LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dsyrfsx()

subroutine dsyrfsx ( character  UPLO,
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( * )  S,
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 
)

DSYRFSX

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Purpose:
    DSYRFSX improves the computed solution to a system of linear
    equations when the coefficient matrix is symmetric indefinite, 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 and S
    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]UPLO
          UPLO is CHARACTER*1
       = 'U':  Upper triangle of A is stored;
       = 'L':  Lower triangle of A is stored.
[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
       = 'Y':  Both row and column equilibration, i.e., A has been
               replaced by diag(S) * A * diag(S).
               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 symmetric matrix A.  If UPLO = 'U', the leading N-by-N
     upper triangular part of A contains the upper triangular
     part of the matrix A, and the strictly lower triangular
     part of A is not referenced.  If UPLO = 'L', the leading
     N-by-N lower triangular part of A contains the lower
     triangular part of the matrix A, and the strictly upper
     triangular part of A is not referenced.
[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 factored form of the matrix A.  AF contains the block
     diagonal matrix D and the multipliers used to obtain the
     factor U or L from the factorization A = U*D*U**T or A =
     L*D*L**T as computed by DSYTRF.
[in]LDAF
          LDAF is INTEGER
     The leading dimension of the array AF.  LDAF >= max(1,N).
[in]IPIV
          IPIV is INTEGER array, dimension (N)
     Details of the interchanges and the block structure of D
     as determined by DSYTRF.
[in,out]S
          S is DOUBLE PRECISION array, dimension (N)
     The scale factors for A.  If EQUED = 'Y', A is multiplied on
     the left and right by diag(S).  S is an input argument if FACT =
     'F'; otherwise, S is an output argument.  If FACT = 'F' and EQUED
     = 'Y', each element of S must be positive.  If S is output, each
     element of S is a power of the radix. If S is input, each element
     of S 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
April 2012

Definition at line 404 of file dsyrfsx.f.

404 *
405 * -- LAPACK computational routine (version 3.7.0) --
406 * -- LAPACK is a software package provided by Univ. of Tennessee, --
407 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
408 * April 2012
409 *
410 * .. Scalar Arguments ..
411  CHARACTER uplo, equed
412  INTEGER info, lda, ldaf, ldb, ldx, n, nrhs, nparams,
413  $ n_err_bnds
414  DOUBLE PRECISION rcond
415 * ..
416 * .. Array Arguments ..
417  INTEGER ipiv( * ), iwork( * )
418  DOUBLE PRECISION a( lda, * ), af( ldaf, * ), b( ldb, * ),
419  $ x( ldx, * ), work( * )
420  DOUBLE PRECISION s( * ), params( * ), berr( * ),
421  $ err_bnds_norm( nrhs, * ),
422  $ err_bnds_comp( nrhs, * )
423 * ..
424 *
425 * ==================================================================
426 *
427 * .. Parameters ..
428  DOUBLE PRECISION zero, one
429  parameter( zero = 0.0d+0, one = 1.0d+0 )
430  DOUBLE PRECISION itref_default, ithresh_default
431  DOUBLE PRECISION componentwise_default, rthresh_default
432  DOUBLE PRECISION dzthresh_default
433  parameter( itref_default = 1.0d+0 )
434  parameter( ithresh_default = 10.0d+0 )
435  parameter( componentwise_default = 1.0d+0 )
436  parameter( rthresh_default = 0.5d+0 )
437  parameter( dzthresh_default = 0.25d+0 )
438  INTEGER la_linrx_itref_i, la_linrx_ithresh_i,
439  $ la_linrx_cwise_i
440  parameter( la_linrx_itref_i = 1,
441  $ la_linrx_ithresh_i = 2 )
442  parameter( la_linrx_cwise_i = 3 )
443  INTEGER la_linrx_trust_i, la_linrx_err_i,
444  $ la_linrx_rcond_i
445  parameter( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
446  parameter( la_linrx_rcond_i = 3 )
447 * ..
448 * .. Local Scalars ..
449  CHARACTER(1) norm
450  LOGICAL rcequ
451  INTEGER j, prec_type, ref_type, n_norms
452  DOUBLE PRECISION anorm, rcond_tmp
453  DOUBLE PRECISION illrcond_thresh, err_lbnd, cwise_wrong
454  LOGICAL ignore_cwise
455  INTEGER ithresh
456  DOUBLE PRECISION rthresh, unstable_thresh
457 * ..
458 * .. External Subroutines ..
460 * ..
461 * .. Intrinsic Functions ..
462  INTRINSIC max, sqrt
463 * ..
464 * .. External Functions ..
465  EXTERNAL lsame, ilaprec
466  EXTERNAL dlamch, dlansy, dla_syrcond
467  DOUBLE PRECISION dlamch, dlansy, dla_syrcond
468  LOGICAL lsame
469  INTEGER ilaprec
470 * ..
471 * .. Executable Statements ..
472 *
473 * Check the input parameters.
474 *
475  info = 0
476  ref_type = int( itref_default )
477  IF ( nparams .GE. la_linrx_itref_i ) THEN
478  IF ( params( la_linrx_itref_i ) .LT. 0.0d+0 ) THEN
479  params( la_linrx_itref_i ) = itref_default
480  ELSE
481  ref_type = params( la_linrx_itref_i )
482  END IF
483  END IF
484 *
485 * Set default parameters.
486 *
487  illrcond_thresh = dble( n )*dlamch( 'Epsilon' )
488  ithresh = int( ithresh_default )
489  rthresh = rthresh_default
490  unstable_thresh = dzthresh_default
491  ignore_cwise = componentwise_default .EQ. 0.0d+0
492 *
493  IF ( nparams.GE.la_linrx_ithresh_i ) THEN
494  IF ( params( la_linrx_ithresh_i ).LT.0.0d+0 ) THEN
495  params( la_linrx_ithresh_i ) = ithresh
496  ELSE
497  ithresh = int( params( la_linrx_ithresh_i ) )
498  END IF
499  END IF
500  IF ( nparams.GE.la_linrx_cwise_i ) THEN
501  IF ( params( la_linrx_cwise_i ).LT.0.0d+0 ) THEN
502  IF ( ignore_cwise ) THEN
503  params( la_linrx_cwise_i ) = 0.0d+0
504  ELSE
505  params( la_linrx_cwise_i ) = 1.0d+0
506  END IF
507  ELSE
508  ignore_cwise = params( la_linrx_cwise_i ) .EQ. 0.0d+0
509  END IF
510  END IF
511  IF ( ref_type .EQ. 0 .OR. n_err_bnds .EQ. 0 ) THEN
512  n_norms = 0
513  ELSE IF ( ignore_cwise ) THEN
514  n_norms = 1
515  ELSE
516  n_norms = 2
517  END IF
518 *
519  rcequ = lsame( equed, 'Y' )
520 *
521 * Test input parameters.
522 *
523  IF ( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
524  info = -1
525  ELSE IF( .NOT.rcequ .AND. .NOT.lsame( equed, 'N' ) ) THEN
526  info = -2
527  ELSE IF( n.LT.0 ) THEN
528  info = -3
529  ELSE IF( nrhs.LT.0 ) THEN
530  info = -4
531  ELSE IF( lda.LT.max( 1, n ) ) THEN
532  info = -6
533  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
534  info = -8
535  ELSE IF( ldb.LT.max( 1, n ) ) THEN
536  info = -12
537  ELSE IF( ldx.LT.max( 1, n ) ) THEN
538  info = -14
539  END IF
540  IF( info.NE.0 ) THEN
541  CALL xerbla( 'DSYRFSX', -info )
542  RETURN
543  END IF
544 *
545 * Quick return if possible.
546 *
547  IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
548  rcond = 1.0d+0
549  DO j = 1, nrhs
550  berr( j ) = 0.0d+0
551  IF ( n_err_bnds .GE. 1 ) THEN
552  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
553  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
554  END IF
555  IF ( n_err_bnds .GE. 2 ) THEN
556  err_bnds_norm( j, la_linrx_err_i ) = 0.0d+0
557  err_bnds_comp( j, la_linrx_err_i ) = 0.0d+0
558  END IF
559  IF ( n_err_bnds .GE. 3 ) THEN
560  err_bnds_norm( j, la_linrx_rcond_i ) = 1.0d+0
561  err_bnds_comp( j, la_linrx_rcond_i ) = 1.0d+0
562  END IF
563  END DO
564  RETURN
565  END IF
566 *
567 * Default to failure.
568 *
569  rcond = 0.0d+0
570  DO j = 1, nrhs
571  berr( j ) = 1.0d+0
572  IF ( n_err_bnds .GE. 1 ) THEN
573  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
574  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
575  END IF
576  IF ( n_err_bnds .GE. 2 ) THEN
577  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
578  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
579  END IF
580  IF ( n_err_bnds .GE. 3 ) THEN
581  err_bnds_norm( j, la_linrx_rcond_i ) = 0.0d+0
582  err_bnds_comp( j, la_linrx_rcond_i ) = 0.0d+0
583  END IF
584  END DO
585 *
586 * Compute the norm of A and the reciprocal of the condition
587 * number of A.
588 *
589  norm = 'I'
590  anorm = dlansy( norm, uplo, n, a, lda, work )
591  CALL dsycon( uplo, n, af, ldaf, ipiv, anorm, rcond, work,
592  $ iwork, info )
593 *
594 * Perform refinement on each right-hand side
595 *
596  IF ( ref_type .NE. 0 ) THEN
597 
598  prec_type = ilaprec( 'E' )
599 
600  CALL dla_syrfsx_extended( prec_type, uplo, n,
601  $ nrhs, a, lda, af, ldaf, ipiv, rcequ, s, b,
602  $ ldb, x, ldx, berr, n_norms, err_bnds_norm, err_bnds_comp,
603  $ work( n+1 ), work( 1 ), work( 2*n+1 ), work( 1 ), rcond,
604  $ ithresh, rthresh, unstable_thresh, ignore_cwise,
605  $ info )
606  END IF
607 
608  err_lbnd = max( 10.0d+0, sqrt( dble( n ) ) )*dlamch( 'Epsilon' )
609  IF (n_err_bnds .GE. 1 .AND. n_norms .GE. 1) THEN
610 *
611 * Compute scaled normwise condition number cond(A*C).
612 *
613  IF ( rcequ ) THEN
614  rcond_tmp = dla_syrcond( uplo, n, a, lda, af, ldaf, ipiv,
615  $ -1, s, info, work, iwork )
616  ELSE
617  rcond_tmp = dla_syrcond( uplo, n, a, lda, af, ldaf, ipiv,
618  $ 0, s, info, work, iwork )
619  END IF
620  DO j = 1, nrhs
621 *
622 * Cap the error at 1.0.
623 *
624  IF (n_err_bnds .GE. la_linrx_err_i
625  $ .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0d+0)
626  $ err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
627 *
628 * Threshold the error (see LAWN).
629 *
630  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
631  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
632  err_bnds_norm( j, la_linrx_trust_i ) = 0.0d+0
633  IF ( info .LE. n ) info = n + j
634  ELSE IF (err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd)
635  $ THEN
636  err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
637  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
638  END IF
639 *
640 * Save the condition number.
641 *
642  IF (n_err_bnds .GE. la_linrx_rcond_i) THEN
643  err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
644  END IF
645  END DO
646  END IF
647 
648  IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 2 ) THEN
649 *
650 * Compute componentwise condition number cond(A*diag(Y(:,J))) for
651 * each right-hand side using the current solution as an estimate of
652 * the true solution. If the componentwise error estimate is too
653 * large, then the solution is a lousy estimate of truth and the
654 * estimated RCOND may be too optimistic. To avoid misleading users,
655 * the inverse condition number is set to 0.0 when the estimated
656 * cwise error is at least CWISE_WRONG.
657 *
658  cwise_wrong = sqrt( dlamch( 'Epsilon' ) )
659  DO j = 1, nrhs
660  IF ( err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
661  $ THEN
662  rcond_tmp = dla_syrcond( uplo, n, a, lda, af, ldaf, ipiv,
663  $ 1, x(1,j), info, work, iwork )
664  ELSE
665  rcond_tmp = 0.0d+0
666  END IF
667 *
668 * Cap the error at 1.0.
669 *
670  IF ( n_err_bnds .GE. la_linrx_err_i
671  $ .AND. err_bnds_comp( j, la_linrx_err_i ) .GT. 1.0d+0 )
672  $ err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
673 *
674 * Threshold the error (see LAWN).
675 *
676  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
677  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
678  err_bnds_comp( j, la_linrx_trust_i ) = 0.0d+0
679  IF ( .NOT. ignore_cwise
680  $ .AND. info.LT.n + j ) info = n + j
681  ELSE IF ( err_bnds_comp( j, la_linrx_err_i )
682  $ .LT. err_lbnd ) THEN
683  err_bnds_comp( j, la_linrx_err_i ) = err_lbnd
684  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
685  END IF
686 *
687 * Save the condition number.
688 *
689  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
690  err_bnds_comp( j, la_linrx_rcond_i ) = rcond_tmp
691  END IF
692 
693  END DO
694  END IF
695 *
696  RETURN
697 *
698 * End of DSYRFSX
699 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
double precision function dlansy(NORM, UPLO, N, A, LDA, WORK)
DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.
Definition: dlansy.f:124
subroutine dla_syrfsx_extended(PREC_TYPE, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, COLEQU, C, B, LDB, Y, LDY, BERR_OUT, N_NORMS, ERR_BNDS_NORM, ERR_BNDS_COMP, RES, AYB, DY, Y_TAIL, RCOND, ITHRESH, RTHRESH, DZ_UB, IGNORE_CWISE, INFO)
DLA_SYRFSX_EXTENDED improves the computed solution to a system of linear equations for symmetric inde...
double precision function dla_syrcond(UPLO, N, A, LDA, AF, LDAF, IPIV, CMODE, C, INFO, WORK, IWORK)
DLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.
Definition: dla_syrcond.f:150
subroutine dsycon(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
DSYCON
Definition: dsycon.f:132
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
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