zgerfsx()

subroutine zgerfsx	(	character	trans,
		character	equed,
		integer	n,
		integer	nrhs,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		complex*16, dimension( ldaf, * )	af,
		integer	ldaf,
		integer, dimension( * )	ipiv,
		double precision, dimension( * )	r,
		double precision, dimension( * )	c,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		complex*16, dimension( ldx , * )	x,
		integer	ldx,
		double precision	rcond,
		double precision, dimension( * )	berr,
		integer	n_err_bnds,
		double precision, dimension( nrhs, * )	err_bnds_norm,
		double precision, dimension( nrhs, * )	err_bnds_comp,
		integer	nparams,
		double precision, dimension( * )	params,
		complex*16, dimension( * )	work,
		double precision, dimension( * )	rwork,
		integer	info )

ZGERFSX

Download ZGERFSX + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!>    ZGERFSX improves the computed solution to a system of linear
!>    equations and provides error bounds and backward error estimates
!>    for the solution.  In addition to normwise error bound, the code
!>    provides maximum componentwise error bound if possible.  See
!>    comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the
!>    error bounds.
!>
!>    The original system of linear equations may have been equilibrated
!>    before calling this routine, as described by arguments EQUED, R
!>    and C below. In this case, the solution and error bounds returned
!>    are for the original unequilibrated system.
!> 

!>     Some optional parameters are bundled in the PARAMS array.  These
!>     settings determine how refinement is performed, but often the
!>     defaults are acceptable.  If the defaults are acceptable, users
!>     can pass NPARAMS = 0 which prevents the source code from accessing
!>     the PARAMS argument.
!> 

Parameters

[in]	TRANS	!> TRANS is CHARACTER*1 !> Specifies the form of the system of equations: !> = 'N': A * X = B (No transpose) !> = 'T': A**T * X = B (Transpose) !> = 'C': A**H * X = B (Conjugate transpose) !>
[in]	EQUED	!> EQUED is CHARACTER*1 !> Specifies the form of equilibration that was done to A !> before calling this routine. This is needed to compute !> the solution and error bounds correctly. !> = 'N': No equilibration !> = 'R': Row equilibration, i.e., A has been premultiplied by !> diag(R). !> = 'C': Column equilibration, i.e., A has been postmultiplied !> by diag(C). !> = 'B': Both row and column equilibration, i.e., A has been !> replaced by diag(R) * A * diag(C). !> The right hand side B has been changed accordingly. !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	NRHS	!> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrices B and X. NRHS >= 0. !>
[in]	A	!> A is COMPLEX*16 array, dimension (LDA,N) !> The original N-by-N matrix A. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[in]	AF	!> AF is COMPLEX*16 array, dimension (LDAF,N) !> The factors L and U from the factorization A = P*L*U !> as computed by ZGETRF. !>
[in]	LDAF	!> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !>
[in]	IPIV	!> IPIV is INTEGER array, dimension (N) !> The pivot indices from ZGETRF; for 1<=i<=N, row i of the !> matrix was interchanged with row IPIV(i). !>
[in]	R	!> R is DOUBLE PRECISION array, dimension (N) !> The row scale factors for A. If EQUED = 'R' or 'B', A is !> multiplied on the left by diag(R); if EQUED = 'N' or 'C', R !> is not accessed. !> If R is accessed, each element of R should be a power of the radix !> to ensure a reliable solution and error estimates. Scaling by !> powers of the radix does not cause rounding errors unless the !> result underflows or overflows. Rounding errors during scaling !> lead to refining with a matrix that is not equivalent to the !> input matrix, producing error estimates that may not be !> reliable. !>
[in]	C	!> C is DOUBLE PRECISION array, dimension (N) !> The column scale factors for A. If EQUED = 'C' or 'B', A is !> multiplied on the right by diag(C); if EQUED = 'N' or 'R', C !> is not accessed. !> If C is accessed, each element of C should be a power of the radix !> to ensure a reliable solution and error estimates. Scaling by !> powers of the radix does not cause rounding errors unless the !> result underflows or overflows. Rounding errors during scaling !> lead to refining with a matrix that is not equivalent to the !> input matrix, producing error estimates that may not be !> reliable. !>
[in]	B	!> B is COMPLEX*16 array, dimension (LDB,NRHS) !> The right hand side matrix B. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>
[in,out]	X	!> X is COMPLEX*16 array, dimension (LDX,NRHS) !> On entry, the solution matrix X, as computed by ZGETRS. !> On exit, the improved solution matrix X. !>
[in]	LDX	!> LDX is INTEGER !> The leading dimension of the array X. LDX >= max(1,N). !>
[out]	RCOND	!> RCOND is DOUBLE PRECISION !> Reciprocal scaled condition number. This is an estimate of the !> reciprocal Skeel condition number of the matrix A after !> equilibration (if done). If this is less than the machine !> precision (in particular, if it is zero), the matrix is singular !> to working precision. Note that the error may still be small even !> if this number is very small and the matrix appears ill- !> conditioned. !>
[out]	BERR	!> BERR is DOUBLE PRECISION array, dimension (NRHS) !> Componentwise relative backward error. This is the !> componentwise relative backward error of each solution vector X(j) !> (i.e., the smallest relative change in any element of A or B that !> makes X(j) an exact solution). !>
[in]	N_ERR_BNDS	!> N_ERR_BNDS is INTEGER !> Number of error bounds to return for each right hand side !> and each type (normwise or componentwise). See ERR_BNDS_NORM and !> ERR_BNDS_COMP below. !>
[out]	ERR_BNDS_NORM	!> ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) !> For each right-hand side, this array contains information about !> various error bounds and condition numbers corresponding to the !> normwise relative error, which is defined as follows: !> !> Normwise relative error in the ith solution vector: !> max_j (abs(XTRUE(j,i) - X(j,i))) !> ------------------------------ !> max_j abs(X(j,i)) !> !> The array is indexed by the type of error information as described !> below. There currently are up to three pieces of information !> returned. !> !> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith !> right-hand side. !> !> The second index in ERR_BNDS_NORM(:,err) contains the following !> three fields: !> err = 1 boolean. Trust the answer if the !> reciprocal condition number is less than the threshold !> sqrt(n) * dlamch('Epsilon'). !> !> err = 2 error bound: The estimated forward error, !> almost certainly within a factor of 10 of the true error !> so long as the next entry is greater than the threshold !> sqrt(n) * dlamch('Epsilon'). This error bound should only !> be trusted if the previous boolean is true. !> !> err = 3 Reciprocal condition number: Estimated normwise !> reciprocal condition number. Compared with the threshold !> sqrt(n) * dlamch('Epsilon') to determine if the error !> estimate is . These reciprocal condition !> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some !> appropriately scaled matrix Z. !> Let Z = S*A, where S scales each row by a power of the !> radix so all absolute row sums of Z are approximately 1. !> !> See Lapack Working Note 165 for further details and extra !> cautions. !>
[out]	ERR_BNDS_COMP	!> ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) !> For each right-hand side, this array contains information about !> various error bounds and condition numbers corresponding to the !> componentwise relative error, which is defined as follows: !> !> Componentwise relative error in the ith solution vector: !> abs(XTRUE(j,i) - X(j,i)) !> max_j ---------------------- !> abs(X(j,i)) !> !> The array is indexed by the right-hand side i (on which the !> componentwise relative error depends), and the type of error !> information as described below. There currently are up to three !> pieces of information returned for each right-hand side. If !> componentwise accuracy is not requested (PARAMS(3) = 0.0), then !> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most !> the first (:,N_ERR_BNDS) entries are returned. !> !> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith !> right-hand side. !> !> The second index in ERR_BNDS_COMP(:,err) contains the following !> three fields: !> err = 1 boolean. Trust the answer if the !> reciprocal condition number is less than the threshold !> sqrt(n) * dlamch('Epsilon'). !> !> err = 2 error bound: The estimated forward error, !> almost certainly within a factor of 10 of the true error !> so long as the next entry is greater than the threshold !> sqrt(n) * dlamch('Epsilon'). This error bound should only !> be trusted if the previous boolean is true. !> !> err = 3 Reciprocal condition number: Estimated componentwise !> reciprocal condition number. Compared with the threshold !> sqrt(n) * dlamch('Epsilon') to determine if the error !> estimate is . These reciprocal condition !> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some !> appropriately scaled matrix Z. !> Let Z = S*(A*diag(x)), where x is the solution for the !> current right-hand side and S scales each row of !> A*diag(x) by a power of the radix so all absolute row !> sums of Z are approximately 1. !> !> See Lapack Working Note 165 for further details and extra !> cautions. !>
[in]	NPARAMS	!> NPARAMS is INTEGER !> Specifies the number of parameters set in PARAMS. If <= 0, the !> PARAMS array is never referenced and default values are used. !>
[in,out]	PARAMS	!> PARAMS is DOUBLE PRECISION array, dimension NPARAMS !> Specifies algorithm parameters. If an entry is < 0.0, then !> that entry will be filled with default value used for that !> parameter. Only positions up to NPARAMS are accessed; defaults !> are used for higher-numbered parameters. !> !> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative !> refinement or not. !> Default: 1.0D+0 !> = 0.0: No refinement is performed, and no error bounds are !> computed. !> = 1.0: Use the double-precision refinement algorithm, !> possibly with doubled-single computations if the !> compilation environment does not support DOUBLE !> PRECISION. !> (other values are reserved for future use) !> !> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual !> computations allowed for refinement. !> Default: 10 !> Aggressive: Set to 100 to permit convergence using approximate !> factorizations or factorizations other than LU. If !> the factorization uses a technique other than !> Gaussian elimination, the guarantees in !> err_bnds_norm and err_bnds_comp may no longer be !> trustworthy. !> !> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code !> will attempt to find a solution with small componentwise !> relative error in the double-precision algorithm. Positive !> is true, 0.0 is false. !> Default: 1.0 (attempt componentwise convergence) !>
[out]	WORK	!> WORK is COMPLEX*16 array, dimension (2*N) !>
[out]	RWORK	!> RWORK is DOUBLE PRECISION array, dimension (2*N) !>
[out]	INFO	!> INFO is INTEGER !> = 0: Successful exit. The solution to every right-hand side is !> guaranteed. !> < 0: If INFO = -i, the i-th argument had an illegal value !> > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization !> has been completed, but the factor U is exactly singular, so !> the solution and error bounds could not be computed. RCOND = 0 !> is returned. !> = N+J: The solution corresponding to the Jth right-hand side is !> not guaranteed. The solutions corresponding to other right- !> hand sides K with K > J may not be guaranteed as well, but !> only the first such right-hand side is reported. If a small !> componentwise error is not requested (PARAMS(3) = 0.0) then !> the Jth right-hand side is the first with a normwise error !> bound that is not guaranteed (the smallest J such !> that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) !> the Jth right-hand side is the first with either a normwise or !> componentwise error bound that is not guaranteed (the smallest !> J such that either ERR_BNDS_NORM(J,1) = 0.0 or !> ERR_BNDS_COMP(J,1) = 0.0). See the definition of !> ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information !> about all of the right-hand sides check ERR_BNDS_NORM or !> ERR_BNDS_COMP. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 408 of file zgerfsx.f.

*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          TRANS, EQUED
      INTEGER            INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
     $                   N_ERR_BNDS
      DOUBLE PRECISION   RCOND
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      COMPLEX*16         A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
     $                   X( LDX , * ), WORK( * )
      DOUBLE PRECISION   R( * ), C( * ), PARAMS( * ), BERR( * ),
     $                   ERR_BNDS_NORM( NRHS, * ),
     $                   ERR_BNDS_COMP( NRHS, * ), RWORK( * )
*     ..
*
*  ==================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
      DOUBLE PRECISION   ITREF_DEFAULT, ITHRESH_DEFAULT
      DOUBLE PRECISION   COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT
      DOUBLE PRECISION   DZTHRESH_DEFAULT
      parameter( itref_default = 1.0d+0 )
      parameter( ithresh_default = 10.0d+0 )
      parameter( componentwise_default = 1.0d+0 )
      parameter( rthresh_default = 0.5d+0 )
      parameter( dzthresh_default = 0.25d+0 )
      INTEGER            LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
     $                   LA_LINRX_CWISE_I
      parameter( la_linrx_itref_i = 1,
     $                   la_linrx_ithresh_i = 2 )
      parameter( la_linrx_cwise_i = 3 )
      INTEGER            LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
     $                   LA_LINRX_RCOND_I
      parameter( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
      parameter( la_linrx_rcond_i = 3 )
*     ..
*     .. Local Scalars ..
      CHARACTER(1)       NORM
      LOGICAL            ROWEQU, COLEQU, NOTRAN
      INTEGER            J, TRANS_TYPE, PREC_TYPE, REF_TYPE
      INTEGER            N_NORMS
      DOUBLE PRECISION   ANORM, RCOND_TMP
      DOUBLE PRECISION   ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
      LOGICAL            IGNORE_CWISE
      INTEGER            ITHRESH
      DOUBLE PRECISION   RTHRESH, UNSTABLE_THRESH
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, zgecon, zla_gerfsx_extended
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, sqrt, transfer
*     ..
*     .. External Functions ..
      EXTERNAL           lsame, ilatrans, ilaprec
      EXTERNAL           dlamch, zlange, zla_gercond_x,
     $                   zla_gercond_c
      DOUBLE PRECISION   DLAMCH, ZLANGE, ZLA_GERCOND_X, ZLA_GERCOND_C
      LOGICAL            LSAME
      INTEGER            ILATRANS, ILAPREC
*     ..
*     .. Executable Statements ..
*
*     Check the input parameters.
*
      info = 0
      trans_type = ilatrans( trans )
      ref_type = int( itref_default )
      IF ( nparams .GE. la_linrx_itref_i ) THEN
         IF ( params( la_linrx_itref_i ) .LT. 0.0d+0 ) THEN
            params( la_linrx_itref_i ) = itref_default
         ELSE
            ref_type = params( la_linrx_itref_i )
         END IF
      END IF
*
*     Set default parameters.
*
      illrcond_thresh = dble( n ) * dlamch( 'Epsilon' )
      ithresh = int( ithresh_default )
      rthresh = rthresh_default
      unstable_thresh = dzthresh_default
      ignore_cwise = componentwise_default .EQ. 0.0d+0
*
      IF ( nparams.GE.la_linrx_ithresh_i ) THEN
         IF ( params( la_linrx_ithresh_i ).LT.0.0d+0 ) THEN
            params(la_linrx_ithresh_i) = ithresh
         ELSE
            ithresh = int( params( la_linrx_ithresh_i ) )
         END IF
      END IF
      IF ( nparams.GE.la_linrx_cwise_i ) THEN
         IF ( params( la_linrx_cwise_i ).LT.0.0d+0 ) THEN
            IF ( ignore_cwise ) THEN
               params( la_linrx_cwise_i ) = 0.0d+0
            ELSE
               params( la_linrx_cwise_i ) = 1.0d+0
            END IF
         ELSE
            ignore_cwise = params( la_linrx_cwise_i ) .EQ. 0.0d+0
         END IF
      END IF
      IF ( ref_type .EQ. 0 .OR. n_err_bnds .EQ. 0 ) THEN
         n_norms = 0
      ELSE IF ( ignore_cwise ) THEN
         n_norms = 1
      ELSE
         n_norms = 2
      END IF
*
      notran = lsame( trans, 'N' )
      rowequ = lsame( equed, 'R' ) .OR. lsame( equed, 'B' )
      colequ = lsame( equed, 'C' ) .OR. lsame( equed, 'B' )
*
*     Test input parameters.
*
      IF( trans_type.EQ.-1 ) THEN
        info = -1
      ELSE IF( .NOT.rowequ .AND. .NOT.colequ .AND.
     $         .NOT.lsame( equed, 'N' ) ) THEN
        info = -2
      ELSE IF( n.LT.0 ) THEN
        info = -3
      ELSE IF( nrhs.LT.0 ) THEN
        info = -4
      ELSE IF( lda.LT.max( 1, n ) ) THEN
        info = -6
      ELSE IF( ldaf.LT.max( 1, n ) ) THEN
        info = -8
      ELSE IF( ldb.LT.max( 1, n ) ) THEN
        info = -13
      ELSE IF( ldx.LT.max( 1, n ) ) THEN
        info = -15
      END IF
      IF( info.NE.0 ) THEN
        CALL xerbla( 'ZGERFSX', -info )
        RETURN
      END IF
*
*     Quick return if possible.
*
      IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
         rcond = 1.0d+0
         DO j = 1, nrhs
            berr( j ) = 0.0d+0
            IF ( n_err_bnds .GE. 1 ) THEN
               err_bnds_norm( j, la_linrx_trust_i ) =  1.0d+0
               err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
            END IF
            IF ( n_err_bnds .GE. 2 ) THEN
               err_bnds_norm( j, la_linrx_err_i ) = 0.0d+0
               err_bnds_comp( j, la_linrx_err_i ) = 0.0d+0
            END IF
            IF ( n_err_bnds .GE. 3 ) THEN
               err_bnds_norm( j, la_linrx_rcond_i ) = 1.0d+0
               err_bnds_comp( j, la_linrx_rcond_i ) = 1.0d+0
            END IF
         END DO
         RETURN
      END IF
*
*     Default to failure.
*
      rcond = 0.0d+0
      DO j = 1, nrhs
         berr( j ) = 1.0d+0
         IF ( n_err_bnds .GE. 1 ) THEN
            err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
            err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
         END IF
         IF ( n_err_bnds .GE. 2 ) THEN
            err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
            err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
         END IF
         IF ( n_err_bnds .GE. 3 ) THEN
            err_bnds_norm( j, la_linrx_rcond_i ) = 0.0d+0
            err_bnds_comp( j, la_linrx_rcond_i ) = 0.0d+0
         END IF
      END DO
*
*     Compute the norm of A and the reciprocal of the condition
*     number of A.
*
      IF( notran ) THEN
         norm = 'I'
      ELSE
         norm = '1'
      END IF
      anorm = zlange( norm, n, n, a, lda, rwork )
      CALL zgecon( norm, n, af, ldaf, anorm, rcond, work, rwork,
     $             info )
*
*     Perform refinement on each right-hand side
*
      IF ( ref_type .NE. 0 ) THEN
 
         prec_type = ilaprec( 'E' )
 
         IF ( notran ) THEN
            CALL zla_gerfsx_extended( prec_type, trans_type,  n,
     $           nrhs, a, lda, af, ldaf, ipiv, colequ, c, b,
     $           ldb, x, ldx, berr, n_norms, err_bnds_norm,
     $           err_bnds_comp, work, rwork, work(n+1),
     $           transfer(rwork(1:2*n), (/ (zero, zero) /), n),
     $           rcond, ithresh, rthresh, unstable_thresh, ignore_cwise,
     $           info )
         ELSE
            CALL zla_gerfsx_extended( prec_type, trans_type,  n,
     $           nrhs, a, lda, af, ldaf, ipiv, rowequ, r, b,
     $           ldb, x, ldx, berr, n_norms, err_bnds_norm,
     $           err_bnds_comp, work, rwork, work(n+1),
     $           transfer(rwork(1:2*n), (/ (zero, zero) /), n),
     $           rcond, ithresh, rthresh, unstable_thresh, ignore_cwise,
     $           info )
         END IF
      END IF
 
      err_lbnd = max( 10.0d+0,
     $                sqrt( dble( n ) ) ) * dlamch( 'Epsilon' )
      IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 1 ) THEN
*
*     Compute scaled normwise condition number cond(A*C).
*
         IF ( colequ .AND. notran ) THEN
            rcond_tmp = zla_gercond_c( trans, n, a, lda, af, ldaf,
     $                                 ipiv,
     $           c, .true., info, work, rwork )
         ELSE IF ( rowequ .AND. .NOT. notran ) THEN
            rcond_tmp = zla_gercond_c( trans, n, a, lda, af, ldaf,
     $                                 ipiv,
     $           r, .true., info, work, rwork )
         ELSE
            rcond_tmp = zla_gercond_c( trans, n, a, lda, af, ldaf,
     $                                 ipiv,
     $           c, .false., info, work, rwork )
         END IF
         DO j = 1, nrhs
*
*     Cap the error at 1.0.
*
            IF ( n_err_bnds .GE. la_linrx_err_i
     $           .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0d+0 )
     $           err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
*
*     Threshold the error (see LAWN).
*
            IF ( rcond_tmp .LT. illrcond_thresh ) THEN
               err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
               err_bnds_norm( j, la_linrx_trust_i ) = 0.0d+0
               IF ( info .LE. n ) info = n + j
            ELSE IF (err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd)
     $              THEN
               err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
               err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
            END IF
*
*     Save the condition number.
*
            IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
               err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
            END IF
         END DO
      END IF
 
      IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 2 ) THEN
*
*     Compute componentwise condition number cond(A*diag(Y(:,J))) for
*     each right-hand side using the current solution as an estimate of
*     the true solution.  If the componentwise error estimate is too
*     large, then the solution is a lousy estimate of truth and the
*     estimated RCOND may be too optimistic.  To avoid misleading users,
*     the inverse condition number is set to 0.0 when the estimated
*     cwise error is at least CWISE_WRONG.
*
         cwise_wrong = sqrt( dlamch( 'Epsilon' ) )
         DO j = 1, nrhs
            IF ( err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
     $     THEN
               rcond_tmp = zla_gercond_x( trans, n, a, lda, af, ldaf,
     $              ipiv, x(1,j), info, work, rwork )
            ELSE
               rcond_tmp = 0.0d+0
            END IF
*
*     Cap the error at 1.0.
*
            IF ( n_err_bnds .GE. la_linrx_err_i
     $           .AND. err_bnds_comp( j, la_linrx_err_i ) .GT. 1.0d+0 )
     $           err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
*
*     Threshold the error (see LAWN).
*
            IF ( rcond_tmp .LT. illrcond_thresh ) THEN
               err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
               err_bnds_comp( j, la_linrx_trust_i ) = 0.0d+0
               IF ( params( la_linrx_cwise_i ) .EQ. 1.0d+0
     $              .AND. info.LT.n + j ) info = n + j
            ELSE IF ( err_bnds_comp( j, la_linrx_err_i )
     $              .LT. err_lbnd ) THEN
               err_bnds_comp( j, la_linrx_err_i ) = err_lbnd
               err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
            END IF
*
*     Save the condition number.
*
            IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
               err_bnds_comp( j, la_linrx_rcond_i ) = rcond_tmp
            END IF
 
         END DO
      END IF
*
      RETURN
*
*     End of ZGERFSX
*

Here is the call graph for this function:

Here is the caller graph for this function: