001:       SUBROUTINE SPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B,
002:      $                    LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
003:      $                    ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
004:      $                    WORK, IWORK, INFO )
005: *
006: *     -- LAPACK routine (version 3.2)                                 --
007: *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
008: *     -- Jason Riedy of Univ. of California Berkeley.                 --
009: *     -- November 2008                                                --
010: *
011: *     -- LAPACK is a software package provided by Univ. of Tennessee, --
012: *     -- Univ. of California Berkeley and NAG Ltd.                    --
013: *
014:       IMPLICIT NONE
015: *     ..
016: *     .. Scalar Arguments ..
017:       CHARACTER          UPLO, EQUED
018:       INTEGER            INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
019:      $                   N_ERR_BNDS
020:       REAL               RCOND
021: *     ..
022: *     .. Array Arguments ..
023:       INTEGER            IWORK( * )
024:       REAL               A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
025:      $                   X( LDX, * ), WORK( * )
026:       REAL               S( * ), PARAMS( * ), BERR( * ),
027:      $                   ERR_BNDS_NORM( NRHS, * ),
028:      $                   ERR_BNDS_COMP( NRHS, * )
029: *     ..
030: *
031: *     Purpose
032: *     =======
033: *
034: *     SPORFSX improves the computed solution to a system of linear
035: *     equations when the coefficient matrix is symmetric positive
036: *     definite, and provides error bounds and backward error estimates
037: *     for the solution.  In addition to normwise error bound, the code
038: *     provides maximum componentwise error bound if possible.  See
039: *     comments for ERR_BNDS for details of the error bounds.
040: *
041: *     The original system of linear equations may have been equilibrated
042: *     before calling this routine, as described by arguments EQUED and S
043: *     below. In this case, the solution and error bounds returned are
044: *     for the original unequilibrated system.
045: *
046: *     Arguments
047: *     =========
048: *
049: *     Some optional parameters are bundled in the PARAMS array.  These
050: *     settings determine how refinement is performed, but often the
051: *     defaults are acceptable.  If the defaults are acceptable, users
052: *     can pass NPARAMS = 0 which prevents the source code from accessing
053: *     the PARAMS argument.
054: *
055: *     UPLO    (input) CHARACTER*1
056: *       = 'U':  Upper triangle of A is stored;
057: *       = 'L':  Lower triangle of A is stored.
058: *
059: *     EQUED   (input) CHARACTER*1
060: *     Specifies the form of equilibration that was done to A
061: *     before calling this routine. This is needed to compute
062: *     the solution and error bounds correctly.
063: *       = 'N':  No equilibration
064: *       = 'Y':  Both row and column equilibration, i.e., A has been
065: *               replaced by diag(S) * A * diag(S).
066: *               The right hand side B has been changed accordingly.
067: *
068: *     N       (input) INTEGER
069: *     The order of the matrix A.  N >= 0.
070: *
071: *     NRHS    (input) INTEGER
072: *     The number of right hand sides, i.e., the number of columns
073: *     of the matrices B and X.  NRHS >= 0.
074: *
075: *     A       (input) REAL array, dimension (LDA,N)
076: *     The symmetric matrix A.  If UPLO = 'U', the leading N-by-N
077: *     upper triangular part of A contains the upper triangular part
078: *     of the matrix A, and the strictly lower triangular part of A
079: *     is not referenced.  If UPLO = 'L', the leading N-by-N lower
080: *     triangular part of A contains the lower triangular part of
081: *     the matrix A, and the strictly upper triangular part of A is
082: *     not referenced.
083: *
084: *     LDA     (input) INTEGER
085: *     The leading dimension of the array A.  LDA >= max(1,N).
086: *
087: *     AF      (input) REAL array, dimension (LDAF,N)
088: *     The triangular factor U or L from the Cholesky factorization
089: *     A = U**T*U or A = L*L**T, as computed by SPOTRF.
090: *
091: *     LDAF    (input) INTEGER
092: *     The leading dimension of the array AF.  LDAF >= max(1,N).
093: *
094: *     S       (input or output) REAL array, dimension (N)
095: *     The row scale factors for A.  If EQUED = 'Y', A is multiplied on
096: *     the left and right by diag(S).  S is an input argument if FACT =
097: *     'F'; otherwise, S is an output argument.  If FACT = 'F' and EQUED
098: *     = 'Y', each element of S must be positive.  If S is output, each
099: *     element of S is a power of the radix. If S is input, each element
100: *     of S should be a power of the radix to ensure a reliable solution
101: *     and error estimates. Scaling by powers of the radix does not cause
102: *     rounding errors unless the result underflows or overflows.
103: *     Rounding errors during scaling lead to refining with a matrix that
104: *     is not equivalent to the input matrix, producing error estimates
105: *     that may not be reliable.
106: *
107: *     B       (input) REAL array, dimension (LDB,NRHS)
108: *     The right hand side matrix B.
109: *
110: *     LDB     (input) INTEGER
111: *     The leading dimension of the array B.  LDB >= max(1,N).
112: *
113: *     X       (input/output) REAL array, dimension (LDX,NRHS)
114: *     On entry, the solution matrix X, as computed by SGETRS.
115: *     On exit, the improved solution matrix X.
116: *
117: *     LDX     (input) INTEGER
118: *     The leading dimension of the array X.  LDX >= max(1,N).
119: *
120: *     RCOND   (output) REAL
121: *     Reciprocal scaled condition number.  This is an estimate of the
122: *     reciprocal Skeel condition number of the matrix A after
123: *     equilibration (if done).  If this is less than the machine
124: *     precision (in particular, if it is zero), the matrix is singular
125: *     to working precision.  Note that the error may still be small even
126: *     if this number is very small and the matrix appears ill-
127: *     conditioned.
128: *
129: *     BERR    (output) REAL array, dimension (NRHS)
130: *     Componentwise relative backward error.  This is the
131: *     componentwise relative backward error of each solution vector X(j)
132: *     (i.e., the smallest relative change in any element of A or B that
133: *     makes X(j) an exact solution).
134: *
135: *     N_ERR_BNDS (input) INTEGER
136: *     Number of error bounds to return for each right hand side
137: *     and each type (normwise or componentwise).  See ERR_BNDS_NORM and
138: *     ERR_BNDS_COMP below.
139: *
140: *     ERR_BNDS_NORM  (output) REAL array, dimension (NRHS, N_ERR_BNDS)
141: *     For each right-hand side, this array contains information about
142: *     various error bounds and condition numbers corresponding to the
143: *     normwise relative error, which is defined as follows:
144: *
145: *     Normwise relative error in the ith solution vector:
146: *             max_j (abs(XTRUE(j,i) - X(j,i)))
147: *            ------------------------------
148: *                  max_j abs(X(j,i))
149: *
150: *     The array is indexed by the type of error information as described
151: *     below. There currently are up to three pieces of information
152: *     returned.
153: *
154: *     The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
155: *     right-hand side.
156: *
157: *     The second index in ERR_BNDS_NORM(:,err) contains the following
158: *     three fields:
159: *     err = 1 "Trust/don't trust" boolean. Trust the answer if the
160: *              reciprocal condition number is less than the threshold
161: *              sqrt(n) * slamch('Epsilon').
162: *
163: *     err = 2 "Guaranteed" error bound: The estimated forward error,
164: *              almost certainly within a factor of 10 of the true error
165: *              so long as the next entry is greater than the threshold
166: *              sqrt(n) * slamch('Epsilon'). This error bound should only
167: *              be trusted if the previous boolean is true.
168: *
169: *     err = 3  Reciprocal condition number: Estimated normwise
170: *              reciprocal condition number.  Compared with the threshold
171: *              sqrt(n) * slamch('Epsilon') to determine if the error
172: *              estimate is "guaranteed". These reciprocal condition
173: *              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
174: *              appropriately scaled matrix Z.
175: *              Let Z = S*A, where S scales each row by a power of the
176: *              radix so all absolute row sums of Z are approximately 1.
177: *
178: *     See Lapack Working Note 165 for further details and extra
179: *     cautions.
180: *
181: *     ERR_BNDS_COMP  (output) REAL array, dimension (NRHS, N_ERR_BNDS)
182: *     For each right-hand side, this array contains information about
183: *     various error bounds and condition numbers corresponding to the
184: *     componentwise relative error, which is defined as follows:
185: *
186: *     Componentwise relative error in the ith solution vector:
187: *                    abs(XTRUE(j,i) - X(j,i))
188: *             max_j ----------------------
189: *                         abs(X(j,i))
190: *
191: *     The array is indexed by the right-hand side i (on which the
192: *     componentwise relative error depends), and the type of error
193: *     information as described below. There currently are up to three
194: *     pieces of information returned for each right-hand side. If
195: *     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
196: *     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
197: *     the first (:,N_ERR_BNDS) entries are returned.
198: *
199: *     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
200: *     right-hand side.
201: *
202: *     The second index in ERR_BNDS_COMP(:,err) contains the following
203: *     three fields:
204: *     err = 1 "Trust/don't trust" boolean. Trust the answer if the
205: *              reciprocal condition number is less than the threshold
206: *              sqrt(n) * slamch('Epsilon').
207: *
208: *     err = 2 "Guaranteed" error bound: The estimated forward error,
209: *              almost certainly within a factor of 10 of the true error
210: *              so long as the next entry is greater than the threshold
211: *              sqrt(n) * slamch('Epsilon'). This error bound should only
212: *              be trusted if the previous boolean is true.
213: *
214: *     err = 3  Reciprocal condition number: Estimated componentwise
215: *              reciprocal condition number.  Compared with the threshold
216: *              sqrt(n) * slamch('Epsilon') to determine if the error
217: *              estimate is "guaranteed". These reciprocal condition
218: *              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
219: *              appropriately scaled matrix Z.
220: *              Let Z = S*(A*diag(x)), where x is the solution for the
221: *              current right-hand side and S scales each row of
222: *              A*diag(x) by a power of the radix so all absolute row
223: *              sums of Z are approximately 1.
224: *
225: *     See Lapack Working Note 165 for further details and extra
226: *     cautions.
227: *
228: *     NPARAMS (input) INTEGER
229: *     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
230: *     PARAMS array is never referenced and default values are used.
231: *
232: *     PARAMS  (input / output) REAL array, dimension NPARAMS
233: *     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
234: *     that entry will be filled with default value used for that
235: *     parameter.  Only positions up to NPARAMS are accessed; defaults
236: *     are used for higher-numbered parameters.
237: *
238: *       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
239: *            refinement or not.
240: *         Default: 1.0
241: *            = 0.0 : No refinement is performed, and no error bounds are
242: *                    computed.
243: *            = 1.0 : Use the double-precision refinement algorithm,
244: *                    possibly with doubled-single computations if the
245: *                    compilation environment does not support DOUBLE
246: *                    PRECISION.
247: *              (other values are reserved for future use)
248: *
249: *       PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
250: *            computations allowed for refinement.
251: *         Default: 10
252: *         Aggressive: Set to 100 to permit convergence using approximate
253: *                     factorizations or factorizations other than LU. If
254: *                     the factorization uses a technique other than
255: *                     Gaussian elimination, the guarantees in
256: *                     err_bnds_norm and err_bnds_comp may no longer be
257: *                     trustworthy.
258: *
259: *       PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
260: *            will attempt to find a solution with small componentwise
261: *            relative error in the double-precision algorithm.  Positive
262: *            is true, 0.0 is false.
263: *         Default: 1.0 (attempt componentwise convergence)
264: *
265: *     WORK    (workspace) REAL array, dimension (4*N)
266: *
267: *     IWORK   (workspace) INTEGER array, dimension (N)
268: *
269: *     INFO    (output) INTEGER
270: *       = 0:  Successful exit. The solution to every right-hand side is
271: *         guaranteed.
272: *       < 0:  If INFO = -i, the i-th argument had an illegal value
273: *       > 0 and <= N:  U(INFO,INFO) is exactly zero.  The factorization
274: *         has been completed, but the factor U is exactly singular, so
275: *         the solution and error bounds could not be computed. RCOND = 0
276: *         is returned.
277: *       = N+J: The solution corresponding to the Jth right-hand side is
278: *         not guaranteed. The solutions corresponding to other right-
279: *         hand sides K with K > J may not be guaranteed as well, but
280: *         only the first such right-hand side is reported. If a small
281: *         componentwise error is not requested (PARAMS(3) = 0.0) then
282: *         the Jth right-hand side is the first with a normwise error
283: *         bound that is not guaranteed (the smallest J such
284: *         that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
285: *         the Jth right-hand side is the first with either a normwise or
286: *         componentwise error bound that is not guaranteed (the smallest
287: *         J such that either ERR_BNDS_NORM(J,1) = 0.0 or
288: *         ERR_BNDS_COMP(J,1) = 0.0). See the definition of
289: *         ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
290: *         about all of the right-hand sides check ERR_BNDS_NORM or
291: *         ERR_BNDS_COMP.
292: *
293: *     ==================================================================
294: *
295: *     .. Parameters ..
296:       REAL               ZERO, ONE
297:       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
298:       REAL               ITREF_DEFAULT, ITHRESH_DEFAULT,
299:      $                   COMPONENTWISE_DEFAULT
300:       REAL               RTHRESH_DEFAULT, DZTHRESH_DEFAULT
301:       PARAMETER          ( ITREF_DEFAULT = 1.0 )
302:       PARAMETER          ( ITHRESH_DEFAULT = 10.0 )
303:       PARAMETER          ( COMPONENTWISE_DEFAULT = 1.0 )
304:       PARAMETER          ( RTHRESH_DEFAULT = 0.5 )
305:       PARAMETER          ( DZTHRESH_DEFAULT = 0.25 )
306:       INTEGER            LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
307:      $                   LA_LINRX_CWISE_I
308:       PARAMETER          ( LA_LINRX_ITREF_I = 1,
309:      $                   LA_LINRX_ITHRESH_I = 2 )
310:       PARAMETER          ( LA_LINRX_CWISE_I = 3 )
311:       INTEGER            LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
312:      $                   LA_LINRX_RCOND_I
313:       PARAMETER          ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
314:       PARAMETER          ( LA_LINRX_RCOND_I = 3 )
315:       INTEGER            LA_LINRX_MAX_N_ERRS
316:       PARAMETER          ( LA_LINRX_MAX_N_ERRS = 3 )
317: *     ..
318: *     .. Local Scalars ..
319:       CHARACTER(1)       NORM
320:       LOGICAL            RCEQU
321:       INTEGER            J, PREC_TYPE, REF_TYPE
322:       INTEGER            N_NORMS
323:       REAL               ANORM, RCOND_TMP
324:       REAL               ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
325:       LOGICAL            IGNORE_CWISE
326:       INTEGER            ITHRESH
327:       REAL               RTHRESH, UNSTABLE_THRESH
328: *     ..
329: *     .. External Subroutines ..
330:       EXTERNAL           XERBLA, SPOCON, SLA_PORFSX_EXTENDED
331: *     ..
332: *     .. Intrinsic Functions ..
333:       INTRINSIC          MAX, SQRT
334: *     ..
335: *     .. External Functions ..
336:       EXTERNAL           LSAME, BLAS_FPINFO_X, ILATRANS, ILAPREC
337:       EXTERNAL           SLAMCH, SLANSY, SLA_PORCOND
338:       REAL               SLAMCH, SLANSY, SLA_PORCOND
339:       LOGICAL            LSAME
340:       INTEGER            BLAS_FPINFO_X
341:       INTEGER            ILATRANS, ILAPREC
342: *     ..
343: *     .. Executable Statements ..
344: *
345: *     Check the input parameters.
346: *
347:       INFO = 0
348:       REF_TYPE = INT( ITREF_DEFAULT )
349:       IF ( NPARAMS .GE. LA_LINRX_ITREF_I ) THEN
350:          IF ( PARAMS( LA_LINRX_ITREF_I ) .LT. 0.0 ) THEN
351:             PARAMS( LA_LINRX_ITREF_I ) = ITREF_DEFAULT
352:          ELSE
353:             REF_TYPE = PARAMS( LA_LINRX_ITREF_I )
354:          END IF
355:       END IF
356: *
357: *     Set default parameters.
358: *
359:       ILLRCOND_THRESH = REAL( N ) * SLAMCH( 'Epsilon' )
360:       ITHRESH = INT( ITHRESH_DEFAULT )
361:       RTHRESH = RTHRESH_DEFAULT
362:       UNSTABLE_THRESH = DZTHRESH_DEFAULT
363:       IGNORE_CWISE = COMPONENTWISE_DEFAULT .EQ. 0.0
364: *
365:       IF ( NPARAMS.GE.LA_LINRX_ITHRESH_I ) THEN
366:          IF ( PARAMS( LA_LINRX_ITHRESH_I ).LT.0.0 ) THEN
367:             PARAMS( LA_LINRX_ITHRESH_I ) = ITHRESH
368:          ELSE
369:             ITHRESH = INT( PARAMS( LA_LINRX_ITHRESH_I ) )
370:          END IF
371:       END IF
372:       IF ( NPARAMS.GE.LA_LINRX_CWISE_I ) THEN
373:          IF ( PARAMS( LA_LINRX_CWISE_I ).LT.0.0 ) THEN
374:             IF ( IGNORE_CWISE ) THEN
375:                PARAMS( LA_LINRX_CWISE_I ) = 0.0
376:             ELSE
377:                PARAMS( LA_LINRX_CWISE_I ) = 1.0
378:             END IF
379:          ELSE
380:             IGNORE_CWISE = PARAMS( LA_LINRX_CWISE_I ) .EQ. 0.0
381:          END IF
382:       END IF
383:       IF ( REF_TYPE .EQ. 0 .OR. N_ERR_BNDS .EQ. 0 ) THEN
384:          N_NORMS = 0
385:       ELSE IF ( IGNORE_CWISE ) THEN
386:          N_NORMS = 1
387:       ELSE
388:          N_NORMS = 2
389:       END IF
390: *
391:       RCEQU = LSAME( EQUED, 'Y' )
392: *
393: *     Test input parameters.
394: *
395:       IF (.NOT.LSAME(UPLO, 'U') .AND. .NOT.LSAME(UPLO, 'L')) THEN
396:         INFO = -1
397:       ELSE IF( .NOT.RCEQU .AND. .NOT.LSAME( EQUED, 'N' ) ) THEN
398:         INFO = -2
399:       ELSE IF( N.LT.0 ) THEN
400:         INFO = -3
401:       ELSE IF( NRHS.LT.0 ) THEN
402:         INFO = -4
403:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
404:         INFO = -6
405:       ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
406:         INFO = -8
407:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
408:         INFO = -11
409:       ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
410:         INFO = -13
411:       END IF
412:       IF( INFO.NE.0 ) THEN
413:         CALL XERBLA( 'SPORFSX', -INFO )
414:         RETURN
415:       END IF
416: *
417: *     Quick return if possible.
418: *
419:       IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN
420:          RCOND = 1.0
421:          DO J = 1, NRHS
422:             BERR( J ) = 0.0
423:             IF ( N_ERR_BNDS .GE. 1 ) THEN
424:                ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0
425:                ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0
426:             ELSE IF ( N_ERR_BNDS .GE. 2 ) THEN
427:                ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 0.0
428:                ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 0.0
429:             ELSE  IF ( N_ERR_BNDS .GE. 3 ) THEN
430:                ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 1.0
431:                ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 1.0
432:             END IF
433:          END DO
434:          RETURN
435:       END IF
436: *
437: *     Default to failure.
438: *
439:       RCOND = 0.0
440:       DO J = 1, NRHS
441:          BERR( J ) = 1.0
442:          IF ( N_ERR_BNDS .GE. 1 ) THEN
443:             ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0
444:             ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0
445:          ELSE IF ( N_ERR_BNDS .GE. 2 ) THEN
446:             ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0
447:             ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0
448:          ELSE IF ( N_ERR_BNDS .GE. 3 ) THEN
449:             ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 0.0
450:             ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 0.0
451:          END IF
452:       END DO
453: *
454: *     Compute the norm of A and the reciprocal of the condition
455: *     number of A.
456: *
457:       NORM = 'I'
458:       ANORM = SLANSY( NORM, UPLO, N, A, LDA, WORK )
459:       CALL SPOCON( UPLO, N, AF, LDAF, ANORM, RCOND, WORK,
460:      $     IWORK, INFO )
461: *
462: *     Perform refinement on each right-hand side
463: *
464:       IF ( REF_TYPE .NE. 0 ) THEN
465: 
466:          PREC_TYPE = ILAPREC( 'D' )
467: 
468:          CALL SLA_PORFSX_EXTENDED( PREC_TYPE, UPLO,  N,
469:      $        NRHS, A, LDA, AF, LDAF, RCEQU, S, B,
470:      $        LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM, ERR_BNDS_COMP,
471:      $        WORK( N+1 ), WORK( 1 ), WORK( 2*N+1 ), WORK( 1 ), RCOND,
472:      $        ITHRESH, RTHRESH, UNSTABLE_THRESH, IGNORE_CWISE,
473:      $        INFO )
474:       END IF
475: 
476:       ERR_LBND = MAX( 10.0, SQRT( REAL( N ) ) ) * SLAMCH( 'Epsilon' )
477:       IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 1 ) THEN
478: *
479: *     Compute scaled normwise condition number cond(A*C).
480: *
481:          IF ( RCEQU ) THEN
482:             RCOND_TMP = SLA_PORCOND( UPLO, N, A, LDA, AF, LDAF,
483:      $           -1, S, INFO, WORK, IWORK )
484:          ELSE
485:             RCOND_TMP = SLA_PORCOND( UPLO, N, A, LDA, AF, LDAF,
486:      $           0, S, INFO, WORK, IWORK )
487:          END IF
488:          DO J = 1, NRHS
489: *
490: *     Cap the error at 1.0.
491: *
492:             IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
493:      $           .AND. ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .GT. 1.0 )
494:      $           ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0
495: *
496: *     Threshold the error (see LAWN).
497: *
498:             IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN
499:                ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0
500:                ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 0.0
501:                IF ( INFO .LE. N ) INFO = N + J
502:             ELSE IF ( ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .LT. ERR_LBND )
503:      $              THEN
504:                ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = ERR_LBND
505:                ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0
506:             END IF
507: *
508: *     Save the condition number.
509: *
510:             IF (N_ERR_BNDS .GE. LA_LINRX_RCOND_I) THEN
511:                ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = RCOND_TMP
512:             END IF
513:          END DO
514:       END IF
515: 
516:       IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 2 ) THEN
517: *
518: *     Compute componentwise condition number cond(A*diag(Y(:,J))) for
519: *     each right-hand side using the current solution as an estimate of
520: *     the true solution.  If the componentwise error estimate is too
521: *     large, then the solution is a lousy estimate of truth and the
522: *     estimated RCOND may be too optimistic.  To avoid misleading users,
523: *     the inverse condition number is set to 0.0 when the estimated
524: *     cwise error is at least CWISE_WRONG.
525: *
526:          CWISE_WRONG = SQRT( SLAMCH( 'Epsilon' ) )
527:          DO J = 1, NRHS
528:             IF (ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .LT. CWISE_WRONG )
529:      $     THEN
530:                RCOND_TMP = SLA_PORCOND( UPLO, N, A, LDA, AF, LDAF, 1,
531:      $              X( 1, J ), INFO, WORK, IWORK )
532:             ELSE
533:                RCOND_TMP = 0.0
534:             END IF
535: *
536: *     Cap the error at 1.0.
537: *
538:             IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
539:      $           .AND. ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .GT. 1.0 )
540:      $           ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0
541: *
542: *     Threshold the error (see LAWN).
543: *
544:             IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN
545:                ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0
546:                ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 0.0
547:                IF ( PARAMS( LA_LINRX_CWISE_I ) .EQ. 1.0
548:      $              .AND. INFO.LT.N + J ) INFO = N + J
549:             ELSE IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I )
550:      $              .LT. ERR_LBND ) THEN
551:                ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = ERR_LBND
552:                ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0
553:             END IF
554: *
555: *     Save the condition number.
556: *
557:             IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
558:                ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = RCOND_TMP
559:             END IF
560: 
561:          END DO
562:       END IF
563: *
564:       RETURN
565: *
566: *     End of SPORFSX
567: *
568:       END
569: