733 lines
27 KiB
Fortran
733 lines
27 KiB
Fortran
*> \brief \b DGERFSX
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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 DGERFSX + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgerfsx.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/dgerfsx.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/dgerfsx.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 DGERFSX( TRANS, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
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* R, C, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
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* ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
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* WORK, IWORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER TRANS, EQUED
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* INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
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* $ N_ERR_BNDS
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* DOUBLE PRECISION RCOND
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * ), IWORK( * )
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* DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
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* $ X( LDX , * ), WORK( * )
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* DOUBLE PRECISION R( * ), C( * ), PARAMS( * ), BERR( * ),
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* $ ERR_BNDS_NORM( NRHS, * ),
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* $ ERR_BNDS_COMP( NRHS, * )
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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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*> DGERFSX improves the computed solution to a system of linear
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*> equations and provides error bounds and backward error estimates
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*> for the solution. In addition to normwise error bound, the code
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*> provides maximum componentwise error bound if possible. See
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*> comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the
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*> error bounds.
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*>
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*> The original system of linear equations may have been equilibrated
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*> before calling this routine, as described by arguments EQUED, R
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*> and C below. In this case, the solution and error bounds returned
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*> are for the original unequilibrated system.
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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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*> \verbatim
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*> Some optional parameters are bundled in the PARAMS array. These
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*> settings determine how refinement is performed, but often the
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*> defaults are acceptable. If the defaults are acceptable, users
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*> can pass NPARAMS = 0 which prevents the source code from accessing
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*> the PARAMS argument.
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*> \endverbatim
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*>
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*> \param[in] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> Specifies the form of the system of equations:
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*> = 'N': A * X = B (No transpose)
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*> = 'T': A**T * X = B (Transpose)
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*> = 'C': A**H * X = B (Conjugate transpose = Transpose)
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*> \endverbatim
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*>
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*> \param[in] EQUED
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*> \verbatim
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*> EQUED is CHARACTER*1
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*> Specifies the form of equilibration that was done to A
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*> before calling this routine. This is needed to compute
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*> the solution and error bounds correctly.
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*> = 'N': No equilibration
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*> = 'R': Row equilibration, i.e., A has been premultiplied by
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*> diag(R).
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*> = 'C': Column equilibration, i.e., A has been postmultiplied
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*> by diag(C).
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*> = 'B': Both row and column equilibration, i.e., A has been
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*> replaced by diag(R) * A * diag(C).
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*> The right hand side B has been changed accordingly.
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*> \endverbatim
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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 order of the 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 matrices B and X. NRHS >= 0.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is DOUBLE PRECISION array, dimension (LDA,N)
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*> The original N-by-N matrix A.
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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[in] AF
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*> \verbatim
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*> AF is DOUBLE PRECISION array, dimension (LDAF,N)
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*> The factors L and U from the factorization A = P*L*U
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*> as computed by DGETRF.
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*> \endverbatim
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*>
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*> \param[in] LDAF
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*> \verbatim
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*> LDAF is INTEGER
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*> The leading dimension of the array AF. LDAF >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*> The pivot indices from DGETRF; for 1<=i<=N, row i of the
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*> matrix was interchanged with row IPIV(i).
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*> \endverbatim
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*>
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*> \param[in] R
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*> \verbatim
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*> R is DOUBLE PRECISION array, dimension (N)
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*> The row scale factors for A. If EQUED = 'R' or 'B', A is
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*> multiplied on the left by diag(R); if EQUED = 'N' or 'C', R
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*> is not accessed.
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*> If R is accessed, each element of R should be a power of the radix
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*> to ensure a reliable solution and error estimates. Scaling by
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*> powers of the radix does not cause rounding errors unless the
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*> result underflows or overflows. Rounding errors during scaling
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*> lead to refining with a matrix that is not equivalent to the
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*> input matrix, producing error estimates that may not be
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*> reliable.
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*> \endverbatim
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*>
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*> \param[in] C
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*> \verbatim
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*> C is DOUBLE PRECISION array, dimension (N)
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*> The column scale factors for A. If EQUED = 'C' or 'B', A is
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*> multiplied on the right by diag(C); if EQUED = 'N' or 'R', C
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*> is not accessed.
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*> If C is accessed, each element of C should be a power of the radix
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*> to ensure a reliable solution and error estimates. Scaling by
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*> powers of the radix does not cause rounding errors unless the
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*> result underflows or overflows. Rounding errors during scaling
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*> lead to refining with a matrix that is not equivalent to the
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*> input matrix, producing error estimates that may not be
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*> reliable.
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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 DOUBLE PRECISION array, dimension (LDB,NRHS)
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*> The 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[in,out] X
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*> \verbatim
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*> X is DOUBLE PRECISION array, dimension (LDX,NRHS)
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*> On entry, the solution matrix X, as computed by DGETRS.
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*> On exit, the improved 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] RCOND
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*> \verbatim
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*> RCOND is DOUBLE PRECISION
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*> Reciprocal scaled condition number. This is an estimate of the
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*> reciprocal Skeel condition number of the matrix A after
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*> equilibration (if done). If this is less than the machine
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*> precision (in particular, if it is zero), the matrix is singular
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*> to working precision. Note that the error may still be small even
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*> if this number is very small and the matrix appears ill-
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*> conditioned.
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*> \endverbatim
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*>
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*> \param[out] BERR
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*> \verbatim
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*> BERR is DOUBLE PRECISION array, dimension (NRHS)
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*> Componentwise relative backward error. This is the
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*> componentwise relative backward error of each solution vector X(j)
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*> (i.e., the smallest relative change in any element of A or B that
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*> makes X(j) an exact solution).
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*> \endverbatim
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*>
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*> \param[in] N_ERR_BNDS
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*> \verbatim
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*> N_ERR_BNDS is INTEGER
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*> Number of error bounds to return for each right hand side
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*> and each type (normwise or componentwise). See ERR_BNDS_NORM and
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*> ERR_BNDS_COMP below.
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*> \endverbatim
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*>
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*> \param[out] ERR_BNDS_NORM
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*> \verbatim
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*> ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
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*> For each right-hand side, this array contains information about
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*> various error bounds and condition numbers corresponding to the
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*> normwise relative error, which is defined as follows:
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*>
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*> Normwise relative error in the ith solution vector:
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*> max_j (abs(XTRUE(j,i) - X(j,i)))
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*> ------------------------------
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*> max_j abs(X(j,i))
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*>
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*> The array is indexed by the type of error information as described
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*> below. There currently are up to three pieces of information
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*> returned.
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*>
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*> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
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*> right-hand side.
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*>
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*> The second index in ERR_BNDS_NORM(:,err) contains the following
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*> three fields:
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*> err = 1 "Trust/don't trust" boolean. Trust the answer if the
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*> reciprocal condition number is less than the threshold
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*> sqrt(n) * dlamch('Epsilon').
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*>
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*> err = 2 "Guaranteed" error bound: The estimated forward error,
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*> almost certainly within a factor of 10 of the true error
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*> so long as the next entry is greater than the threshold
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*> sqrt(n) * dlamch('Epsilon'). This error bound should only
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*> be trusted if the previous boolean is true.
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*>
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*> err = 3 Reciprocal condition number: Estimated normwise
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*> reciprocal condition number. Compared with the threshold
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*> sqrt(n) * dlamch('Epsilon') to determine if the error
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*> estimate is "guaranteed". These reciprocal condition
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*> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
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*> appropriately scaled matrix Z.
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*> Let Z = S*A, where S scales each row by a power of the
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*> radix so all absolute row sums of Z are approximately 1.
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*>
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*> See Lapack Working Note 165 for further details and extra
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*> cautions.
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*> \endverbatim
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*>
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*> \param[out] ERR_BNDS_COMP
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*> \verbatim
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*> ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
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*> For each right-hand side, this array contains information about
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*> various error bounds and condition numbers corresponding to the
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*> componentwise relative error, which is defined as follows:
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*>
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*> Componentwise relative error in the ith solution vector:
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*> abs(XTRUE(j,i) - X(j,i))
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*> max_j ----------------------
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*> abs(X(j,i))
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*>
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*> The array is indexed by the right-hand side i (on which the
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*> componentwise relative error depends), and the type of error
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*> information as described below. There currently are up to three
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*> pieces of information returned for each right-hand side. If
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*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
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*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
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*> the first (:,N_ERR_BNDS) entries are returned.
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*>
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*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
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*> right-hand side.
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*>
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*> The second index in ERR_BNDS_COMP(:,err) contains the following
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*> three fields:
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*> err = 1 "Trust/don't trust" boolean. Trust the answer if the
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*> reciprocal condition number is less than the threshold
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*> sqrt(n) * dlamch('Epsilon').
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*>
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*> err = 2 "Guaranteed" error bound: The estimated forward error,
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*> almost certainly within a factor of 10 of the true error
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*> so long as the next entry is greater than the threshold
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*> sqrt(n) * dlamch('Epsilon'). This error bound should only
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*> be trusted if the previous boolean is true.
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*>
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*> err = 3 Reciprocal condition number: Estimated componentwise
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*> reciprocal condition number. Compared with the threshold
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*> sqrt(n) * dlamch('Epsilon') to determine if the error
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*> estimate is "guaranteed". These reciprocal condition
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*> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
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*> appropriately scaled matrix Z.
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*> Let Z = S*(A*diag(x)), where x is the solution for the
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*> current right-hand side and S scales each row of
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*> A*diag(x) by a power of the radix so all absolute row
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*> sums of Z are approximately 1.
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*>
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*> See Lapack Working Note 165 for further details and extra
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*> cautions.
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*> \endverbatim
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*>
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*> \param[in] NPARAMS
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*> \verbatim
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*> NPARAMS is INTEGER
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*> Specifies the number of parameters set in PARAMS. If .LE. 0, the
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*> PARAMS array is never referenced and default values are used.
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*> \endverbatim
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*>
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*> \param[in,out] PARAMS
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*> \verbatim
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*> PARAMS is DOUBLE PRECISION array, dimension (NPARAMS)
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*> Specifies algorithm parameters. If an entry is .LT. 0.0, then
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*> that entry will be filled with default value used for that
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*> parameter. Only positions up to NPARAMS are accessed; defaults
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*> are used for higher-numbered parameters.
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*>
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*> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
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*> refinement or not.
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*> Default: 1.0D+0
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*> = 0.0 : No refinement is performed, and no error bounds are
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*> computed.
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*> = 1.0 : Use the double-precision refinement algorithm,
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*> possibly with doubled-single computations if the
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*> compilation environment does not support DOUBLE
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*> PRECISION.
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*> (other values are reserved for future use)
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*>
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*> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
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*> computations allowed for refinement.
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*> Default: 10
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*> Aggressive: Set to 100 to permit convergence using approximate
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*> factorizations or factorizations other than LU. If
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*> the factorization uses a technique other than
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*> Gaussian elimination, the guarantees in
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*> err_bnds_norm and err_bnds_comp may no longer be
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*> trustworthy.
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*>
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*> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
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*> will attempt to find a solution with small componentwise
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*> relative error in the double-precision algorithm. Positive
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*> is true, 0.0 is false.
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*> Default: 1.0 (attempt componentwise convergence)
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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 DOUBLE PRECISION array, dimension (4*N)
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*> \endverbatim
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*>
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*> \param[out] IWORK
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*> \verbatim
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*> IWORK is INTEGER array, dimension (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. The solution to every right-hand side is
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*> guaranteed.
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*> < 0: If INFO = -i, the i-th argument had an illegal value
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*> > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization
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*> has been completed, but the factor U is exactly singular, so
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*> the solution and error bounds could not be computed. RCOND = 0
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*> is returned.
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*> = N+J: The solution corresponding to the Jth right-hand side is
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*> not guaranteed. The solutions corresponding to other right-
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*> hand sides K with K > J may not be guaranteed as well, but
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*> only the first such right-hand side is reported. If a small
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*> componentwise error is not requested (PARAMS(3) = 0.0) then
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*> the Jth right-hand side is the first with a normwise error
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*> bound that is not guaranteed (the smallest J such
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*> that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
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*> the Jth right-hand side is the first with either a normwise or
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*> componentwise error bound that is not guaranteed (the smallest
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*> J such that either ERR_BNDS_NORM(J,1) = 0.0 or
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*> ERR_BNDS_COMP(J,1) = 0.0). See the definition of
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*> ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
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*> about all of the right-hand sides check ERR_BNDS_NORM or
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*> ERR_BNDS_COMP.
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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 doubleGEcomputational
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*
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* =====================================================================
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SUBROUTINE DGERFSX( TRANS, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
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$ R, C, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
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$ ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
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$ WORK, IWORK, INFO )
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*
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* -- LAPACK computational routine (version 3.4.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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CHARACTER TRANS, EQUED
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INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
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$ N_ERR_BNDS
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DOUBLE PRECISION RCOND
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * ), IWORK( * )
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DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
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$ X( LDX , * ), WORK( * )
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DOUBLE PRECISION R( * ), C( * ), PARAMS( * ), BERR( * ),
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$ ERR_BNDS_NORM( NRHS, * ),
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$ ERR_BNDS_COMP( NRHS, * )
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* ..
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*
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* ==================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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DOUBLE PRECISION ITREF_DEFAULT, ITHRESH_DEFAULT
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DOUBLE PRECISION COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT
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DOUBLE PRECISION DZTHRESH_DEFAULT
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PARAMETER ( ITREF_DEFAULT = 1.0D+0 )
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PARAMETER ( ITHRESH_DEFAULT = 10.0D+0 )
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PARAMETER ( COMPONENTWISE_DEFAULT = 1.0D+0 )
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PARAMETER ( RTHRESH_DEFAULT = 0.5D+0 )
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PARAMETER ( DZTHRESH_DEFAULT = 0.25D+0 )
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INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
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$ LA_LINRX_CWISE_I
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PARAMETER ( LA_LINRX_ITREF_I = 1,
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$ LA_LINRX_ITHRESH_I = 2 )
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PARAMETER ( LA_LINRX_CWISE_I = 3 )
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INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
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$ LA_LINRX_RCOND_I
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PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
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PARAMETER ( LA_LINRX_RCOND_I = 3 )
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* ..
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* .. Local Scalars ..
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CHARACTER(1) NORM
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LOGICAL ROWEQU, COLEQU, NOTRAN
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INTEGER J, TRANS_TYPE, PREC_TYPE, REF_TYPE
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INTEGER N_NORMS
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DOUBLE PRECISION ANORM, RCOND_TMP
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DOUBLE PRECISION ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
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LOGICAL IGNORE_CWISE
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INTEGER ITHRESH
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DOUBLE PRECISION RTHRESH, UNSTABLE_THRESH
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, DGECON, DLA_GERFSX_EXTENDED
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, SQRT
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* ..
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* .. External Functions ..
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EXTERNAL LSAME, BLAS_FPINFO_X, ILATRANS, ILAPREC
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EXTERNAL DLAMCH, DLANGE, DLA_GERCOND
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DOUBLE PRECISION DLAMCH, DLANGE, DLA_GERCOND
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LOGICAL LSAME
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INTEGER BLAS_FPINFO_X
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INTEGER ILATRANS, ILAPREC
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* ..
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* .. Executable Statements ..
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*
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* Check the input parameters.
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*
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INFO = 0
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TRANS_TYPE = ILATRANS( TRANS )
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REF_TYPE = INT( ITREF_DEFAULT )
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IF ( NPARAMS .GE. LA_LINRX_ITREF_I ) THEN
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IF ( PARAMS( LA_LINRX_ITREF_I ) .LT. 0.0D+0 ) THEN
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PARAMS( LA_LINRX_ITREF_I ) = ITREF_DEFAULT
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ELSE
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REF_TYPE = PARAMS( LA_LINRX_ITREF_I )
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END IF
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END IF
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*
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* Set default parameters.
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*
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ILLRCOND_THRESH = DBLE( N ) * DLAMCH( 'Epsilon' )
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ITHRESH = INT( ITHRESH_DEFAULT )
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RTHRESH = RTHRESH_DEFAULT
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UNSTABLE_THRESH = DZTHRESH_DEFAULT
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IGNORE_CWISE = COMPONENTWISE_DEFAULT .EQ. 0.0D+0
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*
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IF ( NPARAMS.GE.LA_LINRX_ITHRESH_I ) THEN
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IF ( PARAMS( LA_LINRX_ITHRESH_I ).LT.0.0D+0 ) THEN
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PARAMS( LA_LINRX_ITHRESH_I ) = ITHRESH
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ELSE
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ITHRESH = INT( PARAMS( LA_LINRX_ITHRESH_I ) )
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END IF
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END IF
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IF ( NPARAMS.GE.LA_LINRX_CWISE_I ) THEN
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IF ( PARAMS( LA_LINRX_CWISE_I ).LT.0.0D+0 ) THEN
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IF ( IGNORE_CWISE ) THEN
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PARAMS( LA_LINRX_CWISE_I ) = 0.0D+0
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ELSE
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PARAMS( LA_LINRX_CWISE_I ) = 1.0D+0
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END IF
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ELSE
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IGNORE_CWISE = PARAMS( LA_LINRX_CWISE_I ) .EQ. 0.0D+0
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END IF
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END IF
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IF ( REF_TYPE .EQ. 0 .OR. N_ERR_BNDS .EQ. 0 ) THEN
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N_NORMS = 0
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ELSE IF ( IGNORE_CWISE ) THEN
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N_NORMS = 1
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ELSE
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N_NORMS = 2
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END IF
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*
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NOTRAN = LSAME( TRANS, 'N' )
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ROWEQU = LSAME( EQUED, 'R' ) .OR. LSAME( EQUED, 'B' )
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COLEQU = LSAME( EQUED, 'C' ) .OR. LSAME( EQUED, 'B' )
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*
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* Test input parameters.
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*
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IF( TRANS_TYPE.EQ.-1 ) THEN
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INFO = -1
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ELSE IF( .NOT.ROWEQU .AND. .NOT.COLEQU .AND.
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$ .NOT.LSAME( EQUED, 'N' ) ) THEN
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INFO = -2
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ELSE IF( N.LT.0 ) THEN
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INFO = -3
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ELSE IF( NRHS.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -6
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ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
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INFO = -8
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -13
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ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
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INFO = -15
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DGERFSX', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible.
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*
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IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN
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RCOND = 1.0D+0
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DO J = 1, NRHS
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BERR( J ) = 0.0D+0
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IF ( N_ERR_BNDS .GE. 1 ) THEN
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ERR_BNDS_NORM( J, LA_LINRX_TRUST_I) = 1.0D+0
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ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
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END IF
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IF ( N_ERR_BNDS .GE. 2 ) THEN
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ERR_BNDS_NORM( J, LA_LINRX_ERR_I) = 0.0D+0
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ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 0.0D+0
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END IF
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IF ( N_ERR_BNDS .GE. 3 ) THEN
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ERR_BNDS_NORM( J, LA_LINRX_RCOND_I) = 1.0D+0
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ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 1.0D+0
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END IF
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END DO
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RETURN
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END IF
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*
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* Default to failure.
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*
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RCOND = 0.0D+0
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DO J = 1, NRHS
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BERR( J ) = 1.0D+0
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IF ( N_ERR_BNDS .GE. 1 ) THEN
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ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
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ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
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END IF
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IF ( N_ERR_BNDS .GE. 2 ) THEN
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ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
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ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
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END IF
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IF ( N_ERR_BNDS .GE. 3 ) THEN
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ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 0.0D+0
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ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 0.0D+0
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END IF
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END DO
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*
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* Compute the norm of A and the reciprocal of the condition
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* number of A.
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*
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IF( NOTRAN ) THEN
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NORM = 'I'
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ELSE
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NORM = '1'
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END IF
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ANORM = DLANGE( NORM, N, N, A, LDA, WORK )
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CALL DGECON( NORM, N, AF, LDAF, ANORM, RCOND, WORK, IWORK, INFO )
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*
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* Perform refinement on each right-hand side
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*
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IF ( REF_TYPE .NE. 0 ) THEN
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PREC_TYPE = ILAPREC( 'E' )
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IF ( NOTRAN ) THEN
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CALL DLA_GERFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N,
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$ NRHS, A, LDA, AF, LDAF, IPIV, COLEQU, C, B,
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$ LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM,
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$ ERR_BNDS_COMP, WORK(N+1), WORK(1), WORK(2*N+1),
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$ WORK(1), RCOND, ITHRESH, RTHRESH, UNSTABLE_THRESH,
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$ IGNORE_CWISE, INFO )
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ELSE
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CALL DLA_GERFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N,
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$ NRHS, A, LDA, AF, LDAF, IPIV, ROWEQU, R, B,
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$ LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM,
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$ ERR_BNDS_COMP, WORK(N+1), WORK(1), WORK(2*N+1),
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$ WORK(1), RCOND, ITHRESH, RTHRESH, UNSTABLE_THRESH,
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$ IGNORE_CWISE, INFO )
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END IF
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END IF
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ERR_LBND = MAX( 10.0D+0, SQRT( DBLE( N ) ) ) * DLAMCH( 'Epsilon' )
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IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 1 ) THEN
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*
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* Compute scaled normwise condition number cond(A*C).
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*
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IF ( COLEQU .AND. NOTRAN ) THEN
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RCOND_TMP = DLA_GERCOND( TRANS, N, A, LDA, AF, LDAF, IPIV,
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$ -1, C, INFO, WORK, IWORK )
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ELSE IF ( ROWEQU .AND. .NOT. NOTRAN ) THEN
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RCOND_TMP = DLA_GERCOND( TRANS, N, A, LDA, AF, LDAF, IPIV,
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$ -1, R, INFO, WORK, IWORK )
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ELSE
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RCOND_TMP = DLA_GERCOND( TRANS, N, A, LDA, AF, LDAF, IPIV,
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$ 0, R, INFO, WORK, IWORK )
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END IF
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DO J = 1, NRHS
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*
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* Cap the error at 1.0.
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*
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IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
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$ .AND. ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 )
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$ ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
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*
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* Threshold the error (see LAWN).
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*
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IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN
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ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
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ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 0.0D+0
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IF ( INFO .LE. N ) INFO = N + J
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ELSE IF ( ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .LT. ERR_LBND )
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$ THEN
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ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = ERR_LBND
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ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
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END IF
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*
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* Save the condition number.
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*
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IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
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ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = RCOND_TMP
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END IF
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END DO
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END IF
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IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 2 ) THEN
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*
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* Compute componentwise condition number cond(A*diag(Y(:,J))) for
|
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* each right-hand side using the current solution as an estimate of
|
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* the true solution. If the componentwise error estimate is too
|
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* large, then the solution is a lousy estimate of truth and the
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* estimated RCOND may be too optimistic. To avoid misleading users,
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* the inverse condition number is set to 0.0 when the estimated
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* cwise error is at least CWISE_WRONG.
|
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*
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CWISE_WRONG = SQRT( DLAMCH( 'Epsilon' ) )
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DO J = 1, NRHS
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IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .LT. CWISE_WRONG )
|
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$ THEN
|
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RCOND_TMP = DLA_GERCOND( TRANS, N, A, LDA, AF, LDAF,
|
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$ IPIV, 1, X(1,J), INFO, WORK, IWORK )
|
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ELSE
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RCOND_TMP = 0.0D+0
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END IF
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*
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* Cap the error at 1.0.
|
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*
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IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
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$ .AND. ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 )
|
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$ ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
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*
|
|
* Threshold the error (see LAWN).
|
|
*
|
|
IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN
|
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ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
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ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 0.0D+0
|
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IF ( PARAMS( LA_LINRX_CWISE_I ) .EQ. 1.0D+0
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$ .AND. INFO.LT.N + J ) INFO = N + J
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ELSE IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I )
|
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$ .LT. ERR_LBND ) THEN
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ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = ERR_LBND
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ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
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END IF
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*
|
|
* Save the condition number.
|
|
*
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|
IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
|
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ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = RCOND_TMP
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END IF
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END DO
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END IF
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*
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RETURN
|
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*
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* End of DGERFSX
|
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*
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END
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