LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ 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

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

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**H*U or A = L*L**H, as computed by ZPOTRF.
!>
[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 ZGETRS.
!>     On exit, the improved solution matrix X.
!>
[in]LDX
!>          LDX is INTEGER
!>     The leading dimension of the array X.  LDX >= max(1,N).
!>
[out]RCOND
!>          RCOND is DOUBLE PRECISION
!>     Reciprocal scaled condition number.  This is an estimate of the
!>     reciprocal Skeel condition number of the matrix A after
!>     equilibration (if done).  If this is less than the machine
!>     precision (in particular, if it is zero), the matrix is singular
!>     to working precision.  Note that the error may still be small even
!>     if this number is very small and the matrix appears ill-
!>     conditioned.
!>
[out]BERR
!>          BERR is DOUBLE PRECISION array, dimension (NRHS)
!>     Componentwise relative backward error.  This is the
!>     componentwise relative backward error of each solution vector X(j)
!>     (i.e., the smallest relative change in any element of A or B that
!>     makes X(j) an exact solution).
!>
[in]N_ERR_BNDS
!>          N_ERR_BNDS is INTEGER
!>     Number of error bounds to return for each right hand side
!>     and each type (normwise or componentwise).  See ERR_BNDS_NORM and
!>     ERR_BNDS_COMP below.
!>
[out]ERR_BNDS_NORM
!>          ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
!>     For each right-hand side, this array contains information about
!>     various error bounds and condition numbers corresponding to the
!>     normwise relative error, which is defined as follows:
!>
!>     Normwise relative error in the ith solution vector:
!>             max_j (abs(XTRUE(j,i) - X(j,i)))
!>            ------------------------------
!>                  max_j abs(X(j,i))
!>
!>     The array is indexed by the type of error information as described
!>     below. There currently are up to three pieces of information
!>     returned.
!>
!>     The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
!>     right-hand side.
!>
!>     The second index in ERR_BNDS_NORM(:,err) contains the following
!>     three fields:
!>     err = 1  boolean. Trust the answer if the
!>              reciprocal condition number is less than the threshold
!>              sqrt(n) * dlamch('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) * 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 . 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  boolean. Trust the answer if the
!>              reciprocal condition number is less than the threshold
!>              sqrt(n) * dlamch('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) * 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 . 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 387 of file zporfsx.f.

392*
393* -- LAPACK computational routine --
394* -- LAPACK is a software package provided by Univ. of Tennessee, --
395* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
396*
397* .. Scalar Arguments ..
398 CHARACTER UPLO, EQUED
399 INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
400 $ N_ERR_BNDS
401 DOUBLE PRECISION RCOND
402* ..
403* .. Array Arguments ..
404 COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
405 $ X( LDX, * ), WORK( * )
406 DOUBLE PRECISION RWORK( * ), S( * ), PARAMS(*), BERR( * ),
407 $ ERR_BNDS_NORM( NRHS, * ),
408 $ ERR_BNDS_COMP( NRHS, * )
409* ..
410*
411* ==================================================================
412*
413* .. Parameters ..
414 DOUBLE PRECISION ZERO, ONE
415 parameter( zero = 0.0d+0, one = 1.0d+0 )
416 DOUBLE PRECISION ITREF_DEFAULT, ITHRESH_DEFAULT
417 DOUBLE PRECISION COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT
418 DOUBLE PRECISION DZTHRESH_DEFAULT
419 parameter( itref_default = 1.0d+0 )
420 parameter( ithresh_default = 10.0d+0 )
421 parameter( componentwise_default = 1.0d+0 )
422 parameter( rthresh_default = 0.5d+0 )
423 parameter( dzthresh_default = 0.25d+0 )
424 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
425 $ LA_LINRX_CWISE_I
426 parameter( la_linrx_itref_i = 1,
427 $ la_linrx_ithresh_i = 2 )
428 parameter( la_linrx_cwise_i = 3 )
429 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
430 $ LA_LINRX_RCOND_I
431 parameter( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
432 parameter( la_linrx_rcond_i = 3 )
433* ..
434* .. Local Scalars ..
435 CHARACTER(1) NORM
436 LOGICAL RCEQU
437 INTEGER J, PREC_TYPE, REF_TYPE
438 INTEGER N_NORMS
439 DOUBLE PRECISION ANORM, RCOND_TMP
440 DOUBLE PRECISION ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
441 LOGICAL IGNORE_CWISE
442 INTEGER ITHRESH
443 DOUBLE PRECISION RTHRESH, UNSTABLE_THRESH
444* ..
445* .. External Subroutines ..
446 EXTERNAL xerbla, zpocon, zla_porfsx_extended
447* ..
448* .. Intrinsic Functions ..
449 INTRINSIC max, sqrt, transfer
450* ..
451* .. External Functions ..
452 EXTERNAL lsame, ilaprec
453 EXTERNAL dlamch, zlanhe, zla_porcond_x,
454 $ zla_porcond_c
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.
512 $ .NOT.lsame( uplo, 'L' ) ) THEN
513 info = -1
514 ELSE IF( .NOT.rcequ .AND. .NOT.lsame( equed, 'N' ) ) THEN
515 info = -2
516 ELSE IF( n.LT.0 ) THEN
517 info = -3
518 ELSE IF( nrhs.LT.0 ) THEN
519 info = -4
520 ELSE IF( lda.LT.max( 1, n ) ) THEN
521 info = -6
522 ELSE IF( ldaf.LT.max( 1, n ) ) THEN
523 info = -8
524 ELSE IF( ldb.LT.max( 1, n ) ) THEN
525 info = -11
526 ELSE IF( ldx.LT.max( 1, n ) ) THEN
527 info = -13
528 END IF
529 IF( info.NE.0 ) THEN
530 CALL xerbla( 'ZPORFSX', -info )
531 RETURN
532 END IF
533*
534* Quick return if possible.
535*
536 IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
537 rcond = 1.0d+0
538 DO j = 1, nrhs
539 berr( j ) = 0.0d+0
540 IF ( n_err_bnds .GE. 1 ) THEN
541 err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
542 err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
543 END IF
544 IF ( n_err_bnds .GE. 2 ) THEN
545 err_bnds_norm( j, la_linrx_err_i ) = 0.0d+0
546 err_bnds_comp( j, la_linrx_err_i ) = 0.0d+0
547 END IF
548 IF ( n_err_bnds .GE. 3 ) THEN
549 err_bnds_norm( j, la_linrx_rcond_i ) = 1.0d+0
550 err_bnds_comp( j, la_linrx_rcond_i ) = 1.0d+0
551 END IF
552 END DO
553 RETURN
554 END IF
555*
556* Default to failure.
557*
558 rcond = 0.0d+0
559 DO j = 1, nrhs
560 berr( j ) = 1.0d+0
561 IF ( n_err_bnds .GE. 1 ) THEN
562 err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
563 err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
564 END IF
565 IF ( n_err_bnds .GE. 2 ) THEN
566 err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
567 err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
568 END IF
569 IF ( n_err_bnds .GE. 3 ) THEN
570 err_bnds_norm( j, la_linrx_rcond_i ) = 0.0d+0
571 err_bnds_comp( j, la_linrx_rcond_i ) = 0.0d+0
572 END IF
573 END DO
574*
575* Compute the norm of A and the reciprocal of the condition
576* number of A.
577*
578 norm = 'I'
579 anorm = zlanhe( norm, uplo, n, a, lda, rwork )
580 CALL zpocon( uplo, n, af, ldaf, anorm, rcond, work, rwork,
581 $ info )
582*
583* Perform refinement on each right-hand side
584*
585 IF ( ref_type .NE. 0 ) THEN
586
587 prec_type = ilaprec( 'E' )
588
589 CALL zla_porfsx_extended( prec_type, uplo, n,
590 $ nrhs, a, lda, af, ldaf, rcequ, s, b,
591 $ ldb, x, ldx, berr, n_norms, err_bnds_norm, err_bnds_comp,
592 $ work, rwork, work(n+1),
593 $ transfer(rwork(1:2*n), (/ (zero, zero) /), n), rcond,
594 $ ithresh, rthresh, unstable_thresh, ignore_cwise,
595 $ info )
596 END IF
597
598 err_lbnd = max( 10.0d+0,
599 $ sqrt( dble( n ) ) ) * dlamch( 'Epsilon' )
600 IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 1 ) THEN
601*
602* Compute scaled normwise condition number cond(A*C).
603*
604 IF ( rcequ ) THEN
605 rcond_tmp = zla_porcond_c( uplo, n, a, lda, af, ldaf,
606 $ s, .true., info, work, rwork )
607 ELSE
608 rcond_tmp = zla_porcond_c( uplo, n, a, lda, af, ldaf,
609 $ s, .false., info, work, rwork )
610 END IF
611 DO j = 1, nrhs
612*
613* Cap the error at 1.0.
614*
615 IF ( n_err_bnds .GE. la_linrx_err_i
616 $ .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0d+0 )
617 $ err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
618*
619* Threshold the error (see LAWN).
620*
621 IF ( rcond_tmp .LT. illrcond_thresh ) THEN
622 err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
623 err_bnds_norm( j, la_linrx_trust_i ) = 0.0d+0
624 IF ( info .LE. n ) info = n + j
625 ELSE IF ( err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd )
626 $ THEN
627 err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
628 err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
629 END IF
630*
631* Save the condition number.
632*
633 IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
634 err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
635 END IF
636
637 END DO
638 END IF
639
640 IF (n_err_bnds .GE. 1 .AND. n_norms .GE. 2) THEN
641*
642* Compute componentwise condition number cond(A*diag(Y(:,J))) for
643* each right-hand side using the current solution as an estimate of
644* the true solution. If the componentwise error estimate is too
645* large, then the solution is a lousy estimate of truth and the
646* estimated RCOND may be too optimistic. To avoid misleading users,
647* the inverse condition number is set to 0.0 when the estimated
648* cwise error is at least CWISE_WRONG.
649*
650 cwise_wrong = sqrt( dlamch( 'Epsilon' ) )
651 DO j = 1, nrhs
652 IF (err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
653 $ THEN
654 rcond_tmp = zla_porcond_x( uplo, n, a, lda, af, ldaf,
655 $ x(1,j), info, work, rwork )
656 ELSE
657 rcond_tmp = 0.0d+0
658 END IF
659*
660* Cap the error at 1.0.
661*
662 IF ( n_err_bnds .GE. la_linrx_err_i
663 $ .AND. err_bnds_comp( j, la_linrx_err_i ) .GT. 1.0d+0 )
664 $ err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
665*
666* Threshold the error (see LAWN).
667*
668 IF (rcond_tmp .LT. illrcond_thresh) THEN
669 err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
670 err_bnds_comp( j, la_linrx_trust_i ) = 0.0d+0
671 IF ( params( la_linrx_cwise_i ) .EQ. 1.0d+0
672 $ .AND. info.LT.n + j ) info = n + j
673 ELSE IF ( err_bnds_comp( j, la_linrx_err_i )
674 $ .LT. err_lbnd ) THEN
675 err_bnds_comp( j, la_linrx_err_i ) = err_lbnd
676 err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
677 END IF
678*
679* Save the condition number.
680*
681 IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
682 err_bnds_comp( j, la_linrx_rcond_i ) = rcond_tmp
683 END IF
684
685 END DO
686 END IF
687*
688 RETURN
689*
690* End of ZPORFSX
691*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
ilaprec
integer function ilaprec(prec)
ILAPREC
Definition ilaprec.f:56
zla_porcond_c
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...
Definition zla_porcond_c.f:130
zla_porcond_x
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...
Definition zla_porcond_x.f:123
zla_porfsx_extended
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...
Definition zla_porfsx_extended.f:386
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
zlanhe
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:122
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
zpocon
subroutine zpocon(uplo, n, a, lda, anorm, rcond, work, rwork, info)
ZPOCON
Definition zpocon.f:119
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