LAPACK  3.9.1
LAPACK: Linear Algebra PACKage

◆ zporfsx()

subroutine zporfsx ( character  UPLO,
character  EQUED,
integer  N,
integer  NRHS,
complex*16, dimension( lda, * )  A,
integer  LDA,
complex*16, dimension( ldaf, * )  AF,
integer  LDAF,
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 
)

ZPORFSX

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Purpose:
    ZPORFSX improves the computed solution to a system of linear
    equations when the coefficient matrix is Hermitian positive
    definite, 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       = 'Y':  Both row and column equilibration, i.e., A has been
               replaced by diag(S) * A * diag(S).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 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*16 array, dimension (LDAF,N)
     The triangular factor U or L from the Cholesky factorization
     A = U**T*U or A = L*L**T, as computed by DPOTRF.
[in]LDAF
          LDAF is INTEGER
     The leading dimension of the array AF.  LDAF >= max(1,N).
[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 < 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 389 of file zporfsx.f.

393 *
394 * -- LAPACK computational routine --
395 * -- LAPACK is a software package provided by Univ. of Tennessee, --
396 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
397 *
398 * .. Scalar Arguments ..
399  CHARACTER UPLO, EQUED
400  INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
401  $ N_ERR_BNDS
402  DOUBLE PRECISION RCOND
403 * ..
404 * .. Array Arguments ..
405  COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
406  $ X( LDX, * ), WORK( * )
407  DOUBLE PRECISION RWORK( * ), S( * ), PARAMS(*), BERR( * ),
408  $ ERR_BNDS_NORM( NRHS, * ),
409  $ ERR_BNDS_COMP( NRHS, * )
410 * ..
411 *
412 * ==================================================================
413 *
414 * .. Parameters ..
415  DOUBLE PRECISION ZERO, ONE
416  parameter( zero = 0.0d+0, one = 1.0d+0 )
417  DOUBLE PRECISION ITREF_DEFAULT, ITHRESH_DEFAULT
418  DOUBLE PRECISION COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT
419  DOUBLE PRECISION DZTHRESH_DEFAULT
420  parameter( itref_default = 1.0d+0 )
421  parameter( ithresh_default = 10.0d+0 )
422  parameter( componentwise_default = 1.0d+0 )
423  parameter( rthresh_default = 0.5d+0 )
424  parameter( dzthresh_default = 0.25d+0 )
425  INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
426  $ LA_LINRX_CWISE_I
427  parameter( la_linrx_itref_i = 1,
428  $ la_linrx_ithresh_i = 2 )
429  parameter( la_linrx_cwise_i = 3 )
430  INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
431  $ LA_LINRX_RCOND_I
432  parameter( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
433  parameter( la_linrx_rcond_i = 3 )
434 * ..
435 * .. Local Scalars ..
436  CHARACTER(1) NORM
437  LOGICAL RCEQU
438  INTEGER J, PREC_TYPE, REF_TYPE
439  INTEGER N_NORMS
440  DOUBLE PRECISION ANORM, RCOND_TMP
441  DOUBLE PRECISION ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
442  LOGICAL IGNORE_CWISE
443  INTEGER ITHRESH
444  DOUBLE PRECISION RTHRESH, UNSTABLE_THRESH
445 * ..
446 * .. External Subroutines ..
448 * ..
449 * .. Intrinsic Functions ..
450  INTRINSIC max, sqrt, transfer
451 * ..
452 * .. External Functions ..
453  EXTERNAL lsame, ilaprec
455  DOUBLE PRECISION DLAMCH, ZLANHE, ZLA_PORCOND_X, ZLA_PORCOND_C
456  LOGICAL LSAME
457  INTEGER ILAPREC
458 * ..
459 * .. Executable Statements ..
460 *
461 * Check the input parameters.
462 *
463  info = 0
464  ref_type = int( itref_default )
465  IF ( nparams .GE. la_linrx_itref_i ) THEN
466  IF ( params( la_linrx_itref_i ) .LT. 0.0d+0 ) THEN
467  params( la_linrx_itref_i ) = itref_default
468  ELSE
469  ref_type = params( la_linrx_itref_i )
470  END IF
471  END IF
472 *
473 * Set default parameters.
474 *
475  illrcond_thresh = dble( n ) * dlamch( 'Epsilon' )
476  ithresh = int( ithresh_default )
477  rthresh = rthresh_default
478  unstable_thresh = dzthresh_default
479  ignore_cwise = componentwise_default .EQ. 0.0d+0
480 *
481  IF ( nparams.GE.la_linrx_ithresh_i ) THEN
482  IF ( params(la_linrx_ithresh_i ).LT.0.0d+0 ) THEN
483  params( la_linrx_ithresh_i ) = ithresh
484  ELSE
485  ithresh = int( params( la_linrx_ithresh_i ) )
486  END IF
487  END IF
488  IF ( nparams.GE.la_linrx_cwise_i ) THEN
489  IF ( params(la_linrx_cwise_i ).LT.0.0d+0 ) THEN
490  IF ( ignore_cwise ) THEN
491  params( la_linrx_cwise_i ) = 0.0d+0
492  ELSE
493  params( la_linrx_cwise_i ) = 1.0d+0
494  END IF
495  ELSE
496  ignore_cwise = params( la_linrx_cwise_i ) .EQ. 0.0d+0
497  END IF
498  END IF
499  IF ( ref_type .EQ. 0 .OR. n_err_bnds .EQ. 0 ) THEN
500  n_norms = 0
501  ELSE IF ( ignore_cwise ) THEN
502  n_norms = 1
503  ELSE
504  n_norms = 2
505  END IF
506 *
507  rcequ = lsame( equed, 'Y' )
508 *
509 * Test input parameters.
510 *
511  IF (.NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
512  info = -1
513  ELSE IF( .NOT.rcequ .AND. .NOT.lsame( equed, 'N' ) ) THEN
514  info = -2
515  ELSE IF( n.LT.0 ) THEN
516  info = -3
517  ELSE IF( nrhs.LT.0 ) THEN
518  info = -4
519  ELSE IF( lda.LT.max( 1, n ) ) THEN
520  info = -6
521  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
522  info = -8
523  ELSE IF( ldb.LT.max( 1, n ) ) THEN
524  info = -11
525  ELSE IF( ldx.LT.max( 1, n ) ) THEN
526  info = -13
527  END IF
528  IF( info.NE.0 ) THEN
529  CALL xerbla( 'ZPORFSX', -info )
530  RETURN
531  END IF
532 *
533 * Quick return if possible.
534 *
535  IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
536  rcond = 1.0d+0
537  DO j = 1, nrhs
538  berr( j ) = 0.0d+0
539  IF ( n_err_bnds .GE. 1 ) THEN
540  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
541  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
542  END IF
543  IF ( n_err_bnds .GE. 2 ) THEN
544  err_bnds_norm( j, la_linrx_err_i ) = 0.0d+0
545  err_bnds_comp( j, la_linrx_err_i ) = 0.0d+0
546  END IF
547  IF ( n_err_bnds .GE. 3 ) THEN
548  err_bnds_norm( j, la_linrx_rcond_i ) = 1.0d+0
549  err_bnds_comp( j, la_linrx_rcond_i ) = 1.0d+0
550  END IF
551  END DO
552  RETURN
553  END IF
554 *
555 * Default to failure.
556 *
557  rcond = 0.0d+0
558  DO j = 1, nrhs
559  berr( j ) = 1.0d+0
560  IF ( n_err_bnds .GE. 1 ) THEN
561  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
562  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
563  END IF
564  IF ( n_err_bnds .GE. 2 ) THEN
565  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
566  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
567  END IF
568  IF ( n_err_bnds .GE. 3 ) THEN
569  err_bnds_norm( j, la_linrx_rcond_i ) = 0.0d+0
570  err_bnds_comp( j, la_linrx_rcond_i ) = 0.0d+0
571  END IF
572  END DO
573 *
574 * Compute the norm of A and the reciprocal of the condition
575 * number of A.
576 *
577  norm = 'I'
578  anorm = zlanhe( norm, uplo, n, a, lda, rwork )
579  CALL zpocon( uplo, n, af, ldaf, anorm, rcond, work, rwork,
580  $ info )
581 *
582 * Perform refinement on each right-hand side
583 *
584  IF ( ref_type .NE. 0 ) THEN
585 
586  prec_type = ilaprec( 'E' )
587 
588  CALL zla_porfsx_extended( prec_type, uplo, n,
589  $ nrhs, a, lda, af, ldaf, rcequ, s, b,
590  $ ldb, x, ldx, berr, n_norms, err_bnds_norm, err_bnds_comp,
591  $ work, rwork, work(n+1),
592  $ transfer(rwork(1:2*n), (/ (zero, zero) /), n), rcond,
593  $ ithresh, rthresh, unstable_thresh, ignore_cwise,
594  $ info )
595  END IF
596 
597  err_lbnd = max( 10.0d+0, sqrt( dble( n ) ) ) * dlamch( 'Epsilon' )
598  IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 1 ) THEN
599 *
600 * Compute scaled normwise condition number cond(A*C).
601 *
602  IF ( rcequ ) THEN
603  rcond_tmp = zla_porcond_c( uplo, n, a, lda, af, ldaf,
604  $ s, .true., info, work, rwork )
605  ELSE
606  rcond_tmp = zla_porcond_c( uplo, n, a, lda, af, ldaf,
607  $ s, .false., info, work, rwork )
608  END IF
609  DO j = 1, nrhs
610 *
611 * Cap the error at 1.0.
612 *
613  IF ( n_err_bnds .GE. la_linrx_err_i
614  $ .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0d+0 )
615  $ err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
616 *
617 * Threshold the error (see LAWN).
618 *
619  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
620  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
621  err_bnds_norm( j, la_linrx_trust_i ) = 0.0d+0
622  IF ( info .LE. n ) info = n + j
623  ELSE IF ( err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd )
624  $ THEN
625  err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
626  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
627  END IF
628 *
629 * Save the condition number.
630 *
631  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
632  err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
633  END IF
634 
635  END DO
636  END IF
637 
638  IF (n_err_bnds .GE. 1 .AND. n_norms .GE. 2) THEN
639 *
640 * Compute componentwise condition number cond(A*diag(Y(:,J))) for
641 * each right-hand side using the current solution as an estimate of
642 * the true solution. If the componentwise error estimate is too
643 * large, then the solution is a lousy estimate of truth and the
644 * estimated RCOND may be too optimistic. To avoid misleading users,
645 * the inverse condition number is set to 0.0 when the estimated
646 * cwise error is at least CWISE_WRONG.
647 *
648  cwise_wrong = sqrt( dlamch( 'Epsilon' ) )
649  DO j = 1, nrhs
650  IF (err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
651  $ THEN
652  rcond_tmp = zla_porcond_x( uplo, n, a, lda, af, ldaf,
653  $ x(1,j), info, work, rwork )
654  ELSE
655  rcond_tmp = 0.0d+0
656  END IF
657 *
658 * Cap the error at 1.0.
659 *
660  IF ( n_err_bnds .GE. la_linrx_err_i
661  $ .AND. err_bnds_comp( j, la_linrx_err_i ) .GT. 1.0d+0 )
662  $ err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
663 *
664 * Threshold the error (see LAWN).
665 *
666  IF (rcond_tmp .LT. illrcond_thresh) THEN
667  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
668  err_bnds_comp( j, la_linrx_trust_i ) = 0.0d+0
669  IF ( params( la_linrx_cwise_i ) .EQ. 1.0d+0
670  $ .AND. info.LT.n + j ) info = n + j
671  ELSE IF ( err_bnds_comp( j, la_linrx_err_i )
672  $ .LT. err_lbnd ) THEN
673  err_bnds_comp( j, la_linrx_err_i ) = err_lbnd
674  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
675  END IF
676 *
677 * Save the condition number.
678 *
679  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
680  err_bnds_comp( j, la_linrx_rcond_i ) = rcond_tmp
681  END IF
682 
683  END DO
684  END IF
685 *
686  RETURN
687 *
688 * End of ZPORFSX
689 *
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 zlanhe(NORM, UPLO, N, A, LDA, WORK)
ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlanhe.f:124
double precision function zla_porcond_c(UPLO, N, A, LDA, AF, LDAF, C, CAPPLY, INFO, WORK, RWORK)
ZLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positiv...
subroutine zpocon(UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK, INFO)
ZPOCON
Definition: zpocon.f:121
subroutine zla_porfsx_extended(PREC_TYPE, UPLO, N, NRHS, A, LDA, AF, LDAF, 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_PORFSX_EXTENDED improves the computed solution to a system of linear equations for symmetric or H...
double precision function zla_porcond_x(UPLO, N, A, LDA, AF, LDAF, X, INFO, WORK, RWORK)
ZLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-def...
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