LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
subroutine zgbrfsx ( character  TRANS,
character  EQUED,
integer  N,
integer  KL,
integer  KU,
integer  NRHS,
complex*16, dimension( ldab, * )  AB,
integer  LDAB,
complex*16, dimension( ldafb, * )  AFB,
integer  LDAFB,
integer, dimension( * )  IPIV,
double precision, dimension( * )  R,
double precision, dimension( * )  C,
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 
)

ZGBRFSX

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

Purpose:
    ZGBRFSX improves the computed solution to a system of linear
    equations 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, R
    and C 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]TRANS
          TRANS is CHARACTER*1
     Specifies the form of the system of equations:
       = 'N':  A * X = B     (No transpose)
       = 'T':  A**T * X = B  (Transpose)
       = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
[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
       = 'R':  Row equilibration, i.e., A has been premultiplied by
               diag(R).
       = 'C':  Column equilibration, i.e., A has been postmultiplied
               by diag(C).
       = 'B':  Both row and column equilibration, i.e., A has been
               replaced by diag(R) * A * diag(C).
               The right hand side B has been changed accordingly.
[in]N
          N is INTEGER
     The order of the matrix A.  N >= 0.
[in]KL
          KL is INTEGER
     The number of subdiagonals within the band of A.  KL >= 0.
[in]KU
          KU is INTEGER
     The number of superdiagonals within the band of A.  KU >= 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]AB
          AB is COMPLEX*16 array, dimension (LDAB,N)
     The original band matrix A, stored in rows 1 to KL+KU+1.
     The j-th column of A is stored in the j-th column of the
     array AB as follows:
     AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
[in]LDAB
          LDAB is INTEGER
     The leading dimension of the array AB.  LDAB >= KL+KU+1.
[in]AFB
          AFB is COMPLEX*16 array, dimension (LDAFB,N)
     Details of the LU factorization of the band matrix A, as
     computed by DGBTRF.  U is stored as an upper triangular band
     matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
     the multipliers used during the factorization are stored in
     rows KL+KU+2 to 2*KL+KU+1.
[in]LDAFB
          LDAFB is INTEGER
     The leading dimension of the array AFB.  LDAFB >= 2*KL*KU+1.
[in]IPIV
          IPIV is INTEGER array, dimension (N)
     The pivot indices from DGETRF; for 1<=i<=N, row i of the
     matrix was interchanged with row IPIV(i).
[in,out]R
          R is DOUBLE PRECISION array, dimension (N)
     The row scale factors for A.  If EQUED = 'R' or 'B', A is
     multiplied on the left by diag(R); if EQUED = 'N' or 'C', R
     is not accessed.  R is an input argument if FACT = 'F';
     otherwise, R is an output argument.  If FACT = 'F' and
     EQUED = 'R' or 'B', each element of R must be positive.
     If R is output, each element of R is a power of the radix.
     If R is input, each element of R 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,out]C
          C is DOUBLE PRECISION array, dimension (N)
     The column scale factors for A.  If EQUED = 'C' or 'B', A is
     multiplied on the right by diag(C); if EQUED = 'N' or 'R', C
     is not accessed.  C is an input argument if FACT = 'F';
     otherwise, C is an output argument.  If FACT = 'F' and
     EQUED = 'C' or 'B', each element of C must be positive.
     If C is output, each element of C is a power of the radix.
     If C is input, each element of C 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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
April 2012

Definition at line 442 of file zgbrfsx.f.

442 *
443 * -- LAPACK computational routine (version 3.6.1) --
444 * -- LAPACK is a software package provided by Univ. of Tennessee, --
445 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
446 * April 2012
447 *
448 * .. Scalar Arguments ..
449  CHARACTER trans, equed
450  INTEGER info, ldab, ldafb, ldb, ldx, n, kl, ku, nrhs,
451  $ nparams, n_err_bnds
452  DOUBLE PRECISION rcond
453 * ..
454 * .. Array Arguments ..
455  INTEGER ipiv( * )
456  COMPLEX*16 ab( ldab, * ), afb( ldafb, * ), b( ldb, * ),
457  $ x( ldx , * ),work( * )
458  DOUBLE PRECISION r( * ), c( * ), params( * ), berr( * ),
459  $ err_bnds_norm( nrhs, * ),
460  $ err_bnds_comp( nrhs, * ), rwork( * )
461 * ..
462 *
463 * ==================================================================
464 *
465 * .. Parameters ..
466  DOUBLE PRECISION zero, one
467  parameter ( zero = 0.0d+0, one = 1.0d+0 )
468  DOUBLE PRECISION itref_default, ithresh_default
469  DOUBLE PRECISION componentwise_default, rthresh_default
470  DOUBLE PRECISION dzthresh_default
471  parameter ( itref_default = 1.0d+0 )
472  parameter ( ithresh_default = 10.0d+0 )
473  parameter ( componentwise_default = 1.0d+0 )
474  parameter ( rthresh_default = 0.5d+0 )
475  parameter ( dzthresh_default = 0.25d+0 )
476  INTEGER la_linrx_itref_i, la_linrx_ithresh_i,
477  $ la_linrx_cwise_i
478  parameter ( la_linrx_itref_i = 1,
479  $ la_linrx_ithresh_i = 2 )
480  parameter ( la_linrx_cwise_i = 3 )
481  INTEGER la_linrx_trust_i, la_linrx_err_i,
482  $ la_linrx_rcond_i
483  parameter ( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
484  parameter ( la_linrx_rcond_i = 3 )
485 * ..
486 * .. Local Scalars ..
487  CHARACTER(1) norm
488  LOGICAL rowequ, colequ, notran, ignore_cwise
489  INTEGER j, trans_type, prec_type, ref_type, n_norms,
490  $ ithresh
491  DOUBLE PRECISION anorm, rcond_tmp, illrcond_thresh, err_lbnd,
492  $ cwise_wrong, rthresh, unstable_thresh
493 * ..
494 * .. External Subroutines ..
496 * ..
497 * .. Intrinsic Functions ..
498  INTRINSIC max, sqrt, transfer
499 * ..
500 * .. External Functions ..
501  EXTERNAL lsame, blas_fpinfo_x, ilatrans, ilaprec
503  DOUBLE PRECISION dlamch, zlangb, zla_gbrcond_x, zla_gbrcond_c
504  LOGICAL lsame
505  INTEGER blas_fpinfo_x
506  INTEGER ilatrans, ilaprec
507 * ..
508 * .. Executable Statements ..
509 *
510 * Check the input parameters.
511 *
512  info = 0
513  trans_type = ilatrans( trans )
514  ref_type = int( itref_default )
515  IF ( nparams .GE. la_linrx_itref_i ) THEN
516  IF ( params( la_linrx_itref_i ) .LT. 0.0d+0 ) THEN
517  params( la_linrx_itref_i ) = itref_default
518  ELSE
519  ref_type = params( la_linrx_itref_i )
520  END IF
521  END IF
522 *
523 * Set default parameters.
524 *
525  illrcond_thresh = dble( n ) * dlamch( 'Epsilon' )
526  ithresh = int( ithresh_default )
527  rthresh = rthresh_default
528  unstable_thresh = dzthresh_default
529  ignore_cwise = componentwise_default .EQ. 0.0d+0
530 *
531  IF ( nparams.GE.la_linrx_ithresh_i ) THEN
532  IF ( params( la_linrx_ithresh_i ).LT.0.0d+0 ) THEN
533  params( la_linrx_ithresh_i ) = ithresh
534  ELSE
535  ithresh = int( params( la_linrx_ithresh_i ) )
536  END IF
537  END IF
538  IF ( nparams.GE.la_linrx_cwise_i ) THEN
539  IF ( params( la_linrx_cwise_i ).LT.0.0d+0 ) THEN
540  IF ( ignore_cwise ) THEN
541  params( la_linrx_cwise_i ) = 0.0d+0
542  ELSE
543  params( la_linrx_cwise_i ) = 1.0d+0
544  END IF
545  ELSE
546  ignore_cwise = params( la_linrx_cwise_i ) .EQ. 0.0d+0
547  END IF
548  END IF
549  IF ( ref_type .EQ. 0 .OR. n_err_bnds .EQ. 0 ) THEN
550  n_norms = 0
551  ELSE IF ( ignore_cwise ) THEN
552  n_norms = 1
553  ELSE
554  n_norms = 2
555  END IF
556 *
557  notran = lsame( trans, 'N' )
558  rowequ = lsame( equed, 'R' ) .OR. lsame( equed, 'B' )
559  colequ = lsame( equed, 'C' ) .OR. lsame( equed, 'B' )
560 *
561 * Test input parameters.
562 *
563  IF( trans_type.EQ.-1 ) THEN
564  info = -1
565  ELSE IF( .NOT.rowequ .AND. .NOT.colequ .AND.
566  $ .NOT.lsame( equed, 'N' ) ) THEN
567  info = -2
568  ELSE IF( n.LT.0 ) THEN
569  info = -3
570  ELSE IF( kl.LT.0 ) THEN
571  info = -4
572  ELSE IF( ku.LT.0 ) THEN
573  info = -5
574  ELSE IF( nrhs.LT.0 ) THEN
575  info = -6
576  ELSE IF( ldab.LT.kl+ku+1 ) THEN
577  info = -8
578  ELSE IF( ldafb.LT.2*kl+ku+1 ) THEN
579  info = -10
580  ELSE IF( ldb.LT.max( 1, n ) ) THEN
581  info = -13
582  ELSE IF( ldx.LT.max( 1, n ) ) THEN
583  info = -15
584  END IF
585  IF( info.NE.0 ) THEN
586  CALL xerbla( 'ZGBRFSX', -info )
587  RETURN
588  END IF
589 *
590 * Quick return if possible.
591 *
592  IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
593  rcond = 1.0d+0
594  DO j = 1, nrhs
595  berr( j ) = 0.0d+0
596  IF ( n_err_bnds .GE. 1 ) THEN
597  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
598  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
599  END IF
600  IF ( n_err_bnds .GE. 2 ) THEN
601  err_bnds_norm( j, la_linrx_err_i ) = 0.0d+0
602  err_bnds_comp( j, la_linrx_err_i ) = 0.0d+0
603  END IF
604  IF ( n_err_bnds .GE. 3 ) THEN
605  err_bnds_norm( j, la_linrx_rcond_i ) = 1.0d+0
606  err_bnds_comp( j, la_linrx_rcond_i ) = 1.0d+0
607  END IF
608  END DO
609  RETURN
610  END IF
611 *
612 * Default to failure.
613 *
614  rcond = 0.0d+0
615  DO j = 1, nrhs
616  berr( j ) = 1.0d+0
617  IF ( n_err_bnds .GE. 1 ) THEN
618  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
619  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
620  END IF
621  IF ( n_err_bnds .GE. 2 ) THEN
622  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
623  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
624  END IF
625  IF ( n_err_bnds .GE. 3 ) THEN
626  err_bnds_norm( j, la_linrx_rcond_i ) = 0.0d+0
627  err_bnds_comp( j, la_linrx_rcond_i ) = 0.0d+0
628  END IF
629  END DO
630 *
631 * Compute the norm of A and the reciprocal of the condition
632 * number of A.
633 *
634  IF( notran ) THEN
635  norm = 'I'
636  ELSE
637  norm = '1'
638  END IF
639  anorm = zlangb( norm, n, kl, ku, ab, ldab, rwork )
640  CALL zgbcon( norm, n, kl, ku, afb, ldafb, ipiv, anorm, rcond,
641  $ work, rwork, info )
642 *
643 * Perform refinement on each right-hand side
644 *
645  IF ( ref_type .NE. 0 .AND. info .EQ. 0 ) THEN
646 
647  prec_type = ilaprec( 'E' )
648 
649  IF ( notran ) THEN
650  CALL zla_gbrfsx_extended( prec_type, trans_type, n, kl, ku,
651  $ nrhs, ab, ldab, afb, ldafb, ipiv, colequ, c, b,
652  $ ldb, x, ldx, berr, n_norms, err_bnds_norm,
653  $ err_bnds_comp, work, rwork, work(n+1),
654  $ transfer(rwork(1:2*n), (/ (zero, zero) /), n),
655  $ rcond, ithresh, rthresh, unstable_thresh, ignore_cwise,
656  $ info )
657  ELSE
658  CALL zla_gbrfsx_extended( prec_type, trans_type, n, kl, ku,
659  $ nrhs, ab, ldab, afb, ldafb, ipiv, rowequ, r, b,
660  $ ldb, x, ldx, berr, n_norms, err_bnds_norm,
661  $ err_bnds_comp, work, rwork, work(n+1),
662  $ transfer(rwork(1:2*n), (/ (zero, zero) /), n),
663  $ rcond, ithresh, rthresh, unstable_thresh, ignore_cwise,
664  $ info )
665  END IF
666  END IF
667 
668  err_lbnd = max( 10.0d+0, sqrt( dble( n ) ) ) * dlamch( 'Epsilon' )
669  IF (n_err_bnds .GE. 1 .AND. n_norms .GE. 1) THEN
670 *
671 * Compute scaled normwise condition number cond(A*C).
672 *
673  IF ( colequ .AND. notran ) THEN
674  rcond_tmp = zla_gbrcond_c( trans, n, kl, ku, ab, ldab, afb,
675  $ ldafb, ipiv, c, .true., info, work, rwork )
676  ELSE IF ( rowequ .AND. .NOT. notran ) THEN
677  rcond_tmp = zla_gbrcond_c( trans, n, kl, ku, ab, ldab, afb,
678  $ ldafb, ipiv, r, .true., info, work, rwork )
679  ELSE
680  rcond_tmp = zla_gbrcond_c( trans, n, kl, ku, ab, ldab, afb,
681  $ ldafb, ipiv, c, .false., info, work, rwork )
682  END IF
683  DO j = 1, nrhs
684 *
685 * Cap the error at 1.0.
686 *
687  IF ( n_err_bnds .GE. la_linrx_err_i
688  $ .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0d+0)
689  $ err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
690 *
691 * Threshold the error (see LAWN).
692 *
693  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
694  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
695  err_bnds_norm( j, la_linrx_trust_i ) = 0.0d+0
696  IF ( info .LE. n ) info = n + j
697  ELSE IF ( err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd )
698  $ THEN
699  err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
700  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
701  END IF
702 *
703 * Save the condition number.
704 *
705  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
706  err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
707  END IF
708 
709  END DO
710  END IF
711 
712  IF (n_err_bnds .GE. 1 .AND. n_norms .GE. 2) THEN
713 *
714 * Compute componentwise condition number cond(A*diag(Y(:,J))) for
715 * each right-hand side using the current solution as an estimate of
716 * the true solution. If the componentwise error estimate is too
717 * large, then the solution is a lousy estimate of truth and the
718 * estimated RCOND may be too optimistic. To avoid misleading users,
719 * the inverse condition number is set to 0.0 when the estimated
720 * cwise error is at least CWISE_WRONG.
721 *
722  cwise_wrong = sqrt( dlamch( 'Epsilon' ) )
723  DO j = 1, nrhs
724  IF (err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
725  $ THEN
726  rcond_tmp = zla_gbrcond_x( trans, n, kl, ku, ab, ldab,
727  $ afb, ldafb, ipiv, x( 1, j ), info, work, rwork )
728  ELSE
729  rcond_tmp = 0.0d+0
730  END IF
731 *
732 * Cap the error at 1.0.
733 *
734  IF ( n_err_bnds .GE. la_linrx_err_i
735  $ .AND. err_bnds_comp( j, la_linrx_err_i ) .GT. 1.0d+0 )
736  $ err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
737 *
738 * Threshold the error (see LAWN).
739 *
740  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
741  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
742  err_bnds_comp( j, la_linrx_trust_i ) = 0.0d+0
743  IF ( params( la_linrx_cwise_i ) .EQ. 1.0d+0
744  $ .AND. info.LT.n + j ) info = n + j
745  ELSE IF ( err_bnds_comp( j, la_linrx_err_i )
746  $ .LT. err_lbnd ) THEN
747  err_bnds_comp( j, la_linrx_err_i ) = err_lbnd
748  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
749  END IF
750 *
751 * Save the condition number.
752 *
753  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
754  err_bnds_comp( j, la_linrx_rcond_i ) = rcond_tmp
755  END IF
756 
757  END DO
758  END IF
759 *
760  RETURN
761 *
762 * End of ZGBRFSX
763 *
integer function ilatrans(TRANS)
ILATRANS
Definition: ilatrans.f:60
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine zgbcon(NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK, RWORK, INFO)
ZGBCON
Definition: zgbcon.f:149
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
double precision function zla_gbrcond_x(TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, X, INFO, WORK, RWORK)
ZLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrice...
integer function ilaprec(PREC)
ILAPREC
Definition: ilaprec.f:60
double precision function zla_gbrcond_c(TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, C, CAPPLY, INFO, WORK, RWORK)
ZLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded ma...
double precision function zlangb(NORM, N, KL, KU, AB, LDAB, WORK)
ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlangb.f:127
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine zla_gbrfsx_extended(PREC_TYPE, TRANS_TYPE, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, 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)
ZLA_GBRFSX_EXTENDED improves the computed solution to a system of linear equations for general banded...

Here is the call graph for this function:

Here is the caller graph for this function: