LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ dla_porfsx_extended()

subroutine dla_porfsx_extended ( integer  PREC_TYPE,
character  UPLO,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldaf, * )  AF,
integer  LDAF,
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_PORFSX_EXTENDED improves the computed solution to a system of linear equations for symmetric or Hermitian positive-definite matrices by performing extra-precise iterative refinement and provides error bounds and backward error estimates for the solution.

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Purpose:
 DLA_PORFSX_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 DPORFSX 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' 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 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 triangular factor U or L from the Cholesky factorization
     A = U**T*U or A = L*L**T, as computed by DPOTRF.
[in]LDAF
          LDAF is INTEGER
     The leading dimension of the array AF.  LDAF >= max(1,N).
[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 DPOTRS.
     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 < 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 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 DPOTRS had an illegal
             value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 380 of file dla_porfsx_extended.f.

387 *
388 * -- LAPACK computational routine --
389 * -- LAPACK is a software package provided by Univ. of Tennessee, --
390 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
391 *
392 * .. Scalar Arguments ..
393  INTEGER INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
394  $ N_NORMS, ITHRESH
395  CHARACTER UPLO
396  LOGICAL COLEQU, IGNORE_CWISE
397  DOUBLE PRECISION RTHRESH, DZ_UB
398 * ..
399 * .. Array Arguments ..
400  DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
401  $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
402  DOUBLE PRECISION C( * ), AYB(*), RCOND, BERR_OUT( * ),
403  $ ERR_BNDS_NORM( NRHS, * ),
404  $ ERR_BNDS_COMP( NRHS, * )
405 * ..
406 *
407 * =====================================================================
408 *
409 * .. Local Scalars ..
410  INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE
411  DOUBLE PRECISION YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT,
412  $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX,
413  $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z,
414  $ EPS, HUGEVAL, INCR_THRESH
415  LOGICAL INCR_PREC
416 * ..
417 * .. Parameters ..
418  INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE,
419  $ NOPROG_STATE, Y_PREC_STATE, BASE_RESIDUAL,
420  $ EXTRA_RESIDUAL, EXTRA_Y
421  parameter( unstable_state = 0, working_state = 1,
422  $ conv_state = 2, noprog_state = 3 )
423  parameter( base_residual = 0, extra_residual = 1,
424  $ extra_y = 2 )
425  INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
426  INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
427  INTEGER CMP_ERR_I, PIV_GROWTH_I
428  parameter( final_nrm_err_i = 1, final_cmp_err_i = 2,
429  $ berr_i = 3 )
430  parameter( rcond_i = 4, nrm_rcond_i = 5, nrm_err_i = 6 )
431  parameter( cmp_rcond_i = 7, cmp_err_i = 8,
432  $ piv_growth_i = 9 )
433  INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
434  $ LA_LINRX_CWISE_I
435  parameter( la_linrx_itref_i = 1,
436  $ la_linrx_ithresh_i = 2 )
437  parameter( la_linrx_cwise_i = 3 )
438  INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
439  $ LA_LINRX_RCOND_I
440  parameter( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
441  parameter( la_linrx_rcond_i = 3 )
442 * ..
443 * .. External Functions ..
444  LOGICAL LSAME
445  EXTERNAL ilauplo
446  INTEGER ILAUPLO
447 * ..
448 * .. External Subroutines ..
449  EXTERNAL daxpy, dcopy, dpotrs, dsymv, blas_dsymv_x,
450  $ blas_dsymv2_x, dla_syamv, dla_wwaddw,
451  $ dla_lin_berr
452  DOUBLE PRECISION DLAMCH
453 * ..
454 * .. Intrinsic Functions ..
455  INTRINSIC abs, max, min
456 * ..
457 * .. Executable Statements ..
458 *
459  IF (info.NE.0) RETURN
460  eps = dlamch( 'Epsilon' )
461  hugeval = dlamch( 'Overflow' )
462 * Force HUGEVAL to Inf
463  hugeval = hugeval * hugeval
464 * Using HUGEVAL may lead to spurious underflows.
465  incr_thresh = dble( n ) * eps
466 
467  IF ( lsame( uplo, 'L' ) ) THEN
468  uplo2 = ilauplo( 'L' )
469  ELSE
470  uplo2 = ilauplo( 'U' )
471  ENDIF
472 
473  DO j = 1, nrhs
474  y_prec_state = extra_residual
475  IF ( y_prec_state .EQ. extra_y ) THEN
476  DO i = 1, n
477  y_tail( i ) = 0.0d+0
478  END DO
479  END IF
480 
481  dxrat = 0.0d+0
482  dxratmax = 0.0d+0
483  dzrat = 0.0d+0
484  dzratmax = 0.0d+0
485  final_dx_x = hugeval
486  final_dz_z = hugeval
487  prevnormdx = hugeval
488  prev_dz_z = hugeval
489  dz_z = hugeval
490  dx_x = hugeval
491 
492  x_state = working_state
493  z_state = unstable_state
494  incr_prec = .false.
495 
496  DO cnt = 1, ithresh
497 *
498 * Compute residual RES = B_s - op(A_s) * Y,
499 * op(A) = A, A**T, or A**H depending on TRANS (and type).
500 *
501  CALL dcopy( n, b( 1, j ), 1, res, 1 )
502  IF ( y_prec_state .EQ. base_residual ) THEN
503  CALL dsymv( uplo, n, -1.0d+0, a, lda, y(1,j), 1,
504  $ 1.0d+0, res, 1 )
505  ELSE IF ( y_prec_state .EQ. extra_residual ) THEN
506  CALL blas_dsymv_x( uplo2, n, -1.0d+0, a, lda,
507  $ y( 1, j ), 1, 1.0d+0, res, 1, prec_type )
508  ELSE
509  CALL blas_dsymv2_x(uplo2, n, -1.0d+0, a, lda,
510  $ y(1, j), y_tail, 1, 1.0d+0, res, 1, prec_type)
511  END IF
512 
513 ! XXX: RES is no longer needed.
514  CALL dcopy( n, res, 1, dy, 1 )
515  CALL dpotrs( uplo, n, 1, af, ldaf, dy, n, info )
516 *
517 * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
518 *
519  normx = 0.0d+0
520  normy = 0.0d+0
521  normdx = 0.0d+0
522  dz_z = 0.0d+0
523  ymin = hugeval
524 
525  DO i = 1, n
526  yk = abs( y( i, j ) )
527  dyk = abs( dy( i ) )
528 
529  IF ( yk .NE. 0.0d+0 ) THEN
530  dz_z = max( dz_z, dyk / yk )
531  ELSE IF ( dyk .NE. 0.0d+0 ) THEN
532  dz_z = hugeval
533  END IF
534 
535  ymin = min( ymin, yk )
536 
537  normy = max( normy, yk )
538 
539  IF ( colequ ) THEN
540  normx = max( normx, yk * c( i ) )
541  normdx = max( normdx, dyk * c( i ) )
542  ELSE
543  normx = normy
544  normdx = max( normdx, dyk )
545  END IF
546  END DO
547 
548  IF ( normx .NE. 0.0d+0 ) THEN
549  dx_x = normdx / normx
550  ELSE IF ( normdx .EQ. 0.0d+0 ) THEN
551  dx_x = 0.0d+0
552  ELSE
553  dx_x = hugeval
554  END IF
555 
556  dxrat = normdx / prevnormdx
557  dzrat = dz_z / prev_dz_z
558 *
559 * Check termination criteria.
560 *
561  IF ( ymin*rcond .LT. incr_thresh*normy
562  $ .AND. y_prec_state .LT. extra_y )
563  $ incr_prec = .true.
564 
565  IF ( x_state .EQ. noprog_state .AND. dxrat .LE. rthresh )
566  $ x_state = working_state
567  IF ( x_state .EQ. working_state ) THEN
568  IF ( dx_x .LE. eps ) THEN
569  x_state = conv_state
570  ELSE IF ( dxrat .GT. rthresh ) THEN
571  IF ( y_prec_state .NE. extra_y ) THEN
572  incr_prec = .true.
573  ELSE
574  x_state = noprog_state
575  END IF
576  ELSE
577  IF ( dxrat .GT. dxratmax ) dxratmax = dxrat
578  END IF
579  IF ( x_state .GT. working_state ) final_dx_x = dx_x
580  END IF
581 
582  IF ( z_state .EQ. unstable_state .AND. dz_z .LE. dz_ub )
583  $ z_state = working_state
584  IF ( z_state .EQ. noprog_state .AND. dzrat .LE. rthresh )
585  $ z_state = working_state
586  IF ( z_state .EQ. working_state ) THEN
587  IF ( dz_z .LE. eps ) THEN
588  z_state = conv_state
589  ELSE IF ( dz_z .GT. dz_ub ) THEN
590  z_state = unstable_state
591  dzratmax = 0.0d+0
592  final_dz_z = hugeval
593  ELSE IF ( dzrat .GT. rthresh ) THEN
594  IF ( y_prec_state .NE. extra_y ) THEN
595  incr_prec = .true.
596  ELSE
597  z_state = noprog_state
598  END IF
599  ELSE
600  IF ( dzrat .GT. dzratmax ) dzratmax = dzrat
601  END IF
602  IF ( z_state .GT. working_state ) final_dz_z = dz_z
603  END IF
604 
605  IF ( x_state.NE.working_state.AND.
606  $ ( ignore_cwise.OR.z_state.NE.working_state ) )
607  $ GOTO 666
608 
609  IF ( incr_prec ) THEN
610  incr_prec = .false.
611  y_prec_state = y_prec_state + 1
612  DO i = 1, n
613  y_tail( i ) = 0.0d+0
614  END DO
615  END IF
616 
617  prevnormdx = normdx
618  prev_dz_z = dz_z
619 *
620 * Update soluton.
621 *
622  IF (y_prec_state .LT. extra_y) THEN
623  CALL daxpy( n, 1.0d+0, dy, 1, y(1,j), 1 )
624  ELSE
625  CALL dla_wwaddw( n, y( 1, j ), y_tail, dy )
626  END IF
627 
628  END DO
629 * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT.
630  666 CONTINUE
631 *
632 * Set final_* when cnt hits ithresh.
633 *
634  IF ( x_state .EQ. working_state ) final_dx_x = dx_x
635  IF ( z_state .EQ. working_state ) final_dz_z = dz_z
636 *
637 * Compute error bounds.
638 *
639  IF ( n_norms .GE. 1 ) THEN
640  err_bnds_norm( j, la_linrx_err_i ) =
641  $ final_dx_x / (1 - dxratmax)
642  END IF
643  IF ( n_norms .GE. 2 ) THEN
644  err_bnds_comp( j, la_linrx_err_i ) =
645  $ final_dz_z / (1 - dzratmax)
646  END IF
647 *
648 * Compute componentwise relative backward error from formula
649 * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
650 * where abs(Z) is the componentwise absolute value of the matrix
651 * or vector Z.
652 *
653 * Compute residual RES = B_s - op(A_s) * Y,
654 * op(A) = A, A**T, or A**H depending on TRANS (and type).
655 *
656  CALL dcopy( n, b( 1, j ), 1, res, 1 )
657  CALL dsymv( uplo, n, -1.0d+0, a, lda, y(1,j), 1, 1.0d+0, res,
658  $ 1 )
659 
660  DO i = 1, n
661  ayb( i ) = abs( b( i, j ) )
662  END DO
663 *
664 * Compute abs(op(A_s))*abs(Y) + abs(B_s).
665 *
666  CALL dla_syamv( uplo2, n, 1.0d+0,
667  $ a, lda, y(1, j), 1, 1.0d+0, ayb, 1 )
668 
669  CALL dla_lin_berr( n, n, 1, res, ayb, berr_out( j ) )
670 *
671 * End of loop for each RHS.
672 *
673  END DO
674 *
675  RETURN
676 *
677 * End of DLA_PORFSX_EXTENDED
678 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
integer function ilauplo(UPLO)
ILAUPLO
Definition: ilauplo.f:58
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:82
subroutine daxpy(N, DA, DX, INCX, DY, INCY)
DAXPY
Definition: daxpy.f:89
subroutine dsymv(UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DSYMV
Definition: dsymv.f:152
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:101
subroutine dla_wwaddw(N, X, Y, W)
DLA_WWADDW adds a vector into a doubled-single vector.
Definition: dla_wwaddw.f:81
subroutine dpotrs(UPLO, N, NRHS, A, LDA, B, LDB, INFO)
DPOTRS
Definition: dpotrs.f:110
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:177
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