LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ dgbrfsx()

subroutine dgbrfsx ( character  TRANS,
character  EQUED,
integer  N,
integer  KL,
integer  KU,
integer  NRHS,
double precision, dimension( ldab, * )  AB,
integer  LDAB,
double precision, dimension( ldafb, * )  AFB,
integer  LDAFB,
integer, dimension( * )  IPIV,
double precision, dimension( * )  R,
double precision, dimension( * )  C,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, 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,
double precision, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  INFO 
)

DGBRFSX

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Purpose:
    DGBRFSX 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 < 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 <= 0, the
     PARAMS array is never referenced and default values are used.
[in,out]PARAMS
          PARAMS is DOUBLE PRECISION array, dimension (NPARAMS)
     Specifies algorithm parameters.  If an entry is < 0.0, then
     that entry will be filled with default value used for that
     parameter.  Only positions up to NPARAMS are accessed; defaults
     are used for higher-numbered parameters.

       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
            refinement or not.
         Default: 1.0D+0
            = 0.0:  No refinement is performed, and no error bounds are
                    computed.
            = 1.0:  Use the double-precision refinement algorithm,
                    possibly with doubled-single computations if the
                    compilation environment does not support DOUBLE
                    PRECISION.
              (other values are reserved for future use)

       PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
            computations allowed for refinement.
         Default: 10
         Aggressive: Set to 100 to permit convergence using approximate
                     factorizations or factorizations other than LU. If
                     the factorization uses a technique other than
                     Gaussian elimination, the guarantees in
                     err_bnds_norm and err_bnds_comp may no longer be
                     trustworthy.

       PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
            will attempt to find a solution with small componentwise
            relative error in the double-precision algorithm.  Positive
            is true, 0.0 is false.
         Default: 1.0 (attempt componentwise convergence)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (4*N)
[out]IWORK
          IWORK is INTEGER array, dimension (N)
[out]INFO
          INFO is INTEGER
       = 0:  Successful exit. The solution to every right-hand side is
         guaranteed.
       < 0:  If INFO = -i, the i-th argument had an illegal value
       > 0 and <= N:  U(INFO,INFO) is exactly zero.  The factorization
         has been completed, but the factor U is exactly singular, so
         the solution and error bounds could not be computed. RCOND = 0
         is returned.
       = N+J: The solution corresponding to the Jth right-hand side is
         not guaranteed. The solutions corresponding to other right-
         hand sides K with K > J may not be guaranteed as well, but
         only the first such right-hand side is reported. If a small
         componentwise error is not requested (PARAMS(3) = 0.0) then
         the Jth right-hand side is the first with a normwise error
         bound that is not guaranteed (the smallest J such
         that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
         the Jth right-hand side is the first with either a normwise or
         componentwise error bound that is not guaranteed (the smallest
         J such that either ERR_BNDS_NORM(J,1) = 0.0 or
         ERR_BNDS_COMP(J,1) = 0.0). See the definition of
         ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
         about all of the right-hand sides check ERR_BNDS_NORM or
         ERR_BNDS_COMP.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 435 of file dgbrfsx.f.

440 *
441 * -- LAPACK computational routine --
442 * -- LAPACK is a software package provided by Univ. of Tennessee, --
443 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
444 *
445 * .. Scalar Arguments ..
446  CHARACTER TRANS, EQUED
447  INTEGER INFO, LDAB, LDAFB, LDB, LDX, N, KL, KU, NRHS,
448  $ NPARAMS, N_ERR_BNDS
449  DOUBLE PRECISION RCOND
450 * ..
451 * .. Array Arguments ..
452  INTEGER IPIV( * ), IWORK( * )
453  DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ),
454  $ X( LDX , * ),WORK( * )
455  DOUBLE PRECISION R( * ), C( * ), PARAMS( * ), BERR( * ),
456  $ ERR_BNDS_NORM( NRHS, * ),
457  $ ERR_BNDS_COMP( NRHS, * )
458 * ..
459 *
460 * ==================================================================
461 *
462 * .. Parameters ..
463  DOUBLE PRECISION ZERO, ONE
464  parameter( zero = 0.0d+0, one = 1.0d+0 )
465  DOUBLE PRECISION ITREF_DEFAULT, ITHRESH_DEFAULT
466  DOUBLE PRECISION COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT
467  DOUBLE PRECISION DZTHRESH_DEFAULT
468  parameter( itref_default = 1.0d+0 )
469  parameter( ithresh_default = 10.0d+0 )
470  parameter( componentwise_default = 1.0d+0 )
471  parameter( rthresh_default = 0.5d+0 )
472  parameter( dzthresh_default = 0.25d+0 )
473  INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
474  $ LA_LINRX_CWISE_I
475  parameter( la_linrx_itref_i = 1,
476  $ la_linrx_ithresh_i = 2 )
477  parameter( la_linrx_cwise_i = 3 )
478  INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
479  $ LA_LINRX_RCOND_I
480  parameter( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
481  parameter( la_linrx_rcond_i = 3 )
482 * ..
483 * .. Local Scalars ..
484  CHARACTER(1) NORM
485  LOGICAL ROWEQU, COLEQU, NOTRAN
486  INTEGER J, TRANS_TYPE, PREC_TYPE, REF_TYPE
487  INTEGER N_NORMS
488  DOUBLE PRECISION ANORM, RCOND_TMP
489  DOUBLE PRECISION ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
490  LOGICAL IGNORE_CWISE
491  INTEGER ITHRESH
492  DOUBLE PRECISION RTHRESH, UNSTABLE_THRESH
493 * ..
494 * .. External Subroutines ..
495  EXTERNAL xerbla, dgbcon
496  EXTERNAL dla_gbrfsx_extended
497 * ..
498 * .. Intrinsic Functions ..
499  INTRINSIC max, sqrt
500 * ..
501 * .. External Functions ..
502  EXTERNAL lsame, ilatrans, ilaprec
503  EXTERNAL dlamch, dlangb, dla_gbrcond
504  DOUBLE PRECISION DLAMCH, DLANGB, DLA_GBRCOND
505  LOGICAL LSAME
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( 'DGBRFSX', -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 = dlangb( norm, n, kl, ku, ab, ldab, work )
640  CALL dgbcon( norm, n, kl, ku, afb, ldafb, ipiv, anorm, rcond,
641  $ work, iwork, 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 dla_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( n+1 ), work( 1 ), work( 2*n+1 ),
654  $ work( 1 ), rcond, ithresh, rthresh, unstable_thresh,
655  $ ignore_cwise, info )
656  ELSE
657  CALL dla_gbrfsx_extended( prec_type, trans_type, n, kl, ku,
658  $ nrhs, ab, ldab, afb, ldafb, ipiv, rowequ, r, b,
659  $ ldb, x, ldx, berr, n_norms, err_bnds_norm,
660  $ err_bnds_comp, work( n+1 ), work( 1 ), work( 2*n+1 ),
661  $ work( 1 ), rcond, ithresh, rthresh, unstable_thresh,
662  $ ignore_cwise, info )
663  END IF
664  END IF
665 
666  err_lbnd = max( 10.0d+0, sqrt( dble( n ) ) ) * dlamch( 'Epsilon' )
667  IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 1 ) THEN
668 *
669 * Compute scaled normwise condition number cond(A*C).
670 *
671  IF ( colequ .AND. notran ) THEN
672  rcond_tmp = dla_gbrcond( trans, n, kl, ku, ab, ldab, afb,
673  $ ldafb, ipiv, -1, c, info, work, iwork )
674  ELSE IF ( rowequ .AND. .NOT. notran ) THEN
675  rcond_tmp = dla_gbrcond( trans, n, kl, ku, ab, ldab, afb,
676  $ ldafb, ipiv, -1, r, info, work, iwork )
677  ELSE
678  rcond_tmp = dla_gbrcond( trans, n, kl, ku, ab, ldab, afb,
679  $ ldafb, ipiv, 0, r, info, work, iwork )
680  END IF
681  DO j = 1, nrhs
682 *
683 * Cap the error at 1.0.
684 *
685  IF ( n_err_bnds .GE. la_linrx_err_i
686  $ .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0d+0 )
687  $ err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
688 *
689 * Threshold the error (see LAWN).
690 *
691  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
692  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
693  err_bnds_norm( j, la_linrx_trust_i ) = 0.0d+0
694  IF ( info .LE. n ) info = n + j
695  ELSE IF ( err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd )
696  $ THEN
697  err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
698  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
699  END IF
700 *
701 * Save the condition number.
702 *
703  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
704  err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
705  END IF
706 
707  END DO
708  END IF
709 
710  IF (n_err_bnds .GE. 1 .AND. n_norms .GE. 2) THEN
711 *
712 * Compute componentwise condition number cond(A*diag(Y(:,J))) for
713 * each right-hand side using the current solution as an estimate of
714 * the true solution. If the componentwise error estimate is too
715 * large, then the solution is a lousy estimate of truth and the
716 * estimated RCOND may be too optimistic. To avoid misleading users,
717 * the inverse condition number is set to 0.0 when the estimated
718 * cwise error is at least CWISE_WRONG.
719 *
720  cwise_wrong = sqrt( dlamch( 'Epsilon' ) )
721  DO j = 1, nrhs
722  IF ( err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
723  $ THEN
724  rcond_tmp = dla_gbrcond( trans, n, kl, ku, ab, ldab, afb,
725  $ ldafb, ipiv, 1, x( 1, j ), info, work, iwork )
726  ELSE
727  rcond_tmp = 0.0d+0
728  END IF
729 *
730 * Cap the error at 1.0.
731 *
732  IF ( n_err_bnds .GE. la_linrx_err_i
733  $ .AND. err_bnds_comp( j, la_linrx_err_i ) .GT. 1.0d+0 )
734  $ err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
735 *
736 * Threshold the error (see LAWN).
737 *
738  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
739  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
740  err_bnds_comp( j, la_linrx_trust_i ) = 0.0d+0
741  IF ( params( la_linrx_cwise_i ) .EQ. 1.0d+0
742  $ .AND. info.LT.n + j ) info = n + j
743  ELSE IF ( err_bnds_comp( j, la_linrx_err_i )
744  $ .LT. err_lbnd ) THEN
745  err_bnds_comp( j, la_linrx_err_i ) = err_lbnd
746  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
747  END IF
748 *
749 * Save the condition number.
750 *
751  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
752  err_bnds_comp( j, la_linrx_rcond_i ) = rcond_tmp
753  END IF
754 
755  END DO
756  END IF
757 *
758  RETURN
759 *
760 * End of DGBRFSX
761 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
integer function ilaprec(PREC)
ILAPREC
Definition: ilaprec.f:58
integer function ilatrans(TRANS)
ILATRANS
Definition: ilatrans.f:58
double precision function dlangb(NORM, N, KL, KU, AB, LDAB, WORK)
DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlangb.f:124
subroutine dla_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)
DLA_GBRFSX_EXTENDED improves the computed solution to a system of linear equations for general banded...
double precision function dla_gbrcond(TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, CMODE, C, INFO, WORK, IWORK)
DLA_GBRCOND estimates the Skeel condition number for a general banded matrix.
Definition: dla_gbrcond.f:170
subroutine dgbcon(NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
DGBCON
Definition: dgbcon.f:146
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