LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dgerfsx()

subroutine dgerfsx ( character  TRANS,
character  EQUED,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldaf, * )  AF,
integer  LDAF,
integer, dimension( * )  IPIV,
double precision, dimension( * )  R,
double precision, dimension( * )  C,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, 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,
double precision, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  INFO 
)

DGERFSX

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Purpose:
    DGERFSX 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 = 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDAF,N)
     The factors L and U from the factorization A = P*L*U
     as computed by DGETRF.
[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 DGETRF; 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDX,NRHS)
     On entry, the solution matrix X, as computed by DGETRS.
     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 "Trust/don't trust" boolean. Trust the answer if the
              reciprocal condition number is less than the threshold
              sqrt(n) * dlamch('Epsilon').

     err = 2 "Guaranteed" 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 "guaranteed". 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 .LT. 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 "Trust/don't trust" boolean. Trust the answer if the
              reciprocal condition number is less than the threshold
              sqrt(n) * dlamch('Epsilon').

     err = 2 "Guaranteed" 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 "guaranteed". 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 .LE. 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 .LT. 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 DOUBLE PRECISION array, dimension (4*N)
[out]IWORK
          IWORK is INTEGER array, dimension (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.
Date
December 2016

Definition at line 416 of file dgerfsx.f.

416 *
417 * -- LAPACK computational routine (version 3.7.0) --
418 * -- LAPACK is a software package provided by Univ. of Tennessee, --
419 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
420 * December 2016
421 *
422 * .. Scalar Arguments ..
423  CHARACTER trans, equed
424  INTEGER info, lda, ldaf, ldb, ldx, n, nrhs, nparams,
425  $ n_err_bnds
426  DOUBLE PRECISION rcond
427 * ..
428 * .. Array Arguments ..
429  INTEGER ipiv( * ), iwork( * )
430  DOUBLE PRECISION a( lda, * ), af( ldaf, * ), b( ldb, * ),
431  $ x( ldx , * ), work( * )
432  DOUBLE PRECISION r( * ), c( * ), params( * ), berr( * ),
433  $ err_bnds_norm( nrhs, * ),
434  $ err_bnds_comp( nrhs, * )
435 * ..
436 *
437 * ==================================================================
438 *
439 * .. Parameters ..
440  DOUBLE PRECISION zero, one
441  parameter( zero = 0.0d+0, one = 1.0d+0 )
442  DOUBLE PRECISION itref_default, ithresh_default
443  DOUBLE PRECISION componentwise_default, rthresh_default
444  DOUBLE PRECISION dzthresh_default
445  parameter( itref_default = 1.0d+0 )
446  parameter( ithresh_default = 10.0d+0 )
447  parameter( componentwise_default = 1.0d+0 )
448  parameter( rthresh_default = 0.5d+0 )
449  parameter( dzthresh_default = 0.25d+0 )
450  INTEGER la_linrx_itref_i, la_linrx_ithresh_i,
451  $ la_linrx_cwise_i
452  parameter( la_linrx_itref_i = 1,
453  $ la_linrx_ithresh_i = 2 )
454  parameter( la_linrx_cwise_i = 3 )
455  INTEGER la_linrx_trust_i, la_linrx_err_i,
456  $ la_linrx_rcond_i
457  parameter( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
458  parameter( la_linrx_rcond_i = 3 )
459 * ..
460 * .. Local Scalars ..
461  CHARACTER(1) norm
462  LOGICAL rowequ, colequ, notran
463  INTEGER j, trans_type, prec_type, ref_type
464  INTEGER n_norms
465  DOUBLE PRECISION anorm, rcond_tmp
466  DOUBLE PRECISION illrcond_thresh, err_lbnd, cwise_wrong
467  LOGICAL ignore_cwise
468  INTEGER ithresh
469  DOUBLE PRECISION rthresh, unstable_thresh
470 * ..
471 * .. External Subroutines ..
473 * ..
474 * .. Intrinsic Functions ..
475  INTRINSIC max, sqrt
476 * ..
477 * .. External Functions ..
478  EXTERNAL lsame, ilatrans, ilaprec
479  EXTERNAL dlamch, dlange, dla_gercond
480  DOUBLE PRECISION dlamch, dlange, dla_gercond
481  LOGICAL lsame
482  INTEGER ilatrans, ilaprec
483 * ..
484 * .. Executable Statements ..
485 *
486 * Check the input parameters.
487 *
488  info = 0
489  trans_type = ilatrans( trans )
490  ref_type = int( itref_default )
491  IF ( nparams .GE. la_linrx_itref_i ) THEN
492  IF ( params( la_linrx_itref_i ) .LT. 0.0d+0 ) THEN
493  params( la_linrx_itref_i ) = itref_default
494  ELSE
495  ref_type = params( la_linrx_itref_i )
496  END IF
497  END IF
498 *
499 * Set default parameters.
500 *
501  illrcond_thresh = dble( n ) * dlamch( 'Epsilon' )
502  ithresh = int( ithresh_default )
503  rthresh = rthresh_default
504  unstable_thresh = dzthresh_default
505  ignore_cwise = componentwise_default .EQ. 0.0d+0
506 *
507  IF ( nparams.GE.la_linrx_ithresh_i ) THEN
508  IF ( params( la_linrx_ithresh_i ).LT.0.0d+0 ) THEN
509  params( la_linrx_ithresh_i ) = ithresh
510  ELSE
511  ithresh = int( params( la_linrx_ithresh_i ) )
512  END IF
513  END IF
514  IF ( nparams.GE.la_linrx_cwise_i ) THEN
515  IF ( params( la_linrx_cwise_i ).LT.0.0d+0 ) THEN
516  IF ( ignore_cwise ) THEN
517  params( la_linrx_cwise_i ) = 0.0d+0
518  ELSE
519  params( la_linrx_cwise_i ) = 1.0d+0
520  END IF
521  ELSE
522  ignore_cwise = params( la_linrx_cwise_i ) .EQ. 0.0d+0
523  END IF
524  END IF
525  IF ( ref_type .EQ. 0 .OR. n_err_bnds .EQ. 0 ) THEN
526  n_norms = 0
527  ELSE IF ( ignore_cwise ) THEN
528  n_norms = 1
529  ELSE
530  n_norms = 2
531  END IF
532 *
533  notran = lsame( trans, 'N' )
534  rowequ = lsame( equed, 'R' ) .OR. lsame( equed, 'B' )
535  colequ = lsame( equed, 'C' ) .OR. lsame( equed, 'B' )
536 *
537 * Test input parameters.
538 *
539  IF( trans_type.EQ.-1 ) THEN
540  info = -1
541  ELSE IF( .NOT.rowequ .AND. .NOT.colequ .AND.
542  $ .NOT.lsame( equed, 'N' ) ) THEN
543  info = -2
544  ELSE IF( n.LT.0 ) THEN
545  info = -3
546  ELSE IF( nrhs.LT.0 ) THEN
547  info = -4
548  ELSE IF( lda.LT.max( 1, n ) ) THEN
549  info = -6
550  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
551  info = -8
552  ELSE IF( ldb.LT.max( 1, n ) ) THEN
553  info = -13
554  ELSE IF( ldx.LT.max( 1, n ) ) THEN
555  info = -15
556  END IF
557  IF( info.NE.0 ) THEN
558  CALL xerbla( 'DGERFSX', -info )
559  RETURN
560  END IF
561 *
562 * Quick return if possible.
563 *
564  IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
565  rcond = 1.0d+0
566  DO j = 1, nrhs
567  berr( j ) = 0.0d+0
568  IF ( n_err_bnds .GE. 1 ) THEN
569  err_bnds_norm( j, la_linrx_trust_i) = 1.0d+0
570  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
571  END IF
572  IF ( n_err_bnds .GE. 2 ) THEN
573  err_bnds_norm( j, la_linrx_err_i) = 0.0d+0
574  err_bnds_comp( j, la_linrx_err_i ) = 0.0d+0
575  END IF
576  IF ( n_err_bnds .GE. 3 ) THEN
577  err_bnds_norm( j, la_linrx_rcond_i) = 1.0d+0
578  err_bnds_comp( j, la_linrx_rcond_i ) = 1.0d+0
579  END IF
580  END DO
581  RETURN
582  END IF
583 *
584 * Default to failure.
585 *
586  rcond = 0.0d+0
587  DO j = 1, nrhs
588  berr( j ) = 1.0d+0
589  IF ( n_err_bnds .GE. 1 ) THEN
590  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
591  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
592  END IF
593  IF ( n_err_bnds .GE. 2 ) THEN
594  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
595  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
596  END IF
597  IF ( n_err_bnds .GE. 3 ) THEN
598  err_bnds_norm( j, la_linrx_rcond_i ) = 0.0d+0
599  err_bnds_comp( j, la_linrx_rcond_i ) = 0.0d+0
600  END IF
601  END DO
602 *
603 * Compute the norm of A and the reciprocal of the condition
604 * number of A.
605 *
606  IF( notran ) THEN
607  norm = 'I'
608  ELSE
609  norm = '1'
610  END IF
611  anorm = dlange( norm, n, n, a, lda, work )
612  CALL dgecon( norm, n, af, ldaf, anorm, rcond, work, iwork, info )
613 *
614 * Perform refinement on each right-hand side
615 *
616  IF ( ref_type .NE. 0 ) THEN
617 
618  prec_type = ilaprec( 'E' )
619 
620  IF ( notran ) THEN
621  CALL dla_gerfsx_extended( prec_type, trans_type, n,
622  $ nrhs, a, lda, af, ldaf, ipiv, colequ, c, b,
623  $ ldb, x, ldx, berr, n_norms, err_bnds_norm,
624  $ err_bnds_comp, work(n+1), work(1), work(2*n+1),
625  $ work(1), rcond, ithresh, rthresh, unstable_thresh,
626  $ ignore_cwise, info )
627  ELSE
628  CALL dla_gerfsx_extended( prec_type, trans_type, n,
629  $ nrhs, a, lda, af, ldaf, ipiv, rowequ, r, b,
630  $ ldb, x, ldx, berr, n_norms, err_bnds_norm,
631  $ err_bnds_comp, work(n+1), work(1), work(2*n+1),
632  $ work(1), rcond, ithresh, rthresh, unstable_thresh,
633  $ ignore_cwise, info )
634  END IF
635  END IF
636 
637  err_lbnd = max( 10.0d+0, sqrt( dble( n ) ) ) * dlamch( 'Epsilon' )
638  IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 1 ) THEN
639 *
640 * Compute scaled normwise condition number cond(A*C).
641 *
642  IF ( colequ .AND. notran ) THEN
643  rcond_tmp = dla_gercond( trans, n, a, lda, af, ldaf, ipiv,
644  $ -1, c, info, work, iwork )
645  ELSE IF ( rowequ .AND. .NOT. notran ) THEN
646  rcond_tmp = dla_gercond( trans, n, a, lda, af, ldaf, ipiv,
647  $ -1, r, info, work, iwork )
648  ELSE
649  rcond_tmp = dla_gercond( trans, n, a, lda, af, ldaf, ipiv,
650  $ 0, r, info, work, iwork )
651  END IF
652  DO j = 1, nrhs
653 *
654 * Cap the error at 1.0.
655 *
656  IF ( n_err_bnds .GE. la_linrx_err_i
657  $ .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0d+0 )
658  $ err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
659 *
660 * Threshold the error (see LAWN).
661 *
662  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
663  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
664  err_bnds_norm( j, la_linrx_trust_i ) = 0.0d+0
665  IF ( info .LE. n ) info = n + j
666  ELSE IF ( err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd )
667  $ THEN
668  err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
669  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
670  END IF
671 *
672 * Save the condition number.
673 *
674  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
675  err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
676  END IF
677  END DO
678  END IF
679 
680  IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 2 ) THEN
681 *
682 * Compute componentwise condition number cond(A*diag(Y(:,J))) for
683 * each right-hand side using the current solution as an estimate of
684 * the true solution. If the componentwise error estimate is too
685 * large, then the solution is a lousy estimate of truth and the
686 * estimated RCOND may be too optimistic. To avoid misleading users,
687 * the inverse condition number is set to 0.0 when the estimated
688 * cwise error is at least CWISE_WRONG.
689 *
690  cwise_wrong = sqrt( dlamch( 'Epsilon' ) )
691  DO j = 1, nrhs
692  IF ( err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
693  $ THEN
694  rcond_tmp = dla_gercond( trans, n, a, lda, af, ldaf,
695  $ ipiv, 1, x(1,j), info, work, iwork )
696  ELSE
697  rcond_tmp = 0.0d+0
698  END IF
699 *
700 * Cap the error at 1.0.
701 *
702  IF ( n_err_bnds .GE. la_linrx_err_i
703  $ .AND. err_bnds_comp( j, la_linrx_err_i ) .GT. 1.0d+0 )
704  $ err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
705 *
706 * Threshold the error (see LAWN).
707 *
708  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
709  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
710  err_bnds_comp( j, la_linrx_trust_i ) = 0.0d+0
711  IF ( params( la_linrx_cwise_i ) .EQ. 1.0d+0
712  $ .AND. info.LT.n + j ) info = n + j
713  ELSE IF ( err_bnds_comp( j, la_linrx_err_i )
714  $ .LT. err_lbnd ) THEN
715  err_bnds_comp( j, la_linrx_err_i ) = err_lbnd
716  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
717  END IF
718 *
719 * Save the condition number.
720 *
721  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
722  err_bnds_comp( j, la_linrx_rcond_i ) = rcond_tmp
723  END IF
724  END DO
725  END IF
726 *
727  RETURN
728 *
729 * End of DGERFSX
730 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
double precision function dla_gercond(TRANS, N, A, LDA, AF, LDAF, IPIV, CMODE, C, INFO, WORK, IWORK)
DLA_GERCOND estimates the Skeel condition number for a general matrix.
Definition: dla_gercond.f:154
double precision function dlange(NORM, M, N, A, LDA, WORK)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlange.f:116
integer function ilatrans(TRANS)
ILATRANS
Definition: ilatrans.f:60
integer function ilaprec(PREC)
ILAPREC
Definition: ilaprec.f:60
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine dla_gerfsx_extended(PREC_TYPE, TRANS_TYPE, N, NRHS, A, LDA, AF, LDAF, IPIV, COLEQU, C, B, LDB, Y, LDY, BERR_OUT, N_NORMS, ERRS_N, ERRS_C, RES, AYB, DY, Y_TAIL, RCOND, ITHRESH, RTHRESH, DZ_UB, IGNORE_CWISE, INFO)
DLA_GERFSX_EXTENDED improves the computed solution to a system of linear equations for general matric...
subroutine dgecon(NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK, INFO)
DGECON
Definition: dgecon.f:126
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