version 1.9, 2011/07/22 07:38:13
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version 1.10, 2011/11/21 20:43:07
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*> \brief <b> ZCGESV computes the solution to system of linear equations A * X = B for GE matrices</b> (mixed precision with iterative refinement) |
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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 ZCGESV + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zcgesv.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/zcgesv.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/zcgesv.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 ZCGESV( N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, |
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* SWORK, RWORK, ITER, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INFO, ITER, LDA, LDB, LDX, N, NRHS |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IPIV( * ) |
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* DOUBLE PRECISION RWORK( * ) |
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* COMPLEX SWORK( * ) |
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* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( N, * ), |
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* $ X( LDX, * ) |
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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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*> ZCGESV computes the solution to a complex 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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*> ZCGESV first attempts to factorize the matrix in COMPLEX and use this |
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*> factorization within an iterative refinement procedure to produce a |
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*> solution with COMPLEX*16 normwise backward error quality (see below). |
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*> If the approach fails the method switches to a COMPLEX*16 |
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*> factorization and solve. |
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*> |
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*> The iterative refinement is not going to be a winning strategy if |
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*> the ratio COMPLEX performance over COMPLEX*16 performance is too |
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*> small. A reasonable strategy should take the number of right-hand |
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*> sides and the size of the matrix into account. This might be done |
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*> with a call to ILAENV in the future. Up to now, we always try |
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*> iterative refinement. |
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*> |
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*> The iterative refinement process is stopped if |
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*> ITER > ITERMAX |
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*> or for all the RHS we have: |
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*> RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX |
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*> where |
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*> o ITER is the number of the current iteration in the iterative |
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*> refinement process |
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*> o RNRM is the infinity-norm of the residual |
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*> o XNRM is the infinity-norm of the solution |
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*> o ANRM is the infinity-operator-norm of the matrix A |
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*> o EPS is the machine epsilon returned by DLAMCH('Epsilon') |
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*> The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 |
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*> respectively. |
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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 COMPLEX*16 array, |
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*> dimension (LDA,N) |
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*> On entry, the N-by-N coefficient matrix A. |
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*> On exit, if iterative refinement has been successfully used |
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*> (INFO.EQ.0 and ITER.GE.0, see description below), then A is |
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*> unchanged, if double precision factorization has been used |
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*> (INFO.EQ.0 and ITER.LT.0, see description below), then the |
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*> array A contains 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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*> Corresponds either to the single precision factorization |
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*> (if INFO.EQ.0 and ITER.GE.0) or the double precision |
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*> factorization (if INFO.EQ.0 and ITER.LT.0). |
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*> \endverbatim |
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*> |
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*> \param[in] B |
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*> \verbatim |
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*> B is COMPLEX*16 array, dimension (LDB,NRHS) |
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*> The N-by-NRHS right hand side matrix B. |
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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] X |
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*> \verbatim |
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*> X is COMPLEX*16 array, dimension (LDX,NRHS) |
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*> 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] LDX |
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*> \verbatim |
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*> LDX is INTEGER |
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*> The leading dimension of the array X. LDX >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[out] WORK |
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*> \verbatim |
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*> WORK is COMPLEX*16 array, dimension (N*NRHS) |
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*> This array is used to hold the residual vectors. |
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*> \endverbatim |
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*> |
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*> \param[out] SWORK |
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*> \verbatim |
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*> SWORK is COMPLEX array, dimension (N*(N+NRHS)) |
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*> This array is used to use the single precision matrix and the |
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*> right-hand sides or solutions in single precision. |
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*> \endverbatim |
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*> |
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*> \param[out] RWORK |
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*> \verbatim |
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*> RWORK is DOUBLE PRECISION array, dimension (N) |
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*> \endverbatim |
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*> |
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*> \param[out] ITER |
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*> \verbatim |
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*> ITER is INTEGER |
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*> < 0: iterative refinement has failed, COMPLEX*16 |
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*> factorization has been performed |
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*> -1 : the routine fell back to full precision for |
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*> implementation- or machine-specific reasons |
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*> -2 : narrowing the precision induced an overflow, |
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*> the routine fell back to full precision |
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*> -3 : failure of CGETRF |
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*> -31: stop the iterative refinement after the 30th |
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*> iterations |
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*> > 0: iterative refinement has been sucessfully used. |
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*> Returns the number of iterations |
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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) computed in COMPLEX*16 is exactly |
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*> zero. The factorization has been completed, but the |
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*> factor U is exactly singular, so the solution |
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*> 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 complex16GEsolve |
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* |
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* ===================================================================== |
SUBROUTINE ZCGESV( N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, |
SUBROUTINE ZCGESV( N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, |
$ SWORK, RWORK, ITER, INFO ) |
$ SWORK, RWORK, ITER, INFO ) |
* |
* |
* -- LAPACK PROTOTYPE driver routine (version 3.3.1) -- |
* -- 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..-- |
* -- April 2011 -- |
* November 2011 |
* |
* |
* .. |
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* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, ITER, LDA, LDB, LDX, N, NRHS |
INTEGER INFO, ITER, LDA, LDB, LDX, N, NRHS |
* .. |
* .. |
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$ X( LDX, * ) |
$ X( LDX, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZCGESV computes the solution to a complex 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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* ZCGESV first attempts to factorize the matrix in COMPLEX and use this |
|
* factorization within an iterative refinement procedure to produce a |
|
* solution with COMPLEX*16 normwise backward error quality (see below). |
|
* If the approach fails the method switches to a COMPLEX*16 |
|
* factorization and solve. |
|
* |
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* The iterative refinement is not going to be a winning strategy if |
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* the ratio COMPLEX performance over COMPLEX*16 performance is too |
|
* small. A reasonable strategy should take the number of right-hand |
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* sides and the size of the matrix into account. This might be done |
|
* with a call to ILAENV in the future. Up to now, we always try |
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* iterative refinement. |
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* |
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* The iterative refinement process is stopped if |
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* ITER > ITERMAX |
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* or for all the RHS we have: |
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* RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX |
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* where |
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* o ITER is the number of the current iteration in the iterative |
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* refinement process |
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* o RNRM is the infinity-norm of the residual |
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* o XNRM is the infinity-norm of the solution |
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* o ANRM is the infinity-operator-norm of the matrix A |
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* o EPS is the machine epsilon returned by DLAMCH('Epsilon') |
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* The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 |
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* respectively. |
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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) COMPLEX*16 array, |
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* dimension (LDA,N) |
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* On entry, the N-by-N coefficient matrix A. |
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* On exit, if iterative refinement has been successfully used |
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* (INFO.EQ.0 and ITER.GE.0, see description below), then A is |
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* unchanged, if double precision factorization has been used |
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* (INFO.EQ.0 and ITER.LT.0, see description below), then the |
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* array A contains 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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* Corresponds either to the single precision factorization |
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* (if INFO.EQ.0 and ITER.GE.0) or the double precision |
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* factorization (if INFO.EQ.0 and ITER.LT.0). |
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* |
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* B (input) COMPLEX*16 array, dimension (LDB,NRHS) |
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* The N-by-NRHS right hand side matrix B. |
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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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* X (output) COMPLEX*16 array, dimension (LDX,NRHS) |
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* If INFO = 0, the N-by-NRHS solution matrix X. |
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* |
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* LDX (input) INTEGER |
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* The leading dimension of the array X. LDX >= max(1,N). |
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* |
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* WORK (workspace) COMPLEX*16 array, dimension (N*NRHS) |
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* This array is used to hold the residual vectors. |
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* |
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* SWORK (workspace) COMPLEX array, dimension (N*(N+NRHS)) |
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* This array is used to use the single precision matrix and the |
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* right-hand sides or solutions in single precision. |
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* |
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* RWORK (workspace) DOUBLE PRECISION array, dimension (N) |
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* |
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* ITER (output) INTEGER |
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* < 0: iterative refinement has failed, COMPLEX*16 |
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* factorization has been performed |
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* -1 : the routine fell back to full precision for |
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* implementation- or machine-specific reasons |
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* -2 : narrowing the precision induced an overflow, |
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* the routine fell back to full precision |
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* -3 : failure of CGETRF |
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* -31: stop the iterative refinement after the 30th |
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* iterations |
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* > 0: iterative refinement has been sucessfully used. |
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* Returns the number of iterations |
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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) computed in COMPLEX*16 is exactly |
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* zero. The factorization has been completed, but the |
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* factor U is exactly singular, so the solution |
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* could not be computed. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |