LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ 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

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

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       = 'Y':  Both row and column equilibration, i.e., A has been
               replaced by diag(S) * A * diag(S).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