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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/ctpt05.f | |
parent | 5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff) |
Integrating Doxygen in comments
Diffstat (limited to 'TESTING/LIN/ctpt05.f')
-rw-r--r-- | TESTING/LIN/ctpt05.f | 270 |
1 files changed, 179 insertions, 91 deletions
diff --git a/TESTING/LIN/ctpt05.f b/TESTING/LIN/ctpt05.f index f32eb567..79d1eaa8 100644 --- a/TESTING/LIN/ctpt05.f +++ b/TESTING/LIN/ctpt05.f @@ -1,9 +1,186 @@ +*> \brief \b CTPT05 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CTPT05( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, +* XACT, LDXACT, FERR, BERR, RESLTS ) +* +* .. Scalar Arguments .. +* CHARACTER DIAG, TRANS, UPLO +* INTEGER LDB, LDX, LDXACT, N, NRHS +* .. +* .. Array Arguments .. +* REAL BERR( * ), FERR( * ), RESLTS( * ) +* COMPLEX AP( * ), B( LDB, * ), X( LDX, * ), +* $ XACT( LDXACT, * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> CTPT05 tests the error bounds from iterative refinement for the +*> computed solution to a system of equations A*X = B, where A is a +*> triangular matrix in packed storage format. +*> +*> 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 / ( (n+1)*EPS + (*) ), where +*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> Specifies whether the matrix A is upper or lower triangular. +*> = 'U': Upper triangular +*> = 'L': Lower triangular +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> Specifies the form of the system of equations. +*> = 'N': A * X = B (No transpose) +*> = 'T': A'* X = B (Transpose) +*> = 'C': A'* X = B (Conjugate transpose = Transpose) +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> Specifies whether or not the matrix A is unit triangular. +*> = 'N': Non-unit triangular +*> = 'U': Unit triangular +*> \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] NRHS +*> \verbatim +*> NRHS is INTEGER +*> The number of columns of the matrices X, B, and XACT. +*> NRHS >= 0. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is COMPLEX array, dimension (N*(N+1)/2) +*> The upper or lower triangular matrix A, packed columnwise in +*> a linear array. The j-th column of A is stored in the array +*> AP as follows: +*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; +*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. +*> If DIAG = 'U', the diagonal elements of A are not referenced +*> and are assumed to be 1. +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is COMPLEX 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 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 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 REAL 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 REAL 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 REAL array, dimension (2) +*> The maximum over the NRHS solution vectors of the ratios: +*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) +*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) ) +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_lin +* +* ===================================================================== SUBROUTINE CTPT05( UPLO, TRANS, DIAG, N, NRHS, AP, 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 DIAG, TRANS, UPLO @@ -15,95 +192,6 @@ $ XACT( LDXACT, * ) * .. * -* Purpose -* ======= -* -* CTPT05 tests the error bounds from iterative refinement for the -* computed solution to a system of equations A*X = B, where A is a -* triangular matrix in packed storage format. -* -* 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 / ( (n+1)*EPS + (*) ), where -* (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) -* -* Arguments -* ========= -* -* UPLO (input) CHARACTER*1 -* Specifies whether the matrix A is upper or lower triangular. -* = 'U': Upper triangular -* = 'L': Lower triangular -* -* TRANS (input) CHARACTER*1 -* Specifies the form of the system of equations. -* = 'N': A * X = B (No transpose) -* = 'T': A'* X = B (Transpose) -* = 'C': A'* X = B (Conjugate transpose = Transpose) -* -* DIAG (input) CHARACTER*1 -* Specifies whether or not the matrix A is unit triangular. -* = 'N': Non-unit triangular -* = 'U': Unit triangular -* -* N (input) INTEGER -* The number of rows of the matrices X, B, and XACT, and the -* order of the matrix A. N >= 0. -* -* NRHS (input) INTEGER -* The number of columns of the matrices X, B, and XACT. -* NRHS >= 0. -* -* AP (input) COMPLEX array, dimension (N*(N+1)/2) -* The upper or lower triangular matrix A, packed columnwise in -* a linear array. The j-th column of A is stored in the array -* AP as follows: -* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; -* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -* If DIAG = 'U', the diagonal elements of A are not referenced -* and are assumed to be 1. -* -* B (input) COMPLEX 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 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 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) REAL 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) REAL 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) REAL array, dimension (2) -* The maximum over the NRHS solution vectors of the ratios: -* RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) -* RESLTS(2) = BERR / ( (n+1)*EPS + (*) ) -* * ===================================================================== * * .. Parameters .. |