LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine sgbrfsx ( character TRANS, character EQUED, integer N, integer KL, integer KU, integer NRHS, real, dimension( ldab, * ) AB, integer LDAB, real, dimension( ldafb, * ) AFB, integer LDAFB, integer, dimension( * ) IPIV, real, dimension( * ) R, real, dimension( * ) C, real, dimension( ldb, * ) B, integer LDB, real, 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, real, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO )

SGBRFSX

Purpose:
```    SGBRFSX 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 = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).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 REAL 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 REAL 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 SGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).``` [in,out] R ``` R is REAL 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 REAL 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 REAL 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 REAL 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 REAL 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.```
Date
April 2012

Definition at line 442 of file sgbrfsx.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  REAL rcond
453 * ..
454 * .. Array Arguments ..
455  INTEGER ipiv( * ), iwork( * )
456  REAL ab( ldab, * ), afb( ldafb, * ), b( ldb, * ),
457  \$ x( ldx , * ),work( * )
458  REAL r( * ), c( * ), params( * ), berr( * ),
459  \$ err_bnds_norm( nrhs, * ),
460  \$ err_bnds_comp( nrhs, * )
461 * ..
462 *
463 * ==================================================================
464 *
465 * .. Parameters ..
466  REAL zero, one
467  parameter ( zero = 0.0e+0, one = 1.0e+0 )
468  REAL itref_default, ithresh_default,
469  \$ componentwise_default
470  REAL rthresh_default, dzthresh_default
471  parameter ( itref_default = 1.0 )
472  parameter ( ithresh_default = 10.0 )
473  parameter ( componentwise_default = 1.0 )
474  parameter ( rthresh_default = 0.5 )
475  parameter ( dzthresh_default = 0.25 )
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
489  INTEGER j, trans_type, prec_type, ref_type
490  INTEGER n_norms
491  REAL anorm, rcond_tmp
492  REAL illrcond_thresh, err_lbnd, cwise_wrong
493  LOGICAL ignore_cwise
494  INTEGER ithresh
495  REAL rthresh, unstable_thresh
496 * ..
497 * .. External Subroutines ..
498  EXTERNAL xerbla, sgbcon
499  EXTERNAL sla_gbrfsx_extended
500 * ..
501 * .. Intrinsic Functions ..
502  INTRINSIC max, sqrt
503 * ..
504 * .. External Functions ..
505  EXTERNAL lsame, blas_fpinfo_x, ilatrans, ilaprec
506  EXTERNAL slamch, slangb, sla_gbrcond
507  REAL slamch, slangb, sla_gbrcond
508  LOGICAL lsame
509  INTEGER blas_fpinfo_x
510  INTEGER ilatrans, ilaprec
511 * ..
512 * .. Executable Statements ..
513 *
514 * Check the input parameters.
515 *
516  info = 0
517  trans_type = ilatrans( trans )
518  ref_type = int( itref_default )
519  IF ( nparams .GE. la_linrx_itref_i ) THEN
520  IF ( params( la_linrx_itref_i ) .LT. 0.0 ) THEN
521  params( la_linrx_itref_i ) = itref_default
522  ELSE
523  ref_type = params( la_linrx_itref_i )
524  END IF
525  END IF
526 *
527 * Set default parameters.
528 *
529  illrcond_thresh = REAL( N ) * slamch( 'Epsilon' )
530  ithresh = int( ithresh_default )
531  rthresh = rthresh_default
532  unstable_thresh = dzthresh_default
533  ignore_cwise = componentwise_default .EQ. 0.0
534 *
535  IF ( nparams.GE.la_linrx_ithresh_i ) THEN
536  IF ( params( la_linrx_ithresh_i ).LT.0.0 ) THEN
537  params( la_linrx_ithresh_i ) = ithresh
538  ELSE
539  ithresh = int( params( la_linrx_ithresh_i ) )
540  END IF
541  END IF
542  IF ( nparams.GE.la_linrx_cwise_i ) THEN
543  IF ( params( la_linrx_cwise_i ).LT.0.0 ) THEN
544  IF ( ignore_cwise ) THEN
545  params( la_linrx_cwise_i ) = 0.0
546  ELSE
547  params( la_linrx_cwise_i ) = 1.0
548  END IF
549  ELSE
550  ignore_cwise = params( la_linrx_cwise_i ) .EQ. 0.0
551  END IF
552  END IF
553  IF ( ref_type .EQ. 0 .OR. n_err_bnds .EQ. 0 ) THEN
554  n_norms = 0
555  ELSE IF ( ignore_cwise ) THEN
556  n_norms = 1
557  ELSE
558  n_norms = 2
559  END IF
560 *
561  notran = lsame( trans, 'N' )
562  rowequ = lsame( equed, 'R' ) .OR. lsame( equed, 'B' )
563  colequ = lsame( equed, 'C' ) .OR. lsame( equed, 'B' )
564 *
565 * Test input parameters.
566 *
567  IF( trans_type.EQ.-1 ) THEN
568  info = -1
569  ELSE IF( .NOT.rowequ .AND. .NOT.colequ .AND.
570  \$ .NOT.lsame( equed, 'N' ) ) THEN
571  info = -2
572  ELSE IF( n.LT.0 ) THEN
573  info = -3
574  ELSE IF( kl.LT.0 ) THEN
575  info = -4
576  ELSE IF( ku.LT.0 ) THEN
577  info = -5
578  ELSE IF( nrhs.LT.0 ) THEN
579  info = -6
580  ELSE IF( ldab.LT.kl+ku+1 ) THEN
581  info = -8
582  ELSE IF( ldafb.LT.2*kl+ku+1 ) THEN
583  info = -10
584  ELSE IF( ldb.LT.max( 1, n ) ) THEN
585  info = -13
586  ELSE IF( ldx.LT.max( 1, n ) ) THEN
587  info = -15
588  END IF
589  IF( info.NE.0 ) THEN
590  CALL xerbla( 'SGBRFSX', -info )
591  RETURN
592  END IF
593 *
594 * Quick return if possible.
595 *
596  IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
597  rcond = 1.0
598  DO j = 1, nrhs
599  berr( j ) = 0.0
600  IF ( n_err_bnds .GE. 1 ) THEN
601  err_bnds_norm( j, la_linrx_trust_i ) = 1.0
602  err_bnds_comp( j, la_linrx_trust_i ) = 1.0
603  END IF
604  IF ( n_err_bnds .GE. 2 ) THEN
605  err_bnds_norm( j, la_linrx_err_i ) = 0.0
606  err_bnds_comp( j, la_linrx_err_i ) = 0.0
607  END IF
608  IF ( n_err_bnds .GE. 3 ) THEN
609  err_bnds_norm( j, la_linrx_rcond_i ) = 1.0
610  err_bnds_comp( j, la_linrx_rcond_i ) = 1.0
611  END IF
612  END DO
613  RETURN
614  END IF
615 *
616 * Default to failure.
617 *
618  rcond = 0.0
619  DO j = 1, nrhs
620  berr( j ) = 1.0
621  IF ( n_err_bnds .GE. 1 ) THEN
622  err_bnds_norm( j, la_linrx_trust_i ) = 1.0
623  err_bnds_comp( j, la_linrx_trust_i ) = 1.0
624  END IF
625  IF ( n_err_bnds .GE. 2 ) THEN
626  err_bnds_norm( j, la_linrx_err_i ) = 1.0
627  err_bnds_comp( j, la_linrx_err_i ) = 1.0
628  END IF
629  IF ( n_err_bnds .GE. 3 ) THEN
630  err_bnds_norm( j, la_linrx_rcond_i ) = 0.0
631  err_bnds_comp( j, la_linrx_rcond_i ) = 0.0
632  END IF
633  END DO
634 *
635 * Compute the norm of A and the reciprocal of the condition
636 * number of A.
637 *
638  IF( notran ) THEN
639  norm = 'I'
640  ELSE
641  norm = '1'
642  END IF
643  anorm = slangb( norm, n, kl, ku, ab, ldab, work )
644  CALL sgbcon( norm, n, kl, ku, afb, ldafb, ipiv, anorm, rcond,
645  \$ work, iwork, info )
646 *
647 * Perform refinement on each right-hand side
648 *
649  IF ( ref_type .NE. 0 .AND. info .EQ. 0 ) THEN
650
651  prec_type = ilaprec( 'D' )
652
653  IF ( notran ) THEN
654  CALL sla_gbrfsx_extended( prec_type, trans_type, n, kl, ku,
655  \$ nrhs, ab, ldab, afb, ldafb, ipiv, colequ, c, b,
656  \$ ldb, x, ldx, berr, n_norms, err_bnds_norm,
657  \$ err_bnds_comp, work( n+1 ), work( 1 ), work( 2*n+1 ),
658  \$ work( 1 ), rcond, ithresh, rthresh, unstable_thresh,
659  \$ ignore_cwise, info )
660  ELSE
661  CALL sla_gbrfsx_extended( prec_type, trans_type, n, kl, ku,
662  \$ nrhs, ab, ldab, afb, ldafb, ipiv, rowequ, r, b,
663  \$ ldb, x, ldx, berr, n_norms, err_bnds_norm,
664  \$ err_bnds_comp, work( n+1 ), work( 1 ), work( 2*n+1 ),
665  \$ work( 1 ), rcond, ithresh, rthresh, unstable_thresh,
666  \$ ignore_cwise, info )
667  END IF
668  END IF
669
670  err_lbnd = max( 10.0, sqrt( REAL( N ) ) ) * slamch( 'Epsilon' )
671  IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 1 ) THEN
672 *
673 * Compute scaled normwise condition number cond(A*C).
674 *
675  IF ( colequ .AND. notran ) THEN
676  rcond_tmp = sla_gbrcond( trans, n, kl, ku, ab, ldab, afb,
677  \$ ldafb, ipiv, -1, c, info, work, iwork )
678  ELSE IF ( rowequ .AND. .NOT. notran ) THEN
679  rcond_tmp = sla_gbrcond( trans, n, kl, ku, ab, ldab, afb,
680  \$ ldafb, ipiv, -1, r, info, work, iwork )
681  ELSE
682  rcond_tmp = sla_gbrcond( trans, n, kl, ku, ab, ldab, afb,
683  \$ ldafb, ipiv, 0, r, info, work, iwork )
684  END IF
685  DO j = 1, nrhs
686 *
687 * Cap the error at 1.0.
688 *
689  IF ( n_err_bnds .GE. la_linrx_err_i
690  \$ .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0 )
691  \$ err_bnds_norm( j, la_linrx_err_i ) = 1.0
692 *
693 * Threshold the error (see LAWN).
694 *
695  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
696  err_bnds_norm( j, la_linrx_err_i ) = 1.0
697  err_bnds_norm( j, la_linrx_trust_i ) = 0.0
698  IF ( info .LE. n ) info = n + j
699  ELSE IF ( err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd )
700  \$ THEN
701  err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
702  err_bnds_norm( j, la_linrx_trust_i ) = 1.0
703  END IF
704 *
705 * Save the condition number.
706 *
707  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
708  err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
709  END IF
710
711  END DO
712  END IF
713
714  IF (n_err_bnds .GE. 1 .AND. n_norms .GE. 2) THEN
715 *
716 * Compute componentwise condition number cond(A*diag(Y(:,J))) for
717 * each right-hand side using the current solution as an estimate of
718 * the true solution. If the componentwise error estimate is too
719 * large, then the solution is a lousy estimate of truth and the
720 * estimated RCOND may be too optimistic. To avoid misleading users,
721 * the inverse condition number is set to 0.0 when the estimated
722 * cwise error is at least CWISE_WRONG.
723 *
724  cwise_wrong = sqrt( slamch( 'Epsilon' ) )
725  DO j = 1, nrhs
726  IF ( err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
727  \$ THEN
728  rcond_tmp = sla_gbrcond( trans, n, kl, ku, ab, ldab, afb,
729  \$ ldafb, ipiv, 1, x( 1, j ), info, work, iwork )
730  ELSE
731  rcond_tmp = 0.0
732  END IF
733 *
734 * Cap the error at 1.0.
735 *
736  IF ( n_err_bnds .GE. la_linrx_err_i
737  \$ .AND. err_bnds_comp( j, la_linrx_err_i ) .GT. 1.0 )
738  \$ err_bnds_comp( j, la_linrx_err_i ) = 1.0
739 *
740 * Threshold the error (see LAWN).
741 *
742  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
743  err_bnds_comp( j, la_linrx_err_i ) = 1.0
744  err_bnds_comp( j, la_linrx_trust_i ) = 0.0
745  IF ( params( la_linrx_cwise_i ) .EQ. 1.0
746  \$ .AND. info.LT.n + j ) info = n + j
747  ELSE IF ( err_bnds_comp( j, la_linrx_err_i )
748  \$ .LT. err_lbnd ) THEN
749  err_bnds_comp( j, la_linrx_err_i ) = err_lbnd
750  err_bnds_comp( j, la_linrx_trust_i ) = 1.0
751  END IF
752 *
753 * Save the condition number.
754 *
755  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
756  err_bnds_comp( j, la_linrx_rcond_i ) = rcond_tmp
757  END IF
758
759  END DO
760  END IF
761 *
762  RETURN
763 *
764 * End of SGBRFSX
765 *
integer function ilatrans(TRANS)
ILATRANS
Definition: ilatrans.f:60
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
real function sla_gbrcond(TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, CMODE, C, INFO, WORK, IWORK)
SLA_GBRCOND estimates the Skeel condition number for a general banded matrix.
Definition: sla_gbrcond.f:170
integer function ilaprec(PREC)
ILAPREC
Definition: ilaprec.f:60
subroutine sgbcon(NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
SGBCON
Definition: sgbcon.f:148
subroutine sla_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)
SLA_GBRFSX_EXTENDED improves the computed solution to a system of linear equations for general banded...
real function slangb(NORM, N, KL, KU, AB, LDAB, WORK)
SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slangb.f:126
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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