version 1.5, 2010/08/07 13:18:06
|
version 1.21, 2023/08/07 08:38:49
|
Line 1
|
Line 1
|
|
*> \brief \b DGESC2 solves a system of linear equations using the LU factorization with complete pivoting computed by sgetc2. |
|
* |
|
* =========== DOCUMENTATION =========== |
|
* |
|
* Online html documentation available at |
|
* http://www.netlib.org/lapack/explore-html/ |
|
* |
|
*> \htmlonly |
|
*> Download DGESC2 + dependencies |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgesc2.f"> |
|
*> [TGZ]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgesc2.f"> |
|
*> [ZIP]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgesc2.f"> |
|
*> [TXT]</a> |
|
*> \endhtmlonly |
|
* |
|
* Definition: |
|
* =========== |
|
* |
|
* SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE ) |
|
* |
|
* .. Scalar Arguments .. |
|
* INTEGER LDA, N |
|
* DOUBLE PRECISION SCALE |
|
* .. |
|
* .. Array Arguments .. |
|
* INTEGER IPIV( * ), JPIV( * ) |
|
* DOUBLE PRECISION A( LDA, * ), RHS( * ) |
|
* .. |
|
* |
|
* |
|
*> \par Purpose: |
|
* ============= |
|
*> |
|
*> \verbatim |
|
*> |
|
*> DGESC2 solves a system of linear equations |
|
*> |
|
*> A * X = scale* RHS |
|
*> |
|
*> with a general N-by-N matrix A using the LU factorization with |
|
*> complete pivoting computed by DGETC2. |
|
*> \endverbatim |
|
* |
|
* Arguments: |
|
* ========== |
|
* |
|
*> \param[in] N |
|
*> \verbatim |
|
*> N is INTEGER |
|
*> The order of the matrix A. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] A |
|
*> \verbatim |
|
*> A is DOUBLE PRECISION array, dimension (LDA,N) |
|
*> On entry, the LU part of the factorization of the n-by-n |
|
*> matrix A computed by DGETC2: A = P * L * U * Q |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDA |
|
*> \verbatim |
|
*> LDA is INTEGER |
|
*> The leading dimension of the array A. LDA >= max(1, N). |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] RHS |
|
*> \verbatim |
|
*> RHS is DOUBLE PRECISION array, dimension (N). |
|
*> On entry, the right hand side vector b. |
|
*> On exit, the solution vector X. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] IPIV |
|
*> \verbatim |
|
*> IPIV is INTEGER array, dimension (N). |
|
*> The pivot indices; for 1 <= i <= N, row i of the |
|
*> matrix has been interchanged with row IPIV(i). |
|
*> \endverbatim |
|
*> |
|
*> \param[in] JPIV |
|
*> \verbatim |
|
*> JPIV is INTEGER array, dimension (N). |
|
*> The pivot indices; for 1 <= j <= N, column j of the |
|
*> matrix has been interchanged with column JPIV(j). |
|
*> \endverbatim |
|
*> |
|
*> \param[out] SCALE |
|
*> \verbatim |
|
*> SCALE is DOUBLE PRECISION |
|
*> On exit, SCALE contains the scale factor. SCALE is chosen |
|
*> 0 <= SCALE <= 1 to prevent overflow in the solution. |
|
*> \endverbatim |
|
* |
|
* Authors: |
|
* ======== |
|
* |
|
*> \author Univ. of Tennessee |
|
*> \author Univ. of California Berkeley |
|
*> \author Univ. of Colorado Denver |
|
*> \author NAG Ltd. |
|
* |
|
*> \ingroup doubleGEauxiliary |
|
* |
|
*> \par Contributors: |
|
* ================== |
|
*> |
|
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science, |
|
*> Umea University, S-901 87 Umea, Sweden. |
|
* |
|
* ===================================================================== |
SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE ) |
SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2.2) -- |
* -- LAPACK auxiliary routine -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* June 2010 |
|
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER LDA, N |
INTEGER LDA, N |
Line 14
|
Line 125
|
DOUBLE PRECISION A( LDA, * ), RHS( * ) |
DOUBLE PRECISION A( LDA, * ), RHS( * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* DGESC2 solves a system of linear equations |
|
* |
|
* A * X = scale* RHS |
|
* |
|
* with a general N-by-N matrix A using the LU factorization with |
|
* complete pivoting computed by DGETC2. |
|
* |
|
* Arguments |
|
* ========= |
|
* |
|
* N (input) INTEGER |
|
* The order of the matrix A. |
|
* |
|
* A (input) DOUBLE PRECISION array, dimension (LDA,N) |
|
* On entry, the LU part of the factorization of the n-by-n |
|
* matrix A computed by DGETC2: A = P * L * U * Q |
|
* |
|
* LDA (input) INTEGER |
|
* The leading dimension of the array A. LDA >= max(1, N). |
|
* |
|
* RHS (input/output) DOUBLE PRECISION array, dimension (N). |
|
* On entry, the right hand side vector b. |
|
* On exit, the solution vector X. |
|
* |
|
* IPIV (input) INTEGER array, dimension (N). |
|
* The pivot indices; for 1 <= i <= N, row i of the |
|
* matrix has been interchanged with row IPIV(i). |
|
* |
|
* JPIV (input) INTEGER array, dimension (N). |
|
* The pivot indices; for 1 <= j <= N, column j of the |
|
* matrix has been interchanged with column JPIV(j). |
|
* |
|
* SCALE (output) DOUBLE PRECISION |
|
* On exit, SCALE contains the scale factor. SCALE is chosen |
|
* 0 <= SCALE <= 1 to prevent owerflow in the solution. |
|
* |
|
* Further Details |
|
* =============== |
|
* |
|
* Based on contributions by |
|
* Bo Kagstrom and Peter Poromaa, Department of Computing Science, |
|
* Umea University, S-901 87 Umea, Sweden. |
|
* |
|
* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
Line 71
|
Line 136
|
DOUBLE PRECISION BIGNUM, EPS, SMLNUM, TEMP |
DOUBLE PRECISION BIGNUM, EPS, SMLNUM, TEMP |
* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL DLASWP, DSCAL |
EXTERNAL DLASWP, DSCAL, DLABAD |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
INTEGER IDAMAX |
INTEGER IDAMAX |
Line 83
|
Line 148
|
* .. |
* .. |
* .. Executable Statements .. |
* .. Executable Statements .. |
* |
* |
* Set constant to control owerflow |
* Set constant to control overflow |
* |
* |
EPS = DLAMCH( 'P' ) |
EPS = DLAMCH( 'P' ) |
SMLNUM = DLAMCH( 'S' ) / EPS |
SMLNUM = DLAMCH( 'S' ) / EPS |