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author | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
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committer | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
commit | e1d39294aee16fa6db9ba079b14442358217db71 (patch) | |
tree | 30e5aa04c1f6596991fda5334f63dfb9b8027849 /TESTING/LIN/zgbt05.f | |
parent | 5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff) |
Integrating Doxygen in comments
Diffstat (limited to 'TESTING/LIN/zgbt05.f')
-rw-r--r-- | TESTING/LIN/zgbt05.f | 269 |
1 files changed, 180 insertions, 89 deletions
diff --git a/TESTING/LIN/zgbt05.f b/TESTING/LIN/zgbt05.f index 4d5cd05e..abf8fe9d 100644 --- a/TESTING/LIN/zgbt05.f +++ b/TESTING/LIN/zgbt05.f @@ -1,9 +1,187 @@ +*> \brief \b ZGBT05 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZGBT05( TRANS, N, KL, KU, NRHS, AB, LDAB, B, LDB, X, +* LDX, XACT, LDXACT, FERR, BERR, RESLTS ) +* +* .. Scalar Arguments .. +* CHARACTER TRANS +* INTEGER KL, KU, LDAB, LDB, LDX, LDXACT, N, NRHS +* .. +* .. Array Arguments .. +* DOUBLE PRECISION BERR( * ), FERR( * ), RESLTS( * ) +* COMPLEX*16 AB( LDAB, * ), B( LDB, * ), X( LDX, * ), +* $ XACT( LDXACT, * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> ZGBT05 tests the error bounds from iterative refinement for the +*> computed solution to a system of equations op(A)*X = B, where A is a +*> general band matrix of order n with kl subdiagonals and ku +*> superdiagonals and op(A) = A or A**T, depending on TRANS. +*> +*> RESLTS(1) = test of the error bound +*> = norm(X - XACT) / ( norm(X) * FERR ) +*> +*> A large value is returned if this ratio is not less than one. +*> +*> RESLTS(2) = residual from the iterative refinement routine +*> = the maximum of BERR / ( NZ*EPS + (*) ), where +*> (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i ) +*> and NZ = max. number of nonzeros in any row of A, plus 1 +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> Specifies the form of the system of equations. +*> = 'N': A * X = B (No transpose) +*> = 'T': A**T * X = B (Transpose) +*> = 'C': A**H * X = B (Conjugate transpose = Transpose) +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of rows of the matrices X, B, and XACT, and the +*> order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> The number of subdiagonals within the band of A. KL >= 0. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> The number of superdiagonals within the band of A. KU >= 0. +*> \endverbatim +*> +*> \param[in] NRHS +*> \verbatim +*> NRHS is INTEGER +*> The number of columns of the matrices X, B, and XACT. +*> NRHS >= 0. +*> \endverbatim +*> +*> \param[in] AB +*> \verbatim +*> AB is COMPLEX*16 array, dimension (LDAB,N) +*> The original band matrix A, stored in rows 1 to KL+KU+1. +*> The j-th column of A is stored in the j-th column of the +*> array AB as follows: +*> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl). +*> \endverbatim +*> +*> \param[in] LDAB +*> \verbatim +*> LDAB is INTEGER +*> The leading dimension of the array AB. LDAB >= KL+KU+1. +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is COMPLEX*16 array, dimension (LDB,NRHS) +*> The right hand side vectors for the system of linear +*> equations. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of the array B. LDB >= max(1,N). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX*16 array, dimension (LDX,NRHS) +*> The computed solution vectors. Each vector is stored as a +*> column of the matrix X. +*> \endverbatim +*> +*> \param[in] LDX +*> \verbatim +*> LDX is INTEGER +*> The leading dimension of the array X. LDX >= max(1,N). +*> \endverbatim +*> +*> \param[in] XACT +*> \verbatim +*> XACT is COMPLEX*16 array, dimension (LDX,NRHS) +*> The exact solution vectors. Each vector is stored as a +*> column of the matrix XACT. +*> \endverbatim +*> +*> \param[in] LDXACT +*> \verbatim +*> LDXACT is INTEGER +*> The leading dimension of the array XACT. LDXACT >= max(1,N). +*> \endverbatim +*> +*> \param[in] FERR +*> \verbatim +*> FERR is DOUBLE PRECISION array, dimension (NRHS) +*> The estimated forward error bounds for each solution vector +*> X. If XTRUE is the true solution, FERR bounds the magnitude +*> of the largest entry in (X - XTRUE) divided by the magnitude +*> of the largest entry in X. +*> \endverbatim +*> +*> \param[in] BERR +*> \verbatim +*> BERR is DOUBLE PRECISION array, dimension (NRHS) +*> The componentwise relative backward error of each solution +*> vector (i.e., the smallest relative change in any entry of A +*> or B that makes X an exact solution). +*> \endverbatim +*> +*> \param[out] RESLTS +*> \verbatim +*> RESLTS is DOUBLE PRECISION array, dimension (2) +*> The maximum over the NRHS solution vectors of the ratios: +*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) +*> RESLTS(2) = BERR / ( NZ*EPS + (*) ) +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_lin +* +* ===================================================================== SUBROUTINE ZGBT05( TRANS, N, KL, KU, NRHS, AB, LDAB, B, LDB, X, $ LDX, XACT, LDXACT, FERR, BERR, RESLTS ) * * -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 +* -- 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 TRANS @@ -15,93 +193,6 @@ $ XACT( LDXACT, * ) * .. * -* Purpose -* ======= -* -* ZGBT05 tests the error bounds from iterative refinement for the -* computed solution to a system of equations op(A)*X = B, where A is a -* general band matrix of order n with kl subdiagonals and ku -* superdiagonals and op(A) = A or A**T, depending on TRANS. -* -* RESLTS(1) = test of the error bound -* = norm(X - XACT) / ( norm(X) * FERR ) -* -* A large value is returned if this ratio is not less than one. -* -* RESLTS(2) = residual from the iterative refinement routine -* = the maximum of BERR / ( NZ*EPS + (*) ), where -* (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i ) -* and NZ = max. number of nonzeros in any row of A, plus 1 -* -* Arguments -* ========= -* -* TRANS (input) CHARACTER*1 -* Specifies the form of the system of equations. -* = 'N': A * X = B (No transpose) -* = 'T': A**T * X = B (Transpose) -* = 'C': A**H * X = B (Conjugate transpose = Transpose) -* -* N (input) INTEGER -* The number of rows of the matrices X, B, and XACT, and the -* order of the matrix A. N >= 0. -* -* KL (input) INTEGER -* The number of subdiagonals within the band of A. KL >= 0. -* -* KU (input) INTEGER -* The number of superdiagonals within the band of A. KU >= 0. -* -* NRHS (input) INTEGER -* The number of columns of the matrices X, B, and XACT. -* NRHS >= 0. -* -* AB (input) COMPLEX*16 array, dimension (LDAB,N) -* The original band matrix A, stored in rows 1 to KL+KU+1. -* The j-th column of A is stored in the j-th column of the -* array AB as follows: -* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl). -* -* LDAB (input) INTEGER -* The leading dimension of the array AB. LDAB >= KL+KU+1. -* -* B (input) COMPLEX*16 array, dimension (LDB,NRHS) -* The right hand side vectors for the system of linear -* equations. -* -* LDB (input) INTEGER -* The leading dimension of the array B. LDB >= max(1,N). -* -* X (input) COMPLEX*16 array, dimension (LDX,NRHS) -* The computed solution vectors. Each vector is stored as a -* column of the matrix X. -* -* LDX (input) INTEGER -* The leading dimension of the array X. LDX >= max(1,N). -* -* XACT (input) COMPLEX*16 array, dimension (LDX,NRHS) -* The exact solution vectors. Each vector is stored as a -* column of the matrix XACT. -* -* LDXACT (input) INTEGER -* The leading dimension of the array XACT. LDXACT >= max(1,N). -* -* FERR (input) DOUBLE PRECISION array, dimension (NRHS) -* The estimated forward error bounds for each solution vector -* X. If XTRUE is the true solution, FERR bounds the magnitude -* of the largest entry in (X - XTRUE) divided by the magnitude -* of the largest entry in X. -* -* BERR (input) DOUBLE PRECISION array, dimension (NRHS) -* The componentwise relative backward error of each solution -* vector (i.e., the smallest relative change in any entry of A -* or B that makes X an exact solution). -* -* RESLTS (output) DOUBLE PRECISION array, dimension (2) -* The maximum over the NRHS solution vectors of the ratios: -* RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) -* RESLTS(2) = BERR / ( NZ*EPS + (*) ) -* * ===================================================================== * * .. Parameters .. |