LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine cgbrfsx ( character TRANS, character EQUED, integer N, integer KL, integer KU, integer NRHS, complex, dimension( ldab, * ) AB, integer LDAB, complex, dimension( ldafb, * ) AFB, integer LDAFB, integer, dimension( * ) IPIV, real, dimension( * ) R, real, dimension( * ) C, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldx , * ) X, integer LDX, real RCOND, real, dimension( * ) BERR, integer N_ERR_BNDS, real, dimension( nrhs, * ) ERR_BNDS_NORM, real, dimension( nrhs, * ) ERR_BNDS_COMP, integer NPARAMS, real, dimension( * ) PARAMS, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO )

CGBRFSX

Purpose:
```    CGBRFSX 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 = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).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 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 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 COMPLEX array, dimension (LDB,NRHS) The right hand side matrix B.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [in,out] X ``` X is COMPLEX array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by SGETRS. On exit, the improved solution matrix X.``` [in] LDX ``` LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).``` [out] RCOND ``` RCOND is REAL Reciprocal scaled condition number. This is an estimate of the reciprocal Skeel condition number of the matrix A after equilibration (if done). If this is less than the machine precision (in particular, if it is zero), the matrix is singular to working precision. Note that the error may still be small even if this number is very small and the matrix appears ill- conditioned.``` [out] BERR ``` BERR is REAL array, dimension (NRHS) Componentwise relative backward error. This is the componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).``` [in] N_ERR_BNDS ``` N_ERR_BNDS is INTEGER Number of error bounds to return for each right hand side and each type (normwise or componentwise). See ERR_BNDS_NORM and ERR_BNDS_COMP below.``` [out] ERR_BNDS_NORM ``` ERR_BNDS_NORM is REAL array, dimension (NRHS, N_ERR_BNDS) For each right-hand side, this array contains information about various error bounds and condition numbers corresponding to the normwise relative error, which is defined as follows: Normwise relative error in the ith solution vector: max_j (abs(XTRUE(j,i) - X(j,i))) ------------------------------ max_j abs(X(j,i)) The array is indexed by the type of error information as described below. There currently are up to three pieces of information returned. The first index in ERR_BNDS_NORM(i,:) corresponds to the ith right-hand side. The second index in ERR_BNDS_NORM(:,err) contains the following three fields: err = 1 "Trust/don't trust" boolean. Trust the answer if the reciprocal condition number is less than the threshold sqrt(n) * slamch('Epsilon'). err = 2 "Guaranteed" error bound: The estimated forward error, almost certainly within a factor of 10 of the true error so long as the next entry is greater than the threshold sqrt(n) * slamch('Epsilon'). This error bound should only be trusted if the previous boolean is true. err = 3 Reciprocal condition number: Estimated normwise reciprocal condition number. Compared with the threshold sqrt(n) * slamch('Epsilon') to determine if the error estimate is "guaranteed". These reciprocal condition numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some appropriately scaled matrix Z. Let Z = S*A, where S scales each row by a power of the radix so all absolute row sums of Z are approximately 1. See Lapack Working Note 165 for further details and extra cautions.``` [out] ERR_BNDS_COMP ``` ERR_BNDS_COMP is REAL array, dimension (NRHS, N_ERR_BNDS) For each right-hand side, this array contains information about various error bounds and condition numbers corresponding to the componentwise relative error, which is defined as follows: Componentwise relative error in the ith solution vector: abs(XTRUE(j,i) - X(j,i)) max_j ---------------------- abs(X(j,i)) The array is indexed by the right-hand side i (on which the componentwise relative error depends), and the type of error information as described below. There currently are up to three pieces of information returned for each right-hand side. If componentwise accuracy is not requested (PARAMS(3) = 0.0), then ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most the first (:,N_ERR_BNDS) entries are returned. The first index in ERR_BNDS_COMP(i,:) corresponds to the ith right-hand side. The second index in ERR_BNDS_COMP(:,err) contains the following three fields: err = 1 "Trust/don't trust" boolean. Trust the answer if the reciprocal condition number is less than the threshold sqrt(n) * slamch('Epsilon'). err = 2 "Guaranteed" error bound: The estimated forward error, almost certainly within a factor of 10 of the true error so long as the next entry is greater than the threshold sqrt(n) * slamch('Epsilon'). This error bound should only be trusted if the previous boolean is true. err = 3 Reciprocal condition number: Estimated componentwise reciprocal condition number. Compared with the threshold sqrt(n) * slamch('Epsilon') to determine if the error estimate is "guaranteed". These reciprocal condition numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some appropriately scaled matrix Z. Let Z = S*(A*diag(x)), where x is the solution for the current right-hand side and S scales each row of A*diag(x) by a power of the radix so all absolute row sums of Z are approximately 1. See Lapack Working Note 165 for further details and extra cautions.``` [in] NPARAMS ``` NPARAMS is INTEGER Specifies the number of parameters set in PARAMS. If .LE. 0, the PARAMS array is never referenced and default values are used.``` [in,out] PARAMS ``` PARAMS is REAL array, dimension NPARAMS Specifies algorithm parameters. If an entry is .LT. 0.0, then that entry will be filled with default value used for that parameter. Only positions up to NPARAMS are accessed; defaults are used for higher-numbered parameters. PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative refinement or not. Default: 1.0 = 0.0 : No refinement is performed, and no error bounds are computed. = 1.0 : Use the double-precision refinement algorithm, possibly with doubled-single computations if the compilation environment does not support DOUBLE PRECISION. (other values are reserved for future use) PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual computations allowed for refinement. Default: 10 Aggressive: Set to 100 to permit convergence using approximate factorizations or factorizations other than LU. If the factorization uses a technique other than Gaussian elimination, the guarantees in err_bnds_norm and err_bnds_comp may no longer be trustworthy. PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code will attempt to find a solution with small componentwise relative error in the double-precision algorithm. Positive is true, 0.0 is false. Default: 1.0 (attempt componentwise convergence)``` [out] WORK ` WORK is COMPLEX array, dimension (2*N)` [out] RWORK ` RWORK is REAL array, dimension (2*N)` [out] INFO ``` INFO is INTEGER = 0: Successful exit. The solution to every right-hand side is guaranteed. < 0: If INFO = -i, the i-th argument had an illegal value > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution and error bounds could not be computed. RCOND = 0 is returned. = N+J: The solution corresponding to the Jth right-hand side is not guaranteed. The solutions corresponding to other right- hand sides K with K > J may not be guaranteed as well, but only the first such right-hand side is reported. If a small componentwise error is not requested (PARAMS(3) = 0.0) then the Jth right-hand side is the first with a normwise error bound that is not guaranteed (the smallest J such that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) the Jth right-hand side is the first with either a normwise or componentwise error bound that is not guaranteed (the smallest J such that either ERR_BNDS_NORM(J,1) = 0.0 or ERR_BNDS_COMP(J,1) = 0.0). See the definition of ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information about all of the right-hand sides check ERR_BNDS_NORM or ERR_BNDS_COMP.```
Date
April 2012

Definition at line 442 of file cgbrfsx.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( * )
456  COMPLEX 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, * ), rwork( * )
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, ignore_cwise
489  INTEGER j, trans_type, prec_type, ref_type, n_norms,
490  \$ ithresh
491  REAL 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
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. 0.0 ) 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 = REAL( N ) * slamch( 'Epsilon' )
526  ithresh = int( ithresh_default )
527  rthresh = rthresh_default
528  unstable_thresh = dzthresh_default
529  ignore_cwise = componentwise_default .EQ. 0.0
530 *
531  IF ( nparams.GE.la_linrx_ithresh_i ) THEN
532  IF ( params( la_linrx_ithresh_i ).LT.0.0 ) 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.0.0 ) THEN
540  IF ( ignore_cwise ) THEN
541  params( la_linrx_cwise_i ) = 0.0
542  ELSE
543  params( la_linrx_cwise_i ) = 1.0
544  END IF
545  ELSE
546  ignore_cwise = params( la_linrx_cwise_i ) .EQ. 0.0
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( 'CGBRFSX', -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 = 1.0
594  DO j = 1, nrhs
595  berr( j ) = 0.0
596  IF ( n_err_bnds .GE. 1 ) THEN
597  err_bnds_norm( j, la_linrx_trust_i ) = 1.0
598  err_bnds_comp( j, la_linrx_trust_i ) = 1.0
599  END IF
600  IF ( n_err_bnds .GE. 2 ) THEN
601  err_bnds_norm( j, la_linrx_err_i ) = 0.0
602  err_bnds_comp( j, la_linrx_err_i ) = 0.0
603  END IF
604  IF ( n_err_bnds .GE. 3 ) THEN
605  err_bnds_norm( j, la_linrx_rcond_i ) = 1.0
606  err_bnds_comp( j, la_linrx_rcond_i ) = 1.0
607  END IF
608  END DO
609  RETURN
610  END IF
611 *
612 * Default to failure.
613 *
614  rcond = 0.0
615  DO j = 1, nrhs
616  berr( j ) = 1.0
617  IF ( n_err_bnds .GE. 1 ) THEN
618  err_bnds_norm( j, la_linrx_trust_i ) = 1.0
619  err_bnds_comp( j, la_linrx_trust_i ) = 1.0
620  END IF
621  IF ( n_err_bnds .GE. 2 ) THEN
622  err_bnds_norm( j, la_linrx_err_i ) = 1.0
623  err_bnds_comp( j, la_linrx_err_i ) = 1.0
624  END IF
625  IF ( n_err_bnds .GE. 3 ) THEN
626  err_bnds_norm( j, la_linrx_rcond_i ) = 0.0
627  err_bnds_comp( j, la_linrx_rcond_i ) = 0.0
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 = clangb( norm, n, kl, ku, ab, ldab, rwork )
640  CALL cgbcon( 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( 'D' )
648
649  IF ( notran ) THEN
650  CALL cla_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 cla_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( 10.0, sqrt( REAL( N ) ) ) * slamch( '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 = cla_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 = cla_gbrcond_c( trans, n, kl, ku, ab, ldab, afb,
678  \$ ldafb, ipiv, r, .true., info, work, rwork )
679  ELSE
680  rcond_tmp = cla_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. 1.0)
689  \$ err_bnds_norm( j, la_linrx_err_i ) = 1.0
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 ) = 1.0
695  err_bnds_norm( j, la_linrx_trust_i ) = 0.0
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 ) = 1.0
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( slamch( 'Epsilon' ) )
723  DO j = 1, nrhs
724  IF (err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
725  \$ THEN
726  rcond_tmp = cla_gbrcond_x( trans, n, kl, ku, ab, ldab,
727  \$ afb, ldafb, ipiv, x( 1, j ), info, work, rwork )
728  ELSE
729  rcond_tmp = 0.0
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. 1.0 )
736  \$ err_bnds_comp( j, la_linrx_err_i ) = 1.0
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 ) = 1.0
742  err_bnds_comp( j, la_linrx_trust_i ) = 0.0
743  IF ( params( la_linrx_cwise_i ) .EQ. 1.0
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 ) = 1.0
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 CGBRFSX
763 *
integer function ilatrans(TRANS)
ILATRANS
Definition: ilatrans.f:60
subroutine cla_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)
CLA_GBRFSX_EXTENDED improves the computed solution to a system of linear equations for general banded...
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
integer function ilaprec(PREC)
ILAPREC
Definition: ilaprec.f:60
real function cla_gbrcond_x(TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, X, INFO, WORK, RWORK)
CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrice...
subroutine cgbcon(NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK, RWORK, INFO)
CGBCON
Definition: cgbcon.f:149
real function clangb(NORM, N, KL, KU, AB, LDAB, WORK)
CLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clangb.f:127
real function cla_gbrcond_c(TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, C, CAPPLY, INFO, WORK, RWORK)
CLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded ma...
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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