LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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

Purpose:
```    ZPORFSX 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 = 'N': No equilibration = 'Y': Both row and column equilibration, i.e., A has been replaced by diag(S) * A * diag(S).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 COMPLEX*16 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*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 row 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 .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) * 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 .LE. 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 .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: 1.0D+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.```
Date
April 2012

Definition at line 395 of file zporfsx.f.

395 *
396 * -- LAPACK computational routine (version 3.4.1) --
397 * -- LAPACK is a software package provided by Univ. of Tennessee, --
398 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
399 * April 2012
400 *
401 * .. Scalar Arguments ..
402  CHARACTER uplo, equed
403  INTEGER info, lda, ldaf, ldb, ldx, n, nrhs, nparams,
404  \$ n_err_bnds
405  DOUBLE PRECISION rcond
406 * ..
407 * .. Array Arguments ..
408  COMPLEX*16 a( lda, * ), af( ldaf, * ), b( ldb, * ),
409  \$ x( ldx, * ), work( * )
410  DOUBLE PRECISION rwork( * ), s( * ), params(*), berr( * ),
411  \$ err_bnds_norm( nrhs, * ),
412  \$ err_bnds_comp( nrhs, * )
413 * ..
414 *
415 * ==================================================================
416 *
417 * .. Parameters ..
418  DOUBLE PRECISION zero, one
419  parameter ( zero = 0.0d+0, one = 1.0d+0 )
420  DOUBLE PRECISION itref_default, ithresh_default
421  DOUBLE PRECISION componentwise_default, rthresh_default
422  DOUBLE PRECISION dzthresh_default
423  parameter ( itref_default = 1.0d+0 )
424  parameter ( ithresh_default = 10.0d+0 )
425  parameter ( componentwise_default = 1.0d+0 )
426  parameter ( rthresh_default = 0.5d+0 )
427  parameter ( dzthresh_default = 0.25d+0 )
428  INTEGER la_linrx_itref_i, la_linrx_ithresh_i,
429  \$ la_linrx_cwise_i
430  parameter ( la_linrx_itref_i = 1,
431  \$ la_linrx_ithresh_i = 2 )
432  parameter ( la_linrx_cwise_i = 3 )
433  INTEGER la_linrx_trust_i, la_linrx_err_i,
434  \$ la_linrx_rcond_i
435  parameter ( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
436  parameter ( la_linrx_rcond_i = 3 )
437 * ..
438 * .. Local Scalars ..
439  CHARACTER(1) norm
440  LOGICAL rcequ
441  INTEGER j, prec_type, ref_type
442  INTEGER n_norms
443  DOUBLE PRECISION anorm, rcond_tmp
444  DOUBLE PRECISION illrcond_thresh, err_lbnd, cwise_wrong
445  LOGICAL ignore_cwise
446  INTEGER ithresh
447  DOUBLE PRECISION rthresh, unstable_thresh
448 * ..
449 * .. External Subroutines ..
451 * ..
452 * .. Intrinsic Functions ..
453  INTRINSIC max, sqrt, transfer
454 * ..
455 * .. External Functions ..
456  EXTERNAL lsame, blas_fpinfo_x, ilatrans, ilaprec
458  DOUBLE PRECISION dlamch, zlanhe, zla_porcond_x, zla_porcond_c
459  LOGICAL lsame
460  INTEGER blas_fpinfo_x
461  INTEGER ilatrans, ilaprec
462 * ..
463 * .. Executable Statements ..
464 *
465 * Check the input parameters.
466 *
467  info = 0
468  ref_type = int( itref_default )
469  IF ( nparams .GE. la_linrx_itref_i ) THEN
470  IF ( params( la_linrx_itref_i ) .LT. 0.0d+0 ) THEN
471  params( la_linrx_itref_i ) = itref_default
472  ELSE
473  ref_type = params( la_linrx_itref_i )
474  END IF
475  END IF
476 *
477 * Set default parameters.
478 *
479  illrcond_thresh = dble( n ) * dlamch( 'Epsilon' )
480  ithresh = int( ithresh_default )
481  rthresh = rthresh_default
482  unstable_thresh = dzthresh_default
483  ignore_cwise = componentwise_default .EQ. 0.0d+0
484 *
485  IF ( nparams.GE.la_linrx_ithresh_i ) THEN
486  IF ( params(la_linrx_ithresh_i ).LT.0.0d+0 ) THEN
487  params( la_linrx_ithresh_i ) = ithresh
488  ELSE
489  ithresh = int( params( la_linrx_ithresh_i ) )
490  END IF
491  END IF
492  IF ( nparams.GE.la_linrx_cwise_i ) THEN
493  IF ( params(la_linrx_cwise_i ).LT.0.0d+0 ) THEN
494  IF ( ignore_cwise ) THEN
495  params( la_linrx_cwise_i ) = 0.0d+0
496  ELSE
497  params( la_linrx_cwise_i ) = 1.0d+0
498  END IF
499  ELSE
500  ignore_cwise = params( la_linrx_cwise_i ) .EQ. 0.0d+0
501  END IF
502  END IF
503  IF ( ref_type .EQ. 0 .OR. n_err_bnds .EQ. 0 ) THEN
504  n_norms = 0
505  ELSE IF ( ignore_cwise ) THEN
506  n_norms = 1
507  ELSE
508  n_norms = 2
509  END IF
510 *
511  rcequ = lsame( equed, 'Y' )
512 *
513 * Test input parameters.
514 *
515  IF (.NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
516  info = -1
517  ELSE IF( .NOT.rcequ .AND. .NOT.lsame( equed, 'N' ) ) THEN
518  info = -2
519  ELSE IF( n.LT.0 ) THEN
520  info = -3
521  ELSE IF( nrhs.LT.0 ) THEN
522  info = -4
523  ELSE IF( lda.LT.max( 1, n ) ) THEN
524  info = -6
525  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
526  info = -8
527  ELSE IF( ldb.LT.max( 1, n ) ) THEN
528  info = -11
529  ELSE IF( ldx.LT.max( 1, n ) ) THEN
530  info = -13
531  END IF
532  IF( info.NE.0 ) THEN
533  CALL xerbla( 'ZPORFSX', -info )
534  RETURN
535  END IF
536 *
537 * Quick return if possible.
538 *
539  IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
540  rcond = 1.0d+0
541  DO j = 1, nrhs
542  berr( j ) = 0.0d+0
543  IF ( n_err_bnds .GE. 1 ) THEN
544  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
545  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
546  END IF
547  IF ( n_err_bnds .GE. 2 ) THEN
548  err_bnds_norm( j, la_linrx_err_i ) = 0.0d+0
549  err_bnds_comp( j, la_linrx_err_i ) = 0.0d+0
550  END IF
551  IF ( n_err_bnds .GE. 3 ) THEN
552  err_bnds_norm( j, la_linrx_rcond_i ) = 1.0d+0
553  err_bnds_comp( j, la_linrx_rcond_i ) = 1.0d+0
554  END IF
555  END DO
556  RETURN
557  END IF
558 *
559 * Default to failure.
560 *
561  rcond = 0.0d+0
562  DO j = 1, nrhs
563  berr( j ) = 1.0d+0
564  IF ( n_err_bnds .GE. 1 ) THEN
565  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
566  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
567  END IF
568  IF ( n_err_bnds .GE. 2 ) THEN
569  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
570  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
571  END IF
572  IF ( n_err_bnds .GE. 3 ) THEN
573  err_bnds_norm( j, la_linrx_rcond_i ) = 0.0d+0
574  err_bnds_comp( j, la_linrx_rcond_i ) = 0.0d+0
575  END IF
576  END DO
577 *
578 * Compute the norm of A and the reciprocal of the condition
579 * number of A.
580 *
581  norm = 'I'
582  anorm = zlanhe( norm, uplo, n, a, lda, rwork )
583  CALL zpocon( uplo, n, af, ldaf, anorm, rcond, work, rwork,
584  \$ info )
585 *
586 * Perform refinement on each right-hand side
587 *
588  IF ( ref_type .NE. 0 ) THEN
589
590  prec_type = ilaprec( 'E' )
591
592  CALL zla_porfsx_extended( prec_type, uplo, n,
593  \$ nrhs, a, lda, af, ldaf, rcequ, s, b,
594  \$ ldb, x, ldx, berr, n_norms, err_bnds_norm, err_bnds_comp,
595  \$ work, rwork, work(n+1),
596  \$ transfer(rwork(1:2*n), (/ (zero, zero) /), n), rcond,
597  \$ ithresh, rthresh, unstable_thresh, ignore_cwise,
598  \$ info )
599  END IF
600
601  err_lbnd = max( 10.0d+0, sqrt( dble( n ) ) ) * dlamch( 'Epsilon' )
602  IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 1 ) THEN
603 *
604 * Compute scaled normwise condition number cond(A*C).
605 *
606  IF ( rcequ ) THEN
607  rcond_tmp = zla_porcond_c( uplo, n, a, lda, af, ldaf,
608  \$ s, .true., info, work, rwork )
609  ELSE
610  rcond_tmp = zla_porcond_c( uplo, n, a, lda, af, ldaf,
611  \$ s, .false., info, work, rwork )
612  END IF
613  DO j = 1, nrhs
614 *
615 * Cap the error at 1.0.
616 *
617  IF ( n_err_bnds .GE. la_linrx_err_i
618  \$ .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0d+0 )
619  \$ err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
620 *
621 * Threshold the error (see LAWN).
622 *
623  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
624  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
625  err_bnds_norm( j, la_linrx_trust_i ) = 0.0d+0
626  IF ( info .LE. n ) info = n + j
627  ELSE IF ( err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd )
628  \$ THEN
629  err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
630  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
631  END IF
632 *
633 * Save the condition number.
634 *
635  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
636  err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
637  END IF
638
639  END DO
640  END IF
641
642  IF (n_err_bnds .GE. 1 .AND. n_norms .GE. 2) THEN
643 *
644 * Compute componentwise condition number cond(A*diag(Y(:,J))) for
645 * each right-hand side using the current solution as an estimate of
646 * the true solution. If the componentwise error estimate is too
647 * large, then the solution is a lousy estimate of truth and the
648 * estimated RCOND may be too optimistic. To avoid misleading users,
649 * the inverse condition number is set to 0.0 when the estimated
650 * cwise error is at least CWISE_WRONG.
651 *
652  cwise_wrong = sqrt( dlamch( 'Epsilon' ) )
653  DO j = 1, nrhs
654  IF (err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
655  \$ THEN
656  rcond_tmp = zla_porcond_x( uplo, n, a, lda, af, ldaf,
657  \$ x(1,j), info, work, rwork )
658  ELSE
659  rcond_tmp = 0.0d+0
660  END IF
661 *
662 * Cap the error at 1.0.
663 *
664  IF ( n_err_bnds .GE. la_linrx_err_i
665  \$ .AND. err_bnds_comp( j, la_linrx_err_i ) .GT. 1.0d+0 )
666  \$ err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
667 *
668 * Threshold the error (see LAWN).
669 *
670  IF (rcond_tmp .LT. illrcond_thresh) THEN
671  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
672  err_bnds_comp( j, la_linrx_trust_i ) = 0.0d+0
673  IF ( params( la_linrx_cwise_i ) .EQ. 1.0d+0
674  \$ .AND. info.LT.n + j ) info = n + j
675  ELSE IF ( err_bnds_comp( j, la_linrx_err_i )
676  \$ .LT. err_lbnd ) THEN
677  err_bnds_comp( j, la_linrx_err_i ) = err_lbnd
678  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
679  END IF
680 *
681 * Save the condition number.
682 *
683  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
684  err_bnds_comp( j, la_linrx_rcond_i ) = rcond_tmp
685  END IF
686
687  END DO
688  END IF
689 *
690  RETURN
691 *
692 * End of ZPORFSX
693 *
integer function ilatrans(TRANS)
ILATRANS
Definition: ilatrans.f:60
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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 zlanhe(NORM, UPLO, N, A, LDA, WORK)
ZLANHE 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: zlanhe.f:126
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
integer function ilaprec(PREC)
ILAPREC
Definition: ilaprec.f:60
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...
subroutine zpocon(UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK, INFO)
ZPOCON
Definition: zpocon.f:123
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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...

Here is the call graph for this function:

Here is the caller graph for this function: