LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ cporfsx()

 subroutine cporfsx ( character uplo, character equed, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, real, dimension( * ) s, 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 )

CPORFSX

Purpose:
```    CPORFSX improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian positive
definite, 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 and S
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] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.``` [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 = 'N': No equilibration = 'Y': Both row and column equilibration, i.e., A has been replaced by diag(S) * A * diag(S). The right hand side B has been changed accordingly.``` [in] N ``` N is INTEGER 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 matrices B and X. NRHS >= 0.``` [in] A ``` A is COMPLEX array, dimension (LDA,N) The Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.``` [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 triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by CPOTRF.``` [in] LDAF ``` LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N).``` [in,out] S ``` S is REAL array, dimension (N) The scale factors for A. If EQUED = 'Y', A is multiplied on the left and right by diag(S). S is an input argument if FACT = 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED = 'Y', each element of S must be positive. If S is output, each element of S is a power of the radix. If S is input, each element of S 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 < 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 <= 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 < 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.```

Definition at line 389 of file cporfsx.f.

393*
394* -- LAPACK computational routine --
395* -- LAPACK is a software package provided by Univ. of Tennessee, --
396* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
397*
398* .. Scalar Arguments ..
399 CHARACTER UPLO, EQUED
400 INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
401 \$ N_ERR_BNDS
402 REAL RCOND
403* ..
404* .. Array Arguments ..
405 COMPLEX A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
406 \$ X( LDX, * ), WORK( * )
407 REAL RWORK( * ), S( * ), PARAMS(*), BERR( * ),
408 \$ ERR_BNDS_NORM( NRHS, * ),
409 \$ ERR_BNDS_COMP( NRHS, * )
410* ..
411*
412* ==================================================================
413*
414* .. Parameters ..
415 REAL ZERO, ONE
416 parameter( zero = 0.0e+0, one = 1.0e+0 )
417 REAL ITREF_DEFAULT, ITHRESH_DEFAULT,
418 \$ COMPONENTWISE_DEFAULT
419 REAL RTHRESH_DEFAULT, DZTHRESH_DEFAULT
420 parameter( itref_default = 1.0 )
421 parameter( ithresh_default = 10.0 )
422 parameter( componentwise_default = 1.0 )
423 parameter( rthresh_default = 0.5 )
424 parameter( dzthresh_default = 0.25 )
425 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
426 \$ LA_LINRX_CWISE_I
427 parameter( la_linrx_itref_i = 1,
428 \$ la_linrx_ithresh_i = 2 )
429 parameter( la_linrx_cwise_i = 3 )
430 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
431 \$ LA_LINRX_RCOND_I
432 parameter( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
433 parameter( la_linrx_rcond_i = 3 )
434* ..
435* .. Local Scalars ..
436 CHARACTER(1) NORM
437 LOGICAL RCEQU
438 INTEGER J, PREC_TYPE, REF_TYPE
439 INTEGER N_NORMS
440 REAL ANORM, RCOND_TMP
441 REAL ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
442 LOGICAL IGNORE_CWISE
443 INTEGER ITHRESH
444 REAL RTHRESH, UNSTABLE_THRESH
445* ..
446* .. External Subroutines ..
448* ..
449* .. Intrinsic Functions ..
450 INTRINSIC max, sqrt, transfer
451* ..
452* .. External Functions ..
453 EXTERNAL lsame, ilaprec
455 REAL SLAMCH, CLANHE, CLA_PORCOND_X, CLA_PORCOND_C
456 LOGICAL LSAME
457 INTEGER ILAPREC
458* ..
459* .. Executable Statements ..
460*
461* Check the input parameters.
462*
463 info = 0
464 ref_type = int( itref_default )
465 IF ( nparams .GE. la_linrx_itref_i ) THEN
466 IF ( params( la_linrx_itref_i ) .LT. 0.0 ) THEN
467 params( la_linrx_itref_i ) = itref_default
468 ELSE
469 ref_type = params( la_linrx_itref_i )
470 END IF
471 END IF
472*
473* Set default parameters.
474*
475 illrcond_thresh = real( n ) * slamch( 'Epsilon' )
476 ithresh = int( ithresh_default )
477 rthresh = rthresh_default
478 unstable_thresh = dzthresh_default
479 ignore_cwise = componentwise_default .EQ. 0.0
480*
481 IF ( nparams.GE.la_linrx_ithresh_i ) THEN
482 IF ( params(la_linrx_ithresh_i ).LT.0.0 ) THEN
483 params( la_linrx_ithresh_i ) = ithresh
484 ELSE
485 ithresh = int( params( la_linrx_ithresh_i ) )
486 END IF
487 END IF
488 IF ( nparams.GE.la_linrx_cwise_i ) THEN
489 IF ( params(la_linrx_cwise_i ).LT.0.0 ) THEN
490 IF ( ignore_cwise ) THEN
491 params( la_linrx_cwise_i ) = 0.0
492 ELSE
493 params( la_linrx_cwise_i ) = 1.0
494 END IF
495 ELSE
496 ignore_cwise = params( la_linrx_cwise_i ) .EQ. 0.0
497 END IF
498 END IF
499 IF ( ref_type .EQ. 0 .OR. n_err_bnds .EQ. 0 ) THEN
500 n_norms = 0
501 ELSE IF ( ignore_cwise ) THEN
502 n_norms = 1
503 ELSE
504 n_norms = 2
505 END IF
506*
507 rcequ = lsame( equed, 'Y' )
508*
509* Test input parameters.
510*
511 IF (.NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
512 info = -1
513 ELSE IF( .NOT.rcequ .AND. .NOT.lsame( equed, 'N' ) ) THEN
514 info = -2
515 ELSE IF( n.LT.0 ) THEN
516 info = -3
517 ELSE IF( nrhs.LT.0 ) THEN
518 info = -4
519 ELSE IF( lda.LT.max( 1, n ) ) THEN
520 info = -6
521 ELSE IF( ldaf.LT.max( 1, n ) ) THEN
522 info = -8
523 ELSE IF( ldb.LT.max( 1, n ) ) THEN
524 info = -11
525 ELSE IF( ldx.LT.max( 1, n ) ) THEN
526 info = -13
527 END IF
528 IF( info.NE.0 ) THEN
529 CALL xerbla( 'CPORFSX', -info )
530 RETURN
531 END IF
532*
533* Quick return if possible.
534*
535 IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
536 rcond = 1.0
537 DO j = 1, nrhs
538 berr( j ) = 0.0
539 IF ( n_err_bnds .GE. 1 ) THEN
540 err_bnds_norm( j, la_linrx_trust_i ) = 1.0
541 err_bnds_comp( j, la_linrx_trust_i ) = 1.0
542 END IF
543 IF ( n_err_bnds .GE. 2 ) THEN
544 err_bnds_norm( j, la_linrx_err_i ) = 0.0
545 err_bnds_comp( j, la_linrx_err_i ) = 0.0
546 END IF
547 IF ( n_err_bnds .GE. 3 ) THEN
548 err_bnds_norm( j, la_linrx_rcond_i ) = 1.0
549 err_bnds_comp( j, la_linrx_rcond_i ) = 1.0
550 END IF
551 END DO
552 RETURN
553 END IF
554*
555* Default to failure.
556*
557 rcond = 0.0
558 DO j = 1, nrhs
559 berr( j ) = 1.0
560 IF ( n_err_bnds .GE. 1 ) THEN
561 err_bnds_norm( j, la_linrx_trust_i ) = 1.0
562 err_bnds_comp( j, la_linrx_trust_i ) = 1.0
563 END IF
564 IF ( n_err_bnds .GE. 2 ) THEN
565 err_bnds_norm( j, la_linrx_err_i ) = 1.0
566 err_bnds_comp( j, la_linrx_err_i ) = 1.0
567 END IF
568 IF ( n_err_bnds .GE. 3 ) THEN
569 err_bnds_norm( j, la_linrx_rcond_i ) = 0.0
570 err_bnds_comp( j, la_linrx_rcond_i ) = 0.0
571 END IF
572 END DO
573*
574* Compute the norm of A and the reciprocal of the condition
575* number of A.
576*
577 norm = 'I'
578 anorm = clanhe( norm, uplo, n, a, lda, rwork )
579 CALL cpocon( uplo, n, af, ldaf, anorm, rcond, work, rwork,
580 \$ info )
581*
582* Perform refinement on each right-hand side
583*
584 IF ( ref_type .NE. 0 ) THEN
585
586 prec_type = ilaprec( 'D' )
587
588 CALL cla_porfsx_extended( prec_type, uplo, n,
589 \$ nrhs, a, lda, af, ldaf, rcequ, s, b,
590 \$ ldb, x, ldx, berr, n_norms, err_bnds_norm, err_bnds_comp,
591 \$ work, rwork, work(n+1),
592 \$ transfer(rwork(1:2*n), (/ (zero, zero) /), n), rcond,
593 \$ ithresh, rthresh, unstable_thresh, ignore_cwise,
594 \$ info )
595 END IF
596
597 err_lbnd = max( 10.0, sqrt( real( n ) ) ) * slamch( 'Epsilon' )
598 IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 1 ) THEN
599*
600* Compute scaled normwise condition number cond(A*C).
601*
602 IF ( rcequ ) THEN
603 rcond_tmp = cla_porcond_c( uplo, n, a, lda, af, ldaf,
604 \$ s, .true., info, work, rwork )
605 ELSE
606 rcond_tmp = cla_porcond_c( uplo, n, a, lda, af, ldaf,
607 \$ s, .false., info, work, rwork )
608 END IF
609 DO j = 1, nrhs
610*
611* Cap the error at 1.0.
612*
613 IF ( n_err_bnds .GE. la_linrx_err_i
614 \$ .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0 )
615 \$ err_bnds_norm( j, la_linrx_err_i ) = 1.0
616*
617* Threshold the error (see LAWN).
618*
619 IF ( rcond_tmp .LT. illrcond_thresh ) THEN
620 err_bnds_norm( j, la_linrx_err_i ) = 1.0
621 err_bnds_norm( j, la_linrx_trust_i ) = 0.0
622 IF ( info .LE. n ) info = n + j
623 ELSE IF ( err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd )
624 \$ THEN
625 err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
626 err_bnds_norm( j, la_linrx_trust_i ) = 1.0
627 END IF
628*
629* Save the condition number.
630*
631 IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
632 err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
633 END IF
634
635 END DO
636 END IF
637
638 IF (n_err_bnds .GE. 1 .AND. n_norms .GE. 2) THEN
639*
640* Compute componentwise condition number cond(A*diag(Y(:,J))) for
641* each right-hand side using the current solution as an estimate of
642* the true solution. If the componentwise error estimate is too
643* large, then the solution is a lousy estimate of truth and the
644* estimated RCOND may be too optimistic. To avoid misleading users,
645* the inverse condition number is set to 0.0 when the estimated
646* cwise error is at least CWISE_WRONG.
647*
648 cwise_wrong = sqrt( slamch( 'Epsilon' ) )
649 DO j = 1, nrhs
650 IF (err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
651 \$ THEN
652 rcond_tmp = cla_porcond_x( uplo, n, a, lda, af, ldaf,
653 \$ x(1,j), info, work, rwork )
654 ELSE
655 rcond_tmp = 0.0
656 END IF
657*
658* Cap the error at 1.0.
659*
660 IF ( n_err_bnds .GE. la_linrx_err_i
661 \$ .AND. err_bnds_comp( j, la_linrx_err_i ) .GT. 1.0 )
662 \$ err_bnds_comp( j, la_linrx_err_i ) = 1.0
663*
664* Threshold the error (see LAWN).
665*
666 IF (rcond_tmp .LT. illrcond_thresh) THEN
667 err_bnds_comp( j, la_linrx_err_i ) = 1.0
668 err_bnds_comp( j, la_linrx_trust_i ) = 0.0
669 IF ( params( la_linrx_cwise_i ) .EQ. 1.0
670 \$ .AND. info.LT.n + j ) info = n + j
671 ELSE IF ( err_bnds_comp( j, la_linrx_err_i )
672 \$ .LT. err_lbnd ) THEN
673 err_bnds_comp( j, la_linrx_err_i ) = err_lbnd
674 err_bnds_comp( j, la_linrx_trust_i ) = 1.0
675 END IF
676*
677* Save the condition number.
678*
679 IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
680 err_bnds_comp( j, la_linrx_rcond_i ) = rcond_tmp
681 END IF
682
683 END DO
684 END IF
685*
686 RETURN
687*
688* End of CPORFSX
689*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
integer function ilaprec(prec)
ILAPREC
Definition ilaprec.f:58
real function cla_porcond_x(uplo, n, a, lda, af, ldaf, x, info, work, rwork)
CLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-def...
real function cla_porcond_c(uplo, n, a, lda, af, ldaf, c, capply, info, work, rwork)
CLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positiv...
subroutine cla_porfsx_extended(prec_type, uplo, n, nrhs, a, lda, af, ldaf, 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_PORFSX_EXTENDED improves the computed solution to a system of linear equations for symmetric or H...
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
real function clanhe(norm, uplo, n, a, lda, work)
CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition clanhe.f:124
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine cpocon(uplo, n, a, lda, anorm, rcond, work, rwork, info)
CPOCON
Definition cpocon.f:121
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