LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ cherfsx()

subroutine cherfsx ( character uplo,
character equed,
integer n,
integer nrhs,
complex, dimension( lda, * ) a,
integer lda,
complex, dimension( ldaf, * ) af,
integer ldaf,
integer, dimension( * ) ipiv,
real, dimension( * ) s,
complex, dimension( ldb, * ) b,
integer ldb,
complex, dimension( ldx, * ) x,
integer ldx,
real rcond,
real, dimension( * ) berr,
integer n_err_bnds,
real, dimension( nrhs, * ) err_bnds_norm,
real, dimension( nrhs, * ) err_bnds_comp,
integer nparams,
real, dimension( * ) params,
complex, dimension( * ) work,
real, dimension( * ) rwork,
integer info )

CHERFSX

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Purpose:
!> !> CHERFSX improves the computed solution to a system of linear !> equations when the coefficient matrix is Hermitian 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 array, dimension (LDA,N) !> The Hermitian 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 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**H or A = !> L*D*L**H as computed by CHETRF. !>
[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 CHETRF. !>
[in,out]S
!> S is REAL 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 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 array, dimension (LDX,NRHS) !> On entry, the solution matrix X, as computed by CHETRS. !> 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 REAL !> 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 REAL 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 REAL 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 boolean. Trust the answer if the !> reciprocal condition number is less than the threshold !> sqrt(n) * slamch('Epsilon'). !> !> err = 2 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) * slamch('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) * slamch('Epsilon') to determine if the error !> estimate is . 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 REAL 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 boolean. Trust the answer if the !> reciprocal condition number is less than the threshold !> sqrt(n) * slamch('Epsilon'). !> !> err = 2 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) * slamch('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) * slamch('Epsilon') to determine if the error !> estimate is . 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 REAL 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: 1.0 !> = 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 array, dimension (2*N) !>
[out]RWORK
!> RWORK is REAL 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 395 of file cherfsx.f.

400*
401* -- LAPACK computational routine --
402* -- LAPACK is a software package provided by Univ. of Tennessee, --
403* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
404*
405* .. Scalar Arguments ..
406 CHARACTER UPLO, EQUED
407 INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
408 $ N_ERR_BNDS
409 REAL RCOND
410* ..
411* .. Array Arguments ..
412 INTEGER IPIV( * )
413 COMPLEX A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
414 $ X( LDX, * ), WORK( * )
415 REAL S( * ), PARAMS( * ), BERR( * ), RWORK( * ),
416 $ ERR_BNDS_NORM( NRHS, * ),
417 $ ERR_BNDS_COMP( NRHS, * )
418*
419* ==================================================================
420*
421* .. Parameters ..
422 REAL ZERO, ONE
423 parameter( zero = 0.0e+0, one = 1.0e+0 )
424 REAL ITREF_DEFAULT, ITHRESH_DEFAULT,
425 $ COMPONENTWISE_DEFAULT
426 REAL RTHRESH_DEFAULT, DZTHRESH_DEFAULT
427 parameter( itref_default = 1.0 )
428 parameter( ithresh_default = 10.0 )
429 parameter( componentwise_default = 1.0 )
430 parameter( rthresh_default = 0.5 )
431 parameter( dzthresh_default = 0.25 )
432 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
433 $ LA_LINRX_CWISE_I
434 parameter( la_linrx_itref_i = 1,
435 $ la_linrx_ithresh_i = 2 )
436 parameter( la_linrx_cwise_i = 3 )
437 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
438 $ LA_LINRX_RCOND_I
439 parameter( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
440 parameter( la_linrx_rcond_i = 3 )
441* ..
442* .. Local Scalars ..
443 CHARACTER(1) NORM
444 LOGICAL RCEQU
445 INTEGER J, PREC_TYPE, REF_TYPE
446 INTEGER N_NORMS
447 REAL ANORM, RCOND_TMP
448 REAL ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
449 LOGICAL IGNORE_CWISE
450 INTEGER ITHRESH
451 REAL RTHRESH, UNSTABLE_THRESH
452* ..
453* .. External Subroutines ..
455* ..
456* .. Intrinsic Functions ..
457 INTRINSIC max, sqrt, transfer
458* ..
459* .. External Functions ..
460 EXTERNAL lsame, ilaprec
461 EXTERNAL slamch, clanhe, cla_hercond_x,
463 REAL SLAMCH, CLANHE, CLA_HERCOND_X, CLA_HERCOND_C
464 LOGICAL LSAME
465 INTEGER ILAPREC
466* ..
467* .. Executable Statements ..
468*
469* Check the input parameters.
470*
471 info = 0
472 ref_type = int( itref_default )
473 IF ( nparams .GE. la_linrx_itref_i ) THEN
474 IF ( params( la_linrx_itref_i ) .LT. 0.0 ) THEN
475 params( la_linrx_itref_i ) = itref_default
476 ELSE
477 ref_type = params( la_linrx_itref_i )
478 END IF
479 END IF
480*
481* Set default parameters.
482*
483 illrcond_thresh = real( n ) * slamch( 'Epsilon' )
484 ithresh = int( ithresh_default )
485 rthresh = rthresh_default
486 unstable_thresh = dzthresh_default
487 ignore_cwise = componentwise_default .EQ. 0.0
488*
489 IF ( nparams.GE.la_linrx_ithresh_i ) THEN
490 IF ( params( la_linrx_ithresh_i ).LT.0.0 ) THEN
491 params( la_linrx_ithresh_i ) = ithresh
492 ELSE
493 ithresh = int( params( la_linrx_ithresh_i ) )
494 END IF
495 END IF
496 IF ( nparams.GE.la_linrx_cwise_i ) THEN
497 IF ( params(la_linrx_cwise_i ).LT.0.0 ) THEN
498 IF ( ignore_cwise ) THEN
499 params( la_linrx_cwise_i ) = 0.0
500 ELSE
501 params( la_linrx_cwise_i ) = 1.0
502 END IF
503 ELSE
504 ignore_cwise = params( la_linrx_cwise_i ) .EQ. 0.0
505 END IF
506 END IF
507 IF ( ref_type .EQ. 0 .OR. n_err_bnds .EQ. 0 ) THEN
508 n_norms = 0
509 ELSE IF ( ignore_cwise ) THEN
510 n_norms = 1
511 ELSE
512 n_norms = 2
513 END IF
514*
515 rcequ = lsame( equed, 'Y' )
516*
517* Test input parameters.
518*
519 IF (.NOT.lsame( uplo, 'U' ) .AND.
520 $ .NOT.lsame( uplo, 'L' ) ) THEN
521 info = -1
522 ELSE IF( .NOT.rcequ .AND. .NOT.lsame( equed, 'N' ) ) THEN
523 info = -2
524 ELSE IF( n.LT.0 ) THEN
525 info = -3
526 ELSE IF( nrhs.LT.0 ) THEN
527 info = -4
528 ELSE IF( lda.LT.max( 1, n ) ) THEN
529 info = -6
530 ELSE IF( ldaf.LT.max( 1, n ) ) THEN
531 info = -8
532 ELSE IF( ldb.LT.max( 1, n ) ) THEN
533 info = -12
534 ELSE IF( ldx.LT.max( 1, n ) ) THEN
535 info = -14
536 END IF
537 IF( info.NE.0 ) THEN
538 CALL xerbla( 'CHERFSX', -info )
539 RETURN
540 END IF
541*
542* Quick return if possible.
543*
544 IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
545 rcond = 1.0
546 DO j = 1, nrhs
547 berr( j ) = 0.0
548 IF ( n_err_bnds .GE. 1 ) THEN
549 err_bnds_norm( j, la_linrx_trust_i ) = 1.0
550 err_bnds_comp( j, la_linrx_trust_i ) = 1.0
551 END IF
552 IF ( n_err_bnds .GE. 2 ) THEN
553 err_bnds_norm( j, la_linrx_err_i ) = 0.0
554 err_bnds_comp( j, la_linrx_err_i ) = 0.0
555 END IF
556 IF ( n_err_bnds .GE. 3 ) THEN
557 err_bnds_norm( j, la_linrx_rcond_i ) = 1.0
558 err_bnds_comp( j, la_linrx_rcond_i ) = 1.0
559 END IF
560 END DO
561 RETURN
562 END IF
563*
564* Default to failure.
565*
566 rcond = 0.0
567 DO j = 1, nrhs
568 berr( j ) = 1.0
569 IF ( n_err_bnds .GE. 1 ) THEN
570 err_bnds_norm( j, la_linrx_trust_i ) = 1.0
571 err_bnds_comp( j, la_linrx_trust_i ) = 1.0
572 END IF
573 IF ( n_err_bnds .GE. 2 ) THEN
574 err_bnds_norm( j, la_linrx_err_i ) = 1.0
575 err_bnds_comp( j, la_linrx_err_i ) = 1.0
576 END IF
577 IF ( n_err_bnds .GE. 3 ) THEN
578 err_bnds_norm( j, la_linrx_rcond_i ) = 0.0
579 err_bnds_comp( j, la_linrx_rcond_i ) = 0.0
580 END IF
581 END DO
582*
583* Compute the norm of A and the reciprocal of the condition
584* number of A.
585*
586 norm = 'I'
587 anorm = clanhe( norm, uplo, n, a, lda, rwork )
588 CALL checon( uplo, n, af, ldaf, ipiv, anorm, rcond, work,
589 $ info )
590*
591* Perform refinement on each right-hand side
592*
593 IF ( ref_type .NE. 0 ) THEN
594
595 prec_type = ilaprec( 'D' )
596
597 CALL cla_herfsx_extended( prec_type, uplo, n,
598 $ nrhs, a, lda, af, ldaf, ipiv, rcequ, s, b,
599 $ ldb, x, ldx, berr, n_norms, err_bnds_norm, err_bnds_comp,
600 $ work, rwork, work(n+1),
601 $ transfer(rwork(1:2*n), (/ (zero, zero) /), n), rcond,
602 $ ithresh, rthresh, unstable_thresh, ignore_cwise,
603 $ info )
604 END IF
605
606 err_lbnd = max( 10.0, sqrt( real( n ) ) ) * slamch( 'Epsilon' )
607 IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 1 ) THEN
608*
609* Compute scaled normwise condition number cond(A*C).
610*
611 IF ( rcequ ) THEN
612 rcond_tmp = cla_hercond_c( uplo, n, a, lda, af, ldaf,
613 $ ipiv,
614 $ s, .true., info, work, rwork )
615 ELSE
616 rcond_tmp = cla_hercond_c( uplo, n, a, lda, af, ldaf,
617 $ ipiv,
618 $ s, .false., info, work, rwork )
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. 1.0 )
626 $ err_bnds_norm( j, la_linrx_err_i ) = 1.0
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 ) = 1.0
632 err_bnds_norm( j, la_linrx_trust_i ) = 0.0
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 ) = 1.0
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( slamch( 'Epsilon' ) )
659 DO j = 1, nrhs
660 IF ( err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
661 $ THEN
662 rcond_tmp = cla_hercond_x( uplo, n, a, lda, af, ldaf,
663 $ ipiv, x( 1, j ), info, work, rwork )
664 ELSE
665 rcond_tmp = 0.0
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. 1.0 )
672 $ err_bnds_comp( j, la_linrx_err_i ) = 1.0
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 ) = 1.0
678 err_bnds_comp( j, la_linrx_trust_i ) = 0.0
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 ) = 1.0
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 CHERFSX
699*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine checon(uplo, n, a, lda, ipiv, anorm, rcond, work, info)
CHECON
Definition checon.f:123
integer function ilaprec(prec)
ILAPREC
Definition ilaprec.f:56
real function cla_hercond_c(uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
CLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefin...
real function cla_hercond_x(uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)
CLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite m...
subroutine cla_herfsx_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)
CLA_HERFSX_EXTENDED improves the computed solution to a system of linear equations for Hermitian inde...
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
real function clanhe(norm, uplo, n, a, lda, work)
CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition clanhe.f:122
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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