version 1.12, 2017/06/17 10:54:25
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version 1.16, 2023/08/07 08:39:34
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*> \verbatim |
*> \verbatim |
*> |
*> |
*> ZPORFSX improves the computed solution to a system of linear |
*> ZPORFSX improves the computed solution to a system of linear |
*> equations when the coefficient matrix is symmetric positive |
*> equations when the coefficient matrix is Hermitian positive |
*> definite, and provides error bounds and backward error estimates |
*> definite, and provides error bounds and backward error estimates |
*> for the solution. In addition to normwise error bound, the code |
*> for the solution. In addition to normwise error bound, the code |
*> provides maximum componentwise error bound if possible. See |
*> provides maximum componentwise error bound if possible. See |
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*> \param[in] A |
*> \param[in] A |
*> \verbatim |
*> \verbatim |
*> A is COMPLEX*16 array, dimension (LDA,N) |
*> A is COMPLEX*16 array, dimension (LDA,N) |
*> The symmetric matrix A. If UPLO = 'U', the leading N-by-N |
*> The Hermitian matrix A. If UPLO = 'U', the leading N-by-N |
*> upper triangular part of A contains the upper triangular part |
*> upper triangular part of A contains the upper triangular part |
*> of the matrix A, and the strictly lower triangular part of A |
*> of the matrix A, and the strictly lower triangular part of A |
*> is not referenced. If UPLO = 'L', the leading N-by-N lower |
*> is not referenced. If UPLO = 'L', the leading N-by-N lower |
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*> \verbatim |
*> \verbatim |
*> AF is COMPLEX*16 array, dimension (LDAF,N) |
*> AF is COMPLEX*16 array, dimension (LDAF,N) |
*> The triangular factor U or L from the Cholesky factorization |
*> The triangular factor U or L from the Cholesky factorization |
*> A = U**T*U or A = L*L**T, as computed by DPOTRF. |
*> A = U**H*U or A = L*L**H, as computed by ZPOTRF. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] LDAF |
*> \param[in] LDAF |
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*> \param[in,out] S |
*> \param[in,out] S |
*> \verbatim |
*> \verbatim |
*> S is DOUBLE PRECISION array, dimension (N) |
*> S is DOUBLE PRECISION array, dimension (N) |
*> The row scale factors for A. If EQUED = 'Y', A is multiplied on |
*> The scale factors for A. If EQUED = 'Y', A is multiplied on |
*> the left and right by diag(S). S is an input argument if FACT = |
*> the left and right by diag(S). S is an input argument if FACT = |
*> 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED |
*> 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED |
*> = 'Y', each element of S must be positive. If S is output, each |
*> = 'Y', each element of S must be positive. If S is output, each |
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*> \param[in,out] X |
*> \param[in,out] X |
*> \verbatim |
*> \verbatim |
*> X is COMPLEX*16 array, dimension (LDX,NRHS) |
*> X is COMPLEX*16 array, dimension (LDX,NRHS) |
*> On entry, the solution matrix X, as computed by DGETRS. |
*> On entry, the solution matrix X, as computed by ZGETRS. |
*> On exit, the improved solution matrix X. |
*> On exit, the improved solution matrix X. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
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*> information as described below. There currently are up to three |
*> information as described below. There currently are up to three |
*> pieces of information returned for each right-hand side. If |
*> pieces of information returned for each right-hand side. If |
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then |
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then |
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most |
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most |
*> the first (:,N_ERR_BNDS) entries are returned. |
*> the first (:,N_ERR_BNDS) entries are returned. |
*> |
*> |
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith |
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith |
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*> \param[in] NPARAMS |
*> \param[in] NPARAMS |
*> \verbatim |
*> \verbatim |
*> NPARAMS is INTEGER |
*> NPARAMS is INTEGER |
*> Specifies the number of parameters set in PARAMS. If .LE. 0, the |
*> Specifies the number of parameters set in PARAMS. If <= 0, the |
*> PARAMS array is never referenced and default values are used. |
*> PARAMS array is never referenced and default values are used. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in,out] PARAMS |
*> \param[in,out] PARAMS |
*> \verbatim |
*> \verbatim |
*> PARAMS is DOUBLE PRECISION array, dimension NPARAMS |
*> PARAMS is DOUBLE PRECISION array, dimension NPARAMS |
*> Specifies algorithm parameters. If an entry is .LT. 0.0, then |
*> Specifies algorithm parameters. If an entry is < 0.0, then |
*> that entry will be filled with default value used for that |
*> that entry will be filled with default value used for that |
*> parameter. Only positions up to NPARAMS are accessed; defaults |
*> parameter. Only positions up to NPARAMS are accessed; defaults |
*> are used for higher-numbered parameters. |
*> are used for higher-numbered parameters. |
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*> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative |
*> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative |
*> refinement or not. |
*> refinement or not. |
*> Default: 1.0D+0 |
*> Default: 1.0D+0 |
*> = 0.0 : No refinement is performed, and no error bounds are |
*> = 0.0: No refinement is performed, and no error bounds are |
*> computed. |
*> computed. |
*> = 1.0 : Use the double-precision refinement algorithm, |
*> = 1.0: Use the double-precision refinement algorithm, |
*> possibly with doubled-single computations if the |
*> possibly with doubled-single computations if the |
*> compilation environment does not support DOUBLE |
*> compilation environment does not support DOUBLE |
*> PRECISION. |
*> PRECISION. |
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*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
* |
*> \date April 2012 |
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* |
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*> \ingroup complex16POcomputational |
*> \ingroup complex16POcomputational |
* |
* |
* ===================================================================== |
* ===================================================================== |
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$ ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS, |
$ ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS, |
$ WORK, RWORK, INFO ) |
$ WORK, RWORK, INFO ) |
* |
* |
* -- LAPACK computational routine (version 3.7.0) -- |
* -- LAPACK computational 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..-- |
* April 2012 |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO, EQUED |
CHARACTER UPLO, EQUED |