LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ cla_herfsx_extended()

subroutine cla_herfsx_extended ( integer prec_type,
character uplo,
integer n,
integer nrhs,
complex, dimension( lda, * ) a,
integer lda,
complex, dimension( ldaf, * ) af,
integer ldaf,
integer, dimension( * ) ipiv,
logical colequ,
real, dimension( * ) c,
complex, dimension( ldb, * ) b,
integer ldb,
complex, dimension( ldy, * ) y,
integer ldy,
real, dimension( * ) berr_out,
integer n_norms,
real, dimension( nrhs, * ) err_bnds_norm,
real, dimension( nrhs, * ) err_bnds_comp,
complex, dimension( * ) res,
real, dimension( * ) ayb,
complex, dimension( * ) dy,
complex, dimension( * ) y_tail,
real rcond,
integer ithresh,
real rthresh,
real dz_ub,
logical ignore_cwise,
integer info )

CLA_HERFSX_EXTENDED improves the computed solution to a system of linear equations for Hermitian indefinite matrices by performing extra-precise iterative refinement and provides error bounds and backward error estimates for the solution.

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

Purpose:
!>
!> CLA_HERFSX_EXTENDED improves the computed solution to a system of
!> linear equations by performing extra-precise iterative refinement
!> and provides error bounds and backward error estimates for the solution.
!> This subroutine is called by CHERFSX to perform iterative refinement.
!> 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. Note that this
!> subroutine is only responsible for setting the second fields of
!> ERR_BNDS_NORM and ERR_BNDS_COMP.
!>
Parameters
[in]PREC_TYPE
!>          PREC_TYPE is INTEGER
!>     Specifies the intermediate precision to be used in refinement.
!>     The value is defined by ILAPREC(P) where P is a CHARACTER and P
!>          = 'S':  Single
!>          = 'D':  Double
!>          = 'I':  Indigenous
!>          = 'X' or 'E':  Extra
!>
[in]UPLO
!>          UPLO is CHARACTER*1
!>       = 'U':  Upper triangle of A is stored;
!>       = 'L':  Lower triangle of A is stored.
!>
[in]N
!>          N is INTEGER
!>     The number of linear equations, i.e., the order of the
!>     matrix A.  N >= 0.
!>
[in]NRHS
!>          NRHS is INTEGER
!>     The number of right-hand-sides, i.e., the number of columns of the
!>     matrix B.
!>
[in]A
!>          A is COMPLEX array, dimension (LDA,N)
!>     On entry, the N-by-N matrix A.
!>
[in]LDA
!>          LDA is INTEGER
!>     The leading dimension of the array A.  LDA >= max(1,N).
!>
[in]AF
!>          AF is COMPLEX array, dimension (LDAF,N)
!>     The block diagonal matrix D and the multipliers used to
!>     obtain the factor U or L as computed by CHETRF.
!>
[in]LDAF
!>          LDAF is INTEGER
!>     The leading dimension of the array AF.  LDAF >= max(1,N).
!>
[in]IPIV
!>          IPIV is INTEGER array, dimension (N)
!>     Details of the interchanges and the block structure of D
!>     as determined by CHETRF.
!>
[in]COLEQU
!>          COLEQU is LOGICAL
!>     If .TRUE. then column equilibration was done to A before calling
!>     this routine. This is needed to compute the solution and error
!>     bounds correctly.
!>
[in]C
!>          C is REAL array, dimension (N)
!>     The column scale factors for A. If COLEQU = .FALSE., C
!>     is not accessed. 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]Y
!>          Y is COMPLEX array, dimension (LDY,NRHS)
!>     On entry, the solution matrix X, as computed by CHETRS.
!>     On exit, the improved solution matrix Y.
!>
[in]LDY
!>          LDY is INTEGER
!>     The leading dimension of the array Y.  LDY >= max(1,N).
!>
[out]BERR_OUT
!>          BERR_OUT is REAL array, dimension (NRHS)
!>     On exit, BERR_OUT(j) contains the componentwise relative backward
!>     error for right-hand-side j from the formula
!>         max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
!>     where abs(Z) is the componentwise absolute value of the matrix
!>     or vector Z. This is computed by CLA_LIN_BERR.
!>
[in]N_NORMS
!>          N_NORMS is INTEGER
!>     Determines which error bounds to return (see ERR_BNDS_NORM
!>     and ERR_BNDS_COMP).
!>     If N_NORMS >= 1 return normwise error bounds.
!>     If N_NORMS >= 2 return componentwise error bounds.
!>
[in,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  boolean. Trust the answer if the
!>              reciprocal condition number is less than the threshold
!>              sqrt(n) * slamch('Epsilon').
!>
!>     err = 2  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 . 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.
!>
!>     This subroutine is only responsible for setting the second field
!>     above.
!>     See Lapack Working Note 165 for further details and extra
!>     cautions.
!>
[in,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 < 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  boolean. Trust the answer if the
!>              reciprocal condition number is less than the threshold
!>              sqrt(n) * slamch('Epsilon').
!>
!>     err = 2  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 . 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.
!>
!>     This subroutine is only responsible for setting the second field
!>     above.
!>     See Lapack Working Note 165 for further details and extra
!>     cautions.
!>
[in]RES
!>          RES is COMPLEX array, dimension (N)
!>     Workspace to hold the intermediate residual.
!>
[in]AYB
!>          AYB is REAL array, dimension (N)
!>     Workspace.
!>
[in]DY
!>          DY is COMPLEX array, dimension (N)
!>     Workspace to hold the intermediate solution.
!>
[in]Y_TAIL
!>          Y_TAIL is COMPLEX array, dimension (N)
!>     Workspace to hold the trailing bits of the intermediate solution.
!>
[in]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.
!>
[in]ITHRESH
!>          ITHRESH is INTEGER
!>     The maximum number of residual computations allowed for
!>     refinement. The default is 10. For '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.
!>
[in]RTHRESH
!>          RTHRESH is REAL
!>     Determines when to stop refinement if the error estimate stops
!>     decreasing. Refinement will stop when the next solution no longer
!>     satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is
!>     the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The
!>     default value is 0.5. For 'aggressive' set to 0.9 to permit
!>     convergence on extremely ill-conditioned matrices. See LAWN 165
!>     for more details.
!>
[in]DZ_UB
!>          DZ_UB is REAL
!>     Determines when to start considering componentwise convergence.
!>     Componentwise convergence is only considered after each component
!>     of the solution Y is stable, which we define as the relative
!>     change in each component being less than DZ_UB. The default value
!>     is 0.25, requiring the first bit to be stable. See LAWN 165 for
!>     more details.
!>
[in]IGNORE_CWISE
!>          IGNORE_CWISE is LOGICAL
!>     If .TRUE. then ignore componentwise convergence. Default value
!>     is .FALSE..
!>
[out]INFO
!>          INFO is INTEGER
!>       = 0:  Successful exit.
!>       < 0:  if INFO = -i, the ith argument to CLA_HERFSX_EXTENDED had an illegal
!>             value
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 386 of file cla_herfsx_extended.f.

394*
395* -- LAPACK computational routine --
396* -- LAPACK is a software package provided by Univ. of Tennessee, --
397* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
398*
399* .. Scalar Arguments ..
400 INTEGER INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
401 $ N_NORMS, ITHRESH
402 CHARACTER UPLO
403 LOGICAL COLEQU, IGNORE_CWISE
404 REAL RTHRESH, DZ_UB
405* ..
406* .. Array Arguments ..
407 INTEGER IPIV( * )
408 COMPLEX A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
409 $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
410 REAL C( * ), AYB( * ), RCOND, BERR_OUT( * ),
411 $ ERR_BNDS_NORM( NRHS, * ),
412 $ ERR_BNDS_COMP( NRHS, * )
413* ..
414*
415* =====================================================================
416*
417* .. Local Scalars ..
418 INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE,
419 $ Y_PREC_STATE
420 REAL YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT,
421 $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX,
422 $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z,
423 $ EPS, HUGEVAL, INCR_THRESH
424 LOGICAL INCR_PREC, UPPER
425 COMPLEX ZDUM
426* ..
427* .. Parameters ..
428 INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE,
429 $ NOPROG_STATE, BASE_RESIDUAL, EXTRA_RESIDUAL,
430 $ EXTRA_Y
431 parameter( unstable_state = 0, working_state = 1,
432 $ conv_state = 2, noprog_state = 3 )
433 parameter( base_residual = 0, extra_residual = 1,
434 $ extra_y = 2 )
435 INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
436 INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
437 INTEGER CMP_ERR_I, PIV_GROWTH_I
438 parameter( final_nrm_err_i = 1, final_cmp_err_i = 2,
439 $ berr_i = 3 )
440 parameter( rcond_i = 4, nrm_rcond_i = 5, nrm_err_i = 6 )
441 parameter( cmp_rcond_i = 7, cmp_err_i = 8,
442 $ piv_growth_i = 9 )
443 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
444 $ LA_LINRX_CWISE_I
445 parameter( la_linrx_itref_i = 1,
446 $ la_linrx_ithresh_i = 2 )
447 parameter( la_linrx_cwise_i = 3 )
448 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
449 $ LA_LINRX_RCOND_I
450 parameter( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
451 parameter( la_linrx_rcond_i = 3 )
452* ..
453* .. External Functions ..
454 LOGICAL LSAME
455 EXTERNAL ilauplo
456 INTEGER ILAUPLO
457* ..
458* .. External Subroutines ..
459 EXTERNAL caxpy, ccopy, chetrs, chemv,
460 $ blas_chemv_x,
461 $ blas_chemv2_x, cla_heamv, cla_wwaddw,
462 $ cla_lin_berr
463 REAL SLAMCH
464* ..
465* .. Intrinsic Functions ..
466 INTRINSIC abs, real, aimag, max, min
467* ..
468* .. Statement Functions ..
469 REAL CABS1
470* ..
471* .. Statement Function Definitions ..
472 cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
473* ..
474* .. Executable Statements ..
475*
476 info = 0
477 upper = lsame( uplo, 'U' )
478 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
479 info = -2
480 ELSE IF( n.LT.0 ) THEN
481 info = -3
482 ELSE IF( nrhs.LT.0 ) THEN
483 info = -4
484 ELSE IF( lda.LT.max( 1, n ) ) THEN
485 info = -6
486 ELSE IF( ldaf.LT.max( 1, n ) ) THEN
487 info = -8
488 ELSE IF( ldb.LT.max( 1, n ) ) THEN
489 info = -13
490 ELSE IF( ldy.LT.max( 1, n ) ) THEN
491 info = -15
492 END IF
493 IF( info.NE.0 ) THEN
494 CALL xerbla( 'CLA_HERFSX_EXTENDED', -info )
495 RETURN
496 END IF
497 eps = slamch( 'Epsilon' )
498 hugeval = slamch( 'Overflow' )
499* Force HUGEVAL to Inf
500 hugeval = hugeval * hugeval
501* Using HUGEVAL may lead to spurious underflows.
502 incr_thresh = real( n ) * eps
503
504 IF ( lsame( uplo, 'L' ) ) THEN
505 uplo2 = ilauplo( 'L' )
506 ELSE
507 uplo2 = ilauplo( 'U' )
508 ENDIF
509
510 DO j = 1, nrhs
511 y_prec_state = extra_residual
512 IF ( y_prec_state .EQ. extra_y ) THEN
513 DO i = 1, n
514 y_tail( i ) = 0.0
515 END DO
516 END IF
517
518 dxrat = 0.0
519 dxratmax = 0.0
520 dzrat = 0.0
521 dzratmax = 0.0
522 final_dx_x = hugeval
523 final_dz_z = hugeval
524 prevnormdx = hugeval
525 prev_dz_z = hugeval
526 dz_z = hugeval
527 dx_x = hugeval
528
529 x_state = working_state
530 z_state = unstable_state
531 incr_prec = .false.
532
533 DO cnt = 1, ithresh
534*
535* Compute residual RES = B_s - op(A_s) * Y,
536* op(A) = A, A**T, or A**H depending on TRANS (and type).
537*
538 CALL ccopy( n, b( 1, j ), 1, res, 1 )
539 IF ( y_prec_state .EQ. base_residual ) THEN
540 CALL chemv( uplo, n, cmplx(-1.0), a, lda, y( 1, j ),
541 $ 1,
542 $ cmplx(1.0), res, 1 )
543 ELSE IF ( y_prec_state .EQ. extra_residual ) THEN
544 CALL blas_chemv_x( uplo2, n, cmplx(-1.0), a, lda,
545 $ y( 1, j ), 1, cmplx(1.0), res, 1, prec_type)
546 ELSE
547 CALL blas_chemv2_x(uplo2, n, cmplx(-1.0), a, lda,
548 $ y(1, j), y_tail, 1, cmplx(1.0), res, 1, prec_type)
549 END IF
550
551! XXX: RES is no longer needed.
552 CALL ccopy( n, res, 1, dy, 1 )
553 CALL chetrs( uplo, n, 1, af, ldaf, ipiv, dy, n, info )
554*
555* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
556*
557 normx = 0.0
558 normy = 0.0
559 normdx = 0.0
560 dz_z = 0.0
561 ymin = hugeval
562
563 DO i = 1, n
564 yk = cabs1( y( i, j ) )
565 dyk = cabs1( dy( i ) )
566
567 IF (yk .NE. 0.0) THEN
568 dz_z = max( dz_z, dyk / yk )
569 ELSE IF ( dyk .NE. 0.0 ) THEN
570 dz_z = hugeval
571 END IF
572
573 ymin = min( ymin, yk )
574
575 normy = max( normy, yk )
576
577 IF ( colequ ) THEN
578 normx = max( normx, yk * c( i ) )
579 normdx = max( normdx, dyk * c( i ) )
580 ELSE
581 normx = normy
582 normdx = max( normdx, dyk )
583 END IF
584 END DO
585
586 IF ( normx .NE. 0.0 ) THEN
587 dx_x = normdx / normx
588 ELSE IF ( normdx .EQ. 0.0 ) THEN
589 dx_x = 0.0
590 ELSE
591 dx_x = hugeval
592 END IF
593
594 dxrat = normdx / prevnormdx
595 dzrat = dz_z / prev_dz_z
596*
597* Check termination criteria.
598*
599 IF ( ymin*rcond .LT. incr_thresh*normy
600 $ .AND. y_prec_state .LT. extra_y )
601 $ incr_prec = .true.
602
603 IF ( x_state .EQ. noprog_state .AND. dxrat .LE. rthresh )
604 $ x_state = working_state
605 IF ( x_state .EQ. working_state ) THEN
606 IF ( dx_x .LE. eps ) THEN
607 x_state = conv_state
608 ELSE IF ( dxrat .GT. rthresh ) THEN
609 IF ( y_prec_state .NE. extra_y ) THEN
610 incr_prec = .true.
611 ELSE
612 x_state = noprog_state
613 END IF
614 ELSE
615 IF (dxrat .GT. dxratmax) dxratmax = dxrat
616 END IF
617 IF ( x_state .GT. working_state ) final_dx_x = dx_x
618 END IF
619
620 IF ( z_state .EQ. unstable_state .AND. dz_z .LE. dz_ub )
621 $ z_state = working_state
622 IF ( z_state .EQ. noprog_state .AND. dzrat .LE. rthresh )
623 $ z_state = working_state
624 IF ( z_state .EQ. working_state ) THEN
625 IF ( dz_z .LE. eps ) THEN
626 z_state = conv_state
627 ELSE IF ( dz_z .GT. dz_ub ) THEN
628 z_state = unstable_state
629 dzratmax = 0.0
630 final_dz_z = hugeval
631 ELSE IF ( dzrat .GT. rthresh ) THEN
632 IF ( y_prec_state .NE. extra_y ) THEN
633 incr_prec = .true.
634 ELSE
635 z_state = noprog_state
636 END IF
637 ELSE
638 IF ( dzrat .GT. dzratmax ) dzratmax = dzrat
639 END IF
640 IF ( z_state .GT. working_state ) final_dz_z = dz_z
641 END IF
642
643 IF ( x_state.NE.working_state.AND.
644 $ ( ignore_cwise.OR.z_state.NE.working_state ) )
645 $ GOTO 666
646
647 IF ( incr_prec ) THEN
648 incr_prec = .false.
649 y_prec_state = y_prec_state + 1
650 DO i = 1, n
651 y_tail( i ) = 0.0
652 END DO
653 END IF
654
655 prevnormdx = normdx
656 prev_dz_z = dz_z
657*
658* Update solution.
659*
660 IF ( y_prec_state .LT. extra_y ) THEN
661 CALL caxpy( n, cmplx(1.0), dy, 1, y(1,j), 1 )
662 ELSE
663 CALL cla_wwaddw( n, y(1,j), y_tail, dy )
664 END IF
665
666 END DO
667* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT.
668 666 CONTINUE
669*
670* Set final_* when cnt hits ithresh.
671*
672 IF ( x_state .EQ. working_state ) final_dx_x = dx_x
673 IF ( z_state .EQ. working_state ) final_dz_z = dz_z
674*
675* Compute error bounds.
676*
677 IF ( n_norms .GE. 1 ) THEN
678 err_bnds_norm( j, la_linrx_err_i ) =
679 $ final_dx_x / (1 - dxratmax)
680 END IF
681 IF (n_norms .GE. 2) THEN
682 err_bnds_comp( j, la_linrx_err_i ) =
683 $ final_dz_z / (1 - dzratmax)
684 END IF
685*
686* Compute componentwise relative backward error from formula
687* max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
688* where abs(Z) is the componentwise absolute value of the matrix
689* or vector Z.
690*
691* Compute residual RES = B_s - op(A_s) * Y,
692* op(A) = A, A**T, or A**H depending on TRANS (and type).
693*
694 CALL ccopy( n, b( 1, j ), 1, res, 1 )
695 CALL chemv( uplo, n, cmplx(-1.0), a, lda, y(1,j), 1,
696 $ cmplx(1.0), res, 1 )
697
698 DO i = 1, n
699 ayb( i ) = cabs1( b( i, j ) )
700 END DO
701*
702* Compute abs(op(A_s))*abs(Y) + abs(B_s).
703*
704 CALL cla_heamv( uplo2, n, 1.0,
705 $ a, lda, y(1, j), 1, 1.0, ayb, 1 )
706
707 CALL cla_lin_berr( n, n, 1, res, ayb, berr_out( j ) )
708*
709* End of loop for each RHS.
710*
711 END DO
712*
713 RETURN
714*
715* End of CLA_HERFSX_EXTENDED
716*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
caxpy
subroutine caxpy(n, ca, cx, incx, cy, incy)
CAXPY
Definition caxpy.f:88
ccopy
subroutine ccopy(n, cx, incx, cy, incy)
CCOPY
Definition ccopy.f:81
chemv
subroutine chemv(uplo, n, alpha, a, lda, x, incx, beta, y, incy)
CHEMV
Definition chemv.f:154
chetrs
subroutine chetrs(uplo, n, nrhs, a, lda, ipiv, b, ldb, info)
CHETRS
Definition chetrs.f:118
ilauplo
integer function ilauplo(uplo)
ILAUPLO
Definition ilauplo.f:56
cla_heamv
subroutine cla_heamv(uplo, n, alpha, a, lda, x, incx, beta, y, incy)
CLA_HEAMV computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bou...
Definition cla_heamv.f:176
cla_lin_berr
subroutine cla_lin_berr(n, nz, nrhs, res, ayb, berr)
CLA_LIN_BERR computes a component-wise relative backward error.
Definition cla_lin_berr.f:99
cla_wwaddw
subroutine cla_wwaddw(n, x, y, w)
CLA_WWADDW adds a vector into a doubled-single vector.
Definition cla_wwaddw.f:79
slamch
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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