LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
subroutine dla_syrfsx_extended ( integer  PREC_TYPE,
character  UPLO,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldaf, * )  AF,
integer  LDAF,
integer, dimension( * )  IPIV,
logical  COLEQU,
double precision, dimension( * )  C,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( ldy, * )  Y,
integer  LDY,
double precision, dimension( * )  BERR_OUT,
integer  N_NORMS,
double precision, dimension( nrhs, * )  ERR_BNDS_NORM,
double precision, dimension( nrhs, * )  ERR_BNDS_COMP,
double precision, dimension( * )  RES,
double precision, dimension( * )  AYB,
double precision, dimension( * )  DY,
double precision, dimension( * )  Y_TAIL,
double precision  RCOND,
integer  ITHRESH,
double precision  RTHRESH,
double precision  DZ_UB,
logical  IGNORE_CWISE,
integer  INFO 
)

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

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Purpose:
 DLA_SYRFSX_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 DSYRFSX 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 resonsible 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', '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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDAF,N)
     The block diagonal matrix D and the multipliers used to
     obtain the factor U or L as computed by DSYTRF.
[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 DSYTRF.
[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 DOUBLE PRECISION 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 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]Y
          Y is DOUBLE PRECISION array, dimension
                    (LDY,NRHS)
     On entry, the solution matrix X, as computed by DSYTRS.
     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 DOUBLE PRECISION 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 DLA_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 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) * 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.

     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 DOUBLE PRECISION array, dimension
                    (NRHS, N_ERR_BNDS)
     For each right-hand side, this array contains information about
     various error bounds and condition numbers corresponding to the
     componentwise relative error, which is defined as follows:

     Componentwise relative error in the ith solution vector:
                    abs(XTRUE(j,i) - X(j,i))
             max_j ----------------------
                         abs(X(j,i))

     The array is indexed by the right-hand side i (on which the
     componentwise relative error depends), and the type of error
     information as described below. There currently are up to three
     pieces of information returned for each right-hand side. If
     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
     the first (:,N_ERR_BNDS) entries are returned.

     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
     right-hand side.

     The second index in ERR_BNDS_COMP(:,err) contains the following
     three fields:
     err = 1 "Trust/don't trust" boolean. Trust the answer if the
              reciprocal condition number is less than the threshold
              sqrt(n) * 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.

     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 DOUBLE PRECISION array, dimension (N)
     Workspace to hold the intermediate residual.
[in]AYB
          AYB is DOUBLE PRECISION array, dimension (N)
     Workspace. This can be the same workspace passed for Y_TAIL.
[in]DY
          DY is DOUBLE PRECISION array, dimension (N)
     Workspace to hold the intermediate solution.
[in]Y_TAIL
          Y_TAIL is DOUBLE PRECISION array, dimension (N)
     Workspace to hold the trailing bits of the intermediate solution.
[in]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.
[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 DOUBLE PRECISION
     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 DOUBLE PRECISION
     Determines when to start considering componentwise convergence.
     Componentwise convergence is only considered after each component
     of the solution Y is stable, which we definte 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 DLA_SYRFSX_EXTENDED had an illegal
             value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
September 2012

Definition at line 401 of file dla_syrfsx_extended.f.

401 *
402 * -- LAPACK computational routine (version 3.4.2) --
403 * -- LAPACK is a software package provided by Univ. of Tennessee, --
404 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
405 * September 2012
406 *
407 * .. Scalar Arguments ..
408  INTEGER info, lda, ldaf, ldb, ldy, n, nrhs, prec_type,
409  $ n_norms, ithresh
410  CHARACTER uplo
411  LOGICAL colequ, ignore_cwise
412  DOUBLE PRECISION rthresh, dz_ub
413 * ..
414 * .. Array Arguments ..
415  INTEGER ipiv( * )
416  DOUBLE PRECISION a( lda, * ), af( ldaf, * ), b( ldb, * ),
417  $ y( ldy, * ), res( * ), dy( * ), y_tail( * )
418  DOUBLE PRECISION c( * ), ayb( * ), rcond, berr_out( * ),
419  $ err_bnds_norm( nrhs, * ),
420  $ err_bnds_comp( nrhs, * )
421 * ..
422 *
423 * =====================================================================
424 *
425 * .. Local Scalars ..
426  INTEGER uplo2, cnt, i, j, x_state, z_state
427  DOUBLE PRECISION yk, dyk, ymin, normy, normx, normdx, dxrat,
428  $ dzrat, prevnormdx, prev_dz_z, dxratmax,
429  $ dzratmax, dx_x, dz_z, final_dx_x, final_dz_z,
430  $ eps, hugeval, incr_thresh
431  LOGICAL incr_prec, upper
432 * ..
433 * .. Parameters ..
434  INTEGER unstable_state, working_state, conv_state,
435  $ noprog_state, y_prec_state, base_residual,
436  $ extra_residual, extra_y
437  parameter ( unstable_state = 0, working_state = 1,
438  $ conv_state = 2, noprog_state = 3 )
439  parameter ( base_residual = 0, extra_residual = 1,
440  $ extra_y = 2 )
441  INTEGER final_nrm_err_i, final_cmp_err_i, berr_i
442  INTEGER rcond_i, nrm_rcond_i, nrm_err_i, cmp_rcond_i
443  INTEGER cmp_err_i, piv_growth_i
444  parameter ( final_nrm_err_i = 1, final_cmp_err_i = 2,
445  $ berr_i = 3 )
446  parameter ( rcond_i = 4, nrm_rcond_i = 5, nrm_err_i = 6 )
447  parameter ( cmp_rcond_i = 7, cmp_err_i = 8,
448  $ piv_growth_i = 9 )
449  INTEGER la_linrx_itref_i, la_linrx_ithresh_i,
450  $ la_linrx_cwise_i
451  parameter ( la_linrx_itref_i = 1,
452  $ la_linrx_ithresh_i = 2 )
453  parameter ( la_linrx_cwise_i = 3 )
454  INTEGER la_linrx_trust_i, la_linrx_err_i,
455  $ la_linrx_rcond_i
456  parameter ( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
457  parameter ( la_linrx_rcond_i = 3 )
458 * ..
459 * .. External Functions ..
460  LOGICAL lsame
461  EXTERNAL ilauplo
462  INTEGER ilauplo
463 * ..
464 * .. External Subroutines ..
465  EXTERNAL daxpy, dcopy, dsytrs, dsymv, blas_dsymv_x,
466  $ blas_dsymv2_x, dla_syamv, dla_wwaddw,
467  $ dla_lin_berr
468  DOUBLE PRECISION dlamch
469 * ..
470 * .. Intrinsic Functions ..
471  INTRINSIC abs, max, min
472 * ..
473 * .. Executable Statements ..
474 *
475  info = 0
476  upper = lsame( uplo, 'U' )
477  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
478  info = -2
479  ELSE IF( n.LT.0 ) THEN
480  info = -3
481  ELSE IF( nrhs.LT.0 ) THEN
482  info = -4
483  ELSE IF( lda.LT.max( 1, n ) ) THEN
484  info = -6
485  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
486  info = -8
487  ELSE IF( ldb.LT.max( 1, n ) ) THEN
488  info = -13
489  ELSE IF( ldy.LT.max( 1, n ) ) THEN
490  info = -15
491  END IF
492  IF( info.NE.0 ) THEN
493  CALL xerbla( 'DLA_SYRFSX_EXTENDED', -info )
494  RETURN
495  END IF
496  eps = dlamch( 'Epsilon' )
497  hugeval = dlamch( 'Overflow' )
498 * Force HUGEVAL to Inf
499  hugeval = hugeval * hugeval
500 * Using HUGEVAL may lead to spurious underflows.
501  incr_thresh = dble( n )*eps
502 
503  IF ( lsame( uplo, 'L' ) ) THEN
504  uplo2 = ilauplo( 'L' )
505  ELSE
506  uplo2 = ilauplo( 'U' )
507  ENDIF
508 
509  DO j = 1, nrhs
510  y_prec_state = extra_residual
511  IF ( y_prec_state .EQ. extra_y ) THEN
512  DO i = 1, n
513  y_tail( i ) = 0.0d+0
514  END DO
515  END IF
516 
517  dxrat = 0.0d+0
518  dxratmax = 0.0d+0
519  dzrat = 0.0d+0
520  dzratmax = 0.0d+0
521  final_dx_x = hugeval
522  final_dz_z = hugeval
523  prevnormdx = hugeval
524  prev_dz_z = hugeval
525  dz_z = hugeval
526  dx_x = hugeval
527 
528  x_state = working_state
529  z_state = unstable_state
530  incr_prec = .false.
531 
532  DO cnt = 1, ithresh
533 *
534 * Compute residual RES = B_s - op(A_s) * Y,
535 * op(A) = A, A**T, or A**H depending on TRANS (and type).
536 *
537  CALL dcopy( n, b( 1, j ), 1, res, 1 )
538  IF (y_prec_state .EQ. base_residual) THEN
539  CALL dsymv( uplo, n, -1.0d+0, a, lda, y(1,j), 1,
540  $ 1.0d+0, res, 1 )
541  ELSE IF (y_prec_state .EQ. extra_residual) THEN
542  CALL blas_dsymv_x( uplo2, n, -1.0d+0, a, lda,
543  $ y( 1, j ), 1, 1.0d+0, res, 1, prec_type )
544  ELSE
545  CALL blas_dsymv2_x(uplo2, n, -1.0d+0, a, lda,
546  $ y(1, j), y_tail, 1, 1.0d+0, res, 1, prec_type)
547  END IF
548 
549 ! XXX: RES is no longer needed.
550  CALL dcopy( n, res, 1, dy, 1 )
551  CALL dsytrs( uplo, n, 1, af, ldaf, ipiv, dy, n, info )
552 *
553 * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
554 *
555  normx = 0.0d+0
556  normy = 0.0d+0
557  normdx = 0.0d+0
558  dz_z = 0.0d+0
559  ymin = hugeval
560 
561  DO i = 1, n
562  yk = abs( y( i, j ) )
563  dyk = abs( dy( i ) )
564 
565  IF ( yk .NE. 0.0d+0 ) THEN
566  dz_z = max( dz_z, dyk / yk )
567  ELSE IF ( dyk .NE. 0.0d+0 ) THEN
568  dz_z = hugeval
569  END IF
570 
571  ymin = min( ymin, yk )
572 
573  normy = max( normy, yk )
574 
575  IF ( colequ ) THEN
576  normx = max( normx, yk * c( i ) )
577  normdx = max( normdx, dyk * c( i ) )
578  ELSE
579  normx = normy
580  normdx = max(normdx, dyk)
581  END IF
582  END DO
583 
584  IF ( normx .NE. 0.0d+0 ) THEN
585  dx_x = normdx / normx
586  ELSE IF ( normdx .EQ. 0.0d+0 ) THEN
587  dx_x = 0.0d+0
588  ELSE
589  dx_x = hugeval
590  END IF
591 
592  dxrat = normdx / prevnormdx
593  dzrat = dz_z / prev_dz_z
594 *
595 * Check termination criteria.
596 *
597  IF ( ymin*rcond .LT. incr_thresh*normy
598  $ .AND. y_prec_state .LT. extra_y )
599  $ incr_prec = .true.
600 
601  IF ( x_state .EQ. noprog_state .AND. dxrat .LE. rthresh )
602  $ x_state = working_state
603  IF ( x_state .EQ. working_state ) THEN
604  IF ( dx_x .LE. eps ) THEN
605  x_state = conv_state
606  ELSE IF ( dxrat .GT. rthresh ) THEN
607  IF ( y_prec_state .NE. extra_y ) THEN
608  incr_prec = .true.
609  ELSE
610  x_state = noprog_state
611  END IF
612  ELSE
613  IF ( dxrat .GT. dxratmax ) dxratmax = dxrat
614  END IF
615  IF ( x_state .GT. working_state ) final_dx_x = dx_x
616  END IF
617 
618  IF ( z_state .EQ. unstable_state .AND. dz_z .LE. dz_ub )
619  $ z_state = working_state
620  IF ( z_state .EQ. noprog_state .AND. dzrat .LE. rthresh )
621  $ z_state = working_state
622  IF ( z_state .EQ. working_state ) THEN
623  IF ( dz_z .LE. eps ) THEN
624  z_state = conv_state
625  ELSE IF ( dz_z .GT. dz_ub ) THEN
626  z_state = unstable_state
627  dzratmax = 0.0d+0
628  final_dz_z = hugeval
629  ELSE IF ( dzrat .GT. rthresh ) THEN
630  IF ( y_prec_state .NE. extra_y ) THEN
631  incr_prec = .true.
632  ELSE
633  z_state = noprog_state
634  END IF
635  ELSE
636  IF ( dzrat .GT. dzratmax ) dzratmax = dzrat
637  END IF
638  IF ( z_state .GT. working_state ) final_dz_z = dz_z
639  END IF
640 
641  IF ( x_state.NE.working_state.AND.
642  $ ( ignore_cwise.OR.z_state.NE.working_state ) )
643  $ GOTO 666
644 
645  IF ( incr_prec ) THEN
646  incr_prec = .false.
647  y_prec_state = y_prec_state + 1
648  DO i = 1, n
649  y_tail( i ) = 0.0d+0
650  END DO
651  END IF
652 
653  prevnormdx = normdx
654  prev_dz_z = dz_z
655 *
656 * Update soluton.
657 *
658  IF (y_prec_state .LT. extra_y) THEN
659  CALL daxpy( n, 1.0d+0, dy, 1, y(1,j), 1 )
660  ELSE
661  CALL dla_wwaddw( n, y(1,j), y_tail, dy )
662  END IF
663 
664  END DO
665 * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT.
666  666 CONTINUE
667 *
668 * Set final_* when cnt hits ithresh.
669 *
670  IF ( x_state .EQ. working_state ) final_dx_x = dx_x
671  IF ( z_state .EQ. working_state ) final_dz_z = dz_z
672 *
673 * Compute error bounds.
674 *
675  IF ( n_norms .GE. 1 ) THEN
676  err_bnds_norm( j, la_linrx_err_i ) =
677  $ final_dx_x / (1 - dxratmax)
678  END IF
679  IF ( n_norms .GE. 2 ) THEN
680  err_bnds_comp( j, la_linrx_err_i ) =
681  $ final_dz_z / (1 - dzratmax)
682  END IF
683 *
684 * Compute componentwise relative backward error from formula
685 * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
686 * where abs(Z) is the componentwise absolute value of the matrix
687 * or vector Z.
688 *
689 * Compute residual RES = B_s - op(A_s) * Y,
690 * op(A) = A, A**T, or A**H depending on TRANS (and type).
691  CALL dcopy( n, b( 1, j ), 1, res, 1 )
692  CALL dsymv( uplo, n, -1.0d+0, a, lda, y(1,j), 1, 1.0d+0, res,
693  $ 1 )
694 
695  DO i = 1, n
696  ayb( i ) = abs( b( i, j ) )
697  END DO
698 *
699 * Compute abs(op(A_s))*abs(Y) + abs(B_s).
700 *
701  CALL dla_syamv( uplo2, n, 1.0d+0,
702  $ a, lda, y(1, j), 1, 1.0d+0, ayb, 1 )
703 
704  CALL dla_lin_berr( n, n, 1, res, ayb, berr_out( j ) )
705 *
706 * End of loop for each RHS.
707 *
708  END DO
709 *
710  RETURN
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:53
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine dla_lin_berr(N, NZ, NRHS, RES, AYB, BERR)
DLA_LIN_BERR computes a component-wise relative backward error.
Definition: dla_lin_berr.f:103
subroutine daxpy(N, DA, DX, INCX, DY, INCY)
DAXPY
Definition: daxpy.f:54
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
integer function ilauplo(UPLO)
ILAUPLO
Definition: ilauplo.f:60
subroutine dsytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DSYTRS
Definition: dsytrs.f:122
subroutine dla_wwaddw(N, X, Y, W)
DLA_WWADDW adds a vector into a doubled-single vector.
Definition: dla_wwaddw.f:83
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine dla_syamv(UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bou...
Definition: dla_syamv.f:179
subroutine dsymv(UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DSYMV
Definition: dsymv.f:154

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