LAPACK  3.8.0
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       = 'Y':  Both row and column equilibration, i.e., A has been
               replaced by diag(S) * A * diag(S).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 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 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 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 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.
Date
April 2012

Definition at line 404 of file zsyrfsx.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( * )
418  COMPLEX*16 a( lda, * ), af( ldaf, * ), b( ldb, * ),
419  $ x( ldx, * ), work( * )
420  DOUBLE PRECISION s( * ), params( * ), berr( * ), rwork( * ),
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
452  INTEGER n_norms
453  DOUBLE PRECISION anorm, rcond_tmp
454  DOUBLE PRECISION illrcond_thresh, err_lbnd, cwise_wrong
455  LOGICAL ignore_cwise
456  INTEGER ithresh
457  DOUBLE PRECISION rthresh, unstable_thresh
458 * ..
459 * .. External Subroutines ..
461 * ..
462 * .. Intrinsic Functions ..
463  INTRINSIC max, sqrt, transfer
464 * ..
465 * .. External Functions ..
466  EXTERNAL lsame, ilaprec
468  DOUBLE PRECISION dlamch, zlansy, zla_syrcond_x, zla_syrcond_c
469  LOGICAL lsame
470  INTEGER ilaprec
471 * ..
472 * .. Executable Statements ..
473 *
474 * Check the input parameters.
475 *
476  info = 0
477  ref_type = int( itref_default )
478  IF ( nparams .GE. la_linrx_itref_i ) THEN
479  IF ( params( la_linrx_itref_i ) .LT. 0.0d+0 ) THEN
480  params( la_linrx_itref_i ) = itref_default
481  ELSE
482  ref_type = params( la_linrx_itref_i )
483  END IF
484  END IF
485 *
486 * Set default parameters.
487 *
488  illrcond_thresh = dble( n ) * dlamch( 'Epsilon' )
489  ithresh = int( ithresh_default )
490  rthresh = rthresh_default
491  unstable_thresh = dzthresh_default
492  ignore_cwise = componentwise_default .EQ. 0.0d+0
493 *
494  IF ( nparams.GE.la_linrx_ithresh_i ) THEN
495  IF ( params( la_linrx_ithresh_i ).LT.0.0d+0 ) THEN
496  params( la_linrx_ithresh_i ) = ithresh
497  ELSE
498  ithresh = int( params( la_linrx_ithresh_i ) )
499  END IF
500  END IF
501  IF ( nparams.GE.la_linrx_cwise_i ) THEN
502  IF ( params( la_linrx_cwise_i ).LT.0.0d+0 ) THEN
503  IF ( ignore_cwise ) THEN
504  params( la_linrx_cwise_i ) = 0.0d+0
505  ELSE
506  params( la_linrx_cwise_i ) = 1.0d+0
507  END IF
508  ELSE
509  ignore_cwise = params( la_linrx_cwise_i ) .EQ. 0.0d+0
510  END IF
511  END IF
512  IF ( ref_type .EQ. 0 .OR. n_err_bnds .EQ. 0 ) THEN
513  n_norms = 0
514  ELSE IF ( ignore_cwise ) THEN
515  n_norms = 1
516  ELSE
517  n_norms = 2
518  END IF
519 *
520  rcequ = lsame( equed, 'Y' )
521 *
522 * Test input parameters.
523 *
524  IF ( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
525  info = -1
526  ELSE IF( .NOT.rcequ .AND. .NOT.lsame( equed, 'N' ) ) THEN
527  info = -2
528  ELSE IF( n.LT.0 ) THEN
529  info = -3
530  ELSE IF( nrhs.LT.0 ) THEN
531  info = -4
532  ELSE IF( lda.LT.max( 1, n ) ) THEN
533  info = -6
534  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
535  info = -8
536  ELSE IF( ldb.LT.max( 1, n ) ) THEN
537  info = -12
538  ELSE IF( ldx.LT.max( 1, n ) ) THEN
539  info = -14
540  END IF
541  IF( info.NE.0 ) THEN
542  CALL xerbla( 'ZSYRFSX', -info )
543  RETURN
544  END IF
545 *
546 * Quick return if possible.
547 *
548  IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
549  rcond = 1.0d+0
550  DO j = 1, nrhs
551  berr( j ) = 0.0d+0
552  IF ( n_err_bnds .GE. 1 ) THEN
553  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
554  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
555  END IF
556  IF ( n_err_bnds .GE. 2 ) THEN
557  err_bnds_norm( j, la_linrx_err_i ) = 0.0d+0
558  err_bnds_comp( j, la_linrx_err_i ) = 0.0d+0
559  END IF
560  IF ( n_err_bnds .GE. 3 ) THEN
561  err_bnds_norm( j, la_linrx_rcond_i ) = 1.0d+0
562  err_bnds_comp( j, la_linrx_rcond_i ) = 1.0d+0
563  END IF
564  END DO
565  RETURN
566  END IF
567 *
568 * Default to failure.
569 *
570  rcond = 0.0d+0
571  DO j = 1, nrhs
572  berr( j ) = 1.0d+0
573  IF ( n_err_bnds .GE. 1 ) THEN
574  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
575  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
576  END IF
577  IF ( n_err_bnds .GE. 2 ) THEN
578  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
579  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
580  END IF
581  IF ( n_err_bnds .GE. 3 ) THEN
582  err_bnds_norm( j, la_linrx_rcond_i ) = 0.0d+0
583  err_bnds_comp( j, la_linrx_rcond_i ) = 0.0d+0
584  END IF
585  END DO
586 *
587 * Compute the norm of A and the reciprocal of the condition
588 * number of A.
589 *
590  norm = 'I'
591  anorm = zlansy( norm, uplo, n, a, lda, rwork )
592  CALL zsycon( uplo, n, af, ldaf, ipiv, anorm, rcond, work,
593  $ info )
594 *
595 * Perform refinement on each right-hand side
596 *
597  IF ( ref_type .NE. 0 ) THEN
598 
599  prec_type = ilaprec( 'E' )
600 
601  CALL zla_syrfsx_extended( prec_type, uplo, n,
602  $ nrhs, a, lda, af, ldaf, ipiv, rcequ, s, b,
603  $ ldb, x, ldx, berr, n_norms, err_bnds_norm, err_bnds_comp,
604  $ work, rwork, work(n+1),
605  $ transfer(rwork(1:2*n), (/ (zero, zero) /), n), rcond,
606  $ ithresh, rthresh, unstable_thresh, ignore_cwise,
607  $ info )
608  END IF
609 
610  err_lbnd = max( 10.0d+0, sqrt( dble( n ) ) ) * dlamch( 'Epsilon' )
611  IF (n_err_bnds .GE. 1 .AND. n_norms .GE. 1) THEN
612 *
613 * Compute scaled normwise condition number cond(A*C).
614 *
615  IF ( rcequ ) THEN
616  rcond_tmp = zla_syrcond_c( uplo, n, a, lda, af, ldaf, ipiv,
617  $ s, .true., info, work, rwork )
618  ELSE
619  rcond_tmp = zla_syrcond_c( uplo, n, a, lda, af, ldaf, ipiv,
620  $ s, .false., info, work, rwork )
621  END IF
622  DO j = 1, nrhs
623 *
624 * Cap the error at 1.0.
625 *
626  IF ( n_err_bnds .GE. la_linrx_err_i
627  $ .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0d+0 )
628  $ err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
629 *
630 * Threshold the error (see LAWN).
631 *
632  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
633  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
634  err_bnds_norm( j, la_linrx_trust_i ) = 0.0d+0
635  IF ( info .LE. n ) info = n + j
636  ELSE IF ( err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd )
637  $ THEN
638  err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
639  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
640  END IF
641 *
642 * Save the condition number.
643 *
644  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
645  err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
646  END IF
647  END DO
648  END IF
649 
650  IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 2 ) THEN
651 *
652 * Compute componentwise condition number cond(A*diag(Y(:,J))) for
653 * each right-hand side using the current solution as an estimate of
654 * the true solution. If the componentwise error estimate is too
655 * large, then the solution is a lousy estimate of truth and the
656 * estimated RCOND may be too optimistic. To avoid misleading users,
657 * the inverse condition number is set to 0.0 when the estimated
658 * cwise error is at least CWISE_WRONG.
659 *
660  cwise_wrong = sqrt( dlamch( 'Epsilon' ) )
661  DO j = 1, nrhs
662  IF ( err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
663  $ THEN
664  rcond_tmp = zla_syrcond_x( uplo, n, a, lda, af, ldaf,
665  $ ipiv, x(1,j), info, work, rwork )
666  ELSE
667  rcond_tmp = 0.0d+0
668  END IF
669 *
670 * Cap the error at 1.0.
671 *
672  IF ( n_err_bnds .GE. la_linrx_err_i
673  $ .AND. err_bnds_comp( j, la_linrx_err_i ) .GT. 1.0d+0 )
674  $ err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
675 
676 *
677 * Threshold the error (see LAWN).
678 *
679  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
680  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
681  err_bnds_comp( j, la_linrx_trust_i ) = 0.0d+0
682  IF (.NOT. ignore_cwise
683  $ .AND. info.LT.n + j ) info = n + j
684  ELSE IF ( err_bnds_comp( j, la_linrx_err_i )
685  $ .LT. err_lbnd ) THEN
686  err_bnds_comp( j, la_linrx_err_i ) = err_lbnd
687  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
688  END IF
689 *
690 * Save the condition number.
691 *
692  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
693  err_bnds_comp( j, la_linrx_rcond_i ) = rcond_tmp
694  END IF
695 
696  END DO
697  END IF
698 *
699  RETURN
700 *
701 * End of ZSYRFSX
702 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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...
subroutine zsycon(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO)
ZSYCON
Definition: zsycon.f:127
integer function ilaprec(PREC)
ILAPREC
Definition: ilaprec.f:60
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...
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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, or the element of largest absolute value of a complex symmetric matrix.
Definition: zlansy.f:125
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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...
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