LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ zsyrfsx()

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

ZSYRFSX

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Purpose:
    ZSYRFSX 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       = 'Y':  Both row and column equilibration, i.e., A has been
               replaced by diag(S) * A * diag(S).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 COMPLEX*16 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 COMPLEX*16 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 ZSYTRF.
[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 ZSYTRF.
[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 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 "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 < 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 <= 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 398 of file zsyrfsx.f.

402 *
403 * -- LAPACK computational routine --
404 * -- LAPACK is a software package provided by Univ. of Tennessee, --
405 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
406 *
407 * .. Scalar Arguments ..
408  CHARACTER UPLO, EQUED
409  INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
410  $ N_ERR_BNDS
411  DOUBLE PRECISION RCOND
412 * ..
413 * .. Array Arguments ..
414  INTEGER IPIV( * )
415  COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
416  $ X( LDX, * ), WORK( * )
417  DOUBLE PRECISION S( * ), PARAMS( * ), BERR( * ), RWORK( * ),
418  $ ERR_BNDS_NORM( NRHS, * ),
419  $ ERR_BNDS_COMP( NRHS, * )
420 * ..
421 *
422 * ==================================================================
423 *
424 * .. Parameters ..
425  DOUBLE PRECISION ZERO, ONE
426  parameter( zero = 0.0d+0, one = 1.0d+0 )
427  DOUBLE PRECISION ITREF_DEFAULT, ITHRESH_DEFAULT
428  DOUBLE PRECISION COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT
429  DOUBLE PRECISION DZTHRESH_DEFAULT
430  parameter( itref_default = 1.0d+0 )
431  parameter( ithresh_default = 10.0d+0 )
432  parameter( componentwise_default = 1.0d+0 )
433  parameter( rthresh_default = 0.5d+0 )
434  parameter( dzthresh_default = 0.25d+0 )
435  INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
436  $ LA_LINRX_CWISE_I
437  parameter( la_linrx_itref_i = 1,
438  $ la_linrx_ithresh_i = 2 )
439  parameter( la_linrx_cwise_i = 3 )
440  INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
441  $ LA_LINRX_RCOND_I
442  parameter( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
443  parameter( la_linrx_rcond_i = 3 )
444 * ..
445 * .. Local Scalars ..
446  CHARACTER(1) NORM
447  LOGICAL RCEQU
448  INTEGER J, PREC_TYPE, REF_TYPE
449  INTEGER N_NORMS
450  DOUBLE PRECISION ANORM, RCOND_TMP
451  DOUBLE PRECISION ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
452  LOGICAL IGNORE_CWISE
453  INTEGER ITHRESH
454  DOUBLE PRECISION RTHRESH, UNSTABLE_THRESH
455 * ..
456 * .. External Subroutines ..
458 * ..
459 * .. Intrinsic Functions ..
460  INTRINSIC max, sqrt, transfer
461 * ..
462 * .. External Functions ..
463  EXTERNAL lsame, ilaprec
465  DOUBLE PRECISION DLAMCH, ZLANSY, ZLA_SYRCOND_X, ZLA_SYRCOND_C
466  LOGICAL LSAME
467  INTEGER ILAPREC
468 * ..
469 * .. Executable Statements ..
470 *
471 * Check the input parameters.
472 *
473  info = 0
474  ref_type = int( itref_default )
475  IF ( nparams .GE. la_linrx_itref_i ) THEN
476  IF ( params( la_linrx_itref_i ) .LT. 0.0d+0 ) THEN
477  params( la_linrx_itref_i ) = itref_default
478  ELSE
479  ref_type = params( la_linrx_itref_i )
480  END IF
481  END IF
482 *
483 * Set default parameters.
484 *
485  illrcond_thresh = dble( n ) * dlamch( 'Epsilon' )
486  ithresh = int( ithresh_default )
487  rthresh = rthresh_default
488  unstable_thresh = dzthresh_default
489  ignore_cwise = componentwise_default .EQ. 0.0d+0
490 *
491  IF ( nparams.GE.la_linrx_ithresh_i ) THEN
492  IF ( params( la_linrx_ithresh_i ).LT.0.0d+0 ) THEN
493  params( la_linrx_ithresh_i ) = ithresh
494  ELSE
495  ithresh = int( params( la_linrx_ithresh_i ) )
496  END IF
497  END IF
498  IF ( nparams.GE.la_linrx_cwise_i ) THEN
499  IF ( params( la_linrx_cwise_i ).LT.0.0d+0 ) THEN
500  IF ( ignore_cwise ) THEN
501  params( la_linrx_cwise_i ) = 0.0d+0
502  ELSE
503  params( la_linrx_cwise_i ) = 1.0d+0
504  END IF
505  ELSE
506  ignore_cwise = params( la_linrx_cwise_i ) .EQ. 0.0d+0
507  END IF
508  END IF
509  IF ( ref_type .EQ. 0 .OR. n_err_bnds .EQ. 0 ) THEN
510  n_norms = 0
511  ELSE IF ( ignore_cwise ) THEN
512  n_norms = 1
513  ELSE
514  n_norms = 2
515  END IF
516 *
517  rcequ = lsame( equed, 'Y' )
518 *
519 * Test input parameters.
520 *
521  IF ( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
522  info = -1
523  ELSE IF( .NOT.rcequ .AND. .NOT.lsame( equed, 'N' ) ) THEN
524  info = -2
525  ELSE IF( n.LT.0 ) THEN
526  info = -3
527  ELSE IF( nrhs.LT.0 ) THEN
528  info = -4
529  ELSE IF( lda.LT.max( 1, n ) ) THEN
530  info = -6
531  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
532  info = -8
533  ELSE IF( ldb.LT.max( 1, n ) ) THEN
534  info = -12
535  ELSE IF( ldx.LT.max( 1, n ) ) THEN
536  info = -14
537  END IF
538  IF( info.NE.0 ) THEN
539  CALL xerbla( 'ZSYRFSX', -info )
540  RETURN
541  END IF
542 *
543 * Quick return if possible.
544 *
545  IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
546  rcond = 1.0d+0
547  DO j = 1, nrhs
548  berr( j ) = 0.0d+0
549  IF ( n_err_bnds .GE. 1 ) THEN
550  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
551  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
552  END IF
553  IF ( n_err_bnds .GE. 2 ) THEN
554  err_bnds_norm( j, la_linrx_err_i ) = 0.0d+0
555  err_bnds_comp( j, la_linrx_err_i ) = 0.0d+0
556  END IF
557  IF ( n_err_bnds .GE. 3 ) THEN
558  err_bnds_norm( j, la_linrx_rcond_i ) = 1.0d+0
559  err_bnds_comp( j, la_linrx_rcond_i ) = 1.0d+0
560  END IF
561  END DO
562  RETURN
563  END IF
564 *
565 * Default to failure.
566 *
567  rcond = 0.0d+0
568  DO j = 1, nrhs
569  berr( j ) = 1.0d+0
570  IF ( n_err_bnds .GE. 1 ) THEN
571  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
572  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
573  END IF
574  IF ( n_err_bnds .GE. 2 ) THEN
575  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
576  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
577  END IF
578  IF ( n_err_bnds .GE. 3 ) THEN
579  err_bnds_norm( j, la_linrx_rcond_i ) = 0.0d+0
580  err_bnds_comp( j, la_linrx_rcond_i ) = 0.0d+0
581  END IF
582  END DO
583 *
584 * Compute the norm of A and the reciprocal of the condition
585 * number of A.
586 *
587  norm = 'I'
588  anorm = zlansy( norm, uplo, n, a, lda, rwork )
589  CALL zsycon( uplo, n, af, ldaf, ipiv, anorm, rcond, work,
590  $ info )
591 *
592 * Perform refinement on each right-hand side
593 *
594  IF ( ref_type .NE. 0 ) THEN
595 
596  prec_type = ilaprec( 'E' )
597 
598  CALL zla_syrfsx_extended( prec_type, uplo, n,
599  $ nrhs, a, lda, af, ldaf, ipiv, rcequ, s, b,
600  $ ldb, x, ldx, berr, n_norms, err_bnds_norm, err_bnds_comp,
601  $ work, rwork, work(n+1),
602  $ transfer(rwork(1:2*n), (/ (zero, zero) /), n), rcond,
603  $ ithresh, rthresh, unstable_thresh, ignore_cwise,
604  $ info )
605  END IF
606 
607  err_lbnd = max( 10.0d+0, sqrt( dble( n ) ) ) * dlamch( 'Epsilon' )
608  IF (n_err_bnds .GE. 1 .AND. n_norms .GE. 1) THEN
609 *
610 * Compute scaled normwise condition number cond(A*C).
611 *
612  IF ( rcequ ) THEN
613  rcond_tmp = zla_syrcond_c( uplo, n, a, lda, af, ldaf, ipiv,
614  $ s, .true., info, work, rwork )
615  ELSE
616  rcond_tmp = zla_syrcond_c( uplo, n, a, lda, af, ldaf, ipiv,
617  $ s, .false., info, work, rwork )
618  END IF
619  DO j = 1, nrhs
620 *
621 * Cap the error at 1.0.
622 *
623  IF ( n_err_bnds .GE. la_linrx_err_i
624  $ .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0d+0 )
625  $ err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
626 *
627 * Threshold the error (see LAWN).
628 *
629  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
630  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
631  err_bnds_norm( j, la_linrx_trust_i ) = 0.0d+0
632  IF ( info .LE. n ) info = n + j
633  ELSE IF ( err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd )
634  $ THEN
635  err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
636  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
637  END IF
638 *
639 * Save the condition number.
640 *
641  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
642  err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
643  END IF
644  END DO
645  END IF
646 
647  IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 2 ) THEN
648 *
649 * Compute componentwise condition number cond(A*diag(Y(:,J))) for
650 * each right-hand side using the current solution as an estimate of
651 * the true solution. If the componentwise error estimate is too
652 * large, then the solution is a lousy estimate of truth and the
653 * estimated RCOND may be too optimistic. To avoid misleading users,
654 * the inverse condition number is set to 0.0 when the estimated
655 * cwise error is at least CWISE_WRONG.
656 *
657  cwise_wrong = sqrt( dlamch( 'Epsilon' ) )
658  DO j = 1, nrhs
659  IF ( err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
660  $ THEN
661  rcond_tmp = zla_syrcond_x( uplo, n, a, lda, af, ldaf,
662  $ ipiv, x(1,j), info, work, rwork )
663  ELSE
664  rcond_tmp = 0.0d+0
665  END IF
666 *
667 * Cap the error at 1.0.
668 *
669  IF ( n_err_bnds .GE. la_linrx_err_i
670  $ .AND. err_bnds_comp( j, la_linrx_err_i ) .GT. 1.0d+0 )
671  $ err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
672 
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 ZSYRFSX
699 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
integer function ilaprec(PREC)
ILAPREC
Definition: ilaprec.f:58
double precision function zlansy(NORM, UPLO, N, A, LDA, WORK)
ZLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlansy.f:123
subroutine zla_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)
ZLA_SYRFSX_EXTENDED improves the computed solution to a system of linear equations for symmetric inde...
subroutine zsycon(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO)
ZSYCON
Definition: zsycon.f:125
double precision function zla_syrcond_c(UPLO, N, A, LDA, AF, LDAF, IPIV, C, CAPPLY, INFO, WORK, RWORK)
ZLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefin...
double precision function zla_syrcond_x(UPLO, N, A, LDA, AF, LDAF, IPIV, X, INFO, WORK, RWORK)
ZLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite m...
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