001:       SUBROUTINE CHERFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
002:      $                    S, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
003:      $                    ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
004:      $                    WORK, RWORK, INFO )
005: *
006: *     -- LAPACK routine (version 3.2.1)                                 --
007: *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
008: *     -- Jason Riedy of Univ. of California Berkeley.                 --
009: *     -- April 2009                                                   --
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            IPIV( * )
024:       COMPLEX            A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
025:      $                   X( LDX, * ), WORK( * )
026:       REAL               S( * ), PARAMS( * ), BERR( * ), RWORK( * ),
027:      $                   ERR_BNDS_NORM( NRHS, * ),
028:      $                   ERR_BNDS_COMP( NRHS, * )
029: *
030: *     Purpose
031: *     =======
032: *
033: *     CHERFSX improves the computed solution to a system of linear
034: *     equations when the coefficient matrix is Hermitian indefinite, and
035: *     provides error bounds and backward error estimates for the
036: *     solution.  In addition to normwise error bound, the code provides
037: *     maximum componentwise error bound if possible.  See comments for
038: *     ERR_BNDS_NORM and ERR_BNDS_COMP for details of the error bounds.
039: *
040: *     The original system of linear equations may have been equilibrated
041: *     before calling this routine, as described by arguments EQUED and S
042: *     below. In this case, the solution and error bounds returned are
043: *     for the original unequilibrated system.
044: *
045: *     Arguments
046: *     =========
047: *
048: *     Some optional parameters are bundled in the PARAMS array.  These
049: *     settings determine how refinement is performed, but often the
050: *     defaults are acceptable.  If the defaults are acceptable, users
051: *     can pass NPARAMS = 0 which prevents the source code from accessing
052: *     the PARAMS argument.
053: *
054: *     UPLO    (input) CHARACTER*1
055: *       = 'U':  Upper triangle of A is stored;
056: *       = 'L':  Lower triangle of A is stored.
057: *
058: *     EQUED   (input) CHARACTER*1
059: *     Specifies the form of equilibration that was done to A
060: *     before calling this routine. This is needed to compute
061: *     the solution and error bounds correctly.
062: *       = 'N':  No equilibration
063: *       = 'Y':  Both row and column equilibration, i.e., A has been
064: *               replaced by diag(S) * A * diag(S).
065: *               The right hand side B has been changed accordingly.
066: *
067: *     N       (input) INTEGER
068: *     The order of the matrix A.  N >= 0.
069: *
070: *     NRHS    (input) INTEGER
071: *     The number of right hand sides, i.e., the number of columns
072: *     of the matrices B and X.  NRHS >= 0.
073: *
074: *     A       (input) COMPLEX array, dimension (LDA,N)
075: *     The symmetric matrix A.  If UPLO = 'U', the leading N-by-N
076: *     upper triangular part of A contains the upper triangular
077: *     part of the matrix A, and the strictly lower triangular
078: *     part of A is not referenced.  If UPLO = 'L', the leading
079: *     N-by-N lower triangular part of A contains the lower
080: *     triangular part of the matrix A, and the strictly upper
081: *     triangular part of A is not referenced.
082: *
083: *     LDA     (input) INTEGER
084: *     The leading dimension of the array A.  LDA >= max(1,N).
085: *
086: *     AF      (input) COMPLEX array, dimension (LDAF,N)
087: *     The factored form of the matrix A.  AF contains the block
088: *     diagonal matrix D and the multipliers used to obtain the
089: *     factor U or L from the factorization A = U*D*U**T or A =
090: *     L*D*L**T as computed by SSYTRF.
091: *
092: *     LDAF    (input) INTEGER
093: *     The leading dimension of the array AF.  LDAF >= max(1,N).
094: *
095: *     IPIV    (input) INTEGER array, dimension (N)
096: *     Details of the interchanges and the block structure of D
097: *     as determined by SSYTRF.
098: *
099: *     S       (input or output) REAL array, dimension (N)
100: *     The scale factors for A.  If EQUED = 'Y', A is multiplied on
101: *     the left and right by diag(S).  S is an input argument if FACT =
102: *     'F'; otherwise, S is an output argument.  If FACT = 'F' and EQUED
103: *     = 'Y', each element of S must be positive.  If S is output, each
104: *     element of S is a power of the radix. If S is input, each element
105: *     of S should be a power of the radix to ensure a reliable solution
106: *     and error estimates. Scaling by powers of the radix does not cause
107: *     rounding errors unless the result underflows or overflows.
108: *     Rounding errors during scaling lead to refining with a matrix that
109: *     is not equivalent to the input matrix, producing error estimates
110: *     that may not be reliable.
111: *
112: *     B       (input) COMPLEX array, dimension (LDB,NRHS)
113: *     The right hand side matrix B.
114: *
115: *     LDB     (input) INTEGER
116: *     The leading dimension of the array B.  LDB >= max(1,N).
117: *
118: *     X       (input/output) COMPLEX array, dimension (LDX,NRHS)
119: *     On entry, the solution matrix X, as computed by SGETRS.
120: *     On exit, the improved solution matrix X.
121: *
122: *     LDX     (input) INTEGER
123: *     The leading dimension of the array X.  LDX >= max(1,N).
124: *
125: *     RCOND   (output) REAL
126: *     Reciprocal scaled condition number.  This is an estimate of the
127: *     reciprocal Skeel condition number of the matrix A after
128: *     equilibration (if done).  If this is less than the machine
129: *     precision (in particular, if it is zero), the matrix is singular
130: *     to working precision.  Note that the error may still be small even
131: *     if this number is very small and the matrix appears ill-
132: *     conditioned.
133: *
134: *     BERR    (output) REAL array, dimension (NRHS)
135: *     Componentwise relative backward error.  This is the
136: *     componentwise relative backward error of each solution vector X(j)
137: *     (i.e., the smallest relative change in any element of A or B that
138: *     makes X(j) an exact solution).
139: *
140: *     N_ERR_BNDS (input) INTEGER
141: *     Number of error bounds to return for each right hand side
142: *     and each type (normwise or componentwise).  See ERR_BNDS_NORM and
143: *     ERR_BNDS_COMP below.
144: *
145: *     ERR_BNDS_NORM  (output) REAL array, dimension (NRHS, N_ERR_BNDS)
146: *     For each right-hand side, this array contains information about
147: *     various error bounds and condition numbers corresponding to the
148: *     normwise relative error, which is defined as follows:
149: *
150: *     Normwise relative error in the ith solution vector:
151: *             max_j (abs(XTRUE(j,i) - X(j,i)))
152: *            ------------------------------
153: *                  max_j abs(X(j,i))
154: *
155: *     The array is indexed by the type of error information as described
156: *     below. There currently are up to three pieces of information
157: *     returned.
158: *
159: *     The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
160: *     right-hand side.
161: *
162: *     The second index in ERR_BNDS_NORM(:,err) contains the following
163: *     three fields:
164: *     err = 1 "Trust/don't trust" boolean. Trust the answer if the
165: *              reciprocal condition number is less than the threshold
166: *              sqrt(n) * slamch('Epsilon').
167: *
168: *     err = 2 "Guaranteed" error bound: The estimated forward error,
169: *              almost certainly within a factor of 10 of the true error
170: *              so long as the next entry is greater than the threshold
171: *              sqrt(n) * slamch('Epsilon'). This error bound should only
172: *              be trusted if the previous boolean is true.
173: *
174: *     err = 3  Reciprocal condition number: Estimated normwise
175: *              reciprocal condition number.  Compared with the threshold
176: *              sqrt(n) * slamch('Epsilon') to determine if the error
177: *              estimate is "guaranteed". These reciprocal condition
178: *              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
179: *              appropriately scaled matrix Z.
180: *              Let Z = S*A, where S scales each row by a power of the
181: *              radix so all absolute row sums of Z are approximately 1.
182: *
183: *     See Lapack Working Note 165 for further details and extra
184: *     cautions.
185: *
186: *     ERR_BNDS_COMP  (output) REAL array, dimension (NRHS, N_ERR_BNDS)
187: *     For each right-hand side, this array contains information about
188: *     various error bounds and condition numbers corresponding to the
189: *     componentwise relative error, which is defined as follows:
190: *
191: *     Componentwise relative error in the ith solution vector:
192: *                    abs(XTRUE(j,i) - X(j,i))
193: *             max_j ----------------------
194: *                         abs(X(j,i))
195: *
196: *     The array is indexed by the right-hand side i (on which the
197: *     componentwise relative error depends), and the type of error
198: *     information as described below. There currently are up to three
199: *     pieces of information returned for each right-hand side. If
200: *     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
201: *     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
202: *     the first (:,N_ERR_BNDS) entries are returned.
203: *
204: *     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
205: *     right-hand side.
206: *
207: *     The second index in ERR_BNDS_COMP(:,err) contains the following
208: *     three fields:
209: *     err = 1 "Trust/don't trust" boolean. Trust the answer if the
210: *              reciprocal condition number is less than the threshold
211: *              sqrt(n) * slamch('Epsilon').
212: *
213: *     err = 2 "Guaranteed" error bound: The estimated forward error,
214: *              almost certainly within a factor of 10 of the true error
215: *              so long as the next entry is greater than the threshold
216: *              sqrt(n) * slamch('Epsilon'). This error bound should only
217: *              be trusted if the previous boolean is true.
218: *
219: *     err = 3  Reciprocal condition number: Estimated componentwise
220: *              reciprocal condition number.  Compared with the threshold
221: *              sqrt(n) * slamch('Epsilon') to determine if the error
222: *              estimate is "guaranteed". These reciprocal condition
223: *              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
224: *              appropriately scaled matrix Z.
225: *              Let Z = S*(A*diag(x)), where x is the solution for the
226: *              current right-hand side and S scales each row of
227: *              A*diag(x) by a power of the radix so all absolute row
228: *              sums of Z are approximately 1.
229: *
230: *     See Lapack Working Note 165 for further details and extra
231: *     cautions.
232: *
233: *     NPARAMS (input) INTEGER
234: *     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
235: *     PARAMS array is never referenced and default values are used.
236: *
237: *     PARAMS  (input / output) REAL array, dimension NPARAMS
238: *     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
239: *     that entry will be filled with default value used for that
240: *     parameter.  Only positions up to NPARAMS are accessed; defaults
241: *     are used for higher-numbered parameters.
242: *
243: *       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
244: *            refinement or not.
245: *         Default: 1.0
246: *            = 0.0 : No refinement is performed, and no error bounds are
247: *                    computed.
248: *            = 1.0 : Use the double-precision refinement algorithm,
249: *                    possibly with doubled-single computations if the
250: *                    compilation environment does not support DOUBLE
251: *                    PRECISION.
252: *              (other values are reserved for future use)
253: *
254: *       PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
255: *            computations allowed for refinement.
256: *         Default: 10
257: *         Aggressive: Set to 100 to permit convergence using approximate
258: *                     factorizations or factorizations other than LU. If
259: *                     the factorization uses a technique other than
260: *                     Gaussian elimination, the guarantees in
261: *                     err_bnds_norm and err_bnds_comp may no longer be
262: *                     trustworthy.
263: *
264: *       PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
265: *            will attempt to find a solution with small componentwise
266: *            relative error in the double-precision algorithm.  Positive
267: *            is true, 0.0 is false.
268: *         Default: 1.0 (attempt componentwise convergence)
269: *
270: *     WORK    (workspace) COMPLEX array, dimension (2*N)
271: *
272: *     RWORK   (workspace) REAL array, dimension (2*N)
273: *
274: *     INFO    (output) INTEGER
275: *       = 0:  Successful exit. The solution to every right-hand side is
276: *         guaranteed.
277: *       < 0:  If INFO = -i, the i-th argument had an illegal value
278: *       > 0 and <= N:  U(INFO,INFO) is exactly zero.  The factorization
279: *         has been completed, but the factor U is exactly singular, so
280: *         the solution and error bounds could not be computed. RCOND = 0
281: *         is returned.
282: *       = N+J: The solution corresponding to the Jth right-hand side is
283: *         not guaranteed. The solutions corresponding to other right-
284: *         hand sides K with K > J may not be guaranteed as well, but
285: *         only the first such right-hand side is reported. If a small
286: *         componentwise error is not requested (PARAMS(3) = 0.0) then
287: *         the Jth right-hand side is the first with a normwise error
288: *         bound that is not guaranteed (the smallest J such
289: *         that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
290: *         the Jth right-hand side is the first with either a normwise or
291: *         componentwise error bound that is not guaranteed (the smallest
292: *         J such that either ERR_BNDS_NORM(J,1) = 0.0 or
293: *         ERR_BNDS_COMP(J,1) = 0.0). See the definition of
294: *         ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
295: *         about all of the right-hand sides check ERR_BNDS_NORM or
296: *         ERR_BNDS_COMP.
297: *
298: *     ==================================================================
299: *
300: *     .. Parameters ..
301:       REAL               ZERO, ONE
302:       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
303:       REAL               ITREF_DEFAULT, ITHRESH_DEFAULT,
304:      $                   COMPONENTWISE_DEFAULT
305:       REAL               RTHRESH_DEFAULT, DZTHRESH_DEFAULT
306:       PARAMETER          ( ITREF_DEFAULT = 1.0 )
307:       PARAMETER          ( ITHRESH_DEFAULT = 10.0 )
308:       PARAMETER          ( COMPONENTWISE_DEFAULT = 1.0 )
309:       PARAMETER          ( RTHRESH_DEFAULT = 0.5 )
310:       PARAMETER          ( DZTHRESH_DEFAULT = 0.25 )
311:       INTEGER            LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
312:      $                   LA_LINRX_CWISE_I
313:       PARAMETER          ( LA_LINRX_ITREF_I = 1,
314:      $                   LA_LINRX_ITHRESH_I = 2 )
315:       PARAMETER          ( LA_LINRX_CWISE_I = 3 )
316:       INTEGER            LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
317:      $                   LA_LINRX_RCOND_I
318:       PARAMETER          ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
319:       PARAMETER          ( LA_LINRX_RCOND_I = 3 )
320: *     ..
321: *     .. Local Scalars ..
322:       CHARACTER(1)       NORM
323:       LOGICAL            RCEQU
324:       INTEGER            J, PREC_TYPE, REF_TYPE
325:       INTEGER            N_NORMS
326:       REAL               ANORM, RCOND_TMP
327:       REAL               ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
328:       LOGICAL            IGNORE_CWISE
329:       INTEGER            ITHRESH
330:       REAL               RTHRESH, UNSTABLE_THRESH
331: *     ..
332: *     .. External Subroutines ..
333:       EXTERNAL           XERBLA, CHECON, CLA_HERFSX_EXTENDED
334: *     ..
335: *     .. Intrinsic Functions ..
336:       INTRINSIC          MAX, SQRT, TRANSFER
337: *     ..
338: *     .. External Functions ..
339:       EXTERNAL           LSAME, BLAS_FPINFO_X, ILATRANS, ILAPREC
340:       EXTERNAL           SLAMCH, CLANHE, CLA_HERCOND_X, CLA_HERCOND_C
341:       REAL               SLAMCH, CLANHE, CLA_HERCOND_X, CLA_HERCOND_C
342:       LOGICAL            LSAME
343:       INTEGER            BLAS_FPINFO_X
344:       INTEGER            ILATRANS, ILAPREC
345: *     ..
346: *     .. Executable Statements ..
347: *
348: *     Check the input parameters.
349: *
350:       INFO = 0
351:       REF_TYPE = INT( ITREF_DEFAULT )
352:       IF ( NPARAMS .GE. LA_LINRX_ITREF_I ) THEN
353:          IF ( PARAMS( LA_LINRX_ITREF_I ) .LT. 0.0 ) THEN
354:             PARAMS( LA_LINRX_ITREF_I ) = ITREF_DEFAULT
355:          ELSE
356:             REF_TYPE = PARAMS( LA_LINRX_ITREF_I )
357:          END IF
358:       END IF
359: *
360: *     Set default parameters.
361: *
362:       ILLRCOND_THRESH = REAL( N ) * SLAMCH( 'Epsilon' )
363:       ITHRESH = INT( ITHRESH_DEFAULT )
364:       RTHRESH = RTHRESH_DEFAULT
365:       UNSTABLE_THRESH = DZTHRESH_DEFAULT
366:       IGNORE_CWISE = COMPONENTWISE_DEFAULT .EQ. 0.0
367: *
368:       IF ( NPARAMS.GE.LA_LINRX_ITHRESH_I ) THEN
369:          IF ( PARAMS( LA_LINRX_ITHRESH_I ).LT.0.0 ) THEN
370:             PARAMS( LA_LINRX_ITHRESH_I ) = ITHRESH
371:          ELSE
372:             ITHRESH = INT( PARAMS( LA_LINRX_ITHRESH_I ) )
373:          END IF
374:       END IF
375:       IF ( NPARAMS.GE.LA_LINRX_CWISE_I ) THEN
376:          IF ( PARAMS(LA_LINRX_CWISE_I ).LT.0.0 ) THEN
377:             IF ( IGNORE_CWISE ) THEN
378:                PARAMS( LA_LINRX_CWISE_I ) = 0.0
379:             ELSE
380:                PARAMS( LA_LINRX_CWISE_I ) = 1.0
381:             END IF
382:          ELSE
383:             IGNORE_CWISE = PARAMS( LA_LINRX_CWISE_I ) .EQ. 0.0
384:          END IF
385:       END IF
386:       IF ( REF_TYPE .EQ. 0 .OR. N_ERR_BNDS .EQ. 0 ) THEN
387:          N_NORMS = 0
388:       ELSE IF ( IGNORE_CWISE ) THEN
389:          N_NORMS = 1
390:       ELSE
391:          N_NORMS = 2
392:       END IF
393: *
394:       RCEQU = LSAME( EQUED, 'Y' )
395: *
396: *     Test input parameters.
397: *
398:       IF (.NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
399:         INFO = -1
400:       ELSE IF( .NOT.RCEQU .AND. .NOT.LSAME( EQUED, 'N' ) ) THEN
401:         INFO = -2
402:       ELSE IF( N.LT.0 ) THEN
403:         INFO = -3
404:       ELSE IF( NRHS.LT.0 ) THEN
405:         INFO = -4
406:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
407:         INFO = -6
408:       ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
409:         INFO = -8
410:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
411:         INFO = -11
412:       ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
413:         INFO = -13
414:       END IF
415:       IF( INFO.NE.0 ) THEN
416:         CALL XERBLA( 'CHERFSX', -INFO )
417:         RETURN
418:       END IF
419: *
420: *     Quick return if possible.
421: *
422:       IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN
423:          RCOND = 1.0
424:          DO J = 1, NRHS
425:             BERR( J ) = 0.0
426:             IF ( N_ERR_BNDS .GE. 1 ) THEN
427:                ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0
428:                ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0
429:             ELSE IF ( N_ERR_BNDS .GE. 2 ) THEN
430:                ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 0.0
431:                ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 0.0
432:             ELSE IF ( N_ERR_BNDS .GE. 3 ) THEN
433:                ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 1.0
434:                ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 1.0
435:             END IF
436:          END DO
437:          RETURN
438:       END IF
439: *
440: *     Default to failure.
441: *
442:       RCOND = 0.0
443:       DO J = 1, NRHS
444:          BERR( J ) = 1.0
445:          IF ( N_ERR_BNDS .GE. 1 ) THEN
446:             ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0
447:             ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0
448:          ELSE IF ( N_ERR_BNDS .GE. 2 ) THEN
449:             ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0
450:             ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0
451:          ELSE IF ( N_ERR_BNDS .GE. 3 ) THEN
452:             ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 0.0
453:             ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 0.0
454:          END IF
455:       END DO
456: *
457: *     Compute the norm of A and the reciprocal of the condition
458: *     number of A.
459: *
460:       NORM = 'I'
461:       ANORM = CLANHE( NORM, UPLO, N, A, LDA, RWORK )
462:       CALL CHECON( UPLO, N, AF, LDAF, IPIV, ANORM, RCOND, WORK,
463:      $     INFO )
464: *
465: *     Perform refinement on each right-hand side
466: *
467:       IF ( REF_TYPE .NE. 0 ) THEN
468: 
469:          PREC_TYPE = ILAPREC( 'D' )
470: 
471:          CALL CLA_HERFSX_EXTENDED( PREC_TYPE, UPLO,  N,
472:      $        NRHS, A, LDA, AF, LDAF, IPIV, RCEQU, S, B,
473:      $        LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM, ERR_BNDS_COMP,
474:      $        WORK, RWORK, WORK(N+1),
475:      $        TRANSFER (RWORK(1:2*N), (/ (ZERO, ZERO) /), N), RCOND,
476:      $        ITHRESH, RTHRESH, UNSTABLE_THRESH, IGNORE_CWISE,
477:      $        INFO )
478:       END IF
479: 
480:       ERR_LBND = MAX( 10.0, SQRT( REAL( N ) ) ) * SLAMCH( 'Epsilon' )
481:       IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 1 ) THEN
482: *
483: *     Compute scaled normwise condition number cond(A*C).
484: *
485:          IF ( RCEQU ) THEN
486:             RCOND_TMP = CLA_HERCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV,
487:      $           S, .TRUE., INFO, WORK, RWORK )
488:          ELSE
489:             RCOND_TMP = CLA_HERCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV,
490:      $           S, .FALSE., INFO, WORK, RWORK )
491:          END IF
492:          DO J = 1, NRHS
493: *
494: *     Cap the error at 1.0.
495: *
496:             IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
497:      $           .AND. ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .GT. 1.0 )
498:      $           ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0
499: *
500: *     Threshold the error (see LAWN).
501: *
502:             IF (RCOND_TMP .LT. ILLRCOND_THRESH) THEN
503:                ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0
504:                ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 0.0
505:                IF ( INFO .LE. N ) INFO = N + J
506:             ELSE IF ( ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .LT. ERR_LBND )
507:      $              THEN
508:                ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = ERR_LBND
509:                ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0
510:             END IF
511: *
512: *     Save the condition number.
513: *
514:             IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
515:                ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = RCOND_TMP
516:             END IF
517:          END DO
518:       END IF
519: 
520:       IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 2 ) THEN
521: *
522: *     Compute componentwise condition number cond(A*diag(Y(:,J))) for
523: *     each right-hand side using the current solution as an estimate of
524: *     the true solution.  If the componentwise error estimate is too
525: *     large, then the solution is a lousy estimate of truth and the
526: *     estimated RCOND may be too optimistic.  To avoid misleading users,
527: *     the inverse condition number is set to 0.0 when the estimated
528: *     cwise error is at least CWISE_WRONG.
529: *
530:          CWISE_WRONG = SQRT( SLAMCH( 'Epsilon' ) )
531:          DO J = 1, NRHS
532:             IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .LT. CWISE_WRONG )
533:      $     THEN
534:                RCOND_TMP = CLA_HERCOND_X( UPLO, N, A, LDA, AF, LDAF,
535:      $         IPIV, X( 1, J ), INFO, WORK, RWORK )
536:             ELSE
537:                RCOND_TMP = 0.0
538:             END IF
539: *
540: *     Cap the error at 1.0.
541: *
542:             IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
543:      $           .AND. ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .GT. 1.0 )
544:      $           ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0
545: *
546: *     Threshold the error (see LAWN).
547: *
548:             IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN
549:                ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0
550:                ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 0.0
551:                IF ( PARAMS( LA_LINRX_CWISE_I ) .EQ. 1.0
552:      $              .AND. INFO.LT.N + J ) INFO = N + J
553:             ELSE IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I )
554:      $              .LT. ERR_LBND ) THEN
555:                ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = ERR_LBND
556:                ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0
557:             END IF
558: *
559: *     Save the condition number.
560: *
561:             IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
562:                ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = RCOND_TMP
563:             END IF
564: 
565:          END DO
566:       END IF
567: *
568:       RETURN
569: *
570: *     End of CHERFSX
571: *
572:       END
573: