3 * =========== DOCUMENTATION ===========
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
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21 * SUBROUTINE SSYRFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
22 * S, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
23 * ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
26 * .. Scalar Arguments ..
27 * CHARACTER UPLO, EQUED
28 * INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
32 * .. Array Arguments ..
33 * INTEGER IPIV( * ), IWORK( * )
34 * REAL A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
35 * $ X( LDX, * ), WORK( * )
36 * REAL S( * ), PARAMS( * ), BERR( * ),
37 * $ ERR_BNDS_NORM( NRHS, * ),
38 * $ ERR_BNDS_COMP( NRHS, * )
47 *> SSYRFSX improves the computed solution to a system of linear
48 *> equations when the coefficient matrix is symmetric indefinite, and
49 *> provides error bounds and backward error estimates for the
50 *> solution. In addition to normwise error bound, the code provides
51 *> maximum componentwise error bound if possible. See comments for
52 *> ERR_BNDS_NORM and ERR_BNDS_COMP for details of the error bounds.
54 *> The original system of linear equations may have been equilibrated
55 *> before calling this routine, as described by arguments EQUED and S
56 *> below. In this case, the solution and error bounds returned are
57 *> for the original unequilibrated system.
64 *> Some optional parameters are bundled in the PARAMS array. These
65 *> settings determine how refinement is performed, but often the
66 *> defaults are acceptable. If the defaults are acceptable, users
67 *> can pass NPARAMS = 0 which prevents the source code from accessing
68 *> the PARAMS argument.
73 *> UPLO is CHARACTER*1
74 *> = 'U': Upper triangle of A is stored;
75 *> = 'L': Lower triangle of A is stored.
80 *> EQUED is CHARACTER*1
81 *> Specifies the form of equilibration that was done to A
82 *> before calling this routine. This is needed to compute
83 *> the solution and error bounds correctly.
84 *> = 'N': No equilibration
85 *> = 'Y': Both row and column equilibration, i.e., A has been
86 *> replaced by diag(S) * A * diag(S).
87 *> The right hand side B has been changed accordingly.
93 *> The order of the matrix A. N >= 0.
99 *> The number of right hand sides, i.e., the number of columns
100 *> of the matrices B and X. NRHS >= 0.
105 *> A is REAL array, dimension (LDA,N)
106 *> The symmetric matrix A. If UPLO = 'U', the leading N-by-N
107 *> upper triangular part of A contains the upper triangular
108 *> part of the matrix A, and the strictly lower triangular
109 *> part of A is not referenced. If UPLO = 'L', the leading
110 *> N-by-N lower triangular part of A contains the lower
111 *> triangular part of the matrix A, and the strictly upper
112 *> triangular part of A is not referenced.
118 *> The leading dimension of the array A. LDA >= max(1,N).
123 *> AF is REAL array, dimension (LDAF,N)
124 *> The factored form of the matrix A. AF contains the block
125 *> diagonal matrix D and the multipliers used to obtain the
126 *> factor U or L from the factorization A = U*D*U**T or A =
127 *> L*D*L**T as computed by SSYTRF.
133 *> The leading dimension of the array AF. LDAF >= max(1,N).
138 *> IPIV is INTEGER array, dimension (N)
139 *> Details of the interchanges and the block structure of D
140 *> as determined by SSYTRF.
145 *> S is REAL array, dimension (N)
146 *> The scale factors for A. If EQUED = 'Y', A is multiplied on
147 *> the left and right by diag(S). S is an input argument if FACT =
148 *> 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED
149 *> = 'Y', each element of S must be positive. If S is output, each
150 *> element of S is a power of the radix. If S is input, each element
151 *> of S should be a power of the radix to ensure a reliable solution
152 *> and error estimates. Scaling by powers of the radix does not cause
153 *> rounding errors unless the result underflows or overflows.
154 *> Rounding errors during scaling lead to refining with a matrix that
155 *> is not equivalent to the input matrix, producing error estimates
156 *> that may not be reliable.
161 *> B is REAL array, dimension (LDB,NRHS)
162 *> The right hand side matrix B.
168 *> The leading dimension of the array B. LDB >= max(1,N).
173 *> X is REAL array, dimension (LDX,NRHS)
174 *> On entry, the solution matrix X, as computed by SGETRS.
175 *> On exit, the improved solution matrix X.
181 *> The leading dimension of the array X. LDX >= max(1,N).
187 *> Reciprocal scaled condition number. This is an estimate of the
188 *> reciprocal Skeel condition number of the matrix A after
189 *> equilibration (if done). If this is less than the machine
190 *> precision (in particular, if it is zero), the matrix is singular
191 *> to working precision. Note that the error may still be small even
192 *> if this number is very small and the matrix appears ill-
198 *> BERR is REAL array, dimension (NRHS)
199 *> Componentwise relative backward error. This is the
200 *> componentwise relative backward error of each solution vector X(j)
201 *> (i.e., the smallest relative change in any element of A or B that
202 *> makes X(j) an exact solution).
205 *> \param[in] N_ERR_BNDS
207 *> N_ERR_BNDS is INTEGER
208 *> Number of error bounds to return for each right hand side
209 *> and each type (normwise or componentwise). See ERR_BNDS_NORM and
210 *> ERR_BNDS_COMP below.
213 *> \param[out] ERR_BNDS_NORM
215 *> ERR_BNDS_NORM is REAL array, dimension (NRHS, N_ERR_BNDS)
216 *> For each right-hand side, this array contains information about
217 *> various error bounds and condition numbers corresponding to the
218 *> normwise relative error, which is defined as follows:
220 *> Normwise relative error in the ith solution vector:
221 *> max_j (abs(XTRUE(j,i) - X(j,i)))
222 *> ------------------------------
225 *> The array is indexed by the type of error information as described
226 *> below. There currently are up to three pieces of information
229 *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
232 *> The second index in ERR_BNDS_NORM(:,err) contains the following
234 *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
235 *> reciprocal condition number is less than the threshold
236 *> sqrt(n) * slamch('Epsilon').
238 *> err = 2 "Guaranteed" error bound: The estimated forward error,
239 *> almost certainly within a factor of 10 of the true error
240 *> so long as the next entry is greater than the threshold
241 *> sqrt(n) * slamch('Epsilon'). This error bound should only
242 *> be trusted if the previous boolean is true.
244 *> err = 3 Reciprocal condition number: Estimated normwise
245 *> reciprocal condition number. Compared with the threshold
246 *> sqrt(n) * slamch('Epsilon') to determine if the error
247 *> estimate is "guaranteed". These reciprocal condition
248 *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
249 *> appropriately scaled matrix Z.
250 *> Let Z = S*A, where S scales each row by a power of the
251 *> radix so all absolute row sums of Z are approximately 1.
253 *> See Lapack Working Note 165 for further details and extra
257 *> \param[out] ERR_BNDS_COMP
259 *> ERR_BNDS_COMP is REAL array, dimension (NRHS, N_ERR_BNDS)
260 *> For each right-hand side, this array contains information about
261 *> various error bounds and condition numbers corresponding to the
262 *> componentwise relative error, which is defined as follows:
264 *> Componentwise relative error in the ith solution vector:
265 *> abs(XTRUE(j,i) - X(j,i))
266 *> max_j ----------------------
269 *> The array is indexed by the right-hand side i (on which the
270 *> componentwise relative error depends), and the type of error
271 *> information as described below. There currently are up to three
272 *> pieces of information returned for each right-hand side. If
273 *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
274 *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
275 *> the first (:,N_ERR_BNDS) entries are returned.
277 *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
280 *> The second index in ERR_BNDS_COMP(:,err) contains the following
282 *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
283 *> reciprocal condition number is less than the threshold
284 *> sqrt(n) * slamch('Epsilon').
286 *> err = 2 "Guaranteed" error bound: The estimated forward error,
287 *> almost certainly within a factor of 10 of the true error
288 *> so long as the next entry is greater than the threshold
289 *> sqrt(n) * slamch('Epsilon'). This error bound should only
290 *> be trusted if the previous boolean is true.
292 *> err = 3 Reciprocal condition number: Estimated componentwise
293 *> reciprocal condition number. Compared with the threshold
294 *> sqrt(n) * slamch('Epsilon') to determine if the error
295 *> estimate is "guaranteed". These reciprocal condition
296 *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
297 *> appropriately scaled matrix Z.
298 *> Let Z = S*(A*diag(x)), where x is the solution for the
299 *> current right-hand side and S scales each row of
300 *> A*diag(x) by a power of the radix so all absolute row
301 *> sums of Z are approximately 1.
303 *> See Lapack Working Note 165 for further details and extra
307 *> \param[in] NPARAMS
309 *> NPARAMS is INTEGER
310 *> Specifies the number of parameters set in PARAMS. If .LE. 0, the
311 *> PARAMS array is never referenced and default values are used.
314 *> \param[in,out] PARAMS
316 *> PARAMS is REAL array, dimension NPARAMS
317 *> Specifies algorithm parameters. If an entry is .LT. 0.0, then
318 *> that entry will be filled with default value used for that
319 *> parameter. Only positions up to NPARAMS are accessed; defaults
320 *> are used for higher-numbered parameters.
322 *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
323 *> refinement or not.
325 *> = 0.0 : No refinement is performed, and no error bounds are
327 *> = 1.0 : Use the double-precision refinement algorithm,
328 *> possibly with doubled-single computations if the
329 *> compilation environment does not support DOUBLE
331 *> (other values are reserved for future use)
333 *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
334 *> computations allowed for refinement.
336 *> Aggressive: Set to 100 to permit convergence using approximate
337 *> factorizations or factorizations other than LU. If
338 *> the factorization uses a technique other than
339 *> Gaussian elimination, the guarantees in
340 *> err_bnds_norm and err_bnds_comp may no longer be
343 *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
344 *> will attempt to find a solution with small componentwise
345 *> relative error in the double-precision algorithm. Positive
346 *> is true, 0.0 is false.
347 *> Default: 1.0 (attempt componentwise convergence)
352 *> WORK is REAL array, dimension (4*N)
357 *> IWORK is INTEGER array, dimension (N)
363 *> = 0: Successful exit. The solution to every right-hand side is
365 *> < 0: If INFO = -i, the i-th argument had an illegal value
366 *> > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization
367 *> has been completed, but the factor U is exactly singular, so
368 *> the solution and error bounds could not be computed. RCOND = 0
370 *> = N+J: The solution corresponding to the Jth right-hand side is
371 *> not guaranteed. The solutions corresponding to other right-
372 *> hand sides K with K > J may not be guaranteed as well, but
373 *> only the first such right-hand side is reported. If a small
374 *> componentwise error is not requested (PARAMS(3) = 0.0) then
375 *> the Jth right-hand side is the first with a normwise error
376 *> bound that is not guaranteed (the smallest J such
377 *> that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
378 *> the Jth right-hand side is the first with either a normwise or
379 *> componentwise error bound that is not guaranteed (the smallest
380 *> J such that either ERR_BNDS_NORM(J,1) = 0.0 or
381 *> ERR_BNDS_COMP(J,1) = 0.0). See the definition of
382 *> ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
383 *> about all of the right-hand sides check ERR_BNDS_NORM or
390 *> \author Univ. of Tennessee
391 *> \author Univ. of California Berkeley
392 *> \author Univ. of Colorado Denver
397 *> \ingroup realSYcomputational
399 * =====================================================================
400 SUBROUTINE SSYRFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
401 $ S, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
402 $ ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
403 $ WORK, IWORK, INFO )
405 * -- LAPACK computational routine (version 3.4.1) --
406 * -- LAPACK is a software package provided by Univ. of Tennessee, --
407 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
410 * .. Scalar Arguments ..
411 CHARACTER UPLO, EQUED
412 INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
416 * .. Array Arguments ..
417 INTEGER IPIV( * ), IWORK( * )
418 REAL A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
419 $ X( LDX, * ), WORK( * )
420 REAL S( * ), PARAMS( * ), BERR( * ),
421 $ ERR_BNDS_NORM( NRHS, * ),
422 $ ERR_BNDS_COMP( NRHS, * )
425 * ==================================================================
429 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
430 REAL ITREF_DEFAULT, ITHRESH_DEFAULT,
431 $ COMPONENTWISE_DEFAULT
432 REAL RTHRESH_DEFAULT, DZTHRESH_DEFAULT
433 PARAMETER ( ITREF_DEFAULT = 1.0 )
434 PARAMETER ( ITHRESH_DEFAULT = 10.0 )
435 PARAMETER ( COMPONENTWISE_DEFAULT = 1.0 )
436 PARAMETER ( RTHRESH_DEFAULT = 0.5 )
437 PARAMETER ( DZTHRESH_DEFAULT = 0.25 )
438 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
440 PARAMETER ( LA_LINRX_ITREF_I = 1,
441 $ LA_LINRX_ITHRESH_I = 2 )
442 PARAMETER ( LA_LINRX_CWISE_I = 3 )
443 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
445 PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
446 PARAMETER ( LA_LINRX_RCOND_I = 3 )
448 * .. Local Scalars ..
451 INTEGER J, PREC_TYPE, REF_TYPE, N_NORMS
452 REAL ANORM, RCOND_TMP
453 REAL ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
456 REAL RTHRESH, UNSTABLE_THRESH
458 * .. External Subroutines ..
459 EXTERNAL XERBLA, SSYCON, SLA_SYRFSX_EXTENDED
461 * .. Intrinsic Functions ..
464 * .. External Functions ..
465 EXTERNAL LSAME, BLAS_FPINFO_X, ILATRANS, ILAPREC
466 EXTERNAL SLAMCH, SLANSY, SLA_SYRCOND
467 REAL SLAMCH, SLANSY, SLA_SYRCOND
469 INTEGER BLAS_FPINFO_X
470 INTEGER ILATRANS, ILAPREC
472 * .. Executable Statements ..
474 * Check the input parameters.
477 REF_TYPE = INT( ITREF_DEFAULT )
478 IF ( NPARAMS .GE. LA_LINRX_ITREF_I ) THEN
479 IF ( PARAMS( LA_LINRX_ITREF_I ) .LT. 0.0 ) THEN
480 PARAMS( LA_LINRX_ITREF_I ) = ITREF_DEFAULT
482 REF_TYPE = PARAMS( LA_LINRX_ITREF_I )
486 * Set default parameters.
488 ILLRCOND_THRESH = REAL( N )*SLAMCH( 'Epsilon' )
489 ITHRESH = INT( ITHRESH_DEFAULT )
490 RTHRESH = RTHRESH_DEFAULT
491 UNSTABLE_THRESH = DZTHRESH_DEFAULT
492 IGNORE_CWISE = COMPONENTWISE_DEFAULT .EQ. 0.0
494 IF ( NPARAMS.GE.LA_LINRX_ITHRESH_I ) THEN
495 IF ( PARAMS( LA_LINRX_ITHRESH_I ).LT.0.0 ) THEN
496 PARAMS( LA_LINRX_ITHRESH_I ) = ITHRESH
498 ITHRESH = INT( PARAMS( LA_LINRX_ITHRESH_I ) )
501 IF ( NPARAMS.GE.LA_LINRX_CWISE_I ) THEN
502 IF ( PARAMS( LA_LINRX_CWISE_I ).LT.0.0 ) THEN
503 IF ( IGNORE_CWISE ) THEN
504 PARAMS( LA_LINRX_CWISE_I ) = 0.0
506 PARAMS( LA_LINRX_CWISE_I ) = 1.0
509 IGNORE_CWISE = PARAMS( LA_LINRX_CWISE_I ) .EQ. 0.0
512 IF ( REF_TYPE .EQ. 0 .OR. N_ERR_BNDS .EQ. 0 ) THEN
514 ELSE IF ( IGNORE_CWISE ) THEN
520 RCEQU = LSAME( EQUED, 'Y' )
522 * Test input parameters.
524 IF ( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
526 ELSE IF( .NOT.RCEQU .AND. .NOT.LSAME( EQUED, 'N' ) ) THEN
528 ELSE IF( N.LT.0 ) THEN
530 ELSE IF( NRHS.LT.0 ) THEN
532 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
534 ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
536 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
538 ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
542 CALL XERBLA( 'SSYRFSX', -INFO )
546 * Quick return if possible.
548 IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN
552 IF ( N_ERR_BNDS .GE. 1 ) THEN
553 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0
554 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0
556 IF ( N_ERR_BNDS .GE. 2 ) THEN
557 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 0.0
558 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 0.0
560 IF ( N_ERR_BNDS .GE. 3 ) THEN
561 ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 1.0
562 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 1.0
568 * Default to failure.
573 IF ( N_ERR_BNDS .GE. 1 ) THEN
574 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0
575 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0
577 IF ( N_ERR_BNDS .GE. 2 ) THEN
578 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0
579 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0
581 IF ( N_ERR_BNDS .GE. 3 ) THEN
582 ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 0.0
583 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 0.0
587 * Compute the norm of A and the reciprocal of the condition
591 ANORM = SLANSY( NORM, UPLO, N, A, LDA, WORK )
592 CALL SSYCON( UPLO, N, AF, LDAF, IPIV, ANORM, RCOND, WORK,
595 * Perform refinement on each right-hand side
597 IF ( REF_TYPE .NE. 0 ) THEN
599 PREC_TYPE = ILAPREC( 'D' )
601 CALL SLA_SYRFSX_EXTENDED( PREC_TYPE, UPLO, N,
602 $ NRHS, A, LDA, AF, LDAF, IPIV, RCEQU, S, B,
603 $ LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM, ERR_BNDS_COMP,
604 $ WORK( N+1 ), WORK( 1 ), WORK( 2*N+1 ), WORK( 1 ), RCOND,
605 $ ITHRESH, RTHRESH, UNSTABLE_THRESH, IGNORE_CWISE,
609 ERR_LBND = MAX( 10.0, SQRT( REAL( N ) ) )*SLAMCH( 'Epsilon' )
610 IF (N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 1) THEN
612 * Compute scaled normwise condition number cond(A*C).
615 RCOND_TMP = SLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF, IPIV,
616 $ -1, S, INFO, WORK, IWORK )
618 RCOND_TMP = SLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF, IPIV,
619 $ 0, S, INFO, WORK, IWORK )
623 * Cap the error at 1.0.
625 IF (N_ERR_BNDS .GE. LA_LINRX_ERR_I
626 $ .AND. ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .GT. 1.0)
627 $ ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0
629 * Threshold the error (see LAWN).
631 IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN
632 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0
633 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 0.0
634 IF ( INFO .LE. N ) INFO = N + J
635 ELSE IF (ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .LT. ERR_LBND)
637 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = ERR_LBND
638 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0
641 * Save the condition number.
643 IF (N_ERR_BNDS .GE. LA_LINRX_RCOND_I) THEN
644 ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = RCOND_TMP
649 IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 2 ) THEN
651 * Compute componentwise condition number cond(A*diag(Y(:,J))) for
652 * each right-hand side using the current solution as an estimate of
653 * the true solution. If the componentwise error estimate is too
654 * large, then the solution is a lousy estimate of truth and the
655 * estimated RCOND may be too optimistic. To avoid misleading users,
656 * the inverse condition number is set to 0.0 when the estimated
657 * cwise error is at least CWISE_WRONG.
659 CWISE_WRONG = SQRT( SLAMCH( 'Epsilon' ) )
661 IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .LT. CWISE_WRONG )
663 RCOND_TMP = SLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF, IPIV,
664 $ 1, X(1,J), INFO, WORK, IWORK )
669 * Cap the error at 1.0.
671 IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
672 $ .AND. ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .GT. 1.0 )
673 $ ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0
675 * Threshold the error (see LAWN).
677 IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN
678 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0
679 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 0.0
680 IF ( .NOT. IGNORE_CWISE
681 $ .AND. INFO.LT.N + J ) INFO = N + J
682 ELSE IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I )
683 $ .LT. ERR_LBND ) THEN
684 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = ERR_LBND
685 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0
688 * Save the condition number.
690 IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
691 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = RCOND_TMP