 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

◆ cherfsx()

 subroutine cherfsx ( character UPLO, character EQUED, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldaf, * ) AF, integer LDAF, integer, dimension( * ) IPIV, real, dimension( * ) S, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldx, * ) X, integer LDX, real RCOND, real, dimension( * ) BERR, integer N_ERR_BNDS, real, dimension( nrhs, * ) ERR_BNDS_NORM, real, dimension( nrhs, * ) ERR_BNDS_COMP, integer NPARAMS, real, dimension( * ) PARAMS, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO )

CHERFSX

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 = 'N': No equilibration = 'Y': Both row and column equilibration, i.e., A has been replaced by diag(S) * A * diag(S).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 3.7.0) --
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, ilaprec
467  LOGICAL lsame
468  INTEGER ilaprec
469 * ..
470 * .. Executable Statements ..
471 *
472 * Check the input parameters.
473 *
474  info = 0
475  ref_type = int( itref_default )
476  IF ( nparams .GE. la_linrx_itref_i ) THEN
477  IF ( params( la_linrx_itref_i ) .LT. 0.0 ) THEN
478  params( la_linrx_itref_i ) = itref_default
479  ELSE
480  ref_type = params( la_linrx_itref_i )
481  END IF
482  END IF
483 *
484 * Set default parameters.
485 *
486  illrcond_thresh = REAL( N ) * slamch( 'Epsilon' )
487  ithresh = int( ithresh_default )
488  rthresh = rthresh_default
489  unstable_thresh = dzthresh_default
490  ignore_cwise = componentwise_default .EQ. 0.0
491 *
492  IF ( nparams.GE.la_linrx_ithresh_i ) THEN
493  IF ( params( la_linrx_ithresh_i ).LT.0.0 ) THEN
494  params( la_linrx_ithresh_i ) = ithresh
495  ELSE
496  ithresh = int( params( la_linrx_ithresh_i ) )
497  END IF
498  END IF
499  IF ( nparams.GE.la_linrx_cwise_i ) THEN
500  IF ( params(la_linrx_cwise_i ).LT.0.0 ) THEN
501  IF ( ignore_cwise ) THEN
502  params( la_linrx_cwise_i ) = 0.0
503  ELSE
504  params( la_linrx_cwise_i ) = 1.0
505  END IF
506  ELSE
507  ignore_cwise = params( la_linrx_cwise_i ) .EQ. 0.0
508  END IF
509  END IF
510  IF ( ref_type .EQ. 0 .OR. n_err_bnds .EQ. 0 ) THEN
511  n_norms = 0
512  ELSE IF ( ignore_cwise ) THEN
513  n_norms = 1
514  ELSE
515  n_norms = 2
516  END IF
517 *
518  rcequ = lsame( equed, 'Y' )
519 *
520 * Test input parameters.
521 *
522  IF (.NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
523  info = -1
524  ELSE IF( .NOT.rcequ .AND. .NOT.lsame( equed, 'N' ) ) THEN
525  info = -2
526  ELSE IF( n.LT.0 ) THEN
527  info = -3
528  ELSE IF( nrhs.LT.0 ) THEN
529  info = -4
530  ELSE IF( lda.LT.max( 1, n ) ) THEN
531  info = -6
532  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
533  info = -8
534  ELSE IF( ldb.LT.max( 1, n ) ) THEN
535  info = -12
536  ELSE IF( ldx.LT.max( 1, n ) ) THEN
537  info = -14
538  END IF
539  IF( info.NE.0 ) THEN
540  CALL xerbla( 'CHERFSX', -info )
541  RETURN
542  END IF
543 *
544 * Quick return if possible.
545 *
546  IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
547  rcond = 1.0
548  DO j = 1, nrhs
549  berr( j ) = 0.0
550  IF ( n_err_bnds .GE. 1 ) THEN
551  err_bnds_norm( j, la_linrx_trust_i ) = 1.0
552  err_bnds_comp( j, la_linrx_trust_i ) = 1.0
553  END IF
554  IF ( n_err_bnds .GE. 2 ) THEN
555  err_bnds_norm( j, la_linrx_err_i ) = 0.0
556  err_bnds_comp( j, la_linrx_err_i ) = 0.0
557  END IF
558  IF ( n_err_bnds .GE. 3 ) THEN
559  err_bnds_norm( j, la_linrx_rcond_i ) = 1.0
560  err_bnds_comp( j, la_linrx_rcond_i ) = 1.0
561  END IF
562  END DO
563  RETURN
564  END IF
565 *
566 * Default to failure.
567 *
568  rcond = 0.0
569  DO j = 1, nrhs
570  berr( j ) = 1.0
571  IF ( n_err_bnds .GE. 1 ) THEN
572  err_bnds_norm( j, la_linrx_trust_i ) = 1.0
573  err_bnds_comp( j, la_linrx_trust_i ) = 1.0
574  END IF
575  IF ( n_err_bnds .GE. 2 ) THEN
576  err_bnds_norm( j, la_linrx_err_i ) = 1.0
577  err_bnds_comp( j, la_linrx_err_i ) = 1.0
578  END IF
579  IF ( n_err_bnds .GE. 3 ) THEN
580  err_bnds_norm( j, la_linrx_rcond_i ) = 0.0
581  err_bnds_comp( j, la_linrx_rcond_i ) = 0.0
582  END IF
583  END DO
584 *
585 * Compute the norm of A and the reciprocal of the condition
586 * number of A.
587 *
588  norm = 'I'
589  anorm = clanhe( norm, uplo, n, a, lda, rwork )
590  CALL checon( uplo, n, af, ldaf, ipiv, anorm, rcond, work,
591  \$ info )
592 *
593 * Perform refinement on each right-hand side
594 *
595  IF ( ref_type .NE. 0 ) THEN
596
597  prec_type = ilaprec( 'D' )
598
599  CALL cla_herfsx_extended( prec_type, uplo, n,
600  \$ nrhs, a, lda, af, ldaf, ipiv, rcequ, s, b,
601  \$ ldb, x, ldx, berr, n_norms, err_bnds_norm, err_bnds_comp,
602  \$ work, rwork, work(n+1),
603  \$ transfer(rwork(1:2*n), (/ (zero, zero) /), n), rcond,
604  \$ ithresh, rthresh, unstable_thresh, ignore_cwise,
605  \$ info )
606  END IF
607
608  err_lbnd = max( 10.0, sqrt( REAL( N ) ) ) * slamch( 'Epsilon' )
609  IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 1 ) THEN
610 *
611 * Compute scaled normwise condition number cond(A*C).
612 *
613  IF ( rcequ ) THEN
614  rcond_tmp = cla_hercond_c( uplo, n, a, lda, af, ldaf, ipiv,
615  \$ s, .true., info, work, rwork )
616  ELSE
617  rcond_tmp = cla_hercond_c( uplo, n, a, lda, af, ldaf, ipiv,
618  \$ s, .false., info, work, rwork )
619  END IF
620  DO j = 1, nrhs
621 *
622 * Cap the error at 1.0.
623 *
624  IF ( n_err_bnds .GE. la_linrx_err_i
625  \$ .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0 )
626  \$ err_bnds_norm( j, la_linrx_err_i ) = 1.0
627 *
628 * Threshold the error (see LAWN).
629 *
630  IF (rcond_tmp .LT. illrcond_thresh) THEN
631  err_bnds_norm( j, la_linrx_err_i ) = 1.0
632  err_bnds_norm( j, la_linrx_trust_i ) = 0.0
633  IF ( info .LE. n ) info = n + j
634  ELSE IF ( err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd )
635  \$ THEN
636  err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
637  err_bnds_norm( j, la_linrx_trust_i ) = 1.0
638  END IF
639 *
640 * Save the condition number.
641 *
642  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
643  err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
644  END IF
645  END DO
646  END IF
647
648  IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 2 ) THEN
649 *
650 * Compute componentwise condition number cond(A*diag(Y(:,J))) for
651 * each right-hand side using the current solution as an estimate of
652 * the true solution. If the componentwise error estimate is too
653 * large, then the solution is a lousy estimate of truth and the
654 * estimated RCOND may be too optimistic. To avoid misleading users,
655 * the inverse condition number is set to 0.0 when the estimated
656 * cwise error is at least CWISE_WRONG.
657 *
658  cwise_wrong = sqrt( slamch( 'Epsilon' ) )
659  DO j = 1, nrhs
660  IF ( err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
661  \$ THEN
662  rcond_tmp = cla_hercond_x( uplo, n, a, lda, af, ldaf,
663  \$ ipiv, x( 1, j ), info, work, rwork )
664  ELSE
665  rcond_tmp = 0.0
666  END IF
667 *
668 * Cap the error at 1.0.
669 *
670  IF ( n_err_bnds .GE. la_linrx_err_i
671  \$ .AND. err_bnds_comp( j, la_linrx_err_i ) .GT. 1.0 )
672  \$ err_bnds_comp( j, la_linrx_err_i ) = 1.0
673 *
674 * Threshold the error (see LAWN).
675 *
676  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
677  err_bnds_comp( j, la_linrx_err_i ) = 1.0
678  err_bnds_comp( j, la_linrx_trust_i ) = 0.0
679  IF ( .NOT. ignore_cwise
680  \$ .AND. info.LT.n + j ) info = n + j
681  ELSE IF ( err_bnds_comp( j, la_linrx_err_i )
682  \$ .LT. err_lbnd ) THEN
683  err_bnds_comp( j, la_linrx_err_i ) = err_lbnd
684  err_bnds_comp( j, la_linrx_trust_i ) = 1.0
685  END IF
686 *
687 * Save the condition number.
688 *
689  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
690  err_bnds_comp( j, la_linrx_rcond_i ) = rcond_tmp
691  END IF
692
693  END DO
694  END IF
695 *
696  RETURN
697 *
698 * End of CHERFSX
699 *
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 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...
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine checon(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO)
CHECON
Definition: checon.f:127
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
integer function ilaprec(PREC)
ILAPREC
Definition: ilaprec.f:60
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
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...
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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