 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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

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 = 'N': No equilibration = 'Y': Both row and column equilibration, i.e., A has been replaced by diag(S) * A * diag(S).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 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 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**T or A = L*D*L**T as computed by SSYTRF.``` [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 SSYTRF.``` [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 SGETRS. 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 .LT. 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 .LE. 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 .LT. 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.```
Date
April 2012

Definition at line 403 of file cherfsx.f.

403 *
404 * -- LAPACK computational routine (version 3.4.1) --
405 * -- LAPACK is a software package provided by Univ. of Tennessee, --
406 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
407 * April 2012
408 *
409 * .. Scalar Arguments ..
410  CHARACTER uplo, equed
411  INTEGER info, lda, ldaf, ldb, ldx, n, nrhs, nparams,
412  \$ n_err_bnds
413  REAL rcond
414 * ..
415 * .. Array Arguments ..
416  INTEGER ipiv( * )
417  COMPLEX a( lda, * ), af( ldaf, * ), b( ldb, * ),
418  \$ x( ldx, * ), work( * )
419  REAL s( * ), params( * ), berr( * ), rwork( * ),
420  \$ err_bnds_norm( nrhs, * ),
421  \$ err_bnds_comp( nrhs, * )
422 *
423 * ==================================================================
424 *
425 * .. Parameters ..
426  REAL zero, one
427  parameter ( zero = 0.0e+0, one = 1.0e+0 )
428  REAL itref_default, ithresh_default,
429  \$ componentwise_default
430  REAL rthresh_default, dzthresh_default
431  parameter ( itref_default = 1.0 )
432  parameter ( ithresh_default = 10.0 )
433  parameter ( componentwise_default = 1.0 )
434  parameter ( rthresh_default = 0.5 )
435  parameter ( dzthresh_default = 0.25 )
436  INTEGER la_linrx_itref_i, la_linrx_ithresh_i,
437  \$ la_linrx_cwise_i
438  parameter ( la_linrx_itref_i = 1,
439  \$ la_linrx_ithresh_i = 2 )
440  parameter ( la_linrx_cwise_i = 3 )
441  INTEGER la_linrx_trust_i, la_linrx_err_i,
442  \$ la_linrx_rcond_i
443  parameter ( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
444  parameter ( la_linrx_rcond_i = 3 )
445 * ..
446 * .. Local Scalars ..
447  CHARACTER(1) norm
448  LOGICAL rcequ
449  INTEGER j, prec_type, ref_type
450  INTEGER n_norms
451  REAL anorm, rcond_tmp
452  REAL illrcond_thresh, err_lbnd, cwise_wrong
453  LOGICAL ignore_cwise
454  INTEGER ithresh
455  REAL rthresh, unstable_thresh
456 * ..
457 * .. External Subroutines ..
459 * ..
460 * .. Intrinsic Functions ..
461  INTRINSIC max, sqrt, transfer
462 * ..
463 * .. External Functions ..
464  EXTERNAL lsame, blas_fpinfo_x, ilatrans, ilaprec
467  LOGICAL lsame
468  INTEGER blas_fpinfo_x
469  INTEGER ilatrans, ilaprec
470 * ..
471 * .. Executable Statements ..
472 *
473 * Check the input parameters.
474 *
475  info = 0
476  ref_type = int( itref_default )
477  IF ( nparams .GE. la_linrx_itref_i ) THEN
478  IF ( params( la_linrx_itref_i ) .LT. 0.0 ) THEN
479  params( la_linrx_itref_i ) = itref_default
480  ELSE
481  ref_type = params( la_linrx_itref_i )
482  END IF
483  END IF
484 *
485 * Set default parameters.
486 *
487  illrcond_thresh = REAL( N ) * slamch( 'Epsilon' )
488  ithresh = int( ithresh_default )
489  rthresh = rthresh_default
490  unstable_thresh = dzthresh_default
491  ignore_cwise = componentwise_default .EQ. 0.0
492 *
493  IF ( nparams.GE.la_linrx_ithresh_i ) THEN
494  IF ( params( la_linrx_ithresh_i ).LT.0.0 ) THEN
495  params( la_linrx_ithresh_i ) = ithresh
496  ELSE
497  ithresh = int( params( la_linrx_ithresh_i ) )
498  END IF
499  END IF
500  IF ( nparams.GE.la_linrx_cwise_i ) THEN
501  IF ( params(la_linrx_cwise_i ).LT.0.0 ) THEN
502  IF ( ignore_cwise ) THEN
503  params( la_linrx_cwise_i ) = 0.0
504  ELSE
505  params( la_linrx_cwise_i ) = 1.0
506  END IF
507  ELSE
508  ignore_cwise = params( la_linrx_cwise_i ) .EQ. 0.0
509  END IF
510  END IF
511  IF ( ref_type .EQ. 0 .OR. n_err_bnds .EQ. 0 ) THEN
512  n_norms = 0
513  ELSE IF ( ignore_cwise ) THEN
514  n_norms = 1
515  ELSE
516  n_norms = 2
517  END IF
518 *
519  rcequ = lsame( equed, 'Y' )
520 *
521 * Test input parameters.
522 *
523  IF (.NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
524  info = -1
525  ELSE IF( .NOT.rcequ .AND. .NOT.lsame( equed, 'N' ) ) THEN
526  info = -2
527  ELSE IF( n.LT.0 ) THEN
528  info = -3
529  ELSE IF( nrhs.LT.0 ) THEN
530  info = -4
531  ELSE IF( lda.LT.max( 1, n ) ) THEN
532  info = -6
533  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
534  info = -8
535  ELSE IF( ldb.LT.max( 1, n ) ) THEN
536  info = -12
537  ELSE IF( ldx.LT.max( 1, n ) ) THEN
538  info = -14
539  END IF
540  IF( info.NE.0 ) THEN
541  CALL xerbla( 'CHERFSX', -info )
542  RETURN
543  END IF
544 *
545 * Quick return if possible.
546 *
547  IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
548  rcond = 1.0
549  DO j = 1, nrhs
550  berr( j ) = 0.0
551  IF ( n_err_bnds .GE. 1 ) THEN
552  err_bnds_norm( j, la_linrx_trust_i ) = 1.0
553  err_bnds_comp( j, la_linrx_trust_i ) = 1.0
554  END IF
555  IF ( n_err_bnds .GE. 2 ) THEN
556  err_bnds_norm( j, la_linrx_err_i ) = 0.0
557  err_bnds_comp( j, la_linrx_err_i ) = 0.0
558  END IF
559  IF ( n_err_bnds .GE. 3 ) THEN
560  err_bnds_norm( j, la_linrx_rcond_i ) = 1.0
561  err_bnds_comp( j, la_linrx_rcond_i ) = 1.0
562  END IF
563  END DO
564  RETURN
565  END IF
566 *
567 * Default to failure.
568 *
569  rcond = 0.0
570  DO j = 1, nrhs
571  berr( j ) = 1.0
572  IF ( n_err_bnds .GE. 1 ) THEN
573  err_bnds_norm( j, la_linrx_trust_i ) = 1.0
574  err_bnds_comp( j, la_linrx_trust_i ) = 1.0
575  END IF
576  IF ( n_err_bnds .GE. 2 ) THEN
577  err_bnds_norm( j, la_linrx_err_i ) = 1.0
578  err_bnds_comp( j, la_linrx_err_i ) = 1.0
579  END IF
580  IF ( n_err_bnds .GE. 3 ) THEN
581  err_bnds_norm( j, la_linrx_rcond_i ) = 0.0
582  err_bnds_comp( j, la_linrx_rcond_i ) = 0.0
583  END IF
584  END DO
585 *
586 * Compute the norm of A and the reciprocal of the condition
587 * number of A.
588 *
589  norm = 'I'
590  anorm = clanhe( norm, uplo, n, a, lda, rwork )
591  CALL checon( uplo, n, af, ldaf, ipiv, anorm, rcond, work,
592  \$ info )
593 *
594 * Perform refinement on each right-hand side
595 *
596  IF ( ref_type .NE. 0 ) THEN
597
598  prec_type = ilaprec( 'D' )
599
600  CALL cla_herfsx_extended( prec_type, uplo, n,
601  \$ nrhs, a, lda, af, ldaf, ipiv, rcequ, s, b,
602  \$ ldb, x, ldx, berr, n_norms, err_bnds_norm, err_bnds_comp,
603  \$ work, rwork, work(n+1),
604  \$ transfer(rwork(1:2*n), (/ (zero, zero) /), n), rcond,
605  \$ ithresh, rthresh, unstable_thresh, ignore_cwise,
606  \$ info )
607  END IF
608
609  err_lbnd = max( 10.0, sqrt( REAL( N ) ) ) * slamch( 'Epsilon' )
610  IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 1 ) THEN
611 *
612 * Compute scaled normwise condition number cond(A*C).
613 *
614  IF ( rcequ ) THEN
615  rcond_tmp = cla_hercond_c( uplo, n, a, lda, af, ldaf, ipiv,
616  \$ s, .true., info, work, rwork )
617  ELSE
618  rcond_tmp = cla_hercond_c( uplo, n, a, lda, af, ldaf, ipiv,
619  \$ s, .false., info, work, rwork )
620  END IF
621  DO j = 1, nrhs
622 *
623 * Cap the error at 1.0.
624 *
625  IF ( n_err_bnds .GE. la_linrx_err_i
626  \$ .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0 )
627  \$ err_bnds_norm( j, la_linrx_err_i ) = 1.0
628 *
629 * Threshold the error (see LAWN).
630 *
631  IF (rcond_tmp .LT. illrcond_thresh) THEN
632  err_bnds_norm( j, la_linrx_err_i ) = 1.0
633  err_bnds_norm( j, la_linrx_trust_i ) = 0.0
634  IF ( info .LE. n ) info = n + j
635  ELSE IF ( err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd )
636  \$ THEN
637  err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
638  err_bnds_norm( j, la_linrx_trust_i ) = 1.0
639  END IF
640 *
641 * Save the condition number.
642 *
643  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
644  err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
645  END IF
646  END DO
647  END IF
648
649  IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 2 ) THEN
650 *
651 * Compute componentwise condition number cond(A*diag(Y(:,J))) for
652 * each right-hand side using the current solution as an estimate of
653 * the true solution. If the componentwise error estimate is too
654 * large, then the solution is a lousy estimate of truth and the
655 * estimated RCOND may be too optimistic. To avoid misleading users,
656 * the inverse condition number is set to 0.0 when the estimated
657 * cwise error is at least CWISE_WRONG.
658 *
659  cwise_wrong = sqrt( slamch( 'Epsilon' ) )
660  DO j = 1, nrhs
661  IF ( err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
662  \$ THEN
663  rcond_tmp = cla_hercond_x( uplo, n, a, lda, af, ldaf,
664  \$ ipiv, x( 1, j ), info, work, rwork )
665  ELSE
666  rcond_tmp = 0.0
667  END IF
668 *
669 * Cap the error at 1.0.
670 *
671  IF ( n_err_bnds .GE. la_linrx_err_i
672  \$ .AND. err_bnds_comp( j, la_linrx_err_i ) .GT. 1.0 )
673  \$ err_bnds_comp( j, la_linrx_err_i ) = 1.0
674 *
675 * Threshold the error (see LAWN).
676 *
677  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
678  err_bnds_comp( j, la_linrx_err_i ) = 1.0
679  err_bnds_comp( j, la_linrx_trust_i ) = 0.0
680  IF ( .NOT. ignore_cwise
681  \$ .AND. info.LT.n + j ) info = n + j
682  ELSE IF ( err_bnds_comp( j, la_linrx_err_i )
683  \$ .LT. err_lbnd ) THEN
684  err_bnds_comp( j, la_linrx_err_i ) = err_lbnd
685  err_bnds_comp( j, la_linrx_trust_i ) = 1.0
686  END IF
687 *
688 * Save the condition number.
689 *
690  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
691  err_bnds_comp( j, la_linrx_rcond_i ) = rcond_tmp
692  END IF
693
694  END DO
695  END IF
696 *
697  RETURN
698 *
699 * End of CHERFSX
700 *
integer function ilatrans(TRANS)
ILATRANS
Definition: ilatrans.f:60
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 clanhe(NORM, UPLO, N, A, LDA, WORK)
CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.
Definition: clanhe.f:126
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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...
integer function ilaprec(PREC)
ILAPREC
Definition: ilaprec.f:60
subroutine checon(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO)
CHECON
Definition: checon.f:127
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:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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