LAPACK 3.12.0
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

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

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       = 'Y':  Both row and column equilibration, i.e., A has been
               replaced by diag(S) * A * diag(S).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 "Trust/don't trust" boolean. Trust the answer if the
              reciprocal condition number is less than the threshold
              sqrt(n) * slamch('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) * 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 "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 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 "Trust/don't trust" boolean. Trust the answer if the
              reciprocal condition number is less than the threshold
              sqrt(n) * slamch('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) * 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 "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 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 397 of file cherfsx.f.

401*
402* -- LAPACK computational routine --
403* -- LAPACK is a software package provided by Univ. of Tennessee, --
404* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
405*
406* .. Scalar Arguments ..
407 CHARACTER UPLO, EQUED
408 INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
409 $ N_ERR_BNDS
410 REAL RCOND
411* ..
412* .. Array Arguments ..
413 INTEGER IPIV( * )
414 COMPLEX A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
415 $ X( LDX, * ), WORK( * )
416 REAL S( * ), PARAMS( * ), BERR( * ), RWORK( * ),
417 $ ERR_BNDS_NORM( NRHS, * ),
418 $ ERR_BNDS_COMP( NRHS, * )
419*
420* ==================================================================
421*
422* .. Parameters ..
423 REAL ZERO, ONE
424 parameter( zero = 0.0e+0, one = 1.0e+0 )
425 REAL ITREF_DEFAULT, ITHRESH_DEFAULT,
426 $ COMPONENTWISE_DEFAULT
427 REAL RTHRESH_DEFAULT, DZTHRESH_DEFAULT
428 parameter( itref_default = 1.0 )
429 parameter( ithresh_default = 10.0 )
430 parameter( componentwise_default = 1.0 )
431 parameter( rthresh_default = 0.5 )
432 parameter( dzthresh_default = 0.25 )
433 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
434 $ LA_LINRX_CWISE_I
435 parameter( la_linrx_itref_i = 1,
436 $ la_linrx_ithresh_i = 2 )
437 parameter( la_linrx_cwise_i = 3 )
438 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
439 $ LA_LINRX_RCOND_I
440 parameter( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
441 parameter( la_linrx_rcond_i = 3 )
442* ..
443* .. Local Scalars ..
444 CHARACTER(1) NORM
445 LOGICAL RCEQU
446 INTEGER J, PREC_TYPE, REF_TYPE
447 INTEGER N_NORMS
448 REAL ANORM, RCOND_TMP
449 REAL ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
450 LOGICAL IGNORE_CWISE
451 INTEGER ITHRESH
452 REAL RTHRESH, UNSTABLE_THRESH
453* ..
454* .. External Subroutines ..
456* ..
457* .. Intrinsic Functions ..
458 INTRINSIC max, sqrt, transfer
459* ..
460* .. External Functions ..
461 EXTERNAL lsame, ilaprec
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. .NOT.lsame( uplo, 'L' ) ) THEN
520 info = -1
521 ELSE IF( .NOT.rcequ .AND. .NOT.lsame( equed, 'N' ) ) THEN
522 info = -2
523 ELSE IF( n.LT.0 ) THEN
524 info = -3
525 ELSE IF( nrhs.LT.0 ) THEN
526 info = -4
527 ELSE IF( lda.LT.max( 1, n ) ) THEN
528 info = -6
529 ELSE IF( ldaf.LT.max( 1, n ) ) THEN
530 info = -8
531 ELSE IF( ldb.LT.max( 1, n ) ) THEN
532 info = -12
533 ELSE IF( ldx.LT.max( 1, n ) ) THEN
534 info = -14
535 END IF
536 IF( info.NE.0 ) THEN
537 CALL xerbla( 'CHERFSX', -info )
538 RETURN
539 END IF
540*
541* Quick return if possible.
542*
543 IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
544 rcond = 1.0
545 DO j = 1, nrhs
546 berr( j ) = 0.0
547 IF ( n_err_bnds .GE. 1 ) THEN
548 err_bnds_norm( j, la_linrx_trust_i ) = 1.0
549 err_bnds_comp( j, la_linrx_trust_i ) = 1.0
550 END IF
551 IF ( n_err_bnds .GE. 2 ) THEN
552 err_bnds_norm( j, la_linrx_err_i ) = 0.0
553 err_bnds_comp( j, la_linrx_err_i ) = 0.0
554 END IF
555 IF ( n_err_bnds .GE. 3 ) THEN
556 err_bnds_norm( j, la_linrx_rcond_i ) = 1.0
557 err_bnds_comp( j, la_linrx_rcond_i ) = 1.0
558 END IF
559 END DO
560 RETURN
561 END IF
562*
563* Default to failure.
564*
565 rcond = 0.0
566 DO j = 1, nrhs
567 berr( j ) = 1.0
568 IF ( n_err_bnds .GE. 1 ) THEN
569 err_bnds_norm( j, la_linrx_trust_i ) = 1.0
570 err_bnds_comp( j, la_linrx_trust_i ) = 1.0
571 END IF
572 IF ( n_err_bnds .GE. 2 ) THEN
573 err_bnds_norm( j, la_linrx_err_i ) = 1.0
574 err_bnds_comp( j, la_linrx_err_i ) = 1.0
575 END IF
576 IF ( n_err_bnds .GE. 3 ) THEN
577 err_bnds_norm( j, la_linrx_rcond_i ) = 0.0
578 err_bnds_comp( j, la_linrx_rcond_i ) = 0.0
579 END IF
580 END DO
581*
582* Compute the norm of A and the reciprocal of the condition
583* number of A.
584*
585 norm = 'I'
586 anorm = clanhe( norm, uplo, n, a, lda, rwork )
587 CALL checon( uplo, n, af, ldaf, ipiv, anorm, rcond, work,
588 $ info )
589*
590* Perform refinement on each right-hand side
591*
592 IF ( ref_type .NE. 0 ) THEN
593
594 prec_type = ilaprec( 'D' )
595
596 CALL cla_herfsx_extended( prec_type, uplo, n,
597 $ nrhs, a, lda, af, ldaf, ipiv, rcequ, s, b,
598 $ ldb, x, ldx, berr, n_norms, err_bnds_norm, err_bnds_comp,
599 $ work, rwork, work(n+1),
600 $ transfer(rwork(1:2*n), (/ (zero, zero) /), n), rcond,
601 $ ithresh, rthresh, unstable_thresh, ignore_cwise,
602 $ info )
603 END IF
604
605 err_lbnd = max( 10.0, sqrt( real( n ) ) ) * slamch( 'Epsilon' )
606 IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 1 ) THEN
607*
608* Compute scaled normwise condition number cond(A*C).
609*
610 IF ( rcequ ) THEN
611 rcond_tmp = cla_hercond_c( uplo, n, a, lda, af, ldaf, ipiv,
612 $ s, .true., info, work, rwork )
613 ELSE
614 rcond_tmp = cla_hercond_c( uplo, n, a, lda, af, ldaf, ipiv,
615 $ s, .false., info, work, rwork )
616 END IF
617 DO j = 1, nrhs
618*
619* Cap the error at 1.0.
620*
621 IF ( n_err_bnds .GE. la_linrx_err_i
622 $ .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0 )
623 $ err_bnds_norm( j, la_linrx_err_i ) = 1.0
624*
625* Threshold the error (see LAWN).
626*
627 IF (rcond_tmp .LT. illrcond_thresh) THEN
628 err_bnds_norm( j, la_linrx_err_i ) = 1.0
629 err_bnds_norm( j, la_linrx_trust_i ) = 0.0
630 IF ( info .LE. n ) info = n + j
631 ELSE IF ( err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd )
632 $ THEN
633 err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
634 err_bnds_norm( j, la_linrx_trust_i ) = 1.0
635 END IF
636*
637* Save the condition number.
638*
639 IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
640 err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
641 END IF
642 END DO
643 END IF
644
645 IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 2 ) THEN
646*
647* Compute componentwise condition number cond(A*diag(Y(:,J))) for
648* each right-hand side using the current solution as an estimate of
649* the true solution. If the componentwise error estimate is too
650* large, then the solution is a lousy estimate of truth and the
651* estimated RCOND may be too optimistic. To avoid misleading users,
652* the inverse condition number is set to 0.0 when the estimated
653* cwise error is at least CWISE_WRONG.
654*
655 cwise_wrong = sqrt( slamch( 'Epsilon' ) )
656 DO j = 1, nrhs
657 IF ( err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
658 $ THEN
659 rcond_tmp = cla_hercond_x( uplo, n, a, lda, af, ldaf,
660 $ ipiv, x( 1, j ), info, work, rwork )
661 ELSE
662 rcond_tmp = 0.0
663 END IF
664*
665* Cap the error at 1.0.
666*
667 IF ( n_err_bnds .GE. la_linrx_err_i
668 $ .AND. err_bnds_comp( j, la_linrx_err_i ) .GT. 1.0 )
669 $ err_bnds_comp( j, la_linrx_err_i ) = 1.0
670*
671* Threshold the error (see LAWN).
672*
673 IF ( rcond_tmp .LT. illrcond_thresh ) THEN
674 err_bnds_comp( j, la_linrx_err_i ) = 1.0
675 err_bnds_comp( j, la_linrx_trust_i ) = 0.0
676 IF ( .NOT. ignore_cwise
677 $ .AND. info.LT.n + j ) info = n + j
678 ELSE IF ( err_bnds_comp( j, la_linrx_err_i )
679 $ .LT. err_lbnd ) THEN
680 err_bnds_comp( j, la_linrx_err_i ) = err_lbnd
681 err_bnds_comp( j, la_linrx_trust_i ) = 1.0
682 END IF
683*
684* Save the condition number.
685*
686 IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
687 err_bnds_comp( j, la_linrx_rcond_i ) = rcond_tmp
688 END IF
689
690 END DO
691 END IF
692*
693 RETURN
694*
695* End of CHERFSX
696*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine checon(uplo, n, a, lda, ipiv, anorm, rcond, work, info)
CHECON
Definition checon.f:125
integer function ilaprec(prec)
ILAPREC
Definition ilaprec.f:58
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:124
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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