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version 1.10, 2012/08/22 09:48:14
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*> \brief <b> DGESV computes the solution to system of linear equations A * X = B for GE matrices</b> |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download DGESV + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgesv.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgesv.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgesv.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INFO, LDA, LDB, N, NRHS |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IPIV( * ) |
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* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> DGESV computes the solution to a real system of linear equations |
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*> A * X = B, |
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*> where A is an N-by-N matrix and X and B are N-by-NRHS matrices. |
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*> |
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*> The LU decomposition with partial pivoting and row interchanges is |
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*> used to factor A as |
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*> A = P * L * U, |
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*> where P is a permutation matrix, L is unit lower triangular, and U is |
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*> upper triangular. The factored form of A is then used to solve the |
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*> system of equations A * X = B. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The number of linear equations, i.e., the order of the |
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*> matrix A. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] NRHS |
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*> \verbatim |
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*> NRHS is INTEGER |
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*> The number of right hand sides, i.e., the number of columns |
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*> of the matrix B. NRHS >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] A |
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*> \verbatim |
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*> A is DOUBLE PRECISION array, dimension (LDA,N) |
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*> On entry, the N-by-N coefficient matrix A. |
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*> On exit, the factors L and U from the factorization |
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*> A = P*L*U; the unit diagonal elements of L are not stored. |
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*> \endverbatim |
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*> |
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*> \param[in] LDA |
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*> \verbatim |
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*> LDA is INTEGER |
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*> The leading dimension of the array A. LDA >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[out] IPIV |
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*> \verbatim |
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*> IPIV is INTEGER array, dimension (N) |
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*> The pivot indices that define the permutation matrix P; |
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*> row i of the matrix was interchanged with row IPIV(i). |
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*> \endverbatim |
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*> |
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*> \param[in,out] B |
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*> \verbatim |
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*> B is DOUBLE PRECISION array, dimension (LDB,NRHS) |
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*> On entry, the N-by-NRHS matrix of right hand side matrix B. |
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*> On exit, if INFO = 0, the N-by-NRHS solution matrix X. |
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*> \endverbatim |
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*> |
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*> \param[in] LDB |
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*> \verbatim |
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*> LDB is INTEGER |
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*> The leading dimension of the array B. LDB >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[out] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> = 0: successful exit |
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*> < 0: if INFO = -i, the i-th argument had an illegal value |
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*> > 0: if INFO = i, U(i,i) is exactly zero. The factorization |
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*> has been completed, but the factor U is exactly |
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*> singular, so the solution could not be computed. |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date November 2011 |
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* |
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*> \ingroup doubleGEsolve |
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* |
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* ===================================================================== |
SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) |
SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) |
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* -- LAPACK driver routine (version 3.4.0) -- |
* -- 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..-- |
* November 2006 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, LDA, LDB, N, NRHS |
INTEGER INFO, LDA, LDB, N, NRHS |
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DOUBLE PRECISION A( LDA, * ), B( LDB, * ) |
DOUBLE PRECISION A( LDA, * ), B( LDB, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DGESV computes the solution to a real system of linear equations |
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* A * X = B, |
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* where A is an N-by-N matrix and X and B are N-by-NRHS matrices. |
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* |
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* The LU decomposition with partial pivoting and row interchanges is |
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* used to factor A as |
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* A = P * L * U, |
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* where P is a permutation matrix, L is unit lower triangular, and U is |
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* upper triangular. The factored form of A is then used to solve the |
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* system of equations A * X = B. |
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* |
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* Arguments |
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* ========= |
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* |
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* N (input) INTEGER |
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* The number of linear equations, i.e., the order of the |
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* matrix A. N >= 0. |
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* |
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* NRHS (input) INTEGER |
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* The number of right hand sides, i.e., the number of columns |
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* of the matrix B. NRHS >= 0. |
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* |
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* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
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* On entry, the N-by-N coefficient matrix A. |
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* On exit, the factors L and U from the factorization |
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* A = P*L*U; the unit diagonal elements of L are not stored. |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(1,N). |
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* |
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* IPIV (output) INTEGER array, dimension (N) |
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* The pivot indices that define the permutation matrix P; |
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* row i of the matrix was interchanged with row IPIV(i). |
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* |
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* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) |
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* On entry, the N-by-NRHS matrix of right hand side matrix B. |
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* On exit, if INFO = 0, the N-by-NRHS solution matrix X. |
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* |
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* LDB (input) INTEGER |
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* The leading dimension of the array B. LDB >= max(1,N). |
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* |
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* INFO (output) INTEGER |
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* = 0: successful exit |
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* < 0: if INFO = -i, the i-th argument had an illegal value |
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* > 0: if INFO = i, U(i,i) is exactly zero. The factorization |
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* has been completed, but the factor U is exactly |
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* singular, so the solution could not be computed. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. External Subroutines .. |
* .. External Subroutines .. |