 => CONDL less than 1.0, GRADE='L', 'B', 'H', 'S' or 'E', -* and MODEL neither -6, 0 nor 6 -* -16 => MODER not in range -6 to 6 and GRADE= 'R' or 'B' -* -17 => CONDR less than 1.0, GRADE='R' or 'B', and -* MODER neither -6, 0 nor 6 -* -18 => PIVTNG illegal string, or PIVTNG='B' or 'F' and -* M not equal to N, or PIVTNG='L' or 'R' and SYM='S' -* or 'H' -* -19 => IPIVOT contains out of range number and -* PIVTNG not equal to 'N' -* -20 => KL negative -* -21 => KU negative, or SYM='S' or 'H' and KU not equal to KL -* -22 => SPARSE not in range 0. to 1. -* -24 => PACK illegal string, or PACK='U', 'L', 'B' or 'Q' -* and SYM='N', or PACK='C' and SYM='N' and either KL -* not equal to 0 or N not equal to M, or PACK='R' and -* SYM='N', and either KU not equal to 0 or N not equal -* to M -* -26 => LDA too small -* 1 => Error return from CLATM1 (computing D) -* 2 => Cannot scale diagonal to DMAX (max. entry is 0) -* 3 => Error return from CLATM1 (computing DL) -* 4 => Error return from CLATM1 (computing DR) -* 5 => ANORM is positive, but matrix constructed prior to -* attempting to scale it to have norm ANORM, is zero -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/clatms.f b/TESTING/MATGEN/clatms.f index 7fb5c495..7b206d7a 100644 --- a/TESTING/MATGEN/clatms.f +++ b/TESTING/MATGEN/clatms.f @@ -1,9 +1,345 @@ +*> \brief \b CLATMS +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, +* KL, KU, PACK, A, LDA, WORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER DIST, PACK, SYM +* INTEGER INFO, KL, KU, LDA, M, MODE, N +* REAL COND, DMAX +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* REAL D( * ) +* COMPLEX A( LDA, * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> CLATMS generates random matrices with specified singular values +*> (or hermitian with specified eigenvalues) +*> for testing LAPACK programs. +*> +*> CLATMS operates by applying the following sequence of +*> operations: +*> +*> Set the diagonal to D, where D may be input or +*> computed according to MODE, COND, DMAX, and SYM +*> as described below. +*> +*> Generate a matrix with the appropriate band structure, by one +*> of two methods: +*> +*> Method A: +*> Generate a dense M x N matrix by multiplying D on the left +*> and the right by random unitary matrices, then: +*> +*> Reduce the bandwidth according to KL and KU, using +*> Householder transformations. +*> +*> Method B: +*> Convert the bandwidth-0 (i.e., diagonal) matrix to a +*> bandwidth-1 matrix using Givens rotations, "chasing" +*> out-of-band elements back, much as in QR; then convert +*> the bandwidth-1 to a bandwidth-2 matrix, etc. Note +*> that for reasonably small bandwidths (relative to M and +*> N) this requires less storage, as a dense matrix is not +*> generated. Also, for hermitian or symmetric matrices, +*> only one triangle is generated. +*> +*> Method A is chosen if the bandwidth is a large fraction of the +*> order of the matrix, and LDA is at least M (so a dense +*> matrix can be stored.) Method B is chosen if the bandwidth +*> is small (< 1/2 N for hermitian or symmetric, < .3 N+M for +*> non-symmetric), or LDA is less than M and not less than the +*> bandwidth. +*> +*> Pack the matrix if desired. Options specified by PACK are: +*> no packing +*> zero out upper half (if hermitian) +*> zero out lower half (if hermitian) +*> store the upper half columnwise (if hermitian or upper +*> triangular) +*> store the lower half columnwise (if hermitian or lower +*> triangular) +*> store the lower triangle in banded format (if hermitian or +*> lower triangular) +*> store the upper triangle in banded format (if hermitian or +*> upper triangular) +*> store the entire matrix in banded format +*> If Method B is chosen, and band format is specified, then the +*> matrix will be generated in the band format, so no repacking +*> will be necessary. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of A. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of A. N must equal M if the matrix +*> is symmetric or hermitian (i.e., if SYM is not 'N') +*> Not modified. +*> \endverbatim +*> +*> \param[in] DIST +*> \verbatim +*> DIST is CHARACTER*1 +*> On entry, DIST specifies the type of distribution to be used +*> to generate the random eigen-/singular values. +*> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) +*> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) +*> 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. They should lie between 0 and 4095 inclusive, +*> and ISEED(4) should be odd. The random number generator +*> uses a linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to CLATMS +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] SYM +*> \verbatim +*> SYM is CHARACTER*1 +*> If SYM='H', the generated matrix is hermitian, with +*> eigenvalues specified by D, COND, MODE, and DMAX; they +*> may be positive, negative, or zero. +*> If SYM='P', the generated matrix is hermitian, with +*> eigenvalues (= singular values) specified by D, COND, +*> MODE, and DMAX; they will not be negative. +*> If SYM='N', the generated matrix is nonsymmetric, with +*> singular values specified by D, COND, MODE, and DMAX; +*> they will not be negative. +*> If SYM='S', the generated matrix is (complex) symmetric, +*> with singular values specified by D, COND, MODE, and +*> DMAX; they will not be negative. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is REAL array, dimension ( MIN( M, N ) ) +*> This array is used to specify the singular values or +*> eigenvalues of A (see SYM, above.) If MODE=0, then D is +*> assumed to contain the singular/eigenvalues, otherwise +*> they will be computed according to MODE, COND, and DMAX, +*> and placed in D. +*> Modified if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry this describes how the singular/eigenvalues are to +*> be specified: +*> MODE = 0 means use D as input +*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND +*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> If SYM='H', and MODE is neither 0, 6, nor -6, then +*> the elements of D will also be multiplied by a random +*> sign (i.e., +1 or -1.) +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is REAL +*> On entry, this is used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] DMAX +*> \verbatim +*> DMAX is REAL +*> If MODE is neither -6, 0 nor 6, the contents of D, as +*> computed according to MODE and COND, will be scaled by +*> DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or +*> singular value (which is to say the norm) will be abs(DMAX). +*> Note that DMAX need not be positive: if DMAX is negative +*> (or zero), D will be scaled by a negative number (or zero). +*> Not modified. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> This specifies the lower bandwidth of the matrix. For +*> example, KL=0 implies upper triangular, KL=1 implies upper +*> Hessenberg, and KL being at least M-1 means that the matrix +*> has full lower bandwidth. KL must equal KU if the matrix +*> is symmetric or hermitian. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> This specifies the upper bandwidth of the matrix. For +*> example, KU=0 implies lower triangular, KU=1 implies lower +*> Hessenberg, and KU being at least N-1 means that the matrix +*> has full upper bandwidth. KL must equal KU if the matrix +*> is symmetric or hermitian. +*> Not modified. +*> \endverbatim +*> +*> \param[in] PACK +*> \verbatim +*> PACK is CHARACTER*1 +*> This specifies packing of matrix as follows: +*> 'N' => no packing +*> 'U' => zero out all subdiagonal entries (if symmetric +*> or hermitian) +*> 'L' => zero out all superdiagonal entries (if symmetric +*> or hermitian) +*> 'C' => store the upper triangle columnwise (only if the +*> matrix is symmetric, hermitian, or upper triangular) +*> 'R' => store the lower triangle columnwise (only if the +*> matrix is symmetric, hermitian, or lower triangular) +*> 'B' => store the lower triangle in band storage scheme +*> (only if the matrix is symmetric, hermitian, or +*> lower triangular) +*> 'Q' => store the upper triangle in band storage scheme +*> (only if the matrix is symmetric, hermitian, or +*> upper triangular) +*> 'Z' => store the entire matrix in band storage scheme +*> (pivoting can be provided for by using this +*> option to store A in the trailing rows of +*> the allocated storage) +*> \endverbatim +*> \verbatim +*> Using these options, the various LAPACK packed and banded +*> storage schemes can be obtained: +*> GB - use 'Z' +*> PB, SB, HB, or TB - use 'B' or 'Q' +*> PP, SP, HB, or TP - use 'C' or 'R' +*> \endverbatim +*> \verbatim +*> If two calls to CLATMS differ only in the PACK parameter, +*> they will generate mathematically equivalent matrices. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX array, dimension ( LDA, N ) +*> On exit A is the desired test matrix. A is first generated +*> in full (unpacked) form, and then packed, if so specified +*> by PACK. Thus, the first M elements of the first N +*> columns will always be modified. If PACK specifies a +*> packed or banded storage scheme, all LDA elements of the +*> first N columns will be modified; the elements of the +*> array which do not correspond to elements of the generated +*> matrix are set to zero. +*> Modified. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> LDA specifies the first dimension of A as declared in the +*> calling program. If PACK='N', 'U', 'L', 'C', or 'R', then +*> LDA must be at least M. If PACK='B' or 'Q', then LDA must +*> be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). +*> If PACK='Z', LDA must be large enough to hold the packed +*> array: MIN( KU, N-1) + MIN( KL, M-1) + 1. +*> Not modified. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX array, dimension ( 3*MAX( N, M ) ) +*> Workspace. +*> Modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error code. On exit, INFO will be set to one of the +*> following values: +*> 0 => normal return +*> -1 => M negative or unequal to N and SYM='S', 'H', or 'P' +*> -2 => N negative +*> -3 => DIST illegal string +*> -5 => SYM illegal string +*> -7 => MODE not in range -6 to 6 +*> -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 +*> -10 => KL negative +*> -11 => KU negative, or SYM is not 'N' and KU is not equal to +*> KL +*> -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; +*> or PACK='C' or 'Q' and SYM='N' and KL is not zero; +*> or PACK='R' or 'B' and SYM='N' and KU is not zero; +*> or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not +*> N. +*> -14 => LDA is less than M, or PACK='Z' and LDA is less than +*> MIN(KU,N-1) + MIN(KL,M-1) + 1. +*> 1 => Error return from SLATM1 +*> 2 => Cannot scale to DMAX (max. sing. value is 0) +*> 3 => Error return from CLAGGE, CLAGHE or CLAGSY +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_matgen +* +* ===================================================================== SUBROUTINE CLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, $ KL, KU, PACK, A, LDA, WORK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER DIST, PACK, SYM @@ -16,248 +352,6 @@ COMPLEX A( LDA, * ), WORK( * ) * .. * -* Purpose -* ======= -* -* CLATMS generates random matrices with specified singular values -* (or hermitian with specified eigenvalues) -* for testing LAPACK programs. -* -* CLATMS operates by applying the following sequence of -* operations: -* -* Set the diagonal to D, where D may be input or -* computed according to MODE, COND, DMAX, and SYM -* as described below. -* -* Generate a matrix with the appropriate band structure, by one -* of two methods: -* -* Method A: -* Generate a dense M x N matrix by multiplying D on the left -* and the right by random unitary matrices, then: -* -* Reduce the bandwidth according to KL and KU, using -* Householder transformations. -* -* Method B: -* Convert the bandwidth-0 (i.e., diagonal) matrix to a -* bandwidth-1 matrix using Givens rotations, "chasing" -* out-of-band elements back, much as in QR; then convert -* the bandwidth-1 to a bandwidth-2 matrix, etc. Note -* that for reasonably small bandwidths (relative to M and -* N) this requires less storage, as a dense matrix is not -* generated. Also, for hermitian or symmetric matrices, -* only one triangle is generated. -* -* Method A is chosen if the bandwidth is a large fraction of the -* order of the matrix, and LDA is at least M (so a dense -* matrix can be stored.) Method B is chosen if the bandwidth -* is small (< 1/2 N for hermitian or symmetric, < .3 N+M for -* non-symmetric), or LDA is less than M and not less than the -* bandwidth. -* -* Pack the matrix if desired. Options specified by PACK are: -* no packing -* zero out upper half (if hermitian) -* zero out lower half (if hermitian) -* store the upper half columnwise (if hermitian or upper -* triangular) -* store the lower half columnwise (if hermitian or lower -* triangular) -* store the lower triangle in banded format (if hermitian or -* lower triangular) -* store the upper triangle in banded format (if hermitian or -* upper triangular) -* store the entire matrix in banded format -* If Method B is chosen, and band format is specified, then the -* matrix will be generated in the band format, so no repacking -* will be necessary. -* -* Arguments -* ========= -* -* M (input) INTEGER -* The number of rows of A. Not modified. -* -* N (input) INTEGER -* The number of columns of A. N must equal M if the matrix -* is symmetric or hermitian (i.e., if SYM is not 'N') -* Not modified. -* -* DIST (input) CHARACTER*1 -* On entry, DIST specifies the type of distribution to be used -* to generate the random eigen-/singular values. -* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) -* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) -* 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. They should lie between 0 and 4095 inclusive, -* and ISEED(4) should be odd. The random number generator -* uses a linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to CLATMS -* to continue the same random number sequence. -* Changed on exit. -* -* SYM (input) CHARACTER*1 -* If SYM='H', the generated matrix is hermitian, with -* eigenvalues specified by D, COND, MODE, and DMAX; they -* may be positive, negative, or zero. -* If SYM='P', the generated matrix is hermitian, with -* eigenvalues (= singular values) specified by D, COND, -* MODE, and DMAX; they will not be negative. -* If SYM='N', the generated matrix is nonsymmetric, with -* singular values specified by D, COND, MODE, and DMAX; -* they will not be negative. -* If SYM='S', the generated matrix is (complex) symmetric, -* with singular values specified by D, COND, MODE, and -* DMAX; they will not be negative. -* Not modified. -* -* D (input/output) REAL array, dimension ( MIN( M, N ) ) -* This array is used to specify the singular values or -* eigenvalues of A (see SYM, above.) If MODE=0, then D is -* assumed to contain the singular/eigenvalues, otherwise -* they will be computed according to MODE, COND, and DMAX, -* and placed in D. -* Modified if MODE is nonzero. -* -* MODE (input) INTEGER -* On entry this describes how the singular/eigenvalues are to -* be specified: -* MODE = 0 means use D as input -* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND -* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* If SYM='H', and MODE is neither 0, 6, nor -6, then -* the elements of D will also be multiplied by a random -* sign (i.e., +1 or -1.) -* Not modified. -* -* COND (input) REAL -* On entry, this is used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* DMAX (input) REAL -* If MODE is neither -6, 0 nor 6, the contents of D, as -* computed according to MODE and COND, will be scaled by -* DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or -* singular value (which is to say the norm) will be abs(DMAX). -* Note that DMAX need not be positive: if DMAX is negative -* (or zero), D will be scaled by a negative number (or zero). -* Not modified. -* -* KL (input) INTEGER -* This specifies the lower bandwidth of the matrix. For -* example, KL=0 implies upper triangular, KL=1 implies upper -* Hessenberg, and KL being at least M-1 means that the matrix -* has full lower bandwidth. KL must equal KU if the matrix -* is symmetric or hermitian. -* Not modified. -* -* KU (input) INTEGER -* This specifies the upper bandwidth of the matrix. For -* example, KU=0 implies lower triangular, KU=1 implies lower -* Hessenberg, and KU being at least N-1 means that the matrix -* has full upper bandwidth. KL must equal KU if the matrix -* is symmetric or hermitian. -* Not modified. -* -* PACK (input) CHARACTER*1 -* This specifies packing of matrix as follows: -* 'N' => no packing -* 'U' => zero out all subdiagonal entries (if symmetric -* or hermitian) -* 'L' => zero out all superdiagonal entries (if symmetric -* or hermitian) -* 'C' => store the upper triangle columnwise (only if the -* matrix is symmetric, hermitian, or upper triangular) -* 'R' => store the lower triangle columnwise (only if the -* matrix is symmetric, hermitian, or lower triangular) -* 'B' => store the lower triangle in band storage scheme -* (only if the matrix is symmetric, hermitian, or -* lower triangular) -* 'Q' => store the upper triangle in band storage scheme -* (only if the matrix is symmetric, hermitian, or -* upper triangular) -* 'Z' => store the entire matrix in band storage scheme -* (pivoting can be provided for by using this -* option to store A in the trailing rows of -* the allocated storage) -* -* Using these options, the various LAPACK packed and banded -* storage schemes can be obtained: -* GB - use 'Z' -* PB, SB, HB, or TB - use 'B' or 'Q' -* PP, SP, HB, or TP - use 'C' or 'R' -* -* If two calls to CLATMS differ only in the PACK parameter, -* they will generate mathematically equivalent matrices. -* Not modified. -* -* A (input/output) COMPLEX array, dimension ( LDA, N ) -* On exit A is the desired test matrix. A is first generated -* in full (unpacked) form, and then packed, if so specified -* by PACK. Thus, the first M elements of the first N -* columns will always be modified. If PACK specifies a -* packed or banded storage scheme, all LDA elements of the -* first N columns will be modified; the elements of the -* array which do not correspond to elements of the generated -* matrix are set to zero. -* Modified. -* -* LDA (input) INTEGER -* LDA specifies the first dimension of A as declared in the -* calling program. If PACK='N', 'U', 'L', 'C', or 'R', then -* LDA must be at least M. If PACK='B' or 'Q', then LDA must -* be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). -* If PACK='Z', LDA must be large enough to hold the packed -* array: MIN( KU, N-1) + MIN( KL, M-1) + 1. -* Not modified. -* -* WORK (workspace) COMPLEX array, dimension ( 3*MAX( N, M ) ) -* Workspace. -* Modified. -* -* INFO (output) INTEGER -* Error code. On exit, INFO will be set to one of the -* following values: -* 0 => normal return -* -1 => M negative or unequal to N and SYM='S', 'H', or 'P' -* -2 => N negative -* -3 => DIST illegal string -* -5 => SYM illegal string -* -7 => MODE not in range -6 to 6 -* -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 -* -10 => KL negative -* -11 => KU negative, or SYM is not 'N' and KU is not equal to -* KL -* -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; -* or PACK='C' or 'Q' and SYM='N' and KL is not zero; -* or PACK='R' or 'B' and SYM='N' and KU is not zero; -* or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not -* N. -* -14 => LDA is less than M, or PACK='Z' and LDA is less than -* MIN(KU,N-1) + MIN(KL,M-1) + 1. -* 1 => Error return from SLATM1 -* 2 => Cannot scale to DMAX (max. sing. value is 0) -* 3 => Error return from CLAGGE, CLAGHE or CLAGSY -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/clatmt.f b/TESTING/MATGEN/clatmt.f index 1d7a13c7..0a2542be 100644 --- a/TESTING/MATGEN/clatmt.f +++ b/TESTING/MATGEN/clatmt.f @@ -1,9 +1,353 @@ +*> \brief \b CLATMT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CLATMT( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, +* RANK, KL, KU, PACK, A, LDA, WORK, INFO ) +* +* .. Scalar Arguments .. +* REAL COND, DMAX +* INTEGER INFO, KL, KU, LDA, M, MODE, N, RANK +* CHARACTER DIST, PACK, SYM +* .. +* .. Array Arguments .. +* COMPLEX A( LDA, * ), WORK( * ) +* REAL D( * ) +* INTEGER ISEED( 4 ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> CLATMT generates random matrices with specified singular values +*> (or hermitian with specified eigenvalues) +*> for testing LAPACK programs. +*> +*> CLATMT operates by applying the following sequence of +*> operations: +*> +*> Set the diagonal to D, where D may be input or +*> computed according to MODE, COND, DMAX, and SYM +*> as described below. +*> +*> Generate a matrix with the appropriate band structure, by one +*> of two methods: +*> +*> Method A: +*> Generate a dense M x N matrix by multiplying D on the left +*> and the right by random unitary matrices, then: +*> +*> Reduce the bandwidth according to KL and KU, using +*> Householder transformations. +*> +*> Method B: +*> Convert the bandwidth-0 (i.e., diagonal) matrix to a +*> bandwidth-1 matrix using Givens rotations, "chasing" +*> out-of-band elements back, much as in QR; then convert +*> the bandwidth-1 to a bandwidth-2 matrix, etc. Note +*> that for reasonably small bandwidths (relative to M and +*> N) this requires less storage, as a dense matrix is not +*> generated. Also, for hermitian or symmetric matrices, +*> only one triangle is generated. +*> +*> Method A is chosen if the bandwidth is a large fraction of the +*> order of the matrix, and LDA is at least M (so a dense +*> matrix can be stored.) Method B is chosen if the bandwidth +*> is small (< 1/2 N for hermitian or symmetric, < .3 N+M for +*> non-symmetric), or LDA is less than M and not less than the +*> bandwidth. +*> +*> Pack the matrix if desired. Options specified by PACK are: +*> no packing +*> zero out upper half (if hermitian) +*> zero out lower half (if hermitian) +*> store the upper half columnwise (if hermitian or upper +*> triangular) +*> store the lower half columnwise (if hermitian or lower +*> triangular) +*> store the lower triangle in banded format (if hermitian or +*> lower triangular) +*> store the upper triangle in banded format (if hermitian or +*> upper triangular) +*> store the entire matrix in banded format +*> If Method B is chosen, and band format is specified, then the +*> matrix will be generated in the band format, so no repacking +*> will be necessary. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of A. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of A. N must equal M if the matrix +*> is symmetric or hermitian (i.e., if SYM is not 'N') +*> Not modified. +*> \endverbatim +*> +*> \param[in] DIST +*> \verbatim +*> DIST is CHARACTER*1 +*> On entry, DIST specifies the type of distribution to be used +*> to generate the random eigen-/singular values. +*> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) +*> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) +*> 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. They should lie between 0 and 4095 inclusive, +*> and ISEED(4) should be odd. The random number generator +*> uses a linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to CLATMT +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] SYM +*> \verbatim +*> SYM is CHARACTER*1 +*> If SYM='H', the generated matrix is hermitian, with +*> eigenvalues specified by D, COND, MODE, and DMAX; they +*> may be positive, negative, or zero. +*> If SYM='P', the generated matrix is hermitian, with +*> eigenvalues (= singular values) specified by D, COND, +*> MODE, and DMAX; they will not be negative. +*> If SYM='N', the generated matrix is nonsymmetric, with +*> singular values specified by D, COND, MODE, and DMAX; +*> they will not be negative. +*> If SYM='S', the generated matrix is (complex) symmetric, +*> with singular values specified by D, COND, MODE, and +*> DMAX; they will not be negative. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is REAL array, dimension ( MIN( M, N ) ) +*> This array is used to specify the singular values or +*> eigenvalues of A (see SYM, above.) If MODE=0, then D is +*> assumed to contain the singular/eigenvalues, otherwise +*> they will be computed according to MODE, COND, and DMAX, +*> and placed in D. +*> Modified if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry this describes how the singular/eigenvalues are to +*> be specified: +*> MODE = 0 means use D as input +*> MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND +*> MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> If SYM='H', and MODE is neither 0, 6, nor -6, then +*> the elements of D will also be multiplied by a random +*> sign (i.e., +1 or -1.) +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is REAL +*> On entry, this is used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] DMAX +*> \verbatim +*> DMAX is REAL +*> If MODE is neither -6, 0 nor 6, the contents of D, as +*> computed according to MODE and COND, will be scaled by +*> DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or +*> singular value (which is to say the norm) will be abs(DMAX). +*> Note that DMAX need not be positive: if DMAX is negative +*> (or zero), D will be scaled by a negative number (or zero). +*> Not modified. +*> \endverbatim +*> +*> \param[in] RANK +*> \verbatim +*> RANK is INTEGER +*> The rank of matrix to be generated for modes 1,2,3 only. +*> D( RANK+1:N ) = 0. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> This specifies the lower bandwidth of the matrix. For +*> example, KL=0 implies upper triangular, KL=1 implies upper +*> Hessenberg, and KL being at least M-1 means that the matrix +*> has full lower bandwidth. KL must equal KU if the matrix +*> is symmetric or hermitian. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> This specifies the upper bandwidth of the matrix. For +*> example, KU=0 implies lower triangular, KU=1 implies lower +*> Hessenberg, and KU being at least N-1 means that the matrix +*> has full upper bandwidth. KL must equal KU if the matrix +*> is symmetric or hermitian. +*> Not modified. +*> \endverbatim +*> +*> \param[in] PACK +*> \verbatim +*> PACK is CHARACTER*1 +*> This specifies packing of matrix as follows: +*> 'N' => no packing +*> 'U' => zero out all subdiagonal entries (if symmetric +*> or hermitian) +*> 'L' => zero out all superdiagonal entries (if symmetric +*> or hermitian) +*> 'C' => store the upper triangle columnwise (only if the +*> matrix is symmetric, hermitian, or upper triangular) +*> 'R' => store the lower triangle columnwise (only if the +*> matrix is symmetric, hermitian, or lower triangular) +*> 'B' => store the lower triangle in band storage scheme +*> (only if the matrix is symmetric, hermitian, or +*> lower triangular) +*> 'Q' => store the upper triangle in band storage scheme +*> (only if the matrix is symmetric, hermitian, or +*> upper triangular) +*> 'Z' => store the entire matrix in band storage scheme +*> (pivoting can be provided for by using this +*> option to store A in the trailing rows of +*> the allocated storage) +*> \endverbatim +*> \verbatim +*> Using these options, the various LAPACK packed and banded +*> storage schemes can be obtained: +*> GB - use 'Z' +*> PB, SB, HB, or TB - use 'B' or 'Q' +*> PP, SP, HB, or TP - use 'C' or 'R' +*> \endverbatim +*> \verbatim +*> If two calls to CLATMT differ only in the PACK parameter, +*> they will generate mathematically equivalent matrices. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX array, dimension ( LDA, N ) +*> On exit A is the desired test matrix. A is first generated +*> in full (unpacked) form, and then packed, if so specified +*> by PACK. Thus, the first M elements of the first N +*> columns will always be modified. If PACK specifies a +*> packed or banded storage scheme, all LDA elements of the +*> first N columns will be modified; the elements of the +*> array which do not correspond to elements of the generated +*> matrix are set to zero. +*> Modified. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> LDA specifies the first dimension of A as declared in the +*> calling program. If PACK='N', 'U', 'L', 'C', or 'R', then +*> LDA must be at least M. If PACK='B' or 'Q', then LDA must +*> be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). +*> If PACK='Z', LDA must be large enough to hold the packed +*> array: MIN( KU, N-1) + MIN( KL, M-1) + 1. +*> Not modified. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX array, dimension ( 3*MAX( N, M ) ) +*> Workspace. +*> Modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error code. On exit, INFO will be set to one of the +*> following values: +*> 0 => normal return +*> -1 => M negative or unequal to N and SYM='S', 'H', or 'P' +*> -2 => N negative +*> -3 => DIST illegal string +*> -5 => SYM illegal string +*> -7 => MODE not in range -6 to 6 +*> -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 +*> -10 => KL negative +*> -11 => KU negative, or SYM is not 'N' and KU is not equal to +*> KL +*> -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; +*> or PACK='C' or 'Q' and SYM='N' and KL is not zero; +*> or PACK='R' or 'B' and SYM='N' and KU is not zero; +*> or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not +*> N. +*> -14 => LDA is less than M, or PACK='Z' and LDA is less than +*> MIN(KU,N-1) + MIN(KL,M-1) + 1. +*> 1 => Error return from SLATM7 +*> 2 => Cannot scale to DMAX (max. sing. value is 0) +*> 3 => Error return from CLAGGE, CLAGHE or CLAGSY +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_matgen +* +* ===================================================================== SUBROUTINE CLATMT( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, $ RANK, KL, KU, PACK, A, LDA, WORK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Craig Lucas, University of Manchester / NAG Ltd. -* October, 2008 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. REAL COND, DMAX @@ -16,253 +360,6 @@ INTEGER ISEED( 4 ) * .. * -* Purpose -* ======= -* -* CLATMT generates random matrices with specified singular values -* (or hermitian with specified eigenvalues) -* for testing LAPACK programs. -* -* CLATMT operates by applying the following sequence of -* operations: -* -* Set the diagonal to D, where D may be input or -* computed according to MODE, COND, DMAX, and SYM -* as described below. -* -* Generate a matrix with the appropriate band structure, by one -* of two methods: -* -* Method A: -* Generate a dense M x N matrix by multiplying D on the left -* and the right by random unitary matrices, then: -* -* Reduce the bandwidth according to KL and KU, using -* Householder transformations. -* -* Method B: -* Convert the bandwidth-0 (i.e., diagonal) matrix to a -* bandwidth-1 matrix using Givens rotations, "chasing" -* out-of-band elements back, much as in QR; then convert -* the bandwidth-1 to a bandwidth-2 matrix, etc. Note -* that for reasonably small bandwidths (relative to M and -* N) this requires less storage, as a dense matrix is not -* generated. Also, for hermitian or symmetric matrices, -* only one triangle is generated. -* -* Method A is chosen if the bandwidth is a large fraction of the -* order of the matrix, and LDA is at least M (so a dense -* matrix can be stored.) Method B is chosen if the bandwidth -* is small (< 1/2 N for hermitian or symmetric, < .3 N+M for -* non-symmetric), or LDA is less than M and not less than the -* bandwidth. -* -* Pack the matrix if desired. Options specified by PACK are: -* no packing -* zero out upper half (if hermitian) -* zero out lower half (if hermitian) -* store the upper half columnwise (if hermitian or upper -* triangular) -* store the lower half columnwise (if hermitian or lower -* triangular) -* store the lower triangle in banded format (if hermitian or -* lower triangular) -* store the upper triangle in banded format (if hermitian or -* upper triangular) -* store the entire matrix in banded format -* If Method B is chosen, and band format is specified, then the -* matrix will be generated in the band format, so no repacking -* will be necessary. -* -* Arguments -* ========= -* -* M (input) INTEGER -* The number of rows of A. Not modified. -* -* N (input) INTEGER -* The number of columns of A. N must equal M if the matrix -* is symmetric or hermitian (i.e., if SYM is not 'N') -* Not modified. -* -* DIST (input) CHARACTER*1 -* On entry, DIST specifies the type of distribution to be used -* to generate the random eigen-/singular values. -* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) -* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) -* 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. They should lie between 0 and 4095 inclusive, -* and ISEED(4) should be odd. The random number generator -* uses a linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to CLATMT -* to continue the same random number sequence. -* Changed on exit. -* -* SYM (input) CHARACTER*1 -* If SYM='H', the generated matrix is hermitian, with -* eigenvalues specified by D, COND, MODE, and DMAX; they -* may be positive, negative, or zero. -* If SYM='P', the generated matrix is hermitian, with -* eigenvalues (= singular values) specified by D, COND, -* MODE, and DMAX; they will not be negative. -* If SYM='N', the generated matrix is nonsymmetric, with -* singular values specified by D, COND, MODE, and DMAX; -* they will not be negative. -* If SYM='S', the generated matrix is (complex) symmetric, -* with singular values specified by D, COND, MODE, and -* DMAX; they will not be negative. -* Not modified. -* -* D (input/output) REAL array, dimension ( MIN( M, N ) ) -* This array is used to specify the singular values or -* eigenvalues of A (see SYM, above.) If MODE=0, then D is -* assumed to contain the singular/eigenvalues, otherwise -* they will be computed according to MODE, COND, and DMAX, -* and placed in D. -* Modified if MODE is nonzero. -* -* MODE (input) INTEGER -* On entry this describes how the singular/eigenvalues are to -* be specified: -* MODE = 0 means use D as input -* MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND -* MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* If SYM='H', and MODE is neither 0, 6, nor -6, then -* the elements of D will also be multiplied by a random -* sign (i.e., +1 or -1.) -* Not modified. -* -* COND (input) REAL -* On entry, this is used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* DMAX (input) REAL -* If MODE is neither -6, 0 nor 6, the contents of D, as -* computed according to MODE and COND, will be scaled by -* DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or -* singular value (which is to say the norm) will be abs(DMAX). -* Note that DMAX need not be positive: if DMAX is negative -* (or zero), D will be scaled by a negative number (or zero). -* Not modified. -* -* RANK (input) INTEGER -* The rank of matrix to be generated for modes 1,2,3 only. -* D( RANK+1:N ) = 0. -* Not modified. -* -* KL (input) INTEGER -* This specifies the lower bandwidth of the matrix. For -* example, KL=0 implies upper triangular, KL=1 implies upper -* Hessenberg, and KL being at least M-1 means that the matrix -* has full lower bandwidth. KL must equal KU if the matrix -* is symmetric or hermitian. -* Not modified. -* -* KU (input) INTEGER -* This specifies the upper bandwidth of the matrix. For -* example, KU=0 implies lower triangular, KU=1 implies lower -* Hessenberg, and KU being at least N-1 means that the matrix -* has full upper bandwidth. KL must equal KU if the matrix -* is symmetric or hermitian. -* Not modified. -* -* PACK (input) CHARACTER*1 -* This specifies packing of matrix as follows: -* 'N' => no packing -* 'U' => zero out all subdiagonal entries (if symmetric -* or hermitian) -* 'L' => zero out all superdiagonal entries (if symmetric -* or hermitian) -* 'C' => store the upper triangle columnwise (only if the -* matrix is symmetric, hermitian, or upper triangular) -* 'R' => store the lower triangle columnwise (only if the -* matrix is symmetric, hermitian, or lower triangular) -* 'B' => store the lower triangle in band storage scheme -* (only if the matrix is symmetric, hermitian, or -* lower triangular) -* 'Q' => store the upper triangle in band storage scheme -* (only if the matrix is symmetric, hermitian, or -* upper triangular) -* 'Z' => store the entire matrix in band storage scheme -* (pivoting can be provided for by using this -* option to store A in the trailing rows of -* the allocated storage) -* -* Using these options, the various LAPACK packed and banded -* storage schemes can be obtained: -* GB - use 'Z' -* PB, SB, HB, or TB - use 'B' or 'Q' -* PP, SP, HB, or TP - use 'C' or 'R' -* -* If two calls to CLATMT differ only in the PACK parameter, -* they will generate mathematically equivalent matrices. -* Not modified. -* -* A (input/output) COMPLEX array, dimension ( LDA, N ) -* On exit A is the desired test matrix. A is first generated -* in full (unpacked) form, and then packed, if so specified -* by PACK. Thus, the first M elements of the first N -* columns will always be modified. If PACK specifies a -* packed or banded storage scheme, all LDA elements of the -* first N columns will be modified; the elements of the -* array which do not correspond to elements of the generated -* matrix are set to zero. -* Modified. -* -* LDA (input) INTEGER -* LDA specifies the first dimension of A as declared in the -* calling program. If PACK='N', 'U', 'L', 'C', or 'R', then -* LDA must be at least M. If PACK='B' or 'Q', then LDA must -* be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). -* If PACK='Z', LDA must be large enough to hold the packed -* array: MIN( KU, N-1) + MIN( KL, M-1) + 1. -* Not modified. -* -* WORK (workspace) COMPLEX array, dimension ( 3*MAX( N, M ) ) -* Workspace. -* Modified. -* -* INFO (output) INTEGER -* Error code. On exit, INFO will be set to one of the -* following values: -* 0 => normal return -* -1 => M negative or unequal to N and SYM='S', 'H', or 'P' -* -2 => N negative -* -3 => DIST illegal string -* -5 => SYM illegal string -* -7 => MODE not in range -6 to 6 -* -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 -* -10 => KL negative -* -11 => KU negative, or SYM is not 'N' and KU is not equal to -* KL -* -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; -* or PACK='C' or 'Q' and SYM='N' and KL is not zero; -* or PACK='R' or 'B' and SYM='N' and KU is not zero; -* or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not -* N. -* -14 => LDA is less than M, or PACK='Z' and LDA is less than -* MIN(KU,N-1) + MIN(KL,M-1) + 1. -* 1 => Error return from SLATM7 -* 2 => Cannot scale to DMAX (max. sing. value is 0) -* 3 => Error return from CLAGGE, CLAGHE or CLAGSY -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/dlagge.f b/TESTING/MATGEN/dlagge.f index f0ae2168..1a3b2a5c 100644 --- a/TESTING/MATGEN/dlagge.f +++ b/TESTING/MATGEN/dlagge.f @@ -1,62 +1,132 @@ - SUBROUTINE DLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) -* -* -- LAPACK auxiliary test routine (version 3.1) -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER INFO, KL, KU, LDA, M, N -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) - DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * ) -* .. -* +*> \brief \b DLAGGE +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, KL, KU, LDA, M, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * ) +* .. +* * Purpose * ======= * -* DLAGGE generates a real general m by n matrix A, by pre- and post- -* multiplying a real diagonal matrix D with random orthogonal matrices: -* A = U*D*V. The lower and upper bandwidths may then be reduced to -* kl and ku by additional orthogonal transformations. +*>\details \b Purpose: +*>\verbatim +*> +*> DLAGGE generates a real general m by n matrix A, by pre- and post- +*> multiplying a real diagonal matrix D with random orthogonal matrices: +*> A = U*D*V. The lower and upper bandwidths may then be reduced to +*> kl and ku by additional orthogonal transformations. +*> +*>\endverbatim * * Arguments * ========= * -* M (input) INTEGER -* The number of rows of the matrix A. M >= 0. -* -* N (input) INTEGER -* The number of columns of the matrix A. N >= 0. -* -* KL (input) INTEGER -* The number of nonzero subdiagonals within the band of A. -* 0 <= KL <= M-1. -* -* KU (input) INTEGER -* The number of nonzero superdiagonals within the band of A. -* 0 <= KU <= N-1. +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> The number of nonzero subdiagonals within the band of A. +*> 0 <= KL <= M-1. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> The number of nonzero superdiagonals within the band of A. +*> 0 <= KU <= N-1. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (min(M,N)) +*> The diagonal elements of the diagonal matrix D. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> The generated m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= M. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (M+N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= * -* D (input) DOUBLE PRECISION array, dimension (min(M,N)) -* The diagonal elements of the diagonal matrix D. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (output) DOUBLE PRECISION array, dimension (LDA,N) -* The generated m by n matrix A. +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= M. +*> \ingroup double_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. +* ===================================================================== + SUBROUTINE DLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) * -* WORK (workspace) DOUBLE PRECISION array, dimension (M+N) +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value +* .. Scalar Arguments .. + INTEGER INFO, KL, KU, LDA, M, N +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) + DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/dlagsy.f b/TESTING/MATGEN/dlagsy.f index d9e81fbf..43853036 100644 --- a/TESTING/MATGEN/dlagsy.f +++ b/TESTING/MATGEN/dlagsy.f @@ -1,56 +1,120 @@ - SUBROUTINE DLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO ) -* -* -- LAPACK auxiliary test routine (version 3.1) -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, N -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) - DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * ) -* .. -* +*> \brief \b DLAGSY +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, K, LDA, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * ) +* .. +* * Purpose * ======= * -* DLAGSY generates a real symmetric matrix A, by pre- and post- -* multiplying a real diagonal matrix D with a random orthogonal matrix: -* A = U*D*U'. The semi-bandwidth may then be reduced to k by additional -* orthogonal transformations. +*>\details \b Purpose: +*>\verbatim +*> +*> DLAGSY generates a real symmetric matrix A, by pre- and post- +*> multiplying a real diagonal matrix D with a random orthogonal matrix: +*> A = U*D*U'. The semi-bandwidth may then be reduced to k by additional +*> orthogonal transformations. +*> +*>\endverbatim * * Arguments * ========= * -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* K (input) INTEGER -* The number of nonzero subdiagonals within the band of A. -* 0 <= K <= N-1. +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The number of nonzero subdiagonals within the band of A. +*> 0 <= K <= N-1. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> The diagonal elements of the diagonal matrix D. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> The generated n by n symmetric matrix A (the full matrix is +*> stored). +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= N. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (2*N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= * -* D (input) DOUBLE PRECISION array, dimension (N) -* The diagonal elements of the diagonal matrix D. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (output) DOUBLE PRECISION array, dimension (LDA,N) -* The generated n by n symmetric matrix A (the full matrix is -* stored). +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= N. +*> \ingroup double_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. +* ===================================================================== + SUBROUTINE DLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO ) * -* WORK (workspace) DOUBLE PRECISION array, dimension (2*N) +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value +* .. Scalar Arguments .. + INTEGER INFO, K, LDA, N +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) + DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/dlahilb.f b/TESTING/MATGEN/dlahilb.f index 7fa091f0..b35f40ee 100644 --- a/TESTING/MATGEN/dlahilb.f +++ b/TESTING/MATGEN/dlahilb.f @@ -1,107 +1,167 @@ +C> \brief \b DLAHILB +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DLAHILB( N, NRHS, A, LDA, X, LDX, B, LDB, WORK, INFO) +* +* .. Scalar Arguments .. +* INTEGER N, NRHS, LDA, LDX, LDB, INFO +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA, N), X(LDX, NRHS), B(LDB, NRHS), WORK(N) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> DLAHILB generates an N by N scaled Hilbert matrix in A along with +*> NRHS right-hand sides in B and solutions in X such that A*X=B. +*> +*> The Hilbert matrix is scaled by M = LCM(1, 2, ..., 2*N-1) so that all +*> entries are integers. The right-hand sides are the first NRHS +*> columns of M * the identity matrix, and the solutions are the +*> first NRHS columns of the inverse Hilbert matrix. +*> +*> The condition number of the Hilbert matrix grows exponentially with +*> its size, roughly as O(e ** (3.5*N)). Additionally, the inverse +*> Hilbert matrices beyond a relatively small dimension cannot be +*> generated exactly without extra precision. Precision is exhausted +*> when the largest entry in the inverse Hilbert matrix is greater than +*> 2 to the power of the number of bits in the fraction of the data type +*> used plus one, which is 24 for single precision. +*> +*> In single, the generated solution is exact for N <= 6 and has +*> small componentwise error for 7 <= N <= 11. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The dimension of the matrix A. +*> \endverbatim +*> +*> \param[in] NRHS +*> \verbatim +*> NRHS is INTEGER +*> The requested number of right-hand sides. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA, N) +*> The generated scaled Hilbert matrix. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= N. +*> \endverbatim +*> +*> \param[out] X +*> \verbatim +*> X is DOUBLE PRECISION array, dimension (LDX, NRHS) +*> The generated exact solutions. Currently, the first NRHS +*> columns of the inverse Hilbert matrix. +*> \endverbatim +*> +*> \param[in] LDX +*> \verbatim +*> LDX is INTEGER +*> The leading dimension of the array X. LDX >= N. +*> \endverbatim +*> +*> \param[out] B +*> \verbatim +*> B is DOUBLE PRECISION array, dimension (LDB, NRHS) +*> The generated right-hand sides. Currently, the first NRHS +*> columns of LCM(1, 2, ..., 2*N-1) * the identity matrix. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of the array B. LDB >= N. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> = 1: N is too large; the data is still generated but may not +*> be not exact. +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_matgen +* +* ===================================================================== SUBROUTINE DLAHILB( N, NRHS, A, LDA, X, LDX, B, LDB, WORK, INFO) -! -! -- LAPACK auxiliary test routine (version 3.2.2) -- -! Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., -! Courant Institute, Argonne National Lab, and Rice University -* June 2010 -! -! David Vu <dtv@cs.berkeley.edu> -! Yozo Hida <yozo@cs.berkeley.edu> -! Jason Riedy <ejr@cs.berkeley.edu> -! D. Halligan <dhalligan@berkeley.edu> -! - IMPLICIT NONE -! .. Scalar Arguments .. +* +* -- LAPACK test routine (version 3.2.2) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. INTEGER N, NRHS, LDA, LDX, LDB, INFO -! .. Array Arguments .. +* .. Array Arguments .. DOUBLE PRECISION A(LDA, N), X(LDX, NRHS), B(LDB, NRHS), WORK(N) -! .. -! -! Purpose -! ======= -! -! DLAHILB generates an N by N scaled Hilbert matrix in A along with -! NRHS right-hand sides in B and solutions in X such that A*X=B. -! -! The Hilbert matrix is scaled by M = LCM(1, 2, ..., 2*N-1) so that all -! entries are integers. The right-hand sides are the first NRHS -! columns of M * the identity matrix, and the solutions are the -! first NRHS columns of the inverse Hilbert matrix. -! -! The condition number of the Hilbert matrix grows exponentially with -! its size, roughly as O(e ** (3.5*N)). Additionally, the inverse -! Hilbert matrices beyond a relatively small dimension cannot be -! generated exactly without extra precision. Precision is exhausted -! when the largest entry in the inverse Hilbert matrix is greater than -! 2 to the power of the number of bits in the fraction of the data type -! used plus one, which is 24 for single precision. -! -! In single, the generated solution is exact for N <= 6 and has -! small componentwise error for 7 <= N <= 11. -! -! Arguments -! ========= -! -! N (input) INTEGER -! The dimension of the matrix A. -! -! NRHS (input) INTEGER -! The requested number of right-hand sides. -! -! A (output) DOUBLE PRECISION array, dimension (LDA, N) -! The generated scaled Hilbert matrix. -! -! LDA (input) INTEGER -! The leading dimension of the array A. LDA >= N. -! -! X (output) DOUBLE PRECISION array, dimension (LDX, NRHS) -! The generated exact solutions. Currently, the first NRHS -! columns of the inverse Hilbert matrix. -! -! LDX (input) INTEGER -! The leading dimension of the array X. LDX >= N. -! -! B (output) DOUBLE PRECISION array, dimension (LDB, NRHS) -! The generated right-hand sides. Currently, the first NRHS -! columns of LCM(1, 2, ..., 2*N-1) * the identity matrix. -! -! LDB (input) INTEGER -! The leading dimension of the array B. LDB >= N. -! -! WORK (workspace) DOUBLE PRECISION array, dimension (N) -! -! -! INFO (output) INTEGER -! = 0: successful exit -! = 1: N is too large; the data is still generated but may not -! be not exact. -! < 0: if INFO = -i, the i-th argument had an illegal value -! -! ===================================================================== +* .. +* +* ===================================================================== -! .. Local Scalars .. +* .. Local Scalars .. INTEGER TM, TI, R INTEGER M INTEGER I, J COMPLEX*16 TMP -! .. Parameters .. -! NMAX_EXACT the largest dimension where the generated data is -! exact. -! NMAX_APPROX the largest dimension where the generated data has -! a small componentwise relative error. +* .. Parameters .. +* NMAX_EXACT the largest dimension where the generated data is +* exact. +* NMAX_APPROX the largest dimension where the generated data has +* a small componentwise relative error. INTEGER NMAX_EXACT, NMAX_APPROX PARAMETER (NMAX_EXACT = 6, NMAX_APPROX = 11) -! .. -! .. External Functions +* .. +* .. External Functions EXTERNAL DLASET INTRINSIC DBLE -! .. -! .. Executable Statements .. -! -! Test the input arguments -! +* .. +* .. Executable Statements .. +* +* Test the input arguments +* INFO = 0 IF (N .LT. 0 .OR. N .GT. NMAX_APPROX) THEN INFO = -1 @@ -122,8 +182,8 @@ INFO = 1 END IF -! Compute M = the LCM of the integers [1, 2*N-1]. The largest -! reasonable N is small enough that integers suffice (up to N = 11). +* Compute M = the LCM of the integers [1, 2*N-1]. The largest +* reasonable N is small enough that integers suffice (up to N = 11). M = 1 DO I = 2, (2*N-1) TM = M @@ -137,21 +197,21 @@ M = (M / TI) * I END DO -! Generate the scaled Hilbert matrix in A +* Generate the scaled Hilbert matrix in A DO J = 1, N DO I = 1, N A(I, J) = DBLE(M) / (I + J - 1) END DO END DO -! Generate matrix B as simply the first NRHS columns of M * the -! identity. +* Generate matrix B as simply the first NRHS columns of M * the +* identity. TMP = DBLE(M) CALL DLASET('Full', N, NRHS, 0.0D+0, TMP, B, LDB) -! Generate the true solutions in X. Because B = the first NRHS -! columns of M*I, the true solutions are just the first NRHS columns -! of the inverse Hilbert matrix. +* Generate the true solutions in X. Because B = the first NRHS +* columns of M*I, the true solutions are just the first NRHS columns +* of the inverse Hilbert matrix. WORK(1) = N DO J = 2, N WORK(J) = ( ( (WORK(J-1)/(J-1)) * (J-1 - N) ) /(J-1) ) diff --git a/TESTING/MATGEN/dlakf2.f b/TESTING/MATGEN/dlakf2.f index 052719b8..57fe12aa 100644 --- a/TESTING/MATGEN/dlakf2.f +++ b/TESTING/MATGEN/dlakf2.f @@ -1,54 +1,125 @@ - SUBROUTINE DLAKF2( M, N, A, LDA, B, D, E, Z, LDZ ) -* -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER LDA, LDZ, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), B( LDA, * ), D( LDA, * ), - $ E( LDA, * ), Z( LDZ, * ) -* .. -* +*> \brief \b DLAKF2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DLAKF2( M, N, A, LDA, B, D, E, Z, LDZ ) +* +* .. Scalar Arguments .. +* INTEGER LDA, LDZ, M, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ), B( LDA, * ), D( LDA, * ), +* $ E( LDA, * ), Z( LDZ, * ) +* .. +* * Purpose * ======= * -* Form the 2*M*N by 2*M*N matrix -* -* Z = [ kron(In, A) -kron(B', Im) ] -* [ kron(In, D) -kron(E', Im) ], -* -* where In is the identity matrix of size n and X' is the transpose -* of X. kron(X, Y) is the Kronecker product between the matrices X -* and Y. +*>\details \b Purpose: +*>\verbatim +*> +*> Form the 2*M*N by 2*M*N matrix +*> +*> Z = [ kron(In, A) -kron(B', Im) ] +*> [ kron(In, D) -kron(E', Im) ], +*> +*> where In is the identity matrix of size n and X' is the transpose +*> of X. kron(X, Y) is the Kronecker product between the matrices X +*> and Y. +*> +*>\endverbatim * * Arguments * ========= * -* M (input) INTEGER -* Size of matrix, must be >= 1. +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Size of matrix, must be >= 1. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Size of matrix, must be >= 1. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION, dimension ( LDA, M ) +*> The matrix A in the output matrix Z. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of A, B, D, and E. ( LDA >= M+N ) +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is DOUBLE PRECISION, dimension ( LDA, N ) +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION, dimension ( LDA, M ) +*> \endverbatim +*> +*> \param[in] E +*> \verbatim +*> E is DOUBLE PRECISION, dimension ( LDA, N ) +*> \endverbatim +*> \verbatim +*> The matrices used in forming the output matrix Z. +*> \endverbatim +*> +*> \param[out] Z +*> \verbatim +*> Z is DOUBLE PRECISION, dimension ( LDZ, 2*M*N ) +*> The resultant Kronecker M*N*2 by M*N*2 matrix (see above.) +*> \endverbatim +*> +*> \param[in] LDZ +*> \verbatim +*> LDZ is INTEGER +*> The leading dimension of Z. ( LDZ >= 2*M*N ) +*> \endverbatim +*> +* +* Authors +* ======= * -* N (input) INTEGER -* Size of matrix, must be >= 1. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (input) DOUBLE PRECISION, dimension ( LDA, M ) -* The matrix A in the output matrix Z. +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of A, B, D, and E. ( LDA >= M+N ) +*> \ingroup double_matgen * -* B (input) DOUBLE PRECISION, dimension ( LDA, N ) -* D (input) DOUBLE PRECISION, dimension ( LDA, M ) -* E (input) DOUBLE PRECISION, dimension ( LDA, N ) -* The matrices used in forming the output matrix Z. +* ===================================================================== + SUBROUTINE DLAKF2( M, N, A, LDA, B, D, E, Z, LDZ ) * -* Z (output) DOUBLE PRECISION, dimension ( LDZ, 2*M*N ) -* The resultant Kronecker M*N*2 by M*N*2 matrix (see above.) +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* LDZ (input) INTEGER -* The leading dimension of Z. ( LDZ >= 2*M*N ) +* .. Scalar Arguments .. + INTEGER LDA, LDZ, M, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), B( LDA, * ), D( LDA, * ), + $ E( LDA, * ), Z( LDZ, * ) +* .. * * ==================================================================== * diff --git a/TESTING/MATGEN/dlaran.f b/TESTING/MATGEN/dlaran.f index cb4481b4..cfd008ee 100644 --- a/TESTING/MATGEN/dlaran.f +++ b/TESTING/MATGEN/dlaran.f @@ -1,40 +1,84 @@ - DOUBLE PRECISION FUNCTION DLARAN( ISEED ) +*> \brief \b DLARAN * -* -- LAPACK auxiliary routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 +* =========== DOCUMENTATION =========== * -* .. Array Arguments .. - INTEGER ISEED( 4 ) -* .. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* DOUBLE PRECISION FUNCTION DLARAN( ISEED ) +* +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* .. +* * Purpose * ======= * -* DLARAN returns a random real number from a uniform (0,1) -* distribution. +*>\details \b Purpose: +*>\verbatim +*> +*> DLARAN returns a random real number from a uniform (0,1) +*> distribution. +*> +*>\endverbatim * * Arguments * ========= * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup list_temp +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> This routine uses a multiplicative congruential method with modulus +*> 2**48 and multiplier 33952834046453 (see G.S.Fishman, +*> 'Multiplicative congruential random number generators with modulus +*> 2**b: an exhaustive analysis for b = 32 and a partial analysis for +*> b = 48', Math. Comp. 189, pp 331-344, 1990). +*> +*> 48-bit integers are stored in 4 integer array elements with 12 bits +*> per element. Hence the routine is portable across machines with +*> integers of 32 bits or more. +*> +*> \endverbatim +*> +* ===================================================================== + DOUBLE PRECISION FUNCTION DLARAN( ISEED ) * -* This routine uses a multiplicative congruential method with modulus -* 2**48 and multiplier 33952834046453 (see G.S.Fishman, -* 'Multiplicative congruential random number generators with modulus -* 2**b: an exhaustive analysis for b = 32 and a partial analysis for -* b = 48', Math. Comp. 189, pp 331-344, 1990). +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* 48-bit integers are stored in 4 integer array elements with 12 bits -* per element. Hence the routine is portable across machines with -* integers of 32 bits or more. +* .. Array Arguments .. + INTEGER ISEED( 4 ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/dlarge.f b/TESTING/MATGEN/dlarge.f index 3b6d444e..e7e77e2a 100644 --- a/TESTING/MATGEN/dlarge.f +++ b/TESTING/MATGEN/dlarge.f @@ -1,48 +1,106 @@ - SUBROUTINE DLARGE( N, A, LDA, ISEED, WORK, INFO ) -* -* -- LAPACK auxiliary test routine (version 3.1) -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) - DOUBLE PRECISION A( LDA, * ), WORK( * ) -* .. -* +*> \brief \b DLARGE +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DLARGE( N, A, LDA, ISEED, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* DOUBLE PRECISION A( LDA, * ), WORK( * ) +* .. +* * Purpose * ======= * -* DLARGE pre- and post-multiplies a real general n by n matrix A -* with a random orthogonal matrix: A = U*D*U'. +*>\details \b Purpose: +*>\verbatim +*> +*> DLARGE pre- and post-multiplies a real general n by n matrix A +*> with a random orthogonal matrix: A = U*D*U'. +*> +*>\endverbatim * * Arguments * ========= * -* N (input) INTEGER -* The order of the matrix A. N >= 0. +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> On entry, the original n by n matrix A. +*> On exit, A is overwritten by U*A*U' for some random +*> orthogonal matrix U. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= N. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (2*N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -* On entry, the original n by n matrix A. -* On exit, A is overwritten by U*A*U' for some random -* orthogonal matrix U. +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= N. +*> \ingroup double_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. +* ===================================================================== + SUBROUTINE DLARGE( N, A, LDA, ISEED, WORK, INFO ) * -* WORK (workspace) DOUBLE PRECISION array, dimension (2*N) +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value +* .. Scalar Arguments .. + INTEGER INFO, LDA, N +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) + DOUBLE PRECISION A( LDA, * ), WORK( * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/dlarnd.f b/TESTING/MATGEN/dlarnd.f index a84ec8a9..3716cddd 100644 --- a/TESTING/MATGEN/dlarnd.f +++ b/TESTING/MATGEN/dlarnd.f @@ -1,43 +1,93 @@ - DOUBLE PRECISION FUNCTION DLARND( IDIST, ISEED ) +*> \brief \b DLARND * -* -- LAPACK auxiliary routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 +* =========== DOCUMENTATION =========== * -* .. Scalar Arguments .. - INTEGER IDIST -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) -* .. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* DOUBLE PRECISION FUNCTION DLARND( IDIST, ISEED ) +* +* .. Scalar Arguments .. +* INTEGER IDIST +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* .. +* * Purpose * ======= * -* DLARND returns a random real number from a uniform or normal -* distribution. +*>\details \b Purpose: +*>\verbatim +*> +*> DLARND returns a random real number from a uniform or normal +*> distribution. +*> +*>\endverbatim * * Arguments * ========= * -* IDIST (input) INTEGER -* Specifies the distribution of the random numbers: -* = 1: uniform (0,1) -* = 2: uniform (-1,1) -* = 3: normal (0,1) +*> \param[in] IDIST +*> \verbatim +*> IDIST is INTEGER +*> Specifies the distribution of the random numbers: +*> = 1: uniform (0,1) +*> = 2: uniform (-1,1) +*> = 3: normal (0,1) +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> This routine calls the auxiliary routine DLARAN to generate a random +*> real number from a uniform (0,1) distribution. The Box-Muller method +*> is used to transform numbers from a uniform to a normal distribution. +*> +*> \endverbatim +*> +* ===================================================================== + DOUBLE PRECISION FUNCTION DLARND( IDIST, ISEED ) * -* This routine calls the auxiliary routine DLARAN to generate a random -* real number from a uniform (0,1) distribution. The Box-Muller method -* is used to transform numbers from a uniform to a normal distribution. +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER IDIST +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/dlaror.f b/TESTING/MATGEN/dlaror.f index 468e37cd..e4a62686 100644 --- a/TESTING/MATGEN/dlaror.f +++ b/TESTING/MATGEN/dlaror.f @@ -1,8 +1,161 @@ +*> \brief \b DLAROR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DLAROR( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER INIT, SIDE +* INTEGER INFO, LDA, M, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* DOUBLE PRECISION A( LDA, * ), X( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> DLAROR pre- or post-multiplies an M by N matrix A by a random +*> orthogonal matrix U, overwriting A. A may optionally be initialized +*> to the identity matrix before multiplying by U. U is generated using +*> the method of G.W. Stewart (SIAM J. Numer. Anal. 17, 1980, 403-409). +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> Specifies whether A is multiplied on the left or right by U. +*> = 'L': Multiply A on the left (premultiply) by U +*> = 'R': Multiply A on the right (postmultiply) by U' +*> = 'C' or 'T': Multiply A on the left by U and the right +*> by U' (Here, U' means U-transpose.) +*> \endverbatim +*> +*> \param[in] INIT +*> \verbatim +*> INIT is CHARACTER*1 +*> Specifies whether or not A should be initialized to the +*> identity matrix. +*> = 'I': Initialize A to (a section of) the identity matrix +*> before applying U. +*> = 'N': No initialization. Apply U to the input matrix A. +*> \endverbatim +*> \verbatim +*> INIT = 'I' may be used to generate square or rectangular +*> orthogonal matrices: +*> \endverbatim +*> \verbatim +*> For M = N and SIDE = 'L' or 'R', the rows will be orthogonal +*> to each other, as will the columns. +*> \endverbatim +*> \verbatim +*> If M < N, SIDE = 'R' produces a dense matrix whose rows are +*> orthogonal and whose columns are not, while SIDE = 'L' +*> produces a matrix whose rows are orthogonal, and whose first +*> M columns are orthogonal, and whose remaining columns are +*> zero. +*> \endverbatim +*> \verbatim +*> If M > N, SIDE = 'L' produces a dense matrix whose columns +*> are orthogonal and whose rows are not, while SIDE = 'R' +*> produces a matrix whose columns are orthogonal, and whose +*> first M rows are orthogonal, and whose remaining rows are +*> zero. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of A. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA, N) +*> On entry, the array A. +*> On exit, overwritten by U A ( if SIDE = 'L' ), +*> or by A U ( if SIDE = 'R' ), +*> or by U A U' ( if SIDE = 'C' or 'T'). +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry ISEED specifies the seed of the random number +*> generator. The array elements should be between 0 and 4095; +*> if not they will be reduced mod 4096. Also, ISEED(4) must +*> be odd. The random number generator uses a linear +*> congruential sequence limited to small integers, and so +*> should produce machine independent random numbers. The +*> values of ISEED are changed on exit, and can be used in the +*> next call to DLAROR to continue the same random number +*> sequence. +*> \endverbatim +*> +*> \param[out] X +*> \verbatim +*> X is DOUBLE PRECISION array, dimension (3*MAX( M, N )) +*> Workspace of length +*> 2*M + N if SIDE = 'L', +*> 2*N + M if SIDE = 'R', +*> 3*N if SIDE = 'C' or 'T'. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> An error flag. It is set to: +*> = 0: normal return +*> < 0: if INFO = -k, the k-th argument had an illegal value +*> = 1: if the random numbers generated by DLARND are bad. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_matgen +* +* ===================================================================== SUBROUTINE DLAROR( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER INIT, SIDE @@ -13,87 +166,6 @@ DOUBLE PRECISION A( LDA, * ), X( * ) * .. * -* Purpose -* ======= -* -* DLAROR pre- or post-multiplies an M by N matrix A by a random -* orthogonal matrix U, overwriting A. A may optionally be initialized -* to the identity matrix before multiplying by U. U is generated using -* the method of G.W. Stewart (SIAM J. Numer. Anal. 17, 1980, 403-409). -* -* Arguments -* ========= -* -* SIDE (input) CHARACTER*1 -* Specifies whether A is multiplied on the left or right by U. -* = 'L': Multiply A on the left (premultiply) by U -* = 'R': Multiply A on the right (postmultiply) by U' -* = 'C' or 'T': Multiply A on the left by U and the right -* by U' (Here, U' means U-transpose.) -* -* INIT (input) CHARACTER*1 -* Specifies whether or not A should be initialized to the -* identity matrix. -* = 'I': Initialize A to (a section of) the identity matrix -* before applying U. -* = 'N': No initialization. Apply U to the input matrix A. -* -* INIT = 'I' may be used to generate square or rectangular -* orthogonal matrices: -* -* For M = N and SIDE = 'L' or 'R', the rows will be orthogonal -* to each other, as will the columns. -* -* If M < N, SIDE = 'R' produces a dense matrix whose rows are -* orthogonal and whose columns are not, while SIDE = 'L' -* produces a matrix whose rows are orthogonal, and whose first -* M columns are orthogonal, and whose remaining columns are -* zero. -* -* If M > N, SIDE = 'L' produces a dense matrix whose columns -* are orthogonal and whose rows are not, while SIDE = 'R' -* produces a matrix whose columns are orthogonal, and whose -* first M rows are orthogonal, and whose remaining rows are -* zero. -* -* M (input) INTEGER -* The number of rows of A. -* -* N (input) INTEGER -* The number of columns of A. -* -* A (input/output) DOUBLE PRECISION array, dimension (LDA, N) -* On entry, the array A. -* On exit, overwritten by U A ( if SIDE = 'L' ), -* or by A U ( if SIDE = 'R' ), -* or by U A U' ( if SIDE = 'C' or 'T'). -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,M). -* -* ISEED (input/output) INTEGER array, dimension (4) -* On entry ISEED specifies the seed of the random number -* generator. The array elements should be between 0 and 4095; -* if not they will be reduced mod 4096. Also, ISEED(4) must -* be odd. The random number generator uses a linear -* congruential sequence limited to small integers, and so -* should produce machine independent random numbers. The -* values of ISEED are changed on exit, and can be used in the -* next call to DLAROR to continue the same random number -* sequence. -* -* X (workspace) DOUBLE PRECISION array, dimension (3*MAX( M, N )) -* Workspace of length -* 2*M + N if SIDE = 'L', -* 2*N + M if SIDE = 'R', -* 3*N if SIDE = 'C' or 'T'. -* -* INFO (output) INTEGER -* An error flag. It is set to: -* = 0: normal return -* < 0: if INFO = -k, the k-th argument had an illegal value -* = 1: if the random numbers generated by DLARND are bad. -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/dlarot.f b/TESTING/MATGEN/dlarot.f index 319ab1a8..aa899b2a 100644 --- a/TESTING/MATGEN/dlarot.f +++ b/TESTING/MATGEN/dlarot.f @@ -1,202 +1,254 @@ - SUBROUTINE DLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT, - $ XRIGHT ) -* -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - LOGICAL LLEFT, LRIGHT, LROWS - INTEGER LDA, NL - DOUBLE PRECISION C, S, XLEFT, XRIGHT -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( * ) -* .. -* +*> \brief \b DLAROT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT, +* XRIGHT ) +* +* .. Scalar Arguments .. +* LOGICAL LLEFT, LRIGHT, LROWS +* INTEGER LDA, NL +* DOUBLE PRECISION C, S, XLEFT, XRIGHT +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( * ) +* .. +* * Purpose * ======= * -* DLAROT applies a (Givens) rotation to two adjacent rows or -* columns, where one element of the first and/or last column/row -* for use on matrices stored in some format other than GE, so -* that elements of the matrix may be used or modified for which -* no array element is provided. -* -* One example is a symmetric matrix in SB format (bandwidth=4), for -* which UPLO='L': Two adjacent rows will have the format: -* -* row j: * * * * * . . . . -* row j+1: * * * * * . . . . -* -* '*' indicates elements for which storage is provided, -* '.' indicates elements for which no storage is provided, but -* are not necessarily zero; their values are determined by -* symmetry. ' ' indicates elements which are necessarily zero, -* and have no storage provided. -* -* Those columns which have two '*'s can be handled by DROT. -* Those columns which have no '*'s can be ignored, since as long -* as the Givens rotations are carefully applied to preserve -* symmetry, their values are determined. -* Those columns which have one '*' have to be handled separately, -* by using separate variables "p" and "q": -* -* row j: * * * * * p . . . -* row j+1: q * * * * * . . . . -* -* The element p would have to be set correctly, then that column -* is rotated, setting p to its new value. The next call to -* DLAROT would rotate columns j and j+1, using p, and restore -* symmetry. The element q would start out being zero, and be -* made non-zero by the rotation. Later, rotations would presumably -* be chosen to zero q out. -* -* Typical Calling Sequences: rotating the i-th and (i+1)-st rows. -* ------- ------- --------- -* -* General dense matrix: -* -* CALL DLAROT(.TRUE.,.FALSE.,.FALSE., N, C,S, -* A(i,1),LDA, DUMMY, DUMMY) -* -* General banded matrix in GB format: -* -* j = MAX(1, i-KL ) -* NL = MIN( N, i+KU+1 ) + 1-j -* CALL DLAROT( .TRUE., i-KL.GE.1, i+KU.LT.N, NL, C,S, -* A(KU+i+1-j,j),LDA-1, XLEFT, XRIGHT ) -* -* [ note that i+1-j is just MIN(i,KL+1) ] -* -* Symmetric banded matrix in SY format, bandwidth K, -* lower triangle only: -* -* j = MAX(1, i-K ) -* NL = MIN( K+1, i ) + 1 -* CALL DLAROT( .TRUE., i-K.GE.1, .TRUE., NL, C,S, -* A(i,j), LDA, XLEFT, XRIGHT ) -* -* Same, but upper triangle only: -* -* NL = MIN( K+1, N-i ) + 1 -* CALL DLAROT( .TRUE., .TRUE., i+K.LT.N, NL, C,S, -* A(i,i), LDA, XLEFT, XRIGHT ) -* -* Symmetric banded matrix in SB format, bandwidth K, -* lower triangle only: -* -* [ same as for SY, except:] -* . . . . -* A(i+1-j,j), LDA-1, XLEFT, XRIGHT ) -* -* [ note that i+1-j is just MIN(i,K+1) ] -* -* Same, but upper triangle only: -* . . . -* A(K+1,i), LDA-1, XLEFT, XRIGHT ) -* -* Rotating columns is just the transpose of rotating rows, except -* for GB and SB: (rotating columns i and i+1) -* -* GB: -* j = MAX(1, i-KU ) -* NL = MIN( N, i+KL+1 ) + 1-j -* CALL DLAROT( .TRUE., i-KU.GE.1, i+KL.LT.N, NL, C,S, -* A(KU+j+1-i,i),LDA-1, XTOP, XBOTTM ) -* -* [note that KU+j+1-i is just MAX(1,KU+2-i)] -* -* SB: (upper triangle) -* -* . . . . . . -* A(K+j+1-i,i),LDA-1, XTOP, XBOTTM ) -* -* SB: (lower triangle) -* -* . . . . . . -* A(1,i),LDA-1, XTOP, XBOTTM ) +*>\details \b Purpose: +*>\verbatim +*> +*> DLAROT applies a (Givens) rotation to two adjacent rows or +*> columns, where one element of the first and/or last column/row +*> for use on matrices stored in some format other than GE, so +*> that elements of the matrix may be used or modified for which +*> no array element is provided. +*> +*> One example is a symmetric matrix in SB format (bandwidth=4), for +*> which UPLO='L': Two adjacent rows will have the format: +*> +*> row j: C> C> C> C> C> . . . . +*> row j+1: C> C> C> C> C> . . . . +*> +*> '*' indicates elements for which storage is provided, +*> '.' indicates elements for which no storage is provided, but +*> are not necessarily zero; their values are determined by +*> symmetry. ' ' indicates elements which are necessarily zero, +*> and have no storage provided. +*> +*> Those columns which have two '*'s can be handled by DROT. +*> Those columns which have no '*'s can be ignored, since as long +*> as the Givens rotations are carefully applied to preserve +*> symmetry, their values are determined. +*> Those columns which have one '*' have to be handled separately, +*> by using separate variables "p" and "q": +*> +*> row j: C> C> C> C> C> p . . . +*> row j+1: q C> C> C> C> C> . . . . +*> +*> The element p would have to be set correctly, then that column +*> is rotated, setting p to its new value. The next call to +*> DLAROT would rotate columns j and j+1, using p, and restore +*> symmetry. The element q would start out being zero, and be +*> made non-zero by the rotation. Later, rotations would presumably +*> be chosen to zero q out. +*> +*> Typical Calling Sequences: rotating the i-th and (i+1)-st rows. +*> ------- ------- --------- +*> +*> General dense matrix: +*> +*> CALL DLAROT(.TRUE.,.FALSE.,.FALSE., N, C,S, +*> A(i,1),LDA, DUMMY, DUMMY) +*> +*> General banded matrix in GB format: +*> +*> j = MAX(1, i-KL ) +*> NL = MIN( N, i+KU+1 ) + 1-j +*> CALL DLAROT( .TRUE., i-KL.GE.1, i+KU.LT.N, NL, C,S, +*> A(KU+i+1-j,j),LDA-1, XLEFT, XRIGHT ) +*> +*> [ note that i+1-j is just MIN(i,KL+1) ] +*> +*> Symmetric banded matrix in SY format, bandwidth K, +*> lower triangle only: +*> +*> j = MAX(1, i-K ) +*> NL = MIN( K+1, i ) + 1 +*> CALL DLAROT( .TRUE., i-K.GE.1, .TRUE., NL, C,S, +*> A(i,j), LDA, XLEFT, XRIGHT ) +*> +*> Same, but upper triangle only: +*> +*> NL = MIN( K+1, N-i ) + 1 +*> CALL DLAROT( .TRUE., .TRUE., i+K.LT.N, NL, C,S, +*> A(i,i), LDA, XLEFT, XRIGHT ) +*> +*> Symmetric banded matrix in SB format, bandwidth K, +*> lower triangle only: +*> +*> [ same as for SY, except:] +*> . . . . +*> A(i+1-j,j), LDA-1, XLEFT, XRIGHT ) +*> +*> [ note that i+1-j is just MIN(i,K+1) ] +*> +*> Same, but upper triangle only: +*> . . . +*> A(K+1,i), LDA-1, XLEFT, XRIGHT ) +*> +*> Rotating columns is just the transpose of rotating rows, except +*> for GB and SB: (rotating columns i and i+1) +*> +*> GB: +*> j = MAX(1, i-KU ) +*> NL = MIN( N, i+KL+1 ) + 1-j +*> CALL DLAROT( .TRUE., i-KU.GE.1, i+KL.LT.N, NL, C,S, +*> A(KU+j+1-i,i),LDA-1, XTOP, XBOTTM ) +*> +*> [note that KU+j+1-i is just MAX(1,KU+2-i)] +*> +*> SB: (upper triangle) +*> +*> . . . . . . +*> A(K+j+1-i,i),LDA-1, XTOP, XBOTTM ) +*> +*> SB: (lower triangle) +*> +*> . . . . . . +*> A(1,i),LDA-1, XTOP, XBOTTM ) +*> +*>\endverbatim * * Arguments * ========= * -* LROWS - LOGICAL -* If .TRUE., then DLAROT will rotate two rows. If .FALSE., -* then it will rotate two columns. -* Not modified. -* -* LLEFT - LOGICAL -* If .TRUE., then XLEFT will be used instead of the -* corresponding element of A for the first element in the -* second row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) -* If .FALSE., then the corresponding element of A will be -* used. -* Not modified. -* -* LRIGHT - LOGICAL -* If .TRUE., then XRIGHT will be used instead of the -* corresponding element of A for the last element in the -* first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If -* .FALSE., then the corresponding element of A will be used. -* Not modified. +*> \verbatim +*> LROWS - LOGICAL +*> If .TRUE., then DLAROT will rotate two rows. If .FALSE., +*> then it will rotate two columns. +*> Not modified. +*> \endverbatim +*> \verbatim +*> LLEFT - LOGICAL +*> If .TRUE., then XLEFT will be used instead of the +*> corresponding element of A for the first element in the +*> second row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) +*> If .FALSE., then the corresponding element of A will be +*> used. +*> Not modified. +*> \endverbatim +*> \verbatim +*> LRIGHT - LOGICAL +*> If .TRUE., then XRIGHT will be used instead of the +*> corresponding element of A for the last element in the +*> first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If +*> .FALSE., then the corresponding element of A will be used. +*> Not modified. +*> \endverbatim +*> \verbatim +*> NL - INTEGER +*> The length of the rows (if LROWS=.TRUE.) or columns (if +*> LROWS=.FALSE.) to be rotated. If XLEFT and/or XRIGHT are +*> used, the columns/rows they are in should be included in +*> NL, e.g., if LLEFT = LRIGHT = .TRUE., then NL must be at +*> least 2. The number of rows/columns to be rotated +*> exclusive of those involving XLEFT and/or XRIGHT may +*> not be negative, i.e., NL minus how many of LLEFT and +*> LRIGHT are .TRUE. must be at least zero; if not, XERBLA +*> will be called. +*> Not modified. +*> \endverbatim +*> \verbatim +*> C, S - DOUBLE PRECISION +*> Specify the Givens rotation to be applied. If LROWS is +*> true, then the matrix ( c s ) +*> (-s c ) is applied from the left; +*> if false, then the transpose thereof is applied from the +*> right. For a Givens rotation, C**2 + S**2 should be 1, +*> but this is not checked. +*> Not modified. +*> \endverbatim +*> \verbatim +*> A - DOUBLE PRECISION array. +*> The array containing the rows/columns to be rotated. The +*> first element of A should be the upper left element to +*> be rotated. +*> Read and modified. +*> \endverbatim +*> \verbatim +*> LDA - INTEGER +*> The "effective" leading dimension of A. If A contains +*> a matrix stored in GE or SY format, then this is just +*> the leading dimension of A as dimensioned in the calling +*> routine. If A contains a matrix stored in band (GB or SB) +*> format, then this should be *one less* than the leading +*> dimension used in the calling routine. Thus, if +*> A were dimensioned A(LDA,*) in DLAROT, then A(1,j) would +*> be the j-th element in the first of the two rows +*> to be rotated, and A(2,j) would be the j-th in the second, +*> regardless of how the array may be stored in the calling +*> routine. [A cannot, however, actually be dimensioned thus, +*> since for band format, the row number may exceed LDA, which +*> is not legal FORTRAN.] +*> If LROWS=.TRUE., then LDA must be at least 1, otherwise +*> it must be at least NL minus the number of .TRUE. values +*> in XLEFT and XRIGHT. +*> Not modified. +*> \endverbatim +*> \verbatim +*> XLEFT - DOUBLE PRECISION +*> If LLEFT is .TRUE., then XLEFT will be used and modified +*> instead of A(2,1) (if LROWS=.TRUE.) or A(1,2) +*> (if LROWS=.FALSE.). +*> Read and modified. +*> \endverbatim +*> \verbatim +*> XRIGHT - DOUBLE PRECISION +*> If LRIGHT is .TRUE., then XRIGHT will be used and modified +*> instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1) +*> (if LROWS=.FALSE.). +*> Read and modified. +*> \endverbatim +*> +* +* Authors +* ======= * -* NL - INTEGER -* The length of the rows (if LROWS=.TRUE.) or columns (if -* LROWS=.FALSE.) to be rotated. If XLEFT and/or XRIGHT are -* used, the columns/rows they are in should be included in -* NL, e.g., if LLEFT = LRIGHT = .TRUE., then NL must be at -* least 2. The number of rows/columns to be rotated -* exclusive of those involving XLEFT and/or XRIGHT may -* not be negative, i.e., NL minus how many of LLEFT and -* LRIGHT are .TRUE. must be at least zero; if not, XERBLA -* will be called. -* Not modified. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* C, S - DOUBLE PRECISION -* Specify the Givens rotation to be applied. If LROWS is -* true, then the matrix ( c s ) -* (-s c ) is applied from the left; -* if false, then the transpose thereof is applied from the -* right. For a Givens rotation, C**2 + S**2 should be 1, -* but this is not checked. -* Not modified. +*> \date November 2011 * -* A - DOUBLE PRECISION array. -* The array containing the rows/columns to be rotated. The -* first element of A should be the upper left element to -* be rotated. -* Read and modified. +*> \ingroup double_matgen * -* LDA - INTEGER -* The "effective" leading dimension of A. If A contains -* a matrix stored in GE or SY format, then this is just -* the leading dimension of A as dimensioned in the calling -* routine. If A contains a matrix stored in band (GB or SB) -* format, then this should be *one less* than the leading -* dimension used in the calling routine. Thus, if -* A were dimensioned A(LDA,*) in DLAROT, then A(1,j) would -* be the j-th element in the first of the two rows -* to be rotated, and A(2,j) would be the j-th in the second, -* regardless of how the array may be stored in the calling -* routine. [A cannot, however, actually be dimensioned thus, -* since for band format, the row number may exceed LDA, which -* is not legal FORTRAN.] -* If LROWS=.TRUE., then LDA must be at least 1, otherwise -* it must be at least NL minus the number of .TRUE. values -* in XLEFT and XRIGHT. -* Not modified. +* ===================================================================== + SUBROUTINE DLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT, + $ XRIGHT ) * -* XLEFT - DOUBLE PRECISION -* If LLEFT is .TRUE., then XLEFT will be used and modified -* instead of A(2,1) (if LROWS=.TRUE.) or A(1,2) -* (if LROWS=.FALSE.). -* Read and modified. +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* XRIGHT - DOUBLE PRECISION -* If LRIGHT is .TRUE., then XRIGHT will be used and modified -* instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1) -* (if LROWS=.FALSE.). -* Read and modified. +* .. Scalar Arguments .. + LOGICAL LLEFT, LRIGHT, LROWS + INTEGER LDA, NL + DOUBLE PRECISION C, S, XLEFT, XRIGHT +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/dlatm1.f b/TESTING/MATGEN/dlatm1.f index e113e985..f8cbb9c9 100644 --- a/TESTING/MATGEN/dlatm1.f +++ b/TESTING/MATGEN/dlatm1.f @@ -1,8 +1,146 @@ +*> \brief \b DLATM1 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO ) +* +* .. Scalar Arguments .. +* INTEGER IDIST, INFO, IRSIGN, MODE, N +* DOUBLE PRECISION COND +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* DOUBLE PRECISION D( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> DLATM1 computes the entries of D(1..N) as specified by +*> MODE, COND and IRSIGN. IDIST and ISEED determine the generation +*> of random numbers. DLATM1 is called by SLATMR to generate +*> random test matrices for LAPACK programs. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry describes how D is to be computed: +*> MODE = 0 means do not change D. +*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND +*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is DOUBLE PRECISION +*> On entry, used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] IRSIGN +*> \verbatim +*> IRSIGN is INTEGER +*> On entry, if MODE neither -6, 0 nor 6, determines sign of +*> entries of D +*> 0 => leave entries of D unchanged +*> 1 => multiply each entry of D by 1 or -1 with probability .5 +*> \endverbatim +*> +*> \param[in] IDIST +*> \verbatim +*> IDIST is CHARACTER*1 +*> On entry, IDIST specifies the type of distribution to be +*> used to generate a random matrix . +*> 1 => UNIFORM( 0, 1 ) +*> 2 => UNIFORM( -1, 1 ) +*> 3 => NORMAL( 0, 1 ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. The random number generator uses a +*> linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to DLATM1 +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension ( MIN( M , N ) ) +*> Array to be computed according to MODE, COND and IRSIGN. +*> May be changed on exit if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of entries of D. Not modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> 0 => normal termination +*> -1 => if MODE not in range -6 to 6 +*> -2 => if MODE neither -6, 0 nor 6, and +*> IRSIGN neither 0 nor 1 +*> -3 => if MODE neither -6, 0 nor 6 and COND less than 1 +*> -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3 +*> -7 => if N negative +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_matgen +* +* ===================================================================== SUBROUTINE DLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. INTEGER IDIST, INFO, IRSIGN, MODE, N @@ -13,79 +151,6 @@ DOUBLE PRECISION D( * ) * .. * -* Purpose -* ======= -* -* DLATM1 computes the entries of D(1..N) as specified by -* MODE, COND and IRSIGN. IDIST and ISEED determine the generation -* of random numbers. DLATM1 is called by SLATMR to generate -* random test matrices for LAPACK programs. -* -* Arguments -* ========= -* -* MODE (input) INTEGER -* On entry describes how D is to be computed: -* MODE = 0 means do not change D. -* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND -* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* Not modified. -* -* COND (input) DOUBLE PRECISION -* On entry, used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* IRSIGN (input) INTEGER -* On entry, if MODE neither -6, 0 nor 6, determines sign of -* entries of D -* 0 => leave entries of D unchanged -* 1 => multiply each entry of D by 1 or -1 with probability .5 -* -* IDIST (input) CHARACTER*1 -* On entry, IDIST specifies the type of distribution to be -* used to generate a random matrix . -* 1 => UNIFORM( 0, 1 ) -* 2 => UNIFORM( -1, 1 ) -* 3 => NORMAL( 0, 1 ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. The random number generator uses a -* linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to DLATM1 -* to continue the same random number sequence. -* Changed on exit. -* -* D (input/output) DOUBLE PRECISION array, dimension ( MIN( M , N ) ) -* Array to be computed according to MODE, COND and IRSIGN. -* May be changed on exit if MODE is nonzero. -* -* N (input) INTEGER -* Number of entries of D. Not modified. -* -* INFO (output) INTEGER -* 0 => normal termination -* -1 => if MODE not in range -6 to 6 -* -2 => if MODE neither -6, 0 nor 6, and -* IRSIGN neither 0 nor 1 -* -3 => if MODE neither -6, 0 nor 6 and COND less than 1 -* -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3 -* -7 => if N negative -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/dlatm2.f b/TESTING/MATGEN/dlatm2.f index d803608d..1f3eaf38 100644 --- a/TESTING/MATGEN/dlatm2.f +++ b/TESTING/MATGEN/dlatm2.f @@ -1,9 +1,219 @@ +*> \brief \b DLATM2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* DOUBLE PRECISION FUNCTION DLATM2( M, N, I, J, KL, KU, IDIST, +* ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE ) +* +* .. Scalar Arguments .. +* +* INTEGER I, IDIST, IGRADE, IPVTNG, J, KL, KU, M, N +* DOUBLE PRECISION SPARSE +* .. +* +* .. Array Arguments .. +* +* INTEGER ISEED( 4 ), IWORK( * ) +* DOUBLE PRECISION D( * ), DL( * ), DR( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> DLATM2 returns the (I,J) entry of a random matrix of dimension +*> (M, N) described by the other paramters. It is called by the +*> DLATMR routine in order to build random test matrices. No error +*> checking on parameters is done, because this routine is called in +*> a tight loop by DLATMR which has already checked the parameters. +*> +*> Use of DLATM2 differs from SLATM3 in the order in which the random +*> number generator is called to fill in random matrix entries. +*> With DLATM2, the generator is called to fill in the pivoted matrix +*> columnwise. With DLATM3, the generator is called to fill in the +*> matrix columnwise, after which it is pivoted. Thus, DLATM3 can +*> be used to construct random matrices which differ only in their +*> order of rows and/or columns. DLATM2 is used to construct band +*> matrices while avoiding calling the random number generator for +*> entries outside the band (and therefore generating random numbers +*> +*> The matrix whose (I,J) entry is returned is constructed as +*> follows (this routine only computes one entry): +*> +*> If I is outside (1..M) or J is outside (1..N), return zero +*> (this is convenient for generating matrices in band format). +*> +*> Generate a matrix A with random entries of distribution IDIST. +*> +*> Set the diagonal to D. +*> +*> Grade the matrix, if desired, from the left (by DL) and/or +*> from the right (by DR or DL) as specified by IGRADE. +*> +*> Permute, if desired, the rows and/or columns as specified by +*> IPVTNG and IWORK. +*> +*> Band the matrix to have lower bandwidth KL and upper +*> bandwidth KU. +*> +*> Set random entries to zero as specified by SPARSE. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Number of rows of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of columns of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] I +*> \verbatim +*> I is INTEGER +*> Row of entry to be returned. Not modified. +*> \endverbatim +*> +*> \param[in] J +*> \verbatim +*> J is INTEGER +*> Column of entry to be returned. Not modified. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> Lower bandwidth. Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> Upper bandwidth. Not modified. +*> \endverbatim +*> +*> \param[in] IDIST +*> \verbatim +*> IDIST is INTEGER +*> On entry, IDIST specifies the type of distribution to be +*> used to generate a random matrix . +*> 1 => UNIFORM( 0, 1 ) +*> 2 => UNIFORM( -1, 1 ) +*> 3 => NORMAL( 0, 1 ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array of dimension ( 4 ) +*> Seed for random number generator. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array of dimension ( MIN( I , J ) ) +*> Diagonal entries of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] IGRADE +*> \verbatim +*> IGRADE is INTEGER +*> Specifies grading of matrix as follows: +*> 0 => no grading +*> 1 => matrix premultiplied by diag( DL ) +*> 2 => matrix postmultiplied by diag( DR ) +*> 3 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DR ) +*> 4 => matrix premultiplied by diag( DL ) and +*> postmultiplied by inv( diag( DL ) ) +*> 5 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DL ) +*> Not modified. +*> \endverbatim +*> +*> \param[in] DL +*> \verbatim +*> DL is DOUBLE PRECISION array ( I or J, as appropriate ) +*> Left scale factors for grading matrix. Not modified. +*> \endverbatim +*> +*> \param[in] DR +*> \verbatim +*> DR is DOUBLE PRECISION array ( I or J, as appropriate ) +*> Right scale factors for grading matrix. Not modified. +*> \endverbatim +*> +*> \param[in] IPVTNG +*> \verbatim +*> IPVTNG is INTEGER +*> On entry specifies pivoting permutations as follows: +*> 0 => none. +*> 1 => row pivoting. +*> 2 => column pivoting. +*> 3 => full pivoting, i.e., on both sides. +*> Not modified. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array ( I or J, as appropriate ) +*> This array specifies the permutation used. The +*> row (or column) in position K was originally in +*> position IWORK( K ). +*> This differs from IWORK for DLATM3. Not modified. +*> \endverbatim +*> +*> \param[in] SPARSE +*> \verbatim +*> SPARSE is DOUBLE PRECISION between 0. and 1. +*> On entry specifies the sparsity of the matrix +*> if sparse matix is to be generated. +*> SPARSE should lie between 0 and 1. +*> A uniform ( 0, 1 ) random number x is generated and +*> compared to SPARSE; if x is larger the matrix entry +*> is unchanged and if x is smaller the entry is set +*> to zero. Thus on the average a fraction SPARSE of the +*> entries will be set to zero. +*> Not modified. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_matgen +* +* ===================================================================== DOUBLE PRECISION FUNCTION DLATM2( M, N, I, J, KL, KU, IDIST, $ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. * @@ -17,126 +227,6 @@ DOUBLE PRECISION D( * ), DL( * ), DR( * ) * .. * -* Purpose -* ======= -* -* DLATM2 returns the (I,J) entry of a random matrix of dimension -* (M, N) described by the other paramters. It is called by the -* DLATMR routine in order to build random test matrices. No error -* checking on parameters is done, because this routine is called in -* a tight loop by DLATMR which has already checked the parameters. -* -* Use of DLATM2 differs from SLATM3 in the order in which the random -* number generator is called to fill in random matrix entries. -* With DLATM2, the generator is called to fill in the pivoted matrix -* columnwise. With DLATM3, the generator is called to fill in the -* matrix columnwise, after which it is pivoted. Thus, DLATM3 can -* be used to construct random matrices which differ only in their -* order of rows and/or columns. DLATM2 is used to construct band -* matrices while avoiding calling the random number generator for -* entries outside the band (and therefore generating random numbers -* -* The matrix whose (I,J) entry is returned is constructed as -* follows (this routine only computes one entry): -* -* If I is outside (1..M) or J is outside (1..N), return zero -* (this is convenient for generating matrices in band format). -* -* Generate a matrix A with random entries of distribution IDIST. -* -* Set the diagonal to D. -* -* Grade the matrix, if desired, from the left (by DL) and/or -* from the right (by DR or DL) as specified by IGRADE. -* -* Permute, if desired, the rows and/or columns as specified by -* IPVTNG and IWORK. -* -* Band the matrix to have lower bandwidth KL and upper -* bandwidth KU. -* -* Set random entries to zero as specified by SPARSE. -* -* Arguments -* ========= -* -* M (input) INTEGER -* Number of rows of matrix. Not modified. -* -* N (input) INTEGER -* Number of columns of matrix. Not modified. -* -* I (input) INTEGER -* Row of entry to be returned. Not modified. -* -* J (input) INTEGER -* Column of entry to be returned. Not modified. -* -* KL (input) INTEGER -* Lower bandwidth. Not modified. -* -* KU (input) INTEGER -* Upper bandwidth. Not modified. -* -* IDIST (input) INTEGER -* On entry, IDIST specifies the type of distribution to be -* used to generate a random matrix . -* 1 => UNIFORM( 0, 1 ) -* 2 => UNIFORM( -1, 1 ) -* 3 => NORMAL( 0, 1 ) -* Not modified. -* -* ISEED (input/output) INTEGER array of dimension ( 4 ) -* Seed for random number generator. -* Changed on exit. -* -* D (input) DOUBLE PRECISION array of dimension ( MIN( I , J ) ) -* Diagonal entries of matrix. Not modified. -* -* IGRADE (input) INTEGER -* Specifies grading of matrix as follows: -* 0 => no grading -* 1 => matrix premultiplied by diag( DL ) -* 2 => matrix postmultiplied by diag( DR ) -* 3 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DR ) -* 4 => matrix premultiplied by diag( DL ) and -* postmultiplied by inv( diag( DL ) ) -* 5 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DL ) -* Not modified. -* -* DL (input) DOUBLE PRECISION array ( I or J, as appropriate ) -* Left scale factors for grading matrix. Not modified. -* -* DR (input) DOUBLE PRECISION array ( I or J, as appropriate ) -* Right scale factors for grading matrix. Not modified. -* -* IPVTNG (input) INTEGER -* On entry specifies pivoting permutations as follows: -* 0 => none. -* 1 => row pivoting. -* 2 => column pivoting. -* 3 => full pivoting, i.e., on both sides. -* Not modified. -* -* IWORK (workspace) INTEGER array ( I or J, as appropriate ) -* This array specifies the permutation used. The -* row (or column) in position K was originally in -* position IWORK( K ). -* This differs from IWORK for DLATM3. Not modified. -* -* SPARSE (input) DOUBLE PRECISION between 0. and 1. -* On entry specifies the sparsity of the matrix -* if sparse matix is to be generated. -* SPARSE should lie between 0 and 1. -* A uniform ( 0, 1 ) random number x is generated and -* compared to SPARSE; if x is larger the matrix entry -* is unchanged and if x is smaller the entry is set -* to zero. Thus on the average a fraction SPARSE of the -* entries will be set to zero. -* Not modified. -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/dlatm3.f b/TESTING/MATGEN/dlatm3.f index 3b8bb363..10d1b2ba 100644 --- a/TESTING/MATGEN/dlatm3.f +++ b/TESTING/MATGEN/dlatm3.f @@ -1,10 +1,237 @@ +*> \brief \b DLATM3 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* DOUBLE PRECISION FUNCTION DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, +* IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, +* SPARSE ) +* +* .. Scalar Arguments .. +* +* INTEGER I, IDIST, IGRADE, IPVTNG, ISUB, J, JSUB, KL, +* $ KU, M, N +* DOUBLE PRECISION SPARSE +* .. +* +* .. Array Arguments .. +* +* INTEGER ISEED( 4 ), IWORK( * ) +* DOUBLE PRECISION D( * ), DL( * ), DR( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> DLATM3 returns the (ISUB,JSUB) entry of a random matrix of +*> dimension (M, N) described by the other paramters. (ISUB,JSUB) +*> is the final position of the (I,J) entry after pivoting +*> according to IPVTNG and IWORK. DLATM3 is called by the +*> DLATMR routine in order to build random test matrices. No error +*> checking on parameters is done, because this routine is called in +*> a tight loop by DLATMR which has already checked the parameters. +*> +*> Use of DLATM3 differs from SLATM2 in the order in which the random +*> number generator is called to fill in random matrix entries. +*> With DLATM2, the generator is called to fill in the pivoted matrix +*> columnwise. With DLATM3, the generator is called to fill in the +*> matrix columnwise, after which it is pivoted. Thus, DLATM3 can +*> be used to construct random matrices which differ only in their +*> order of rows and/or columns. DLATM2 is used to construct band +*> matrices while avoiding calling the random number generator for +*> entries outside the band (and therefore generating random numbers +*> in different orders for different pivot orders). +*> +*> The matrix whose (ISUB,JSUB) entry is returned is constructed as +*> follows (this routine only computes one entry): +*> +*> If ISUB is outside (1..M) or JSUB is outside (1..N), return zero +*> (this is convenient for generating matrices in band format). +*> +*> Generate a matrix A with random entries of distribution IDIST. +*> +*> Set the diagonal to D. +*> +*> Grade the matrix, if desired, from the left (by DL) and/or +*> from the right (by DR or DL) as specified by IGRADE. +*> +*> Permute, if desired, the rows and/or columns as specified by +*> IPVTNG and IWORK. +*> +*> Band the matrix to have lower bandwidth KL and upper +*> bandwidth KU. +*> +*> Set random entries to zero as specified by SPARSE. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Number of rows of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of columns of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] I +*> \verbatim +*> I is INTEGER +*> Row of unpivoted entry to be returned. Not modified. +*> \endverbatim +*> +*> \param[in] J +*> \verbatim +*> J is INTEGER +*> Column of unpivoted entry to be returned. Not modified. +*> \endverbatim +*> +*> \param[in,out] ISUB +*> \verbatim +*> ISUB is INTEGER +*> Row of pivoted entry to be returned. Changed on exit. +*> \endverbatim +*> +*> \param[in,out] JSUB +*> \verbatim +*> JSUB is INTEGER +*> Column of pivoted entry to be returned. Changed on exit. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> Lower bandwidth. Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> Upper bandwidth. Not modified. +*> \endverbatim +*> +*> \param[in] IDIST +*> \verbatim +*> IDIST is INTEGER +*> On entry, IDIST specifies the type of distribution to be +*> used to generate a random matrix . +*> 1 => UNIFORM( 0, 1 ) +*> 2 => UNIFORM( -1, 1 ) +*> 3 => NORMAL( 0, 1 ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array of dimension ( 4 ) +*> Seed for random number generator. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array of dimension ( MIN( I , J ) ) +*> Diagonal entries of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] IGRADE +*> \verbatim +*> IGRADE is INTEGER +*> Specifies grading of matrix as follows: +*> 0 => no grading +*> 1 => matrix premultiplied by diag( DL ) +*> 2 => matrix postmultiplied by diag( DR ) +*> 3 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DR ) +*> 4 => matrix premultiplied by diag( DL ) and +*> postmultiplied by inv( diag( DL ) ) +*> 5 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DL ) +*> Not modified. +*> \endverbatim +*> +*> \param[in] DL +*> \verbatim +*> DL is DOUBLE PRECISION array ( I or J, as appropriate ) +*> Left scale factors for grading matrix. Not modified. +*> \endverbatim +*> +*> \param[in] DR +*> \verbatim +*> DR is DOUBLE PRECISION array ( I or J, as appropriate ) +*> Right scale factors for grading matrix. Not modified. +*> \endverbatim +*> +*> \param[in] IPVTNG +*> \verbatim +*> IPVTNG is INTEGER +*> On entry specifies pivoting permutations as follows: +*> 0 => none. +*> 1 => row pivoting. +*> 2 => column pivoting. +*> 3 => full pivoting, i.e., on both sides. +*> Not modified. +*> \endverbatim +*> +*> \param[in] IWORK +*> \verbatim +*> IWORK is INTEGER array ( I or J, as appropriate ) +*> This array specifies the permutation used. The +*> row (or column) originally in position K is in +*> position IWORK( K ) after pivoting. +*> This differs from IWORK for DLATM2. Not modified. +*> \endverbatim +*> +*> \param[in] SPARSE +*> \verbatim +*> SPARSE is DOUBLE PRECISION between 0. and 1. +*> On entry specifies the sparsity of the matrix +*> if sparse matix is to be generated. +*> SPARSE should lie between 0 and 1. +*> A uniform ( 0, 1 ) random number x is generated and +*> compared to SPARSE; if x is larger the matrix entry +*> is unchanged and if x is smaller the entry is set +*> to zero. Thus on the average a fraction SPARSE of the +*> entries will be set to zero. +*> Not modified. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_matgen +* +* ===================================================================== DOUBLE PRECISION FUNCTION DLATM3( M, N, I, J, ISUB, JSUB, KL, KU, $ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, $ SPARSE ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. * @@ -19,135 +246,6 @@ DOUBLE PRECISION D( * ), DL( * ), DR( * ) * .. * -* Purpose -* ======= -* -* DLATM3 returns the (ISUB,JSUB) entry of a random matrix of -* dimension (M, N) described by the other paramters. (ISUB,JSUB) -* is the final position of the (I,J) entry after pivoting -* according to IPVTNG and IWORK. DLATM3 is called by the -* DLATMR routine in order to build random test matrices. No error -* checking on parameters is done, because this routine is called in -* a tight loop by DLATMR which has already checked the parameters. -* -* Use of DLATM3 differs from SLATM2 in the order in which the random -* number generator is called to fill in random matrix entries. -* With DLATM2, the generator is called to fill in the pivoted matrix -* columnwise. With DLATM3, the generator is called to fill in the -* matrix columnwise, after which it is pivoted. Thus, DLATM3 can -* be used to construct random matrices which differ only in their -* order of rows and/or columns. DLATM2 is used to construct band -* matrices while avoiding calling the random number generator for -* entries outside the band (and therefore generating random numbers -* in different orders for different pivot orders). -* -* The matrix whose (ISUB,JSUB) entry is returned is constructed as -* follows (this routine only computes one entry): -* -* If ISUB is outside (1..M) or JSUB is outside (1..N), return zero -* (this is convenient for generating matrices in band format). -* -* Generate a matrix A with random entries of distribution IDIST. -* -* Set the diagonal to D. -* -* Grade the matrix, if desired, from the left (by DL) and/or -* from the right (by DR or DL) as specified by IGRADE. -* -* Permute, if desired, the rows and/or columns as specified by -* IPVTNG and IWORK. -* -* Band the matrix to have lower bandwidth KL and upper -* bandwidth KU. -* -* Set random entries to zero as specified by SPARSE. -* -* Arguments -* ========= -* -* M (input) INTEGER -* Number of rows of matrix. Not modified. -* -* N (input) INTEGER -* Number of columns of matrix. Not modified. -* -* I (input) INTEGER -* Row of unpivoted entry to be returned. Not modified. -* -* J (input) INTEGER -* Column of unpivoted entry to be returned. Not modified. -* -* ISUB (input/output) INTEGER -* Row of pivoted entry to be returned. Changed on exit. -* -* JSUB (input/output) INTEGER -* Column of pivoted entry to be returned. Changed on exit. -* -* KL (input) INTEGER -* Lower bandwidth. Not modified. -* -* KU (input) INTEGER -* Upper bandwidth. Not modified. -* -* IDIST (input) INTEGER -* On entry, IDIST specifies the type of distribution to be -* used to generate a random matrix . -* 1 => UNIFORM( 0, 1 ) -* 2 => UNIFORM( -1, 1 ) -* 3 => NORMAL( 0, 1 ) -* Not modified. -* -* ISEED (input/output) INTEGER array of dimension ( 4 ) -* Seed for random number generator. -* Changed on exit. -* -* D (input) DOUBLE PRECISION array of dimension ( MIN( I , J ) ) -* Diagonal entries of matrix. Not modified. -* -* IGRADE (input) INTEGER -* Specifies grading of matrix as follows: -* 0 => no grading -* 1 => matrix premultiplied by diag( DL ) -* 2 => matrix postmultiplied by diag( DR ) -* 3 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DR ) -* 4 => matrix premultiplied by diag( DL ) and -* postmultiplied by inv( diag( DL ) ) -* 5 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DL ) -* Not modified. -* -* DL (input) DOUBLE PRECISION array ( I or J, as appropriate ) -* Left scale factors for grading matrix. Not modified. -* -* DR (input) DOUBLE PRECISION array ( I or J, as appropriate ) -* Right scale factors for grading matrix. Not modified. -* -* IPVTNG (input) INTEGER -* On entry specifies pivoting permutations as follows: -* 0 => none. -* 1 => row pivoting. -* 2 => column pivoting. -* 3 => full pivoting, i.e., on both sides. -* Not modified. -* -* IWORK (input) INTEGER array ( I or J, as appropriate ) -* This array specifies the permutation used. The -* row (or column) originally in position K is in -* position IWORK( K ) after pivoting. -* This differs from IWORK for DLATM2. Not modified. -* -* SPARSE (input) DOUBLE PRECISION between 0. and 1. -* On entry specifies the sparsity of the matrix -* if sparse matix is to be generated. -* SPARSE should lie between 0 and 1. -* A uniform ( 0, 1 ) random number x is generated and -* compared to SPARSE; if x is larger the matrix entry -* is unchanged and if x is smaller the entry is set -* to zero. Thus on the average a fraction SPARSE of the -* entries will be set to zero. -* Not modified. -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/dlatm5.f b/TESTING/MATGEN/dlatm5.f index 3163849c..d3bb66ea 100644 --- a/TESTING/MATGEN/dlatm5.f +++ b/TESTING/MATGEN/dlatm5.f @@ -1,177 +1,292 @@ - SUBROUTINE DLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD, - $ E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA, - $ QBLCKB ) -* -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N, - $ PRTYPE, QBLCKA, QBLCKB - DOUBLE PRECISION ALPHA -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ), - $ D( LDD, * ), E( LDE, * ), F( LDF, * ), - $ L( LDL, * ), R( LDR, * ) -* .. -* +*> \brief \b DLATM5 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD, +* E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA, +* QBLCKB ) +* +* .. Scalar Arguments .. +* INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N, +* $ PRTYPE, QBLCKA, QBLCKB +* DOUBLE PRECISION ALPHA +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ), +* $ D( LDD, * ), E( LDE, * ), F( LDF, * ), +* $ L( LDL, * ), R( LDR, * ) +* .. +* * Purpose * ======= * -* DLATM5 generates matrices involved in the Generalized Sylvester -* equation: -* -* A * R - L * B = C -* D * R - L * E = F -* -* They also satisfy (the diagonalization condition) -* -* [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] ) -* [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] ) -* +*>\details \b Purpose: +*>\verbatim +*> +*> DLATM5 generates matrices involved in the Generalized Sylvester +*> equation: +*> +*> A * R - L * B = C +*> D * R - L * E = F +*> +*> They also satisfy (the diagonalization condition) +*> +*> [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] ) +*> [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] ) +*> +*> +*>\endverbatim * * Arguments * ========= * -* PRTYPE (input) INTEGER -* "Points" to a certian type of the matrices to generate -* (see futher details). -* -* M (input) INTEGER -* Specifies the order of A and D and the number of rows in -* C, F, R and L. -* -* N (input) INTEGER -* Specifies the order of B and E and the number of columns in -* C, F, R and L. -* -* A (output) DOUBLE PRECISION array, dimension (LDA, M). -* On exit A M-by-M is initialized according to PRTYPE. -* -* LDA (input) INTEGER -* The leading dimension of A. -* -* B (output) DOUBLE PRECISION array, dimension (LDB, N). -* On exit B N-by-N is initialized according to PRTYPE. -* -* LDB (input) INTEGER -* The leading dimension of B. -* -* C (output) DOUBLE PRECISION array, dimension (LDC, N). -* On exit C M-by-N is initialized according to PRTYPE. -* -* LDC (input) INTEGER -* The leading dimension of C. -* -* D (output) DOUBLE PRECISION array, dimension (LDD, M). -* On exit D M-by-M is initialized according to PRTYPE. -* -* LDD (input) INTEGER -* The leading dimension of D. -* -* E (output) DOUBLE PRECISION array, dimension (LDE, N). -* On exit E N-by-N is initialized according to PRTYPE. -* -* LDE (input) INTEGER -* The leading dimension of E. -* -* F (output) DOUBLE PRECISION array, dimension (LDF, N). -* On exit F M-by-N is initialized according to PRTYPE. -* -* LDF (input) INTEGER -* The leading dimension of F. -* -* R (output) DOUBLE PRECISION array, dimension (LDR, N). -* On exit R M-by-N is initialized according to PRTYPE. -* -* LDR (input) INTEGER -* The leading dimension of R. -* -* L (output) DOUBLE PRECISION array, dimension (LDL, N). -* On exit L M-by-N is initialized according to PRTYPE. -* -* LDL (input) INTEGER -* The leading dimension of L. +*> \param[in] PRTYPE +*> \verbatim +*> PRTYPE is INTEGER +*> "Points" to a certian type of the matrices to generate +*> (see futher details). +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Specifies the order of A and D and the number of rows in +*> C, F, R and L. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Specifies the order of B and E and the number of columns in +*> C, F, R and L. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA, M). +*> On exit A M-by-M is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of A. +*> \endverbatim +*> +*> \param[out] B +*> \verbatim +*> B is DOUBLE PRECISION array, dimension (LDB, N). +*> On exit B N-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of B. +*> \endverbatim +*> +*> \param[out] C +*> \verbatim +*> C is DOUBLE PRECISION array, dimension (LDC, N). +*> On exit C M-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> The leading dimension of C. +*> \endverbatim +*> +*> \param[out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (LDD, M). +*> On exit D M-by-M is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDD +*> \verbatim +*> LDD is INTEGER +*> The leading dimension of D. +*> \endverbatim +*> +*> \param[out] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (LDE, N). +*> On exit E N-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDE +*> \verbatim +*> LDE is INTEGER +*> The leading dimension of E. +*> \endverbatim +*> +*> \param[out] F +*> \verbatim +*> F is DOUBLE PRECISION array, dimension (LDF, N). +*> On exit F M-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDF +*> \verbatim +*> LDF is INTEGER +*> The leading dimension of F. +*> \endverbatim +*> +*> \param[out] R +*> \verbatim +*> R is DOUBLE PRECISION array, dimension (LDR, N). +*> On exit R M-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDR +*> \verbatim +*> LDR is INTEGER +*> The leading dimension of R. +*> \endverbatim +*> +*> \param[out] L +*> \verbatim +*> L is DOUBLE PRECISION array, dimension (LDL, N). +*> On exit L M-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDL +*> \verbatim +*> LDL is INTEGER +*> The leading dimension of L. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION +*> Parameter used in generating PRTYPE = 1 and 5 matrices. +*> \endverbatim +*> +*> \param[in] QBLCKA +*> \verbatim +*> QBLCKA is INTEGER +*> When PRTYPE = 3, specifies the distance between 2-by-2 +*> blocks on the diagonal in A. Otherwise, QBLCKA is not +*> referenced. QBLCKA > 1. +*> \endverbatim +*> +*> \param[in] QBLCKB +*> \verbatim +*> QBLCKB is INTEGER +*> When PRTYPE = 3, specifies the distance between 2-by-2 +*> blocks on the diagonal in B. Otherwise, QBLCKB is not +*> referenced. QBLCKB > 1. +*> \endverbatim +*> +* +* Authors +* ======= * -* ALPHA (input) DOUBLE PRECISION -* Parameter used in generating PRTYPE = 1 and 5 matrices. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* QBLCKA (input) INTEGER -* When PRTYPE = 3, specifies the distance between 2-by-2 -* blocks on the diagonal in A. Otherwise, QBLCKA is not -* referenced. QBLCKA > 1. +*> \date November 2011 * -* QBLCKB (input) INTEGER -* When PRTYPE = 3, specifies the distance between 2-by-2 -* blocks on the diagonal in B. Otherwise, QBLCKB is not -* referenced. QBLCKB > 1. +*> \ingroup double_matgen * * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices +*> +*> A : if (i == j) then A(i, j) = 1.0 +*> if (j == i + 1) then A(i, j) = -1.0 +*> else A(i, j) = 0.0, i, j = 1...M +*> +*> B : if (i == j) then B(i, j) = 1.0 - ALPHA +*> if (j == i + 1) then B(i, j) = 1.0 +*> else B(i, j) = 0.0, i, j = 1...N +*> +*> D : if (i == j) then D(i, j) = 1.0 +*> else D(i, j) = 0.0, i, j = 1...M +*> +*> E : if (i == j) then E(i, j) = 1.0 +*> else E(i, j) = 0.0, i, j = 1...N +*> +*> L = R are chosen from [-10...10], +*> which specifies the right hand sides (C, F). +*> +*> PRTYPE = 2 or 3: Triangular and/or quasi- triangular. +*> +*> A : if (i <= j) then A(i, j) = [-1...1] +*> else A(i, j) = 0.0, i, j = 1...M +*> +*> if (PRTYPE = 3) then +*> A(k + 1, k + 1) = A(k, k) +*> A(k + 1, k) = [-1...1] +*> sign(A(k, k + 1) = -(sin(A(k + 1, k)) +*> k = 1, M - 1, QBLCKA +*> +*> B : if (i <= j) then B(i, j) = [-1...1] +*> else B(i, j) = 0.0, i, j = 1...N +*> +*> if (PRTYPE = 3) then +*> B(k + 1, k + 1) = B(k, k) +*> B(k + 1, k) = [-1...1] +*> sign(B(k, k + 1) = -(sign(B(k + 1, k)) +*> k = 1, N - 1, QBLCKB +*> +*> D : if (i <= j) then D(i, j) = [-1...1]. +*> else D(i, j) = 0.0, i, j = 1...M +*> +*> +*> E : if (i <= j) then D(i, j) = [-1...1] +*> else E(i, j) = 0.0, i, j = 1...N +*> +*> L, R are chosen from [-10...10], +*> which specifies the right hand sides (C, F). +*> +*> PRTYPE = 4 Full +*> A(i, j) = [-10...10] +*> D(i, j) = [-1...1] i,j = 1...M +*> B(i, j) = [-10...10] +*> E(i, j) = [-1...1] i,j = 1...N +*> R(i, j) = [-10...10] +*> L(i, j) = [-1...1] i = 1..M ,j = 1...N +*> +*> L, R specifies the right hand sides (C, F). +*> +*> PRTYPE = 5 special case common and/or close eigs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD, + $ E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA, + $ QBLCKB ) * -* PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices -* -* A : if (i == j) then A(i, j) = 1.0 -* if (j == i + 1) then A(i, j) = -1.0 -* else A(i, j) = 0.0, i, j = 1...M -* -* B : if (i == j) then B(i, j) = 1.0 - ALPHA -* if (j == i + 1) then B(i, j) = 1.0 -* else B(i, j) = 0.0, i, j = 1...N -* -* D : if (i == j) then D(i, j) = 1.0 -* else D(i, j) = 0.0, i, j = 1...M -* -* E : if (i == j) then E(i, j) = 1.0 -* else E(i, j) = 0.0, i, j = 1...N -* -* L = R are chosen from [-10...10], -* which specifies the right hand sides (C, F). -* -* PRTYPE = 2 or 3: Triangular and/or quasi- triangular. -* -* A : if (i <= j) then A(i, j) = [-1...1] -* else A(i, j) = 0.0, i, j = 1...M -* -* if (PRTYPE = 3) then -* A(k + 1, k + 1) = A(k, k) -* A(k + 1, k) = [-1...1] -* sign(A(k, k + 1) = -(sin(A(k + 1, k)) -* k = 1, M - 1, QBLCKA -* -* B : if (i <= j) then B(i, j) = [-1...1] -* else B(i, j) = 0.0, i, j = 1...N -* -* if (PRTYPE = 3) then -* B(k + 1, k + 1) = B(k, k) -* B(k + 1, k) = [-1...1] -* sign(B(k, k + 1) = -(sign(B(k + 1, k)) -* k = 1, N - 1, QBLCKB -* -* D : if (i <= j) then D(i, j) = [-1...1]. -* else D(i, j) = 0.0, i, j = 1...M -* -* -* E : if (i <= j) then D(i, j) = [-1...1] -* else E(i, j) = 0.0, i, j = 1...N -* -* L, R are chosen from [-10...10], -* which specifies the right hand sides (C, F). -* -* PRTYPE = 4 Full -* A(i, j) = [-10...10] -* D(i, j) = [-1...1] i,j = 1...M -* B(i, j) = [-10...10] -* E(i, j) = [-1...1] i,j = 1...N -* R(i, j) = [-10...10] -* L(i, j) = [-1...1] i = 1..M ,j = 1...N -* -* L, R specifies the right hand sides (C, F). +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* PRTYPE = 5 special case common and/or close eigs. +* .. Scalar Arguments .. + INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N, + $ PRTYPE, QBLCKA, QBLCKB + DOUBLE PRECISION ALPHA +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ), + $ D( LDD, * ), E( LDE, * ), F( LDF, * ), + $ L( LDL, * ), R( LDR, * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/dlatm6.f b/TESTING/MATGEN/dlatm6.f index ddb6e5d0..766cfe18 100644 --- a/TESTING/MATGEN/dlatm6.f +++ b/TESTING/MATGEN/dlatm6.f @@ -1,107 +1,197 @@ - SUBROUTINE DLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA, - $ BETA, WX, WY, S, DIF ) -* -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER LDA, LDX, LDY, N, TYPE - DOUBLE PRECISION ALPHA, BETA, WX, WY -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), B( LDA, * ), DIF( * ), S( * ), - $ X( LDX, * ), Y( LDY, * ) -* .. -* +*> \brief \b DLATM6 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA, +* BETA, WX, WY, S, DIF ) +* +* .. Scalar Arguments .. +* INTEGER LDA, LDX, LDY, N, TYPE +* DOUBLE PRECISION ALPHA, BETA, WX, WY +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ), B( LDA, * ), DIF( * ), S( * ), +* $ X( LDX, * ), Y( LDY, * ) +* .. +* * Purpose * ======= * -* DLATM6 generates test matrices for the generalized eigenvalue -* problem, their corresponding right and left eigenvector matrices, -* and also reciprocal condition numbers for all eigenvalues and -* the reciprocal condition numbers of eigenvectors corresponding to -* the 1th and 5th eigenvalues. -* -* Test Matrices -* ============= -* -* Two kinds of test matrix pairs -* -* (A, B) = inverse(YH) * (Da, Db) * inverse(X) -* -* are used in the tests: -* -* Type 1: -* Da = 1+a 0 0 0 0 Db = 1 0 0 0 0 -* 0 2+a 0 0 0 0 1 0 0 0 -* 0 0 3+a 0 0 0 0 1 0 0 -* 0 0 0 4+a 0 0 0 0 1 0 -* 0 0 0 0 5+a , 0 0 0 0 1 , and -* -* Type 2: -* Da = 1 -1 0 0 0 Db = 1 0 0 0 0 -* 1 1 0 0 0 0 1 0 0 0 -* 0 0 1 0 0 0 0 1 0 0 -* 0 0 0 1+a 1+b 0 0 0 1 0 -* 0 0 0 -1-b 1+a , 0 0 0 0 1 . -* -* In both cases the same inverse(YH) and inverse(X) are used to compute -* (A, B), giving the exact eigenvectors to (A,B) as (YH, X): -* -* YH: = 1 0 -y y -y X = 1 0 -x -x x -* 0 1 -y y -y 0 1 x -x -x -* 0 0 1 0 0 0 0 1 0 0 -* 0 0 0 1 0 0 0 0 1 0 -* 0 0 0 0 1, 0 0 0 0 1 , -* -* where a, b, x and y will have all values independently of each other. +*>\details \b Purpose: +*>\verbatim +*> +*> DLATM6 generates test matrices for the generalized eigenvalue +*> problem, their corresponding right and left eigenvector matrices, +*> and also reciprocal condition numbers for all eigenvalues and +*> the reciprocal condition numbers of eigenvectors corresponding to +*> the 1th and 5th eigenvalues. +*> +*> Test Matrices +*> ============= +*> +*> Two kinds of test matrix pairs +*> +*> (A, B) = inverse(YH) * (Da, Db) * inverse(X) +*> +*> are used in the tests: +*> +*> Type 1: +*> Da = 1+a 0 0 0 0 Db = 1 0 0 0 0 +*> 0 2+a 0 0 0 0 1 0 0 0 +*> 0 0 3+a 0 0 0 0 1 0 0 +*> 0 0 0 4+a 0 0 0 0 1 0 +*> 0 0 0 0 5+a , 0 0 0 0 1 , and +*> +*> Type 2: +*> Da = 1 -1 0 0 0 Db = 1 0 0 0 0 +*> 1 1 0 0 0 0 1 0 0 0 +*> 0 0 1 0 0 0 0 1 0 0 +*> 0 0 0 1+a 1+b 0 0 0 1 0 +*> 0 0 0 -1-b 1+a , 0 0 0 0 1 . +*> +*> In both cases the same inverse(YH) and inverse(X) are used to compute +*> (A, B), giving the exact eigenvectors to (A,B) as (YH, X): +*> +*> YH: = 1 0 -y y -y X = 1 0 -x -x x +*> 0 1 -y y -y 0 1 x -x -x +*> 0 0 1 0 0 0 0 1 0 0 +*> 0 0 0 1 0 0 0 0 1 0 +*> 0 0 0 0 1, 0 0 0 0 1 , +*> +*> where a, b, x and y will have all values independently of each other. +*> +*>\endverbatim * * Arguments * ========= * -* TYPE (input) INTEGER -* Specifies the problem type (see futher details). -* -* N (input) INTEGER -* Size of the matrices A and B. -* -* A (output) DOUBLE PRECISION array, dimension (LDA, N). -* On exit A N-by-N is initialized according to TYPE. -* -* LDA (input) INTEGER -* The leading dimension of A and of B. -* -* B (output) DOUBLE PRECISION array, dimension (LDA, N). -* On exit B N-by-N is initialized according to TYPE. -* -* X (output) DOUBLE PRECISION array, dimension (LDX, N). -* On exit X is the N-by-N matrix of right eigenvectors. -* -* LDX (input) INTEGER -* The leading dimension of X. -* -* Y (output) DOUBLE PRECISION array, dimension (LDY, N). -* On exit Y is the N-by-N matrix of left eigenvectors. +*> \param[in] TYPE +*> \verbatim +*> TYPE is INTEGER +*> Specifies the problem type (see futher details). +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Size of the matrices A and B. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA, N). +*> On exit A N-by-N is initialized according to TYPE. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of A and of B. +*> \endverbatim +*> +*> \param[out] B +*> \verbatim +*> B is DOUBLE PRECISION array, dimension (LDA, N). +*> On exit B N-by-N is initialized according to TYPE. +*> \endverbatim +*> +*> \param[out] X +*> \verbatim +*> X is DOUBLE PRECISION array, dimension (LDX, N). +*> On exit X is the N-by-N matrix of right eigenvectors. +*> \endverbatim +*> +*> \param[in] LDX +*> \verbatim +*> LDX is INTEGER +*> The leading dimension of X. +*> \endverbatim +*> +*> \param[out] Y +*> \verbatim +*> Y is DOUBLE PRECISION array, dimension (LDY, N). +*> On exit Y is the N-by-N matrix of left eigenvectors. +*> \endverbatim +*> +*> \param[in] LDY +*> \verbatim +*> LDY is INTEGER +*> The leading dimension of Y. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is DOUBLE PRECISION +*> \endverbatim +*> \verbatim +*> Weighting constants for matrix A. +*> \endverbatim +*> +*> \param[in] WX +*> \verbatim +*> WX is DOUBLE PRECISION +*> Constant for right eigenvector matrix. +*> \endverbatim +*> +*> \param[in] WY +*> \verbatim +*> WY is DOUBLE PRECISION +*> Constant for left eigenvector matrix. +*> \endverbatim +*> +*> \param[out] S +*> \verbatim +*> S is DOUBLE PRECISION array, dimension (N) +*> S(i) is the reciprocal condition number for eigenvalue i. +*> \endverbatim +*> +*> \param[out] DIF +*> \verbatim +*> DIF is DOUBLE PRECISION array, dimension (N) +*> DIF(i) is the reciprocal condition number for eigenvector i. +*> \endverbatim +*> +* +* Authors +* ======= * -* LDY (input) INTEGER -* The leading dimension of Y. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* ALPHA (input) DOUBLE PRECISION -* BETA (input) DOUBLE PRECISION -* Weighting constants for matrix A. +*> \date November 2011 * -* WX (input) DOUBLE PRECISION -* Constant for right eigenvector matrix. +*> \ingroup double_matgen * -* WY (input) DOUBLE PRECISION -* Constant for left eigenvector matrix. +* ===================================================================== + SUBROUTINE DLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA, + $ BETA, WX, WY, S, DIF ) * -* S (output) DOUBLE PRECISION array, dimension (N) -* S(i) is the reciprocal condition number for eigenvalue i. +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* DIF (output) DOUBLE PRECISION array, dimension (N) -* DIF(i) is the reciprocal condition number for eigenvector i. +* .. Scalar Arguments .. + INTEGER LDA, LDX, LDY, N, TYPE + DOUBLE PRECISION ALPHA, BETA, WX, WY +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), B( LDA, * ), DIF( * ), S( * ), + $ X( LDX, * ), Y( LDY, * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/dlatm7.f b/TESTING/MATGEN/dlatm7.f index 683d46be..4d46cd4b 100644 --- a/TESTING/MATGEN/dlatm7.f +++ b/TESTING/MATGEN/dlatm7.f @@ -1,9 +1,143 @@ +*> \brief \b DLATM7 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DLATM7( MODE, COND, IRSIGN, IDIST, ISEED, D, N, +* RANK, INFO ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION COND +* INTEGER IDIST, INFO, IRSIGN, MODE, N, RANK +* .. +* .. Array Arguments .. +* DOUBLE PRECISION D( * ) +* INTEGER ISEED( 4 ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> DLATM7 computes the entries of D as specified by MODE +*> COND and IRSIGN. IDIST and ISEED determine the generation +*> of random numbers. DLATM7 is called by DLATMT to generate +*> random test matrices. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \verbatim +*> MODE - INTEGER +*> On entry describes how D is to be computed: +*> MODE = 0 means do not change D. +*> \endverbatim +*> \verbatim +*> MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND +*> MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) I=1:RANK +*> \endverbatim +*> \verbatim +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> Not modified. +*> \endverbatim +*> \verbatim +*> COND - DOUBLE PRECISION +*> On entry, used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> \verbatim +*> IRSIGN - INTEGER +*> On entry, if MODE neither -6, 0 nor 6, determines sign of +*> entries of D +*> 0 => leave entries of D unchanged +*> 1 => multiply each entry of D by 1 or -1 with probability .5 +*> \endverbatim +*> \verbatim +*> IDIST - CHARACTER*1 +*> On entry, IDIST specifies the type of distribution to be +*> used to generate a random matrix . +*> 1 => UNIFORM( 0, 1 ) +*> 2 => UNIFORM( -1, 1 ) +*> 3 => NORMAL( 0, 1 ) +*> Not modified. +*> \endverbatim +*> \verbatim +*> ISEED - INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. The random number generator uses a +*> linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to DLATM7 +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> \verbatim +*> D - DOUBLE PRECISION array, dimension ( MIN( M , N ) ) +*> Array to be computed according to MODE, COND and IRSIGN. +*> May be changed on exit if MODE is nonzero. +*> \endverbatim +*> \verbatim +*> N - INTEGER +*> Number of entries of D. Not modified. +*> \endverbatim +*> \verbatim +*> RANK - INTEGER +*> The rank of matrix to be generated for modes 1,2,3 only. +*> D( RANK+1:N ) = 0. +*> Not modified. +*> \endverbatim +*> \verbatim +*> INFO - INTEGER +*> 0 => normal termination +*> -1 => if MODE not in range -6 to 6 +*> -2 => if MODE neither -6, 0 nor 6, and +*> IRSIGN neither 0 nor 1 +*> -3 => if MODE neither -6, 0 nor 6 and COND less than 1 +*> -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3 +*> -7 => if N negative +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_matgen +* +* ===================================================================== SUBROUTINE DLATM7( MODE, COND, IRSIGN, IDIST, ISEED, D, N, $ RANK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Craig Lucas, University of Manchester / NAG Ltd. -* October, 2008 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. DOUBLE PRECISION COND @@ -14,86 +148,6 @@ INTEGER ISEED( 4 ) * .. * -* Purpose -* ======= -* -* DLATM7 computes the entries of D as specified by MODE -* COND and IRSIGN. IDIST and ISEED determine the generation -* of random numbers. DLATM7 is called by DLATMT to generate -* random test matrices. -* -* Arguments -* ========= -* -* MODE - INTEGER -* On entry describes how D is to be computed: -* MODE = 0 means do not change D. -* -* MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND -* MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) I=1:RANK -* -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* Not modified. -* -* COND - DOUBLE PRECISION -* On entry, used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* IRSIGN - INTEGER -* On entry, if MODE neither -6, 0 nor 6, determines sign of -* entries of D -* 0 => leave entries of D unchanged -* 1 => multiply each entry of D by 1 or -1 with probability .5 -* -* IDIST - CHARACTER*1 -* On entry, IDIST specifies the type of distribution to be -* used to generate a random matrix . -* 1 => UNIFORM( 0, 1 ) -* 2 => UNIFORM( -1, 1 ) -* 3 => NORMAL( 0, 1 ) -* Not modified. -* -* ISEED - INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. The random number generator uses a -* linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to DLATM7 -* to continue the same random number sequence. -* Changed on exit. -* -* D - DOUBLE PRECISION array, dimension ( MIN( M , N ) ) -* Array to be computed according to MODE, COND and IRSIGN. -* May be changed on exit if MODE is nonzero. -* -* N - INTEGER -* Number of entries of D. Not modified. -* -* RANK - INTEGER -* The rank of matrix to be generated for modes 1,2,3 only. -* D( RANK+1:N ) = 0. -* Not modified. -* -* INFO - INTEGER -* 0 => normal termination -* -1 => if MODE not in range -6 to 6 -* -2 => if MODE neither -6, 0 nor 6, and -* IRSIGN neither 0 nor 1 -* -3 => if MODE neither -6, 0 nor 6 and COND less than 1 -* -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3 -* -7 => if N negative -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/dlatme.f b/TESTING/MATGEN/dlatme.f index 86bb1f31..9eccb773 100644 --- a/TESTING/MATGEN/dlatme.f +++ b/TESTING/MATGEN/dlatme.f @@ -1,12 +1,343 @@ +*> \brief \b DLATME +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DLATME( N, DIST, ISEED, D, MODE, COND, DMAX, EI, +* RSIGN, +* UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, +* A, +* LDA, WORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER DIST, RSIGN, SIM, UPPER +* INTEGER INFO, KL, KU, LDA, MODE, MODES, N +* DOUBLE PRECISION ANORM, COND, CONDS, DMAX +* .. +* .. Array Arguments .. +* CHARACTER EI( * ) +* INTEGER ISEED( 4 ) +* DOUBLE PRECISION A( LDA, * ), D( * ), DS( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> DLATME generates random non-symmetric square matrices with +*> specified eigenvalues for testing LAPACK programs. +*> +*> DLATME operates by applying the following sequence of +*> operations: +*> +*> 1. Set the diagonal to D, where D may be input or +*> computed according to MODE, COND, DMAX, and RSIGN +*> as described below. +*> +*> 2. If complex conjugate pairs are desired (MODE=0 and EI(1)='R', +*> or MODE=5), certain pairs of adjacent elements of D are +*> interpreted as the real and complex parts of a complex +*> conjugate pair; A thus becomes block diagonal, with 1x1 +*> and 2x2 blocks. +*> +*> 3. If UPPER='T', the upper triangle of A is set to random values +*> out of distribution DIST. +*> +*> 4. If SIM='T', A is multiplied on the left by a random matrix +*> X, whose singular values are specified by DS, MODES, and +*> CONDS, and on the right by X inverse. +*> +*> 5. If KL < N-1, the lower bandwidth is reduced to KL using +*> Householder transformations. If KU < N-1, the upper +*> bandwidth is reduced to KU. +*> +*> 6. If ANORM is not negative, the matrix is scaled to have +*> maximum-element-norm ANORM. +*> +*> (Note: since the matrix cannot be reduced beyond Hessenberg form, +*> no packing options are available.) +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns (or rows) of A. Not modified. +*> \endverbatim +*> +*> \param[in] DIST +*> \verbatim +*> DIST is CHARACTER*1 +*> On entry, DIST specifies the type of distribution to be used +*> to generate the random eigen-/singular values, and for the +*> upper triangle (see UPPER). +*> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) +*> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) +*> 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. They should lie between 0 and 4095 inclusive, +*> and ISEED(4) should be odd. The random number generator +*> uses a linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to DLATME +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension ( N ) +*> This array is used to specify the eigenvalues of A. If +*> MODE=0, then D is assumed to contain the eigenvalues (but +*> see the description of EI), otherwise they will be +*> computed according to MODE, COND, DMAX, and RSIGN and +*> placed in D. +*> Modified if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry this describes how the eigenvalues are to +*> be specified: +*> MODE = 0 means use D (with EI) as input +*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND +*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. Each odd-even pair +*> of elements will be either used as two real +*> eigenvalues or as the real and imaginary part +*> of a complex conjugate pair of eigenvalues; +*> the choice of which is done is random, with +*> 50-50 probability, for each pair. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is between 1 and 4, D has entries ranging +*> from 1 to 1/COND, if between -1 and -4, D has entries +*> ranging from 1/COND to 1, +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is DOUBLE PRECISION +*> On entry, this is used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] DMAX +*> \verbatim +*> DMAX is DOUBLE PRECISION +*> If MODE is neither -6, 0 nor 6, the contents of D, as +*> computed according to MODE and COND, will be scaled by +*> DMAX / max(abs(D(i))). Note that DMAX need not be +*> positive: if DMAX is negative (or zero), D will be +*> scaled by a negative number (or zero). +*> Not modified. +*> \endverbatim +*> +*> \param[in] EI +*> \verbatim +*> EI is CHARACTER*1 array, dimension ( N ) +*> If MODE is 0, and EI(1) is not ' ' (space character), +*> this array specifies which elements of D (on input) are +*> real eigenvalues and which are the real and imaginary parts +*> of a complex conjugate pair of eigenvalues. The elements +*> of EI may then only have the values 'R' and 'I'. If +*> EI(j)='R' and EI(j+1)='I', then the j-th eigenvalue is +*> CMPLX( D(j) , D(j+1) ), and the (j+1)-th is the complex +*> conjugate thereof. If EI(j)=EI(j+1)='R', then the j-th +*> eigenvalue is D(j) (i.e., real). EI(1) may not be 'I', +*> nor may two adjacent elements of EI both have the value 'I'. +*> If MODE is not 0, then EI is ignored. If MODE is 0 and +*> EI(1)=' ', then the eigenvalues will all be real. +*> Not modified. +*> \endverbatim +*> +*> \param[in] RSIGN +*> \verbatim +*> RSIGN is CHARACTER*1 +*> If MODE is not 0, 6, or -6, and RSIGN='T', then the +*> elements of D, as computed according to MODE and COND, will +*> be multiplied by a random sign (+1 or -1). If RSIGN='F', +*> they will not be. RSIGN may only have the values 'T' or +*> 'F'. +*> Not modified. +*> \endverbatim +*> +*> \param[in] UPPER +*> \verbatim +*> UPPER is CHARACTER*1 +*> If UPPER='T', then the elements of A above the diagonal +*> (and above the 2x2 diagonal blocks, if A has complex +*> eigenvalues) will be set to random numbers out of DIST. +*> If UPPER='F', they will not. UPPER may only have the +*> values 'T' or 'F'. +*> Not modified. +*> \endverbatim +*> +*> \param[in] SIM +*> \verbatim +*> SIM is CHARACTER*1 +*> If SIM='T', then A will be operated on by a "similarity +*> transform", i.e., multiplied on the left by a matrix X and +*> on the right by X inverse. X = U S V, where U and V are +*> random unitary matrices and S is a (diagonal) matrix of +*> singular values specified by DS, MODES, and CONDS. If +*> SIM='F', then A will not be transformed. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] DS +*> \verbatim +*> DS is DOUBLE PRECISION array, dimension ( N ) +*> This array is used to specify the singular values of X, +*> in the same way that D specifies the eigenvalues of A. +*> If MODE=0, the DS contains the singular values, which +*> may not be zero. +*> Modified if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODES +*> \verbatim +*> MODES is INTEGER +*> \endverbatim +*> +*> \param[in] CONDS +*> \verbatim +*> CONDS is DOUBLE PRECISION +*> Same as MODE and COND, but for specifying the diagonal +*> of S. MODES=-6 and +6 are not allowed (since they would +*> result in randomly ill-conditioned eigenvalues.) +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> This specifies the lower bandwidth of the matrix. KL=1 +*> specifies upper Hessenberg form. If KL is at least N-1, +*> then A will have full lower bandwidth. KL must be at +*> least 1. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> This specifies the upper bandwidth of the matrix. KU=1 +*> specifies lower Hessenberg form. If KU is at least N-1, +*> then A will have full upper bandwidth; if KU and KL +*> are both at least N-1, then A will be dense. Only one of +*> KU and KL may be less than N-1. KU must be at least 1. +*> Not modified. +*> \endverbatim +*> +*> \param[in] ANORM +*> \verbatim +*> ANORM is DOUBLE PRECISION +*> If ANORM is not negative, then A will be scaled by a non- +*> negative real number to make the maximum-element-norm of A +*> to be ANORM. +*> Not modified. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension ( LDA, N ) +*> On exit A is the desired test matrix. +*> Modified. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> LDA specifies the first dimension of A as declared in the +*> calling program. LDA must be at least N. +*> Not modified. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension ( 3*N ) +*> Workspace. +*> Modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error code. On exit, INFO will be set to one of the +*> following values: +*> 0 => normal return +*> -1 => N negative +*> -2 => DIST illegal string +*> -5 => MODE not in range -6 to 6 +*> -6 => COND less than 1.0, and MODE neither -6, 0 nor 6 +*> -8 => EI(1) is not ' ' or 'R', EI(j) is not 'R' or 'I', or +*> two adjacent elements of EI are 'I'. +*> -9 => RSIGN is not 'T' or 'F' +*> -10 => UPPER is not 'T' or 'F' +*> -11 => SIM is not 'T' or 'F' +*> -12 => MODES=0 and DS has a zero singular value. +*> -13 => MODES is not in the range -5 to 5. +*> -14 => MODES is nonzero and CONDS is less than 1. +*> -15 => KL is less than 1. +*> -16 => KU is less than 1, or KL and KU are both less than +*> N-1. +*> -19 => LDA is less than N. +*> 1 => Error return from DLATM1 (computing D) +*> 2 => Cannot scale to DMAX (max. eigenvalue is 0) +*> 3 => Error return from DLATM1 (computing DS) +*> 4 => Error return from DLARGE +*> 5 => Zero singular value from DLATM1. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_matgen +* +* ===================================================================== SUBROUTINE DLATME( N, DIST, ISEED, D, MODE, COND, DMAX, EI, $ RSIGN, $ UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, $ A, $ LDA, WORK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER DIST, RSIGN, SIM, UPPER @@ -19,227 +350,6 @@ DOUBLE PRECISION A( LDA, * ), D( * ), DS( * ), WORK( * ) * .. * -* Purpose -* ======= -* -* DLATME generates random non-symmetric square matrices with -* specified eigenvalues for testing LAPACK programs. -* -* DLATME operates by applying the following sequence of -* operations: -* -* 1. Set the diagonal to D, where D may be input or -* computed according to MODE, COND, DMAX, and RSIGN -* as described below. -* -* 2. If complex conjugate pairs are desired (MODE=0 and EI(1)='R', -* or MODE=5), certain pairs of adjacent elements of D are -* interpreted as the real and complex parts of a complex -* conjugate pair; A thus becomes block diagonal, with 1x1 -* and 2x2 blocks. -* -* 3. If UPPER='T', the upper triangle of A is set to random values -* out of distribution DIST. -* -* 4. If SIM='T', A is multiplied on the left by a random matrix -* X, whose singular values are specified by DS, MODES, and -* CONDS, and on the right by X inverse. -* -* 5. If KL < N-1, the lower bandwidth is reduced to KL using -* Householder transformations. If KU < N-1, the upper -* bandwidth is reduced to KU. -* -* 6. If ANORM is not negative, the matrix is scaled to have -* maximum-element-norm ANORM. -* -* (Note: since the matrix cannot be reduced beyond Hessenberg form, -* no packing options are available.) -* -* Arguments -* ========= -* -* N (input) INTEGER -* The number of columns (or rows) of A. Not modified. -* -* DIST (input) CHARACTER*1 -* On entry, DIST specifies the type of distribution to be used -* to generate the random eigen-/singular values, and for the -* upper triangle (see UPPER). -* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) -* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) -* 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. They should lie between 0 and 4095 inclusive, -* and ISEED(4) should be odd. The random number generator -* uses a linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to DLATME -* to continue the same random number sequence. -* Changed on exit. -* -* D (input/output) DOUBLE PRECISION array, dimension ( N ) -* This array is used to specify the eigenvalues of A. If -* MODE=0, then D is assumed to contain the eigenvalues (but -* see the description of EI), otherwise they will be -* computed according to MODE, COND, DMAX, and RSIGN and -* placed in D. -* Modified if MODE is nonzero. -* -* MODE (input) INTEGER -* On entry this describes how the eigenvalues are to -* be specified: -* MODE = 0 means use D (with EI) as input -* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND -* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. Each odd-even pair -* of elements will be either used as two real -* eigenvalues or as the real and imaginary part -* of a complex conjugate pair of eigenvalues; -* the choice of which is done is random, with -* 50-50 probability, for each pair. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is between 1 and 4, D has entries ranging -* from 1 to 1/COND, if between -1 and -4, D has entries -* ranging from 1/COND to 1, -* Not modified. -* -* COND (input) DOUBLE PRECISION -* On entry, this is used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* DMAX (input) DOUBLE PRECISION -* If MODE is neither -6, 0 nor 6, the contents of D, as -* computed according to MODE and COND, will be scaled by -* DMAX / max(abs(D(i))). Note that DMAX need not be -* positive: if DMAX is negative (or zero), D will be -* scaled by a negative number (or zero). -* Not modified. -* -* EI (input) CHARACTER*1 array, dimension ( N ) -* If MODE is 0, and EI(1) is not ' ' (space character), -* this array specifies which elements of D (on input) are -* real eigenvalues and which are the real and imaginary parts -* of a complex conjugate pair of eigenvalues. The elements -* of EI may then only have the values 'R' and 'I'. If -* EI(j)='R' and EI(j+1)='I', then the j-th eigenvalue is -* CMPLX( D(j) , D(j+1) ), and the (j+1)-th is the complex -* conjugate thereof. If EI(j)=EI(j+1)='R', then the j-th -* eigenvalue is D(j) (i.e., real). EI(1) may not be 'I', -* nor may two adjacent elements of EI both have the value 'I'. -* If MODE is not 0, then EI is ignored. If MODE is 0 and -* EI(1)=' ', then the eigenvalues will all be real. -* Not modified. -* -* RSIGN (input) CHARACTER*1 -* If MODE is not 0, 6, or -6, and RSIGN='T', then the -* elements of D, as computed according to MODE and COND, will -* be multiplied by a random sign (+1 or -1). If RSIGN='F', -* they will not be. RSIGN may only have the values 'T' or -* 'F'. -* Not modified. -* -* UPPER (input) CHARACTER*1 -* If UPPER='T', then the elements of A above the diagonal -* (and above the 2x2 diagonal blocks, if A has complex -* eigenvalues) will be set to random numbers out of DIST. -* If UPPER='F', they will not. UPPER may only have the -* values 'T' or 'F'. -* Not modified. -* -* SIM (input) CHARACTER*1 -* If SIM='T', then A will be operated on by a "similarity -* transform", i.e., multiplied on the left by a matrix X and -* on the right by X inverse. X = U S V, where U and V are -* random unitary matrices and S is a (diagonal) matrix of -* singular values specified by DS, MODES, and CONDS. If -* SIM='F', then A will not be transformed. -* Not modified. -* -* DS (input/output) DOUBLE PRECISION array, dimension ( N ) -* This array is used to specify the singular values of X, -* in the same way that D specifies the eigenvalues of A. -* If MODE=0, the DS contains the singular values, which -* may not be zero. -* Modified if MODE is nonzero. -* -* MODES (input) INTEGER -* -* CONDS (input) DOUBLE PRECISION -* Same as MODE and COND, but for specifying the diagonal -* of S. MODES=-6 and +6 are not allowed (since they would -* result in randomly ill-conditioned eigenvalues.) -* -* KL (input) INTEGER -* This specifies the lower bandwidth of the matrix. KL=1 -* specifies upper Hessenberg form. If KL is at least N-1, -* then A will have full lower bandwidth. KL must be at -* least 1. -* Not modified. -* -* KU (input) INTEGER -* This specifies the upper bandwidth of the matrix. KU=1 -* specifies lower Hessenberg form. If KU is at least N-1, -* then A will have full upper bandwidth; if KU and KL -* are both at least N-1, then A will be dense. Only one of -* KU and KL may be less than N-1. KU must be at least 1. -* Not modified. -* -* ANORM (input) DOUBLE PRECISION -* If ANORM is not negative, then A will be scaled by a non- -* negative real number to make the maximum-element-norm of A -* to be ANORM. -* Not modified. -* -* A (output) DOUBLE PRECISION array, dimension ( LDA, N ) -* On exit A is the desired test matrix. -* Modified. -* -* LDA (input) INTEGER -* LDA specifies the first dimension of A as declared in the -* calling program. LDA must be at least N. -* Not modified. -* -* WORK (workspace) DOUBLE PRECISION array, dimension ( 3*N ) -* Workspace. -* Modified. -* -* INFO (output) INTEGER -* Error code. On exit, INFO will be set to one of the -* following values: -* 0 => normal return -* -1 => N negative -* -2 => DIST illegal string -* -5 => MODE not in range -6 to 6 -* -6 => COND less than 1.0, and MODE neither -6, 0 nor 6 -* -8 => EI(1) is not ' ' or 'R', EI(j) is not 'R' or 'I', or -* two adjacent elements of EI are 'I'. -* -9 => RSIGN is not 'T' or 'F' -* -10 => UPPER is not 'T' or 'F' -* -11 => SIM is not 'T' or 'F' -* -12 => MODES=0 and DS has a zero singular value. -* -13 => MODES is not in the range -5 to 5. -* -14 => MODES is nonzero and CONDS is less than 1. -* -15 => KL is less than 1. -* -16 => KU is less than 1, or KL and KU are both less than -* N-1. -* -19 => LDA is less than N. -* 1 => Error return from DLATM1 (computing D) -* 2 => Cannot scale to DMAX (max. eigenvalue is 0) -* 3 => Error return from DLATM1 (computing DS) -* 4 => Error return from DLARGE -* 5 => Zero singular value from DLATM1. -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/dlatmr.f b/TESTING/MATGEN/dlatmr.f index 38b38f58..c484e06e 100644 --- a/TESTING/MATGEN/dlatmr.f +++ b/TESTING/MATGEN/dlatmr.f @@ -1,11 +1,485 @@ +*> \brief \b DLATMR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DLATMR( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, +* RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, +* CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, +* PACK, A, LDA, IWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER DIST, GRADE, PACK, PIVTNG, RSIGN, SYM +* INTEGER INFO, KL, KU, LDA, M, MODE, MODEL, MODER, N +* DOUBLE PRECISION ANORM, COND, CONDL, CONDR, DMAX, SPARSE +* .. +* .. Array Arguments .. +* INTEGER IPIVOT( * ), ISEED( 4 ), IWORK( * ) +* DOUBLE PRECISION A( LDA, * ), D( * ), DL( * ), DR( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> DLATMR generates random matrices of various types for testing +*> LAPACK programs. +*> +*> DLATMR operates by applying the following sequence of +*> operations: +*> +*> Generate a matrix A with random entries of distribution DIST +*> which is symmetric if SYM='S', and nonsymmetric +*> if SYM='N'. +*> +*> Set the diagonal to D, where D may be input or +*> computed according to MODE, COND, DMAX and RSIGN +*> as described below. +*> +*> Grade the matrix, if desired, from the left and/or right +*> as specified by GRADE. The inputs DL, MODEL, CONDL, DR, +*> MODER and CONDR also determine the grading as described +*> below. +*> +*> Permute, if desired, the rows and/or columns as specified by +*> PIVTNG and IPIVOT. +*> +*> Set random entries to zero, if desired, to get a random sparse +*> matrix as specified by SPARSE. +*> +*> Make A a band matrix, if desired, by zeroing out the matrix +*> outside a band of lower bandwidth KL and upper bandwidth KU. +*> +*> Scale A, if desired, to have maximum entry ANORM. +*> +*> Pack the matrix if desired. Options specified by PACK are: +*> no packing +*> zero out upper half (if symmetric) +*> zero out lower half (if symmetric) +*> store the upper half columnwise (if symmetric or +*> square upper triangular) +*> store the lower half columnwise (if symmetric or +*> square lower triangular) +*> same as upper half rowwise if symmetric +*> store the lower triangle in banded format (if symmetric) +*> store the upper triangle in banded format (if symmetric) +*> store the entire matrix in banded format +*> +*> Note: If two calls to DLATMR differ only in the PACK parameter, +*> they will generate mathematically equivalent matrices. +*> +*> If two calls to DLATMR both have full bandwidth (KL = M-1 +*> and KU = N-1), and differ only in the PIVTNG and PACK +*> parameters, then the matrices generated will differ only +*> in the order of the rows and/or columns, and otherwise +*> contain the same data. This consistency cannot be and +*> is not maintained with less than full bandwidth. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Number of rows of A. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of columns of A. Not modified. +*> \endverbatim +*> +*> \param[in] DIST +*> \verbatim +*> DIST is CHARACTER*1 +*> On entry, DIST specifies the type of distribution to be used +*> to generate a random matrix . +*> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) +*> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) +*> 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry ISEED specifies the seed of the random number +*> generator. They should lie between 0 and 4095 inclusive, +*> and ISEED(4) should be odd. The random number generator +*> uses a linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to DLATMR +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] SYM +*> \verbatim +*> SYM is CHARACTER*1 +*> If SYM='S' or 'H', generated matrix is symmetric. +*> If SYM='N', generated matrix is nonsymmetric. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (min(M,N)) +*> On entry this array specifies the diagonal entries +*> of the diagonal of A. D may either be specified +*> on entry, or set according to MODE and COND as described +*> below. May be changed on exit if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry describes how D is to be used: +*> MODE = 0 means use D as input +*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND +*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is DOUBLE PRECISION +*> On entry, used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] DMAX +*> \verbatim +*> DMAX is DOUBLE PRECISION +*> If MODE neither -6, 0 nor 6, the diagonal is scaled by +*> DMAX / max(abs(D(i))), so that maximum absolute entry +*> of diagonal is abs(DMAX). If DMAX is negative (or zero), +*> diagonal will be scaled by a negative number (or zero). +*> \endverbatim +*> +*> \param[in] RSIGN +*> \verbatim +*> RSIGN is CHARACTER*1 +*> If MODE neither -6, 0 nor 6, specifies sign of diagonal +*> as follows: +*> 'T' => diagonal entries are multiplied by 1 or -1 +*> with probability .5 +*> 'F' => diagonal unchanged +*> Not modified. +*> \endverbatim +*> +*> \param[in] GRADE +*> \verbatim +*> GRADE is CHARACTER*1 +*> Specifies grading of matrix as follows: +*> 'N' => no grading +*> 'L' => matrix premultiplied by diag( DL ) +*> (only if matrix nonsymmetric) +*> 'R' => matrix postmultiplied by diag( DR ) +*> (only if matrix nonsymmetric) +*> 'B' => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DR ) +*> (only if matrix nonsymmetric) +*> 'S' or 'H' => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DL ) +*> ('S' for symmetric, or 'H' for Hermitian) +*> 'E' => matrix premultiplied by diag( DL ) and +*> postmultiplied by inv( diag( DL ) ) +*> ( 'E' for eigenvalue invariance) +*> (only if matrix nonsymmetric) +*> Note: if GRADE='E', then M must equal N. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] DL +*> \verbatim +*> DL is DOUBLE PRECISION array, dimension (M) +*> If MODEL=0, then on entry this array specifies the diagonal +*> entries of a diagonal matrix used as described under GRADE +*> above. If MODEL is not zero, then DL will be set according +*> to MODEL and CONDL, analogous to the way D is set according +*> to MODE and COND (except there is no DMAX parameter for DL). +*> If GRADE='E', then DL cannot have zero entries. +*> Not referenced if GRADE = 'N' or 'R'. Changed on exit. +*> \endverbatim +*> +*> \param[in] MODEL +*> \verbatim +*> MODEL is INTEGER +*> This specifies how the diagonal array DL is to be computed, +*> just as MODE specifies how D is to be computed. +*> Not modified. +*> \endverbatim +*> +*> \param[in] CONDL +*> \verbatim +*> CONDL is DOUBLE PRECISION +*> When MODEL is not zero, this specifies the condition number +*> of the computed DL. Not modified. +*> \endverbatim +*> +*> \param[in,out] DR +*> \verbatim +*> DR is DOUBLE PRECISION array, dimension (N) +*> If MODER=0, then on entry this array specifies the diagonal +*> entries of a diagonal matrix used as described under GRADE +*> above. If MODER is not zero, then DR will be set according +*> to MODER and CONDR, analogous to the way D is set according +*> to MODE and COND (except there is no DMAX parameter for DR). +*> Not referenced if GRADE = 'N', 'L', 'H', 'S' or 'E'. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] MODER +*> \verbatim +*> MODER is INTEGER +*> This specifies how the diagonal array DR is to be computed, +*> just as MODE specifies how D is to be computed. +*> Not modified. +*> \endverbatim +*> +*> \param[in] CONDR +*> \verbatim +*> CONDR is DOUBLE PRECISION +*> When MODER is not zero, this specifies the condition number +*> of the computed DR. Not modified. +*> \endverbatim +*> +*> \param[in] PIVTNG +*> \verbatim +*> PIVTNG is CHARACTER*1 +*> On entry specifies pivoting permutations as follows: +*> 'N' or ' ' => none. +*> 'L' => left or row pivoting (matrix must be nonsymmetric). +*> 'R' => right or column pivoting (matrix must be +*> nonsymmetric). +*> 'B' or 'F' => both or full pivoting, i.e., on both sides. +*> In this case, M must equal N +*> \endverbatim +*> \verbatim +*> If two calls to DLATMR both have full bandwidth (KL = M-1 +*> and KU = N-1), and differ only in the PIVTNG and PACK +*> parameters, then the matrices generated will differ only +*> in the order of the rows and/or columns, and otherwise +*> contain the same data. This consistency cannot be +*> maintained with less than full bandwidth. +*> \endverbatim +*> +*> \param[in] IPIVOT +*> \verbatim +*> IPIVOT is INTEGER array, dimension (N or M) +*> This array specifies the permutation used. After the +*> basic matrix is generated, the rows, columns, or both +*> are permuted. If, say, row pivoting is selected, DLATMR +*> starts with the *last* row and interchanges the M-th and +*> IPIVOT(M)-th rows, then moves to the next-to-last row, +*> interchanging the (M-1)-th and the IPIVOT(M-1)-th rows, +*> and so on. In terms of "2-cycles", the permutation is +*> (1 IPIVOT(1)) (2 IPIVOT(2)) ... (M IPIVOT(M)) +*> where the rightmost cycle is applied first. This is the +*> *inverse* of the effect of pivoting in LINPACK. The idea +*> is that factoring (with pivoting) an identity matrix +*> which has been inverse-pivoted in this way should +*> result in a pivot vector identical to IPIVOT. +*> Not referenced if PIVTNG = 'N'. Not modified. +*> \endverbatim +*> +*> \param[in] SPARSE +*> \verbatim +*> SPARSE is DOUBLE PRECISION +*> On entry specifies the sparsity of the matrix if a sparse +*> matrix is to be generated. SPARSE should lie between +*> 0 and 1. To generate a sparse matrix, for each matrix entry +*> a uniform ( 0, 1 ) random number x is generated and +*> compared to SPARSE; if x is larger the matrix entry +*> is unchanged and if x is smaller the entry is set +*> to zero. Thus on the average a fraction SPARSE of the +*> entries will be set to zero. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> On entry specifies the lower bandwidth of the matrix. For +*> example, KL=0 implies upper triangular, KL=1 implies upper +*> Hessenberg, and KL at least M-1 implies the matrix is not +*> banded. Must equal KU if matrix is symmetric. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> On entry specifies the upper bandwidth of the matrix. For +*> example, KU=0 implies lower triangular, KU=1 implies lower +*> Hessenberg, and KU at least N-1 implies the matrix is not +*> banded. Must equal KL if matrix is symmetric. +*> Not modified. +*> \endverbatim +*> +*> \param[in] ANORM +*> \verbatim +*> ANORM is DOUBLE PRECISION +*> On entry specifies maximum entry of output matrix +*> (output matrix will by multiplied by a constant so that +*> its largest absolute entry equal ANORM) +*> if ANORM is nonnegative. If ANORM is negative no scaling +*> is done. Not modified. +*> \endverbatim +*> +*> \param[in] PACK +*> \verbatim +*> PACK is CHARACTER*1 +*> On entry specifies packing of matrix as follows: +*> 'N' => no packing +*> 'U' => zero out all subdiagonal entries (if symmetric) +*> 'L' => zero out all superdiagonal entries (if symmetric) +*> 'C' => store the upper triangle columnwise +*> (only if matrix symmetric or square upper triangular) +*> 'R' => store the lower triangle columnwise +*> (only if matrix symmetric or square lower triangular) +*> (same as upper half rowwise if symmetric) +*> 'B' => store the lower triangle in band storage scheme +*> (only if matrix symmetric) +*> 'Q' => store the upper triangle in band storage scheme +*> (only if matrix symmetric) +*> 'Z' => store the entire matrix in band storage scheme +*> (pivoting can be provided for by using this +*> option to store A in the trailing rows of +*> the allocated storage) +*> \endverbatim +*> \verbatim +*> Using these options, the various LAPACK packed and banded +*> storage schemes can be obtained: +*> GB - use 'Z' +*> PB, SB or TB - use 'B' or 'Q' +*> PP, SP or TP - use 'C' or 'R' +*> \endverbatim +*> \verbatim +*> If two calls to DLATMR differ only in the PACK parameter, +*> they will generate mathematically equivalent matrices. +*> Not modified. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> On exit A is the desired test matrix. Only those +*> entries of A which are significant on output +*> will be referenced (even if A is in packed or band +*> storage format). The 'unoccupied corners' of A in +*> band format will be zeroed out. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> on entry LDA specifies the first dimension of A as +*> declared in the calling program. +*> If PACK='N', 'U' or 'L', LDA must be at least max ( 1, M ). +*> If PACK='C' or 'R', LDA must be at least 1. +*> If PACK='B', or 'Q', LDA must be MIN ( KU+1, N ) +*> If PACK='Z', LDA must be at least KUU+KLL+1, where +*> KUU = MIN ( KU, N-1 ) and KLL = MIN ( KL, N-1 ) +*> Not modified. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension ( N or M) +*> Workspace. Not referenced if PIVTNG = 'N'. Changed on exit. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error parameter on exit: +*> 0 => normal return +*> -1 => M negative or unequal to N and SYM='S' or 'H' +*> -2 => N negative +*> -3 => DIST illegal string +*> -5 => SYM illegal string +*> -7 => MODE not in range -6 to 6 +*> -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 +*> -10 => MODE neither -6, 0 nor 6 and RSIGN illegal string +*> -11 => GRADE illegal string, or GRADE='E' and +*> M not equal to N, or GRADE='L', 'R', 'B' or 'E' and +*> SYM = 'S' or 'H' +*> -12 => GRADE = 'E' and DL contains zero +*> -13 => MODEL not in range -6 to 6 and GRADE= 'L', 'B', 'H', +*> 'S' or 'E' +*> -14 => CONDL less than 1.0, GRADE='L', 'B', 'H', 'S' or 'E', +*> and MODEL neither -6, 0 nor 6 +*> -16 => MODER not in range -6 to 6 and GRADE= 'R' or 'B' +*> -17 => CONDR less than 1.0, GRADE='R' or 'B', and +*> MODER neither -6, 0 nor 6 +*> -18 => PIVTNG illegal string, or PIVTNG='B' or 'F' and +*> M not equal to N, or PIVTNG='L' or 'R' and SYM='S' +*> or 'H' +*> -19 => IPIVOT contains out of range number and +*> PIVTNG not equal to 'N' +*> -20 => KL negative +*> -21 => KU negative, or SYM='S' or 'H' and KU not equal to KL +*> -22 => SPARSE not in range 0. to 1. +*> -24 => PACK illegal string, or PACK='U', 'L', 'B' or 'Q' +*> and SYM='N', or PACK='C' and SYM='N' and either KL +*> not equal to 0 or N not equal to M, or PACK='R' and +*> SYM='N', and either KU not equal to 0 or N not equal +*> to M +*> -26 => LDA too small +*> 1 => Error return from DLATM1 (computing D) +*> 2 => Cannot scale diagonal to DMAX (max. entry is 0) +*> 3 => Error return from DLATM1 (computing DL) +*> 4 => Error return from DLATM1 (computing DR) +*> 5 => ANORM is positive, but matrix constructed prior to +*> attempting to scale it to have norm ANORM, is zero +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_matgen +* +* ===================================================================== SUBROUTINE DLATMR( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, $ RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, $ CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, $ PACK, A, LDA, IWORK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER DIST, GRADE, PACK, PIVTNG, RSIGN, SYM @@ -17,348 +491,6 @@ DOUBLE PRECISION A( LDA, * ), D( * ), DL( * ), DR( * ) * .. * -* Purpose -* ======= -* -* DLATMR generates random matrices of various types for testing -* LAPACK programs. -* -* DLATMR operates by applying the following sequence of -* operations: -* -* Generate a matrix A with random entries of distribution DIST -* which is symmetric if SYM='S', and nonsymmetric -* if SYM='N'. -* -* Set the diagonal to D, where D may be input or -* computed according to MODE, COND, DMAX and RSIGN -* as described below. -* -* Grade the matrix, if desired, from the left and/or right -* as specified by GRADE. The inputs DL, MODEL, CONDL, DR, -* MODER and CONDR also determine the grading as described -* below. -* -* Permute, if desired, the rows and/or columns as specified by -* PIVTNG and IPIVOT. -* -* Set random entries to zero, if desired, to get a random sparse -* matrix as specified by SPARSE. -* -* Make A a band matrix, if desired, by zeroing out the matrix -* outside a band of lower bandwidth KL and upper bandwidth KU. -* -* Scale A, if desired, to have maximum entry ANORM. -* -* Pack the matrix if desired. Options specified by PACK are: -* no packing -* zero out upper half (if symmetric) -* zero out lower half (if symmetric) -* store the upper half columnwise (if symmetric or -* square upper triangular) -* store the lower half columnwise (if symmetric or -* square lower triangular) -* same as upper half rowwise if symmetric -* store the lower triangle in banded format (if symmetric) -* store the upper triangle in banded format (if symmetric) -* store the entire matrix in banded format -* -* Note: If two calls to DLATMR differ only in the PACK parameter, -* they will generate mathematically equivalent matrices. -* -* If two calls to DLATMR both have full bandwidth (KL = M-1 -* and KU = N-1), and differ only in the PIVTNG and PACK -* parameters, then the matrices generated will differ only -* in the order of the rows and/or columns, and otherwise -* contain the same data. This consistency cannot be and -* is not maintained with less than full bandwidth. -* -* Arguments -* ========= -* -* M (input) INTEGER -* Number of rows of A. Not modified. -* -* N (input) INTEGER -* Number of columns of A. Not modified. -* -* DIST (input) CHARACTER*1 -* On entry, DIST specifies the type of distribution to be used -* to generate a random matrix . -* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) -* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) -* 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension (4) -* On entry ISEED specifies the seed of the random number -* generator. They should lie between 0 and 4095 inclusive, -* and ISEED(4) should be odd. The random number generator -* uses a linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to DLATMR -* to continue the same random number sequence. -* Changed on exit. -* -* SYM (input) CHARACTER*1 -* If SYM='S' or 'H', generated matrix is symmetric. -* If SYM='N', generated matrix is nonsymmetric. -* Not modified. -* -* D (input/output) DOUBLE PRECISION array, dimension (min(M,N)) -* On entry this array specifies the diagonal entries -* of the diagonal of A. D may either be specified -* on entry, or set according to MODE and COND as described -* below. May be changed on exit if MODE is nonzero. -* -* MODE (input) INTEGER -* On entry describes how D is to be used: -* MODE = 0 means use D as input -* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND -* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* Not modified. -* -* COND (input) DOUBLE PRECISION -* On entry, used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* DMAX (input) DOUBLE PRECISION -* If MODE neither -6, 0 nor 6, the diagonal is scaled by -* DMAX / max(abs(D(i))), so that maximum absolute entry -* of diagonal is abs(DMAX). If DMAX is negative (or zero), -* diagonal will be scaled by a negative number (or zero). -* -* RSIGN (input) CHARACTER*1 -* If MODE neither -6, 0 nor 6, specifies sign of diagonal -* as follows: -* 'T' => diagonal entries are multiplied by 1 or -1 -* with probability .5 -* 'F' => diagonal unchanged -* Not modified. -* -* GRADE (input) CHARACTER*1 -* Specifies grading of matrix as follows: -* 'N' => no grading -* 'L' => matrix premultiplied by diag( DL ) -* (only if matrix nonsymmetric) -* 'R' => matrix postmultiplied by diag( DR ) -* (only if matrix nonsymmetric) -* 'B' => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DR ) -* (only if matrix nonsymmetric) -* 'S' or 'H' => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DL ) -* ('S' for symmetric, or 'H' for Hermitian) -* 'E' => matrix premultiplied by diag( DL ) and -* postmultiplied by inv( diag( DL ) ) -* ( 'E' for eigenvalue invariance) -* (only if matrix nonsymmetric) -* Note: if GRADE='E', then M must equal N. -* Not modified. -* -* DL (input/output) DOUBLE PRECISION array, dimension (M) -* If MODEL=0, then on entry this array specifies the diagonal -* entries of a diagonal matrix used as described under GRADE -* above. If MODEL is not zero, then DL will be set according -* to MODEL and CONDL, analogous to the way D is set according -* to MODE and COND (except there is no DMAX parameter for DL). -* If GRADE='E', then DL cannot have zero entries. -* Not referenced if GRADE = 'N' or 'R'. Changed on exit. -* -* MODEL (input) INTEGER -* This specifies how the diagonal array DL is to be computed, -* just as MODE specifies how D is to be computed. -* Not modified. -* -* CONDL (input) DOUBLE PRECISION -* When MODEL is not zero, this specifies the condition number -* of the computed DL. Not modified. -* -* DR (input/output) DOUBLE PRECISION array, dimension (N) -* If MODER=0, then on entry this array specifies the diagonal -* entries of a diagonal matrix used as described under GRADE -* above. If MODER is not zero, then DR will be set according -* to MODER and CONDR, analogous to the way D is set according -* to MODE and COND (except there is no DMAX parameter for DR). -* Not referenced if GRADE = 'N', 'L', 'H', 'S' or 'E'. -* Changed on exit. -* -* MODER (input) INTEGER -* This specifies how the diagonal array DR is to be computed, -* just as MODE specifies how D is to be computed. -* Not modified. -* -* CONDR (input) DOUBLE PRECISION -* When MODER is not zero, this specifies the condition number -* of the computed DR. Not modified. -* -* PIVTNG (input) CHARACTER*1 -* On entry specifies pivoting permutations as follows: -* 'N' or ' ' => none. -* 'L' => left or row pivoting (matrix must be nonsymmetric). -* 'R' => right or column pivoting (matrix must be -* nonsymmetric). -* 'B' or 'F' => both or full pivoting, i.e., on both sides. -* In this case, M must equal N -* -* If two calls to DLATMR both have full bandwidth (KL = M-1 -* and KU = N-1), and differ only in the PIVTNG and PACK -* parameters, then the matrices generated will differ only -* in the order of the rows and/or columns, and otherwise -* contain the same data. This consistency cannot be -* maintained with less than full bandwidth. -* -* IPIVOT (input) INTEGER array, dimension (N or M) -* This array specifies the permutation used. After the -* basic matrix is generated, the rows, columns, or both -* are permuted. If, say, row pivoting is selected, DLATMR -* starts with the *last* row and interchanges the M-th and -* IPIVOT(M)-th rows, then moves to the next-to-last row, -* interchanging the (M-1)-th and the IPIVOT(M-1)-th rows, -* and so on. In terms of "2-cycles", the permutation is -* (1 IPIVOT(1)) (2 IPIVOT(2)) ... (M IPIVOT(M)) -* where the rightmost cycle is applied first. This is the -* *inverse* of the effect of pivoting in LINPACK. The idea -* is that factoring (with pivoting) an identity matrix -* which has been inverse-pivoted in this way should -* result in a pivot vector identical to IPIVOT. -* Not referenced if PIVTNG = 'N'. Not modified. -* -* SPARSE (input) DOUBLE PRECISION -* On entry specifies the sparsity of the matrix if a sparse -* matrix is to be generated. SPARSE should lie between -* 0 and 1. To generate a sparse matrix, for each matrix entry -* a uniform ( 0, 1 ) random number x is generated and -* compared to SPARSE; if x is larger the matrix entry -* is unchanged and if x is smaller the entry is set -* to zero. Thus on the average a fraction SPARSE of the -* entries will be set to zero. -* Not modified. -* -* KL (input) INTEGER -* On entry specifies the lower bandwidth of the matrix. For -* example, KL=0 implies upper triangular, KL=1 implies upper -* Hessenberg, and KL at least M-1 implies the matrix is not -* banded. Must equal KU if matrix is symmetric. -* Not modified. -* -* KU (input) INTEGER -* On entry specifies the upper bandwidth of the matrix. For -* example, KU=0 implies lower triangular, KU=1 implies lower -* Hessenberg, and KU at least N-1 implies the matrix is not -* banded. Must equal KL if matrix is symmetric. -* Not modified. -* -* ANORM (input) DOUBLE PRECISION -* On entry specifies maximum entry of output matrix -* (output matrix will by multiplied by a constant so that -* its largest absolute entry equal ANORM) -* if ANORM is nonnegative. If ANORM is negative no scaling -* is done. Not modified. -* -* PACK (input) CHARACTER*1 -* On entry specifies packing of matrix as follows: -* 'N' => no packing -* 'U' => zero out all subdiagonal entries (if symmetric) -* 'L' => zero out all superdiagonal entries (if symmetric) -* 'C' => store the upper triangle columnwise -* (only if matrix symmetric or square upper triangular) -* 'R' => store the lower triangle columnwise -* (only if matrix symmetric or square lower triangular) -* (same as upper half rowwise if symmetric) -* 'B' => store the lower triangle in band storage scheme -* (only if matrix symmetric) -* 'Q' => store the upper triangle in band storage scheme -* (only if matrix symmetric) -* 'Z' => store the entire matrix in band storage scheme -* (pivoting can be provided for by using this -* option to store A in the trailing rows of -* the allocated storage) -* -* Using these options, the various LAPACK packed and banded -* storage schemes can be obtained: -* GB - use 'Z' -* PB, SB or TB - use 'B' or 'Q' -* PP, SP or TP - use 'C' or 'R' -* -* If two calls to DLATMR differ only in the PACK parameter, -* they will generate mathematically equivalent matrices. -* Not modified. -* -* A (output) DOUBLE PRECISION array, dimension (LDA,N) -* On exit A is the desired test matrix. Only those -* entries of A which are significant on output -* will be referenced (even if A is in packed or band -* storage format). The 'unoccupied corners' of A in -* band format will be zeroed out. -* -* LDA (input) INTEGER -* on entry LDA specifies the first dimension of A as -* declared in the calling program. -* If PACK='N', 'U' or 'L', LDA must be at least max ( 1, M ). -* If PACK='C' or 'R', LDA must be at least 1. -* If PACK='B', or 'Q', LDA must be MIN ( KU+1, N ) -* If PACK='Z', LDA must be at least KUU+KLL+1, where -* KUU = MIN ( KU, N-1 ) and KLL = MIN ( KL, N-1 ) -* Not modified. -* -* IWORK (workspace) INTEGER array, dimension ( N or M) -* Workspace. Not referenced if PIVTNG = 'N'. Changed on exit. -* -* INFO (output) INTEGER -* Error parameter on exit: -* 0 => normal return -* -1 => M negative or unequal to N and SYM='S' or 'H' -* -2 => N negative -* -3 => DIST illegal string -* -5 => SYM illegal string -* -7 => MODE not in range -6 to 6 -* -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 -* -10 => MODE neither -6, 0 nor 6 and RSIGN illegal string -* -11 => GRADE illegal string, or GRADE='E' and -* M not equal to N, or GRADE='L', 'R', 'B' or 'E' and -* SYM = 'S' or 'H' -* -12 => GRADE = 'E' and DL contains zero -* -13 => MODEL not in range -6 to 6 and GRADE= 'L', 'B', 'H', -* 'S' or 'E' -* -14 => CONDL less than 1.0, GRADE='L', 'B', 'H', 'S' or 'E', -* and MODEL neither -6, 0 nor 6 -* -16 => MODER not in range -6 to 6 and GRADE= 'R' or 'B' -* -17 => CONDR less than 1.0, GRADE='R' or 'B', and -* MODER neither -6, 0 nor 6 -* -18 => PIVTNG illegal string, or PIVTNG='B' or 'F' and -* M not equal to N, or PIVTNG='L' or 'R' and SYM='S' -* or 'H' -* -19 => IPIVOT contains out of range number and -* PIVTNG not equal to 'N' -* -20 => KL negative -* -21 => KU negative, or SYM='S' or 'H' and KU not equal to KL -* -22 => SPARSE not in range 0. to 1. -* -24 => PACK illegal string, or PACK='U', 'L', 'B' or 'Q' -* and SYM='N', or PACK='C' and SYM='N' and either KL -* not equal to 0 or N not equal to M, or PACK='R' and -* SYM='N', and either KU not equal to 0 or N not equal -* to M -* -26 => LDA too small -* 1 => Error return from DLATM1 (computing D) -* 2 => Cannot scale diagonal to DMAX (max. entry is 0) -* 3 => Error return from DLATM1 (computing DL) -* 4 => Error return from DLATM1 (computing DR) -* 5 => ANORM is positive, but matrix constructed prior to -* attempting to scale it to have norm ANORM, is zero -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/dlatms.f b/TESTING/MATGEN/dlatms.f index 9d36d677..a10f5fa7 100644 --- a/TESTING/MATGEN/dlatms.f +++ b/TESTING/MATGEN/dlatms.f @@ -1,9 +1,334 @@ +*> \brief \b DLATMS +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, +* KL, KU, PACK, A, LDA, WORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER DIST, PACK, SYM +* INTEGER INFO, KL, KU, LDA, M, MODE, N +* DOUBLE PRECISION COND, DMAX +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> DLATMS generates random matrices with specified singular values +*> (or symmetric/hermitian with specified eigenvalues) +*> for testing LAPACK programs. +*> +*> DLATMS operates by applying the following sequence of +*> operations: +*> +*> Set the diagonal to D, where D may be input or +*> computed according to MODE, COND, DMAX, and SYM +*> as described below. +*> +*> Generate a matrix with the appropriate band structure, by one +*> of two methods: +*> +*> Method A: +*> Generate a dense M x N matrix by multiplying D on the left +*> and the right by random unitary matrices, then: +*> +*> Reduce the bandwidth according to KL and KU, using +*> Householder transformations. +*> +*> Method B: +*> Convert the bandwidth-0 (i.e., diagonal) matrix to a +*> bandwidth-1 matrix using Givens rotations, "chasing" +*> out-of-band elements back, much as in QR; then +*> convert the bandwidth-1 to a bandwidth-2 matrix, etc. +*> Note that for reasonably small bandwidths (relative to +*> M and N) this requires less storage, as a dense matrix +*> is not generated. Also, for symmetric matrices, only +*> one triangle is generated. +*> +*> Method A is chosen if the bandwidth is a large fraction of the +*> order of the matrix, and LDA is at least M (so a dense +*> matrix can be stored.) Method B is chosen if the bandwidth +*> is small (< 1/2 N for symmetric, < .3 N+M for +*> non-symmetric), or LDA is less than M and not less than the +*> bandwidth. +*> +*> Pack the matrix if desired. Options specified by PACK are: +*> no packing +*> zero out upper half (if symmetric) +*> zero out lower half (if symmetric) +*> store the upper half columnwise (if symmetric or upper +*> triangular) +*> store the lower half columnwise (if symmetric or lower +*> triangular) +*> store the lower triangle in banded format (if symmetric +*> or lower triangular) +*> store the upper triangle in banded format (if symmetric +*> or upper triangular) +*> store the entire matrix in banded format +*> If Method B is chosen, and band format is specified, then the +*> matrix will be generated in the band format, so no repacking +*> will be necessary. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of A. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of A. Not modified. +*> \endverbatim +*> +*> \param[in] DIST +*> \verbatim +*> DIST is CHARACTER*1 +*> On entry, DIST specifies the type of distribution to be used +*> to generate the random eigen-/singular values. +*> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) +*> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) +*> 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. They should lie between 0 and 4095 inclusive, +*> and ISEED(4) should be odd. The random number generator +*> uses a linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to DLATMS +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] SYM +*> \verbatim +*> SYM is CHARACTER*1 +*> If SYM='S' or 'H', the generated matrix is symmetric, with +*> eigenvalues specified by D, COND, MODE, and DMAX; they +*> may be positive, negative, or zero. +*> If SYM='P', the generated matrix is symmetric, with +*> eigenvalues (= singular values) specified by D, COND, +*> MODE, and DMAX; they will not be negative. +*> If SYM='N', the generated matrix is nonsymmetric, with +*> singular values specified by D, COND, MODE, and DMAX; +*> they will not be negative. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension ( MIN( M , N ) ) +*> This array is used to specify the singular values or +*> eigenvalues of A (see SYM, above.) If MODE=0, then D is +*> assumed to contain the singular/eigenvalues, otherwise +*> they will be computed according to MODE, COND, and DMAX, +*> and placed in D. +*> Modified if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry this describes how the singular/eigenvalues are to +*> be specified: +*> MODE = 0 means use D as input +*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND +*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> If SYM='S' or 'H', and MODE is neither 0, 6, nor -6, then +*> the elements of D will also be multiplied by a random +*> sign (i.e., +1 or -1.) +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is DOUBLE PRECISION +*> On entry, this is used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] DMAX +*> \verbatim +*> DMAX is DOUBLE PRECISION +*> If MODE is neither -6, 0 nor 6, the contents of D, as +*> computed according to MODE and COND, will be scaled by +*> DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or +*> singular value (which is to say the norm) will be abs(DMAX). +*> Note that DMAX need not be positive: if DMAX is negative +*> (or zero), D will be scaled by a negative number (or zero). +*> Not modified. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> This specifies the lower bandwidth of the matrix. For +*> example, KL=0 implies upper triangular, KL=1 implies upper +*> Hessenberg, and KL being at least M-1 means that the matrix +*> has full lower bandwidth. KL must equal KU if the matrix +*> is symmetric. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> This specifies the upper bandwidth of the matrix. For +*> example, KU=0 implies lower triangular, KU=1 implies lower +*> Hessenberg, and KU being at least N-1 means that the matrix +*> has full upper bandwidth. KL must equal KU if the matrix +*> is symmetric. +*> Not modified. +*> \endverbatim +*> +*> \param[in] PACK +*> \verbatim +*> PACK is CHARACTER*1 +*> This specifies packing of matrix as follows: +*> 'N' => no packing +*> 'U' => zero out all subdiagonal entries (if symmetric) +*> 'L' => zero out all superdiagonal entries (if symmetric) +*> 'C' => store the upper triangle columnwise +*> (only if the matrix is symmetric or upper triangular) +*> 'R' => store the lower triangle columnwise +*> (only if the matrix is symmetric or lower triangular) +*> 'B' => store the lower triangle in band storage scheme +*> (only if matrix symmetric or lower triangular) +*> 'Q' => store the upper triangle in band storage scheme +*> (only if matrix symmetric or upper triangular) +*> 'Z' => store the entire matrix in band storage scheme +*> (pivoting can be provided for by using this +*> option to store A in the trailing rows of +*> the allocated storage) +*> \endverbatim +*> \verbatim +*> Using these options, the various LAPACK packed and banded +*> storage schemes can be obtained: +*> GB - use 'Z' +*> PB, SB or TB - use 'B' or 'Q' +*> PP, SP or TP - use 'C' or 'R' +*> \endverbatim +*> \verbatim +*> If two calls to DLATMS differ only in the PACK parameter, +*> they will generate mathematically equivalent matrices. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension ( LDA, N ) +*> On exit A is the desired test matrix. A is first generated +*> in full (unpacked) form, and then packed, if so specified +*> by PACK. Thus, the first M elements of the first N +*> columns will always be modified. If PACK specifies a +*> packed or banded storage scheme, all LDA elements of the +*> first N columns will be modified; the elements of the +*> array which do not correspond to elements of the generated +*> matrix are set to zero. +*> Modified. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> LDA specifies the first dimension of A as declared in the +*> calling program. If PACK='N', 'U', 'L', 'C', or 'R', then +*> LDA must be at least M. If PACK='B' or 'Q', then LDA must +*> be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). +*> If PACK='Z', LDA must be large enough to hold the packed +*> array: MIN( KU, N-1) + MIN( KL, M-1) + 1. +*> Not modified. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension ( 3*MAX( N , M ) ) +*> Workspace. +*> Modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error code. On exit, INFO will be set to one of the +*> following values: +*> 0 => normal return +*> -1 => M negative or unequal to N and SYM='S', 'H', or 'P' +*> -2 => N negative +*> -3 => DIST illegal string +*> -5 => SYM illegal string +*> -7 => MODE not in range -6 to 6 +*> -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 +*> -10 => KL negative +*> -11 => KU negative, or SYM='S' or 'H' and KU not equal to KL +*> -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; +*> or PACK='C' or 'Q' and SYM='N' and KL is not zero; +*> or PACK='R' or 'B' and SYM='N' and KU is not zero; +*> or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not +*> N. +*> -14 => LDA is less than M, or PACK='Z' and LDA is less than +*> MIN(KU,N-1) + MIN(KL,M-1) + 1. +*> 1 => Error return from DLATM1 +*> 2 => Cannot scale to DMAX (max. sing. value is 0) +*> 3 => Error return from DLAGGE or SLAGSY +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_matgen +* +* ===================================================================== SUBROUTINE DLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, $ KL, KU, PACK, A, LDA, WORK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER DIST, PACK, SYM @@ -15,238 +340,6 @@ DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * ) * .. * -* Purpose -* ======= -* -* DLATMS generates random matrices with specified singular values -* (or symmetric/hermitian with specified eigenvalues) -* for testing LAPACK programs. -* -* DLATMS operates by applying the following sequence of -* operations: -* -* Set the diagonal to D, where D may be input or -* computed according to MODE, COND, DMAX, and SYM -* as described below. -* -* Generate a matrix with the appropriate band structure, by one -* of two methods: -* -* Method A: -* Generate a dense M x N matrix by multiplying D on the left -* and the right by random unitary matrices, then: -* -* Reduce the bandwidth according to KL and KU, using -* Householder transformations. -* -* Method B: -* Convert the bandwidth-0 (i.e., diagonal) matrix to a -* bandwidth-1 matrix using Givens rotations, "chasing" -* out-of-band elements back, much as in QR; then -* convert the bandwidth-1 to a bandwidth-2 matrix, etc. -* Note that for reasonably small bandwidths (relative to -* M and N) this requires less storage, as a dense matrix -* is not generated. Also, for symmetric matrices, only -* one triangle is generated. -* -* Method A is chosen if the bandwidth is a large fraction of the -* order of the matrix, and LDA is at least M (so a dense -* matrix can be stored.) Method B is chosen if the bandwidth -* is small (< 1/2 N for symmetric, < .3 N+M for -* non-symmetric), or LDA is less than M and not less than the -* bandwidth. -* -* Pack the matrix if desired. Options specified by PACK are: -* no packing -* zero out upper half (if symmetric) -* zero out lower half (if symmetric) -* store the upper half columnwise (if symmetric or upper -* triangular) -* store the lower half columnwise (if symmetric or lower -* triangular) -* store the lower triangle in banded format (if symmetric -* or lower triangular) -* store the upper triangle in banded format (if symmetric -* or upper triangular) -* store the entire matrix in banded format -* If Method B is chosen, and band format is specified, then the -* matrix will be generated in the band format, so no repacking -* will be necessary. -* -* Arguments -* ========= -* -* M (input) INTEGER -* The number of rows of A. Not modified. -* -* N (input) INTEGER -* The number of columns of A. Not modified. -* -* DIST (input) CHARACTER*1 -* On entry, DIST specifies the type of distribution to be used -* to generate the random eigen-/singular values. -* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) -* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) -* 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. They should lie between 0 and 4095 inclusive, -* and ISEED(4) should be odd. The random number generator -* uses a linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to DLATMS -* to continue the same random number sequence. -* Changed on exit. -* -* SYM (input) CHARACTER*1 -* If SYM='S' or 'H', the generated matrix is symmetric, with -* eigenvalues specified by D, COND, MODE, and DMAX; they -* may be positive, negative, or zero. -* If SYM='P', the generated matrix is symmetric, with -* eigenvalues (= singular values) specified by D, COND, -* MODE, and DMAX; they will not be negative. -* If SYM='N', the generated matrix is nonsymmetric, with -* singular values specified by D, COND, MODE, and DMAX; -* they will not be negative. -* Not modified. -* -* D (input/output) DOUBLE PRECISION array, dimension ( MIN( M , N ) ) -* This array is used to specify the singular values or -* eigenvalues of A (see SYM, above.) If MODE=0, then D is -* assumed to contain the singular/eigenvalues, otherwise -* they will be computed according to MODE, COND, and DMAX, -* and placed in D. -* Modified if MODE is nonzero. -* -* MODE (input) INTEGER -* On entry this describes how the singular/eigenvalues are to -* be specified: -* MODE = 0 means use D as input -* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND -* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* If SYM='S' or 'H', and MODE is neither 0, 6, nor -6, then -* the elements of D will also be multiplied by a random -* sign (i.e., +1 or -1.) -* Not modified. -* -* COND (input) DOUBLE PRECISION -* On entry, this is used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* DMAX (input) DOUBLE PRECISION -* If MODE is neither -6, 0 nor 6, the contents of D, as -* computed according to MODE and COND, will be scaled by -* DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or -* singular value (which is to say the norm) will be abs(DMAX). -* Note that DMAX need not be positive: if DMAX is negative -* (or zero), D will be scaled by a negative number (or zero). -* Not modified. -* -* KL (input) INTEGER -* This specifies the lower bandwidth of the matrix. For -* example, KL=0 implies upper triangular, KL=1 implies upper -* Hessenberg, and KL being at least M-1 means that the matrix -* has full lower bandwidth. KL must equal KU if the matrix -* is symmetric. -* Not modified. -* -* KU (input) INTEGER -* This specifies the upper bandwidth of the matrix. For -* example, KU=0 implies lower triangular, KU=1 implies lower -* Hessenberg, and KU being at least N-1 means that the matrix -* has full upper bandwidth. KL must equal KU if the matrix -* is symmetric. -* Not modified. -* -* PACK (input) CHARACTER*1 -* This specifies packing of matrix as follows: -* 'N' => no packing -* 'U' => zero out all subdiagonal entries (if symmetric) -* 'L' => zero out all superdiagonal entries (if symmetric) -* 'C' => store the upper triangle columnwise -* (only if the matrix is symmetric or upper triangular) -* 'R' => store the lower triangle columnwise -* (only if the matrix is symmetric or lower triangular) -* 'B' => store the lower triangle in band storage scheme -* (only if matrix symmetric or lower triangular) -* 'Q' => store the upper triangle in band storage scheme -* (only if matrix symmetric or upper triangular) -* 'Z' => store the entire matrix in band storage scheme -* (pivoting can be provided for by using this -* option to store A in the trailing rows of -* the allocated storage) -* -* Using these options, the various LAPACK packed and banded -* storage schemes can be obtained: -* GB - use 'Z' -* PB, SB or TB - use 'B' or 'Q' -* PP, SP or TP - use 'C' or 'R' -* -* If two calls to DLATMS differ only in the PACK parameter, -* they will generate mathematically equivalent matrices. -* Not modified. -* -* A (input/output) DOUBLE PRECISION array, dimension ( LDA, N ) -* On exit A is the desired test matrix. A is first generated -* in full (unpacked) form, and then packed, if so specified -* by PACK. Thus, the first M elements of the first N -* columns will always be modified. If PACK specifies a -* packed or banded storage scheme, all LDA elements of the -* first N columns will be modified; the elements of the -* array which do not correspond to elements of the generated -* matrix are set to zero. -* Modified. -* -* LDA (input) INTEGER -* LDA specifies the first dimension of A as declared in the -* calling program. If PACK='N', 'U', 'L', 'C', or 'R', then -* LDA must be at least M. If PACK='B' or 'Q', then LDA must -* be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). -* If PACK='Z', LDA must be large enough to hold the packed -* array: MIN( KU, N-1) + MIN( KL, M-1) + 1. -* Not modified. -* -* WORK (workspace) DOUBLE PRECISION array, dimension ( 3*MAX( N , M ) ) -* Workspace. -* Modified. -* -* INFO (output) INTEGER -* Error code. On exit, INFO will be set to one of the -* following values: -* 0 => normal return -* -1 => M negative or unequal to N and SYM='S', 'H', or 'P' -* -2 => N negative -* -3 => DIST illegal string -* -5 => SYM illegal string -* -7 => MODE not in range -6 to 6 -* -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 -* -10 => KL negative -* -11 => KU negative, or SYM='S' or 'H' and KU not equal to KL -* -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; -* or PACK='C' or 'Q' and SYM='N' and KL is not zero; -* or PACK='R' or 'B' and SYM='N' and KU is not zero; -* or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not -* N. -* -14 => LDA is less than M, or PACK='Z' and LDA is less than -* MIN(KU,N-1) + MIN(KL,M-1) + 1. -* 1 => Error return from DLATM1 -* 2 => Cannot scale to DMAX (max. sing. value is 0) -* 3 => Error return from DLAGGE or SLAGSY -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/dlatmt.f b/TESTING/MATGEN/dlatmt.f index 90a0001d..04b80dfb 100644 --- a/TESTING/MATGEN/dlatmt.f +++ b/TESTING/MATGEN/dlatmt.f @@ -1,9 +1,346 @@ +*> \brief \b DLATMT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DLATMT( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, +* RANK, KL, KU, PACK, A, LDA, WORK, INFO ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION COND, DMAX +* INTEGER INFO, KL, KU, LDA, M, MODE, N, RANK +* CHARACTER DIST, PACK, SYM +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * ) +* INTEGER ISEED( 4 ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> DLATMT generates random matrices with specified singular values +*> (or symmetric/hermitian with specified eigenvalues) +*> for testing LAPACK programs. +*> +*> DLATMT operates by applying the following sequence of +*> operations: +*> +*> Set the diagonal to D, where D may be input or +*> computed according to MODE, COND, DMAX, and SYM +*> as described below. +*> +*> Generate a matrix with the appropriate band structure, by one +*> of two methods: +*> +*> Method A: +*> Generate a dense M x N matrix by multiplying D on the left +*> and the right by random unitary matrices, then: +*> +*> Reduce the bandwidth according to KL and KU, using +*> Householder transformations. +*> +*> Method B: +*> Convert the bandwidth-0 (i.e., diagonal) matrix to a +*> bandwidth-1 matrix using Givens rotations, "chasing" +*> out-of-band elements back, much as in QR; then +*> convert the bandwidth-1 to a bandwidth-2 matrix, etc. +*> Note that for reasonably small bandwidths (relative to +*> M and N) this requires less storage, as a dense matrix +*> is not generated. Also, for symmetric matrices, only +*> one triangle is generated. +*> +*> Method A is chosen if the bandwidth is a large fraction of the +*> order of the matrix, and LDA is at least M (so a dense +*> matrix can be stored.) Method B is chosen if the bandwidth +*> is small (< 1/2 N for symmetric, < .3 N+M for +*> non-symmetric), or LDA is less than M and not less than the +*> bandwidth. +*> +*> Pack the matrix if desired. Options specified by PACK are: +*> no packing +*> zero out upper half (if symmetric) +*> zero out lower half (if symmetric) +*> store the upper half columnwise (if symmetric or upper +*> triangular) +*> store the lower half columnwise (if symmetric or lower +*> triangular) +*> store the lower triangle in banded format (if symmetric +*> or lower triangular) +*> store the upper triangle in banded format (if symmetric +*> or upper triangular) +*> store the entire matrix in banded format +*> If Method B is chosen, and band format is specified, then the +*> matrix will be generated in the band format, so no repacking +*> will be necessary. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of A. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of A. Not modified. +*> \endverbatim +*> +*> \param[in] DIST +*> \verbatim +*> DIST is CHARACTER*1 +*> On entry, DIST specifies the type of distribution to be used +*> to generate the random eigen-/singular values. +*> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) +*> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) +*> 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. They should lie between 0 and 4095 inclusive, +*> and ISEED(4) should be odd. The random number generator +*> uses a linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to DLATMT +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] SYM +*> \verbatim +*> SYM is CHARACTER*1 +*> If SYM='S' or 'H', the generated matrix is symmetric, with +*> eigenvalues specified by D, COND, MODE, and DMAX; they +*> may be positive, negative, or zero. +*> If SYM='P', the generated matrix is symmetric, with +*> eigenvalues (= singular values) specified by D, COND, +*> MODE, and DMAX; they will not be negative. +*> If SYM='N', the generated matrix is nonsymmetric, with +*> singular values specified by D, COND, MODE, and DMAX; +*> they will not be negative. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension ( MIN( M , N ) ) +*> This array is used to specify the singular values or +*> eigenvalues of A (see SYM, above.) If MODE=0, then D is +*> assumed to contain the singular/eigenvalues, otherwise +*> they will be computed according to MODE, COND, and DMAX, +*> and placed in D. +*> Modified if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry this describes how the singular/eigenvalues are to +*> be specified: +*> MODE = 0 means use D as input +*> \endverbatim +*> \verbatim +*> MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND +*> MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) +*> \endverbatim +*> \verbatim +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> If SYM='S' or 'H', and MODE is neither 0, 6, nor -6, then +*> the elements of D will also be multiplied by a random +*> sign (i.e., +1 or -1.) +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is DOUBLE PRECISION +*> On entry, this is used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] DMAX +*> \verbatim +*> DMAX is DOUBLE PRECISION +*> If MODE is neither -6, 0 nor 6, the contents of D, as +*> computed according to MODE and COND, will be scaled by +*> DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or +*> singular value (which is to say the norm) will be abs(DMAX). +*> Note that DMAX need not be positive: if DMAX is negative +*> (or zero), D will be scaled by a negative number (or zero). +*> Not modified. +*> \endverbatim +*> +*> \param[in] RANK +*> \verbatim +*> RANK is INTEGER +*> The rank of matrix to be generated for modes 1,2,3 only. +*> D( RANK+1:N ) = 0. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> This specifies the lower bandwidth of the matrix. For +*> example, KL=0 implies upper triangular, KL=1 implies upper +*> Hessenberg, and KL being at least M-1 means that the matrix +*> has full lower bandwidth. KL must equal KU if the matrix +*> is symmetric. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> This specifies the upper bandwidth of the matrix. For +*> example, KU=0 implies lower triangular, KU=1 implies lower +*> Hessenberg, and KU being at least N-1 means that the matrix +*> has full upper bandwidth. KL must equal KU if the matrix +*> is symmetric. +*> Not modified. +*> \endverbatim +*> +*> \param[in] PACK +*> \verbatim +*> PACK is CHARACTER*1 +*> This specifies packing of matrix as follows: +*> 'N' => no packing +*> 'U' => zero out all subdiagonal entries (if symmetric) +*> 'L' => zero out all superdiagonal entries (if symmetric) +*> 'C' => store the upper triangle columnwise +*> (only if the matrix is symmetric or upper triangular) +*> 'R' => store the lower triangle columnwise +*> (only if the matrix is symmetric or lower triangular) +*> 'B' => store the lower triangle in band storage scheme +*> (only if matrix symmetric or lower triangular) +*> 'Q' => store the upper triangle in band storage scheme +*> (only if matrix symmetric or upper triangular) +*> 'Z' => store the entire matrix in band storage scheme +*> (pivoting can be provided for by using this +*> option to store A in the trailing rows of +*> the allocated storage) +*> \endverbatim +*> \verbatim +*> Using these options, the various LAPACK packed and banded +*> storage schemes can be obtained: +*> GB - use 'Z' +*> PB, SB or TB - use 'B' or 'Q' +*> PP, SP or TP - use 'C' or 'R' +*> \endverbatim +*> \verbatim +*> If two calls to DLATMT differ only in the PACK parameter, +*> they will generate mathematically equivalent matrices. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension ( LDA, N ) +*> On exit A is the desired test matrix. A is first generated +*> in full (unpacked) form, and then packed, if so specified +*> by PACK. Thus, the first M elements of the first N +*> columns will always be modified. If PACK specifies a +*> packed or banded storage scheme, all LDA elements of the +*> first N columns will be modified; the elements of the +*> array which do not correspond to elements of the generated +*> matrix are set to zero. +*> Modified. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> LDA specifies the first dimension of A as declared in the +*> calling program. If PACK='N', 'U', 'L', 'C', or 'R', then +*> LDA must be at least M. If PACK='B' or 'Q', then LDA must +*> be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). +*> If PACK='Z', LDA must be large enough to hold the packed +*> array: MIN( KU, N-1) + MIN( KL, M-1) + 1. +*> Not modified. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension ( 3*MAX( N , M ) ) +*> Workspace. +*> Modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error code. On exit, INFO will be set to one of the +*> following values: +*> 0 => normal return +*> -1 => M negative or unequal to N and SYM='S', 'H', or 'P' +*> -2 => N negative +*> -3 => DIST illegal string +*> -5 => SYM illegal string +*> -7 => MODE not in range -6 to 6 +*> -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 +*> -10 => KL negative +*> -11 => KU negative, or SYM='S' or 'H' and KU not equal to KL +*> -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; +*> or PACK='C' or 'Q' and SYM='N' and KL is not zero; +*> or PACK='R' or 'B' and SYM='N' and KU is not zero; +*> or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not +*> N. +*> -14 => LDA is less than M, or PACK='Z' and LDA is less than +*> MIN(KU,N-1) + MIN(KL,M-1) + 1. +*> 1 => Error return from DLATM7 +*> 2 => Cannot scale to DMAX (max. sing. value is 0) +*> 3 => Error return from DLAGGE or DLAGSY +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_matgen +* +* ===================================================================== SUBROUTINE DLATMT( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, $ RANK, KL, KU, PACK, A, LDA, WORK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Craig Lucas, University of Manchester / NAG Ltd. -* October, 2008 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. DOUBLE PRECISION COND, DMAX @@ -15,245 +352,6 @@ INTEGER ISEED( 4 ) * .. * -* Purpose -* ======= -* -* DLATMT generates random matrices with specified singular values -* (or symmetric/hermitian with specified eigenvalues) -* for testing LAPACK programs. -* -* DLATMT operates by applying the following sequence of -* operations: -* -* Set the diagonal to D, where D may be input or -* computed according to MODE, COND, DMAX, and SYM -* as described below. -* -* Generate a matrix with the appropriate band structure, by one -* of two methods: -* -* Method A: -* Generate a dense M x N matrix by multiplying D on the left -* and the right by random unitary matrices, then: -* -* Reduce the bandwidth according to KL and KU, using -* Householder transformations. -* -* Method B: -* Convert the bandwidth-0 (i.e., diagonal) matrix to a -* bandwidth-1 matrix using Givens rotations, "chasing" -* out-of-band elements back, much as in QR; then -* convert the bandwidth-1 to a bandwidth-2 matrix, etc. -* Note that for reasonably small bandwidths (relative to -* M and N) this requires less storage, as a dense matrix -* is not generated. Also, for symmetric matrices, only -* one triangle is generated. -* -* Method A is chosen if the bandwidth is a large fraction of the -* order of the matrix, and LDA is at least M (so a dense -* matrix can be stored.) Method B is chosen if the bandwidth -* is small (< 1/2 N for symmetric, < .3 N+M for -* non-symmetric), or LDA is less than M and not less than the -* bandwidth. -* -* Pack the matrix if desired. Options specified by PACK are: -* no packing -* zero out upper half (if symmetric) -* zero out lower half (if symmetric) -* store the upper half columnwise (if symmetric or upper -* triangular) -* store the lower half columnwise (if symmetric or lower -* triangular) -* store the lower triangle in banded format (if symmetric -* or lower triangular) -* store the upper triangle in banded format (if symmetric -* or upper triangular) -* store the entire matrix in banded format -* If Method B is chosen, and band format is specified, then the -* matrix will be generated in the band format, so no repacking -* will be necessary. -* -* Arguments -* ========= -* -* M (input) INTEGER -* The number of rows of A. Not modified. -* -* N (input) INTEGER -* The number of columns of A. Not modified. -* -* DIST (input) CHARACTER*1 -* On entry, DIST specifies the type of distribution to be used -* to generate the random eigen-/singular values. -* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) -* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) -* 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. They should lie between 0 and 4095 inclusive, -* and ISEED(4) should be odd. The random number generator -* uses a linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to DLATMT -* to continue the same random number sequence. -* Changed on exit. -* -* SYM (input) CHARACTER*1 -* If SYM='S' or 'H', the generated matrix is symmetric, with -* eigenvalues specified by D, COND, MODE, and DMAX; they -* may be positive, negative, or zero. -* If SYM='P', the generated matrix is symmetric, with -* eigenvalues (= singular values) specified by D, COND, -* MODE, and DMAX; they will not be negative. -* If SYM='N', the generated matrix is nonsymmetric, with -* singular values specified by D, COND, MODE, and DMAX; -* they will not be negative. -* Not modified. -* -* D (input/output) DOUBLE PRECISION array, dimension ( MIN( M , N ) ) -* This array is used to specify the singular values or -* eigenvalues of A (see SYM, above.) If MODE=0, then D is -* assumed to contain the singular/eigenvalues, otherwise -* they will be computed according to MODE, COND, and DMAX, -* and placed in D. -* Modified if MODE is nonzero. -* -* MODE (input) INTEGER -* On entry this describes how the singular/eigenvalues are to -* be specified: -* MODE = 0 means use D as input -* -* MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND -* MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) -* -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* If SYM='S' or 'H', and MODE is neither 0, 6, nor -6, then -* the elements of D will also be multiplied by a random -* sign (i.e., +1 or -1.) -* Not modified. -* -* COND (input) DOUBLE PRECISION -* On entry, this is used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* DMAX (input) DOUBLE PRECISION -* If MODE is neither -6, 0 nor 6, the contents of D, as -* computed according to MODE and COND, will be scaled by -* DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or -* singular value (which is to say the norm) will be abs(DMAX). -* Note that DMAX need not be positive: if DMAX is negative -* (or zero), D will be scaled by a negative number (or zero). -* Not modified. -* -* RANK (input) INTEGER -* The rank of matrix to be generated for modes 1,2,3 only. -* D( RANK+1:N ) = 0. -* Not modified. -* -* KL (input) INTEGER -* This specifies the lower bandwidth of the matrix. For -* example, KL=0 implies upper triangular, KL=1 implies upper -* Hessenberg, and KL being at least M-1 means that the matrix -* has full lower bandwidth. KL must equal KU if the matrix -* is symmetric. -* Not modified. -* -* KU (input) INTEGER -* This specifies the upper bandwidth of the matrix. For -* example, KU=0 implies lower triangular, KU=1 implies lower -* Hessenberg, and KU being at least N-1 means that the matrix -* has full upper bandwidth. KL must equal KU if the matrix -* is symmetric. -* Not modified. -* -* PACK (input) CHARACTER*1 -* This specifies packing of matrix as follows: -* 'N' => no packing -* 'U' => zero out all subdiagonal entries (if symmetric) -* 'L' => zero out all superdiagonal entries (if symmetric) -* 'C' => store the upper triangle columnwise -* (only if the matrix is symmetric or upper triangular) -* 'R' => store the lower triangle columnwise -* (only if the matrix is symmetric or lower triangular) -* 'B' => store the lower triangle in band storage scheme -* (only if matrix symmetric or lower triangular) -* 'Q' => store the upper triangle in band storage scheme -* (only if matrix symmetric or upper triangular) -* 'Z' => store the entire matrix in band storage scheme -* (pivoting can be provided for by using this -* option to store A in the trailing rows of -* the allocated storage) -* -* Using these options, the various LAPACK packed and banded -* storage schemes can be obtained: -* GB - use 'Z' -* PB, SB or TB - use 'B' or 'Q' -* PP, SP or TP - use 'C' or 'R' -* -* If two calls to DLATMT differ only in the PACK parameter, -* they will generate mathematically equivalent matrices. -* Not modified. -* -* A (input/output) DOUBLE PRECISION array, dimension ( LDA, N ) -* On exit A is the desired test matrix. A is first generated -* in full (unpacked) form, and then packed, if so specified -* by PACK. Thus, the first M elements of the first N -* columns will always be modified. If PACK specifies a -* packed or banded storage scheme, all LDA elements of the -* first N columns will be modified; the elements of the -* array which do not correspond to elements of the generated -* matrix are set to zero. -* Modified. -* -* LDA (input) INTEGER -* LDA specifies the first dimension of A as declared in the -* calling program. If PACK='N', 'U', 'L', 'C', or 'R', then -* LDA must be at least M. If PACK='B' or 'Q', then LDA must -* be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). -* If PACK='Z', LDA must be large enough to hold the packed -* array: MIN( KU, N-1) + MIN( KL, M-1) + 1. -* Not modified. -* -* WORK (workspace) DOUBLE PRECISION array, dimension ( 3*MAX( N , M ) ) -* Workspace. -* Modified. -* -* INFO (output) INTEGER -* Error code. On exit, INFO will be set to one of the -* following values: -* 0 => normal return -* -1 => M negative or unequal to N and SYM='S', 'H', or 'P' -* -2 => N negative -* -3 => DIST illegal string -* -5 => SYM illegal string -* -7 => MODE not in range -6 to 6 -* -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 -* -10 => KL negative -* -11 => KU negative, or SYM='S' or 'H' and KU not equal to KL -* -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; -* or PACK='C' or 'Q' and SYM='N' and KL is not zero; -* or PACK='R' or 'B' and SYM='N' and KU is not zero; -* or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not -* N. -* -14 => LDA is less than M, or PACK='Z' and LDA is less than -* MIN(KU,N-1) + MIN(KL,M-1) + 1. -* 1 => Error return from DLATM7 -* 2 => Cannot scale to DMAX (max. sing. value is 0) -* 3 => Error return from DLAGGE or DLAGSY -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/slagge.f b/TESTING/MATGEN/slagge.f index f2f7d7aa..e551eee5 100644 --- a/TESTING/MATGEN/slagge.f +++ b/TESTING/MATGEN/slagge.f @@ -1,62 +1,132 @@ - SUBROUTINE SLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) -* -* -- LAPACK auxiliary test routine (version 3.1) -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER INFO, KL, KU, LDA, M, N -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) - REAL A( LDA, * ), D( * ), WORK( * ) -* .. -* +*> \brief \b SLAGGE +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, KL, KU, LDA, M, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* REAL A( LDA, * ), D( * ), WORK( * ) +* .. +* * Purpose * ======= * -* SLAGGE generates a real general m by n matrix A, by pre- and post- -* multiplying a real diagonal matrix D with random orthogonal matrices: -* A = U*D*V. The lower and upper bandwidths may then be reduced to -* kl and ku by additional orthogonal transformations. +*>\details \b Purpose: +*>\verbatim +*> +*> SLAGGE generates a real general m by n matrix A, by pre- and post- +*> multiplying a real diagonal matrix D with random orthogonal matrices: +*> A = U*D*V. The lower and upper bandwidths may then be reduced to +*> kl and ku by additional orthogonal transformations. +*> +*>\endverbatim * * Arguments * ========= * -* M (input) INTEGER -* The number of rows of the matrix A. M >= 0. -* -* N (input) INTEGER -* The number of columns of the matrix A. N >= 0. -* -* KL (input) INTEGER -* The number of nonzero subdiagonals within the band of A. -* 0 <= KL <= M-1. -* -* KU (input) INTEGER -* The number of nonzero superdiagonals within the band of A. -* 0 <= KU <= N-1. +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> The number of nonzero subdiagonals within the band of A. +*> 0 <= KL <= M-1. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> The number of nonzero superdiagonals within the band of A. +*> 0 <= KU <= N-1. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is REAL array, dimension (min(M,N)) +*> The diagonal elements of the diagonal matrix D. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is REAL array, dimension (LDA,N) +*> The generated m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= M. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is REAL array, dimension (M+N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= * -* D (input) REAL array, dimension (min(M,N)) -* The diagonal elements of the diagonal matrix D. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (output) REAL array, dimension (LDA,N) -* The generated m by n matrix A. +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= M. +*> \ingroup real_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. +* ===================================================================== + SUBROUTINE SLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) * -* WORK (workspace) REAL array, dimension (M+N) +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value +* .. Scalar Arguments .. + INTEGER INFO, KL, KU, LDA, M, N +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) + REAL A( LDA, * ), D( * ), WORK( * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/slagsy.f b/TESTING/MATGEN/slagsy.f index 00ff328e..18fdee00 100644 --- a/TESTING/MATGEN/slagsy.f +++ b/TESTING/MATGEN/slagsy.f @@ -1,56 +1,120 @@ - SUBROUTINE SLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO ) -* -* -- LAPACK auxiliary test routine (version 3.1) -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, N -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) - REAL A( LDA, * ), D( * ), WORK( * ) -* .. -* +*> \brief \b SLAGSY +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, K, LDA, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* REAL A( LDA, * ), D( * ), WORK( * ) +* .. +* * Purpose * ======= * -* SLAGSY generates a real symmetric matrix A, by pre- and post- -* multiplying a real diagonal matrix D with a random orthogonal matrix: -* A = U*D*U'. The semi-bandwidth may then be reduced to k by additional -* orthogonal transformations. +*>\details \b Purpose: +*>\verbatim +*> +*> SLAGSY generates a real symmetric matrix A, by pre- and post- +*> multiplying a real diagonal matrix D with a random orthogonal matrix: +*> A = U*D*U'. The semi-bandwidth may then be reduced to k by additional +*> orthogonal transformations. +*> +*>\endverbatim * * Arguments * ========= * -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* K (input) INTEGER -* The number of nonzero subdiagonals within the band of A. -* 0 <= K <= N-1. +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The number of nonzero subdiagonals within the band of A. +*> 0 <= K <= N-1. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is REAL array, dimension (N) +*> The diagonal elements of the diagonal matrix D. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is REAL array, dimension (LDA,N) +*> The generated n by n symmetric matrix A (the full matrix is +*> stored). +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= N. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is REAL array, dimension (2*N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= * -* D (input) REAL array, dimension (N) -* The diagonal elements of the diagonal matrix D. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (output) REAL array, dimension (LDA,N) -* The generated n by n symmetric matrix A (the full matrix is -* stored). +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= N. +*> \ingroup real_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. +* ===================================================================== + SUBROUTINE SLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO ) * -* WORK (workspace) REAL array, dimension (2*N) +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value +* .. Scalar Arguments .. + INTEGER INFO, K, LDA, N +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) + REAL A( LDA, * ), D( * ), WORK( * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/slahilb.f b/TESTING/MATGEN/slahilb.f index 60d6dc8a..ceb9ef25 100644 --- a/TESTING/MATGEN/slahilb.f +++ b/TESTING/MATGEN/slahilb.f @@ -1,106 +1,166 @@ +*> \brief \b SLAHILB +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SLAHILB( N, NRHS, A, LDA, X, LDX, B, LDB, WORK, INFO) +* +* .. Scalar Arguments .. +* INTEGER N, NRHS, LDA, LDX, LDB, INFO +* .. Array Arguments .. +* REAL A(LDA, N), X(LDX, NRHS), B(LDB, NRHS), WORK(N) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> SLAHILB generates an N by N scaled Hilbert matrix in A along with +*> NRHS right-hand sides in B and solutions in X such that A*X=B. +*> +*> The Hilbert matrix is scaled by M = LCM(1, 2, ..., 2*N-1) so that all +*> entries are integers. The right-hand sides are the first NRHS +*> columns of M * the identity matrix, and the solutions are the +*> first NRHS columns of the inverse Hilbert matrix. +*> +*> The condition number of the Hilbert matrix grows exponentially with +*> its size, roughly as O(e ** (3.5*N)). Additionally, the inverse +*> Hilbert matrices beyond a relatively small dimension cannot be +*> generated exactly without extra precision. Precision is exhausted +*> when the largest entry in the inverse Hilbert matrix is greater than +*> 2 to the power of the number of bits in the fraction of the data type +*> used plus one, which is 24 for single precision. +*> +*> In single, the generated solution is exact for N <= 6 and has +*> small componentwise error for 7 <= N <= 11. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The dimension of the matrix A. +*> \endverbatim +*> +*> \param[in] NRHS +*> \verbatim +*> NRHS is INTEGER +*> The requested number of right-hand sides. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is REAL array, dimension (LDA, N) +*> The generated scaled Hilbert matrix. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= N. +*> \endverbatim +*> +*> \param[out] X +*> \verbatim +*> X is REAL array, dimension (LDX, NRHS) +*> The generated exact solutions. Currently, the first NRHS +*> columns of the inverse Hilbert matrix. +*> \endverbatim +*> +*> \param[in] LDX +*> \verbatim +*> LDX is INTEGER +*> The leading dimension of the array X. LDX >= N. +*> \endverbatim +*> +*> \param[out] B +*> \verbatim +*> B is REAL array, dimension (LDB, NRHS) +*> The generated right-hand sides. Currently, the first NRHS +*> columns of LCM(1, 2, ..., 2*N-1) * the identity matrix. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of the array B. LDB >= N. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is REAL array, dimension (N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> = 1: N is too large; the data is still generated but may not +*> be not exact. +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup real_matgen +* +* ===================================================================== SUBROUTINE SLAHILB( N, NRHS, A, LDA, X, LDX, B, LDB, WORK, INFO) -! -! -- LAPACK auxiliary test routine (version 3.2.2) -- -! Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., -! Courant Institute, Argonne National Lab, and Rice University -* June 2010 -! -! David Vu <dtv@cs.berkeley.edu> -! Yozo Hida <yozo@cs.berkeley.edu> -! Jason Riedy <ejr@cs.berkeley.edu> -! D. Halligan <dhalligan@berkeley.edu> -! - IMPLICIT NONE -! .. Scalar Arguments .. +* +* -- LAPACK auxiliary routine (version 3.2.2) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. INTEGER N, NRHS, LDA, LDX, LDB, INFO -! .. Array Arguments .. +* .. Array Arguments .. REAL A(LDA, N), X(LDX, NRHS), B(LDB, NRHS), WORK(N) -! .. -! -! Purpose -! ======= -! -! SLAHILB generates an N by N scaled Hilbert matrix in A along with -! NRHS right-hand sides in B and solutions in X such that A*X=B. -! -! The Hilbert matrix is scaled by M = LCM(1, 2, ..., 2*N-1) so that all -! entries are integers. The right-hand sides are the first NRHS -! columns of M * the identity matrix, and the solutions are the -! first NRHS columns of the inverse Hilbert matrix. -! -! The condition number of the Hilbert matrix grows exponentially with -! its size, roughly as O(e ** (3.5*N)). Additionally, the inverse -! Hilbert matrices beyond a relatively small dimension cannot be -! generated exactly without extra precision. Precision is exhausted -! when the largest entry in the inverse Hilbert matrix is greater than -! 2 to the power of the number of bits in the fraction of the data type -! used plus one, which is 24 for single precision. -! -! In single, the generated solution is exact for N <= 6 and has -! small componentwise error for 7 <= N <= 11. -! -! Arguments -! ========= -! -! N (input) INTEGER -! The dimension of the matrix A. -! -! NRHS (input) INTEGER -! The requested number of right-hand sides. -! -! A (output) REAL array, dimension (LDA, N) -! The generated scaled Hilbert matrix. -! -! LDA (input) INTEGER -! The leading dimension of the array A. LDA >= N. -! -! X (output) REAL array, dimension (LDX, NRHS) -! The generated exact solutions. Currently, the first NRHS -! columns of the inverse Hilbert matrix. -! -! LDX (input) INTEGER -! The leading dimension of the array X. LDX >= N. -! -! B (output) REAL array, dimension (LDB, NRHS) -! The generated right-hand sides. Currently, the first NRHS -! columns of LCM(1, 2, ..., 2*N-1) * the identity matrix. -! -! LDB (input) INTEGER -! The leading dimension of the array B. LDB >= N. -! -! WORK (workspace) REAL array, dimension (N) -! -! -! INFO (output) INTEGER -! = 0: successful exit -! = 1: N is too large; the data is still generated but may not -! be not exact. -! < 0: if INFO = -i, the i-th argument had an illegal value -! -! ===================================================================== +* .. +* +* ===================================================================== -! .. Local Scalars .. +* .. Local Scalars .. INTEGER TM, TI, R INTEGER M INTEGER I, J -! .. Parameters .. -! NMAX_EXACT the largest dimension where the generated data is -! exact. -! NMAX_APPROX the largest dimension where the generated data has -! a small componentwise relative error. +* .. Parameters .. +* NMAX_EXACT the largest dimension where the generated data is +* exact. +* NMAX_APPROX the largest dimension where the generated data has +* a small componentwise relative error. INTEGER NMAX_EXACT, NMAX_APPROX PARAMETER (NMAX_EXACT = 6, NMAX_APPROX = 11) -! .. -! .. External Functions +* .. +* .. External Functions EXTERNAL SLASET INTRINSIC REAL -! .. -! .. Executable Statements .. -! -! Test the input arguments -! +* .. +* .. Executable Statements .. +* +* Test the input arguments +* INFO = 0 IF (N .LT. 0 .OR. N .GT. NMAX_APPROX) THEN INFO = -1 @@ -121,8 +181,8 @@ INFO = 1 END IF -! Compute M = the LCM of the integers [1, 2*N-1]. The largest -! reasonable N is small enough that integers suffice (up to N = 11). +* Compute M = the LCM of the integers [1, 2*N-1]. The largest +* reasonable N is small enough that integers suffice (up to N = 11). M = 1 DO I = 2, (2*N-1) TM = M @@ -136,20 +196,20 @@ M = (M / TI) * I END DO -! Generate the scaled Hilbert matrix in A +* Generate the scaled Hilbert matrix in A DO J = 1, N DO I = 1, N A(I, J) = REAL(M) / (I + J - 1) END DO END DO -! Generate matrix B as simply the first NRHS columns of M * the -! identity. +* Generate matrix B as simply the first NRHS columns of M * the +* identity. CALL SLASET('Full', N, NRHS, 0.0, REAL(M), B, LDB) -! Generate the true solutions in X. Because B = the first NRHS -! columns of M*I, the true solutions are just the first NRHS columns -! of the inverse Hilbert matrix. +* Generate the true solutions in X. Because B = the first NRHS +* columns of M*I, the true solutions are just the first NRHS columns +* of the inverse Hilbert matrix. WORK(1) = N DO J = 2, N WORK(J) = ( ( (WORK(J-1)/(J-1)) * (J-1 - N) ) /(J-1) ) diff --git a/TESTING/MATGEN/slakf2.f b/TESTING/MATGEN/slakf2.f index ef0d38f9..a5bbdad3 100644 --- a/TESTING/MATGEN/slakf2.f +++ b/TESTING/MATGEN/slakf2.f @@ -1,54 +1,125 @@ - SUBROUTINE SLAKF2( M, N, A, LDA, B, D, E, Z, LDZ ) -* -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER LDA, LDZ, M, N -* .. -* .. Array Arguments .. - REAL A( LDA, * ), B( LDA, * ), D( LDA, * ), - $ E( LDA, * ), Z( LDZ, * ) -* .. -* +*> \brief \b SLAKF2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SLAKF2( M, N, A, LDA, B, D, E, Z, LDZ ) +* +* .. Scalar Arguments .. +* INTEGER LDA, LDZ, M, N +* .. +* .. Array Arguments .. +* REAL A( LDA, * ), B( LDA, * ), D( LDA, * ), +* $ E( LDA, * ), Z( LDZ, * ) +* .. +* * Purpose * ======= * -* Form the 2*M*N by 2*M*N matrix -* -* Z = [ kron(In, A) -kron(B', Im) ] -* [ kron(In, D) -kron(E', Im) ], -* -* where In is the identity matrix of size n and X' is the transpose -* of X. kron(X, Y) is the Kronecker product between the matrices X -* and Y. +*>\details \b Purpose: +*>\verbatim +*> +*> Form the 2*M*N by 2*M*N matrix +*> +*> Z = [ kron(In, A) -kron(B', Im) ] +*> [ kron(In, D) -kron(E', Im) ], +*> +*> where In is the identity matrix of size n and X' is the transpose +*> of X. kron(X, Y) is the Kronecker product between the matrices X +*> and Y. +*> +*>\endverbatim * * Arguments * ========= * -* M (input) INTEGER -* Size of matrix, must be >= 1. +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Size of matrix, must be >= 1. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Size of matrix, must be >= 1. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL, dimension ( LDA, M ) +*> The matrix A in the output matrix Z. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of A, B, D, and E. ( LDA >= M+N ) +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is REAL, dimension ( LDA, N ) +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is REAL, dimension ( LDA, M ) +*> \endverbatim +*> +*> \param[in] E +*> \verbatim +*> E is REAL, dimension ( LDA, N ) +*> \endverbatim +*> \verbatim +*> The matrices used in forming the output matrix Z. +*> \endverbatim +*> +*> \param[out] Z +*> \verbatim +*> Z is REAL, dimension ( LDZ, 2*M*N ) +*> The resultant Kronecker M*N*2 by M*N*2 matrix (see above.) +*> \endverbatim +*> +*> \param[in] LDZ +*> \verbatim +*> LDZ is INTEGER +*> The leading dimension of Z. ( LDZ >= 2*M*N ) +*> \endverbatim +*> +* +* Authors +* ======= * -* N (input) INTEGER -* Size of matrix, must be >= 1. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (input) REAL, dimension ( LDA, M ) -* The matrix A in the output matrix Z. +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of A, B, D, and E. ( LDA >= M+N ) +*> \ingroup real_matgen * -* B (input) REAL, dimension ( LDA, N ) -* D (input) REAL, dimension ( LDA, M ) -* E (input) REAL, dimension ( LDA, N ) -* The matrices used in forming the output matrix Z. +* ===================================================================== + SUBROUTINE SLAKF2( M, N, A, LDA, B, D, E, Z, LDZ ) * -* Z (output) REAL, dimension ( LDZ, 2*M*N ) -* The resultant Kronecker M*N*2 by M*N*2 matrix (see above.) +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* LDZ (input) INTEGER -* The leading dimension of Z. ( LDZ >= 2*M*N ) +* .. Scalar Arguments .. + INTEGER LDA, LDZ, M, N +* .. +* .. Array Arguments .. + REAL A( LDA, * ), B( LDA, * ), D( LDA, * ), + $ E( LDA, * ), Z( LDZ, * ) +* .. * * ==================================================================== * diff --git a/TESTING/MATGEN/slaran.f b/TESTING/MATGEN/slaran.f index 97ae5be9..079aa349 100644 --- a/TESTING/MATGEN/slaran.f +++ b/TESTING/MATGEN/slaran.f @@ -1,40 +1,84 @@ - REAL FUNCTION SLARAN( ISEED ) +*> \brief \b SLARAN * -* -- LAPACK auxiliary routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 +* =========== DOCUMENTATION =========== * -* .. Array Arguments .. - INTEGER ISEED( 4 ) -* .. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* REAL FUNCTION SLARAN( ISEED ) +* +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* .. +* * Purpose * ======= * -* SLARAN returns a random real number from a uniform (0,1) -* distribution. +*>\details \b Purpose: +*>\verbatim +*> +*> SLARAN returns a random real number from a uniform (0,1) +*> distribution. +*> +*>\endverbatim * * Arguments * ========= * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup real_matgen +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> This routine uses a multiplicative congruential method with modulus +*> 2**48 and multiplier 33952834046453 (see G.S.Fishman, +*> 'Multiplicative congruential random number generators with modulus +*> 2**b: an exhaustive analysis for b = 32 and a partial analysis for +*> b = 48', Math. Comp. 189, pp 331-344, 1990). +*> +*> 48-bit integers are stored in 4 integer array elements with 12 bits +*> per element. Hence the routine is portable across machines with +*> integers of 32 bits or more. +*> +*> \endverbatim +*> +* ===================================================================== + REAL FUNCTION SLARAN( ISEED ) * -* This routine uses a multiplicative congruential method with modulus -* 2**48 and multiplier 33952834046453 (see G.S.Fishman, -* 'Multiplicative congruential random number generators with modulus -* 2**b: an exhaustive analysis for b = 32 and a partial analysis for -* b = 48', Math. Comp. 189, pp 331-344, 1990). +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* 48-bit integers are stored in 4 integer array elements with 12 bits -* per element. Hence the routine is portable across machines with -* integers of 32 bits or more. +* .. Array Arguments .. + INTEGER ISEED( 4 ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/slarge.f b/TESTING/MATGEN/slarge.f index 7ee18ba6..8293c289 100644 --- a/TESTING/MATGEN/slarge.f +++ b/TESTING/MATGEN/slarge.f @@ -1,48 +1,106 @@ - SUBROUTINE SLARGE( N, A, LDA, ISEED, WORK, INFO ) -* -* -- LAPACK auxiliary test routine (version 3.1) -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) - REAL A( LDA, * ), WORK( * ) -* .. -* +*> \brief \b SLARGE +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SLARGE( N, A, LDA, ISEED, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* REAL A( LDA, * ), WORK( * ) +* .. +* * Purpose * ======= * -* SLARGE pre- and post-multiplies a real general n by n matrix A -* with a random orthogonal matrix: A = U*D*U'. +*>\details \b Purpose: +*>\verbatim +*> +*> SLARGE pre- and post-multiplies a real general n by n matrix A +*> with a random orthogonal matrix: A = U*D*U'. +*> +*>\endverbatim * * Arguments * ========= * -* N (input) INTEGER -* The order of the matrix A. N >= 0. +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is REAL array, dimension (LDA,N) +*> On entry, the original n by n matrix A. +*> On exit, A is overwritten by U*A*U' for some random +*> orthogonal matrix U. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= N. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is REAL array, dimension (2*N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (input/output) REAL array, dimension (LDA,N) -* On entry, the original n by n matrix A. -* On exit, A is overwritten by U*A*U' for some random -* orthogonal matrix U. +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= N. +*> \ingroup real_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. +* ===================================================================== + SUBROUTINE SLARGE( N, A, LDA, ISEED, WORK, INFO ) * -* WORK (workspace) REAL array, dimension (2*N) +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value +* .. Scalar Arguments .. + INTEGER INFO, LDA, N +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) + REAL A( LDA, * ), WORK( * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/slarnd.f b/TESTING/MATGEN/slarnd.f index 9386d6d6..3868af38 100644 --- a/TESTING/MATGEN/slarnd.f +++ b/TESTING/MATGEN/slarnd.f @@ -1,43 +1,93 @@ - REAL FUNCTION SLARND( IDIST, ISEED ) +*> \brief \b SLARND * -* -- LAPACK auxiliary routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 +* =========== DOCUMENTATION =========== * -* .. Scalar Arguments .. - INTEGER IDIST -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) -* .. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* REAL FUNCTION SLARND( IDIST, ISEED ) +* +* .. Scalar Arguments .. +* INTEGER IDIST +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* .. +* * Purpose * ======= * -* SLARND returns a random real number from a uniform or normal -* distribution. +*>\details \b Purpose: +*>\verbatim +*> +*> SLARND returns a random real number from a uniform or normal +*> distribution. +*> +*>\endverbatim * * Arguments * ========= * -* IDIST (input) INTEGER -* Specifies the distribution of the random numbers: -* = 1: uniform (0,1) -* = 2: uniform (-1,1) -* = 3: normal (0,1) +*> \param[in] IDIST +*> \verbatim +*> IDIST is INTEGER +*> Specifies the distribution of the random numbers: +*> = 1: uniform (0,1) +*> = 2: uniform (-1,1) +*> = 3: normal (0,1) +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup real_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> This routine calls the auxiliary routine SLARAN to generate a random +*> real number from a uniform (0,1) distribution. The Box-Muller method +*> is used to transform numbers from a uniform to a normal distribution. +*> +*> \endverbatim +*> +* ===================================================================== + REAL FUNCTION SLARND( IDIST, ISEED ) * -* This routine calls the auxiliary routine SLARAN to generate a random -* real number from a uniform (0,1) distribution. The Box-Muller method -* is used to transform numbers from a uniform to a normal distribution. +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER IDIST +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/slaror.f b/TESTING/MATGEN/slaror.f index 4e5bef53..b1711e1e 100644 --- a/TESTING/MATGEN/slaror.f +++ b/TESTING/MATGEN/slaror.f @@ -1,8 +1,161 @@ +*> \brief \b SLAROR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SLAROR( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER INIT, SIDE +* INTEGER INFO, LDA, M, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* REAL A( LDA, * ), X( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> SLAROR pre- or post-multiplies an M by N matrix A by a random +*> orthogonal matrix U, overwriting A. A may optionally be initialized +*> to the identity matrix before multiplying by U. U is generated using +*> the method of G.W. Stewart (SIAM J. Numer. Anal. 17, 1980, 403-409). +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> Specifies whether A is multiplied on the left or right by U. +*> = 'L': Multiply A on the left (premultiply) by U +*> = 'R': Multiply A on the right (postmultiply) by U' +*> = 'C' or 'T': Multiply A on the left by U and the right +*> by U' (Here, U' means U-transpose.) +*> \endverbatim +*> +*> \param[in] INIT +*> \verbatim +*> INIT is CHARACTER*1 +*> Specifies whether or not A should be initialized to the +*> identity matrix. +*> = 'I': Initialize A to (a section of) the identity matrix +*> before applying U. +*> = 'N': No initialization. Apply U to the input matrix A. +*> \endverbatim +*> \verbatim +*> INIT = 'I' may be used to generate square or rectangular +*> orthogonal matrices: +*> \endverbatim +*> \verbatim +*> For M = N and SIDE = 'L' or 'R', the rows will be orthogonal +*> to each other, as will the columns. +*> \endverbatim +*> \verbatim +*> If M < N, SIDE = 'R' produces a dense matrix whose rows are +*> orthogonal and whose columns are not, while SIDE = 'L' +*> produces a matrix whose rows are orthogonal, and whose first +*> M columns are orthogonal, and whose remaining columns are +*> zero. +*> \endverbatim +*> \verbatim +*> If M > N, SIDE = 'L' produces a dense matrix whose columns +*> are orthogonal and whose rows are not, while SIDE = 'R' +*> produces a matrix whose columns are orthogonal, and whose +*> first M rows are orthogonal, and whose remaining rows are +*> zero. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of A. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is REAL array, dimension (LDA, N) +*> On entry, the array A. +*> On exit, overwritten by U A ( if SIDE = 'L' ), +*> or by A U ( if SIDE = 'R' ), +*> or by U A U' ( if SIDE = 'C' or 'T'). +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry ISEED specifies the seed of the random number +*> generator. The array elements should be between 0 and 4095; +*> if not they will be reduced mod 4096. Also, ISEED(4) must +*> be odd. The random number generator uses a linear +*> congruential sequence limited to small integers, and so +*> should produce machine independent random numbers. The +*> values of ISEED are changed on exit, and can be used in the +*> next call to SLAROR to continue the same random number +*> sequence. +*> \endverbatim +*> +*> \param[out] X +*> \verbatim +*> X is REAL array, dimension (3*MAX( M, N )) +*> Workspace of length +*> 2*M + N if SIDE = 'L', +*> 2*N + M if SIDE = 'R', +*> 3*N if SIDE = 'C' or 'T'. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> An error flag. It is set to: +*> = 0: normal return +*> < 0: if INFO = -k, the k-th argument had an illegal value +*> = 1: if the random numbers generated by SLARND are bad. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup real_matgen +* +* ===================================================================== SUBROUTINE SLAROR( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER INIT, SIDE @@ -13,87 +166,6 @@ REAL A( LDA, * ), X( * ) * .. * -* Purpose -* ======= -* -* SLAROR pre- or post-multiplies an M by N matrix A by a random -* orthogonal matrix U, overwriting A. A may optionally be initialized -* to the identity matrix before multiplying by U. U is generated using -* the method of G.W. Stewart (SIAM J. Numer. Anal. 17, 1980, 403-409). -* -* Arguments -* ========= -* -* SIDE (input) CHARACTER*1 -* Specifies whether A is multiplied on the left or right by U. -* = 'L': Multiply A on the left (premultiply) by U -* = 'R': Multiply A on the right (postmultiply) by U' -* = 'C' or 'T': Multiply A on the left by U and the right -* by U' (Here, U' means U-transpose.) -* -* INIT (input) CHARACTER*1 -* Specifies whether or not A should be initialized to the -* identity matrix. -* = 'I': Initialize A to (a section of) the identity matrix -* before applying U. -* = 'N': No initialization. Apply U to the input matrix A. -* -* INIT = 'I' may be used to generate square or rectangular -* orthogonal matrices: -* -* For M = N and SIDE = 'L' or 'R', the rows will be orthogonal -* to each other, as will the columns. -* -* If M < N, SIDE = 'R' produces a dense matrix whose rows are -* orthogonal and whose columns are not, while SIDE = 'L' -* produces a matrix whose rows are orthogonal, and whose first -* M columns are orthogonal, and whose remaining columns are -* zero. -* -* If M > N, SIDE = 'L' produces a dense matrix whose columns -* are orthogonal and whose rows are not, while SIDE = 'R' -* produces a matrix whose columns are orthogonal, and whose -* first M rows are orthogonal, and whose remaining rows are -* zero. -* -* M (input) INTEGER -* The number of rows of A. -* -* N (input) INTEGER -* The number of columns of A. -* -* A (input/output) REAL array, dimension (LDA, N) -* On entry, the array A. -* On exit, overwritten by U A ( if SIDE = 'L' ), -* or by A U ( if SIDE = 'R' ), -* or by U A U' ( if SIDE = 'C' or 'T'). -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,M). -* -* ISEED (input/output) INTEGER array, dimension (4) -* On entry ISEED specifies the seed of the random number -* generator. The array elements should be between 0 and 4095; -* if not they will be reduced mod 4096. Also, ISEED(4) must -* be odd. The random number generator uses a linear -* congruential sequence limited to small integers, and so -* should produce machine independent random numbers. The -* values of ISEED are changed on exit, and can be used in the -* next call to SLAROR to continue the same random number -* sequence. -* -* X (workspace) REAL array, dimension (3*MAX( M, N )) -* Workspace of length -* 2*M + N if SIDE = 'L', -* 2*N + M if SIDE = 'R', -* 3*N if SIDE = 'C' or 'T'. -* -* INFO (output) INTEGER -* An error flag. It is set to: -* = 0: normal return -* < 0: if INFO = -k, the k-th argument had an illegal value -* = 1: if the random numbers generated by SLARND are bad. -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/slarot.f b/TESTING/MATGEN/slarot.f index 466cb29f..0bf495be 100644 --- a/TESTING/MATGEN/slarot.f +++ b/TESTING/MATGEN/slarot.f @@ -1,202 +1,254 @@ - SUBROUTINE SLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT, - $ XRIGHT ) -* -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - LOGICAL LLEFT, LRIGHT, LROWS - INTEGER LDA, NL - REAL C, S, XLEFT, XRIGHT -* .. -* .. Array Arguments .. - REAL A( * ) -* .. -* +*> \brief \b SLAROT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT, +* XRIGHT ) +* +* .. Scalar Arguments .. +* LOGICAL LLEFT, LRIGHT, LROWS +* INTEGER LDA, NL +* REAL C, S, XLEFT, XRIGHT +* .. +* .. Array Arguments .. +* REAL A( * ) +* .. +* * Purpose * ======= * -* SLAROT applies a (Givens) rotation to two adjacent rows or -* columns, where one element of the first and/or last column/row -* for use on matrices stored in some format other than GE, so -* that elements of the matrix may be used or modified for which -* no array element is provided. -* -* One example is a symmetric matrix in SB format (bandwidth=4), for -* which UPLO='L': Two adjacent rows will have the format: -* -* row j: * * * * * . . . . -* row j+1: * * * * * . . . . -* -* '*' indicates elements for which storage is provided, -* '.' indicates elements for which no storage is provided, but -* are not necessarily zero; their values are determined by -* symmetry. ' ' indicates elements which are necessarily zero, -* and have no storage provided. -* -* Those columns which have two '*'s can be handled by SROT. -* Those columns which have no '*'s can be ignored, since as long -* as the Givens rotations are carefully applied to preserve -* symmetry, their values are determined. -* Those columns which have one '*' have to be handled separately, -* by using separate variables "p" and "q": -* -* row j: * * * * * p . . . -* row j+1: q * * * * * . . . . -* -* The element p would have to be set correctly, then that column -* is rotated, setting p to its new value. The next call to -* SLAROT would rotate columns j and j+1, using p, and restore -* symmetry. The element q would start out being zero, and be -* made non-zero by the rotation. Later, rotations would presumably -* be chosen to zero q out. -* -* Typical Calling Sequences: rotating the i-th and (i+1)-st rows. -* ------- ------- --------- -* -* General dense matrix: -* -* CALL SLAROT(.TRUE.,.FALSE.,.FALSE., N, C,S, -* A(i,1),LDA, DUMMY, DUMMY) -* -* General banded matrix in GB format: -* -* j = MAX(1, i-KL ) -* NL = MIN( N, i+KU+1 ) + 1-j -* CALL SLAROT( .TRUE., i-KL.GE.1, i+KU.LT.N, NL, C,S, -* A(KU+i+1-j,j),LDA-1, XLEFT, XRIGHT ) -* -* [ note that i+1-j is just MIN(i,KL+1) ] -* -* Symmetric banded matrix in SY format, bandwidth K, -* lower triangle only: -* -* j = MAX(1, i-K ) -* NL = MIN( K+1, i ) + 1 -* CALL SLAROT( .TRUE., i-K.GE.1, .TRUE., NL, C,S, -* A(i,j), LDA, XLEFT, XRIGHT ) -* -* Same, but upper triangle only: -* -* NL = MIN( K+1, N-i ) + 1 -* CALL SLAROT( .TRUE., .TRUE., i+K.LT.N, NL, C,S, -* A(i,i), LDA, XLEFT, XRIGHT ) -* -* Symmetric banded matrix in SB format, bandwidth K, -* lower triangle only: -* -* [ same as for SY, except:] -* . . . . -* A(i+1-j,j), LDA-1, XLEFT, XRIGHT ) -* -* [ note that i+1-j is just MIN(i,K+1) ] -* -* Same, but upper triangle only: -* . . . -* A(K+1,i), LDA-1, XLEFT, XRIGHT ) -* -* Rotating columns is just the transpose of rotating rows, except -* for GB and SB: (rotating columns i and i+1) -* -* GB: -* j = MAX(1, i-KU ) -* NL = MIN( N, i+KL+1 ) + 1-j -* CALL SLAROT( .TRUE., i-KU.GE.1, i+KL.LT.N, NL, C,S, -* A(KU+j+1-i,i),LDA-1, XTOP, XBOTTM ) -* -* [note that KU+j+1-i is just MAX(1,KU+2-i)] -* -* SB: (upper triangle) -* -* . . . . . . -* A(K+j+1-i,i),LDA-1, XTOP, XBOTTM ) -* -* SB: (lower triangle) -* -* . . . . . . -* A(1,i),LDA-1, XTOP, XBOTTM ) +*>\details \b Purpose: +*>\verbatim +*> +*> SLAROT applies a (Givens) rotation to two adjacent rows or +*> columns, where one element of the first and/or last column/row +*> for use on matrices stored in some format other than GE, so +*> that elements of the matrix may be used or modified for which +*> no array element is provided. +*> +*> One example is a symmetric matrix in SB format (bandwidth=4), for +*> which UPLO='L': Two adjacent rows will have the format: +*> +*> row j: C> C> C> C> C> . . . . +*> row j+1: C> C> C> C> C> . . . . +*> +*> '*' indicates elements for which storage is provided, +*> '.' indicates elements for which no storage is provided, but +*> are not necessarily zero; their values are determined by +*> symmetry. ' ' indicates elements which are necessarily zero, +*> and have no storage provided. +*> +*> Those columns which have two '*'s can be handled by SROT. +*> Those columns which have no '*'s can be ignored, since as long +*> as the Givens rotations are carefully applied to preserve +*> symmetry, their values are determined. +*> Those columns which have one '*' have to be handled separately, +*> by using separate variables "p" and "q": +*> +*> row j: C> C> C> C> C> p . . . +*> row j+1: q C> C> C> C> C> . . . . +*> +*> The element p would have to be set correctly, then that column +*> is rotated, setting p to its new value. The next call to +*> SLAROT would rotate columns j and j+1, using p, and restore +*> symmetry. The element q would start out being zero, and be +*> made non-zero by the rotation. Later, rotations would presumably +*> be chosen to zero q out. +*> +*> Typical Calling Sequences: rotating the i-th and (i+1)-st rows. +*> ------- ------- --------- +*> +*> General dense matrix: +*> +*> CALL SLAROT(.TRUE.,.FALSE.,.FALSE., N, C,S, +*> A(i,1),LDA, DUMMY, DUMMY) +*> +*> General banded matrix in GB format: +*> +*> j = MAX(1, i-KL ) +*> NL = MIN( N, i+KU+1 ) + 1-j +*> CALL SLAROT( .TRUE., i-KL.GE.1, i+KU.LT.N, NL, C,S, +*> A(KU+i+1-j,j),LDA-1, XLEFT, XRIGHT ) +*> +*> [ note that i+1-j is just MIN(i,KL+1) ] +*> +*> Symmetric banded matrix in SY format, bandwidth K, +*> lower triangle only: +*> +*> j = MAX(1, i-K ) +*> NL = MIN( K+1, i ) + 1 +*> CALL SLAROT( .TRUE., i-K.GE.1, .TRUE., NL, C,S, +*> A(i,j), LDA, XLEFT, XRIGHT ) +*> +*> Same, but upper triangle only: +*> +*> NL = MIN( K+1, N-i ) + 1 +*> CALL SLAROT( .TRUE., .TRUE., i+K.LT.N, NL, C,S, +*> A(i,i), LDA, XLEFT, XRIGHT ) +*> +*> Symmetric banded matrix in SB format, bandwidth K, +*> lower triangle only: +*> +*> [ same as for SY, except:] +*> . . . . +*> A(i+1-j,j), LDA-1, XLEFT, XRIGHT ) +*> +*> [ note that i+1-j is just MIN(i,K+1) ] +*> +*> Same, but upper triangle only: +*> . . . +*> A(K+1,i), LDA-1, XLEFT, XRIGHT ) +*> +*> Rotating columns is just the transpose of rotating rows, except +*> for GB and SB: (rotating columns i and i+1) +*> +*> GB: +*> j = MAX(1, i-KU ) +*> NL = MIN( N, i+KL+1 ) + 1-j +*> CALL SLAROT( .TRUE., i-KU.GE.1, i+KL.LT.N, NL, C,S, +*> A(KU+j+1-i,i),LDA-1, XTOP, XBOTTM ) +*> +*> [note that KU+j+1-i is just MAX(1,KU+2-i)] +*> +*> SB: (upper triangle) +*> +*> . . . . . . +*> A(K+j+1-i,i),LDA-1, XTOP, XBOTTM ) +*> +*> SB: (lower triangle) +*> +*> . . . . . . +*> A(1,i),LDA-1, XTOP, XBOTTM ) +*> +*>\endverbatim * * Arguments * ========= * -* LROWS - LOGICAL -* If .TRUE., then SLAROT will rotate two rows. If .FALSE., -* then it will rotate two columns. -* Not modified. -* -* LLEFT - LOGICAL -* If .TRUE., then XLEFT will be used instead of the -* corresponding element of A for the first element in the -* second row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) -* If .FALSE., then the corresponding element of A will be -* used. -* Not modified. -* -* LRIGHT - LOGICAL -* If .TRUE., then XRIGHT will be used instead of the -* corresponding element of A for the last element in the -* first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If -* .FALSE., then the corresponding element of A will be used. -* Not modified. +*> \verbatim +*> LROWS - LOGICAL +*> If .TRUE., then SLAROT will rotate two rows. If .FALSE., +*> then it will rotate two columns. +*> Not modified. +*> \endverbatim +*> \verbatim +*> LLEFT - LOGICAL +*> If .TRUE., then XLEFT will be used instead of the +*> corresponding element of A for the first element in the +*> second row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) +*> If .FALSE., then the corresponding element of A will be +*> used. +*> Not modified. +*> \endverbatim +*> \verbatim +*> LRIGHT - LOGICAL +*> If .TRUE., then XRIGHT will be used instead of the +*> corresponding element of A for the last element in the +*> first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If +*> .FALSE., then the corresponding element of A will be used. +*> Not modified. +*> \endverbatim +*> \verbatim +*> NL - INTEGER +*> The length of the rows (if LROWS=.TRUE.) or columns (if +*> LROWS=.FALSE.) to be rotated. If XLEFT and/or XRIGHT are +*> used, the columns/rows they are in should be included in +*> NL, e.g., if LLEFT = LRIGHT = .TRUE., then NL must be at +*> least 2. The number of rows/columns to be rotated +*> exclusive of those involving XLEFT and/or XRIGHT may +*> not be negative, i.e., NL minus how many of LLEFT and +*> LRIGHT are .TRUE. must be at least zero; if not, XERBLA +*> will be called. +*> Not modified. +*> \endverbatim +*> \verbatim +*> C, S - REAL +*> Specify the Givens rotation to be applied. If LROWS is +*> true, then the matrix ( c s ) +*> (-s c ) is applied from the left; +*> if false, then the transpose thereof is applied from the +*> right. For a Givens rotation, C**2 + S**2 should be 1, +*> but this is not checked. +*> Not modified. +*> \endverbatim +*> \verbatim +*> A - REAL array. +*> The array containing the rows/columns to be rotated. The +*> first element of A should be the upper left element to +*> be rotated. +*> Read and modified. +*> \endverbatim +*> \verbatim +*> LDA - INTEGER +*> The "effective" leading dimension of A. If A contains +*> a matrix stored in GE or SY format, then this is just +*> the leading dimension of A as dimensioned in the calling +*> routine. If A contains a matrix stored in band (GB or SB) +*> format, then this should be *one less* than the leading +*> dimension used in the calling routine. Thus, if +*> A were dimensioned A(LDA,*) in SLAROT, then A(1,j) would +*> be the j-th element in the first of the two rows +*> to be rotated, and A(2,j) would be the j-th in the second, +*> regardless of how the array may be stored in the calling +*> routine. [A cannot, however, actually be dimensioned thus, +*> since for band format, the row number may exceed LDA, which +*> is not legal FORTRAN.] +*> If LROWS=.TRUE., then LDA must be at least 1, otherwise +*> it must be at least NL minus the number of .TRUE. values +*> in XLEFT and XRIGHT. +*> Not modified. +*> \endverbatim +*> \verbatim +*> XLEFT - REAL +*> If LLEFT is .TRUE., then XLEFT will be used and modified +*> instead of A(2,1) (if LROWS=.TRUE.) or A(1,2) +*> (if LROWS=.FALSE.). +*> Read and modified. +*> \endverbatim +*> \verbatim +*> XRIGHT - REAL +*> If LRIGHT is .TRUE., then XRIGHT will be used and modified +*> instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1) +*> (if LROWS=.FALSE.). +*> Read and modified. +*> \endverbatim +*> +* +* Authors +* ======= * -* NL - INTEGER -* The length of the rows (if LROWS=.TRUE.) or columns (if -* LROWS=.FALSE.) to be rotated. If XLEFT and/or XRIGHT are -* used, the columns/rows they are in should be included in -* NL, e.g., if LLEFT = LRIGHT = .TRUE., then NL must be at -* least 2. The number of rows/columns to be rotated -* exclusive of those involving XLEFT and/or XRIGHT may -* not be negative, i.e., NL minus how many of LLEFT and -* LRIGHT are .TRUE. must be at least zero; if not, XERBLA -* will be called. -* Not modified. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* C, S - REAL -* Specify the Givens rotation to be applied. If LROWS is -* true, then the matrix ( c s ) -* (-s c ) is applied from the left; -* if false, then the transpose thereof is applied from the -* right. For a Givens rotation, C**2 + S**2 should be 1, -* but this is not checked. -* Not modified. +*> \date November 2011 * -* A - REAL array. -* The array containing the rows/columns to be rotated. The -* first element of A should be the upper left element to -* be rotated. -* Read and modified. +*> \ingroup real_matgen * -* LDA - INTEGER -* The "effective" leading dimension of A. If A contains -* a matrix stored in GE or SY format, then this is just -* the leading dimension of A as dimensioned in the calling -* routine. If A contains a matrix stored in band (GB or SB) -* format, then this should be *one less* than the leading -* dimension used in the calling routine. Thus, if -* A were dimensioned A(LDA,*) in SLAROT, then A(1,j) would -* be the j-th element in the first of the two rows -* to be rotated, and A(2,j) would be the j-th in the second, -* regardless of how the array may be stored in the calling -* routine. [A cannot, however, actually be dimensioned thus, -* since for band format, the row number may exceed LDA, which -* is not legal FORTRAN.] -* If LROWS=.TRUE., then LDA must be at least 1, otherwise -* it must be at least NL minus the number of .TRUE. values -* in XLEFT and XRIGHT. -* Not modified. +* ===================================================================== + SUBROUTINE SLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT, + $ XRIGHT ) * -* XLEFT - REAL -* If LLEFT is .TRUE., then XLEFT will be used and modified -* instead of A(2,1) (if LROWS=.TRUE.) or A(1,2) -* (if LROWS=.FALSE.). -* Read and modified. +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* XRIGHT - REAL -* If LRIGHT is .TRUE., then XRIGHT will be used and modified -* instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1) -* (if LROWS=.FALSE.). -* Read and modified. +* .. Scalar Arguments .. + LOGICAL LLEFT, LRIGHT, LROWS + INTEGER LDA, NL + REAL C, S, XLEFT, XRIGHT +* .. +* .. Array Arguments .. + REAL A( * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/slatm1.f b/TESTING/MATGEN/slatm1.f index 507b9df0..55415420 100644 --- a/TESTING/MATGEN/slatm1.f +++ b/TESTING/MATGEN/slatm1.f @@ -1,8 +1,146 @@ +*> \brief \b SLATM1 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO ) +* +* .. Scalar Arguments .. +* INTEGER IDIST, INFO, IRSIGN, MODE, N +* REAL COND +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* REAL D( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> SLATM1 computes the entries of D(1..N) as specified by +*> MODE, COND and IRSIGN. IDIST and ISEED determine the generation +*> of random numbers. SLATM1 is called by SLATMR to generate +*> random test matrices for LAPACK programs. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry describes how D is to be computed: +*> MODE = 0 means do not change D. +*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND +*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is REAL +*> On entry, used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] IRSIGN +*> \verbatim +*> IRSIGN is INTEGER +*> On entry, if MODE neither -6, 0 nor 6, determines sign of +*> entries of D +*> 0 => leave entries of D unchanged +*> 1 => multiply each entry of D by 1 or -1 with probability .5 +*> \endverbatim +*> +*> \param[in] IDIST +*> \verbatim +*> IDIST is CHARACTER*1 +*> On entry, IDIST specifies the type of distribution to be +*> used to generate a random matrix . +*> 1 => UNIFORM( 0, 1 ) +*> 2 => UNIFORM( -1, 1 ) +*> 3 => NORMAL( 0, 1 ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. The random number generator uses a +*> linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to SLATM1 +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is REAL array, dimension ( MIN( M , N ) ) +*> Array to be computed according to MODE, COND and IRSIGN. +*> May be changed on exit if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of entries of D. Not modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> 0 => normal termination +*> -1 => if MODE not in range -6 to 6 +*> -2 => if MODE neither -6, 0 nor 6, and +*> IRSIGN neither 0 nor 1 +*> -3 => if MODE neither -6, 0 nor 6 and COND less than 1 +*> -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3 +*> -7 => if N negative +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup real_matgen +* +* ===================================================================== SUBROUTINE SLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. INTEGER IDIST, INFO, IRSIGN, MODE, N @@ -13,79 +151,6 @@ REAL D( * ) * .. * -* Purpose -* ======= -* -* SLATM1 computes the entries of D(1..N) as specified by -* MODE, COND and IRSIGN. IDIST and ISEED determine the generation -* of random numbers. SLATM1 is called by SLATMR to generate -* random test matrices for LAPACK programs. -* -* Arguments -* ========= -* -* MODE (input) INTEGER -* On entry describes how D is to be computed: -* MODE = 0 means do not change D. -* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND -* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* Not modified. -* -* COND (input) REAL -* On entry, used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* IRSIGN (input) INTEGER -* On entry, if MODE neither -6, 0 nor 6, determines sign of -* entries of D -* 0 => leave entries of D unchanged -* 1 => multiply each entry of D by 1 or -1 with probability .5 -* -* IDIST (input) CHARACTER*1 -* On entry, IDIST specifies the type of distribution to be -* used to generate a random matrix . -* 1 => UNIFORM( 0, 1 ) -* 2 => UNIFORM( -1, 1 ) -* 3 => NORMAL( 0, 1 ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. The random number generator uses a -* linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to SLATM1 -* to continue the same random number sequence. -* Changed on exit. -* -* D (input/output) REAL array, dimension ( MIN( M , N ) ) -* Array to be computed according to MODE, COND and IRSIGN. -* May be changed on exit if MODE is nonzero. -* -* N (input) INTEGER -* Number of entries of D. Not modified. -* -* INFO (output) INTEGER -* 0 => normal termination -* -1 => if MODE not in range -6 to 6 -* -2 => if MODE neither -6, 0 nor 6, and -* IRSIGN neither 0 nor 1 -* -3 => if MODE neither -6, 0 nor 6 and COND less than 1 -* -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3 -* -7 => if N negative -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/slatm2.f b/TESTING/MATGEN/slatm2.f index 3320e249..81fa969b 100644 --- a/TESTING/MATGEN/slatm2.f +++ b/TESTING/MATGEN/slatm2.f @@ -1,9 +1,219 @@ +*> \brief \b SLATM2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* REAL FUNCTION SLATM2( M, N, I, J, KL, KU, IDIST, +* ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE ) +* +* .. Scalar Arguments .. +* +* INTEGER I, IDIST, IGRADE, IPVTNG, J, KL, KU, M, N +* REAL SPARSE +* .. +* +* .. Array Arguments .. +* +* INTEGER ISEED( 4 ), IWORK( * ) +* REAL D( * ), DL( * ), DR( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> SLATM2 returns the (I,J) entry of a random matrix of dimension +*> (M, N) described by the other paramters. It is called by the +*> SLATMR routine in order to build random test matrices. No error +*> checking on parameters is done, because this routine is called in +*> a tight loop by SLATMR which has already checked the parameters. +*> +*> Use of SLATM2 differs from SLATM3 in the order in which the random +*> number generator is called to fill in random matrix entries. +*> With SLATM2, the generator is called to fill in the pivoted matrix +*> columnwise. With SLATM3, the generator is called to fill in the +*> matrix columnwise, after which it is pivoted. Thus, SLATM3 can +*> be used to construct random matrices which differ only in their +*> order of rows and/or columns. SLATM2 is used to construct band +*> matrices while avoiding calling the random number generator for +*> entries outside the band (and therefore generating random numbers +*> +*> The matrix whose (I,J) entry is returned is constructed as +*> follows (this routine only computes one entry): +*> +*> If I is outside (1..M) or J is outside (1..N), return zero +*> (this is convenient for generating matrices in band format). +*> +*> Generate a matrix A with random entries of distribution IDIST. +*> +*> Set the diagonal to D. +*> +*> Grade the matrix, if desired, from the left (by DL) and/or +*> from the right (by DR or DL) as specified by IGRADE. +*> +*> Permute, if desired, the rows and/or columns as specified by +*> IPVTNG and IWORK. +*> +*> Band the matrix to have lower bandwidth KL and upper +*> bandwidth KU. +*> +*> Set random entries to zero as specified by SPARSE. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Number of rows of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of columns of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] I +*> \verbatim +*> I is INTEGER +*> Row of entry to be returned. Not modified. +*> \endverbatim +*> +*> \param[in] J +*> \verbatim +*> J is INTEGER +*> Column of entry to be returned. Not modified. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> Lower bandwidth. Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> Upper bandwidth. Not modified. +*> \endverbatim +*> +*> \param[in] IDIST +*> \verbatim +*> IDIST is INTEGER +*> On entry, IDIST specifies the type of distribution to be +*> used to generate a random matrix . +*> 1 => UNIFORM( 0, 1 ) +*> 2 => UNIFORM( -1, 1 ) +*> 3 => NORMAL( 0, 1 ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array of dimension ( 4 ) +*> Seed for random number generator. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is REAL array of dimension ( MIN( I , J ) ) +*> Diagonal entries of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] IGRADE +*> \verbatim +*> IGRADE is INTEGER +*> Specifies grading of matrix as follows: +*> 0 => no grading +*> 1 => matrix premultiplied by diag( DL ) +*> 2 => matrix postmultiplied by diag( DR ) +*> 3 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DR ) +*> 4 => matrix premultiplied by diag( DL ) and +*> postmultiplied by inv( diag( DL ) ) +*> 5 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DL ) +*> Not modified. +*> \endverbatim +*> +*> \param[in] DL +*> \verbatim +*> DL is REAL array ( I or J, as appropriate ) +*> Left scale factors for grading matrix. Not modified. +*> \endverbatim +*> +*> \param[in] DR +*> \verbatim +*> DR is REAL array ( I or J, as appropriate ) +*> Right scale factors for grading matrix. Not modified. +*> \endverbatim +*> +*> \param[in] IPVTNG +*> \verbatim +*> IPVTNG is INTEGER +*> On entry specifies pivoting permutations as follows: +*> 0 => none. +*> 1 => row pivoting. +*> 2 => column pivoting. +*> 3 => full pivoting, i.e., on both sides. +*> Not modified. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array ( I or J, as appropriate ) +*> This array specifies the permutation used. The +*> row (or column) in position K was originally in +*> position IWORK( K ). +*> This differs from IWORK for SLATM3. Not modified. +*> \endverbatim +*> +*> \param[in] SPARSE +*> \verbatim +*> SPARSE is REAL between 0. and 1. +*> On entry specifies the sparsity of the matrix +*> if sparse matix is to be generated. +*> SPARSE should lie between 0 and 1. +*> A uniform ( 0, 1 ) random number x is generated and +*> compared to SPARSE; if x is larger the matrix entry +*> is unchanged and if x is smaller the entry is set +*> to zero. Thus on the average a fraction SPARSE of the +*> entries will be set to zero. +*> Not modified. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup real_matgen +* +* ===================================================================== REAL FUNCTION SLATM2( M, N, I, J, KL, KU, IDIST, $ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. * @@ -17,126 +227,6 @@ REAL D( * ), DL( * ), DR( * ) * .. * -* Purpose -* ======= -* -* SLATM2 returns the (I,J) entry of a random matrix of dimension -* (M, N) described by the other paramters. It is called by the -* SLATMR routine in order to build random test matrices. No error -* checking on parameters is done, because this routine is called in -* a tight loop by SLATMR which has already checked the parameters. -* -* Use of SLATM2 differs from SLATM3 in the order in which the random -* number generator is called to fill in random matrix entries. -* With SLATM2, the generator is called to fill in the pivoted matrix -* columnwise. With SLATM3, the generator is called to fill in the -* matrix columnwise, after which it is pivoted. Thus, SLATM3 can -* be used to construct random matrices which differ only in their -* order of rows and/or columns. SLATM2 is used to construct band -* matrices while avoiding calling the random number generator for -* entries outside the band (and therefore generating random numbers -* -* The matrix whose (I,J) entry is returned is constructed as -* follows (this routine only computes one entry): -* -* If I is outside (1..M) or J is outside (1..N), return zero -* (this is convenient for generating matrices in band format). -* -* Generate a matrix A with random entries of distribution IDIST. -* -* Set the diagonal to D. -* -* Grade the matrix, if desired, from the left (by DL) and/or -* from the right (by DR or DL) as specified by IGRADE. -* -* Permute, if desired, the rows and/or columns as specified by -* IPVTNG and IWORK. -* -* Band the matrix to have lower bandwidth KL and upper -* bandwidth KU. -* -* Set random entries to zero as specified by SPARSE. -* -* Arguments -* ========= -* -* M (input) INTEGER -* Number of rows of matrix. Not modified. -* -* N (input) INTEGER -* Number of columns of matrix. Not modified. -* -* I (input) INTEGER -* Row of entry to be returned. Not modified. -* -* J (input) INTEGER -* Column of entry to be returned. Not modified. -* -* KL (input) INTEGER -* Lower bandwidth. Not modified. -* -* KU (input) INTEGER -* Upper bandwidth. Not modified. -* -* IDIST (input) INTEGER -* On entry, IDIST specifies the type of distribution to be -* used to generate a random matrix . -* 1 => UNIFORM( 0, 1 ) -* 2 => UNIFORM( -1, 1 ) -* 3 => NORMAL( 0, 1 ) -* Not modified. -* -* ISEED (input/output) INTEGER array of dimension ( 4 ) -* Seed for random number generator. -* Changed on exit. -* -* D (input) REAL array of dimension ( MIN( I , J ) ) -* Diagonal entries of matrix. Not modified. -* -* IGRADE (input) INTEGER -* Specifies grading of matrix as follows: -* 0 => no grading -* 1 => matrix premultiplied by diag( DL ) -* 2 => matrix postmultiplied by diag( DR ) -* 3 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DR ) -* 4 => matrix premultiplied by diag( DL ) and -* postmultiplied by inv( diag( DL ) ) -* 5 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DL ) -* Not modified. -* -* DL (input) REAL array ( I or J, as appropriate ) -* Left scale factors for grading matrix. Not modified. -* -* DR (input) REAL array ( I or J, as appropriate ) -* Right scale factors for grading matrix. Not modified. -* -* IPVTNG (input) INTEGER -* On entry specifies pivoting permutations as follows: -* 0 => none. -* 1 => row pivoting. -* 2 => column pivoting. -* 3 => full pivoting, i.e., on both sides. -* Not modified. -* -* IWORK (workspace) INTEGER array ( I or J, as appropriate ) -* This array specifies the permutation used. The -* row (or column) in position K was originally in -* position IWORK( K ). -* This differs from IWORK for SLATM3. Not modified. -* -* SPARSE (input) REAL between 0. and 1. -* On entry specifies the sparsity of the matrix -* if sparse matix is to be generated. -* SPARSE should lie between 0 and 1. -* A uniform ( 0, 1 ) random number x is generated and -* compared to SPARSE; if x is larger the matrix entry -* is unchanged and if x is smaller the entry is set -* to zero. Thus on the average a fraction SPARSE of the -* entries will be set to zero. -* Not modified. -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/slatm3.f b/TESTING/MATGEN/slatm3.f index 5dc4e29b..3c639920 100644 --- a/TESTING/MATGEN/slatm3.f +++ b/TESTING/MATGEN/slatm3.f @@ -1,10 +1,237 @@ +*> \brief \b SLATM3 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* REAL FUNCTION SLATM3( M, N, I, J, ISUB, JSUB, KL, KU, +* IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, +* SPARSE ) +* +* .. Scalar Arguments .. +* +* INTEGER I, IDIST, IGRADE, IPVTNG, ISUB, J, JSUB, KL, +* $ KU, M, N +* REAL SPARSE +* .. +* +* .. Array Arguments .. +* +* INTEGER ISEED( 4 ), IWORK( * ) +* REAL D( * ), DL( * ), DR( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> SLATM3 returns the (ISUB,JSUB) entry of a random matrix of +*> dimension (M, N) described by the other paramters. (ISUB,JSUB) +*> is the final position of the (I,J) entry after pivoting +*> according to IPVTNG and IWORK. SLATM3 is called by the +*> SLATMR routine in order to build random test matrices. No error +*> checking on parameters is done, because this routine is called in +*> a tight loop by SLATMR which has already checked the parameters. +*> +*> Use of SLATM3 differs from SLATM2 in the order in which the random +*> number generator is called to fill in random matrix entries. +*> With SLATM2, the generator is called to fill in the pivoted matrix +*> columnwise. With SLATM3, the generator is called to fill in the +*> matrix columnwise, after which it is pivoted. Thus, SLATM3 can +*> be used to construct random matrices which differ only in their +*> order of rows and/or columns. SLATM2 is used to construct band +*> matrices while avoiding calling the random number generator for +*> entries outside the band (and therefore generating random numbers +*> in different orders for different pivot orders). +*> +*> The matrix whose (ISUB,JSUB) entry is returned is constructed as +*> follows (this routine only computes one entry): +*> +*> If ISUB is outside (1..M) or JSUB is outside (1..N), return zero +*> (this is convenient for generating matrices in band format). +*> +*> Generate a matrix A with random entries of distribution IDIST. +*> +*> Set the diagonal to D. +*> +*> Grade the matrix, if desired, from the left (by DL) and/or +*> from the right (by DR or DL) as specified by IGRADE. +*> +*> Permute, if desired, the rows and/or columns as specified by +*> IPVTNG and IWORK. +*> +*> Band the matrix to have lower bandwidth KL and upper +*> bandwidth KU. +*> +*> Set random entries to zero as specified by SPARSE. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Number of rows of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of columns of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] I +*> \verbatim +*> I is INTEGER +*> Row of unpivoted entry to be returned. Not modified. +*> \endverbatim +*> +*> \param[in] J +*> \verbatim +*> J is INTEGER +*> Column of unpivoted entry to be returned. Not modified. +*> \endverbatim +*> +*> \param[in,out] ISUB +*> \verbatim +*> ISUB is INTEGER +*> Row of pivoted entry to be returned. Changed on exit. +*> \endverbatim +*> +*> \param[in,out] JSUB +*> \verbatim +*> JSUB is INTEGER +*> Column of pivoted entry to be returned. Changed on exit. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> Lower bandwidth. Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> Upper bandwidth. Not modified. +*> \endverbatim +*> +*> \param[in] IDIST +*> \verbatim +*> IDIST is INTEGER +*> On entry, IDIST specifies the type of distribution to be +*> used to generate a random matrix . +*> 1 => UNIFORM( 0, 1 ) +*> 2 => UNIFORM( -1, 1 ) +*> 3 => NORMAL( 0, 1 ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array of dimension ( 4 ) +*> Seed for random number generator. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is REAL array of dimension ( MIN( I , J ) ) +*> Diagonal entries of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] IGRADE +*> \verbatim +*> IGRADE is INTEGER +*> Specifies grading of matrix as follows: +*> 0 => no grading +*> 1 => matrix premultiplied by diag( DL ) +*> 2 => matrix postmultiplied by diag( DR ) +*> 3 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DR ) +*> 4 => matrix premultiplied by diag( DL ) and +*> postmultiplied by inv( diag( DL ) ) +*> 5 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DL ) +*> Not modified. +*> \endverbatim +*> +*> \param[in] DL +*> \verbatim +*> DL is REAL array ( I or J, as appropriate ) +*> Left scale factors for grading matrix. Not modified. +*> \endverbatim +*> +*> \param[in] DR +*> \verbatim +*> DR is REAL array ( I or J, as appropriate ) +*> Right scale factors for grading matrix. Not modified. +*> \endverbatim +*> +*> \param[in] IPVTNG +*> \verbatim +*> IPVTNG is INTEGER +*> On entry specifies pivoting permutations as follows: +*> 0 => none. +*> 1 => row pivoting. +*> 2 => column pivoting. +*> 3 => full pivoting, i.e., on both sides. +*> Not modified. +*> \endverbatim +*> +*> \param[in] IWORK +*> \verbatim +*> IWORK is INTEGER array ( I or J, as appropriate ) +*> This array specifies the permutation used. The +*> row (or column) originally in position K is in +*> position IWORK( K ) after pivoting. +*> This differs from IWORK for SLATM2. Not modified. +*> \endverbatim +*> +*> \param[in] SPARSE +*> \verbatim +*> SPARSE is REAL between 0. and 1. +*> On entry specifies the sparsity of the matrix +*> if sparse matix is to be generated. +*> SPARSE should lie between 0 and 1. +*> A uniform ( 0, 1 ) random number x is generated and +*> compared to SPARSE; if x is larger the matrix entry +*> is unchanged and if x is smaller the entry is set +*> to zero. Thus on the average a fraction SPARSE of the +*> entries will be set to zero. +*> Not modified. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup real_matgen +* +* ===================================================================== REAL FUNCTION SLATM3( M, N, I, J, ISUB, JSUB, KL, KU, $ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, $ SPARSE ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. * @@ -19,135 +246,6 @@ REAL D( * ), DL( * ), DR( * ) * .. * -* Purpose -* ======= -* -* SLATM3 returns the (ISUB,JSUB) entry of a random matrix of -* dimension (M, N) described by the other paramters. (ISUB,JSUB) -* is the final position of the (I,J) entry after pivoting -* according to IPVTNG and IWORK. SLATM3 is called by the -* SLATMR routine in order to build random test matrices. No error -* checking on parameters is done, because this routine is called in -* a tight loop by SLATMR which has already checked the parameters. -* -* Use of SLATM3 differs from SLATM2 in the order in which the random -* number generator is called to fill in random matrix entries. -* With SLATM2, the generator is called to fill in the pivoted matrix -* columnwise. With SLATM3, the generator is called to fill in the -* matrix columnwise, after which it is pivoted. Thus, SLATM3 can -* be used to construct random matrices which differ only in their -* order of rows and/or columns. SLATM2 is used to construct band -* matrices while avoiding calling the random number generator for -* entries outside the band (and therefore generating random numbers -* in different orders for different pivot orders). -* -* The matrix whose (ISUB,JSUB) entry is returned is constructed as -* follows (this routine only computes one entry): -* -* If ISUB is outside (1..M) or JSUB is outside (1..N), return zero -* (this is convenient for generating matrices in band format). -* -* Generate a matrix A with random entries of distribution IDIST. -* -* Set the diagonal to D. -* -* Grade the matrix, if desired, from the left (by DL) and/or -* from the right (by DR or DL) as specified by IGRADE. -* -* Permute, if desired, the rows and/or columns as specified by -* IPVTNG and IWORK. -* -* Band the matrix to have lower bandwidth KL and upper -* bandwidth KU. -* -* Set random entries to zero as specified by SPARSE. -* -* Arguments -* ========= -* -* M (input) INTEGER -* Number of rows of matrix. Not modified. -* -* N (input) INTEGER -* Number of columns of matrix. Not modified. -* -* I (input) INTEGER -* Row of unpivoted entry to be returned. Not modified. -* -* J (input) INTEGER -* Column of unpivoted entry to be returned. Not modified. -* -* ISUB (input/output) INTEGER -* Row of pivoted entry to be returned. Changed on exit. -* -* JSUB (input/output) INTEGER -* Column of pivoted entry to be returned. Changed on exit. -* -* KL (input) INTEGER -* Lower bandwidth. Not modified. -* -* KU (input) INTEGER -* Upper bandwidth. Not modified. -* -* IDIST (input) INTEGER -* On entry, IDIST specifies the type of distribution to be -* used to generate a random matrix . -* 1 => UNIFORM( 0, 1 ) -* 2 => UNIFORM( -1, 1 ) -* 3 => NORMAL( 0, 1 ) -* Not modified. -* -* ISEED (input/output) INTEGER array of dimension ( 4 ) -* Seed for random number generator. -* Changed on exit. -* -* D (input) REAL array of dimension ( MIN( I , J ) ) -* Diagonal entries of matrix. Not modified. -* -* IGRADE (input) INTEGER -* Specifies grading of matrix as follows: -* 0 => no grading -* 1 => matrix premultiplied by diag( DL ) -* 2 => matrix postmultiplied by diag( DR ) -* 3 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DR ) -* 4 => matrix premultiplied by diag( DL ) and -* postmultiplied by inv( diag( DL ) ) -* 5 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DL ) -* Not modified. -* -* DL (input) REAL array ( I or J, as appropriate ) -* Left scale factors for grading matrix. Not modified. -* -* DR (input) REAL array ( I or J, as appropriate ) -* Right scale factors for grading matrix. Not modified. -* -* IPVTNG (input) INTEGER -* On entry specifies pivoting permutations as follows: -* 0 => none. -* 1 => row pivoting. -* 2 => column pivoting. -* 3 => full pivoting, i.e., on both sides. -* Not modified. -* -* IWORK (input) INTEGER array ( I or J, as appropriate ) -* This array specifies the permutation used. The -* row (or column) originally in position K is in -* position IWORK( K ) after pivoting. -* This differs from IWORK for SLATM2. Not modified. -* -* SPARSE (input) REAL between 0. and 1. -* On entry specifies the sparsity of the matrix -* if sparse matix is to be generated. -* SPARSE should lie between 0 and 1. -* A uniform ( 0, 1 ) random number x is generated and -* compared to SPARSE; if x is larger the matrix entry -* is unchanged and if x is smaller the entry is set -* to zero. Thus on the average a fraction SPARSE of the -* entries will be set to zero. -* Not modified. -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/slatm5.f b/TESTING/MATGEN/slatm5.f index 1239ec64..ef49ad8e 100644 --- a/TESTING/MATGEN/slatm5.f +++ b/TESTING/MATGEN/slatm5.f @@ -1,177 +1,292 @@ - SUBROUTINE SLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD, - $ E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA, - $ QBLCKB ) -* -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N, - $ PRTYPE, QBLCKA, QBLCKB - REAL ALPHA -* .. -* .. Array Arguments .. - REAL A( LDA, * ), B( LDB, * ), C( LDC, * ), - $ D( LDD, * ), E( LDE, * ), F( LDF, * ), - $ L( LDL, * ), R( LDR, * ) -* .. -* +*> \brief \b SLATM5 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD, +* E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA, +* QBLCKB ) +* +* .. Scalar Arguments .. +* INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N, +* $ PRTYPE, QBLCKA, QBLCKB +* REAL ALPHA +* .. +* .. Array Arguments .. +* REAL A( LDA, * ), B( LDB, * ), C( LDC, * ), +* $ D( LDD, * ), E( LDE, * ), F( LDF, * ), +* $ L( LDL, * ), R( LDR, * ) +* .. +* * Purpose * ======= * -* SLATM5 generates matrices involved in the Generalized Sylvester -* equation: -* -* A * R - L * B = C -* D * R - L * E = F -* -* They also satisfy (the diagonalization condition) -* -* [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] ) -* [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] ) -* +*>\details \b Purpose: +*>\verbatim +*> +*> SLATM5 generates matrices involved in the Generalized Sylvester +*> equation: +*> +*> A * R - L * B = C +*> D * R - L * E = F +*> +*> They also satisfy (the diagonalization condition) +*> +*> [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] ) +*> [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] ) +*> +*> +*>\endverbatim * * Arguments * ========= * -* PRTYPE (input) INTEGER -* "Points" to a certian type of the matrices to generate -* (see futher details). -* -* M (input) INTEGER -* Specifies the order of A and D and the number of rows in -* C, F, R and L. -* -* N (input) INTEGER -* Specifies the order of B and E and the number of columns in -* C, F, R and L. -* -* A (output) REAL array, dimension (LDA, M). -* On exit A M-by-M is initialized according to PRTYPE. -* -* LDA (input) INTEGER -* The leading dimension of A. -* -* B (output) REAL array, dimension (LDB, N). -* On exit B N-by-N is initialized according to PRTYPE. -* -* LDB (input) INTEGER -* The leading dimension of B. -* -* C (output) REAL array, dimension (LDC, N). -* On exit C M-by-N is initialized according to PRTYPE. -* -* LDC (input) INTEGER -* The leading dimension of C. -* -* D (output) REAL array, dimension (LDD, M). -* On exit D M-by-M is initialized according to PRTYPE. -* -* LDD (input) INTEGER -* The leading dimension of D. -* -* E (output) REAL array, dimension (LDE, N). -* On exit E N-by-N is initialized according to PRTYPE. -* -* LDE (input) INTEGER -* The leading dimension of E. -* -* F (output) REAL array, dimension (LDF, N). -* On exit F M-by-N is initialized according to PRTYPE. -* -* LDF (input) INTEGER -* The leading dimension of F. -* -* R (output) REAL array, dimension (LDR, N). -* On exit R M-by-N is initialized according to PRTYPE. -* -* LDR (input) INTEGER -* The leading dimension of R. -* -* L (output) REAL array, dimension (LDL, N). -* On exit L M-by-N is initialized according to PRTYPE. -* -* LDL (input) INTEGER -* The leading dimension of L. +*> \param[in] PRTYPE +*> \verbatim +*> PRTYPE is INTEGER +*> "Points" to a certian type of the matrices to generate +*> (see futher details). +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Specifies the order of A and D and the number of rows in +*> C, F, R and L. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Specifies the order of B and E and the number of columns in +*> C, F, R and L. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is REAL array, dimension (LDA, M). +*> On exit A M-by-M is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of A. +*> \endverbatim +*> +*> \param[out] B +*> \verbatim +*> B is REAL array, dimension (LDB, N). +*> On exit B N-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of B. +*> \endverbatim +*> +*> \param[out] C +*> \verbatim +*> C is REAL array, dimension (LDC, N). +*> On exit C M-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> The leading dimension of C. +*> \endverbatim +*> +*> \param[out] D +*> \verbatim +*> D is REAL array, dimension (LDD, M). +*> On exit D M-by-M is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDD +*> \verbatim +*> LDD is INTEGER +*> The leading dimension of D. +*> \endverbatim +*> +*> \param[out] E +*> \verbatim +*> E is REAL array, dimension (LDE, N). +*> On exit E N-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDE +*> \verbatim +*> LDE is INTEGER +*> The leading dimension of E. +*> \endverbatim +*> +*> \param[out] F +*> \verbatim +*> F is REAL array, dimension (LDF, N). +*> On exit F M-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDF +*> \verbatim +*> LDF is INTEGER +*> The leading dimension of F. +*> \endverbatim +*> +*> \param[out] R +*> \verbatim +*> R is REAL array, dimension (LDR, N). +*> On exit R M-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDR +*> \verbatim +*> LDR is INTEGER +*> The leading dimension of R. +*> \endverbatim +*> +*> \param[out] L +*> \verbatim +*> L is REAL array, dimension (LDL, N). +*> On exit L M-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDL +*> \verbatim +*> LDL is INTEGER +*> The leading dimension of L. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> Parameter used in generating PRTYPE = 1 and 5 matrices. +*> \endverbatim +*> +*> \param[in] QBLCKA +*> \verbatim +*> QBLCKA is INTEGER +*> When PRTYPE = 3, specifies the distance between 2-by-2 +*> blocks on the diagonal in A. Otherwise, QBLCKA is not +*> referenced. QBLCKA > 1. +*> \endverbatim +*> +*> \param[in] QBLCKB +*> \verbatim +*> QBLCKB is INTEGER +*> When PRTYPE = 3, specifies the distance between 2-by-2 +*> blocks on the diagonal in B. Otherwise, QBLCKB is not +*> referenced. QBLCKB > 1. +*> \endverbatim +*> +* +* Authors +* ======= * -* ALPHA (input) REAL -* Parameter used in generating PRTYPE = 1 and 5 matrices. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* QBLCKA (input) INTEGER -* When PRTYPE = 3, specifies the distance between 2-by-2 -* blocks on the diagonal in A. Otherwise, QBLCKA is not -* referenced. QBLCKA > 1. +*> \date November 2011 * -* QBLCKB (input) INTEGER -* When PRTYPE = 3, specifies the distance between 2-by-2 -* blocks on the diagonal in B. Otherwise, QBLCKB is not -* referenced. QBLCKB > 1. +*> \ingroup real_matgen * * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices +*> +*> A : if (i == j) then A(i, j) = 1.0 +*> if (j == i + 1) then A(i, j) = -1.0 +*> else A(i, j) = 0.0, i, j = 1...M +*> +*> B : if (i == j) then B(i, j) = 1.0 - ALPHA +*> if (j == i + 1) then B(i, j) = 1.0 +*> else B(i, j) = 0.0, i, j = 1...N +*> +*> D : if (i == j) then D(i, j) = 1.0 +*> else D(i, j) = 0.0, i, j = 1...M +*> +*> E : if (i == j) then E(i, j) = 1.0 +*> else E(i, j) = 0.0, i, j = 1...N +*> +*> L = R are chosen from [-10...10], +*> which specifies the right hand sides (C, F). +*> +*> PRTYPE = 2 or 3: Triangular and/or quasi- triangular. +*> +*> A : if (i <= j) then A(i, j) = [-1...1] +*> else A(i, j) = 0.0, i, j = 1...M +*> +*> if (PRTYPE = 3) then +*> A(k + 1, k + 1) = A(k, k) +*> A(k + 1, k) = [-1...1] +*> sign(A(k, k + 1) = -(sin(A(k + 1, k)) +*> k = 1, M - 1, QBLCKA +*> +*> B : if (i <= j) then B(i, j) = [-1...1] +*> else B(i, j) = 0.0, i, j = 1...N +*> +*> if (PRTYPE = 3) then +*> B(k + 1, k + 1) = B(k, k) +*> B(k + 1, k) = [-1...1] +*> sign(B(k, k + 1) = -(sign(B(k + 1, k)) +*> k = 1, N - 1, QBLCKB +*> +*> D : if (i <= j) then D(i, j) = [-1...1]. +*> else D(i, j) = 0.0, i, j = 1...M +*> +*> +*> E : if (i <= j) then D(i, j) = [-1...1] +*> else E(i, j) = 0.0, i, j = 1...N +*> +*> L, R are chosen from [-10...10], +*> which specifies the right hand sides (C, F). +*> +*> PRTYPE = 4 Full +*> A(i, j) = [-10...10] +*> D(i, j) = [-1...1] i,j = 1...M +*> B(i, j) = [-10...10] +*> E(i, j) = [-1...1] i,j = 1...N +*> R(i, j) = [-10...10] +*> L(i, j) = [-1...1] i = 1..M ,j = 1...N +*> +*> L, R specifies the right hand sides (C, F). +*> +*> PRTYPE = 5 special case common and/or close eigs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD, + $ E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA, + $ QBLCKB ) * -* PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices -* -* A : if (i == j) then A(i, j) = 1.0 -* if (j == i + 1) then A(i, j) = -1.0 -* else A(i, j) = 0.0, i, j = 1...M -* -* B : if (i == j) then B(i, j) = 1.0 - ALPHA -* if (j == i + 1) then B(i, j) = 1.0 -* else B(i, j) = 0.0, i, j = 1...N -* -* D : if (i == j) then D(i, j) = 1.0 -* else D(i, j) = 0.0, i, j = 1...M -* -* E : if (i == j) then E(i, j) = 1.0 -* else E(i, j) = 0.0, i, j = 1...N -* -* L = R are chosen from [-10...10], -* which specifies the right hand sides (C, F). -* -* PRTYPE = 2 or 3: Triangular and/or quasi- triangular. -* -* A : if (i <= j) then A(i, j) = [-1...1] -* else A(i, j) = 0.0, i, j = 1...M -* -* if (PRTYPE = 3) then -* A(k + 1, k + 1) = A(k, k) -* A(k + 1, k) = [-1...1] -* sign(A(k, k + 1) = -(sin(A(k + 1, k)) -* k = 1, M - 1, QBLCKA -* -* B : if (i <= j) then B(i, j) = [-1...1] -* else B(i, j) = 0.0, i, j = 1...N -* -* if (PRTYPE = 3) then -* B(k + 1, k + 1) = B(k, k) -* B(k + 1, k) = [-1...1] -* sign(B(k, k + 1) = -(sign(B(k + 1, k)) -* k = 1, N - 1, QBLCKB -* -* D : if (i <= j) then D(i, j) = [-1...1]. -* else D(i, j) = 0.0, i, j = 1...M -* -* -* E : if (i <= j) then D(i, j) = [-1...1] -* else E(i, j) = 0.0, i, j = 1...N -* -* L, R are chosen from [-10...10], -* which specifies the right hand sides (C, F). -* -* PRTYPE = 4 Full -* A(i, j) = [-10...10] -* D(i, j) = [-1...1] i,j = 1...M -* B(i, j) = [-10...10] -* E(i, j) = [-1...1] i,j = 1...N -* R(i, j) = [-10...10] -* L(i, j) = [-1...1] i = 1..M ,j = 1...N -* -* L, R specifies the right hand sides (C, F). +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* PRTYPE = 5 special case common and/or close eigs. +* .. Scalar Arguments .. + INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N, + $ PRTYPE, QBLCKA, QBLCKB + REAL ALPHA +* .. +* .. Array Arguments .. + REAL A( LDA, * ), B( LDB, * ), C( LDC, * ), + $ D( LDD, * ), E( LDE, * ), F( LDF, * ), + $ L( LDL, * ), R( LDR, * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/slatm6.f b/TESTING/MATGEN/slatm6.f index 093c955b..f209b335 100644 --- a/TESTING/MATGEN/slatm6.f +++ b/TESTING/MATGEN/slatm6.f @@ -1,107 +1,197 @@ - SUBROUTINE SLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA, - $ BETA, WX, WY, S, DIF ) -* -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER LDA, LDX, LDY, N, TYPE - REAL ALPHA, BETA, WX, WY -* .. -* .. Array Arguments .. - REAL A( LDA, * ), B( LDA, * ), DIF( * ), S( * ), - $ X( LDX, * ), Y( LDY, * ) -* .. -* +*> \brief \b SLATM6 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA, +* BETA, WX, WY, S, DIF ) +* +* .. Scalar Arguments .. +* INTEGER LDA, LDX, LDY, N, TYPE +* REAL ALPHA, BETA, WX, WY +* .. +* .. Array Arguments .. +* REAL A( LDA, * ), B( LDA, * ), DIF( * ), S( * ), +* $ X( LDX, * ), Y( LDY, * ) +* .. +* * Purpose * ======= * -* SLATM6 generates test matrices for the generalized eigenvalue -* problem, their corresponding right and left eigenvector matrices, -* and also reciprocal condition numbers for all eigenvalues and -* the reciprocal condition numbers of eigenvectors corresponding to -* the 1th and 5th eigenvalues. -* -* Test Matrices -* ============= -* -* Two kinds of test matrix pairs -* -* (A, B) = inverse(YH) * (Da, Db) * inverse(X) -* -* are used in the tests: -* -* Type 1: -* Da = 1+a 0 0 0 0 Db = 1 0 0 0 0 -* 0 2+a 0 0 0 0 1 0 0 0 -* 0 0 3+a 0 0 0 0 1 0 0 -* 0 0 0 4+a 0 0 0 0 1 0 -* 0 0 0 0 5+a , 0 0 0 0 1 , and -* -* Type 2: -* Da = 1 -1 0 0 0 Db = 1 0 0 0 0 -* 1 1 0 0 0 0 1 0 0 0 -* 0 0 1 0 0 0 0 1 0 0 -* 0 0 0 1+a 1+b 0 0 0 1 0 -* 0 0 0 -1-b 1+a , 0 0 0 0 1 . -* -* In both cases the same inverse(YH) and inverse(X) are used to compute -* (A, B), giving the exact eigenvectors to (A,B) as (YH, X): -* -* YH: = 1 0 -y y -y X = 1 0 -x -x x -* 0 1 -y y -y 0 1 x -x -x -* 0 0 1 0 0 0 0 1 0 0 -* 0 0 0 1 0 0 0 0 1 0 -* 0 0 0 0 1, 0 0 0 0 1 , -* -* where a, b, x and y will have all values independently of each other. +*>\details \b Purpose: +*>\verbatim +*> +*> SLATM6 generates test matrices for the generalized eigenvalue +*> problem, their corresponding right and left eigenvector matrices, +*> and also reciprocal condition numbers for all eigenvalues and +*> the reciprocal condition numbers of eigenvectors corresponding to +*> the 1th and 5th eigenvalues. +*> +*> Test Matrices +*> ============= +*> +*> Two kinds of test matrix pairs +*> +*> (A, B) = inverse(YH) * (Da, Db) * inverse(X) +*> +*> are used in the tests: +*> +*> Type 1: +*> Da = 1+a 0 0 0 0 Db = 1 0 0 0 0 +*> 0 2+a 0 0 0 0 1 0 0 0 +*> 0 0 3+a 0 0 0 0 1 0 0 +*> 0 0 0 4+a 0 0 0 0 1 0 +*> 0 0 0 0 5+a , 0 0 0 0 1 , and +*> +*> Type 2: +*> Da = 1 -1 0 0 0 Db = 1 0 0 0 0 +*> 1 1 0 0 0 0 1 0 0 0 +*> 0 0 1 0 0 0 0 1 0 0 +*> 0 0 0 1+a 1+b 0 0 0 1 0 +*> 0 0 0 -1-b 1+a , 0 0 0 0 1 . +*> +*> In both cases the same inverse(YH) and inverse(X) are used to compute +*> (A, B), giving the exact eigenvectors to (A,B) as (YH, X): +*> +*> YH: = 1 0 -y y -y X = 1 0 -x -x x +*> 0 1 -y y -y 0 1 x -x -x +*> 0 0 1 0 0 0 0 1 0 0 +*> 0 0 0 1 0 0 0 0 1 0 +*> 0 0 0 0 1, 0 0 0 0 1 , +*> +*> where a, b, x and y will have all values independently of each other. +*> +*>\endverbatim * * Arguments * ========= * -* TYPE (input) INTEGER -* Specifies the problem type (see futher details). -* -* N (input) INTEGER -* Size of the matrices A and B. -* -* A (output) REAL array, dimension (LDA, N). -* On exit A N-by-N is initialized according to TYPE. -* -* LDA (input) INTEGER -* The leading dimension of A and of B. -* -* B (output) REAL array, dimension (LDA, N). -* On exit B N-by-N is initialized according to TYPE. -* -* X (output) REAL array, dimension (LDX, N). -* On exit X is the N-by-N matrix of right eigenvectors. -* -* LDX (input) INTEGER -* The leading dimension of X. -* -* Y (output) REAL array, dimension (LDY, N). -* On exit Y is the N-by-N matrix of left eigenvectors. +*> \param[in] TYPE +*> \verbatim +*> TYPE is INTEGER +*> Specifies the problem type (see futher details). +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Size of the matrices A and B. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is REAL array, dimension (LDA, N). +*> On exit A N-by-N is initialized according to TYPE. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of A and of B. +*> \endverbatim +*> +*> \param[out] B +*> \verbatim +*> B is REAL array, dimension (LDA, N). +*> On exit B N-by-N is initialized according to TYPE. +*> \endverbatim +*> +*> \param[out] X +*> \verbatim +*> X is REAL array, dimension (LDX, N). +*> On exit X is the N-by-N matrix of right eigenvectors. +*> \endverbatim +*> +*> \param[in] LDX +*> \verbatim +*> LDX is INTEGER +*> The leading dimension of X. +*> \endverbatim +*> +*> \param[out] Y +*> \verbatim +*> Y is REAL array, dimension (LDY, N). +*> On exit Y is the N-by-N matrix of left eigenvectors. +*> \endverbatim +*> +*> \param[in] LDY +*> \verbatim +*> LDY is INTEGER +*> The leading dimension of Y. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is REAL +*> \endverbatim +*> \verbatim +*> Weighting constants for matrix A. +*> \endverbatim +*> +*> \param[in] WX +*> \verbatim +*> WX is REAL +*> Constant for right eigenvector matrix. +*> \endverbatim +*> +*> \param[in] WY +*> \verbatim +*> WY is REAL +*> Constant for left eigenvector matrix. +*> \endverbatim +*> +*> \param[out] S +*> \verbatim +*> S is REAL array, dimension (N) +*> S(i) is the reciprocal condition number for eigenvalue i. +*> \endverbatim +*> +*> \param[out] DIF +*> \verbatim +*> DIF is REAL array, dimension (N) +*> DIF(i) is the reciprocal condition number for eigenvector i. +*> \endverbatim +*> +* +* Authors +* ======= * -* LDY (input) INTEGER -* The leading dimension of Y. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* ALPHA (input) REAL -* BETA (input) REAL -* Weighting constants for matrix A. +*> \date November 2011 * -* WX (input) REAL -* Constant for right eigenvector matrix. +*> \ingroup real_matgen * -* WY (input) REAL -* Constant for left eigenvector matrix. +* ===================================================================== + SUBROUTINE SLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA, + $ BETA, WX, WY, S, DIF ) * -* S (output) REAL array, dimension (N) -* S(i) is the reciprocal condition number for eigenvalue i. +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* DIF (output) REAL array, dimension (N) -* DIF(i) is the reciprocal condition number for eigenvector i. +* .. Scalar Arguments .. + INTEGER LDA, LDX, LDY, N, TYPE + REAL ALPHA, BETA, WX, WY +* .. +* .. Array Arguments .. + REAL A( LDA, * ), B( LDA, * ), DIF( * ), S( * ), + $ X( LDX, * ), Y( LDY, * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/slatm7.f b/TESTING/MATGEN/slatm7.f index 8fa977f6..a45d1611 100644 --- a/TESTING/MATGEN/slatm7.f +++ b/TESTING/MATGEN/slatm7.f @@ -1,9 +1,143 @@ +*> \brief \b SLATM7 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SLATM7( MODE, COND, IRSIGN, IDIST, ISEED, D, N, +* RANK, INFO ) +* +* .. Scalar Arguments .. +* REAL COND +* INTEGER IDIST, INFO, IRSIGN, MODE, N, RANK +* .. +* .. Array Arguments .. +* REAL D( * ) +* INTEGER ISEED( 4 ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> SLATM7 computes the entries of D as specified by MODE +*> COND and IRSIGN. IDIST and ISEED determine the generation +*> of random numbers. SLATM7 is called by SLATMT to generate +*> random test matrices. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \verbatim +*> MODE - INTEGER +*> On entry describes how D is to be computed: +*> MODE = 0 means do not change D. +*> \endverbatim +*> \verbatim +*> MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND +*> MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) I=1:RANK +*> \endverbatim +*> \verbatim +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> Not modified. +*> \endverbatim +*> \verbatim +*> COND - REAL +*> On entry, used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> \verbatim +*> IRSIGN - INTEGER +*> On entry, if MODE neither -6, 0 nor 6, determines sign of +*> entries of D +*> 0 => leave entries of D unchanged +*> 1 => multiply each entry of D by 1 or -1 with probability .5 +*> \endverbatim +*> \verbatim +*> IDIST - CHARACTER*1 +*> On entry, IDIST specifies the type of distribution to be +*> used to generate a random matrix . +*> 1 => UNIFORM( 0, 1 ) +*> 2 => UNIFORM( -1, 1 ) +*> 3 => NORMAL( 0, 1 ) +*> Not modified. +*> \endverbatim +*> \verbatim +*> ISEED - INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. The random number generator uses a +*> linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to SLATM7 +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> \verbatim +*> D - REAL array, dimension ( MIN( M , N ) ) +*> Array to be computed according to MODE, COND and IRSIGN. +*> May be changed on exit if MODE is nonzero. +*> \endverbatim +*> \verbatim +*> N - INTEGER +*> Number of entries of D. Not modified. +*> \endverbatim +*> \verbatim +*> RANK - INTEGER +*> The rank of matrix to be generated for modes 1,2,3 only. +*> D( RANK+1:N ) = 0. +*> Not modified. +*> \endverbatim +*> \verbatim +*> INFO - INTEGER +*> 0 => normal termination +*> -1 => if MODE not in range -6 to 6 +*> -2 => if MODE neither -6, 0 nor 6, and +*> IRSIGN neither 0 nor 1 +*> -3 => if MODE neither -6, 0 nor 6 and COND less than 1 +*> -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3 +*> -7 => if N negative +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup real_matgen +* +* ===================================================================== SUBROUTINE SLATM7( MODE, COND, IRSIGN, IDIST, ISEED, D, N, $ RANK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Craig Lucas, University of Manchester / NAG Ltd. -* October, 2008 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. REAL COND @@ -14,86 +148,6 @@ INTEGER ISEED( 4 ) * .. * -* Purpose -* ======= -* -* SLATM7 computes the entries of D as specified by MODE -* COND and IRSIGN. IDIST and ISEED determine the generation -* of random numbers. SLATM7 is called by SLATMT to generate -* random test matrices. -* -* Arguments -* ========= -* -* MODE - INTEGER -* On entry describes how D is to be computed: -* MODE = 0 means do not change D. -* -* MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND -* MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) I=1:RANK -* -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* Not modified. -* -* COND - REAL -* On entry, used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* IRSIGN - INTEGER -* On entry, if MODE neither -6, 0 nor 6, determines sign of -* entries of D -* 0 => leave entries of D unchanged -* 1 => multiply each entry of D by 1 or -1 with probability .5 -* -* IDIST - CHARACTER*1 -* On entry, IDIST specifies the type of distribution to be -* used to generate a random matrix . -* 1 => UNIFORM( 0, 1 ) -* 2 => UNIFORM( -1, 1 ) -* 3 => NORMAL( 0, 1 ) -* Not modified. -* -* ISEED - INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. The random number generator uses a -* linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to SLATM7 -* to continue the same random number sequence. -* Changed on exit. -* -* D - REAL array, dimension ( MIN( M , N ) ) -* Array to be computed according to MODE, COND and IRSIGN. -* May be changed on exit if MODE is nonzero. -* -* N - INTEGER -* Number of entries of D. Not modified. -* -* RANK - INTEGER -* The rank of matrix to be generated for modes 1,2,3 only. -* D( RANK+1:N ) = 0. -* Not modified. -* -* INFO - INTEGER -* 0 => normal termination -* -1 => if MODE not in range -6 to 6 -* -2 => if MODE neither -6, 0 nor 6, and -* IRSIGN neither 0 nor 1 -* -3 => if MODE neither -6, 0 nor 6 and COND less than 1 -* -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3 -* -7 => if N negative -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/slatme.f b/TESTING/MATGEN/slatme.f index 60a32068..3deff329 100644 --- a/TESTING/MATGEN/slatme.f +++ b/TESTING/MATGEN/slatme.f @@ -1,12 +1,343 @@ +*> \brief \b SLATME +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SLATME( N, DIST, ISEED, D, MODE, COND, DMAX, EI, +* RSIGN, +* UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, +* A, +* LDA, WORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER DIST, RSIGN, SIM, UPPER +* INTEGER INFO, KL, KU, LDA, MODE, MODES, N +* REAL ANORM, COND, CONDS, DMAX +* .. +* .. Array Arguments .. +* CHARACTER EI( * ) +* INTEGER ISEED( 4 ) +* REAL A( LDA, * ), D( * ), DS( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> SLATME generates random non-symmetric square matrices with +*> specified eigenvalues for testing LAPACK programs. +*> +*> SLATME operates by applying the following sequence of +*> operations: +*> +*> 1. Set the diagonal to D, where D may be input or +*> computed according to MODE, COND, DMAX, and RSIGN +*> as described below. +*> +*> 2. If complex conjugate pairs are desired (MODE=0 and EI(1)='R', +*> or MODE=5), certain pairs of adjacent elements of D are +*> interpreted as the real and complex parts of a complex +*> conjugate pair; A thus becomes block diagonal, with 1x1 +*> and 2x2 blocks. +*> +*> 3. If UPPER='T', the upper triangle of A is set to random values +*> out of distribution DIST. +*> +*> 4. If SIM='T', A is multiplied on the left by a random matrix +*> X, whose singular values are specified by DS, MODES, and +*> CONDS, and on the right by X inverse. +*> +*> 5. If KL < N-1, the lower bandwidth is reduced to KL using +*> Householder transformations. If KU < N-1, the upper +*> bandwidth is reduced to KU. +*> +*> 6. If ANORM is not negative, the matrix is scaled to have +*> maximum-element-norm ANORM. +*> +*> (Note: since the matrix cannot be reduced beyond Hessenberg form, +*> no packing options are available.) +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns (or rows) of A. Not modified. +*> \endverbatim +*> +*> \param[in] DIST +*> \verbatim +*> DIST is CHARACTER*1 +*> On entry, DIST specifies the type of distribution to be used +*> to generate the random eigen-/singular values, and for the +*> upper triangle (see UPPER). +*> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) +*> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) +*> 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. They should lie between 0 and 4095 inclusive, +*> and ISEED(4) should be odd. The random number generator +*> uses a linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to SLATME +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is REAL array, dimension ( N ) +*> This array is used to specify the eigenvalues of A. If +*> MODE=0, then D is assumed to contain the eigenvalues (but +*> see the description of EI), otherwise they will be +*> computed according to MODE, COND, DMAX, and RSIGN and +*> placed in D. +*> Modified if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry this describes how the eigenvalues are to +*> be specified: +*> MODE = 0 means use D (with EI) as input +*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND +*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. Each odd-even pair +*> of elements will be either used as two real +*> eigenvalues or as the real and imaginary part +*> of a complex conjugate pair of eigenvalues; +*> the choice of which is done is random, with +*> 50-50 probability, for each pair. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is between 1 and 4, D has entries ranging +*> from 1 to 1/COND, if between -1 and -4, D has entries +*> ranging from 1/COND to 1, +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is REAL +*> On entry, this is used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] DMAX +*> \verbatim +*> DMAX is REAL +*> If MODE is neither -6, 0 nor 6, the contents of D, as +*> computed according to MODE and COND, will be scaled by +*> DMAX / max(abs(D(i))). Note that DMAX need not be +*> positive: if DMAX is negative (or zero), D will be +*> scaled by a negative number (or zero). +*> Not modified. +*> \endverbatim +*> +*> \param[in] EI +*> \verbatim +*> EI is CHARACTER*1 array, dimension ( N ) +*> If MODE is 0, and EI(1) is not ' ' (space character), +*> this array specifies which elements of D (on input) are +*> real eigenvalues and which are the real and imaginary parts +*> of a complex conjugate pair of eigenvalues. The elements +*> of EI may then only have the values 'R' and 'I'. If +*> EI(j)='R' and EI(j+1)='I', then the j-th eigenvalue is +*> CMPLX( D(j) , D(j+1) ), and the (j+1)-th is the complex +*> conjugate thereof. If EI(j)=EI(j+1)='R', then the j-th +*> eigenvalue is D(j) (i.e., real). EI(1) may not be 'I', +*> nor may two adjacent elements of EI both have the value 'I'. +*> If MODE is not 0, then EI is ignored. If MODE is 0 and +*> EI(1)=' ', then the eigenvalues will all be real. +*> Not modified. +*> \endverbatim +*> +*> \param[in] RSIGN +*> \verbatim +*> RSIGN is CHARACTER*1 +*> If MODE is not 0, 6, or -6, and RSIGN='T', then the +*> elements of D, as computed according to MODE and COND, will +*> be multiplied by a random sign (+1 or -1). If RSIGN='F', +*> they will not be. RSIGN may only have the values 'T' or +*> 'F'. +*> Not modified. +*> \endverbatim +*> +*> \param[in] UPPER +*> \verbatim +*> UPPER is CHARACTER*1 +*> If UPPER='T', then the elements of A above the diagonal +*> (and above the 2x2 diagonal blocks, if A has complex +*> eigenvalues) will be set to random numbers out of DIST. +*> If UPPER='F', they will not. UPPER may only have the +*> values 'T' or 'F'. +*> Not modified. +*> \endverbatim +*> +*> \param[in] SIM +*> \verbatim +*> SIM is CHARACTER*1 +*> If SIM='T', then A will be operated on by a "similarity +*> transform", i.e., multiplied on the left by a matrix X and +*> on the right by X inverse. X = U S V, where U and V are +*> random unitary matrices and S is a (diagonal) matrix of +*> singular values specified by DS, MODES, and CONDS. If +*> SIM='F', then A will not be transformed. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] DS +*> \verbatim +*> DS is REAL array, dimension ( N ) +*> This array is used to specify the singular values of X, +*> in the same way that D specifies the eigenvalues of A. +*> If MODE=0, the DS contains the singular values, which +*> may not be zero. +*> Modified if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODES +*> \verbatim +*> MODES is INTEGER +*> \endverbatim +*> +*> \param[in] CONDS +*> \verbatim +*> CONDS is REAL +*> Same as MODE and COND, but for specifying the diagonal +*> of S. MODES=-6 and +6 are not allowed (since they would +*> result in randomly ill-conditioned eigenvalues.) +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> This specifies the lower bandwidth of the matrix. KL=1 +*> specifies upper Hessenberg form. If KL is at least N-1, +*> then A will have full lower bandwidth. KL must be at +*> least 1. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> This specifies the upper bandwidth of the matrix. KU=1 +*> specifies lower Hessenberg form. If KU is at least N-1, +*> then A will have full upper bandwidth; if KU and KL +*> are both at least N-1, then A will be dense. Only one of +*> KU and KL may be less than N-1. KU must be at least 1. +*> Not modified. +*> \endverbatim +*> +*> \param[in] ANORM +*> \verbatim +*> ANORM is REAL +*> If ANORM is not negative, then A will be scaled by a non- +*> negative real number to make the maximum-element-norm of A +*> to be ANORM. +*> Not modified. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is REAL array, dimension ( LDA, N ) +*> On exit A is the desired test matrix. +*> Modified. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> LDA specifies the first dimension of A as declared in the +*> calling program. LDA must be at least N. +*> Not modified. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is REAL array, dimension ( 3*N ) +*> Workspace. +*> Modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error code. On exit, INFO will be set to one of the +*> following values: +*> 0 => normal return +*> -1 => N negative +*> -2 => DIST illegal string +*> -5 => MODE not in range -6 to 6 +*> -6 => COND less than 1.0, and MODE neither -6, 0 nor 6 +*> -8 => EI(1) is not ' ' or 'R', EI(j) is not 'R' or 'I', or +*> two adjacent elements of EI are 'I'. +*> -9 => RSIGN is not 'T' or 'F' +*> -10 => UPPER is not 'T' or 'F' +*> -11 => SIM is not 'T' or 'F' +*> -12 => MODES=0 and DS has a zero singular value. +*> -13 => MODES is not in the range -5 to 5. +*> -14 => MODES is nonzero and CONDS is less than 1. +*> -15 => KL is less than 1. +*> -16 => KU is less than 1, or KL and KU are both less than +*> N-1. +*> -19 => LDA is less than N. +*> 1 => Error return from SLATM1 (computing D) +*> 2 => Cannot scale to DMAX (max. eigenvalue is 0) +*> 3 => Error return from SLATM1 (computing DS) +*> 4 => Error return from SLARGE +*> 5 => Zero singular value from SLATM1. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup real_matgen +* +* ===================================================================== SUBROUTINE SLATME( N, DIST, ISEED, D, MODE, COND, DMAX, EI, $ RSIGN, $ UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, $ A, $ LDA, WORK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER DIST, RSIGN, SIM, UPPER @@ -19,227 +350,6 @@ REAL A( LDA, * ), D( * ), DS( * ), WORK( * ) * .. * -* Purpose -* ======= -* -* SLATME generates random non-symmetric square matrices with -* specified eigenvalues for testing LAPACK programs. -* -* SLATME operates by applying the following sequence of -* operations: -* -* 1. Set the diagonal to D, where D may be input or -* computed according to MODE, COND, DMAX, and RSIGN -* as described below. -* -* 2. If complex conjugate pairs are desired (MODE=0 and EI(1)='R', -* or MODE=5), certain pairs of adjacent elements of D are -* interpreted as the real and complex parts of a complex -* conjugate pair; A thus becomes block diagonal, with 1x1 -* and 2x2 blocks. -* -* 3. If UPPER='T', the upper triangle of A is set to random values -* out of distribution DIST. -* -* 4. If SIM='T', A is multiplied on the left by a random matrix -* X, whose singular values are specified by DS, MODES, and -* CONDS, and on the right by X inverse. -* -* 5. If KL < N-1, the lower bandwidth is reduced to KL using -* Householder transformations. If KU < N-1, the upper -* bandwidth is reduced to KU. -* -* 6. If ANORM is not negative, the matrix is scaled to have -* maximum-element-norm ANORM. -* -* (Note: since the matrix cannot be reduced beyond Hessenberg form, -* no packing options are available.) -* -* Arguments -* ========= -* -* N (input) INTEGER -* The number of columns (or rows) of A. Not modified. -* -* DIST (input) CHARACTER*1 -* On entry, DIST specifies the type of distribution to be used -* to generate the random eigen-/singular values, and for the -* upper triangle (see UPPER). -* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) -* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) -* 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. They should lie between 0 and 4095 inclusive, -* and ISEED(4) should be odd. The random number generator -* uses a linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to SLATME -* to continue the same random number sequence. -* Changed on exit. -* -* D (input/output) REAL array, dimension ( N ) -* This array is used to specify the eigenvalues of A. If -* MODE=0, then D is assumed to contain the eigenvalues (but -* see the description of EI), otherwise they will be -* computed according to MODE, COND, DMAX, and RSIGN and -* placed in D. -* Modified if MODE is nonzero. -* -* MODE (input) INTEGER -* On entry this describes how the eigenvalues are to -* be specified: -* MODE = 0 means use D (with EI) as input -* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND -* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. Each odd-even pair -* of elements will be either used as two real -* eigenvalues or as the real and imaginary part -* of a complex conjugate pair of eigenvalues; -* the choice of which is done is random, with -* 50-50 probability, for each pair. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is between 1 and 4, D has entries ranging -* from 1 to 1/COND, if between -1 and -4, D has entries -* ranging from 1/COND to 1, -* Not modified. -* -* COND (input) REAL -* On entry, this is used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* DMAX (input) REAL -* If MODE is neither -6, 0 nor 6, the contents of D, as -* computed according to MODE and COND, will be scaled by -* DMAX / max(abs(D(i))). Note that DMAX need not be -* positive: if DMAX is negative (or zero), D will be -* scaled by a negative number (or zero). -* Not modified. -* -* EI (input) CHARACTER*1 array, dimension ( N ) -* If MODE is 0, and EI(1) is not ' ' (space character), -* this array specifies which elements of D (on input) are -* real eigenvalues and which are the real and imaginary parts -* of a complex conjugate pair of eigenvalues. The elements -* of EI may then only have the values 'R' and 'I'. If -* EI(j)='R' and EI(j+1)='I', then the j-th eigenvalue is -* CMPLX( D(j) , D(j+1) ), and the (j+1)-th is the complex -* conjugate thereof. If EI(j)=EI(j+1)='R', then the j-th -* eigenvalue is D(j) (i.e., real). EI(1) may not be 'I', -* nor may two adjacent elements of EI both have the value 'I'. -* If MODE is not 0, then EI is ignored. If MODE is 0 and -* EI(1)=' ', then the eigenvalues will all be real. -* Not modified. -* -* RSIGN (input) CHARACTER*1 -* If MODE is not 0, 6, or -6, and RSIGN='T', then the -* elements of D, as computed according to MODE and COND, will -* be multiplied by a random sign (+1 or -1). If RSIGN='F', -* they will not be. RSIGN may only have the values 'T' or -* 'F'. -* Not modified. -* -* UPPER (input) CHARACTER*1 -* If UPPER='T', then the elements of A above the diagonal -* (and above the 2x2 diagonal blocks, if A has complex -* eigenvalues) will be set to random numbers out of DIST. -* If UPPER='F', they will not. UPPER may only have the -* values 'T' or 'F'. -* Not modified. -* -* SIM (input) CHARACTER*1 -* If SIM='T', then A will be operated on by a "similarity -* transform", i.e., multiplied on the left by a matrix X and -* on the right by X inverse. X = U S V, where U and V are -* random unitary matrices and S is a (diagonal) matrix of -* singular values specified by DS, MODES, and CONDS. If -* SIM='F', then A will not be transformed. -* Not modified. -* -* DS (input/output) REAL array, dimension ( N ) -* This array is used to specify the singular values of X, -* in the same way that D specifies the eigenvalues of A. -* If MODE=0, the DS contains the singular values, which -* may not be zero. -* Modified if MODE is nonzero. -* -* MODES (input) INTEGER -* -* CONDS (input) REAL -* Same as MODE and COND, but for specifying the diagonal -* of S. MODES=-6 and +6 are not allowed (since they would -* result in randomly ill-conditioned eigenvalues.) -* -* KL (input) INTEGER -* This specifies the lower bandwidth of the matrix. KL=1 -* specifies upper Hessenberg form. If KL is at least N-1, -* then A will have full lower bandwidth. KL must be at -* least 1. -* Not modified. -* -* KU (input) INTEGER -* This specifies the upper bandwidth of the matrix. KU=1 -* specifies lower Hessenberg form. If KU is at least N-1, -* then A will have full upper bandwidth; if KU and KL -* are both at least N-1, then A will be dense. Only one of -* KU and KL may be less than N-1. KU must be at least 1. -* Not modified. -* -* ANORM (input) REAL -* If ANORM is not negative, then A will be scaled by a non- -* negative real number to make the maximum-element-norm of A -* to be ANORM. -* Not modified. -* -* A (output) REAL array, dimension ( LDA, N ) -* On exit A is the desired test matrix. -* Modified. -* -* LDA (input) INTEGER -* LDA specifies the first dimension of A as declared in the -* calling program. LDA must be at least N. -* Not modified. -* -* WORK (workspace) REAL array, dimension ( 3*N ) -* Workspace. -* Modified. -* -* INFO (output) INTEGER -* Error code. On exit, INFO will be set to one of the -* following values: -* 0 => normal return -* -1 => N negative -* -2 => DIST illegal string -* -5 => MODE not in range -6 to 6 -* -6 => COND less than 1.0, and MODE neither -6, 0 nor 6 -* -8 => EI(1) is not ' ' or 'R', EI(j) is not 'R' or 'I', or -* two adjacent elements of EI are 'I'. -* -9 => RSIGN is not 'T' or 'F' -* -10 => UPPER is not 'T' or 'F' -* -11 => SIM is not 'T' or 'F' -* -12 => MODES=0 and DS has a zero singular value. -* -13 => MODES is not in the range -5 to 5. -* -14 => MODES is nonzero and CONDS is less than 1. -* -15 => KL is less than 1. -* -16 => KU is less than 1, or KL and KU are both less than -* N-1. -* -19 => LDA is less than N. -* 1 => Error return from SLATM1 (computing D) -* 2 => Cannot scale to DMAX (max. eigenvalue is 0) -* 3 => Error return from SLATM1 (computing DS) -* 4 => Error return from SLARGE -* 5 => Zero singular value from SLATM1. -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/slatmr.f b/TESTING/MATGEN/slatmr.f index 0506ca9f..bf9adcc5 100644 --- a/TESTING/MATGEN/slatmr.f +++ b/TESTING/MATGEN/slatmr.f @@ -1,11 +1,485 @@ +*> \brief \b SLATMR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SLATMR( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, +* RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, +* CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, +* PACK, A, LDA, IWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER DIST, GRADE, PACK, PIVTNG, RSIGN, SYM +* INTEGER INFO, KL, KU, LDA, M, MODE, MODEL, MODER, N +* REAL ANORM, COND, CONDL, CONDR, DMAX, SPARSE +* .. +* .. Array Arguments .. +* INTEGER IPIVOT( * ), ISEED( 4 ), IWORK( * ) +* REAL A( LDA, * ), D( * ), DL( * ), DR( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> SLATMR generates random matrices of various types for testing +*> LAPACK programs. +*> +*> SLATMR operates by applying the following sequence of +*> operations: +*> +*> Generate a matrix A with random entries of distribution DIST +*> which is symmetric if SYM='S', and nonsymmetric +*> if SYM='N'. +*> +*> Set the diagonal to D, where D may be input or +*> computed according to MODE, COND, DMAX and RSIGN +*> as described below. +*> +*> Grade the matrix, if desired, from the left and/or right +*> as specified by GRADE. The inputs DL, MODEL, CONDL, DR, +*> MODER and CONDR also determine the grading as described +*> below. +*> +*> Permute, if desired, the rows and/or columns as specified by +*> PIVTNG and IPIVOT. +*> +*> Set random entries to zero, if desired, to get a random sparse +*> matrix as specified by SPARSE. +*> +*> Make A a band matrix, if desired, by zeroing out the matrix +*> outside a band of lower bandwidth KL and upper bandwidth KU. +*> +*> Scale A, if desired, to have maximum entry ANORM. +*> +*> Pack the matrix if desired. Options specified by PACK are: +*> no packing +*> zero out upper half (if symmetric) +*> zero out lower half (if symmetric) +*> store the upper half columnwise (if symmetric or +*> square upper triangular) +*> store the lower half columnwise (if symmetric or +*> square lower triangular) +*> same as upper half rowwise if symmetric +*> store the lower triangle in banded format (if symmetric) +*> store the upper triangle in banded format (if symmetric) +*> store the entire matrix in banded format +*> +*> Note: If two calls to SLATMR differ only in the PACK parameter, +*> they will generate mathematically equivalent matrices. +*> +*> If two calls to SLATMR both have full bandwidth (KL = M-1 +*> and KU = N-1), and differ only in the PIVTNG and PACK +*> parameters, then the matrices generated will differ only +*> in the order of the rows and/or columns, and otherwise +*> contain the same data. This consistency cannot be and +*> is not maintained with less than full bandwidth. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Number of rows of A. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of columns of A. Not modified. +*> \endverbatim +*> +*> \param[in] DIST +*> \verbatim +*> DIST is CHARACTER*1 +*> On entry, DIST specifies the type of distribution to be used +*> to generate a random matrix . +*> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) +*> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) +*> 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry ISEED specifies the seed of the random number +*> generator. They should lie between 0 and 4095 inclusive, +*> and ISEED(4) should be odd. The random number generator +*> uses a linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to SLATMR +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] SYM +*> \verbatim +*> SYM is CHARACTER*1 +*> If SYM='S' or 'H', generated matrix is symmetric. +*> If SYM='N', generated matrix is nonsymmetric. +*> Not modified. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is REAL array, dimension (min(M,N)) +*> On entry this array specifies the diagonal entries +*> of the diagonal of A. D may either be specified +*> on entry, or set according to MODE and COND as described +*> below. May be changed on exit if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry describes how D is to be used: +*> MODE = 0 means use D as input +*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND +*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is REAL +*> On entry, used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] DMAX +*> \verbatim +*> DMAX is REAL +*> If MODE neither -6, 0 nor 6, the diagonal is scaled by +*> DMAX / max(abs(D(i))), so that maximum absolute entry +*> of diagonal is abs(DMAX). If DMAX is negative (or zero), +*> diagonal will be scaled by a negative number (or zero). +*> \endverbatim +*> +*> \param[in] RSIGN +*> \verbatim +*> RSIGN is CHARACTER*1 +*> If MODE neither -6, 0 nor 6, specifies sign of diagonal +*> as follows: +*> 'T' => diagonal entries are multiplied by 1 or -1 +*> with probability .5 +*> 'F' => diagonal unchanged +*> Not modified. +*> \endverbatim +*> +*> \param[in] GRADE +*> \verbatim +*> GRADE is CHARACTER*1 +*> Specifies grading of matrix as follows: +*> 'N' => no grading +*> 'L' => matrix premultiplied by diag( DL ) +*> (only if matrix nonsymmetric) +*> 'R' => matrix postmultiplied by diag( DR ) +*> (only if matrix nonsymmetric) +*> 'B' => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DR ) +*> (only if matrix nonsymmetric) +*> 'S' or 'H' => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DL ) +*> ('S' for symmetric, or 'H' for Hermitian) +*> 'E' => matrix premultiplied by diag( DL ) and +*> postmultiplied by inv( diag( DL ) ) +*> ( 'E' for eigenvalue invariance) +*> (only if matrix nonsymmetric) +*> Note: if GRADE='E', then M must equal N. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] DL +*> \verbatim +*> DL is REAL array, dimension (M) +*> If MODEL=0, then on entry this array specifies the diagonal +*> entries of a diagonal matrix used as described under GRADE +*> above. If MODEL is not zero, then DL will be set according +*> to MODEL and CONDL, analogous to the way D is set according +*> to MODE and COND (except there is no DMAX parameter for DL). +*> If GRADE='E', then DL cannot have zero entries. +*> Not referenced if GRADE = 'N' or 'R'. Changed on exit. +*> \endverbatim +*> +*> \param[in] MODEL +*> \verbatim +*> MODEL is INTEGER +*> This specifies how the diagonal array DL is to be computed, +*> just as MODE specifies how D is to be computed. +*> Not modified. +*> \endverbatim +*> +*> \param[in] CONDL +*> \verbatim +*> CONDL is REAL +*> When MODEL is not zero, this specifies the condition number +*> of the computed DL. Not modified. +*> \endverbatim +*> +*> \param[in,out] DR +*> \verbatim +*> DR is REAL array, dimension (N) +*> If MODER=0, then on entry this array specifies the diagonal +*> entries of a diagonal matrix used as described under GRADE +*> above. If MODER is not zero, then DR will be set according +*> to MODER and CONDR, analogous to the way D is set according +*> to MODE and COND (except there is no DMAX parameter for DR). +*> Not referenced if GRADE = 'N', 'L', 'H', 'S' or 'E'. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] MODER +*> \verbatim +*> MODER is INTEGER +*> This specifies how the diagonal array DR is to be computed, +*> just as MODE specifies how D is to be computed. +*> Not modified. +*> \endverbatim +*> +*> \param[in] CONDR +*> \verbatim +*> CONDR is REAL +*> When MODER is not zero, this specifies the condition number +*> of the computed DR. Not modified. +*> \endverbatim +*> +*> \param[in] PIVTNG +*> \verbatim +*> PIVTNG is CHARACTER*1 +*> On entry specifies pivoting permutations as follows: +*> 'N' or ' ' => none. +*> 'L' => left or row pivoting (matrix must be nonsymmetric). +*> 'R' => right or column pivoting (matrix must be +*> nonsymmetric). +*> 'B' or 'F' => both or full pivoting, i.e., on both sides. +*> In this case, M must equal N +*> \endverbatim +*> \verbatim +*> If two calls to SLATMR both have full bandwidth (KL = M-1 +*> and KU = N-1), and differ only in the PIVTNG and PACK +*> parameters, then the matrices generated will differ only +*> in the order of the rows and/or columns, and otherwise +*> contain the same data. This consistency cannot be +*> maintained with less than full bandwidth. +*> \endverbatim +*> +*> \param[in] IPIVOT +*> \verbatim +*> IPIVOT is INTEGER array, dimension (N or M) +*> This array specifies the permutation used. After the +*> basic matrix is generated, the rows, columns, or both +*> are permuted. If, say, row pivoting is selected, SLATMR +*> starts with the *last* row and interchanges the M-th and +*> IPIVOT(M)-th rows, then moves to the next-to-last row, +*> interchanging the (M-1)-th and the IPIVOT(M-1)-th rows, +*> and so on. In terms of "2-cycles", the permutation is +*> (1 IPIVOT(1)) (2 IPIVOT(2)) ... (M IPIVOT(M)) +*> where the rightmost cycle is applied first. This is the +*> *inverse* of the effect of pivoting in LINPACK. The idea +*> is that factoring (with pivoting) an identity matrix +*> which has been inverse-pivoted in this way should +*> result in a pivot vector identical to IPIVOT. +*> Not referenced if PIVTNG = 'N'. Not modified. +*> \endverbatim +*> +*> \param[in] SPARSE +*> \verbatim +*> SPARSE is REAL +*> On entry specifies the sparsity of the matrix if a sparse +*> matrix is to be generated. SPARSE should lie between +*> 0 and 1. To generate a sparse matrix, for each matrix entry +*> a uniform ( 0, 1 ) random number x is generated and +*> compared to SPARSE; if x is larger the matrix entry +*> is unchanged and if x is smaller the entry is set +*> to zero. Thus on the average a fraction SPARSE of the +*> entries will be set to zero. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> On entry specifies the lower bandwidth of the matrix. For +*> example, KL=0 implies upper triangular, KL=1 implies upper +*> Hessenberg, and KL at least M-1 implies the matrix is not +*> banded. Must equal KU if matrix is symmetric. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> On entry specifies the upper bandwidth of the matrix. For +*> example, KU=0 implies lower triangular, KU=1 implies lower +*> Hessenberg, and KU at least N-1 implies the matrix is not +*> banded. Must equal KL if matrix is symmetric. +*> Not modified. +*> \endverbatim +*> +*> \param[in] ANORM +*> \verbatim +*> ANORM is REAL +*> On entry specifies maximum entry of output matrix +*> (output matrix will by multiplied by a constant so that +*> its largest absolute entry equal ANORM) +*> if ANORM is nonnegative. If ANORM is negative no scaling +*> is done. Not modified. +*> \endverbatim +*> +*> \param[in] PACK +*> \verbatim +*> PACK is CHARACTER*1 +*> On entry specifies packing of matrix as follows: +*> 'N' => no packing +*> 'U' => zero out all subdiagonal entries (if symmetric) +*> 'L' => zero out all superdiagonal entries (if symmetric) +*> 'C' => store the upper triangle columnwise +*> (only if matrix symmetric or square upper triangular) +*> 'R' => store the lower triangle columnwise +*> (only if matrix symmetric or square lower triangular) +*> (same as upper half rowwise if symmetric) +*> 'B' => store the lower triangle in band storage scheme +*> (only if matrix symmetric) +*> 'Q' => store the upper triangle in band storage scheme +*> (only if matrix symmetric) +*> 'Z' => store the entire matrix in band storage scheme +*> (pivoting can be provided for by using this +*> option to store A in the trailing rows of +*> the allocated storage) +*> \endverbatim +*> \verbatim +*> Using these options, the various LAPACK packed and banded +*> storage schemes can be obtained: +*> GB - use 'Z' +*> PB, SB or TB - use 'B' or 'Q' +*> PP, SP or TP - use 'C' or 'R' +*> \endverbatim +*> \verbatim +*> If two calls to SLATMR differ only in the PACK parameter, +*> they will generate mathematically equivalent matrices. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is REAL array, dimension (LDA,N) +*> On exit A is the desired test matrix. Only those +*> entries of A which are significant on output +*> will be referenced (even if A is in packed or band +*> storage format). The 'unoccupied corners' of A in +*> band format will be zeroed out. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> on entry LDA specifies the first dimension of A as +*> declared in the calling program. +*> If PACK='N', 'U' or 'L', LDA must be at least max ( 1, M ). +*> If PACK='C' or 'R', LDA must be at least 1. +*> If PACK='B', or 'Q', LDA must be MIN ( KU+1, N ) +*> If PACK='Z', LDA must be at least KUU+KLL+1, where +*> KUU = MIN ( KU, N-1 ) and KLL = MIN ( KL, N-1 ) +*> Not modified. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension ( N or M) +*> Workspace. Not referenced if PIVTNG = 'N'. Changed on exit. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error parameter on exit: +*> 0 => normal return +*> -1 => M negative or unequal to N and SYM='S' or 'H' +*> -2 => N negative +*> -3 => DIST illegal string +*> -5 => SYM illegal string +*> -7 => MODE not in range -6 to 6 +*> -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 +*> -10 => MODE neither -6, 0 nor 6 and RSIGN illegal string +*> -11 => GRADE illegal string, or GRADE='E' and +*> M not equal to N, or GRADE='L', 'R', 'B' or 'E' and +*> SYM = 'S' or 'H' +*> -12 => GRADE = 'E' and DL contains zero +*> -13 => MODEL not in range -6 to 6 and GRADE= 'L', 'B', 'H', +*> 'S' or 'E' +*> -14 => CONDL less than 1.0, GRADE='L', 'B', 'H', 'S' or 'E', +*> and MODEL neither -6, 0 nor 6 +*> -16 => MODER not in range -6 to 6 and GRADE= 'R' or 'B' +*> -17 => CONDR less than 1.0, GRADE='R' or 'B', and +*> MODER neither -6, 0 nor 6 +*> -18 => PIVTNG illegal string, or PIVTNG='B' or 'F' and +*> M not equal to N, or PIVTNG='L' or 'R' and SYM='S' +*> or 'H' +*> -19 => IPIVOT contains out of range number and +*> PIVTNG not equal to 'N' +*> -20 => KL negative +*> -21 => KU negative, or SYM='S' or 'H' and KU not equal to KL +*> -22 => SPARSE not in range 0. to 1. +*> -24 => PACK illegal string, or PACK='U', 'L', 'B' or 'Q' +*> and SYM='N', or PACK='C' and SYM='N' and either KL +*> not equal to 0 or N not equal to M, or PACK='R' and +*> SYM='N', and either KU not equal to 0 or N not equal +*> to M +*> -26 => LDA too small +*> 1 => Error return from SLATM1 (computing D) +*> 2 => Cannot scale diagonal to DMAX (max. entry is 0) +*> 3 => Error return from SLATM1 (computing DL) +*> 4 => Error return from SLATM1 (computing DR) +*> 5 => ANORM is positive, but matrix constructed prior to +*> attempting to scale it to have norm ANORM, is zero +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup real_matgen +* +* ===================================================================== SUBROUTINE SLATMR( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, $ RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, $ CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, $ PACK, A, LDA, IWORK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER DIST, GRADE, PACK, PIVTNG, RSIGN, SYM @@ -17,348 +491,6 @@ REAL A( LDA, * ), D( * ), DL( * ), DR( * ) * .. * -* Purpose -* ======= -* -* SLATMR generates random matrices of various types for testing -* LAPACK programs. -* -* SLATMR operates by applying the following sequence of -* operations: -* -* Generate a matrix A with random entries of distribution DIST -* which is symmetric if SYM='S', and nonsymmetric -* if SYM='N'. -* -* Set the diagonal to D, where D may be input or -* computed according to MODE, COND, DMAX and RSIGN -* as described below. -* -* Grade the matrix, if desired, from the left and/or right -* as specified by GRADE. The inputs DL, MODEL, CONDL, DR, -* MODER and CONDR also determine the grading as described -* below. -* -* Permute, if desired, the rows and/or columns as specified by -* PIVTNG and IPIVOT. -* -* Set random entries to zero, if desired, to get a random sparse -* matrix as specified by SPARSE. -* -* Make A a band matrix, if desired, by zeroing out the matrix -* outside a band of lower bandwidth KL and upper bandwidth KU. -* -* Scale A, if desired, to have maximum entry ANORM. -* -* Pack the matrix if desired. Options specified by PACK are: -* no packing -* zero out upper half (if symmetric) -* zero out lower half (if symmetric) -* store the upper half columnwise (if symmetric or -* square upper triangular) -* store the lower half columnwise (if symmetric or -* square lower triangular) -* same as upper half rowwise if symmetric -* store the lower triangle in banded format (if symmetric) -* store the upper triangle in banded format (if symmetric) -* store the entire matrix in banded format -* -* Note: If two calls to SLATMR differ only in the PACK parameter, -* they will generate mathematically equivalent matrices. -* -* If two calls to SLATMR both have full bandwidth (KL = M-1 -* and KU = N-1), and differ only in the PIVTNG and PACK -* parameters, then the matrices generated will differ only -* in the order of the rows and/or columns, and otherwise -* contain the same data. This consistency cannot be and -* is not maintained with less than full bandwidth. -* -* Arguments -* ========= -* -* M (input) INTEGER -* Number of rows of A. Not modified. -* -* N (input) INTEGER -* Number of columns of A. Not modified. -* -* DIST (input) CHARACTER*1 -* On entry, DIST specifies the type of distribution to be used -* to generate a random matrix . -* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) -* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) -* 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension (4) -* On entry ISEED specifies the seed of the random number -* generator. They should lie between 0 and 4095 inclusive, -* and ISEED(4) should be odd. The random number generator -* uses a linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to SLATMR -* to continue the same random number sequence. -* Changed on exit. -* -* SYM (input) CHARACTER*1 -* If SYM='S' or 'H', generated matrix is symmetric. -* If SYM='N', generated matrix is nonsymmetric. -* Not modified. -* -* D (input) REAL array, dimension (min(M,N)) -* On entry this array specifies the diagonal entries -* of the diagonal of A. D may either be specified -* on entry, or set according to MODE and COND as described -* below. May be changed on exit if MODE is nonzero. -* -* MODE (input) INTEGER -* On entry describes how D is to be used: -* MODE = 0 means use D as input -* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND -* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* Not modified. -* -* COND (input) REAL -* On entry, used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* DMAX (input) REAL -* If MODE neither -6, 0 nor 6, the diagonal is scaled by -* DMAX / max(abs(D(i))), so that maximum absolute entry -* of diagonal is abs(DMAX). If DMAX is negative (or zero), -* diagonal will be scaled by a negative number (or zero). -* -* RSIGN (input) CHARACTER*1 -* If MODE neither -6, 0 nor 6, specifies sign of diagonal -* as follows: -* 'T' => diagonal entries are multiplied by 1 or -1 -* with probability .5 -* 'F' => diagonal unchanged -* Not modified. -* -* GRADE (input) CHARACTER*1 -* Specifies grading of matrix as follows: -* 'N' => no grading -* 'L' => matrix premultiplied by diag( DL ) -* (only if matrix nonsymmetric) -* 'R' => matrix postmultiplied by diag( DR ) -* (only if matrix nonsymmetric) -* 'B' => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DR ) -* (only if matrix nonsymmetric) -* 'S' or 'H' => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DL ) -* ('S' for symmetric, or 'H' for Hermitian) -* 'E' => matrix premultiplied by diag( DL ) and -* postmultiplied by inv( diag( DL ) ) -* ( 'E' for eigenvalue invariance) -* (only if matrix nonsymmetric) -* Note: if GRADE='E', then M must equal N. -* Not modified. -* -* DL (input/output) REAL array, dimension (M) -* If MODEL=0, then on entry this array specifies the diagonal -* entries of a diagonal matrix used as described under GRADE -* above. If MODEL is not zero, then DL will be set according -* to MODEL and CONDL, analogous to the way D is set according -* to MODE and COND (except there is no DMAX parameter for DL). -* If GRADE='E', then DL cannot have zero entries. -* Not referenced if GRADE = 'N' or 'R'. Changed on exit. -* -* MODEL (input) INTEGER -* This specifies how the diagonal array DL is to be computed, -* just as MODE specifies how D is to be computed. -* Not modified. -* -* CONDL (input) REAL -* When MODEL is not zero, this specifies the condition number -* of the computed DL. Not modified. -* -* DR (input/output) REAL array, dimension (N) -* If MODER=0, then on entry this array specifies the diagonal -* entries of a diagonal matrix used as described under GRADE -* above. If MODER is not zero, then DR will be set according -* to MODER and CONDR, analogous to the way D is set according -* to MODE and COND (except there is no DMAX parameter for DR). -* Not referenced if GRADE = 'N', 'L', 'H', 'S' or 'E'. -* Changed on exit. -* -* MODER (input) INTEGER -* This specifies how the diagonal array DR is to be computed, -* just as MODE specifies how D is to be computed. -* Not modified. -* -* CONDR (input) REAL -* When MODER is not zero, this specifies the condition number -* of the computed DR. Not modified. -* -* PIVTNG (input) CHARACTER*1 -* On entry specifies pivoting permutations as follows: -* 'N' or ' ' => none. -* 'L' => left or row pivoting (matrix must be nonsymmetric). -* 'R' => right or column pivoting (matrix must be -* nonsymmetric). -* 'B' or 'F' => both or full pivoting, i.e., on both sides. -* In this case, M must equal N -* -* If two calls to SLATMR both have full bandwidth (KL = M-1 -* and KU = N-1), and differ only in the PIVTNG and PACK -* parameters, then the matrices generated will differ only -* in the order of the rows and/or columns, and otherwise -* contain the same data. This consistency cannot be -* maintained with less than full bandwidth. -* -* IPIVOT (input) INTEGER array, dimension (N or M) -* This array specifies the permutation used. After the -* basic matrix is generated, the rows, columns, or both -* are permuted. If, say, row pivoting is selected, SLATMR -* starts with the *last* row and interchanges the M-th and -* IPIVOT(M)-th rows, then moves to the next-to-last row, -* interchanging the (M-1)-th and the IPIVOT(M-1)-th rows, -* and so on. In terms of "2-cycles", the permutation is -* (1 IPIVOT(1)) (2 IPIVOT(2)) ... (M IPIVOT(M)) -* where the rightmost cycle is applied first. This is the -* *inverse* of the effect of pivoting in LINPACK. The idea -* is that factoring (with pivoting) an identity matrix -* which has been inverse-pivoted in this way should -* result in a pivot vector identical to IPIVOT. -* Not referenced if PIVTNG = 'N'. Not modified. -* -* SPARSE (input) REAL -* On entry specifies the sparsity of the matrix if a sparse -* matrix is to be generated. SPARSE should lie between -* 0 and 1. To generate a sparse matrix, for each matrix entry -* a uniform ( 0, 1 ) random number x is generated and -* compared to SPARSE; if x is larger the matrix entry -* is unchanged and if x is smaller the entry is set -* to zero. Thus on the average a fraction SPARSE of the -* entries will be set to zero. -* Not modified. -* -* KL (input) INTEGER -* On entry specifies the lower bandwidth of the matrix. For -* example, KL=0 implies upper triangular, KL=1 implies upper -* Hessenberg, and KL at least M-1 implies the matrix is not -* banded. Must equal KU if matrix is symmetric. -* Not modified. -* -* KU (input) INTEGER -* On entry specifies the upper bandwidth of the matrix. For -* example, KU=0 implies lower triangular, KU=1 implies lower -* Hessenberg, and KU at least N-1 implies the matrix is not -* banded. Must equal KL if matrix is symmetric. -* Not modified. -* -* ANORM (input) REAL -* On entry specifies maximum entry of output matrix -* (output matrix will by multiplied by a constant so that -* its largest absolute entry equal ANORM) -* if ANORM is nonnegative. If ANORM is negative no scaling -* is done. Not modified. -* -* PACK (input) CHARACTER*1 -* On entry specifies packing of matrix as follows: -* 'N' => no packing -* 'U' => zero out all subdiagonal entries (if symmetric) -* 'L' => zero out all superdiagonal entries (if symmetric) -* 'C' => store the upper triangle columnwise -* (only if matrix symmetric or square upper triangular) -* 'R' => store the lower triangle columnwise -* (only if matrix symmetric or square lower triangular) -* (same as upper half rowwise if symmetric) -* 'B' => store the lower triangle in band storage scheme -* (only if matrix symmetric) -* 'Q' => store the upper triangle in band storage scheme -* (only if matrix symmetric) -* 'Z' => store the entire matrix in band storage scheme -* (pivoting can be provided for by using this -* option to store A in the trailing rows of -* the allocated storage) -* -* Using these options, the various LAPACK packed and banded -* storage schemes can be obtained: -* GB - use 'Z' -* PB, SB or TB - use 'B' or 'Q' -* PP, SP or TP - use 'C' or 'R' -* -* If two calls to SLATMR differ only in the PACK parameter, -* they will generate mathematically equivalent matrices. -* Not modified. -* -* A (input/output) REAL array, dimension (LDA,N) -* On exit A is the desired test matrix. Only those -* entries of A which are significant on output -* will be referenced (even if A is in packed or band -* storage format). The 'unoccupied corners' of A in -* band format will be zeroed out. -* -* LDA (input) INTEGER -* on entry LDA specifies the first dimension of A as -* declared in the calling program. -* If PACK='N', 'U' or 'L', LDA must be at least max ( 1, M ). -* If PACK='C' or 'R', LDA must be at least 1. -* If PACK='B', or 'Q', LDA must be MIN ( KU+1, N ) -* If PACK='Z', LDA must be at least KUU+KLL+1, where -* KUU = MIN ( KU, N-1 ) and KLL = MIN ( KL, N-1 ) -* Not modified. -* -* IWORK (workspace) INTEGER array, dimension ( N or M) -* Workspace. Not referenced if PIVTNG = 'N'. Changed on exit. -* -* INFO (output) INTEGER -* Error parameter on exit: -* 0 => normal return -* -1 => M negative or unequal to N and SYM='S' or 'H' -* -2 => N negative -* -3 => DIST illegal string -* -5 => SYM illegal string -* -7 => MODE not in range -6 to 6 -* -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 -* -10 => MODE neither -6, 0 nor 6 and RSIGN illegal string -* -11 => GRADE illegal string, or GRADE='E' and -* M not equal to N, or GRADE='L', 'R', 'B' or 'E' and -* SYM = 'S' or 'H' -* -12 => GRADE = 'E' and DL contains zero -* -13 => MODEL not in range -6 to 6 and GRADE= 'L', 'B', 'H', -* 'S' or 'E' -* -14 => CONDL less than 1.0, GRADE='L', 'B', 'H', 'S' or 'E', -* and MODEL neither -6, 0 nor 6 -* -16 => MODER not in range -6 to 6 and GRADE= 'R' or 'B' -* -17 => CONDR less than 1.0, GRADE='R' or 'B', and -* MODER neither -6, 0 nor 6 -* -18 => PIVTNG illegal string, or PIVTNG='B' or 'F' and -* M not equal to N, or PIVTNG='L' or 'R' and SYM='S' -* or 'H' -* -19 => IPIVOT contains out of range number and -* PIVTNG not equal to 'N' -* -20 => KL negative -* -21 => KU negative, or SYM='S' or 'H' and KU not equal to KL -* -22 => SPARSE not in range 0. to 1. -* -24 => PACK illegal string, or PACK='U', 'L', 'B' or 'Q' -* and SYM='N', or PACK='C' and SYM='N' and either KL -* not equal to 0 or N not equal to M, or PACK='R' and -* SYM='N', and either KU not equal to 0 or N not equal -* to M -* -26 => LDA too small -* 1 => Error return from SLATM1 (computing D) -* 2 => Cannot scale diagonal to DMAX (max. entry is 0) -* 3 => Error return from SLATM1 (computing DL) -* 4 => Error return from SLATM1 (computing DR) -* 5 => ANORM is positive, but matrix constructed prior to -* attempting to scale it to have norm ANORM, is zero -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/slatms.f b/TESTING/MATGEN/slatms.f index c914aaca..da71d288 100644 --- a/TESTING/MATGEN/slatms.f +++ b/TESTING/MATGEN/slatms.f @@ -1,9 +1,334 @@ +*> \brief \b SLATMS +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, +* KL, KU, PACK, A, LDA, WORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER DIST, PACK, SYM +* INTEGER INFO, KL, KU, LDA, M, MODE, N +* REAL COND, DMAX +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* REAL A( LDA, * ), D( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> SLATMS generates random matrices with specified singular values +*> (or symmetric/hermitian with specified eigenvalues) +*> for testing LAPACK programs. +*> +*> SLATMS operates by applying the following sequence of +*> operations: +*> +*> Set the diagonal to D, where D may be input or +*> computed according to MODE, COND, DMAX, and SYM +*> as described below. +*> +*> Generate a matrix with the appropriate band structure, by one +*> of two methods: +*> +*> Method A: +*> Generate a dense M x N matrix by multiplying D on the left +*> and the right by random unitary matrices, then: +*> +*> Reduce the bandwidth according to KL and KU, using +*> Householder transformations. +*> +*> Method B: +*> Convert the bandwidth-0 (i.e., diagonal) matrix to a +*> bandwidth-1 matrix using Givens rotations, "chasing" +*> out-of-band elements back, much as in QR; then +*> convert the bandwidth-1 to a bandwidth-2 matrix, etc. +*> Note that for reasonably small bandwidths (relative to +*> M and N) this requires less storage, as a dense matrix +*> is not generated. Also, for symmetric matrices, only +*> one triangle is generated. +*> +*> Method A is chosen if the bandwidth is a large fraction of the +*> order of the matrix, and LDA is at least M (so a dense +*> matrix can be stored.) Method B is chosen if the bandwidth +*> is small (< 1/2 N for symmetric, < .3 N+M for +*> non-symmetric), or LDA is less than M and not less than the +*> bandwidth. +*> +*> Pack the matrix if desired. Options specified by PACK are: +*> no packing +*> zero out upper half (if symmetric) +*> zero out lower half (if symmetric) +*> store the upper half columnwise (if symmetric or upper +*> triangular) +*> store the lower half columnwise (if symmetric or lower +*> triangular) +*> store the lower triangle in banded format (if symmetric +*> or lower triangular) +*> store the upper triangle in banded format (if symmetric +*> or upper triangular) +*> store the entire matrix in banded format +*> If Method B is chosen, and band format is specified, then the +*> matrix will be generated in the band format, so no repacking +*> will be necessary. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of A. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of A. Not modified. +*> \endverbatim +*> +*> \param[in] DIST +*> \verbatim +*> DIST is CHARACTER*1 +*> On entry, DIST specifies the type of distribution to be used +*> to generate the random eigen-/singular values. +*> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) +*> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) +*> 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. They should lie between 0 and 4095 inclusive, +*> and ISEED(4) should be odd. The random number generator +*> uses a linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to SLATMS +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] SYM +*> \verbatim +*> SYM is CHARACTER*1 +*> If SYM='S' or 'H', the generated matrix is symmetric, with +*> eigenvalues specified by D, COND, MODE, and DMAX; they +*> may be positive, negative, or zero. +*> If SYM='P', the generated matrix is symmetric, with +*> eigenvalues (= singular values) specified by D, COND, +*> MODE, and DMAX; they will not be negative. +*> If SYM='N', the generated matrix is nonsymmetric, with +*> singular values specified by D, COND, MODE, and DMAX; +*> they will not be negative. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is REAL array, dimension ( MIN( M , N ) ) +*> This array is used to specify the singular values or +*> eigenvalues of A (see SYM, above.) If MODE=0, then D is +*> assumed to contain the singular/eigenvalues, otherwise +*> they will be computed according to MODE, COND, and DMAX, +*> and placed in D. +*> Modified if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry this describes how the singular/eigenvalues are to +*> be specified: +*> MODE = 0 means use D as input +*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND +*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> If SYM='S' or 'H', and MODE is neither 0, 6, nor -6, then +*> the elements of D will also be multiplied by a random +*> sign (i.e., +1 or -1.) +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is REAL +*> On entry, this is used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] DMAX +*> \verbatim +*> DMAX is REAL +*> If MODE is neither -6, 0 nor 6, the contents of D, as +*> computed according to MODE and COND, will be scaled by +*> DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or +*> singular value (which is to say the norm) will be abs(DMAX). +*> Note that DMAX need not be positive: if DMAX is negative +*> (or zero), D will be scaled by a negative number (or zero). +*> Not modified. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> This specifies the lower bandwidth of the matrix. For +*> example, KL=0 implies upper triangular, KL=1 implies upper +*> Hessenberg, and KL being at least M-1 means that the matrix +*> has full lower bandwidth. KL must equal KU if the matrix +*> is symmetric. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> This specifies the upper bandwidth of the matrix. For +*> example, KU=0 implies lower triangular, KU=1 implies lower +*> Hessenberg, and KU being at least N-1 means that the matrix +*> has full upper bandwidth. KL must equal KU if the matrix +*> is symmetric. +*> Not modified. +*> \endverbatim +*> +*> \param[in] PACK +*> \verbatim +*> PACK is CHARACTER*1 +*> This specifies packing of matrix as follows: +*> 'N' => no packing +*> 'U' => zero out all subdiagonal entries (if symmetric) +*> 'L' => zero out all superdiagonal entries (if symmetric) +*> 'C' => store the upper triangle columnwise +*> (only if the matrix is symmetric or upper triangular) +*> 'R' => store the lower triangle columnwise +*> (only if the matrix is symmetric or lower triangular) +*> 'B' => store the lower triangle in band storage scheme +*> (only if matrix symmetric or lower triangular) +*> 'Q' => store the upper triangle in band storage scheme +*> (only if matrix symmetric or upper triangular) +*> 'Z' => store the entire matrix in band storage scheme +*> (pivoting can be provided for by using this +*> option to store A in the trailing rows of +*> the allocated storage) +*> \endverbatim +*> \verbatim +*> Using these options, the various LAPACK packed and banded +*> storage schemes can be obtained: +*> GB - use 'Z' +*> PB, SB or TB - use 'B' or 'Q' +*> PP, SP or TP - use 'C' or 'R' +*> \endverbatim +*> \verbatim +*> If two calls to SLATMS differ only in the PACK parameter, +*> they will generate mathematically equivalent matrices. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is REAL array, dimension ( LDA, N ) +*> On exit A is the desired test matrix. A is first generated +*> in full (unpacked) form, and then packed, if so specified +*> by PACK. Thus, the first M elements of the first N +*> columns will always be modified. If PACK specifies a +*> packed or banded storage scheme, all LDA elements of the +*> first N columns will be modified; the elements of the +*> array which do not correspond to elements of the generated +*> matrix are set to zero. +*> Modified. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> LDA specifies the first dimension of A as declared in the +*> calling program. If PACK='N', 'U', 'L', 'C', or 'R', then +*> LDA must be at least M. If PACK='B' or 'Q', then LDA must +*> be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). +*> If PACK='Z', LDA must be large enough to hold the packed +*> array: MIN( KU, N-1) + MIN( KL, M-1) + 1. +*> Not modified. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is REAL array, dimension ( 3*MAX( N , M ) ) +*> Workspace. +*> Modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error code. On exit, INFO will be set to one of the +*> following values: +*> 0 => normal return +*> -1 => M negative or unequal to N and SYM='S', 'H', or 'P' +*> -2 => N negative +*> -3 => DIST illegal string +*> -5 => SYM illegal string +*> -7 => MODE not in range -6 to 6 +*> -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 +*> -10 => KL negative +*> -11 => KU negative, or SYM='S' or 'H' and KU not equal to KL +*> -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; +*> or PACK='C' or 'Q' and SYM='N' and KL is not zero; +*> or PACK='R' or 'B' and SYM='N' and KU is not zero; +*> or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not +*> N. +*> -14 => LDA is less than M, or PACK='Z' and LDA is less than +*> MIN(KU,N-1) + MIN(KL,M-1) + 1. +*> 1 => Error return from SLATM1 +*> 2 => Cannot scale to DMAX (max. sing. value is 0) +*> 3 => Error return from SLAGGE or SLAGSY +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup real_matgen +* +* ===================================================================== SUBROUTINE SLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, $ KL, KU, PACK, A, LDA, WORK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER DIST, PACK, SYM @@ -15,238 +340,6 @@ REAL A( LDA, * ), D( * ), WORK( * ) * .. * -* Purpose -* ======= -* -* SLATMS generates random matrices with specified singular values -* (or symmetric/hermitian with specified eigenvalues) -* for testing LAPACK programs. -* -* SLATMS operates by applying the following sequence of -* operations: -* -* Set the diagonal to D, where D may be input or -* computed according to MODE, COND, DMAX, and SYM -* as described below. -* -* Generate a matrix with the appropriate band structure, by one -* of two methods: -* -* Method A: -* Generate a dense M x N matrix by multiplying D on the left -* and the right by random unitary matrices, then: -* -* Reduce the bandwidth according to KL and KU, using -* Householder transformations. -* -* Method B: -* Convert the bandwidth-0 (i.e., diagonal) matrix to a -* bandwidth-1 matrix using Givens rotations, "chasing" -* out-of-band elements back, much as in QR; then -* convert the bandwidth-1 to a bandwidth-2 matrix, etc. -* Note that for reasonably small bandwidths (relative to -* M and N) this requires less storage, as a dense matrix -* is not generated. Also, for symmetric matrices, only -* one triangle is generated. -* -* Method A is chosen if the bandwidth is a large fraction of the -* order of the matrix, and LDA is at least M (so a dense -* matrix can be stored.) Method B is chosen if the bandwidth -* is small (< 1/2 N for symmetric, < .3 N+M for -* non-symmetric), or LDA is less than M and not less than the -* bandwidth. -* -* Pack the matrix if desired. Options specified by PACK are: -* no packing -* zero out upper half (if symmetric) -* zero out lower half (if symmetric) -* store the upper half columnwise (if symmetric or upper -* triangular) -* store the lower half columnwise (if symmetric or lower -* triangular) -* store the lower triangle in banded format (if symmetric -* or lower triangular) -* store the upper triangle in banded format (if symmetric -* or upper triangular) -* store the entire matrix in banded format -* If Method B is chosen, and band format is specified, then the -* matrix will be generated in the band format, so no repacking -* will be necessary. -* -* Arguments -* ========= -* -* M (input) INTEGER -* The number of rows of A. Not modified. -* -* N (input) INTEGER -* The number of columns of A. Not modified. -* -* DIST (input) CHARACTER*1 -* On entry, DIST specifies the type of distribution to be used -* to generate the random eigen-/singular values. -* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) -* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) -* 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. They should lie between 0 and 4095 inclusive, -* and ISEED(4) should be odd. The random number generator -* uses a linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to SLATMS -* to continue the same random number sequence. -* Changed on exit. -* -* SYM (input) CHARACTER*1 -* If SYM='S' or 'H', the generated matrix is symmetric, with -* eigenvalues specified by D, COND, MODE, and DMAX; they -* may be positive, negative, or zero. -* If SYM='P', the generated matrix is symmetric, with -* eigenvalues (= singular values) specified by D, COND, -* MODE, and DMAX; they will not be negative. -* If SYM='N', the generated matrix is nonsymmetric, with -* singular values specified by D, COND, MODE, and DMAX; -* they will not be negative. -* Not modified. -* -* D (input/output) REAL array, dimension ( MIN( M , N ) ) -* This array is used to specify the singular values or -* eigenvalues of A (see SYM, above.) If MODE=0, then D is -* assumed to contain the singular/eigenvalues, otherwise -* they will be computed according to MODE, COND, and DMAX, -* and placed in D. -* Modified if MODE is nonzero. -* -* MODE (input) INTEGER -* On entry this describes how the singular/eigenvalues are to -* be specified: -* MODE = 0 means use D as input -* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND -* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* If SYM='S' or 'H', and MODE is neither 0, 6, nor -6, then -* the elements of D will also be multiplied by a random -* sign (i.e., +1 or -1.) -* Not modified. -* -* COND (input) REAL -* On entry, this is used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* DMAX (input) REAL -* If MODE is neither -6, 0 nor 6, the contents of D, as -* computed according to MODE and COND, will be scaled by -* DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or -* singular value (which is to say the norm) will be abs(DMAX). -* Note that DMAX need not be positive: if DMAX is negative -* (or zero), D will be scaled by a negative number (or zero). -* Not modified. -* -* KL (input) INTEGER -* This specifies the lower bandwidth of the matrix. For -* example, KL=0 implies upper triangular, KL=1 implies upper -* Hessenberg, and KL being at least M-1 means that the matrix -* has full lower bandwidth. KL must equal KU if the matrix -* is symmetric. -* Not modified. -* -* KU (input) INTEGER -* This specifies the upper bandwidth of the matrix. For -* example, KU=0 implies lower triangular, KU=1 implies lower -* Hessenberg, and KU being at least N-1 means that the matrix -* has full upper bandwidth. KL must equal KU if the matrix -* is symmetric. -* Not modified. -* -* PACK (input) CHARACTER*1 -* This specifies packing of matrix as follows: -* 'N' => no packing -* 'U' => zero out all subdiagonal entries (if symmetric) -* 'L' => zero out all superdiagonal entries (if symmetric) -* 'C' => store the upper triangle columnwise -* (only if the matrix is symmetric or upper triangular) -* 'R' => store the lower triangle columnwise -* (only if the matrix is symmetric or lower triangular) -* 'B' => store the lower triangle in band storage scheme -* (only if matrix symmetric or lower triangular) -* 'Q' => store the upper triangle in band storage scheme -* (only if matrix symmetric or upper triangular) -* 'Z' => store the entire matrix in band storage scheme -* (pivoting can be provided for by using this -* option to store A in the trailing rows of -* the allocated storage) -* -* Using these options, the various LAPACK packed and banded -* storage schemes can be obtained: -* GB - use 'Z' -* PB, SB or TB - use 'B' or 'Q' -* PP, SP or TP - use 'C' or 'R' -* -* If two calls to SLATMS differ only in the PACK parameter, -* they will generate mathematically equivalent matrices. -* Not modified. -* -* A (input/output) REAL array, dimension ( LDA, N ) -* On exit A is the desired test matrix. A is first generated -* in full (unpacked) form, and then packed, if so specified -* by PACK. Thus, the first M elements of the first N -* columns will always be modified. If PACK specifies a -* packed or banded storage scheme, all LDA elements of the -* first N columns will be modified; the elements of the -* array which do not correspond to elements of the generated -* matrix are set to zero. -* Modified. -* -* LDA (input) INTEGER -* LDA specifies the first dimension of A as declared in the -* calling program. If PACK='N', 'U', 'L', 'C', or 'R', then -* LDA must be at least M. If PACK='B' or 'Q', then LDA must -* be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). -* If PACK='Z', LDA must be large enough to hold the packed -* array: MIN( KU, N-1) + MIN( KL, M-1) + 1. -* Not modified. -* -* WORK (workspace) REAL array, dimension ( 3*MAX( N , M ) ) -* Workspace. -* Modified. -* -* INFO (output) INTEGER -* Error code. On exit, INFO will be set to one of the -* following values: -* 0 => normal return -* -1 => M negative or unequal to N and SYM='S', 'H', or 'P' -* -2 => N negative -* -3 => DIST illegal string -* -5 => SYM illegal string -* -7 => MODE not in range -6 to 6 -* -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 -* -10 => KL negative -* -11 => KU negative, or SYM='S' or 'H' and KU not equal to KL -* -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; -* or PACK='C' or 'Q' and SYM='N' and KL is not zero; -* or PACK='R' or 'B' and SYM='N' and KU is not zero; -* or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not -* N. -* -14 => LDA is less than M, or PACK='Z' and LDA is less than -* MIN(KU,N-1) + MIN(KL,M-1) + 1. -* 1 => Error return from SLATM1 -* 2 => Cannot scale to DMAX (max. sing. value is 0) -* 3 => Error return from SLAGGE or SLAGSY -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/slatmt.f b/TESTING/MATGEN/slatmt.f index 6e5007c1..5a75b53c 100644 --- a/TESTING/MATGEN/slatmt.f +++ b/TESTING/MATGEN/slatmt.f @@ -1,9 +1,346 @@ +*> \brief \b SLATMT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SLATMT( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, +* RANK, KL, KU, PACK, A, LDA, WORK, INFO ) +* +* .. Scalar Arguments .. +* REAL COND, DMAX +* INTEGER INFO, KL, KU, LDA, M, MODE, N, RANK +* CHARACTER DIST, PACK, SYM +* .. +* .. Array Arguments .. +* REAL A( LDA, * ), D( * ), WORK( * ) +* INTEGER ISEED( 4 ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> SLATMT generates random matrices with specified singular values +*> (or symmetric/hermitian with specified eigenvalues) +*> for testing LAPACK programs. +*> +*> SLATMT operates by applying the following sequence of +*> operations: +*> +*> Set the diagonal to D, where D may be input or +*> computed according to MODE, COND, DMAX, and SYM +*> as described below. +*> +*> Generate a matrix with the appropriate band structure, by one +*> of two methods: +*> +*> Method A: +*> Generate a dense M x N matrix by multiplying D on the left +*> and the right by random unitary matrices, then: +*> +*> Reduce the bandwidth according to KL and KU, using +*> Householder transformations. +*> +*> Method B: +*> Convert the bandwidth-0 (i.e., diagonal) matrix to a +*> bandwidth-1 matrix using Givens rotations, "chasing" +*> out-of-band elements back, much as in QR; then +*> convert the bandwidth-1 to a bandwidth-2 matrix, etc. +*> Note that for reasonably small bandwidths (relative to +*> M and N) this requires less storage, as a dense matrix +*> is not generated. Also, for symmetric matrices, only +*> one triangle is generated. +*> +*> Method A is chosen if the bandwidth is a large fraction of the +*> order of the matrix, and LDA is at least M (so a dense +*> matrix can be stored.) Method B is chosen if the bandwidth +*> is small (< 1/2 N for symmetric, < .3 N+M for +*> non-symmetric), or LDA is less than M and not less than the +*> bandwidth. +*> +*> Pack the matrix if desired. Options specified by PACK are: +*> no packing +*> zero out upper half (if symmetric) +*> zero out lower half (if symmetric) +*> store the upper half columnwise (if symmetric or upper +*> triangular) +*> store the lower half columnwise (if symmetric or lower +*> triangular) +*> store the lower triangle in banded format (if symmetric +*> or lower triangular) +*> store the upper triangle in banded format (if symmetric +*> or upper triangular) +*> store the entire matrix in banded format +*> If Method B is chosen, and band format is specified, then the +*> matrix will be generated in the band format, so no repacking +*> will be necessary. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of A. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of A. Not modified. +*> \endverbatim +*> +*> \param[in] DIST +*> \verbatim +*> DIST is CHARACTER*1 +*> On entry, DIST specifies the type of distribution to be used +*> to generate the random eigen-/singular values. +*> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) +*> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) +*> 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. They should lie between 0 and 4095 inclusive, +*> and ISEED(4) should be odd. The random number generator +*> uses a linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to SLATMT +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] SYM +*> \verbatim +*> SYM is CHARACTER*1 +*> If SYM='S' or 'H', the generated matrix is symmetric, with +*> eigenvalues specified by D, COND, MODE, and DMAX; they +*> may be positive, negative, or zero. +*> If SYM='P', the generated matrix is symmetric, with +*> eigenvalues (= singular values) specified by D, COND, +*> MODE, and DMAX; they will not be negative. +*> If SYM='N', the generated matrix is nonsymmetric, with +*> singular values specified by D, COND, MODE, and DMAX; +*> they will not be negative. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is REAL array, dimension ( MIN( M , N ) ) +*> This array is used to specify the singular values or +*> eigenvalues of A (see SYM, above.) If MODE=0, then D is +*> assumed to contain the singular/eigenvalues, otherwise +*> they will be computed according to MODE, COND, and DMAX, +*> and placed in D. +*> Modified if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry this describes how the singular/eigenvalues are to +*> be specified: +*> MODE = 0 means use D as input +*> \endverbatim +*> \verbatim +*> MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND +*> MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) +*> \endverbatim +*> \verbatim +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> If SYM='S' or 'H', and MODE is neither 0, 6, nor -6, then +*> the elements of D will also be multiplied by a random +*> sign (i.e., +1 or -1.) +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is REAL +*> On entry, this is used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] DMAX +*> \verbatim +*> DMAX is REAL +*> If MODE is neither -6, 0 nor 6, the contents of D, as +*> computed according to MODE and COND, will be scaled by +*> DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or +*> singular value (which is to say the norm) will be abs(DMAX). +*> Note that DMAX need not be positive: if DMAX is negative +*> (or zero), D will be scaled by a negative number (or zero). +*> Not modified. +*> \endverbatim +*> +*> \param[in] RANK +*> \verbatim +*> RANK is INTEGER +*> The rank of matrix to be generated for modes 1,2,3 only. +*> D( RANK+1:N ) = 0. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> This specifies the lower bandwidth of the matrix. For +*> example, KL=0 implies upper triangular, KL=1 implies upper +*> Hessenberg, and KL being at least M-1 means that the matrix +*> has full lower bandwidth. KL must equal KU if the matrix +*> is symmetric. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> This specifies the upper bandwidth of the matrix. For +*> example, KU=0 implies lower triangular, KU=1 implies lower +*> Hessenberg, and KU being at least N-1 means that the matrix +*> has full upper bandwidth. KL must equal KU if the matrix +*> is symmetric. +*> Not modified. +*> \endverbatim +*> +*> \param[in] PACK +*> \verbatim +*> PACK is CHARACTER*1 +*> This specifies packing of matrix as follows: +*> 'N' => no packing +*> 'U' => zero out all subdiagonal entries (if symmetric) +*> 'L' => zero out all superdiagonal entries (if symmetric) +*> 'C' => store the upper triangle columnwise +*> (only if the matrix is symmetric or upper triangular) +*> 'R' => store the lower triangle columnwise +*> (only if the matrix is symmetric or lower triangular) +*> 'B' => store the lower triangle in band storage scheme +*> (only if matrix symmetric or lower triangular) +*> 'Q' => store the upper triangle in band storage scheme +*> (only if matrix symmetric or upper triangular) +*> 'Z' => store the entire matrix in band storage scheme +*> (pivoting can be provided for by using this +*> option to store A in the trailing rows of +*> the allocated storage) +*> \endverbatim +*> \verbatim +*> Using these options, the various LAPACK packed and banded +*> storage schemes can be obtained: +*> GB - use 'Z' +*> PB, SB or TB - use 'B' or 'Q' +*> PP, SP or TP - use 'C' or 'R' +*> \endverbatim +*> \verbatim +*> If two calls to SLATMT differ only in the PACK parameter, +*> they will generate mathematically equivalent matrices. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is REAL array, dimension ( LDA, N ) +*> On exit A is the desired test matrix. A is first generated +*> in full (unpacked) form, and then packed, if so specified +*> by PACK. Thus, the first M elements of the first N +*> columns will always be modified. If PACK specifies a +*> packed or banded storage scheme, all LDA elements of the +*> first N columns will be modified; the elements of the +*> array which do not correspond to elements of the generated +*> matrix are set to zero. +*> Modified. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> LDA specifies the first dimension of A as declared in the +*> calling program. If PACK='N', 'U', 'L', 'C', or 'R', then +*> LDA must be at least M. If PACK='B' or 'Q', then LDA must +*> be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). +*> If PACK='Z', LDA must be large enough to hold the packed +*> array: MIN( KU, N-1) + MIN( KL, M-1) + 1. +*> Not modified. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is REAL array, dimension ( 3*MAX( N , M ) ) +*> Workspace. +*> Modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error code. On exit, INFO will be set to one of the +*> following values: +*> 0 => normal return +*> -1 => M negative or unequal to N and SYM='S', 'H', or 'P' +*> -2 => N negative +*> -3 => DIST illegal string +*> -5 => SYM illegal string +*> -7 => MODE not in range -6 to 6 +*> -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 +*> -10 => KL negative +*> -11 => KU negative, or SYM='S' or 'H' and KU not equal to KL +*> -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; +*> or PACK='C' or 'Q' and SYM='N' and KL is not zero; +*> or PACK='R' or 'B' and SYM='N' and KU is not zero; +*> or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not +*> N. +*> -14 => LDA is less than M, or PACK='Z' and LDA is less than +*> MIN(KU,N-1) + MIN(KL,M-1) + 1. +*> 1 => Error return from SLATM7 +*> 2 => Cannot scale to DMAX (max. sing. value is 0) +*> 3 => Error return from SLAGGE or SLAGSY +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup real_matgen +* +* ===================================================================== SUBROUTINE SLATMT( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, $ RANK, KL, KU, PACK, A, LDA, WORK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Craig Lucas, University of Manchester / NAG Ltd. -* October, 2008 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. REAL COND, DMAX @@ -15,245 +352,6 @@ INTEGER ISEED( 4 ) * .. * -* Purpose -* ======= -* -* SLATMT generates random matrices with specified singular values -* (or symmetric/hermitian with specified eigenvalues) -* for testing LAPACK programs. -* -* SLATMT operates by applying the following sequence of -* operations: -* -* Set the diagonal to D, where D may be input or -* computed according to MODE, COND, DMAX, and SYM -* as described below. -* -* Generate a matrix with the appropriate band structure, by one -* of two methods: -* -* Method A: -* Generate a dense M x N matrix by multiplying D on the left -* and the right by random unitary matrices, then: -* -* Reduce the bandwidth according to KL and KU, using -* Householder transformations. -* -* Method B: -* Convert the bandwidth-0 (i.e., diagonal) matrix to a -* bandwidth-1 matrix using Givens rotations, "chasing" -* out-of-band elements back, much as in QR; then -* convert the bandwidth-1 to a bandwidth-2 matrix, etc. -* Note that for reasonably small bandwidths (relative to -* M and N) this requires less storage, as a dense matrix -* is not generated. Also, for symmetric matrices, only -* one triangle is generated. -* -* Method A is chosen if the bandwidth is a large fraction of the -* order of the matrix, and LDA is at least M (so a dense -* matrix can be stored.) Method B is chosen if the bandwidth -* is small (< 1/2 N for symmetric, < .3 N+M for -* non-symmetric), or LDA is less than M and not less than the -* bandwidth. -* -* Pack the matrix if desired. Options specified by PACK are: -* no packing -* zero out upper half (if symmetric) -* zero out lower half (if symmetric) -* store the upper half columnwise (if symmetric or upper -* triangular) -* store the lower half columnwise (if symmetric or lower -* triangular) -* store the lower triangle in banded format (if symmetric -* or lower triangular) -* store the upper triangle in banded format (if symmetric -* or upper triangular) -* store the entire matrix in banded format -* If Method B is chosen, and band format is specified, then the -* matrix will be generated in the band format, so no repacking -* will be necessary. -* -* Arguments -* ========= -* -* M (input) INTEGER -* The number of rows of A. Not modified. -* -* N (input) INTEGER -* The number of columns of A. Not modified. -* -* DIST (input) CHARACTER*1 -* On entry, DIST specifies the type of distribution to be used -* to generate the random eigen-/singular values. -* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) -* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) -* 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. They should lie between 0 and 4095 inclusive, -* and ISEED(4) should be odd. The random number generator -* uses a linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to SLATMT -* to continue the same random number sequence. -* Changed on exit. -* -* SYM (input) CHARACTER*1 -* If SYM='S' or 'H', the generated matrix is symmetric, with -* eigenvalues specified by D, COND, MODE, and DMAX; they -* may be positive, negative, or zero. -* If SYM='P', the generated matrix is symmetric, with -* eigenvalues (= singular values) specified by D, COND, -* MODE, and DMAX; they will not be negative. -* If SYM='N', the generated matrix is nonsymmetric, with -* singular values specified by D, COND, MODE, and DMAX; -* they will not be negative. -* Not modified. -* -* D (input/output) REAL array, dimension ( MIN( M , N ) ) -* This array is used to specify the singular values or -* eigenvalues of A (see SYM, above.) If MODE=0, then D is -* assumed to contain the singular/eigenvalues, otherwise -* they will be computed according to MODE, COND, and DMAX, -* and placed in D. -* Modified if MODE is nonzero. -* -* MODE (input) INTEGER -* On entry this describes how the singular/eigenvalues are to -* be specified: -* MODE = 0 means use D as input -* -* MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND -* MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) -* -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* If SYM='S' or 'H', and MODE is neither 0, 6, nor -6, then -* the elements of D will also be multiplied by a random -* sign (i.e., +1 or -1.) -* Not modified. -* -* COND (input) REAL -* On entry, this is used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* DMAX (input) REAL -* If MODE is neither -6, 0 nor 6, the contents of D, as -* computed according to MODE and COND, will be scaled by -* DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or -* singular value (which is to say the norm) will be abs(DMAX). -* Note that DMAX need not be positive: if DMAX is negative -* (or zero), D will be scaled by a negative number (or zero). -* Not modified. -* -* RANK (input) INTEGER -* The rank of matrix to be generated for modes 1,2,3 only. -* D( RANK+1:N ) = 0. -* Not modified. -* -* KL (input) INTEGER -* This specifies the lower bandwidth of the matrix. For -* example, KL=0 implies upper triangular, KL=1 implies upper -* Hessenberg, and KL being at least M-1 means that the matrix -* has full lower bandwidth. KL must equal KU if the matrix -* is symmetric. -* Not modified. -* -* KU (input) INTEGER -* This specifies the upper bandwidth of the matrix. For -* example, KU=0 implies lower triangular, KU=1 implies lower -* Hessenberg, and KU being at least N-1 means that the matrix -* has full upper bandwidth. KL must equal KU if the matrix -* is symmetric. -* Not modified. -* -* PACK (input) CHARACTER*1 -* This specifies packing of matrix as follows: -* 'N' => no packing -* 'U' => zero out all subdiagonal entries (if symmetric) -* 'L' => zero out all superdiagonal entries (if symmetric) -* 'C' => store the upper triangle columnwise -* (only if the matrix is symmetric or upper triangular) -* 'R' => store the lower triangle columnwise -* (only if the matrix is symmetric or lower triangular) -* 'B' => store the lower triangle in band storage scheme -* (only if matrix symmetric or lower triangular) -* 'Q' => store the upper triangle in band storage scheme -* (only if matrix symmetric or upper triangular) -* 'Z' => store the entire matrix in band storage scheme -* (pivoting can be provided for by using this -* option to store A in the trailing rows of -* the allocated storage) -* -* Using these options, the various LAPACK packed and banded -* storage schemes can be obtained: -* GB - use 'Z' -* PB, SB or TB - use 'B' or 'Q' -* PP, SP or TP - use 'C' or 'R' -* -* If two calls to SLATMT differ only in the PACK parameter, -* they will generate mathematically equivalent matrices. -* Not modified. -* -* A (input/output) REAL array, dimension ( LDA, N ) -* On exit A is the desired test matrix. A is first generated -* in full (unpacked) form, and then packed, if so specified -* by PACK. Thus, the first M elements of the first N -* columns will always be modified. If PACK specifies a -* packed or banded storage scheme, all LDA elements of the -* first N columns will be modified; the elements of the -* array which do not correspond to elements of the generated -* matrix are set to zero. -* Modified. -* -* LDA (input) INTEGER -* LDA specifies the first dimension of A as declared in the -* calling program. If PACK='N', 'U', 'L', 'C', or 'R', then -* LDA must be at least M. If PACK='B' or 'Q', then LDA must -* be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). -* If PACK='Z', LDA must be large enough to hold the packed -* array: MIN( KU, N-1) + MIN( KL, M-1) + 1. -* Not modified. -* -* WORK (workspace) REAL array, dimension ( 3*MAX( N , M ) ) -* Workspace. -* Modified. -* -* INFO (output) INTEGER -* Error code. On exit, INFO will be set to one of the -* following values: -* 0 => normal return -* -1 => M negative or unequal to N and SYM='S', 'H', or 'P' -* -2 => N negative -* -3 => DIST illegal string -* -5 => SYM illegal string -* -7 => MODE not in range -6 to 6 -* -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 -* -10 => KL negative -* -11 => KU negative, or SYM='S' or 'H' and KU not equal to KL -* -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; -* or PACK='C' or 'Q' and SYM='N' and KL is not zero; -* or PACK='R' or 'B' and SYM='N' and KU is not zero; -* or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not -* N. -* -14 => LDA is less than M, or PACK='Z' and LDA is less than -* MIN(KU,N-1) + MIN(KL,M-1) + 1. -* 1 => Error return from SLATM7 -* 2 => Cannot scale to DMAX (max. sing. value is 0) -* 3 => Error return from SLAGGE or SLAGSY -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/zlagge.f b/TESTING/MATGEN/zlagge.f index ce5b7358..5963699d 100644 --- a/TESTING/MATGEN/zlagge.f +++ b/TESTING/MATGEN/zlagge.f @@ -1,63 +1,134 @@ - SUBROUTINE ZLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) -* -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER INFO, KL, KU, LDA, M, N -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) - DOUBLE PRECISION D( * ) - COMPLEX*16 A( LDA, * ), WORK( * ) -* .. -* +*> \brief \b ZLAGGE +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, KL, KU, LDA, M, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* DOUBLE PRECISION D( * ) +* COMPLEX*16 A( LDA, * ), WORK( * ) +* .. +* * Purpose * ======= * -* ZLAGGE generates a complex general m by n matrix A, by pre- and post- -* multiplying a real diagonal matrix D with random unitary matrices: -* A = U*D*V. The lower and upper bandwidths may then be reduced to -* kl and ku by additional unitary transformations. +*>\details \b Purpose: +*>\verbatim +*> +*> ZLAGGE generates a complex general m by n matrix A, by pre- and post- +*> multiplying a real diagonal matrix D with random unitary matrices: +*> A = U*D*V. The lower and upper bandwidths may then be reduced to +*> kl and ku by additional unitary transformations. +*> +*>\endverbatim * * Arguments * ========= * -* M (input) INTEGER -* The number of rows of the matrix A. M >= 0. -* -* N (input) INTEGER -* The number of columns of the matrix A. N >= 0. -* -* KL (input) INTEGER -* The number of nonzero subdiagonals within the band of A. -* 0 <= KL <= M-1. -* -* KU (input) INTEGER -* The number of nonzero superdiagonals within the band of A. -* 0 <= KU <= N-1. +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> The number of nonzero subdiagonals within the band of A. +*> 0 <= KL <= M-1. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> The number of nonzero superdiagonals within the band of A. +*> 0 <= KU <= N-1. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (min(M,N)) +*> The diagonal elements of the diagonal matrix D. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> The generated m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= M. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension (M+N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= * -* D (input) DOUBLE PRECISION array, dimension (min(M,N)) -* The diagonal elements of the diagonal matrix D. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (output) COMPLEX*16 array, dimension (LDA,N) -* The generated m by n matrix A. +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= M. +*> \ingroup complex16_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. +* ===================================================================== + SUBROUTINE ZLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) * -* WORK (workspace) COMPLEX*16 array, dimension (M+N) +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value +* .. Scalar Arguments .. + INTEGER INFO, KL, KU, LDA, M, N +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) + DOUBLE PRECISION D( * ) + COMPLEX*16 A( LDA, * ), WORK( * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/zlaghe.f b/TESTING/MATGEN/zlaghe.f index 0e86fc33..8e9c6e3c 100644 --- a/TESTING/MATGEN/zlaghe.f +++ b/TESTING/MATGEN/zlaghe.f @@ -1,57 +1,122 @@ - SUBROUTINE ZLAGHE( N, K, D, A, LDA, ISEED, WORK, INFO ) -* -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, N -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) - DOUBLE PRECISION D( * ) - COMPLEX*16 A( LDA, * ), WORK( * ) -* .. -* +*> \brief \b ZLAGHE +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZLAGHE( N, K, D, A, LDA, ISEED, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, K, LDA, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* DOUBLE PRECISION D( * ) +* COMPLEX*16 A( LDA, * ), WORK( * ) +* .. +* * Purpose * ======= * -* ZLAGHE generates a complex hermitian matrix A, by pre- and post- -* multiplying a real diagonal matrix D with a random unitary matrix: -* A = U*D*U'. The semi-bandwidth may then be reduced to k by additional -* unitary transformations. +*>\details \b Purpose: +*>\verbatim +*> +*> ZLAGHE generates a complex hermitian matrix A, by pre- and post- +*> multiplying a real diagonal matrix D with a random unitary matrix: +*> A = U*D*U'. The semi-bandwidth may then be reduced to k by additional +*> unitary transformations. +*> +*>\endverbatim * * Arguments * ========= * -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* K (input) INTEGER -* The number of nonzero subdiagonals within the band of A. -* 0 <= K <= N-1. +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The number of nonzero subdiagonals within the band of A. +*> 0 <= K <= N-1. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> The diagonal elements of the diagonal matrix D. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> The generated n by n hermitian matrix A (the full matrix is +*> stored). +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= N. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension (2*N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= * -* D (input) DOUBLE PRECISION array, dimension (N) -* The diagonal elements of the diagonal matrix D. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (output) COMPLEX*16 array, dimension (LDA,N) -* The generated n by n hermitian matrix A (the full matrix is -* stored). +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= N. +*> \ingroup complex16_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. +* ===================================================================== + SUBROUTINE ZLAGHE( N, K, D, A, LDA, ISEED, WORK, INFO ) * -* WORK (workspace) COMPLEX*16 array, dimension (2*N) +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value +* .. Scalar Arguments .. + INTEGER INFO, K, LDA, N +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) + DOUBLE PRECISION D( * ) + COMPLEX*16 A( LDA, * ), WORK( * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/zlagsy.f b/TESTING/MATGEN/zlagsy.f index 7adb609b..317d2489 100644 --- a/TESTING/MATGEN/zlagsy.f +++ b/TESTING/MATGEN/zlagsy.f @@ -1,57 +1,122 @@ - SUBROUTINE ZLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO ) -* -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, N -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) - DOUBLE PRECISION D( * ) - COMPLEX*16 A( LDA, * ), WORK( * ) -* .. -* +*> \brief \b ZLAGSY +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, K, LDA, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* DOUBLE PRECISION D( * ) +* COMPLEX*16 A( LDA, * ), WORK( * ) +* .. +* * Purpose * ======= * -* ZLAGSY generates a complex symmetric matrix A, by pre- and post- -* multiplying a real diagonal matrix D with a random unitary matrix: -* A = U*D*U**T. The semi-bandwidth may then be reduced to k by -* additional unitary transformations. +*>\details \b Purpose: +*>\verbatim +*> +*> ZLAGSY generates a complex symmetric matrix A, by pre- and post- +*> multiplying a real diagonal matrix D with a random unitary matrix: +*> A = U*D*U**T. The semi-bandwidth may then be reduced to k by +*> additional unitary transformations. +*> +*>\endverbatim * * Arguments * ========= * -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* K (input) INTEGER -* The number of nonzero subdiagonals within the band of A. -* 0 <= K <= N-1. +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The number of nonzero subdiagonals within the band of A. +*> 0 <= K <= N-1. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> The diagonal elements of the diagonal matrix D. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> The generated n by n symmetric matrix A (the full matrix is +*> stored). +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= N. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension (2*N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= * -* D (input) DOUBLE PRECISION array, dimension (N) -* The diagonal elements of the diagonal matrix D. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (output) COMPLEX*16 array, dimension (LDA,N) -* The generated n by n symmetric matrix A (the full matrix is -* stored). +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= N. +*> \ingroup complex16_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. +* ===================================================================== + SUBROUTINE ZLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO ) * -* WORK (workspace) COMPLEX*16 array, dimension (2*N) +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value +* .. Scalar Arguments .. + INTEGER INFO, K, LDA, N +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) + DOUBLE PRECISION D( * ) + COMPLEX*16 A( LDA, * ), WORK( * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/zlahilb.f b/TESTING/MATGEN/zlahilb.f index a9378c4c..53df5089 100644 --- a/TESTING/MATGEN/zlahilb.f +++ b/TESTING/MATGEN/zlahilb.f @@ -1,104 +1,167 @@ +*> \brief \b ZLAHILB +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZLAHILB( N, NRHS, A, LDA, X, LDX, B, LDB, WORK, +* INFO, PATH) +* +* .. Scalar Arguments .. +* INTEGER N, NRHS, LDA, LDX, LDB, INFO +* .. Array Arguments .. +* DOUBLE PRECISION WORK(N) +* COMPLEX*16 A(LDA,N), X(LDX, NRHS), B(LDB, NRHS) +* CHARACTER*3 PATH +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> ZLAHILB generates an N by N scaled Hilbert matrix in A along with +*> NRHS right-hand sides in B and solutions in X such that A*X=B. +*> +*> The Hilbert matrix is scaled by M = LCM(1, 2, ..., 2*N-1) so that all +*> entries are integers. The right-hand sides are the first NRHS +*> columns of M * the identity matrix, and the solutions are the +*> first NRHS columns of the inverse Hilbert matrix. +*> +*> The condition number of the Hilbert matrix grows exponentially with +*> its size, roughly as O(e ** (3.5*N)). Additionally, the inverse +*> Hilbert matrices beyond a relatively small dimension cannot be +*> generated exactly without extra precision. Precision is exhausted +*> when the largest entry in the inverse Hilbert matrix is greater than +*> 2 to the power of the number of bits in the fraction of the data type +*> used plus one, which is 24 for single precision. +*> +*> In single, the generated solution is exact for N <= 6 and has +*> small componentwise error for 7 <= N <= 11. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The dimension of the matrix A. +*> \endverbatim +*> +*> \param[in] NRHS +*> \verbatim +*> NRHS is INTEGER +*> The requested number of right-hand sides. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is COMPLEX array, dimension (LDA, N) +*> The generated scaled Hilbert matrix. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= N. +*> \endverbatim +*> +*> \param[out] X +*> \verbatim +*> X is COMPLEX array, dimension (LDX, NRHS) +*> The generated exact solutions. Currently, the first NRHS +*> columns of the inverse Hilbert matrix. +*> \endverbatim +*> +*> \param[in] LDX +*> \verbatim +*> LDX is INTEGER +*> The leading dimension of the array X. LDX >= N. +*> \endverbatim +*> +*> \param[out] B +*> \verbatim +*> B is REAL array, dimension (LDB, NRHS) +*> The generated right-hand sides. Currently, the first NRHS +*> columns of LCM(1, 2, ..., 2*N-1) * the identity matrix. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of the array B. LDB >= N. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is REAL array, dimension (N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> = 1: N is too large; the data is still generated but may not +*> be not exact. +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_matgen +* +* ===================================================================== SUBROUTINE ZLAHILB( N, NRHS, A, LDA, X, LDX, B, LDB, WORK, $ INFO, PATH) -! -! -- LAPACK auxiliary test routine (version 3.2.2) -- -! Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., -! Courant Institute, Argonne National Lab, and Rice University -* June 2010 -! -! David Vu <dtv@cs.berkeley.edu> -! Yozo Hida <yozo@cs.berkeley.edu> -! Jason Riedy <ejr@cs.berkeley.edu> -! D. Halligan <dhalligan@berkeley.edu> -! - IMPLICIT NONE -! .. Scalar Arguments .. +* +* -- LAPACK auxiliary routine (version 3.2.2) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. INTEGER N, NRHS, LDA, LDX, LDB, INFO -! .. Array Arguments .. +* .. Array Arguments .. DOUBLE PRECISION WORK(N) COMPLEX*16 A(LDA,N), X(LDX, NRHS), B(LDB, NRHS) CHARACTER*3 PATH -! .. -! -! Purpose -! ======= -! -! ZLAHILB generates an N by N scaled Hilbert matrix in A along with -! NRHS right-hand sides in B and solutions in X such that A*X=B. -! -! The Hilbert matrix is scaled by M = LCM(1, 2, ..., 2*N-1) so that all -! entries are integers. The right-hand sides are the first NRHS -! columns of M * the identity matrix, and the solutions are the -! first NRHS columns of the inverse Hilbert matrix. -! -! The condition number of the Hilbert matrix grows exponentially with -! its size, roughly as O(e ** (3.5*N)). Additionally, the inverse -! Hilbert matrices beyond a relatively small dimension cannot be -! generated exactly without extra precision. Precision is exhausted -! when the largest entry in the inverse Hilbert matrix is greater than -! 2 to the power of the number of bits in the fraction of the data type -! used plus one, which is 24 for single precision. -! -! In single, the generated solution is exact for N <= 6 and has -! small componentwise error for 7 <= N <= 11. -! -! Arguments -! ========= -! -! N (input) INTEGER -! The dimension of the matrix A. -! -! NRHS (input) INTEGER -! The requested number of right-hand sides. -! -! A (output) COMPLEX array, dimension (LDA, N) -! The generated scaled Hilbert matrix. -! -! LDA (input) INTEGER -! The leading dimension of the array A. LDA >= N. -! -! X (output) COMPLEX array, dimension (LDX, NRHS) -! The generated exact solutions. Currently, the first NRHS -! columns of the inverse Hilbert matrix. -! -! LDX (input) INTEGER -! The leading dimension of the array X. LDX >= N. -! -! B (output) REAL array, dimension (LDB, NRHS) -! The generated right-hand sides. Currently, the first NRHS -! columns of LCM(1, 2, ..., 2*N-1) * the identity matrix. -! -! LDB (input) INTEGER -! The leading dimension of the array B. LDB >= N. -! -! WORK (workspace) REAL array, dimension (N) -! -! -! INFO (output) INTEGER -! = 0: successful exit -! = 1: N is too large; the data is still generated but may not -! be not exact. -! < 0: if INFO = -i, the i-th argument had an illegal value -! -! ===================================================================== +* .. +* +* ===================================================================== -! .. Local Scalars .. +* .. Local Scalars .. INTEGER TM, TI, R INTEGER M INTEGER I, J COMPLEX*16 TMP CHARACTER*2 C2 -! .. Parameters .. -! NMAX_EXACT the largest dimension where the generated data is -! exact. -! NMAX_APPROX the largest dimension where the generated data has -! a small componentwise relative error. -! ??? complex uses how many bits ??? +* .. Parameters .. +* NMAX_EXACT the largest dimension where the generated data is +* exact. +* NMAX_APPROX the largest dimension where the generated data has +* a small componentwise relative error. +* ??? complex uses how many bits ??? INTEGER NMAX_EXACT, NMAX_APPROX, SIZE_D PARAMETER (NMAX_EXACT = 6, NMAX_APPROX = 11, SIZE_D = 8) -! d's are generated from random permuation of those eight elements. +* d's are generated from random permuation of those eight elements. COMPLEX*16 d1(8), d2(8), invd1(8), invd2(8) DATA D1 /(-1,0),(0,1),(-1,-1),(0,-1),(1,0),(-1,1),(1,1),(1,-1)/ DATA D2 /(-1,0),(0,-1),(-1,1),(0,1),(1,0),(-1,-1),(1,-1),(1,1)/ @@ -107,17 +170,17 @@ $ (-.5,-.5),(.5,-.5),(.5,.5)/ DATA INVD2 /(-1,0),(0,1),(-.5,-.5),(0,-1),(1,0), $ (-.5,.5),(.5,.5),(.5,-.5)/ -! .. -! .. External Functions +* .. +* .. External Functions EXTERNAL ZLASET, LSAMEN INTRINSIC DBLE LOGICAL LSAMEN -! .. -! .. Executable Statements .. +* .. +* .. Executable Statements .. C2 = PATH( 2: 3 ) -! -! Test the input arguments -! +* +* Test the input arguments +* INFO = 0 IF (N .LT. 0 .OR. N .GT. NMAX_APPROX) THEN INFO = -1 @@ -138,8 +201,8 @@ INFO = 1 END IF -! Compute M = the LCM of the integers [1, 2*N-1]. The largest -! reasonable N is small enough that integers suffice (up to N = 11). +* Compute M = the LCM of the integers [1, 2*N-1]. The largest +* reasonable N is small enough that integers suffice (up to N = 11). M = 1 DO I = 2, (2*N-1) TM = M @@ -153,9 +216,9 @@ M = (M / TI) * I END DO -! Generate the scaled Hilbert matrix in A -! If we are testing SY routines, -! take D1_i = D2_i, else, D1_i = D2_i* +* Generate the scaled Hilbert matrix in A +* If we are testing SY routines, +* take D1_i = D2_i, else, D1_i = D2_i* IF ( LSAMEN( 2, C2, 'SY' ) ) THEN DO J = 1, N DO I = 1, N @@ -172,22 +235,22 @@ END DO END IF -! Generate matrix B as simply the first NRHS columns of M * the -! identity. +* Generate matrix B as simply the first NRHS columns of M * the +* identity. TMP = DBLE(M) CALL ZLASET('Full', N, NRHS, (0.0D+0,0.0D+0), TMP, B, LDB) -! Generate the true solutions in X. Because B = the first NRHS -! columns of M*I, the true solutions are just the first NRHS columns -! of the inverse Hilbert matrix. +* Generate the true solutions in X. Because B = the first NRHS +* columns of M*I, the true solutions are just the first NRHS columns +* of the inverse Hilbert matrix. WORK(1) = N DO J = 2, N WORK(J) = ( ( (WORK(J-1)/(J-1)) * (J-1 - N) ) /(J-1) ) $ * (N +J -1) END DO -! If we are testing SY routines, -! take D1_i = D2_i, else, D1_i = D2_i* +* If we are testing SY routines, +* take D1_i = D2_i, else, D1_i = D2_i* IF ( LSAMEN( 2, C2, 'SY' ) ) THEN DO J = 1, NRHS DO I = 1, N diff --git a/TESTING/MATGEN/zlakf2.f b/TESTING/MATGEN/zlakf2.f index 58c7eb27..48afb3f4 100644 --- a/TESTING/MATGEN/zlakf2.f +++ b/TESTING/MATGEN/zlakf2.f @@ -1,54 +1,125 @@ - SUBROUTINE ZLAKF2( M, N, A, LDA, B, D, E, Z, LDZ ) -* -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER LDA, LDZ, M, N -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ), B( LDA, * ), D( LDA, * ), - $ E( LDA, * ), Z( LDZ, * ) -* .. -* +*> \brief \b ZLAKF2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZLAKF2( M, N, A, LDA, B, D, E, Z, LDZ ) +* +* .. Scalar Arguments .. +* INTEGER LDA, LDZ, M, N +* .. +* .. Array Arguments .. +* COMPLEX*16 A( LDA, * ), B( LDA, * ), D( LDA, * ), +* $ E( LDA, * ), Z( LDZ, * ) +* .. +* * Purpose * ======= * -* Form the 2*M*N by 2*M*N matrix -* -* Z = [ kron(In, A) -kron(B', Im) ] -* [ kron(In, D) -kron(E', Im) ], -* -* where In is the identity matrix of size n and X' is the transpose -* of X. kron(X, Y) is the Kronecker product between the matrices X -* and Y. +*>\details \b Purpose: +*>\verbatim +*> +*> Form the 2*M*N by 2*M*N matrix +*> +*> Z = [ kron(In, A) -kron(B', Im) ] +*> [ kron(In, D) -kron(E', Im) ], +*> +*> where In is the identity matrix of size n and X' is the transpose +*> of X. kron(X, Y) is the Kronecker product between the matrices X +*> and Y. +*> +*>\endverbatim * * Arguments * ========= * -* M (input) INTEGER -* Size of matrix, must be >= 1. +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Size of matrix, must be >= 1. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Size of matrix, must be >= 1. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16, dimension ( LDA, M ) +*> The matrix A in the output matrix Z. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of A, B, D, and E. ( LDA >= M+N ) +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is COMPLEX*16, dimension ( LDA, N ) +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is COMPLEX*16, dimension ( LDA, M ) +*> \endverbatim +*> +*> \param[in] E +*> \verbatim +*> E is COMPLEX*16, dimension ( LDA, N ) +*> \endverbatim +*> \verbatim +*> The matrices used in forming the output matrix Z. +*> \endverbatim +*> +*> \param[out] Z +*> \verbatim +*> Z is COMPLEX*16, dimension ( LDZ, 2*M*N ) +*> The resultant Kronecker M*N*2 by M*N*2 matrix (see above.) +*> \endverbatim +*> +*> \param[in] LDZ +*> \verbatim +*> LDZ is INTEGER +*> The leading dimension of Z. ( LDZ >= 2*M*N ) +*> \endverbatim +*> +* +* Authors +* ======= * -* N (input) INTEGER -* Size of matrix, must be >= 1. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (input) COMPLEX*16, dimension ( LDA, M ) -* The matrix A in the output matrix Z. +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of A, B, D, and E. ( LDA >= M+N ) +*> \ingroup complex16_matgen * -* B (input) COMPLEX*16, dimension ( LDA, N ) -* D (input) COMPLEX*16, dimension ( LDA, M ) -* E (input) COMPLEX*16, dimension ( LDA, N ) -* The matrices used in forming the output matrix Z. +* ===================================================================== + SUBROUTINE ZLAKF2( M, N, A, LDA, B, D, E, Z, LDZ ) * -* Z (output) COMPLEX*16, dimension ( LDZ, 2*M*N ) -* The resultant Kronecker M*N*2 by M*N*2 matrix (see above.) +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* LDZ (input) INTEGER -* The leading dimension of Z. ( LDZ >= 2*M*N ) +* .. Scalar Arguments .. + INTEGER LDA, LDZ, M, N +* .. +* .. Array Arguments .. + COMPLEX*16 A( LDA, * ), B( LDA, * ), D( LDA, * ), + $ E( LDA, * ), Z( LDZ, * ) +* .. * * ==================================================================== * diff --git a/TESTING/MATGEN/zlarge.f b/TESTING/MATGEN/zlarge.f index 7cb187e5..895afc48 100644 --- a/TESTING/MATGEN/zlarge.f +++ b/TESTING/MATGEN/zlarge.f @@ -1,48 +1,106 @@ - SUBROUTINE ZLARGE( N, A, LDA, ISEED, WORK, INFO ) -* -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) - COMPLEX*16 A( LDA, * ), WORK( * ) -* .. -* +*> \brief \b ZLARGE +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZLARGE( N, A, LDA, ISEED, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* COMPLEX*16 A( LDA, * ), WORK( * ) +* .. +* * Purpose * ======= * -* ZLARGE pre- and post-multiplies a complex general n by n matrix A -* with a random unitary matrix: A = U*D*U'. +*>\details \b Purpose: +*>\verbatim +*> +*> ZLARGE pre- and post-multiplies a complex general n by n matrix A +*> with a random unitary matrix: A = U*D*U'. +*> +*>\endverbatim * * Arguments * ========= * -* N (input) INTEGER -* The order of the matrix A. N >= 0. +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> On entry, the original n by n matrix A. +*> On exit, A is overwritten by U*A*U' for some random +*> unitary matrix U. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= N. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension (2*N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* A (input/output) COMPLEX*16 array, dimension (LDA,N) -* On entry, the original n by n matrix A. -* On exit, A is overwritten by U*A*U' for some random -* unitary matrix U. +*> \date November 2011 * -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= N. +*> \ingroup complex16_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. +* ===================================================================== + SUBROUTINE ZLARGE( N, A, LDA, ISEED, WORK, INFO ) * -* WORK (workspace) COMPLEX*16 array, dimension (2*N) +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value +* .. Scalar Arguments .. + INTEGER INFO, LDA, N +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) + COMPLEX*16 A( LDA, * ), WORK( * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/zlarnd.f b/TESTING/MATGEN/zlarnd.f index 09a20c4f..15919f27 100644 --- a/TESTING/MATGEN/zlarnd.f +++ b/TESTING/MATGEN/zlarnd.f @@ -1,45 +1,95 @@ - COMPLEX*16 FUNCTION ZLARND( IDIST, ISEED ) +*> \brief \b ZLARND * -* -- LAPACK auxiliary routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 +* =========== DOCUMENTATION =========== * -* .. Scalar Arguments .. - INTEGER IDIST -* .. -* .. Array Arguments .. - INTEGER ISEED( 4 ) -* .. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* COMPLEX*16 FUNCTION ZLARND( IDIST, ISEED ) +* +* .. Scalar Arguments .. +* INTEGER IDIST +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* .. +* * Purpose * ======= * -* ZLARND returns a random complex number from a uniform or normal -* distribution. +*>\details \b Purpose: +*>\verbatim +*> +*> ZLARND returns a random complex number from a uniform or normal +*> distribution. +*> +*>\endverbatim * * Arguments * ========= * -* IDIST (input) INTEGER -* Specifies the distribution of the random numbers: -* = 1: real and imaginary parts each uniform (0,1) -* = 2: real and imaginary parts each uniform (-1,1) -* = 3: real and imaginary parts each normal (0,1) -* = 4: uniformly distributed on the disc abs(z) <= 1 -* = 5: uniformly distributed on the circle abs(z) = 1 +*> \param[in] IDIST +*> \verbatim +*> IDIST is INTEGER +*> Specifies the distribution of the random numbers: +*> = 1: real and imaginary parts each uniform (0,1) +*> = 2: real and imaginary parts each uniform (-1,1) +*> = 3: real and imaginary parts each normal (0,1) +*> = 4: uniformly distributed on the disc abs(z) <= 1 +*> = 5: uniformly distributed on the circle abs(z) = 1 +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_matgen * -* ISEED (input/output) INTEGER array, dimension (4) -* On entry, the seed of the random number generator; the array -* elements must be between 0 and 4095, and ISEED(4) must be -* odd. -* On exit, the seed is updated. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> This routine calls the auxiliary routine DLARAN to generate a random +*> real number from a uniform (0,1) distribution. The Box-Muller method +*> is used to transform numbers from a uniform to a normal distribution. +*> +*> \endverbatim +*> +* ===================================================================== + COMPLEX*16 FUNCTION ZLARND( IDIST, ISEED ) * -* This routine calls the auxiliary routine DLARAN to generate a random -* real number from a uniform (0,1) distribution. The Box-Muller method -* is used to transform numbers from a uniform to a normal distribution. +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER IDIST +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/zlaror.f b/TESTING/MATGEN/zlaror.f index 73f75136..34d32223 100644 --- a/TESTING/MATGEN/zlaror.f +++ b/TESTING/MATGEN/zlaror.f @@ -1,8 +1,170 @@ +*> \brief \b ZLAROR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZLAROR( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER INIT, SIDE +* INTEGER INFO, LDA, M, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* COMPLEX*16 A( LDA, * ), X( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> ZLAROR pre- or post-multiplies an M by N matrix A by a random +*> unitary matrix U, overwriting A. A may optionally be +*> initialized to the identity matrix before multiplying by U. +*> U is generated using the method of G.W. Stewart +*> ( SIAM J. Numer. Anal. 17, 1980, pp. 403-409 ). +*> (BLAS-2 version) +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> SIDE specifies whether A is multiplied on the left or right +*> by U. +*> SIDE = 'L' Multiply A on the left (premultiply) by U +*> SIDE = 'R' Multiply A on the right (postmultiply) by UC> SIDE = 'C' Multiply A on the left by U and the right by UC> SIDE = 'T' Multiply A on the left by U and the right by U' +*> Not modified. +*> \endverbatim +*> +*> \param[in] INIT +*> \verbatim +*> INIT is CHARACTER*1 +*> INIT specifies whether or not A should be initialized to +*> the identity matrix. +*> INIT = 'I' Initialize A to (a section of) the +*> identity matrix before applying U. +*> INIT = 'N' No initialization. Apply U to the +*> input matrix A. +*> \endverbatim +*> \verbatim +*> INIT = 'I' may be used to generate square (i.e., unitary) +*> or rectangular orthogonal matrices (orthogonality being +*> in the sense of ZDOTC): +*> \endverbatim +*> \verbatim +*> For square matrices, M=N, and SIDE many be either 'L' or +*> 'R'; the rows will be orthogonal to each other, as will the +*> columns. +*> For rectangular matrices where M < N, SIDE = 'R' will +*> produce a dense matrix whose rows will be orthogonal and +*> whose columns will not, while SIDE = 'L' will produce a +*> matrix whose rows will be orthogonal, and whose first M +*> columns will be orthogonal, the remaining columns being +*> zero. +*> For matrices where M > N, just use the previous +*> explanation, interchanging 'L' and 'R' and "rows" and +*> "columns". +*> \endverbatim +*> \verbatim +*> Not modified. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Number of rows of A. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of columns of A. Not modified. +*> \endverbatim +*> \verbatim +*> A COMPLEX*16 array, dimension ( LDA, N ) +*> Input and output array. Overwritten by U A ( if SIDE = 'L' ) +*> or by A U ( if SIDE = 'R' ) +*> or by U A U* ( if SIDE = 'C') +*> or by U A U' ( if SIDE = 'T') on exit. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> Leading dimension of A. Must be at least MAX ( 1, M ). +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. The array elements should be between 0 and 4095; +*> if not they will be reduced mod 4096. Also, ISEED(4) must +*> be odd. The random number generator uses a linear +*> congruential sequence limited to small integers, and so +*> should produce machine independent random numbers. The +*> values of ISEED are changed on exit, and can be used in the +*> next call to ZLAROR to continue the same random number +*> sequence. +*> Modified. +*> \endverbatim +*> +*> \param[out] X +*> \verbatim +*> X is COMPLEX*16 array, dimension ( 3*MAX( M, N ) ) +*> Workspace. Of length: +*> 2*M + N if SIDE = 'L', +*> 2*N + M if SIDE = 'R', +*> 3*N if SIDE = 'C' or 'T'. +*> Modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> An error flag. It is set to: +*> 0 if no error. +*> 1 if ZLARND returned a bad random number (installation +*> problem) +*> -1 if SIDE is not L, R, C, or T. +*> -3 if M is negative. +*> -4 if N is negative or if SIDE is C or T and N is not equal +*> to M. +*> -6 if LDA is less than M. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_matgen +* +* ===================================================================== SUBROUTINE ZLAROR( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER INIT, SIDE @@ -13,101 +175,6 @@ COMPLEX*16 A( LDA, * ), X( * ) * .. * -* Purpose -* ======= -* -* ZLAROR pre- or post-multiplies an M by N matrix A by a random -* unitary matrix U, overwriting A. A may optionally be -* initialized to the identity matrix before multiplying by U. -* U is generated using the method of G.W. Stewart -* ( SIAM J. Numer. Anal. 17, 1980, pp. 403-409 ). -* (BLAS-2 version) -* -* Arguments -* ========= -* -* SIDE (input) CHARACTER*1 -* SIDE specifies whether A is multiplied on the left or right -* by U. -* SIDE = 'L' Multiply A on the left (premultiply) by U -* SIDE = 'R' Multiply A on the right (postmultiply) by U* -* SIDE = 'C' Multiply A on the left by U and the right by U* -* SIDE = 'T' Multiply A on the left by U and the right by U' -* Not modified. -* -* INIT (input) CHARACTER*1 -* INIT specifies whether or not A should be initialized to -* the identity matrix. -* INIT = 'I' Initialize A to (a section of) the -* identity matrix before applying U. -* INIT = 'N' No initialization. Apply U to the -* input matrix A. -* -* INIT = 'I' may be used to generate square (i.e., unitary) -* or rectangular orthogonal matrices (orthogonality being -* in the sense of ZDOTC): -* -* For square matrices, M=N, and SIDE many be either 'L' or -* 'R'; the rows will be orthogonal to each other, as will the -* columns. -* For rectangular matrices where M < N, SIDE = 'R' will -* produce a dense matrix whose rows will be orthogonal and -* whose columns will not, while SIDE = 'L' will produce a -* matrix whose rows will be orthogonal, and whose first M -* columns will be orthogonal, the remaining columns being -* zero. -* For matrices where M > N, just use the previous -* explanation, interchanging 'L' and 'R' and "rows" and -* "columns". -* -* Not modified. -* -* M (input) INTEGER -* Number of rows of A. Not modified. -* -* N (input) INTEGER -* Number of columns of A. Not modified. -* -* A COMPLEX*16 array, dimension ( LDA, N ) -* Input and output array. Overwritten by U A ( if SIDE = 'L' ) -* or by A U ( if SIDE = 'R' ) -* or by U A U* ( if SIDE = 'C') -* or by U A U' ( if SIDE = 'T') on exit. -* -* LDA (input) INTEGER -* Leading dimension of A. Must be at least MAX ( 1, M ). -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. The array elements should be between 0 and 4095; -* if not they will be reduced mod 4096. Also, ISEED(4) must -* be odd. The random number generator uses a linear -* congruential sequence limited to small integers, and so -* should produce machine independent random numbers. The -* values of ISEED are changed on exit, and can be used in the -* next call to ZLAROR to continue the same random number -* sequence. -* Modified. -* -* X (workspace) COMPLEX*16 array, dimension ( 3*MAX( M, N ) ) -* Workspace. Of length: -* 2*M + N if SIDE = 'L', -* 2*N + M if SIDE = 'R', -* 3*N if SIDE = 'C' or 'T'. -* Modified. -* -* INFO (output) INTEGER -* An error flag. It is set to: -* 0 if no error. -* 1 if ZLARND returned a bad random number (installation -* problem) -* -1 if SIDE is not L, R, C, or T. -* -3 if M is negative. -* -4 if N is negative or if SIDE is C or T and N is not equal -* to M. -* -6 if LDA is less than M. -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/zlarot.f b/TESTING/MATGEN/zlarot.f index 106a4d9f..68c986de 100644 --- a/TESTING/MATGEN/zlarot.f +++ b/TESTING/MATGEN/zlarot.f @@ -1,9 +1,248 @@ +*> \brief \b ZLAROT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT, +* XRIGHT ) +* +* .. Scalar Arguments .. +* LOGICAL LLEFT, LRIGHT, LROWS +* INTEGER LDA, NL +* COMPLEX*16 C, S, XLEFT, XRIGHT +* .. +* .. Array Arguments .. +* COMPLEX*16 A( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> ZLAROT applies a (Givens) rotation to two adjacent rows or +*> columns, where one element of the first and/or last column/row +*> for use on matrices stored in some format other than GE, so +*> that elements of the matrix may be used or modified for which +*> no array element is provided. +*> +*> One example is a symmetric matrix in SB format (bandwidth=4), for +*> which UPLO='L': Two adjacent rows will have the format: +*> +*> row j: C> C> C> C> C> . . . . +*> row j+1: C> C> C> C> C> . . . . +*> +*> '*' indicates elements for which storage is provided, +*> '.' indicates elements for which no storage is provided, but +*> are not necessarily zero; their values are determined by +*> symmetry. ' ' indicates elements which are necessarily zero, +*> and have no storage provided. +*> +*> Those columns which have two '*'s can be handled by DROT. +*> Those columns which have no '*'s can be ignored, since as long +*> as the Givens rotations are carefully applied to preserve +*> symmetry, their values are determined. +*> Those columns which have one '*' have to be handled separately, +*> by using separate variables "p" and "q": +*> +*> row j: C> C> C> C> C> p . . . +*> row j+1: q C> C> C> C> C> . . . . +*> +*> The element p would have to be set correctly, then that column +*> is rotated, setting p to its new value. The next call to +*> ZLAROT would rotate columns j and j+1, using p, and restore +*> symmetry. The element q would start out being zero, and be +*> made non-zero by the rotation. Later, rotations would presumably +*> be chosen to zero q out. +*> +*> Typical Calling Sequences: rotating the i-th and (i+1)-st rows. +*> ------- ------- --------- +*> +*> General dense matrix: +*> +*> CALL ZLAROT(.TRUE.,.FALSE.,.FALSE., N, C,S, +*> A(i,1),LDA, DUMMY, DUMMY) +*> +*> General banded matrix in GB format: +*> +*> j = MAX(1, i-KL ) +*> NL = MIN( N, i+KU+1 ) + 1-j +*> CALL ZLAROT( .TRUE., i-KL.GE.1, i+KU.LT.N, NL, C,S, +*> A(KU+i+1-j,j),LDA-1, XLEFT, XRIGHT ) +*> +*> [ note that i+1-j is just MIN(i,KL+1) ] +*> +*> Symmetric banded matrix in SY format, bandwidth K, +*> lower triangle only: +*> +*> j = MAX(1, i-K ) +*> NL = MIN( K+1, i ) + 1 +*> CALL ZLAROT( .TRUE., i-K.GE.1, .TRUE., NL, C,S, +*> A(i,j), LDA, XLEFT, XRIGHT ) +*> +*> Same, but upper triangle only: +*> +*> NL = MIN( K+1, N-i ) + 1 +*> CALL ZLAROT( .TRUE., .TRUE., i+K.LT.N, NL, C,S, +*> A(i,i), LDA, XLEFT, XRIGHT ) +*> +*> Symmetric banded matrix in SB format, bandwidth K, +*> lower triangle only: +*> +*> [ same as for SY, except:] +*> . . . . +*> A(i+1-j,j), LDA-1, XLEFT, XRIGHT ) +*> +*> [ note that i+1-j is just MIN(i,K+1) ] +*> +*> Same, but upper triangle only: +*> . . . +*> A(K+1,i), LDA-1, XLEFT, XRIGHT ) +*> +*> Rotating columns is just the transpose of rotating rows, except +*> for GB and SB: (rotating columns i and i+1) +*> +*> GB: +*> j = MAX(1, i-KU ) +*> NL = MIN( N, i+KL+1 ) + 1-j +*> CALL ZLAROT( .TRUE., i-KU.GE.1, i+KL.LT.N, NL, C,S, +*> A(KU+j+1-i,i),LDA-1, XTOP, XBOTTM ) +*> +*> [note that KU+j+1-i is just MAX(1,KU+2-i)] +*> +*> SB: (upper triangle) +*> +*> . . . . . . +*> A(K+j+1-i,i),LDA-1, XTOP, XBOTTM ) +*> +*> SB: (lower triangle) +*> +*> . . . . . . +*> A(1,i),LDA-1, XTOP, XBOTTM ) +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \verbatim +*> LROWS - LOGICAL +*> If .TRUE., then ZLAROT will rotate two rows. If .FALSE., +*> then it will rotate two columns. +*> Not modified. +*> \endverbatim +*> \verbatim +*> LLEFT - LOGICAL +*> If .TRUE., then XLEFT will be used instead of the +*> corresponding element of A for the first element in the +*> second row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) +*> If .FALSE., then the corresponding element of A will be +*> used. +*> Not modified. +*> \endverbatim +*> \verbatim +*> LRIGHT - LOGICAL +*> If .TRUE., then XRIGHT will be used instead of the +*> corresponding element of A for the last element in the +*> first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If +*> .FALSE., then the corresponding element of A will be used. +*> Not modified. +*> \endverbatim +*> \verbatim +*> NL - INTEGER +*> The length of the rows (if LROWS=.TRUE.) or columns (if +*> LROWS=.FALSE.) to be rotated. If XLEFT and/or XRIGHT are +*> used, the columns/rows they are in should be included in +*> NL, e.g., if LLEFT = LRIGHT = .TRUE., then NL must be at +*> least 2. The number of rows/columns to be rotated +*> exclusive of those involving XLEFT and/or XRIGHT may +*> not be negative, i.e., NL minus how many of LLEFT and +*> LRIGHT are .TRUE. must be at least zero; if not, XERBLA +*> will be called. +*> Not modified. +*> \endverbatim +*> \verbatim +*> C, S - COMPLEX*16 +*> Specify the Givens rotation to be applied. If LROWS is +*> true, then the matrix ( c s ) +*> ( _ _ ) +*> (-s c ) is applied from the left; +*> if false, then the transpose (not conjugated) thereof is +*> applied from the right. Note that in contrast to the +*> output of ZROTG or to most versions of ZROT, both C and S +*> are complex. For a Givens rotation, |C|**2 + |S|**2 should +*> be 1, but this is not checked. +*> Not modified. +*> \endverbatim +*> \verbatim +*> A - COMPLEX*16 array. +*> The array containing the rows/columns to be rotated. The +*> first element of A should be the upper left element to +*> be rotated. +*> Read and modified. +*> \endverbatim +*> \verbatim +*> LDA - INTEGER +*> The "effective" leading dimension of A. If A contains +*> a matrix stored in GE, HE, or SY format, then this is just +*> the leading dimension of A as dimensioned in the calling +*> routine. If A contains a matrix stored in band (GB, HB, or +*> SB) format, then this should be *one less* than the leading +*> dimension used in the calling routine. Thus, if A were +*> dimensioned A(LDA,*) in ZLAROT, then A(1,j) would be the +*> j-th element in the first of the two rows to be rotated, +*> and A(2,j) would be the j-th in the second, regardless of +*> how the array may be stored in the calling routine. [A +*> cannot, however, actually be dimensioned thus, since for +*> band format, the row number may exceed LDA, which is not +*> legal FORTRAN.] +*> If LROWS=.TRUE., then LDA must be at least 1, otherwise +*> it must be at least NL minus the number of .TRUE. values +*> in XLEFT and XRIGHT. +*> Not modified. +*> \endverbatim +*> \verbatim +*> XLEFT - COMPLEX*16 +*> If LLEFT is .TRUE., then XLEFT will be used and modified +*> instead of A(2,1) (if LROWS=.TRUE.) or A(1,2) +*> (if LROWS=.FALSE.). +*> Read and modified. +*> \endverbatim +*> \verbatim +*> XRIGHT - COMPLEX*16 +*> If LRIGHT is .TRUE., then XRIGHT will be used and modified +*> instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1) +*> (if LROWS=.FALSE.). +*> Read and modified. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_matgen +* +* ===================================================================== SUBROUTINE ZLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT, $ XRIGHT ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. LOGICAL LLEFT, LRIGHT, LROWS @@ -14,193 +253,6 @@ COMPLEX*16 A( * ) * .. * -* Purpose -* ======= -* -* ZLAROT applies a (Givens) rotation to two adjacent rows or -* columns, where one element of the first and/or last column/row -* for use on matrices stored in some format other than GE, so -* that elements of the matrix may be used or modified for which -* no array element is provided. -* -* One example is a symmetric matrix in SB format (bandwidth=4), for -* which UPLO='L': Two adjacent rows will have the format: -* -* row j: * * * * * . . . . -* row j+1: * * * * * . . . . -* -* '*' indicates elements for which storage is provided, -* '.' indicates elements for which no storage is provided, but -* are not necessarily zero; their values are determined by -* symmetry. ' ' indicates elements which are necessarily zero, -* and have no storage provided. -* -* Those columns which have two '*'s can be handled by DROT. -* Those columns which have no '*'s can be ignored, since as long -* as the Givens rotations are carefully applied to preserve -* symmetry, their values are determined. -* Those columns which have one '*' have to be handled separately, -* by using separate variables "p" and "q": -* -* row j: * * * * * p . . . -* row j+1: q * * * * * . . . . -* -* The element p would have to be set correctly, then that column -* is rotated, setting p to its new value. The next call to -* ZLAROT would rotate columns j and j+1, using p, and restore -* symmetry. The element q would start out being zero, and be -* made non-zero by the rotation. Later, rotations would presumably -* be chosen to zero q out. -* -* Typical Calling Sequences: rotating the i-th and (i+1)-st rows. -* ------- ------- --------- -* -* General dense matrix: -* -* CALL ZLAROT(.TRUE.,.FALSE.,.FALSE., N, C,S, -* A(i,1),LDA, DUMMY, DUMMY) -* -* General banded matrix in GB format: -* -* j = MAX(1, i-KL ) -* NL = MIN( N, i+KU+1 ) + 1-j -* CALL ZLAROT( .TRUE., i-KL.GE.1, i+KU.LT.N, NL, C,S, -* A(KU+i+1-j,j),LDA-1, XLEFT, XRIGHT ) -* -* [ note that i+1-j is just MIN(i,KL+1) ] -* -* Symmetric banded matrix in SY format, bandwidth K, -* lower triangle only: -* -* j = MAX(1, i-K ) -* NL = MIN( K+1, i ) + 1 -* CALL ZLAROT( .TRUE., i-K.GE.1, .TRUE., NL, C,S, -* A(i,j), LDA, XLEFT, XRIGHT ) -* -* Same, but upper triangle only: -* -* NL = MIN( K+1, N-i ) + 1 -* CALL ZLAROT( .TRUE., .TRUE., i+K.LT.N, NL, C,S, -* A(i,i), LDA, XLEFT, XRIGHT ) -* -* Symmetric banded matrix in SB format, bandwidth K, -* lower triangle only: -* -* [ same as for SY, except:] -* . . . . -* A(i+1-j,j), LDA-1, XLEFT, XRIGHT ) -* -* [ note that i+1-j is just MIN(i,K+1) ] -* -* Same, but upper triangle only: -* . . . -* A(K+1,i), LDA-1, XLEFT, XRIGHT ) -* -* Rotating columns is just the transpose of rotating rows, except -* for GB and SB: (rotating columns i and i+1) -* -* GB: -* j = MAX(1, i-KU ) -* NL = MIN( N, i+KL+1 ) + 1-j -* CALL ZLAROT( .TRUE., i-KU.GE.1, i+KL.LT.N, NL, C,S, -* A(KU+j+1-i,i),LDA-1, XTOP, XBOTTM ) -* -* [note that KU+j+1-i is just MAX(1,KU+2-i)] -* -* SB: (upper triangle) -* -* . . . . . . -* A(K+j+1-i,i),LDA-1, XTOP, XBOTTM ) -* -* SB: (lower triangle) -* -* . . . . . . -* A(1,i),LDA-1, XTOP, XBOTTM ) -* -* Arguments -* ========= -* -* LROWS - LOGICAL -* If .TRUE., then ZLAROT will rotate two rows. If .FALSE., -* then it will rotate two columns. -* Not modified. -* -* LLEFT - LOGICAL -* If .TRUE., then XLEFT will be used instead of the -* corresponding element of A for the first element in the -* second row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) -* If .FALSE., then the corresponding element of A will be -* used. -* Not modified. -* -* LRIGHT - LOGICAL -* If .TRUE., then XRIGHT will be used instead of the -* corresponding element of A for the last element in the -* first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If -* .FALSE., then the corresponding element of A will be used. -* Not modified. -* -* NL - INTEGER -* The length of the rows (if LROWS=.TRUE.) or columns (if -* LROWS=.FALSE.) to be rotated. If XLEFT and/or XRIGHT are -* used, the columns/rows they are in should be included in -* NL, e.g., if LLEFT = LRIGHT = .TRUE., then NL must be at -* least 2. The number of rows/columns to be rotated -* exclusive of those involving XLEFT and/or XRIGHT may -* not be negative, i.e., NL minus how many of LLEFT and -* LRIGHT are .TRUE. must be at least zero; if not, XERBLA -* will be called. -* Not modified. -* -* C, S - COMPLEX*16 -* Specify the Givens rotation to be applied. If LROWS is -* true, then the matrix ( c s ) -* ( _ _ ) -* (-s c ) is applied from the left; -* if false, then the transpose (not conjugated) thereof is -* applied from the right. Note that in contrast to the -* output of ZROTG or to most versions of ZROT, both C and S -* are complex. For a Givens rotation, |C|**2 + |S|**2 should -* be 1, but this is not checked. -* Not modified. -* -* A - COMPLEX*16 array. -* The array containing the rows/columns to be rotated. The -* first element of A should be the upper left element to -* be rotated. -* Read and modified. -* -* LDA - INTEGER -* The "effective" leading dimension of A. If A contains -* a matrix stored in GE, HE, or SY format, then this is just -* the leading dimension of A as dimensioned in the calling -* routine. If A contains a matrix stored in band (GB, HB, or -* SB) format, then this should be *one less* than the leading -* dimension used in the calling routine. Thus, if A were -* dimensioned A(LDA,*) in ZLAROT, then A(1,j) would be the -* j-th element in the first of the two rows to be rotated, -* and A(2,j) would be the j-th in the second, regardless of -* how the array may be stored in the calling routine. [A -* cannot, however, actually be dimensioned thus, since for -* band format, the row number may exceed LDA, which is not -* legal FORTRAN.] -* If LROWS=.TRUE., then LDA must be at least 1, otherwise -* it must be at least NL minus the number of .TRUE. values -* in XLEFT and XRIGHT. -* Not modified. -* -* XLEFT - COMPLEX*16 -* If LLEFT is .TRUE., then XLEFT will be used and modified -* instead of A(2,1) (if LROWS=.TRUE.) or A(1,2) -* (if LROWS=.FALSE.). -* Read and modified. -* -* XRIGHT - COMPLEX*16 -* If LRIGHT is .TRUE., then XRIGHT will be used and modified -* instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1) -* (if LROWS=.FALSE.). -* Read and modified. -* * ===================================================================== * * .. Local Scalars .. diff --git a/TESTING/MATGEN/zlatm1.f b/TESTING/MATGEN/zlatm1.f index aa0133a1..8e6829bf 100644 --- a/TESTING/MATGEN/zlatm1.f +++ b/TESTING/MATGEN/zlatm1.f @@ -1,8 +1,148 @@ +*> \brief \b ZLATM1 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO ) +* +* .. Scalar Arguments .. +* INTEGER IDIST, INFO, IRSIGN, MODE, N +* DOUBLE PRECISION COND +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* COMPLEX*16 D( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> ZLATM1 computes the entries of D(1..N) as specified by +*> MODE, COND and IRSIGN. IDIST and ISEED determine the generation +*> of random numbers. ZLATM1 is called by CLATMR to generate +*> random test matrices for LAPACK programs. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry describes how D is to be computed: +*> MODE = 0 means do not change D. +*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND +*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is DOUBLE PRECISION +*> On entry, used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] IRSIGN +*> \verbatim +*> IRSIGN is INTEGER +*> On entry, if MODE neither -6, 0 nor 6, determines sign of +*> entries of D +*> 0 => leave entries of D unchanged +*> 1 => multiply each entry of D by random complex number +*> uniformly distributed with absolute value 1 +*> \endverbatim +*> +*> \param[in] IDIST +*> \verbatim +*> IDIST is CHARACTER*1 +*> On entry, IDIST specifies the type of distribution to be +*> used to generate a random matrix . +*> 1 => real and imaginary parts each UNIFORM( 0, 1 ) +*> 2 => real and imaginary parts each UNIFORM( -1, 1 ) +*> 3 => real and imaginary parts each NORMAL( 0, 1 ) +*> 4 => complex number uniform in DISK( 0, 1 ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. The random number generator uses a +*> linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to ZLATM1 +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is COMPLEX*16 array, dimension ( MIN( M , N ) ) +*> Array to be computed according to MODE, COND and IRSIGN. +*> May be changed on exit if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of entries of D. Not modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> 0 => normal termination +*> -1 => if MODE not in range -6 to 6 +*> -2 => if MODE neither -6, 0 nor 6, and +*> IRSIGN neither 0 nor 1 +*> -3 => if MODE neither -6, 0 nor 6 and COND less than 1 +*> -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 4 +*> -7 => if N negative +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_matgen +* +* ===================================================================== SUBROUTINE ZLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. INTEGER IDIST, INFO, IRSIGN, MODE, N @@ -13,81 +153,6 @@ COMPLEX*16 D( * ) * .. * -* Purpose -* ======= -* -* ZLATM1 computes the entries of D(1..N) as specified by -* MODE, COND and IRSIGN. IDIST and ISEED determine the generation -* of random numbers. ZLATM1 is called by CLATMR to generate -* random test matrices for LAPACK programs. -* -* Arguments -* ========= -* -* MODE (input) INTEGER -* On entry describes how D is to be computed: -* MODE = 0 means do not change D. -* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND -* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* Not modified. -* -* COND (input) DOUBLE PRECISION -* On entry, used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* IRSIGN (input) INTEGER -* On entry, if MODE neither -6, 0 nor 6, determines sign of -* entries of D -* 0 => leave entries of D unchanged -* 1 => multiply each entry of D by random complex number -* uniformly distributed with absolute value 1 -* -* IDIST (input) CHARACTER*1 -* On entry, IDIST specifies the type of distribution to be -* used to generate a random matrix . -* 1 => real and imaginary parts each UNIFORM( 0, 1 ) -* 2 => real and imaginary parts each UNIFORM( -1, 1 ) -* 3 => real and imaginary parts each NORMAL( 0, 1 ) -* 4 => complex number uniform in DISK( 0, 1 ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. The random number generator uses a -* linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to ZLATM1 -* to continue the same random number sequence. -* Changed on exit. -* -* D (input/output) COMPLEX*16 array, dimension ( MIN( M , N ) ) -* Array to be computed according to MODE, COND and IRSIGN. -* May be changed on exit if MODE is nonzero. -* -* N (input) INTEGER -* Number of entries of D. Not modified. -* -* INFO (output) INTEGER -* 0 => normal termination -* -1 => if MODE not in range -6 to 6 -* -2 => if MODE neither -6, 0 nor 6, and -* IRSIGN neither 0 nor 1 -* -3 => if MODE neither -6, 0 nor 6 and COND less than 1 -* -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 4 -* -7 => if N negative -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/zlatm2.f b/TESTING/MATGEN/zlatm2.f index c5c2d950..76b0152d 100644 --- a/TESTING/MATGEN/zlatm2.f +++ b/TESTING/MATGEN/zlatm2.f @@ -1,9 +1,222 @@ +*> \brief \b ZLATM2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* COMPLEX*16 FUNCTION ZLATM2( M, N, I, J, KL, KU, IDIST, +* ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE ) +* +* .. Scalar Arguments .. +* +* INTEGER I, IDIST, IGRADE, IPVTNG, J, KL, KU, M, N +* DOUBLE PRECISION SPARSE +* .. +* +* .. Array Arguments .. +* +* INTEGER ISEED( 4 ), IWORK( * ) +* COMPLEX*16 D( * ), DL( * ), DR( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> ZLATM2 returns the (I,J) entry of a random matrix of dimension +*> (M, N) described by the other paramters. It is called by the +*> ZLATMR routine in order to build random test matrices. No error +*> checking on parameters is done, because this routine is called in +*> a tight loop by ZLATMR which has already checked the parameters. +*> +*> Use of ZLATM2 differs from CLATM3 in the order in which the random +*> number generator is called to fill in random matrix entries. +*> With ZLATM2, the generator is called to fill in the pivoted matrix +*> columnwise. With ZLATM3, the generator is called to fill in the +*> matrix columnwise, after which it is pivoted. Thus, ZLATM3 can +*> be used to construct random matrices which differ only in their +*> order of rows and/or columns. ZLATM2 is used to construct band +*> matrices while avoiding calling the random number generator for +*> entries outside the band (and therefore generating random numbers +*> +*> The matrix whose (I,J) entry is returned is constructed as +*> follows (this routine only computes one entry): +*> +*> If I is outside (1..M) or J is outside (1..N), return zero +*> (this is convenient for generating matrices in band format). +*> +*> Generate a matrix A with random entries of distribution IDIST. +*> +*> Set the diagonal to D. +*> +*> Grade the matrix, if desired, from the left (by DL) and/or +*> from the right (by DR or DL) as specified by IGRADE. +*> +*> Permute, if desired, the rows and/or columns as specified by +*> IPVTNG and IWORK. +*> +*> Band the matrix to have lower bandwidth KL and upper +*> bandwidth KU. +*> +*> Set random entries to zero as specified by SPARSE. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Number of rows of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of columns of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] I +*> \verbatim +*> I is INTEGER +*> Row of entry to be returned. Not modified. +*> \endverbatim +*> +*> \param[in] J +*> \verbatim +*> J is INTEGER +*> Column of entry to be returned. Not modified. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> Lower bandwidth. Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> Upper bandwidth. Not modified. +*> \endverbatim +*> +*> \param[in] IDIST +*> \verbatim +*> IDIST is INTEGER +*> On entry, IDIST specifies the type of distribution to be +*> used to generate a random matrix . +*> 1 => real and imaginary parts each UNIFORM( 0, 1 ) +*> 2 => real and imaginary parts each UNIFORM( -1, 1 ) +*> 3 => real and imaginary parts each NORMAL( 0, 1 ) +*> 4 => complex number uniform in DISK( 0 , 1 ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array of dimension ( 4 ) +*> Seed for random number generator. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is COMPLEX*16 array of dimension ( MIN( I , J ) ) +*> Diagonal entries of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] IGRADE +*> \verbatim +*> IGRADE is INTEGER +*> Specifies grading of matrix as follows: +*> 0 => no grading +*> 1 => matrix premultiplied by diag( DL ) +*> 2 => matrix postmultiplied by diag( DR ) +*> 3 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DR ) +*> 4 => matrix premultiplied by diag( DL ) and +*> postmultiplied by inv( diag( DL ) ) +*> 5 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( CONJG(DL) ) +*> 6 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DL ) +*> Not modified. +*> \endverbatim +*> +*> \param[in] DL +*> \verbatim +*> DL is COMPLEX*16 array ( I or J, as appropriate ) +*> Left scale factors for grading matrix. Not modified. +*> \endverbatim +*> +*> \param[in] DR +*> \verbatim +*> DR is COMPLEX*16 array ( I or J, as appropriate ) +*> Right scale factors for grading matrix. Not modified. +*> \endverbatim +*> +*> \param[in] IPVTNG +*> \verbatim +*> IPVTNG is INTEGER +*> On entry specifies pivoting permutations as follows: +*> 0 => none. +*> 1 => row pivoting. +*> 2 => column pivoting. +*> 3 => full pivoting, i.e., on both sides. +*> Not modified. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array ( I or J, as appropriate ) +*> This array specifies the permutation used. The +*> row (or column) in position K was originally in +*> position IWORK( K ). +*> This differs from IWORK for ZLATM3. Not modified. +*> \endverbatim +*> +*> \param[in] SPARSE +*> \verbatim +*> SPARSE is DOUBLE PRECISION between 0. and 1. +*> On entry specifies the sparsity of the matrix +*> if sparse matix is to be generated. +*> SPARSE should lie between 0 and 1. +*> A uniform ( 0, 1 ) random number x is generated and +*> compared to SPARSE; if x is larger the matrix entry +*> is unchanged and if x is smaller the entry is set +*> to zero. Thus on the average a fraction SPARSE of the +*> entries will be set to zero. +*> Not modified. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_matgen +* +* ===================================================================== COMPLEX*16 FUNCTION ZLATM2( M, N, I, J, KL, KU, IDIST, $ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. * @@ -17,129 +230,6 @@ COMPLEX*16 D( * ), DL( * ), DR( * ) * .. * -* Purpose -* ======= -* -* ZLATM2 returns the (I,J) entry of a random matrix of dimension -* (M, N) described by the other paramters. It is called by the -* ZLATMR routine in order to build random test matrices. No error -* checking on parameters is done, because this routine is called in -* a tight loop by ZLATMR which has already checked the parameters. -* -* Use of ZLATM2 differs from CLATM3 in the order in which the random -* number generator is called to fill in random matrix entries. -* With ZLATM2, the generator is called to fill in the pivoted matrix -* columnwise. With ZLATM3, the generator is called to fill in the -* matrix columnwise, after which it is pivoted. Thus, ZLATM3 can -* be used to construct random matrices which differ only in their -* order of rows and/or columns. ZLATM2 is used to construct band -* matrices while avoiding calling the random number generator for -* entries outside the band (and therefore generating random numbers -* -* The matrix whose (I,J) entry is returned is constructed as -* follows (this routine only computes one entry): -* -* If I is outside (1..M) or J is outside (1..N), return zero -* (this is convenient for generating matrices in band format). -* -* Generate a matrix A with random entries of distribution IDIST. -* -* Set the diagonal to D. -* -* Grade the matrix, if desired, from the left (by DL) and/or -* from the right (by DR or DL) as specified by IGRADE. -* -* Permute, if desired, the rows and/or columns as specified by -* IPVTNG and IWORK. -* -* Band the matrix to have lower bandwidth KL and upper -* bandwidth KU. -* -* Set random entries to zero as specified by SPARSE. -* -* Arguments -* ========= -* -* M (input) INTEGER -* Number of rows of matrix. Not modified. -* -* N (input) INTEGER -* Number of columns of matrix. Not modified. -* -* I (input) INTEGER -* Row of entry to be returned. Not modified. -* -* J (input) INTEGER -* Column of entry to be returned. Not modified. -* -* KL (input) INTEGER -* Lower bandwidth. Not modified. -* -* KU (input) INTEGER -* Upper bandwidth. Not modified. -* -* IDIST (input) INTEGER -* On entry, IDIST specifies the type of distribution to be -* used to generate a random matrix . -* 1 => real and imaginary parts each UNIFORM( 0, 1 ) -* 2 => real and imaginary parts each UNIFORM( -1, 1 ) -* 3 => real and imaginary parts each NORMAL( 0, 1 ) -* 4 => complex number uniform in DISK( 0 , 1 ) -* Not modified. -* -* ISEED (input/output) INTEGER array of dimension ( 4 ) -* Seed for random number generator. -* Changed on exit. -* -* D (input) COMPLEX*16 array of dimension ( MIN( I , J ) ) -* Diagonal entries of matrix. Not modified. -* -* IGRADE (input) INTEGER -* Specifies grading of matrix as follows: -* 0 => no grading -* 1 => matrix premultiplied by diag( DL ) -* 2 => matrix postmultiplied by diag( DR ) -* 3 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DR ) -* 4 => matrix premultiplied by diag( DL ) and -* postmultiplied by inv( diag( DL ) ) -* 5 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( CONJG(DL) ) -* 6 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DL ) -* Not modified. -* -* DL (input) COMPLEX*16 array ( I or J, as appropriate ) -* Left scale factors for grading matrix. Not modified. -* -* DR (input) COMPLEX*16 array ( I or J, as appropriate ) -* Right scale factors for grading matrix. Not modified. -* -* IPVTNG (input) INTEGER -* On entry specifies pivoting permutations as follows: -* 0 => none. -* 1 => row pivoting. -* 2 => column pivoting. -* 3 => full pivoting, i.e., on both sides. -* Not modified. -* -* IWORK (workspace) INTEGER array ( I or J, as appropriate ) -* This array specifies the permutation used. The -* row (or column) in position K was originally in -* position IWORK( K ). -* This differs from IWORK for ZLATM3. Not modified. -* -* SPARSE (input) DOUBLE PRECISION between 0. and 1. -* On entry specifies the sparsity of the matrix -* if sparse matix is to be generated. -* SPARSE should lie between 0 and 1. -* A uniform ( 0, 1 ) random number x is generated and -* compared to SPARSE; if x is larger the matrix entry -* is unchanged and if x is smaller the entry is set -* to zero. Thus on the average a fraction SPARSE of the -* entries will be set to zero. -* Not modified. -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/zlatm3.f b/TESTING/MATGEN/zlatm3.f index e07ae49e..b3aac8ed 100644 --- a/TESTING/MATGEN/zlatm3.f +++ b/TESTING/MATGEN/zlatm3.f @@ -1,10 +1,240 @@ +*> \brief \b ZLATM3 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* COMPLEX*16 FUNCTION ZLATM3( M, N, I, J, ISUB, JSUB, KL, KU, +* IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, +* SPARSE ) +* +* .. Scalar Arguments .. +* +* INTEGER I, IDIST, IGRADE, IPVTNG, ISUB, J, JSUB, KL, +* $ KU, M, N +* DOUBLE PRECISION SPARSE +* .. +* +* .. Array Arguments .. +* +* INTEGER ISEED( 4 ), IWORK( * ) +* COMPLEX*16 D( * ), DL( * ), DR( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> ZLATM3 returns the (ISUB,JSUB) entry of a random matrix of +*> dimension (M, N) described by the other paramters. (ISUB,JSUB) +*> is the final position of the (I,J) entry after pivoting +*> according to IPVTNG and IWORK. ZLATM3 is called by the +*> ZLATMR routine in order to build random test matrices. No error +*> checking on parameters is done, because this routine is called in +*> a tight loop by ZLATMR which has already checked the parameters. +*> +*> Use of ZLATM3 differs from CLATM2 in the order in which the random +*> number generator is called to fill in random matrix entries. +*> With ZLATM2, the generator is called to fill in the pivoted matrix +*> columnwise. With ZLATM3, the generator is called to fill in the +*> matrix columnwise, after which it is pivoted. Thus, ZLATM3 can +*> be used to construct random matrices which differ only in their +*> order of rows and/or columns. ZLATM2 is used to construct band +*> matrices while avoiding calling the random number generator for +*> entries outside the band (and therefore generating random numbers +*> in different orders for different pivot orders). +*> +*> The matrix whose (ISUB,JSUB) entry is returned is constructed as +*> follows (this routine only computes one entry): +*> +*> If ISUB is outside (1..M) or JSUB is outside (1..N), return zero +*> (this is convenient for generating matrices in band format). +*> +*> Generate a matrix A with random entries of distribution IDIST. +*> +*> Set the diagonal to D. +*> +*> Grade the matrix, if desired, from the left (by DL) and/or +*> from the right (by DR or DL) as specified by IGRADE. +*> +*> Permute, if desired, the rows and/or columns as specified by +*> IPVTNG and IWORK. +*> +*> Band the matrix to have lower bandwidth KL and upper +*> bandwidth KU. +*> +*> Set random entries to zero as specified by SPARSE. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Number of rows of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of columns of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] I +*> \verbatim +*> I is INTEGER +*> Row of unpivoted entry to be returned. Not modified. +*> \endverbatim +*> +*> \param[in] J +*> \verbatim +*> J is INTEGER +*> Column of unpivoted entry to be returned. Not modified. +*> \endverbatim +*> +*> \param[in,out] ISUB +*> \verbatim +*> ISUB is INTEGER +*> Row of pivoted entry to be returned. Changed on exit. +*> \endverbatim +*> +*> \param[in,out] JSUB +*> \verbatim +*> JSUB is INTEGER +*> Column of pivoted entry to be returned. Changed on exit. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> Lower bandwidth. Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> Upper bandwidth. Not modified. +*> \endverbatim +*> +*> \param[in] IDIST +*> \verbatim +*> IDIST is INTEGER +*> On entry, IDIST specifies the type of distribution to be +*> used to generate a random matrix . +*> 1 => real and imaginary parts each UNIFORM( 0, 1 ) +*> 2 => real and imaginary parts each UNIFORM( -1, 1 ) +*> 3 => real and imaginary parts each NORMAL( 0, 1 ) +*> 4 => complex number uniform in DISK( 0 , 1 ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array of dimension ( 4 ) +*> Seed for random number generator. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is COMPLEX*16 array of dimension ( MIN( I , J ) ) +*> Diagonal entries of matrix. Not modified. +*> \endverbatim +*> +*> \param[in] IGRADE +*> \verbatim +*> IGRADE is INTEGER +*> Specifies grading of matrix as follows: +*> 0 => no grading +*> 1 => matrix premultiplied by diag( DL ) +*> 2 => matrix postmultiplied by diag( DR ) +*> 3 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DR ) +*> 4 => matrix premultiplied by diag( DL ) and +*> postmultiplied by inv( diag( DL ) ) +*> 5 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( CONJG(DL) ) +*> 6 => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DL ) +*> Not modified. +*> \endverbatim +*> +*> \param[in] DL +*> \verbatim +*> DL is COMPLEX*16 array ( I or J, as appropriate ) +*> Left scale factors for grading matrix. Not modified. +*> \endverbatim +*> +*> \param[in] DR +*> \verbatim +*> DR is COMPLEX*16 array ( I or J, as appropriate ) +*> Right scale factors for grading matrix. Not modified. +*> \endverbatim +*> +*> \param[in] IPVTNG +*> \verbatim +*> IPVTNG is INTEGER +*> On entry specifies pivoting permutations as follows: +*> 0 => none. +*> 1 => row pivoting. +*> 2 => column pivoting. +*> 3 => full pivoting, i.e., on both sides. +*> Not modified. +*> \endverbatim +*> +*> \param[in] IWORK +*> \verbatim +*> IWORK is INTEGER array ( I or J, as appropriate ) +*> This array specifies the permutation used. The +*> row (or column) originally in position K is in +*> position IWORK( K ) after pivoting. +*> This differs from IWORK for ZLATM2. Not modified. +*> \endverbatim +*> +*> \param[in] SPARSE +*> \verbatim +*> SPARSE is DOUBLE PRECISION between 0. and 1. +*> On entry specifies the sparsity of the matrix +*> if sparse matix is to be generated. +*> SPARSE should lie between 0 and 1. +*> A uniform ( 0, 1 ) random number x is generated and +*> compared to SPARSE; if x is larger the matrix entry +*> is unchanged and if x is smaller the entry is set +*> to zero. Thus on the average a fraction SPARSE of the +*> entries will be set to zero. +*> Not modified. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_matgen +* +* ===================================================================== COMPLEX*16 FUNCTION ZLATM3( M, N, I, J, ISUB, JSUB, KL, KU, $ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, $ SPARSE ) * -* -- LAPACK auxiliary test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK auxiliary routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. * @@ -19,138 +249,6 @@ COMPLEX*16 D( * ), DL( * ), DR( * ) * .. * -* Purpose -* ======= -* -* ZLATM3 returns the (ISUB,JSUB) entry of a random matrix of -* dimension (M, N) described by the other paramters. (ISUB,JSUB) -* is the final position of the (I,J) entry after pivoting -* according to IPVTNG and IWORK. ZLATM3 is called by the -* ZLATMR routine in order to build random test matrices. No error -* checking on parameters is done, because this routine is called in -* a tight loop by ZLATMR which has already checked the parameters. -* -* Use of ZLATM3 differs from CLATM2 in the order in which the random -* number generator is called to fill in random matrix entries. -* With ZLATM2, the generator is called to fill in the pivoted matrix -* columnwise. With ZLATM3, the generator is called to fill in the -* matrix columnwise, after which it is pivoted. Thus, ZLATM3 can -* be used to construct random matrices which differ only in their -* order of rows and/or columns. ZLATM2 is used to construct band -* matrices while avoiding calling the random number generator for -* entries outside the band (and therefore generating random numbers -* in different orders for different pivot orders). -* -* The matrix whose (ISUB,JSUB) entry is returned is constructed as -* follows (this routine only computes one entry): -* -* If ISUB is outside (1..M) or JSUB is outside (1..N), return zero -* (this is convenient for generating matrices in band format). -* -* Generate a matrix A with random entries of distribution IDIST. -* -* Set the diagonal to D. -* -* Grade the matrix, if desired, from the left (by DL) and/or -* from the right (by DR or DL) as specified by IGRADE. -* -* Permute, if desired, the rows and/or columns as specified by -* IPVTNG and IWORK. -* -* Band the matrix to have lower bandwidth KL and upper -* bandwidth KU. -* -* Set random entries to zero as specified by SPARSE. -* -* Arguments -* ========= -* -* M (input) INTEGER -* Number of rows of matrix. Not modified. -* -* N (input) INTEGER -* Number of columns of matrix. Not modified. -* -* I (input) INTEGER -* Row of unpivoted entry to be returned. Not modified. -* -* J (input) INTEGER -* Column of unpivoted entry to be returned. Not modified. -* -* ISUB (input/output) INTEGER -* Row of pivoted entry to be returned. Changed on exit. -* -* JSUB (input/output) INTEGER -* Column of pivoted entry to be returned. Changed on exit. -* -* KL (input) INTEGER -* Lower bandwidth. Not modified. -* -* KU (input) INTEGER -* Upper bandwidth. Not modified. -* -* IDIST (input) INTEGER -* On entry, IDIST specifies the type of distribution to be -* used to generate a random matrix . -* 1 => real and imaginary parts each UNIFORM( 0, 1 ) -* 2 => real and imaginary parts each UNIFORM( -1, 1 ) -* 3 => real and imaginary parts each NORMAL( 0, 1 ) -* 4 => complex number uniform in DISK( 0 , 1 ) -* Not modified. -* -* ISEED (input/output) INTEGER array of dimension ( 4 ) -* Seed for random number generator. -* Changed on exit. -* -* D (input) COMPLEX*16 array of dimension ( MIN( I , J ) ) -* Diagonal entries of matrix. Not modified. -* -* IGRADE (input) INTEGER -* Specifies grading of matrix as follows: -* 0 => no grading -* 1 => matrix premultiplied by diag( DL ) -* 2 => matrix postmultiplied by diag( DR ) -* 3 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DR ) -* 4 => matrix premultiplied by diag( DL ) and -* postmultiplied by inv( diag( DL ) ) -* 5 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( CONJG(DL) ) -* 6 => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DL ) -* Not modified. -* -* DL (input) COMPLEX*16 array ( I or J, as appropriate ) -* Left scale factors for grading matrix. Not modified. -* -* DR (input) COMPLEX*16 array ( I or J, as appropriate ) -* Right scale factors for grading matrix. Not modified. -* -* IPVTNG (input) INTEGER -* On entry specifies pivoting permutations as follows: -* 0 => none. -* 1 => row pivoting. -* 2 => column pivoting. -* 3 => full pivoting, i.e., on both sides. -* Not modified. -* -* IWORK (input) INTEGER array ( I or J, as appropriate ) -* This array specifies the permutation used. The -* row (or column) originally in position K is in -* position IWORK( K ) after pivoting. -* This differs from IWORK for ZLATM2. Not modified. -* -* SPARSE (input) DOUBLE PRECISION between 0. and 1. -* On entry specifies the sparsity of the matrix -* if sparse matix is to be generated. -* SPARSE should lie between 0 and 1. -* A uniform ( 0, 1 ) random number x is generated and -* compared to SPARSE; if x is larger the matrix entry -* is unchanged and if x is smaller the entry is set -* to zero. Thus on the average a fraction SPARSE of the -* entries will be set to zero. -* Not modified. -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/zlatm5.f b/TESTING/MATGEN/zlatm5.f index a1c0a6ca..6e3ce53d 100644 --- a/TESTING/MATGEN/zlatm5.f +++ b/TESTING/MATGEN/zlatm5.f @@ -1,177 +1,292 @@ - SUBROUTINE ZLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD, - $ E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA, - $ QBLCKB ) -* -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N, - $ PRTYPE, QBLCKA, QBLCKB - DOUBLE PRECISION ALPHA -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * ), - $ D( LDD, * ), E( LDE, * ), F( LDF, * ), - $ L( LDL, * ), R( LDR, * ) -* .. -* +*> \brief \b ZLATM5 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD, +* E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA, +* QBLCKB ) +* +* .. Scalar Arguments .. +* INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N, +* $ PRTYPE, QBLCKA, QBLCKB +* DOUBLE PRECISION ALPHA +* .. +* .. Array Arguments .. +* COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * ), +* $ D( LDD, * ), E( LDE, * ), F( LDF, * ), +* $ L( LDL, * ), R( LDR, * ) +* .. +* * Purpose * ======= * -* ZLATM5 generates matrices involved in the Generalized Sylvester -* equation: -* -* A * R - L * B = C -* D * R - L * E = F -* -* They also satisfy (the diagonalization condition) -* -* [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] ) -* [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] ) -* +*>\details \b Purpose: +*>\verbatim +*> +*> ZLATM5 generates matrices involved in the Generalized Sylvester +*> equation: +*> +*> A * R - L * B = C +*> D * R - L * E = F +*> +*> They also satisfy (the diagonalization condition) +*> +*> [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] ) +*> [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] ) +*> +*> +*>\endverbatim * * Arguments * ========= * -* PRTYPE (input) INTEGER -* "Points" to a certian type of the matrices to generate -* (see futher details). -* -* M (input) INTEGER -* Specifies the order of A and D and the number of rows in -* C, F, R and L. -* -* N (input) INTEGER -* Specifies the order of B and E and the number of columns in -* C, F, R and L. -* -* A (output) COMPLEX*16 array, dimension (LDA, M). -* On exit A M-by-M is initialized according to PRTYPE. -* -* LDA (input) INTEGER -* The leading dimension of A. -* -* B (output) COMPLEX*16 array, dimension (LDB, N). -* On exit B N-by-N is initialized according to PRTYPE. -* -* LDB (input) INTEGER -* The leading dimension of B. -* -* C (output) COMPLEX*16 array, dimension (LDC, N). -* On exit C M-by-N is initialized according to PRTYPE. -* -* LDC (input) INTEGER -* The leading dimension of C. -* -* D (output) COMPLEX*16 array, dimension (LDD, M). -* On exit D M-by-M is initialized according to PRTYPE. -* -* LDD (input) INTEGER -* The leading dimension of D. -* -* E (output) COMPLEX*16 array, dimension (LDE, N). -* On exit E N-by-N is initialized according to PRTYPE. -* -* LDE (input) INTEGER -* The leading dimension of E. -* -* F (output) COMPLEX*16 array, dimension (LDF, N). -* On exit F M-by-N is initialized according to PRTYPE. -* -* LDF (input) INTEGER -* The leading dimension of F. -* -* R (output) COMPLEX*16 array, dimension (LDR, N). -* On exit R M-by-N is initialized according to PRTYPE. -* -* LDR (input) INTEGER -* The leading dimension of R. -* -* L (output) COMPLEX*16 array, dimension (LDL, N). -* On exit L M-by-N is initialized according to PRTYPE. -* -* LDL (input) INTEGER -* The leading dimension of L. +*> \param[in] PRTYPE +*> \verbatim +*> PRTYPE is INTEGER +*> "Points" to a certian type of the matrices to generate +*> (see futher details). +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Specifies the order of A and D and the number of rows in +*> C, F, R and L. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Specifies the order of B and E and the number of columns in +*> C, F, R and L. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA, M). +*> On exit A M-by-M is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of A. +*> \endverbatim +*> +*> \param[out] B +*> \verbatim +*> B is COMPLEX*16 array, dimension (LDB, N). +*> On exit B N-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of B. +*> \endverbatim +*> +*> \param[out] C +*> \verbatim +*> C is COMPLEX*16 array, dimension (LDC, N). +*> On exit C M-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> The leading dimension of C. +*> \endverbatim +*> +*> \param[out] D +*> \verbatim +*> D is COMPLEX*16 array, dimension (LDD, M). +*> On exit D M-by-M is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDD +*> \verbatim +*> LDD is INTEGER +*> The leading dimension of D. +*> \endverbatim +*> +*> \param[out] E +*> \verbatim +*> E is COMPLEX*16 array, dimension (LDE, N). +*> On exit E N-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDE +*> \verbatim +*> LDE is INTEGER +*> The leading dimension of E. +*> \endverbatim +*> +*> \param[out] F +*> \verbatim +*> F is COMPLEX*16 array, dimension (LDF, N). +*> On exit F M-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDF +*> \verbatim +*> LDF is INTEGER +*> The leading dimension of F. +*> \endverbatim +*> +*> \param[out] R +*> \verbatim +*> R is COMPLEX*16 array, dimension (LDR, N). +*> On exit R M-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDR +*> \verbatim +*> LDR is INTEGER +*> The leading dimension of R. +*> \endverbatim +*> +*> \param[out] L +*> \verbatim +*> L is COMPLEX*16 array, dimension (LDL, N). +*> On exit L M-by-N is initialized according to PRTYPE. +*> \endverbatim +*> +*> \param[in] LDL +*> \verbatim +*> LDL is INTEGER +*> The leading dimension of L. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION +*> Parameter used in generating PRTYPE = 1 and 5 matrices. +*> \endverbatim +*> +*> \param[in] QBLCKA +*> \verbatim +*> QBLCKA is INTEGER +*> When PRTYPE = 3, specifies the distance between 2-by-2 +*> blocks on the diagonal in A. Otherwise, QBLCKA is not +*> referenced. QBLCKA > 1. +*> \endverbatim +*> +*> \param[in] QBLCKB +*> \verbatim +*> QBLCKB is INTEGER +*> When PRTYPE = 3, specifies the distance between 2-by-2 +*> blocks on the diagonal in B. Otherwise, QBLCKB is not +*> referenced. QBLCKB > 1. +*> \endverbatim +*> +* +* Authors +* ======= * -* ALPHA (input) DOUBLE PRECISION -* Parameter used in generating PRTYPE = 1 and 5 matrices. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* QBLCKA (input) INTEGER -* When PRTYPE = 3, specifies the distance between 2-by-2 -* blocks on the diagonal in A. Otherwise, QBLCKA is not -* referenced. QBLCKA > 1. +*> \date November 2011 * -* QBLCKB (input) INTEGER -* When PRTYPE = 3, specifies the distance between 2-by-2 -* blocks on the diagonal in B. Otherwise, QBLCKB is not -* referenced. QBLCKB > 1. +*> \ingroup complex16_matgen * * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices +*> +*> A : if (i == j) then A(i, j) = 1.0 +*> if (j == i + 1) then A(i, j) = -1.0 +*> else A(i, j) = 0.0, i, j = 1...M +*> +*> B : if (i == j) then B(i, j) = 1.0 - ALPHA +*> if (j == i + 1) then B(i, j) = 1.0 +*> else B(i, j) = 0.0, i, j = 1...N +*> +*> D : if (i == j) then D(i, j) = 1.0 +*> else D(i, j) = 0.0, i, j = 1...M +*> +*> E : if (i == j) then E(i, j) = 1.0 +*> else E(i, j) = 0.0, i, j = 1...N +*> +*> L = R are chosen from [-10...10], +*> which specifies the right hand sides (C, F). +*> +*> PRTYPE = 2 or 3: Triangular and/or quasi- triangular. +*> +*> A : if (i <= j) then A(i, j) = [-1...1] +*> else A(i, j) = 0.0, i, j = 1...M +*> +*> if (PRTYPE = 3) then +*> A(k + 1, k + 1) = A(k, k) +*> A(k + 1, k) = [-1...1] +*> sign(A(k, k + 1) = -(sin(A(k + 1, k)) +*> k = 1, M - 1, QBLCKA +*> +*> B : if (i <= j) then B(i, j) = [-1...1] +*> else B(i, j) = 0.0, i, j = 1...N +*> +*> if (PRTYPE = 3) then +*> B(k + 1, k + 1) = B(k, k) +*> B(k + 1, k) = [-1...1] +*> sign(B(k, k + 1) = -(sign(B(k + 1, k)) +*> k = 1, N - 1, QBLCKB +*> +*> D : if (i <= j) then D(i, j) = [-1...1]. +*> else D(i, j) = 0.0, i, j = 1...M +*> +*> +*> E : if (i <= j) then D(i, j) = [-1...1] +*> else E(i, j) = 0.0, i, j = 1...N +*> +*> L, R are chosen from [-10...10], +*> which specifies the right hand sides (C, F). +*> +*> PRTYPE = 4 Full +*> A(i, j) = [-10...10] +*> D(i, j) = [-1...1] i,j = 1...M +*> B(i, j) = [-10...10] +*> E(i, j) = [-1...1] i,j = 1...N +*> R(i, j) = [-10...10] +*> L(i, j) = [-1...1] i = 1..M ,j = 1...N +*> +*> L, R specifies the right hand sides (C, F). +*> +*> PRTYPE = 5 special case common and/or close eigs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD, + $ E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA, + $ QBLCKB ) * -* PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices -* -* A : if (i == j) then A(i, j) = 1.0 -* if (j == i + 1) then A(i, j) = -1.0 -* else A(i, j) = 0.0, i, j = 1...M -* -* B : if (i == j) then B(i, j) = 1.0 - ALPHA -* if (j == i + 1) then B(i, j) = 1.0 -* else B(i, j) = 0.0, i, j = 1...N -* -* D : if (i == j) then D(i, j) = 1.0 -* else D(i, j) = 0.0, i, j = 1...M -* -* E : if (i == j) then E(i, j) = 1.0 -* else E(i, j) = 0.0, i, j = 1...N -* -* L = R are chosen from [-10...10], -* which specifies the right hand sides (C, F). -* -* PRTYPE = 2 or 3: Triangular and/or quasi- triangular. -* -* A : if (i <= j) then A(i, j) = [-1...1] -* else A(i, j) = 0.0, i, j = 1...M -* -* if (PRTYPE = 3) then -* A(k + 1, k + 1) = A(k, k) -* A(k + 1, k) = [-1...1] -* sign(A(k, k + 1) = -(sin(A(k + 1, k)) -* k = 1, M - 1, QBLCKA -* -* B : if (i <= j) then B(i, j) = [-1...1] -* else B(i, j) = 0.0, i, j = 1...N -* -* if (PRTYPE = 3) then -* B(k + 1, k + 1) = B(k, k) -* B(k + 1, k) = [-1...1] -* sign(B(k, k + 1) = -(sign(B(k + 1, k)) -* k = 1, N - 1, QBLCKB -* -* D : if (i <= j) then D(i, j) = [-1...1]. -* else D(i, j) = 0.0, i, j = 1...M -* -* -* E : if (i <= j) then D(i, j) = [-1...1] -* else E(i, j) = 0.0, i, j = 1...N -* -* L, R are chosen from [-10...10], -* which specifies the right hand sides (C, F). -* -* PRTYPE = 4 Full -* A(i, j) = [-10...10] -* D(i, j) = [-1...1] i,j = 1...M -* B(i, j) = [-10...10] -* E(i, j) = [-1...1] i,j = 1...N -* R(i, j) = [-10...10] -* L(i, j) = [-1...1] i = 1..M ,j = 1...N -* -* L, R specifies the right hand sides (C, F). +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* PRTYPE = 5 special case common and/or close eigs. +* .. Scalar Arguments .. + INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N, + $ PRTYPE, QBLCKA, QBLCKB + DOUBLE PRECISION ALPHA +* .. +* .. Array Arguments .. + COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * ), + $ D( LDD, * ), E( LDE, * ), F( LDF, * ), + $ L( LDL, * ), R( LDR, * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/zlatm6.f b/TESTING/MATGEN/zlatm6.f index 6dd7241d..04a52d8b 100644 --- a/TESTING/MATGEN/zlatm6.f +++ b/TESTING/MATGEN/zlatm6.f @@ -1,105 +1,195 @@ - SUBROUTINE ZLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA, - $ BETA, WX, WY, S, DIF ) -* -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER LDA, LDX, LDY, N, TYPE - COMPLEX*16 ALPHA, BETA, WX, WY -* .. -* .. Array Arguments .. - DOUBLE PRECISION DIF( * ), S( * ) - COMPLEX*16 A( LDA, * ), B( LDA, * ), X( LDX, * ), - $ Y( LDY, * ) -* .. -* +*> \brief \b ZLATM6 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA, +* BETA, WX, WY, S, DIF ) +* +* .. Scalar Arguments .. +* INTEGER LDA, LDX, LDY, N, TYPE +* COMPLEX*16 ALPHA, BETA, WX, WY +* .. +* .. Array Arguments .. +* DOUBLE PRECISION DIF( * ), S( * ) +* COMPLEX*16 A( LDA, * ), B( LDA, * ), X( LDX, * ), +* $ Y( LDY, * ) +* .. +* * Purpose * ======= * -* ZLATM6 generates test matrices for the generalized eigenvalue -* problem, their corresponding right and left eigenvector matrices, -* and also reciprocal condition numbers for all eigenvalues and -* the reciprocal condition numbers of eigenvectors corresponding to -* the 1th and 5th eigenvalues. -* -* Test Matrices -* ============= -* -* Two kinds of test matrix pairs -* (A, B) = inverse(YH) * (Da, Db) * inverse(X) -* are used in the tests: -* -* Type 1: -* Da = 1+a 0 0 0 0 Db = 1 0 0 0 0 -* 0 2+a 0 0 0 0 1 0 0 0 -* 0 0 3+a 0 0 0 0 1 0 0 -* 0 0 0 4+a 0 0 0 0 1 0 -* 0 0 0 0 5+a , 0 0 0 0 1 -* and Type 2: -* Da = 1+i 0 0 0 0 Db = 1 0 0 0 0 -* 0 1-i 0 0 0 0 1 0 0 0 -* 0 0 1 0 0 0 0 1 0 0 -* 0 0 0 (1+a)+(1+b)i 0 0 0 0 1 0 -* 0 0 0 0 (1+a)-(1+b)i, 0 0 0 0 1 . -* -* In both cases the same inverse(YH) and inverse(X) are used to compute -* (A, B), giving the exact eigenvectors to (A,B) as (YH, X): -* -* YH: = 1 0 -y y -y X = 1 0 -x -x x -* 0 1 -y y -y 0 1 x -x -x -* 0 0 1 0 0 0 0 1 0 0 -* 0 0 0 1 0 0 0 0 1 0 -* 0 0 0 0 1, 0 0 0 0 1 , where -* -* a, b, x and y will have all values independently of each other. +*>\details \b Purpose: +*>\verbatim +*> +*> ZLATM6 generates test matrices for the generalized eigenvalue +*> problem, their corresponding right and left eigenvector matrices, +*> and also reciprocal condition numbers for all eigenvalues and +*> the reciprocal condition numbers of eigenvectors corresponding to +*> the 1th and 5th eigenvalues. +*> +*> Test Matrices +*> ============= +*> +*> Two kinds of test matrix pairs +*> (A, B) = inverse(YH) * (Da, Db) * inverse(X) +*> are used in the tests: +*> +*> Type 1: +*> Da = 1+a 0 0 0 0 Db = 1 0 0 0 0 +*> 0 2+a 0 0 0 0 1 0 0 0 +*> 0 0 3+a 0 0 0 0 1 0 0 +*> 0 0 0 4+a 0 0 0 0 1 0 +*> 0 0 0 0 5+a , 0 0 0 0 1 +*> and Type 2: +*> Da = 1+i 0 0 0 0 Db = 1 0 0 0 0 +*> 0 1-i 0 0 0 0 1 0 0 0 +*> 0 0 1 0 0 0 0 1 0 0 +*> 0 0 0 (1+a)+(1+b)i 0 0 0 0 1 0 +*> 0 0 0 0 (1+a)-(1+b)i, 0 0 0 0 1 . +*> +*> In both cases the same inverse(YH) and inverse(X) are used to compute +*> (A, B), giving the exact eigenvectors to (A,B) as (YH, X): +*> +*> YH: = 1 0 -y y -y X = 1 0 -x -x x +*> 0 1 -y y -y 0 1 x -x -x +*> 0 0 1 0 0 0 0 1 0 0 +*> 0 0 0 1 0 0 0 0 1 0 +*> 0 0 0 0 1, 0 0 0 0 1 , where +*> +*> a, b, x and y will have all values independently of each other. +*> +*>\endverbatim * * Arguments * ========= * -* TYPE (input) INTEGER -* Specifies the problem type (see futher details). -* -* N (input) INTEGER -* Size of the matrices A and B. -* -* A (output) COMPLEX*16 array, dimension (LDA, N). -* On exit A N-by-N is initialized according to TYPE. -* -* LDA (input) INTEGER -* The leading dimension of A and of B. -* -* B (output) COMPLEX*16 array, dimension (LDA, N). -* On exit B N-by-N is initialized according to TYPE. -* -* X (output) COMPLEX*16 array, dimension (LDX, N). -* On exit X is the N-by-N matrix of right eigenvectors. -* -* LDX (input) INTEGER -* The leading dimension of X. -* -* Y (output) COMPLEX*16 array, dimension (LDY, N). -* On exit Y is the N-by-N matrix of left eigenvectors. +*> \param[in] TYPE +*> \verbatim +*> TYPE is INTEGER +*> Specifies the problem type (see futher details). +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Size of the matrices A and B. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA, N). +*> On exit A N-by-N is initialized according to TYPE. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of A and of B. +*> \endverbatim +*> +*> \param[out] B +*> \verbatim +*> B is COMPLEX*16 array, dimension (LDA, N). +*> On exit B N-by-N is initialized according to TYPE. +*> \endverbatim +*> +*> \param[out] X +*> \verbatim +*> X is COMPLEX*16 array, dimension (LDX, N). +*> On exit X is the N-by-N matrix of right eigenvectors. +*> \endverbatim +*> +*> \param[in] LDX +*> \verbatim +*> LDX is INTEGER +*> The leading dimension of X. +*> \endverbatim +*> +*> \param[out] Y +*> \verbatim +*> Y is COMPLEX*16 array, dimension (LDY, N). +*> On exit Y is the N-by-N matrix of left eigenvectors. +*> \endverbatim +*> +*> \param[in] LDY +*> \verbatim +*> LDY is INTEGER +*> The leading dimension of Y. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX*16 +*> \verbatim +*> Weighting constants for matrix A. +*> \endverbatim +*> +*> \param[in] WX +*> \verbatim +*> WX is COMPLEX*16 +*> Constant for right eigenvector matrix. +*> \endverbatim +*> +*> \param[in] WY +*> \verbatim +*> WY is COMPLEX*16 +*> Constant for left eigenvector matrix. +*> \endverbatim +*> +*> \param[out] S +*> \verbatim +*> S is DOUBLE PRECISION array, dimension (N) +*> S(i) is the reciprocal condition number for eigenvalue i. +*> \endverbatim +*> +*> \param[out] DIF +*> \verbatim +*> DIF is DOUBLE PRECISION array, dimension (N) +*> DIF(i) is the reciprocal condition number for eigenvector i. +*> \endverbatim +*> +* +* Authors +* ======= * -* LDY (input) INTEGER -* The leading dimension of Y. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* ALPHA (input) COMPLEX*16 -* BETA (input) COMPLEX*16 -* Weighting constants for matrix A. +*> \date November 2011 * -* WX (input) COMPLEX*16 -* Constant for right eigenvector matrix. +*> \ingroup complex16_matgen * -* WY (input) COMPLEX*16 -* Constant for left eigenvector matrix. +* ===================================================================== + SUBROUTINE ZLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA, + $ BETA, WX, WY, S, DIF ) * -* S (output) DOUBLE PRECISION array, dimension (N) -* S(i) is the reciprocal condition number for eigenvalue i. +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* DIF (output) DOUBLE PRECISION array, dimension (N) -* DIF(i) is the reciprocal condition number for eigenvector i. +* .. Scalar Arguments .. + INTEGER LDA, LDX, LDY, N, TYPE + COMPLEX*16 ALPHA, BETA, WX, WY +* .. +* .. Array Arguments .. + DOUBLE PRECISION DIF( * ), S( * ) + COMPLEX*16 A( LDA, * ), B( LDA, * ), X( LDX, * ), + $ Y( LDY, * ) +* .. * * ===================================================================== * diff --git a/TESTING/MATGEN/zlatme.f b/TESTING/MATGEN/zlatme.f index 0063b06c..51dbb2d1 100644 --- a/TESTING/MATGEN/zlatme.f +++ b/TESTING/MATGEN/zlatme.f @@ -1,12 +1,312 @@ +*> \brief \b ZLATME +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZLATME( N, DIST, ISEED, D, MODE, COND, DMAX, +* RSIGN, +* UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, +* A, +* LDA, WORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER DIST, RSIGN, SIM, UPPER +* INTEGER INFO, KL, KU, LDA, MODE, MODES, N +* DOUBLE PRECISION ANORM, COND, CONDS +* COMPLEX*16 DMAX +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* DOUBLE PRECISION DS( * ) +* COMPLEX*16 A( LDA, * ), D( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> ZLATME generates random non-symmetric square matrices with +*> specified eigenvalues for testing LAPACK programs. +*> +*> ZLATME operates by applying the following sequence of +*> operations: +*> +*> 1. Set the diagonal to D, where D may be input or +*> computed according to MODE, COND, DMAX, and RSIGN +*> as described below. +*> +*> 2. If UPPER='T', the upper triangle of A is set to random values +*> out of distribution DIST. +*> +*> 3. If SIM='T', A is multiplied on the left by a random matrix +*> X, whose singular values are specified by DS, MODES, and +*> CONDS, and on the right by X inverse. +*> +*> 4. If KL < N-1, the lower bandwidth is reduced to KL using +*> Householder transformations. If KU < N-1, the upper +*> bandwidth is reduced to KU. +*> +*> 5. If ANORM is not negative, the matrix is scaled to have +*> maximum-element-norm ANORM. +*> +*> (Note: since the matrix cannot be reduced beyond Hessenberg form, +*> no packing options are available.) +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns (or rows) of A. Not modified. +*> \endverbatim +*> +*> \param[in] DIST +*> \verbatim +*> DIST is CHARACTER*1 +*> On entry, DIST specifies the type of distribution to be used +*> to generate the random eigen-/singular values, and on the +*> upper triangle (see UPPER). +*> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) +*> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) +*> 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) +*> 'D' => uniform on the complex disc |z| < 1. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. They should lie between 0 and 4095 inclusive, +*> and ISEED(4) should be odd. The random number generator +*> uses a linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to ZLATME +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is COMPLEX*16 array, dimension ( N ) +*> This array is used to specify the eigenvalues of A. If +*> MODE=0, then D is assumed to contain the eigenvalues +*> otherwise they will be computed according to MODE, COND, +*> DMAX, and RSIGN and placed in D. +*> Modified if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry this describes how the eigenvalues are to +*> be specified: +*> MODE = 0 means use D as input +*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND +*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is between 1 and 4, D has entries ranging +*> from 1 to 1/COND, if between -1 and -4, D has entries +*> ranging from 1/COND to 1, +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is DOUBLE PRECISION +*> On entry, this is used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] DMAX +*> \verbatim +*> DMAX is COMPLEX*16 +*> If MODE is neither -6, 0 nor 6, the contents of D, as +*> computed according to MODE and COND, will be scaled by +*> DMAX / max(abs(D(i))). Note that DMAX need not be +*> positive or real: if DMAX is negative or complex (or zero), +*> D will be scaled by a negative or complex number (or zero). +*> If RSIGN='F' then the largest (absolute) eigenvalue will be +*> equal to DMAX. +*> Not modified. +*> \endverbatim +*> +*> \param[in] RSIGN +*> \verbatim +*> RSIGN is CHARACTER*1 +*> If MODE is not 0, 6, or -6, and RSIGN='T', then the +*> elements of D, as computed according to MODE and COND, will +*> be multiplied by a random complex number from the unit +*> circle |z| = 1. If RSIGN='F', they will not be. RSIGN may +*> only have the values 'T' or 'F'. +*> Not modified. +*> \endverbatim +*> +*> \param[in] UPPER +*> \verbatim +*> UPPER is CHARACTER*1 +*> If UPPER='T', then the elements of A above the diagonal +*> will be set to random numbers out of DIST. If UPPER='F', +*> they will not. UPPER may only have the values 'T' or 'F'. +*> Not modified. +*> \endverbatim +*> +*> \param[in] SIM +*> \verbatim +*> SIM is CHARACTER*1 +*> If SIM='T', then A will be operated on by a "similarity +*> transform", i.e., multiplied on the left by a matrix X and +*> on the right by X inverse. X = U S V, where U and V are +*> random unitary matrices and S is a (diagonal) matrix of +*> singular values specified by DS, MODES, and CONDS. If +*> SIM='F', then A will not be transformed. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] DS +*> \verbatim +*> DS is DOUBLE PRECISION array, dimension ( N ) +*> This array is used to specify the singular values of X, +*> in the same way that D specifies the eigenvalues of A. +*> If MODE=0, the DS contains the singular values, which +*> may not be zero. +*> Modified if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODES +*> \verbatim +*> MODES is INTEGER +*> \endverbatim +*> +*> \param[in] CONDS +*> \verbatim +*> CONDS is DOUBLE PRECISION +*> Similar to MODE and COND, but for specifying the diagonal +*> of S. MODES=-6 and +6 are not allowed (since they would +*> result in randomly ill-conditioned eigenvalues.) +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> This specifies the lower bandwidth of the matrix. KL=1 +*> specifies upper Hessenberg form. If KL is at least N-1, +*> then A will have full lower bandwidth. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> This specifies the upper bandwidth of the matrix. KU=1 +*> specifies lower Hessenberg form. If KU is at least N-1, +*> then A will have full upper bandwidth; if KU and KL +*> are both at least N-1, then A will be dense. Only one of +*> KU and KL may be less than N-1. +*> Not modified. +*> \endverbatim +*> +*> \param[in] ANORM +*> \verbatim +*> ANORM is DOUBLE PRECISION +*> If ANORM is not negative, then A will be scaled by a non- +*> negative real number to make the maximum-element-norm of A +*> to be ANORM. +*> Not modified. +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension ( LDA, N ) +*> On exit A is the desired test matrix. +*> Modified. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> LDA specifies the first dimension of A as declared in the +*> calling program. LDA must be at least M. +*> Not modified. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension ( 3*N ) +*> Workspace. +*> Modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error code. On exit, INFO will be set to one of the +*> following values: +*> 0 => normal return +*> -1 => N negative +*> -2 => DIST illegal string +*> -5 => MODE not in range -6 to 6 +*> -6 => COND less than 1.0, and MODE neither -6, 0 nor 6 +*> -9 => RSIGN is not 'T' or 'F' +*> -10 => UPPER is not 'T' or 'F' +*> -11 => SIM is not 'T' or 'F' +*> -12 => MODES=0 and DS has a zero singular value. +*> -13 => MODES is not in the range -5 to 5. +*> -14 => MODES is nonzero and CONDS is less than 1. +*> -15 => KL is less than 1. +*> -16 => KU is less than 1, or KL and KU are both less than +*> N-1. +*> -19 => LDA is less than M. +*> 1 => Error return from ZLATM1 (computing D) +*> 2 => Cannot scale to DMAX (max. eigenvalue is 0) +*> 3 => Error return from DLATM1 (computing DS) +*> 4 => Error return from ZLARGE +*> 5 => Zero singular value from DLATM1. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_matgen +* +* ===================================================================== SUBROUTINE ZLATME( N, DIST, ISEED, D, MODE, COND, DMAX, $ RSIGN, $ UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, $ A, $ LDA, WORK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER DIST, RSIGN, SIM, UPPER @@ -20,198 +320,6 @@ COMPLEX*16 A( LDA, * ), D( * ), WORK( * ) * .. * -* Purpose -* ======= -* -* ZLATME generates random non-symmetric square matrices with -* specified eigenvalues for testing LAPACK programs. -* -* ZLATME operates by applying the following sequence of -* operations: -* -* 1. Set the diagonal to D, where D may be input or -* computed according to MODE, COND, DMAX, and RSIGN -* as described below. -* -* 2. If UPPER='T', the upper triangle of A is set to random values -* out of distribution DIST. -* -* 3. If SIM='T', A is multiplied on the left by a random matrix -* X, whose singular values are specified by DS, MODES, and -* CONDS, and on the right by X inverse. -* -* 4. If KL < N-1, the lower bandwidth is reduced to KL using -* Householder transformations. If KU < N-1, the upper -* bandwidth is reduced to KU. -* -* 5. If ANORM is not negative, the matrix is scaled to have -* maximum-element-norm ANORM. -* -* (Note: since the matrix cannot be reduced beyond Hessenberg form, -* no packing options are available.) -* -* Arguments -* ========= -* -* N (input) INTEGER -* The number of columns (or rows) of A. Not modified. -* -* DIST (input) CHARACTER*1 -* On entry, DIST specifies the type of distribution to be used -* to generate the random eigen-/singular values, and on the -* upper triangle (see UPPER). -* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) -* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) -* 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) -* 'D' => uniform on the complex disc |z| < 1. -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. They should lie between 0 and 4095 inclusive, -* and ISEED(4) should be odd. The random number generator -* uses a linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to ZLATME -* to continue the same random number sequence. -* Changed on exit. -* -* D (input/output) COMPLEX*16 array, dimension ( N ) -* This array is used to specify the eigenvalues of A. If -* MODE=0, then D is assumed to contain the eigenvalues -* otherwise they will be computed according to MODE, COND, -* DMAX, and RSIGN and placed in D. -* Modified if MODE is nonzero. -* -* MODE (input) INTEGER -* On entry this describes how the eigenvalues are to -* be specified: -* MODE = 0 means use D as input -* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND -* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is between 1 and 4, D has entries ranging -* from 1 to 1/COND, if between -1 and -4, D has entries -* ranging from 1/COND to 1, -* Not modified. -* -* COND (input) DOUBLE PRECISION -* On entry, this is used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* DMAX (input) COMPLEX*16 -* If MODE is neither -6, 0 nor 6, the contents of D, as -* computed according to MODE and COND, will be scaled by -* DMAX / max(abs(D(i))). Note that DMAX need not be -* positive or real: if DMAX is negative or complex (or zero), -* D will be scaled by a negative or complex number (or zero). -* If RSIGN='F' then the largest (absolute) eigenvalue will be -* equal to DMAX. -* Not modified. -* -* RSIGN (input) CHARACTER*1 -* If MODE is not 0, 6, or -6, and RSIGN='T', then the -* elements of D, as computed according to MODE and COND, will -* be multiplied by a random complex number from the unit -* circle |z| = 1. If RSIGN='F', they will not be. RSIGN may -* only have the values 'T' or 'F'. -* Not modified. -* -* UPPER (input) CHARACTER*1 -* If UPPER='T', then the elements of A above the diagonal -* will be set to random numbers out of DIST. If UPPER='F', -* they will not. UPPER may only have the values 'T' or 'F'. -* Not modified. -* -* SIM (input) CHARACTER*1 -* If SIM='T', then A will be operated on by a "similarity -* transform", i.e., multiplied on the left by a matrix X and -* on the right by X inverse. X = U S V, where U and V are -* random unitary matrices and S is a (diagonal) matrix of -* singular values specified by DS, MODES, and CONDS. If -* SIM='F', then A will not be transformed. -* Not modified. -* -* DS (input/output) DOUBLE PRECISION array, dimension ( N ) -* This array is used to specify the singular values of X, -* in the same way that D specifies the eigenvalues of A. -* If MODE=0, the DS contains the singular values, which -* may not be zero. -* Modified if MODE is nonzero. -* -* MODES (input) INTEGER -* -* CONDS (input) DOUBLE PRECISION -* Similar to MODE and COND, but for specifying the diagonal -* of S. MODES=-6 and +6 are not allowed (since they would -* result in randomly ill-conditioned eigenvalues.) -* -* KL (input) INTEGER -* This specifies the lower bandwidth of the matrix. KL=1 -* specifies upper Hessenberg form. If KL is at least N-1, -* then A will have full lower bandwidth. -* Not modified. -* -* KU (input) INTEGER -* This specifies the upper bandwidth of the matrix. KU=1 -* specifies lower Hessenberg form. If KU is at least N-1, -* then A will have full upper bandwidth; if KU and KL -* are both at least N-1, then A will be dense. Only one of -* KU and KL may be less than N-1. -* Not modified. -* -* ANORM (input) DOUBLE PRECISION -* If ANORM is not negative, then A will be scaled by a non- -* negative real number to make the maximum-element-norm of A -* to be ANORM. -* Not modified. -* -* A (output) COMPLEX*16 array, dimension ( LDA, N ) -* On exit A is the desired test matrix. -* Modified. -* -* LDA (input) INTEGER -* LDA specifies the first dimension of A as declared in the -* calling program. LDA must be at least M. -* Not modified. -* -* WORK (workspace) COMPLEX*16 array, dimension ( 3*N ) -* Workspace. -* Modified. -* -* INFO (output) INTEGER -* Error code. On exit, INFO will be set to one of the -* following values: -* 0 => normal return -* -1 => N negative -* -2 => DIST illegal string -* -5 => MODE not in range -6 to 6 -* -6 => COND less than 1.0, and MODE neither -6, 0 nor 6 -* -9 => RSIGN is not 'T' or 'F' -* -10 => UPPER is not 'T' or 'F' -* -11 => SIM is not 'T' or 'F' -* -12 => MODES=0 and DS has a zero singular value. -* -13 => MODES is not in the range -5 to 5. -* -14 => MODES is nonzero and CONDS is less than 1. -* -15 => KL is less than 1. -* -16 => KU is less than 1, or KL and KU are both less than -* N-1. -* -19 => LDA is less than M. -* 1 => Error return from ZLATM1 (computing D) -* 2 => Cannot scale to DMAX (max. eigenvalue is 0) -* 3 => Error return from DLATM1 (computing DS) -* 4 => Error return from ZLARGE -* 5 => Zero singular value from DLATM1. -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/zlatmr.f b/TESTING/MATGEN/zlatmr.f index 5c2e4f34..5fd1accb 100644 --- a/TESTING/MATGEN/zlatmr.f +++ b/TESTING/MATGEN/zlatmr.f @@ -1,11 +1,504 @@ +*> \brief \b ZLATMR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZLATMR( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, +* RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, +* CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, +* PACK, A, LDA, IWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER DIST, GRADE, PACK, PIVTNG, RSIGN, SYM +* INTEGER INFO, KL, KU, LDA, M, MODE, MODEL, MODER, N +* DOUBLE PRECISION ANORM, COND, CONDL, CONDR, SPARSE +* COMPLEX*16 DMAX +* .. +* .. Array Arguments .. +* INTEGER IPIVOT( * ), ISEED( 4 ), IWORK( * ) +* COMPLEX*16 A( LDA, * ), D( * ), DL( * ), DR( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> ZLATMR generates random matrices of various types for testing +*> LAPACK programs. +*> +*> ZLATMR operates by applying the following sequence of +*> operations: +*> +*> Generate a matrix A with random entries of distribution DIST +*> which is symmetric if SYM='S', Hermitian if SYM='H', and +*> nonsymmetric if SYM='N'. +*> +*> Set the diagonal to D, where D may be input or +*> computed according to MODE, COND, DMAX and RSIGN +*> as described below. +*> +*> Grade the matrix, if desired, from the left and/or right +*> as specified by GRADE. The inputs DL, MODEL, CONDL, DR, +*> MODER and CONDR also determine the grading as described +*> below. +*> +*> Permute, if desired, the rows and/or columns as specified by +*> PIVTNG and IPIVOT. +*> +*> Set random entries to zero, if desired, to get a random sparse +*> matrix as specified by SPARSE. +*> +*> Make A a band matrix, if desired, by zeroing out the matrix +*> outside a band of lower bandwidth KL and upper bandwidth KU. +*> +*> Scale A, if desired, to have maximum entry ANORM. +*> +*> Pack the matrix if desired. Options specified by PACK are: +*> no packing +*> zero out upper half (if symmetric or Hermitian) +*> zero out lower half (if symmetric or Hermitian) +*> store the upper half columnwise (if symmetric or Hermitian +*> or square upper triangular) +*> store the lower half columnwise (if symmetric or Hermitian +*> or square lower triangular) +*> same as upper half rowwise if symmetric +*> same as conjugate upper half rowwise if Hermitian +*> store the lower triangle in banded format +*> (if symmetric or Hermitian) +*> store the upper triangle in banded format +*> (if symmetric or Hermitian) +*> store the entire matrix in banded format +*> +*> Note: If two calls to ZLATMR differ only in the PACK parameter, +*> they will generate mathematically equivalent matrices. +*> +*> If two calls to ZLATMR both have full bandwidth (KL = M-1 +*> and KU = N-1), and differ only in the PIVTNG and PACK +*> parameters, then the matrices generated will differ only +*> in the order of the rows and/or columns, and otherwise +*> contain the same data. This consistency cannot be and +*> is not maintained with less than full bandwidth. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> Number of rows of A. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> Number of columns of A. Not modified. +*> \endverbatim +*> +*> \param[in] DIST +*> \verbatim +*> DIST is CHARACTER*1 +*> On entry, DIST specifies the type of distribution to be used +*> to generate a random matrix . +*> 'U' => real and imaginary parts are independent +*> UNIFORM( 0, 1 ) ( 'U' for uniform ) +*> 'S' => real and imaginary parts are independent +*> UNIFORM( -1, 1 ) ( 'S' for symmetric ) +*> 'N' => real and imaginary parts are independent +*> NORMAL( 0, 1 ) ( 'N' for normal ) +*> 'D' => uniform on interior of unit disk ( 'D' for disk ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry ISEED specifies the seed of the random number +*> generator. They should lie between 0 and 4095 inclusive, +*> and ISEED(4) should be odd. The random number generator +*> uses a linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to ZLATMR +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] SYM +*> \verbatim +*> SYM is CHARACTER*1 +*> If SYM='S', generated matrix is symmetric. +*> If SYM='H', generated matrix is Hermitian. +*> If SYM='N', generated matrix is nonsymmetric. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is COMPLEX*16 array, dimension (min(M,N)) +*> On entry this array specifies the diagonal entries +*> of the diagonal of A. D may either be specified +*> on entry, or set according to MODE and COND as described +*> below. If the matrix is Hermitian, the real part of D +*> will be taken. May be changed on exit if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry describes how D is to be used: +*> MODE = 0 means use D as input +*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND +*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is DOUBLE PRECISION +*> On entry, used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] DMAX +*> \verbatim +*> DMAX is COMPLEX*16 +*> If MODE neither -6, 0 nor 6, the diagonal is scaled by +*> DMAX / max(abs(D(i))), so that maximum absolute entry +*> of diagonal is abs(DMAX). If DMAX is complex (or zero), +*> diagonal will be scaled by a complex number (or zero). +*> \endverbatim +*> +*> \param[in] RSIGN +*> \verbatim +*> RSIGN is CHARACTER*1 +*> If MODE neither -6, 0 nor 6, specifies sign of diagonal +*> as follows: +*> 'T' => diagonal entries are multiplied by a random complex +*> number uniformly distributed with absolute value 1 +*> 'F' => diagonal unchanged +*> Not modified. +*> \endverbatim +*> +*> \param[in] GRADE +*> \verbatim +*> GRADE is CHARACTER*1 +*> Specifies grading of matrix as follows: +*> 'N' => no grading +*> 'L' => matrix premultiplied by diag( DL ) +*> (only if matrix nonsymmetric) +*> 'R' => matrix postmultiplied by diag( DR ) +*> (only if matrix nonsymmetric) +*> 'B' => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DR ) +*> (only if matrix nonsymmetric) +*> 'H' => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( CONJG(DL) ) +*> (only if matrix Hermitian or nonsymmetric) +*> 'S' => matrix premultiplied by diag( DL ) and +*> postmultiplied by diag( DL ) +*> (only if matrix symmetric or nonsymmetric) +*> 'E' => matrix premultiplied by diag( DL ) and +*> postmultiplied by inv( diag( DL ) ) +*> ( 'S' for similarity ) +*> (only if matrix nonsymmetric) +*> Note: if GRADE='S', then M must equal N. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] DL +*> \verbatim +*> DL is COMPLEX*16 array, dimension (M) +*> If MODEL=0, then on entry this array specifies the diagonal +*> entries of a diagonal matrix used as described under GRADE +*> above. If MODEL is not zero, then DL will be set according +*> to MODEL and CONDL, analogous to the way D is set according +*> to MODE and COND (except there is no DMAX parameter for DL). +*> If GRADE='E', then DL cannot have zero entries. +*> Not referenced if GRADE = 'N' or 'R'. Changed on exit. +*> \endverbatim +*> +*> \param[in] MODEL +*> \verbatim +*> MODEL is INTEGER +*> This specifies how the diagonal array DL is to be computed, +*> just as MODE specifies how D is to be computed. +*> Not modified. +*> \endverbatim +*> +*> \param[in] CONDL +*> \verbatim +*> CONDL is DOUBLE PRECISION +*> When MODEL is not zero, this specifies the condition number +*> of the computed DL. Not modified. +*> \endverbatim +*> +*> \param[in,out] DR +*> \verbatim +*> DR is COMPLEX*16 array, dimension (N) +*> If MODER=0, then on entry this array specifies the diagonal +*> entries of a diagonal matrix used as described under GRADE +*> above. If MODER is not zero, then DR will be set according +*> to MODER and CONDR, analogous to the way D is set according +*> to MODE and COND (except there is no DMAX parameter for DR). +*> Not referenced if GRADE = 'N', 'L', 'H' or 'S'. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] MODER +*> \verbatim +*> MODER is INTEGER +*> This specifies how the diagonal array DR is to be computed, +*> just as MODE specifies how D is to be computed. +*> Not modified. +*> \endverbatim +*> +*> \param[in] CONDR +*> \verbatim +*> CONDR is DOUBLE PRECISION +*> When MODER is not zero, this specifies the condition number +*> of the computed DR. Not modified. +*> \endverbatim +*> +*> \param[in] PIVTNG +*> \verbatim +*> PIVTNG is CHARACTER*1 +*> On entry specifies pivoting permutations as follows: +*> 'N' or ' ' => none. +*> 'L' => left or row pivoting (matrix must be nonsymmetric). +*> 'R' => right or column pivoting (matrix must be +*> nonsymmetric). +*> 'B' or 'F' => both or full pivoting, i.e., on both sides. +*> In this case, M must equal N +*> \endverbatim +*> \verbatim +*> If two calls to ZLATMR both have full bandwidth (KL = M-1 +*> and KU = N-1), and differ only in the PIVTNG and PACK +*> parameters, then the matrices generated will differ only +*> in the order of the rows and/or columns, and otherwise +*> contain the same data. This consistency cannot be +*> maintained with less than full bandwidth. +*> \endverbatim +*> +*> \param[in] IPIVOT +*> \verbatim +*> IPIVOT is INTEGER array, dimension (N or M) +*> This array specifies the permutation used. After the +*> basic matrix is generated, the rows, columns, or both +*> are permuted. If, say, row pivoting is selected, ZLATMR +*> starts with the *last* row and interchanges the M-th and +*> IPIVOT(M)-th rows, then moves to the next-to-last row, +*> interchanging the (M-1)-th and the IPIVOT(M-1)-th rows, +*> and so on. In terms of "2-cycles", the permutation is +*> (1 IPIVOT(1)) (2 IPIVOT(2)) ... (M IPIVOT(M)) +*> where the rightmost cycle is applied first. This is the +*> *inverse* of the effect of pivoting in LINPACK. The idea +*> is that factoring (with pivoting) an identity matrix +*> which has been inverse-pivoted in this way should +*> result in a pivot vector identical to IPIVOT. +*> Not referenced if PIVTNG = 'N'. Not modified. +*> \endverbatim +*> +*> \param[in] SPARSE +*> \verbatim +*> SPARSE is DOUBLE PRECISION +*> On entry specifies the sparsity of the matrix if a sparse +*> matrix is to be generated. SPARSE should lie between +*> 0 and 1. To generate a sparse matrix, for each matrix entry +*> a uniform ( 0, 1 ) random number x is generated and +*> compared to SPARSE; if x is larger the matrix entry +*> is unchanged and if x is smaller the entry is set +*> to zero. Thus on the average a fraction SPARSE of the +*> entries will be set to zero. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> On entry specifies the lower bandwidth of the matrix. For +*> example, KL=0 implies upper triangular, KL=1 implies upper +*> Hessenberg, and KL at least M-1 implies the matrix is not +*> banded. Must equal KU if matrix is symmetric or Hermitian. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> On entry specifies the upper bandwidth of the matrix. For +*> example, KU=0 implies lower triangular, KU=1 implies lower +*> Hessenberg, and KU at least N-1 implies the matrix is not +*> banded. Must equal KL if matrix is symmetric or Hermitian. +*> Not modified. +*> \endverbatim +*> +*> \param[in] ANORM +*> \verbatim +*> ANORM is DOUBLE PRECISION +*> On entry specifies maximum entry of output matrix +*> (output matrix will by multiplied by a constant so that +*> its largest absolute entry equal ANORM) +*> if ANORM is nonnegative. If ANORM is negative no scaling +*> is done. Not modified. +*> \endverbatim +*> +*> \param[in] PACK +*> \verbatim +*> PACK is CHARACTER*1 +*> On entry specifies packing of matrix as follows: +*> 'N' => no packing +*> 'U' => zero out all subdiagonal entries +*> (if symmetric or Hermitian) +*> 'L' => zero out all superdiagonal entries +*> (if symmetric or Hermitian) +*> 'C' => store the upper triangle columnwise +*> (only if matrix symmetric or Hermitian or +*> square upper triangular) +*> 'R' => store the lower triangle columnwise +*> (only if matrix symmetric or Hermitian or +*> square lower triangular) +*> (same as upper half rowwise if symmetric) +*> (same as conjugate upper half rowwise if Hermitian) +*> 'B' => store the lower triangle in band storage scheme +*> (only if matrix symmetric or Hermitian) +*> 'Q' => store the upper triangle in band storage scheme +*> (only if matrix symmetric or Hermitian) +*> 'Z' => store the entire matrix in band storage scheme +*> (pivoting can be provided for by using this +*> option to store A in the trailing rows of +*> the allocated storage) +*> \endverbatim +*> \verbatim +*> Using these options, the various LAPACK packed and banded +*> storage schemes can be obtained: +*> GB - use 'Z' +*> PB, HB or TB - use 'B' or 'Q' +*> PP, HP or TP - use 'C' or 'R' +*> \endverbatim +*> \verbatim +*> If two calls to ZLATMR differ only in the PACK parameter, +*> they will generate mathematically equivalent matrices. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> On exit A is the desired test matrix. Only those +*> entries of A which are significant on output +*> will be referenced (even if A is in packed or band +*> storage format). The 'unoccupied corners' of A in +*> band format will be zeroed out. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> on entry LDA specifies the first dimension of A as +*> declared in the calling program. +*> If PACK='N', 'U' or 'L', LDA must be at least max ( 1, M ). +*> If PACK='C' or 'R', LDA must be at least 1. +*> If PACK='B', or 'Q', LDA must be MIN ( KU+1, N ) +*> If PACK='Z', LDA must be at least KUU+KLL+1, where +*> KUU = MIN ( KU, N-1 ) and KLL = MIN ( KL, N-1 ) +*> Not modified. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (N or M) +*> Workspace. Not referenced if PIVTNG = 'N'. Changed on exit. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error parameter on exit: +*> 0 => normal return +*> -1 => M negative or unequal to N and SYM='S' or 'H' +*> -2 => N negative +*> -3 => DIST illegal string +*> -5 => SYM illegal string +*> -7 => MODE not in range -6 to 6 +*> -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 +*> -10 => MODE neither -6, 0 nor 6 and RSIGN illegal string +*> -11 => GRADE illegal string, or GRADE='E' and +*> M not equal to N, or GRADE='L', 'R', 'B', 'S' or 'E' +*> and SYM = 'H', or GRADE='L', 'R', 'B', 'H' or 'E' +*> and SYM = 'S' +*> -12 => GRADE = 'E' and DL contains zero +*> -13 => MODEL not in range -6 to 6 and GRADE= 'L', 'B', 'H', +*> 'S' or 'E' +*> -14 => CONDL less than 1.0, GRADE='L', 'B', 'H', 'S' or 'E', +*> and MODEL neither -6, 0 nor 6 +*> -16 => MODER not in range -6 to 6 and GRADE= 'R' or 'B' +*> -17 => CONDR less than 1.0, GRADE='R' or 'B', and +*> MODER neither -6, 0 nor 6 +*> -18 => PIVTNG illegal string, or PIVTNG='B' or 'F' and +*> M not equal to N, or PIVTNG='L' or 'R' and SYM='S' +*> or 'H' +*> -19 => IPIVOT contains out of range number and +*> PIVTNG not equal to 'N' +*> -20 => KL negative +*> -21 => KU negative, or SYM='S' or 'H' and KU not equal to KL +*> -22 => SPARSE not in range 0. to 1. +*> -24 => PACK illegal string, or PACK='U', 'L', 'B' or 'Q' +*> and SYM='N', or PACK='C' and SYM='N' and either KL +*> not equal to 0 or N not equal to M, or PACK='R' and +*> SYM='N', and either KU not equal to 0 or N not equal +*> to M +*> -26 => LDA too small +*> 1 => Error return from ZLATM1 (computing D) +*> 2 => Cannot scale diagonal to DMAX (max. entry is 0) +*> 3 => Error return from ZLATM1 (computing DL) +*> 4 => Error return from ZLATM1 (computing DR) +*> 5 => ANORM is positive, but matrix constructed prior to +*> attempting to scale it to have norm ANORM, is zero +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_matgen +* +* ===================================================================== SUBROUTINE ZLATMR( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, $ RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, $ CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, $ PACK, A, LDA, IWORK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER DIST, GRADE, PACK, PIVTNG, RSIGN, SYM @@ -18,366 +511,6 @@ COMPLEX*16 A( LDA, * ), D( * ), DL( * ), DR( * ) * .. * -* Purpose -* ======= -* -* ZLATMR generates random matrices of various types for testing -* LAPACK programs. -* -* ZLATMR operates by applying the following sequence of -* operations: -* -* Generate a matrix A with random entries of distribution DIST -* which is symmetric if SYM='S', Hermitian if SYM='H', and -* nonsymmetric if SYM='N'. -* -* Set the diagonal to D, where D may be input or -* computed according to MODE, COND, DMAX and RSIGN -* as described below. -* -* Grade the matrix, if desired, from the left and/or right -* as specified by GRADE. The inputs DL, MODEL, CONDL, DR, -* MODER and CONDR also determine the grading as described -* below. -* -* Permute, if desired, the rows and/or columns as specified by -* PIVTNG and IPIVOT. -* -* Set random entries to zero, if desired, to get a random sparse -* matrix as specified by SPARSE. -* -* Make A a band matrix, if desired, by zeroing out the matrix -* outside a band of lower bandwidth KL and upper bandwidth KU. -* -* Scale A, if desired, to have maximum entry ANORM. -* -* Pack the matrix if desired. Options specified by PACK are: -* no packing -* zero out upper half (if symmetric or Hermitian) -* zero out lower half (if symmetric or Hermitian) -* store the upper half columnwise (if symmetric or Hermitian -* or square upper triangular) -* store the lower half columnwise (if symmetric or Hermitian -* or square lower triangular) -* same as upper half rowwise if symmetric -* same as conjugate upper half rowwise if Hermitian -* store the lower triangle in banded format -* (if symmetric or Hermitian) -* store the upper triangle in banded format -* (if symmetric or Hermitian) -* store the entire matrix in banded format -* -* Note: If two calls to ZLATMR differ only in the PACK parameter, -* they will generate mathematically equivalent matrices. -* -* If two calls to ZLATMR both have full bandwidth (KL = M-1 -* and KU = N-1), and differ only in the PIVTNG and PACK -* parameters, then the matrices generated will differ only -* in the order of the rows and/or columns, and otherwise -* contain the same data. This consistency cannot be and -* is not maintained with less than full bandwidth. -* -* Arguments -* ========= -* -* M (input) INTEGER -* Number of rows of A. Not modified. -* -* N (input) INTEGER -* Number of columns of A. Not modified. -* -* DIST (input) CHARACTER*1 -* On entry, DIST specifies the type of distribution to be used -* to generate a random matrix . -* 'U' => real and imaginary parts are independent -* UNIFORM( 0, 1 ) ( 'U' for uniform ) -* 'S' => real and imaginary parts are independent -* UNIFORM( -1, 1 ) ( 'S' for symmetric ) -* 'N' => real and imaginary parts are independent -* NORMAL( 0, 1 ) ( 'N' for normal ) -* 'D' => uniform on interior of unit disk ( 'D' for disk ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension (4) -* On entry ISEED specifies the seed of the random number -* generator. They should lie between 0 and 4095 inclusive, -* and ISEED(4) should be odd. The random number generator -* uses a linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to ZLATMR -* to continue the same random number sequence. -* Changed on exit. -* -* SYM (input) CHARACTER*1 -* If SYM='S', generated matrix is symmetric. -* If SYM='H', generated matrix is Hermitian. -* If SYM='N', generated matrix is nonsymmetric. -* Not modified. -* -* D (input/output) COMPLEX*16 array, dimension (min(M,N)) -* On entry this array specifies the diagonal entries -* of the diagonal of A. D may either be specified -* on entry, or set according to MODE and COND as described -* below. If the matrix is Hermitian, the real part of D -* will be taken. May be changed on exit if MODE is nonzero. -* -* MODE (input) INTEGER -* On entry describes how D is to be used: -* MODE = 0 means use D as input -* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND -* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* Not modified. -* -* COND (input) DOUBLE PRECISION -* On entry, used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* DMAX (input) COMPLEX*16 -* If MODE neither -6, 0 nor 6, the diagonal is scaled by -* DMAX / max(abs(D(i))), so that maximum absolute entry -* of diagonal is abs(DMAX). If DMAX is complex (or zero), -* diagonal will be scaled by a complex number (or zero). -* -* RSIGN (input) CHARACTER*1 -* If MODE neither -6, 0 nor 6, specifies sign of diagonal -* as follows: -* 'T' => diagonal entries are multiplied by a random complex -* number uniformly distributed with absolute value 1 -* 'F' => diagonal unchanged -* Not modified. -* -* GRADE (input) CHARACTER*1 -* Specifies grading of matrix as follows: -* 'N' => no grading -* 'L' => matrix premultiplied by diag( DL ) -* (only if matrix nonsymmetric) -* 'R' => matrix postmultiplied by diag( DR ) -* (only if matrix nonsymmetric) -* 'B' => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DR ) -* (only if matrix nonsymmetric) -* 'H' => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( CONJG(DL) ) -* (only if matrix Hermitian or nonsymmetric) -* 'S' => matrix premultiplied by diag( DL ) and -* postmultiplied by diag( DL ) -* (only if matrix symmetric or nonsymmetric) -* 'E' => matrix premultiplied by diag( DL ) and -* postmultiplied by inv( diag( DL ) ) -* ( 'S' for similarity ) -* (only if matrix nonsymmetric) -* Note: if GRADE='S', then M must equal N. -* Not modified. -* -* DL (input/output) COMPLEX*16 array, dimension (M) -* If MODEL=0, then on entry this array specifies the diagonal -* entries of a diagonal matrix used as described under GRADE -* above. If MODEL is not zero, then DL will be set according -* to MODEL and CONDL, analogous to the way D is set according -* to MODE and COND (except there is no DMAX parameter for DL). -* If GRADE='E', then DL cannot have zero entries. -* Not referenced if GRADE = 'N' or 'R'. Changed on exit. -* -* MODEL (input) INTEGER -* This specifies how the diagonal array DL is to be computed, -* just as MODE specifies how D is to be computed. -* Not modified. -* -* CONDL (input) DOUBLE PRECISION -* When MODEL is not zero, this specifies the condition number -* of the computed DL. Not modified. -* -* DR (input/output) COMPLEX*16 array, dimension (N) -* If MODER=0, then on entry this array specifies the diagonal -* entries of a diagonal matrix used as described under GRADE -* above. If MODER is not zero, then DR will be set according -* to MODER and CONDR, analogous to the way D is set according -* to MODE and COND (except there is no DMAX parameter for DR). -* Not referenced if GRADE = 'N', 'L', 'H' or 'S'. -* Changed on exit. -* -* MODER (input) INTEGER -* This specifies how the diagonal array DR is to be computed, -* just as MODE specifies how D is to be computed. -* Not modified. -* -* CONDR (input) DOUBLE PRECISION -* When MODER is not zero, this specifies the condition number -* of the computed DR. Not modified. -* -* PIVTNG (input) CHARACTER*1 -* On entry specifies pivoting permutations as follows: -* 'N' or ' ' => none. -* 'L' => left or row pivoting (matrix must be nonsymmetric). -* 'R' => right or column pivoting (matrix must be -* nonsymmetric). -* 'B' or 'F' => both or full pivoting, i.e., on both sides. -* In this case, M must equal N -* -* If two calls to ZLATMR both have full bandwidth (KL = M-1 -* and KU = N-1), and differ only in the PIVTNG and PACK -* parameters, then the matrices generated will differ only -* in the order of the rows and/or columns, and otherwise -* contain the same data. This consistency cannot be -* maintained with less than full bandwidth. -* -* IPIVOT (input) INTEGER array, dimension (N or M) -* This array specifies the permutation used. After the -* basic matrix is generated, the rows, columns, or both -* are permuted. If, say, row pivoting is selected, ZLATMR -* starts with the *last* row and interchanges the M-th and -* IPIVOT(M)-th rows, then moves to the next-to-last row, -* interchanging the (M-1)-th and the IPIVOT(M-1)-th rows, -* and so on. In terms of "2-cycles", the permutation is -* (1 IPIVOT(1)) (2 IPIVOT(2)) ... (M IPIVOT(M)) -* where the rightmost cycle is applied first. This is the -* *inverse* of the effect of pivoting in LINPACK. The idea -* is that factoring (with pivoting) an identity matrix -* which has been inverse-pivoted in this way should -* result in a pivot vector identical to IPIVOT. -* Not referenced if PIVTNG = 'N'. Not modified. -* -* SPARSE (input) DOUBLE PRECISION -* On entry specifies the sparsity of the matrix if a sparse -* matrix is to be generated. SPARSE should lie between -* 0 and 1. To generate a sparse matrix, for each matrix entry -* a uniform ( 0, 1 ) random number x is generated and -* compared to SPARSE; if x is larger the matrix entry -* is unchanged and if x is smaller the entry is set -* to zero. Thus on the average a fraction SPARSE of the -* entries will be set to zero. -* Not modified. -* -* KL (input) INTEGER -* On entry specifies the lower bandwidth of the matrix. For -* example, KL=0 implies upper triangular, KL=1 implies upper -* Hessenberg, and KL at least M-1 implies the matrix is not -* banded. Must equal KU if matrix is symmetric or Hermitian. -* Not modified. -* -* KU (input) INTEGER -* On entry specifies the upper bandwidth of the matrix. For -* example, KU=0 implies lower triangular, KU=1 implies lower -* Hessenberg, and KU at least N-1 implies the matrix is not -* banded. Must equal KL if matrix is symmetric or Hermitian. -* Not modified. -* -* ANORM (input) DOUBLE PRECISION -* On entry specifies maximum entry of output matrix -* (output matrix will by multiplied by a constant so that -* its largest absolute entry equal ANORM) -* if ANORM is nonnegative. If ANORM is negative no scaling -* is done. Not modified. -* -* PACK (input) CHARACTER*1 -* On entry specifies packing of matrix as follows: -* 'N' => no packing -* 'U' => zero out all subdiagonal entries -* (if symmetric or Hermitian) -* 'L' => zero out all superdiagonal entries -* (if symmetric or Hermitian) -* 'C' => store the upper triangle columnwise -* (only if matrix symmetric or Hermitian or -* square upper triangular) -* 'R' => store the lower triangle columnwise -* (only if matrix symmetric or Hermitian or -* square lower triangular) -* (same as upper half rowwise if symmetric) -* (same as conjugate upper half rowwise if Hermitian) -* 'B' => store the lower triangle in band storage scheme -* (only if matrix symmetric or Hermitian) -* 'Q' => store the upper triangle in band storage scheme -* (only if matrix symmetric or Hermitian) -* 'Z' => store the entire matrix in band storage scheme -* (pivoting can be provided for by using this -* option to store A in the trailing rows of -* the allocated storage) -* -* Using these options, the various LAPACK packed and banded -* storage schemes can be obtained: -* GB - use 'Z' -* PB, HB or TB - use 'B' or 'Q' -* PP, HP or TP - use 'C' or 'R' -* -* If two calls to ZLATMR differ only in the PACK parameter, -* they will generate mathematically equivalent matrices. -* Not modified. -* -* A (input/output) COMPLEX*16 array, dimension (LDA,N) -* On exit A is the desired test matrix. Only those -* entries of A which are significant on output -* will be referenced (even if A is in packed or band -* storage format). The 'unoccupied corners' of A in -* band format will be zeroed out. -* -* LDA (input) INTEGER -* on entry LDA specifies the first dimension of A as -* declared in the calling program. -* If PACK='N', 'U' or 'L', LDA must be at least max ( 1, M ). -* If PACK='C' or 'R', LDA must be at least 1. -* If PACK='B', or 'Q', LDA must be MIN ( KU+1, N ) -* If PACK='Z', LDA must be at least KUU+KLL+1, where -* KUU = MIN ( KU, N-1 ) and KLL = MIN ( KL, N-1 ) -* Not modified. -* -* IWORK (workspace) INTEGER array, dimension (N or M) -* Workspace. Not referenced if PIVTNG = 'N'. Changed on exit. -* -* INFO (output) INTEGER -* Error parameter on exit: -* 0 => normal return -* -1 => M negative or unequal to N and SYM='S' or 'H' -* -2 => N negative -* -3 => DIST illegal string -* -5 => SYM illegal string -* -7 => MODE not in range -6 to 6 -* -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 -* -10 => MODE neither -6, 0 nor 6 and RSIGN illegal string -* -11 => GRADE illegal string, or GRADE='E' and -* M not equal to N, or GRADE='L', 'R', 'B', 'S' or 'E' -* and SYM = 'H', or GRADE='L', 'R', 'B', 'H' or 'E' -* and SYM = 'S' -* -12 => GRADE = 'E' and DL contains zero -* -13 => MODEL not in range -6 to 6 and GRADE= 'L', 'B', 'H', -* 'S' or 'E' -* -14 => CONDL less than 1.0, GRADE='L', 'B', 'H', 'S' or 'E', -* and MODEL neither -6, 0 nor 6 -* -16 => MODER not in range -6 to 6 and GRADE= 'R' or 'B' -* -17 => CONDR less than 1.0, GRADE='R' or 'B', and -* MODER neither -6, 0 nor 6 -* -18 => PIVTNG illegal string, or PIVTNG='B' or 'F' and -* M not equal to N, or PIVTNG='L' or 'R' and SYM='S' -* or 'H' -* -19 => IPIVOT contains out of range number and -* PIVTNG not equal to 'N' -* -20 => KL negative -* -21 => KU negative, or SYM='S' or 'H' and KU not equal to KL -* -22 => SPARSE not in range 0. to 1. -* -24 => PACK illegal string, or PACK='U', 'L', 'B' or 'Q' -* and SYM='N', or PACK='C' and SYM='N' and either KL -* not equal to 0 or N not equal to M, or PACK='R' and -* SYM='N', and either KU not equal to 0 or N not equal -* to M -* -26 => LDA too small -* 1 => Error return from ZLATM1 (computing D) -* 2 => Cannot scale diagonal to DMAX (max. entry is 0) -* 3 => Error return from ZLATM1 (computing DL) -* 4 => Error return from ZLATM1 (computing DR) -* 5 => ANORM is positive, but matrix constructed prior to -* attempting to scale it to have norm ANORM, is zero -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/zlatms.f b/TESTING/MATGEN/zlatms.f index 53e8a4c6..481d6719 100644 --- a/TESTING/MATGEN/zlatms.f +++ b/TESTING/MATGEN/zlatms.f @@ -1,9 +1,345 @@ +*> \brief \b ZLATMS +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, +* KL, KU, PACK, A, LDA, WORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER DIST, PACK, SYM +* INTEGER INFO, KL, KU, LDA, M, MODE, N +* DOUBLE PRECISION COND, DMAX +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* DOUBLE PRECISION D( * ) +* COMPLEX*16 A( LDA, * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> ZLATMS generates random matrices with specified singular values +*> (or hermitian with specified eigenvalues) +*> for testing LAPACK programs. +*> +*> ZLATMS operates by applying the following sequence of +*> operations: +*> +*> Set the diagonal to D, where D may be input or +*> computed according to MODE, COND, DMAX, and SYM +*> as described below. +*> +*> Generate a matrix with the appropriate band structure, by one +*> of two methods: +*> +*> Method A: +*> Generate a dense M x N matrix by multiplying D on the left +*> and the right by random unitary matrices, then: +*> +*> Reduce the bandwidth according to KL and KU, using +*> Householder transformations. +*> +*> Method B: +*> Convert the bandwidth-0 (i.e., diagonal) matrix to a +*> bandwidth-1 matrix using Givens rotations, "chasing" +*> out-of-band elements back, much as in QR; then convert +*> the bandwidth-1 to a bandwidth-2 matrix, etc. Note +*> that for reasonably small bandwidths (relative to M and +*> N) this requires less storage, as a dense matrix is not +*> generated. Also, for hermitian or symmetric matrices, +*> only one triangle is generated. +*> +*> Method A is chosen if the bandwidth is a large fraction of the +*> order of the matrix, and LDA is at least M (so a dense +*> matrix can be stored.) Method B is chosen if the bandwidth +*> is small (< 1/2 N for hermitian or symmetric, < .3 N+M for +*> non-symmetric), or LDA is less than M and not less than the +*> bandwidth. +*> +*> Pack the matrix if desired. Options specified by PACK are: +*> no packing +*> zero out upper half (if hermitian) +*> zero out lower half (if hermitian) +*> store the upper half columnwise (if hermitian or upper +*> triangular) +*> store the lower half columnwise (if hermitian or lower +*> triangular) +*> store the lower triangle in banded format (if hermitian or +*> lower triangular) +*> store the upper triangle in banded format (if hermitian or +*> upper triangular) +*> store the entire matrix in banded format +*> If Method B is chosen, and band format is specified, then the +*> matrix will be generated in the band format, so no repacking +*> will be necessary. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of A. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of A. N must equal M if the matrix +*> is symmetric or hermitian (i.e., if SYM is not 'N') +*> Not modified. +*> \endverbatim +*> +*> \param[in] DIST +*> \verbatim +*> DIST is CHARACTER*1 +*> On entry, DIST specifies the type of distribution to be used +*> to generate the random eigen-/singular values. +*> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) +*> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) +*> 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. They should lie between 0 and 4095 inclusive, +*> and ISEED(4) should be odd. The random number generator +*> uses a linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to ZLATMS +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] SYM +*> \verbatim +*> SYM is CHARACTER*1 +*> If SYM='H', the generated matrix is hermitian, with +*> eigenvalues specified by D, COND, MODE, and DMAX; they +*> may be positive, negative, or zero. +*> If SYM='P', the generated matrix is hermitian, with +*> eigenvalues (= singular values) specified by D, COND, +*> MODE, and DMAX; they will not be negative. +*> If SYM='N', the generated matrix is nonsymmetric, with +*> singular values specified by D, COND, MODE, and DMAX; +*> they will not be negative. +*> If SYM='S', the generated matrix is (complex) symmetric, +*> with singular values specified by D, COND, MODE, and +*> DMAX; they will not be negative. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension ( MIN( M, N ) ) +*> This array is used to specify the singular values or +*> eigenvalues of A (see SYM, above.) If MODE=0, then D is +*> assumed to contain the singular/eigenvalues, otherwise +*> they will be computed according to MODE, COND, and DMAX, +*> and placed in D. +*> Modified if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry this describes how the singular/eigenvalues are to +*> be specified: +*> MODE = 0 means use D as input +*> MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND +*> MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> If SYM='H', and MODE is neither 0, 6, nor -6, then +*> the elements of D will also be multiplied by a random +*> sign (i.e., +1 or -1.) +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is DOUBLE PRECISION +*> On entry, this is used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] DMAX +*> \verbatim +*> DMAX is DOUBLE PRECISION +*> If MODE is neither -6, 0 nor 6, the contents of D, as +*> computed according to MODE and COND, will be scaled by +*> DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or +*> singular value (which is to say the norm) will be abs(DMAX). +*> Note that DMAX need not be positive: if DMAX is negative +*> (or zero), D will be scaled by a negative number (or zero). +*> Not modified. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> This specifies the lower bandwidth of the matrix. For +*> example, KL=0 implies upper triangular, KL=1 implies upper +*> Hessenberg, and KL being at least M-1 means that the matrix +*> has full lower bandwidth. KL must equal KU if the matrix +*> is symmetric or hermitian. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> This specifies the upper bandwidth of the matrix. For +*> example, KU=0 implies lower triangular, KU=1 implies lower +*> Hessenberg, and KU being at least N-1 means that the matrix +*> has full upper bandwidth. KL must equal KU if the matrix +*> is symmetric or hermitian. +*> Not modified. +*> \endverbatim +*> +*> \param[in] PACK +*> \verbatim +*> PACK is CHARACTER*1 +*> This specifies packing of matrix as follows: +*> 'N' => no packing +*> 'U' => zero out all subdiagonal entries (if symmetric +*> or hermitian) +*> 'L' => zero out all superdiagonal entries (if symmetric +*> or hermitian) +*> 'C' => store the upper triangle columnwise (only if the +*> matrix is symmetric, hermitian, or upper triangular) +*> 'R' => store the lower triangle columnwise (only if the +*> matrix is symmetric, hermitian, or lower triangular) +*> 'B' => store the lower triangle in band storage scheme +*> (only if the matrix is symmetric, hermitian, or +*> lower triangular) +*> 'Q' => store the upper triangle in band storage scheme +*> (only if the matrix is symmetric, hermitian, or +*> upper triangular) +*> 'Z' => store the entire matrix in band storage scheme +*> (pivoting can be provided for by using this +*> option to store A in the trailing rows of +*> the allocated storage) +*> \endverbatim +*> \verbatim +*> Using these options, the various LAPACK packed and banded +*> storage schemes can be obtained: +*> GB - use 'Z' +*> PB, SB, HB, or TB - use 'B' or 'Q' +*> PP, SP, HB, or TP - use 'C' or 'R' +*> \endverbatim +*> \verbatim +*> If two calls to ZLATMS differ only in the PACK parameter, +*> they will generate mathematically equivalent matrices. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension ( LDA, N ) +*> On exit A is the desired test matrix. A is first generated +*> in full (unpacked) form, and then packed, if so specified +*> by PACK. Thus, the first M elements of the first N +*> columns will always be modified. If PACK specifies a +*> packed or banded storage scheme, all LDA elements of the +*> first N columns will be modified; the elements of the +*> array which do not correspond to elements of the generated +*> matrix are set to zero. +*> Modified. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> LDA specifies the first dimension of A as declared in the +*> calling program. If PACK='N', 'U', 'L', 'C', or 'R', then +*> LDA must be at least M. If PACK='B' or 'Q', then LDA must +*> be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). +*> If PACK='Z', LDA must be large enough to hold the packed +*> array: MIN( KU, N-1) + MIN( KL, M-1) + 1. +*> Not modified. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension ( 3*MAX( N, M ) ) +*> Workspace. +*> Modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error code. On exit, INFO will be set to one of the +*> following values: +*> 0 => normal return +*> -1 => M negative or unequal to N and SYM='S', 'H', or 'P' +*> -2 => N negative +*> -3 => DIST illegal string +*> -5 => SYM illegal string +*> -7 => MODE not in range -6 to 6 +*> -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 +*> -10 => KL negative +*> -11 => KU negative, or SYM is not 'N' and KU is not equal to +*> KL +*> -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; +*> or PACK='C' or 'Q' and SYM='N' and KL is not zero; +*> or PACK='R' or 'B' and SYM='N' and KU is not zero; +*> or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not +*> N. +*> -14 => LDA is less than M, or PACK='Z' and LDA is less than +*> MIN(KU,N-1) + MIN(KL,M-1) + 1. +*> 1 => Error return from DLATM1 +*> 2 => Cannot scale to DMAX (max. sing. value is 0) +*> 3 => Error return from ZLAGGE, CLAGHE or CLAGSY +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_matgen +* +* ===================================================================== SUBROUTINE ZLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, $ KL, KU, PACK, A, LDA, WORK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* June 2010 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER DIST, PACK, SYM @@ -16,248 +352,6 @@ COMPLEX*16 A( LDA, * ), WORK( * ) * .. * -* Purpose -* ======= -* -* ZLATMS generates random matrices with specified singular values -* (or hermitian with specified eigenvalues) -* for testing LAPACK programs. -* -* ZLATMS operates by applying the following sequence of -* operations: -* -* Set the diagonal to D, where D may be input or -* computed according to MODE, COND, DMAX, and SYM -* as described below. -* -* Generate a matrix with the appropriate band structure, by one -* of two methods: -* -* Method A: -* Generate a dense M x N matrix by multiplying D on the left -* and the right by random unitary matrices, then: -* -* Reduce the bandwidth according to KL and KU, using -* Householder transformations. -* -* Method B: -* Convert the bandwidth-0 (i.e., diagonal) matrix to a -* bandwidth-1 matrix using Givens rotations, "chasing" -* out-of-band elements back, much as in QR; then convert -* the bandwidth-1 to a bandwidth-2 matrix, etc. Note -* that for reasonably small bandwidths (relative to M and -* N) this requires less storage, as a dense matrix is not -* generated. Also, for hermitian or symmetric matrices, -* only one triangle is generated. -* -* Method A is chosen if the bandwidth is a large fraction of the -* order of the matrix, and LDA is at least M (so a dense -* matrix can be stored.) Method B is chosen if the bandwidth -* is small (< 1/2 N for hermitian or symmetric, < .3 N+M for -* non-symmetric), or LDA is less than M and not less than the -* bandwidth. -* -* Pack the matrix if desired. Options specified by PACK are: -* no packing -* zero out upper half (if hermitian) -* zero out lower half (if hermitian) -* store the upper half columnwise (if hermitian or upper -* triangular) -* store the lower half columnwise (if hermitian or lower -* triangular) -* store the lower triangle in banded format (if hermitian or -* lower triangular) -* store the upper triangle in banded format (if hermitian or -* upper triangular) -* store the entire matrix in banded format -* If Method B is chosen, and band format is specified, then the -* matrix will be generated in the band format, so no repacking -* will be necessary. -* -* Arguments -* ========= -* -* M (input) INTEGER -* The number of rows of A. Not modified. -* -* N (input) INTEGER -* The number of columns of A. N must equal M if the matrix -* is symmetric or hermitian (i.e., if SYM is not 'N') -* Not modified. -* -* DIST (input) CHARACTER*1 -* On entry, DIST specifies the type of distribution to be used -* to generate the random eigen-/singular values. -* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) -* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) -* 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. They should lie between 0 and 4095 inclusive, -* and ISEED(4) should be odd. The random number generator -* uses a linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to ZLATMS -* to continue the same random number sequence. -* Changed on exit. -* -* SYM (input) CHARACTER*1 -* If SYM='H', the generated matrix is hermitian, with -* eigenvalues specified by D, COND, MODE, and DMAX; they -* may be positive, negative, or zero. -* If SYM='P', the generated matrix is hermitian, with -* eigenvalues (= singular values) specified by D, COND, -* MODE, and DMAX; they will not be negative. -* If SYM='N', the generated matrix is nonsymmetric, with -* singular values specified by D, COND, MODE, and DMAX; -* they will not be negative. -* If SYM='S', the generated matrix is (complex) symmetric, -* with singular values specified by D, COND, MODE, and -* DMAX; they will not be negative. -* Not modified. -* -* D (input/output) DOUBLE PRECISION array, dimension ( MIN( M, N ) ) -* This array is used to specify the singular values or -* eigenvalues of A (see SYM, above.) If MODE=0, then D is -* assumed to contain the singular/eigenvalues, otherwise -* they will be computed according to MODE, COND, and DMAX, -* and placed in D. -* Modified if MODE is nonzero. -* -* MODE (input) INTEGER -* On entry this describes how the singular/eigenvalues are to -* be specified: -* MODE = 0 means use D as input -* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND -* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* If SYM='H', and MODE is neither 0, 6, nor -6, then -* the elements of D will also be multiplied by a random -* sign (i.e., +1 or -1.) -* Not modified. -* -* COND (input) DOUBLE PRECISION -* On entry, this is used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* DMAX (input) DOUBLE PRECISION -* If MODE is neither -6, 0 nor 6, the contents of D, as -* computed according to MODE and COND, will be scaled by -* DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or -* singular value (which is to say the norm) will be abs(DMAX). -* Note that DMAX need not be positive: if DMAX is negative -* (or zero), D will be scaled by a negative number (or zero). -* Not modified. -* -* KL (input) INTEGER -* This specifies the lower bandwidth of the matrix. For -* example, KL=0 implies upper triangular, KL=1 implies upper -* Hessenberg, and KL being at least M-1 means that the matrix -* has full lower bandwidth. KL must equal KU if the matrix -* is symmetric or hermitian. -* Not modified. -* -* KU (input) INTEGER -* This specifies the upper bandwidth of the matrix. For -* example, KU=0 implies lower triangular, KU=1 implies lower -* Hessenberg, and KU being at least N-1 means that the matrix -* has full upper bandwidth. KL must equal KU if the matrix -* is symmetric or hermitian. -* Not modified. -* -* PACK (input) CHARACTER*1 -* This specifies packing of matrix as follows: -* 'N' => no packing -* 'U' => zero out all subdiagonal entries (if symmetric -* or hermitian) -* 'L' => zero out all superdiagonal entries (if symmetric -* or hermitian) -* 'C' => store the upper triangle columnwise (only if the -* matrix is symmetric, hermitian, or upper triangular) -* 'R' => store the lower triangle columnwise (only if the -* matrix is symmetric, hermitian, or lower triangular) -* 'B' => store the lower triangle in band storage scheme -* (only if the matrix is symmetric, hermitian, or -* lower triangular) -* 'Q' => store the upper triangle in band storage scheme -* (only if the matrix is symmetric, hermitian, or -* upper triangular) -* 'Z' => store the entire matrix in band storage scheme -* (pivoting can be provided for by using this -* option to store A in the trailing rows of -* the allocated storage) -* -* Using these options, the various LAPACK packed and banded -* storage schemes can be obtained: -* GB - use 'Z' -* PB, SB, HB, or TB - use 'B' or 'Q' -* PP, SP, HB, or TP - use 'C' or 'R' -* -* If two calls to ZLATMS differ only in the PACK parameter, -* they will generate mathematically equivalent matrices. -* Not modified. -* -* A (input/output) COMPLEX*16 array, dimension ( LDA, N ) -* On exit A is the desired test matrix. A is first generated -* in full (unpacked) form, and then packed, if so specified -* by PACK. Thus, the first M elements of the first N -* columns will always be modified. If PACK specifies a -* packed or banded storage scheme, all LDA elements of the -* first N columns will be modified; the elements of the -* array which do not correspond to elements of the generated -* matrix are set to zero. -* Modified. -* -* LDA (input) INTEGER -* LDA specifies the first dimension of A as declared in the -* calling program. If PACK='N', 'U', 'L', 'C', or 'R', then -* LDA must be at least M. If PACK='B' or 'Q', then LDA must -* be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). -* If PACK='Z', LDA must be large enough to hold the packed -* array: MIN( KU, N-1) + MIN( KL, M-1) + 1. -* Not modified. -* -* WORK (workspace) COMPLEX*16 array, dimension ( 3*MAX( N, M ) ) -* Workspace. -* Modified. -* -* INFO (output) INTEGER -* Error code. On exit, INFO will be set to one of the -* following values: -* 0 => normal return -* -1 => M negative or unequal to N and SYM='S', 'H', or 'P' -* -2 => N negative -* -3 => DIST illegal string -* -5 => SYM illegal string -* -7 => MODE not in range -6 to 6 -* -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 -* -10 => KL negative -* -11 => KU negative, or SYM is not 'N' and KU is not equal to -* KL -* -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; -* or PACK='C' or 'Q' and SYM='N' and KL is not zero; -* or PACK='R' or 'B' and SYM='N' and KU is not zero; -* or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not -* N. -* -14 => LDA is less than M, or PACK='Z' and LDA is less than -* MIN(KU,N-1) + MIN(KL,M-1) + 1. -* 1 => Error return from DLATM1 -* 2 => Cannot scale to DMAX (max. sing. value is 0) -* 3 => Error return from ZLAGGE, CLAGHE or CLAGSY -* * ===================================================================== * * .. Parameters .. diff --git a/TESTING/MATGEN/zlatmt.f b/TESTING/MATGEN/zlatmt.f index b5840306..0e2c319a 100644 --- a/TESTING/MATGEN/zlatmt.f +++ b/TESTING/MATGEN/zlatmt.f @@ -1,9 +1,353 @@ +*> \brief \b ZLATMT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZLATMT( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, +* RANK, KL, KU, PACK, A, LDA, WORK, INFO ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION COND, DMAX +* INTEGER INFO, KL, KU, LDA, M, MODE, N, RANK +* CHARACTER DIST, PACK, SYM +* .. +* .. Array Arguments .. +* COMPLEX*16 A( LDA, * ), WORK( * ) +* DOUBLE PRECISION D( * ) +* INTEGER ISEED( 4 ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> ZLATMT generates random matrices with specified singular values +*> (or hermitian with specified eigenvalues) +*> for testing LAPACK programs. +*> +*> ZLATMT operates by applying the following sequence of +*> operations: +*> +*> Set the diagonal to D, where D may be input or +*> computed according to MODE, COND, DMAX, and SYM +*> as described below. +*> +*> Generate a matrix with the appropriate band structure, by one +*> of two methods: +*> +*> Method A: +*> Generate a dense M x N matrix by multiplying D on the left +*> and the right by random unitary matrices, then: +*> +*> Reduce the bandwidth according to KL and KU, using +*> Householder transformations. +*> +*> Method B: +*> Convert the bandwidth-0 (i.e., diagonal) matrix to a +*> bandwidth-1 matrix using Givens rotations, "chasing" +*> out-of-band elements back, much as in QR; then convert +*> the bandwidth-1 to a bandwidth-2 matrix, etc. Note +*> that for reasonably small bandwidths (relative to M and +*> N) this requires less storage, as a dense matrix is not +*> generated. Also, for hermitian or symmetric matrices, +*> only one triangle is generated. +*> +*> Method A is chosen if the bandwidth is a large fraction of the +*> order of the matrix, and LDA is at least M (so a dense +*> matrix can be stored.) Method B is chosen if the bandwidth +*> is small (< 1/2 N for hermitian or symmetric, < .3 N+M for +*> non-symmetric), or LDA is less than M and not less than the +*> bandwidth. +*> +*> Pack the matrix if desired. Options specified by PACK are: +*> no packing +*> zero out upper half (if hermitian) +*> zero out lower half (if hermitian) +*> store the upper half columnwise (if hermitian or upper +*> triangular) +*> store the lower half columnwise (if hermitian or lower +*> triangular) +*> store the lower triangle in banded format (if hermitian or +*> lower triangular) +*> store the upper triangle in banded format (if hermitian or +*> upper triangular) +*> store the entire matrix in banded format +*> If Method B is chosen, and band format is specified, then the +*> matrix will be generated in the band format, so no repacking +*> will be necessary. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of A. Not modified. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of A. N must equal M if the matrix +*> is symmetric or hermitian (i.e., if SYM is not 'N') +*> Not modified. +*> \endverbatim +*> +*> \param[in] DIST +*> \verbatim +*> DIST is CHARACTER*1 +*> On entry, DIST specifies the type of distribution to be used +*> to generate the random eigen-/singular values. +*> 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) +*> 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) +*> 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension ( 4 ) +*> On entry ISEED specifies the seed of the random number +*> generator. They should lie between 0 and 4095 inclusive, +*> and ISEED(4) should be odd. The random number generator +*> uses a linear congruential sequence limited to small +*> integers, and so should produce machine independent +*> random numbers. The values of ISEED are changed on +*> exit, and can be used in the next call to ZLATMT +*> to continue the same random number sequence. +*> Changed on exit. +*> \endverbatim +*> +*> \param[in] SYM +*> \verbatim +*> SYM is CHARACTER*1 +*> If SYM='H', the generated matrix is hermitian, with +*> eigenvalues specified by D, COND, MODE, and DMAX; they +*> may be positive, negative, or zero. +*> If SYM='P', the generated matrix is hermitian, with +*> eigenvalues (= singular values) specified by D, COND, +*> MODE, and DMAX; they will not be negative. +*> If SYM='N', the generated matrix is nonsymmetric, with +*> singular values specified by D, COND, MODE, and DMAX; +*> they will not be negative. +*> If SYM='S', the generated matrix is (complex) symmetric, +*> with singular values specified by D, COND, MODE, and +*> DMAX; they will not be negative. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension ( MIN( M, N ) ) +*> This array is used to specify the singular values or +*> eigenvalues of A (see SYM, above.) If MODE=0, then D is +*> assumed to contain the singular/eigenvalues, otherwise +*> they will be computed according to MODE, COND, and DMAX, +*> and placed in D. +*> Modified if MODE is nonzero. +*> \endverbatim +*> +*> \param[in] MODE +*> \verbatim +*> MODE is INTEGER +*> On entry this describes how the singular/eigenvalues are to +*> be specified: +*> MODE = 0 means use D as input +*> MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND +*> MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND +*> MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) +*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) +*> MODE = 5 sets D to random numbers in the range +*> ( 1/COND , 1 ) such that their logarithms +*> are uniformly distributed. +*> MODE = 6 set D to random numbers from same distribution +*> as the rest of the matrix. +*> MODE < 0 has the same meaning as ABS(MODE), except that +*> the order of the elements of D is reversed. +*> Thus if MODE is positive, D has entries ranging from +*> 1 to 1/COND, if negative, from 1/COND to 1, +*> If SYM='H', and MODE is neither 0, 6, nor -6, then +*> the elements of D will also be multiplied by a random +*> sign (i.e., +1 or -1.) +*> Not modified. +*> \endverbatim +*> +*> \param[in] COND +*> \verbatim +*> COND is DOUBLE PRECISION +*> On entry, this is used as described under MODE above. +*> If used, it must be >= 1. Not modified. +*> \endverbatim +*> +*> \param[in] DMAX +*> \verbatim +*> DMAX is DOUBLE PRECISION +*> If MODE is neither -6, 0 nor 6, the contents of D, as +*> computed according to MODE and COND, will be scaled by +*> DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or +*> singular value (which is to say the norm) will be abs(DMAX). +*> Note that DMAX need not be positive: if DMAX is negative +*> (or zero), D will be scaled by a negative number (or zero). +*> Not modified. +*> \endverbatim +*> +*> \param[in] RANK +*> \verbatim +*> RANK is INTEGER +*> The rank of matrix to be generated for modes 1,2,3 only. +*> D( RANK+1:N ) = 0. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> This specifies the lower bandwidth of the matrix. For +*> example, KL=0 implies upper triangular, KL=1 implies upper +*> Hessenberg, and KL being at least M-1 means that the matrix +*> has full lower bandwidth. KL must equal KU if the matrix +*> is symmetric or hermitian. +*> Not modified. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> This specifies the upper bandwidth of the matrix. For +*> example, KU=0 implies lower triangular, KU=1 implies lower +*> Hessenberg, and KU being at least N-1 means that the matrix +*> has full upper bandwidth. KL must equal KU if the matrix +*> is symmetric or hermitian. +*> Not modified. +*> \endverbatim +*> +*> \param[in] PACK +*> \verbatim +*> PACK is CHARACTER*1 +*> This specifies packing of matrix as follows: +*> 'N' => no packing +*> 'U' => zero out all subdiagonal entries (if symmetric +*> or hermitian) +*> 'L' => zero out all superdiagonal entries (if symmetric +*> or hermitian) +*> 'C' => store the upper triangle columnwise (only if the +*> matrix is symmetric, hermitian, or upper triangular) +*> 'R' => store the lower triangle columnwise (only if the +*> matrix is symmetric, hermitian, or lower triangular) +*> 'B' => store the lower triangle in band storage scheme +*> (only if the matrix is symmetric, hermitian, or +*> lower triangular) +*> 'Q' => store the upper triangle in band storage scheme +*> (only if the matrix is symmetric, hermitian, or +*> upper triangular) +*> 'Z' => store the entire matrix in band storage scheme +*> (pivoting can be provided for by using this +*> option to store A in the trailing rows of +*> the allocated storage) +*> \endverbatim +*> \verbatim +*> Using these options, the various LAPACK packed and banded +*> storage schemes can be obtained: +*> GB - use 'Z' +*> PB, SB, HB, or TB - use 'B' or 'Q' +*> PP, SP, HB, or TP - use 'C' or 'R' +*> \endverbatim +*> \verbatim +*> If two calls to ZLATMT differ only in the PACK parameter, +*> they will generate mathematically equivalent matrices. +*> Not modified. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension ( LDA, N ) +*> On exit A is the desired test matrix. A is first generated +*> in full (unpacked) form, and then packed, if so specified +*> by PACK. Thus, the first M elements of the first N +*> columns will always be modified. If PACK specifies a +*> packed or banded storage scheme, all LDA elements of the +*> first N columns will be modified; the elements of the +*> array which do not correspond to elements of the generated +*> matrix are set to zero. +*> Modified. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> LDA specifies the first dimension of A as declared in the +*> calling program. If PACK='N', 'U', 'L', 'C', or 'R', then +*> LDA must be at least M. If PACK='B' or 'Q', then LDA must +*> be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). +*> If PACK='Z', LDA must be large enough to hold the packed +*> array: MIN( KU, N-1) + MIN( KL, M-1) + 1. +*> Not modified. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension ( 3*MAX( N, M ) ) +*> Workspace. +*> Modified. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error code. On exit, INFO will be set to one of the +*> following values: +*> 0 => normal return +*> -1 => M negative or unequal to N and SYM='S', 'H', or 'P' +*> -2 => N negative +*> -3 => DIST illegal string +*> -5 => SYM illegal string +*> -7 => MODE not in range -6 to 6 +*> -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 +*> -10 => KL negative +*> -11 => KU negative, or SYM is not 'N' and KU is not equal to +*> KL +*> -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; +*> or PACK='C' or 'Q' and SYM='N' and KL is not zero; +*> or PACK='R' or 'B' and SYM='N' and KU is not zero; +*> or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not +*> N. +*> -14 => LDA is less than M, or PACK='Z' and LDA is less than +*> MIN(KU,N-1) + MIN(KL,M-1) + 1. +*> 1 => Error return from DLATM7 +*> 2 => Cannot scale to DMAX (max. sing. value is 0) +*> 3 => Error return from ZLAGGE, ZLAGHE or ZLAGSY +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_matgen +* +* ===================================================================== SUBROUTINE ZLATMT( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, $ RANK, KL, KU, PACK, A, LDA, WORK, INFO ) * -* -- LAPACK test routine (version 3.1) -- -* Craig Lucas, University of Manchester / NAG Ltd. -* October, 2008 +* -- LAPACK computational routine (version 3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. DOUBLE PRECISION COND, DMAX @@ -16,253 +360,6 @@ INTEGER ISEED( 4 ) * .. * -* Purpose -* ======= -* -* ZLATMT generates random matrices with specified singular values -* (or hermitian with specified eigenvalues) -* for testing LAPACK programs. -* -* ZLATMT operates by applying the following sequence of -* operations: -* -* Set the diagonal to D, where D may be input or -* computed according to MODE, COND, DMAX, and SYM -* as described below. -* -* Generate a matrix with the appropriate band structure, by one -* of two methods: -* -* Method A: -* Generate a dense M x N matrix by multiplying D on the left -* and the right by random unitary matrices, then: -* -* Reduce the bandwidth according to KL and KU, using -* Householder transformations. -* -* Method B: -* Convert the bandwidth-0 (i.e., diagonal) matrix to a -* bandwidth-1 matrix using Givens rotations, "chasing" -* out-of-band elements back, much as in QR; then convert -* the bandwidth-1 to a bandwidth-2 matrix, etc. Note -* that for reasonably small bandwidths (relative to M and -* N) this requires less storage, as a dense matrix is not -* generated. Also, for hermitian or symmetric matrices, -* only one triangle is generated. -* -* Method A is chosen if the bandwidth is a large fraction of the -* order of the matrix, and LDA is at least M (so a dense -* matrix can be stored.) Method B is chosen if the bandwidth -* is small (< 1/2 N for hermitian or symmetric, < .3 N+M for -* non-symmetric), or LDA is less than M and not less than the -* bandwidth. -* -* Pack the matrix if desired. Options specified by PACK are: -* no packing -* zero out upper half (if hermitian) -* zero out lower half (if hermitian) -* store the upper half columnwise (if hermitian or upper -* triangular) -* store the lower half columnwise (if hermitian or lower -* triangular) -* store the lower triangle in banded format (if hermitian or -* lower triangular) -* store the upper triangle in banded format (if hermitian or -* upper triangular) -* store the entire matrix in banded format -* If Method B is chosen, and band format is specified, then the -* matrix will be generated in the band format, so no repacking -* will be necessary. -* -* Arguments -* ========= -* -* M (input) INTEGER -* The number of rows of A. Not modified. -* -* N (input) INTEGER -* The number of columns of A. N must equal M if the matrix -* is symmetric or hermitian (i.e., if SYM is not 'N') -* Not modified. -* -* DIST (input) CHARACTER*1 -* On entry, DIST specifies the type of distribution to be used -* to generate the random eigen-/singular values. -* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) -* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) -* 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) -* Not modified. -* -* ISEED (input/output) INTEGER array, dimension ( 4 ) -* On entry ISEED specifies the seed of the random number -* generator. They should lie between 0 and 4095 inclusive, -* and ISEED(4) should be odd. The random number generator -* uses a linear congruential sequence limited to small -* integers, and so should produce machine independent -* random numbers. The values of ISEED are changed on -* exit, and can be used in the next call to ZLATMT -* to continue the same random number sequence. -* Changed on exit. -* -* SYM (input) CHARACTER*1 -* If SYM='H', the generated matrix is hermitian, with -* eigenvalues specified by D, COND, MODE, and DMAX; they -* may be positive, negative, or zero. -* If SYM='P', the generated matrix is hermitian, with -* eigenvalues (= singular values) specified by D, COND, -* MODE, and DMAX; they will not be negative. -* If SYM='N', the generated matrix is nonsymmetric, with -* singular values specified by D, COND, MODE, and DMAX; -* they will not be negative. -* If SYM='S', the generated matrix is (complex) symmetric, -* with singular values specified by D, COND, MODE, and -* DMAX; they will not be negative. -* Not modified. -* -* D (input/output) DOUBLE PRECISION array, dimension ( MIN( M, N ) ) -* This array is used to specify the singular values or -* eigenvalues of A (see SYM, above.) If MODE=0, then D is -* assumed to contain the singular/eigenvalues, otherwise -* they will be computed according to MODE, COND, and DMAX, -* and placed in D. -* Modified if MODE is nonzero. -* -* MODE (input) INTEGER -* On entry this describes how the singular/eigenvalues are to -* be specified: -* MODE = 0 means use D as input -* MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND -* MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND -* MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) -* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) -* MODE = 5 sets D to random numbers in the range -* ( 1/COND , 1 ) such that their logarithms -* are uniformly distributed. -* MODE = 6 set D to random numbers from same distribution -* as the rest of the matrix. -* MODE < 0 has the same meaning as ABS(MODE), except that -* the order of the elements of D is reversed. -* Thus if MODE is positive, D has entries ranging from -* 1 to 1/COND, if negative, from 1/COND to 1, -* If SYM='H', and MODE is neither 0, 6, nor -6, then -* the elements of D will also be multiplied by a random -* sign (i.e., +1 or -1.) -* Not modified. -* -* COND (input) DOUBLE PRECISION -* On entry, this is used as described under MODE above. -* If used, it must be >= 1. Not modified. -* -* DMAX (input) DOUBLE PRECISION -* If MODE is neither -6, 0 nor 6, the contents of D, as -* computed according to MODE and COND, will be scaled by -* DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or -* singular value (which is to say the norm) will be abs(DMAX). -* Note that DMAX need not be positive: if DMAX is negative -* (or zero), D will be scaled by a negative number (or zero). -* Not modified. -* -* RANK (input) INTEGER -* The rank of matrix to be generated for modes 1,2,3 only. -* D( RANK+1:N ) = 0. -* Not modified. -* -* KL (input) INTEGER -* This specifies the lower bandwidth of the matrix. For -* example, KL=0 implies upper triangular, KL=1 implies upper -* Hessenberg, and KL being at least M-1 means that the matrix -* has full lower bandwidth. KL must equal KU if the matrix -* is symmetric or hermitian. -* Not modified. -* -* KU (input) INTEGER -* This specifies the upper bandwidth of the matrix. For -* example, KU=0 implies lower triangular, KU=1 implies lower -* Hessenberg, and KU being at least N-1 means that the matrix -* has full upper bandwidth. KL must equal KU if the matrix -* is symmetric or hermitian. -* Not modified. -* -* PACK (input) CHARACTER*1 -* This specifies packing of matrix as follows: -* 'N' => no packing -* 'U' => zero out all subdiagonal entries (if symmetric -* or hermitian) -* 'L' => zero out all superdiagonal entries (if symmetric -* or hermitian) -* 'C' => store the upper triangle columnwise (only if the -* matrix is symmetric, hermitian, or upper triangular) -* 'R' => store the lower triangle columnwise (only if the -* matrix is symmetric, hermitian, or lower triangular) -* 'B' => store the lower triangle in band storage scheme -* (only if the matrix is symmetric, hermitian, or -* lower triangular) -* 'Q' => store the upper triangle in band storage scheme -* (only if the matrix is symmetric, hermitian, or -* upper triangular) -* 'Z' => store the entire matrix in band storage scheme -* (pivoting can be provided for by using this -* option to store A in the trailing rows of -* the allocated storage) -* -* Using these options, the various LAPACK packed and banded -* storage schemes can be obtained: -* GB - use 'Z' -* PB, SB, HB, or TB - use 'B' or 'Q' -* PP, SP, HB, or TP - use 'C' or 'R' -* -* If two calls to ZLATMT differ only in the PACK parameter, -* they will generate mathematically equivalent matrices. -* Not modified. -* -* A (input/output) COMPLEX*16 array, dimension ( LDA, N ) -* On exit A is the desired test matrix. A is first generated -* in full (unpacked) form, and then packed, if so specified -* by PACK. Thus, the first M elements of the first N -* columns will always be modified. If PACK specifies a -* packed or banded storage scheme, all LDA elements of the -* first N columns will be modified; the elements of the -* array which do not correspond to elements of the generated -* matrix are set to zero. -* Modified. -* -* LDA (input) INTEGER -* LDA specifies the first dimension of A as declared in the -* calling program. If PACK='N', 'U', 'L', 'C', or 'R', then -* LDA must be at least M. If PACK='B' or 'Q', then LDA must -* be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)). -* If PACK='Z', LDA must be large enough to hold the packed -* array: MIN( KU, N-1) + MIN( KL, M-1) + 1. -* Not modified. -* -* WORK (workspace) COMPLEX*16 array, dimension ( 3*MAX( N, M ) ) -* Workspace. -* Modified. -* -* INFO (output) INTEGER -* Error code. On exit, INFO will be set to one of the -* following values: -* 0 => normal return -* -1 => M negative or unequal to N and SYM='S', 'H', or 'P' -* -2 => N negative -* -3 => DIST illegal string -* -5 => SYM illegal string -* -7 => MODE not in range -6 to 6 -* -8 => COND less than 1.0, and MODE neither -6, 0 nor 6 -* -10 => KL negative -* -11 => KU negative, or SYM is not 'N' and KU is not equal to -* KL -* -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N'; -* or PACK='C' or 'Q' and SYM='N' and KL is not zero; -* or PACK='R' or 'B' and SYM='N' and KU is not zero; -* or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not -* N. -* -14 => LDA is less than M, or PACK='Z' and LDA is less than -* MIN(KU,N-1) + MIN(KL,M-1) + 1. -* 1 => Error return from DLATM7 -* 2 => Cannot scale to DMAX (max. sing. value is 0) -* 3 => Error return from ZLAGGE, ZLAGHE or ZLAGSY -* * ===================================================================== * * .. Parameters .. |