LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ dporfsx()

subroutine dporfsx ( character  UPLO,
character  EQUED,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldaf, * )  AF,
integer  LDAF,
double precision, dimension( * )  S,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, 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,
double precision, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  INFO 
)

DPORFSX

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Purpose:
    DPORFSX improves the computed solution to a system of linear
    equations when the coefficient matrix is symmetric 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       = 'Y':  Both row and column equilibration, i.e., A has been
               replaced by diag(S) * A * diag(S).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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (4*N)
[out]IWORK
          IWORK is INTEGER array, dimension (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 390 of file dporfsx.f.

394 *
395 * -- LAPACK computational routine --
396 * -- LAPACK is a software package provided by Univ. of Tennessee, --
397 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
398 *
399 * .. Scalar Arguments ..
400  CHARACTER UPLO, EQUED
401  INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
402  $ N_ERR_BNDS
403  DOUBLE PRECISION RCOND
404 * ..
405 * .. Array Arguments ..
406  INTEGER IWORK( * )
407  DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
408  $ X( LDX, * ), WORK( * )
409  DOUBLE PRECISION S( * ), PARAMS( * ), BERR( * ),
410  $ ERR_BNDS_NORM( NRHS, * ),
411  $ ERR_BNDS_COMP( NRHS, * )
412 * ..
413 *
414 * ==================================================================
415 *
416 * .. Parameters ..
417  DOUBLE PRECISION ZERO, ONE
418  parameter( zero = 0.0d+0, one = 1.0d+0 )
419  DOUBLE PRECISION ITREF_DEFAULT, ITHRESH_DEFAULT
420  DOUBLE PRECISION COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT
421  DOUBLE PRECISION DZTHRESH_DEFAULT
422  parameter( itref_default = 1.0d+0 )
423  parameter( ithresh_default = 10.0d+0 )
424  parameter( componentwise_default = 1.0d+0 )
425  parameter( rthresh_default = 0.5d+0 )
426  parameter( dzthresh_default = 0.25d+0 )
427  INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
428  $ LA_LINRX_CWISE_I
429  parameter( la_linrx_itref_i = 1,
430  $ la_linrx_ithresh_i = 2 )
431  parameter( la_linrx_cwise_i = 3 )
432  INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
433  $ LA_LINRX_RCOND_I
434  parameter( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
435  parameter( la_linrx_rcond_i = 3 )
436 * ..
437 * .. Local Scalars ..
438  CHARACTER(1) NORM
439  LOGICAL RCEQU
440  INTEGER J, PREC_TYPE, REF_TYPE
441  INTEGER N_NORMS
442  DOUBLE PRECISION ANORM, RCOND_TMP
443  DOUBLE PRECISION ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
444  LOGICAL IGNORE_CWISE
445  INTEGER ITHRESH
446  DOUBLE PRECISION RTHRESH, UNSTABLE_THRESH
447 * ..
448 * .. External Subroutines ..
450 * ..
451 * .. Intrinsic Functions ..
452  INTRINSIC max, sqrt
453 * ..
454 * .. External Functions ..
455  EXTERNAL lsame, ilaprec
456  EXTERNAL dlamch, dlansy, dla_porcond
457  DOUBLE PRECISION DLAMCH, DLANSY, DLA_PORCOND
458  LOGICAL LSAME
459  INTEGER ILAPREC
460 * ..
461 * .. Executable Statements ..
462 *
463 * Check the input parameters.
464 *
465  info = 0
466  ref_type = int( itref_default )
467  IF ( nparams .GE. la_linrx_itref_i ) THEN
468  IF ( params( la_linrx_itref_i ) .LT. 0.0d+0 ) THEN
469  params( la_linrx_itref_i ) = itref_default
470  ELSE
471  ref_type = params( la_linrx_itref_i )
472  END IF
473  END IF
474 *
475 * Set default parameters.
476 *
477  illrcond_thresh = dble( n ) * dlamch( 'Epsilon' )
478  ithresh = int( ithresh_default )
479  rthresh = rthresh_default
480  unstable_thresh = dzthresh_default
481  ignore_cwise = componentwise_default .EQ. 0.0d+0
482 *
483  IF ( nparams.GE.la_linrx_ithresh_i ) THEN
484  IF ( params( la_linrx_ithresh_i ).LT.0.0d+0 ) THEN
485  params( la_linrx_ithresh_i ) = ithresh
486  ELSE
487  ithresh = int( params( la_linrx_ithresh_i ) )
488  END IF
489  END IF
490  IF ( nparams.GE.la_linrx_cwise_i ) THEN
491  IF ( params( la_linrx_cwise_i ).LT.0.0d+0 ) THEN
492  IF ( ignore_cwise ) THEN
493  params( la_linrx_cwise_i ) = 0.0d+0
494  ELSE
495  params( la_linrx_cwise_i ) = 1.0d+0
496  END IF
497  ELSE
498  ignore_cwise = params( la_linrx_cwise_i ) .EQ. 0.0d+0
499  END IF
500  END IF
501  IF ( ref_type .EQ. 0 .OR. n_err_bnds .EQ. 0 ) THEN
502  n_norms = 0
503  ELSE IF ( ignore_cwise ) THEN
504  n_norms = 1
505  ELSE
506  n_norms = 2
507  END IF
508 *
509  rcequ = lsame( equed, 'Y' )
510 *
511 * Test input parameters.
512 *
513  IF (.NOT.lsame(uplo, 'U') .AND. .NOT.lsame(uplo, 'L')) THEN
514  info = -1
515  ELSE IF( .NOT.rcequ .AND. .NOT.lsame( equed, 'N' ) ) THEN
516  info = -2
517  ELSE IF( n.LT.0 ) THEN
518  info = -3
519  ELSE IF( nrhs.LT.0 ) THEN
520  info = -4
521  ELSE IF( lda.LT.max( 1, n ) ) THEN
522  info = -6
523  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
524  info = -8
525  ELSE IF( ldb.LT.max( 1, n ) ) THEN
526  info = -11
527  ELSE IF( ldx.LT.max( 1, n ) ) THEN
528  info = -13
529  END IF
530  IF( info.NE.0 ) THEN
531  CALL xerbla( 'DPORFSX', -info )
532  RETURN
533  END IF
534 *
535 * Quick return if possible.
536 *
537  IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
538  rcond = 1.0d+0
539  DO j = 1, nrhs
540  berr( j ) = 0.0d+0
541  IF ( n_err_bnds .GE. 1 ) THEN
542  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
543  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
544  END IF
545  IF ( n_err_bnds .GE. 2 ) THEN
546  err_bnds_norm( j, la_linrx_err_i ) = 0.0d+0
547  err_bnds_comp( j, la_linrx_err_i ) = 0.0d+0
548  END IF
549  IF ( n_err_bnds .GE. 3 ) THEN
550  err_bnds_norm( j, la_linrx_rcond_i ) = 1.0d+0
551  err_bnds_comp( j, la_linrx_rcond_i ) = 1.0d+0
552  END IF
553  END DO
554  RETURN
555  END IF
556 *
557 * Default to failure.
558 *
559  rcond = 0.0d+0
560  DO j = 1, nrhs
561  berr( j ) = 1.0d+0
562  IF ( n_err_bnds .GE. 1 ) THEN
563  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
564  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
565  END IF
566  IF ( n_err_bnds .GE. 2 ) THEN
567  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
568  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
569  END IF
570  IF ( n_err_bnds .GE. 3 ) THEN
571  err_bnds_norm( j, la_linrx_rcond_i ) = 0.0d+0
572  err_bnds_comp( j, la_linrx_rcond_i ) = 0.0d+0
573  END IF
574  END DO
575 *
576 * Compute the norm of A and the reciprocal of the condition
577 * number of A.
578 *
579  norm = 'I'
580  anorm = dlansy( norm, uplo, n, a, lda, work )
581  CALL dpocon( uplo, n, af, ldaf, anorm, rcond, work,
582  $ iwork, info )
583 *
584 * Perform refinement on each right-hand side
585 *
586  IF ( ref_type .NE. 0 ) THEN
587 
588  prec_type = ilaprec( 'E' )
589 
590  CALL dla_porfsx_extended( prec_type, uplo, n,
591  $ nrhs, a, lda, af, ldaf, rcequ, s, b,
592  $ ldb, x, ldx, berr, n_norms, err_bnds_norm, err_bnds_comp,
593  $ work( n+1 ), work( 1 ), work( 2*n+1 ), work( 1 ), rcond,
594  $ ithresh, rthresh, unstable_thresh, ignore_cwise,
595  $ info )
596  END IF
597 
598  err_lbnd = max( 10.0d+0, sqrt( dble( n ) ) ) * dlamch( 'Epsilon' )
599  IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 1 ) THEN
600 *
601 * Compute scaled normwise condition number cond(A*C).
602 *
603  IF ( rcequ ) THEN
604  rcond_tmp = dla_porcond( uplo, n, a, lda, af, ldaf,
605  $ -1, s, info, work, iwork )
606  ELSE
607  rcond_tmp = dla_porcond( uplo, n, a, lda, af, ldaf,
608  $ 0, s, info, work, iwork )
609  END IF
610  DO j = 1, nrhs
611 *
612 * Cap the error at 1.0.
613 *
614  IF ( n_err_bnds .GE. la_linrx_err_i
615  $ .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0d+0 )
616  $ err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
617 *
618 * Threshold the error (see LAWN).
619 *
620  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
621  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
622  err_bnds_norm( j, la_linrx_trust_i ) = 0.0d+0
623  IF ( info .LE. n ) info = n + j
624  ELSE IF ( err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd )
625  $ THEN
626  err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
627  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
628  END IF
629 *
630 * Save the condition number.
631 *
632  IF (n_err_bnds .GE. la_linrx_rcond_i) THEN
633  err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
634  END IF
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 = dla_porcond( uplo, n, a, lda, af, ldaf, 1,
653  $ x( 1, j ), info, work, iwork )
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 DPORFSX
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
subroutine dla_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)
DLA_PORFSX_EXTENDED improves the computed solution to a system of linear equations for symmetric or H...
subroutine dpocon(UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK, INFO)
DPOCON
Definition: dpocon.f:121
double precision function dla_porcond(UPLO, N, A, LDA, AF, LDAF, CMODE, C, INFO, WORK, IWORK)
DLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix.
Definition: dla_porcond.f:142
double precision function dlansy(NORM, UPLO, N, A, LDA, WORK)
DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlansy.f:122
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