LAPACK  3.5.0
LAPACK: Linear Algebra PACKage
 All Classes Files Functions Variables Typedefs Macros
zporfsx.f
Go to the documentation of this file.
1 *> \brief \b ZPORFSX
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download ZPORFSX + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zporfsx.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zporfsx.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zporfsx.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B,
22 * LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
23 * ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
24 * WORK, RWORK, INFO )
25 *
26 * .. Scalar Arguments ..
27 * CHARACTER UPLO, EQUED
28 * INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
29 * $ N_ERR_BNDS
30 * DOUBLE PRECISION RCOND
31 * ..
32 * .. Array Arguments ..
33 * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
34 * $ X( LDX, * ), WORK( * )
35 * DOUBLE PRECISION RWORK( * ), S( * ), PARAMS(*), BERR( * ),
36 * $ ERR_BNDS_NORM( NRHS, * ),
37 * $ ERR_BNDS_COMP( NRHS, * )
38 * ..
39 *
40 *
41 *> \par Purpose:
42 * =============
43 *>
44 *> \verbatim
45 *>
46 *> ZPORFSX improves the computed solution to a system of linear
47 *> equations when the coefficient matrix is symmetric positive
48 *> definite, and provides error bounds and backward error estimates
49 *> for the solution. In addition to normwise error bound, the code
50 *> provides maximum componentwise error bound if possible. See
51 *> comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the
52 *> error bounds.
53 *>
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.
58 *> \endverbatim
59 *
60 * Arguments:
61 * ==========
62 *
63 *> \verbatim
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.
69 *> \endverbatim
70 *>
71 *> \param[in] UPLO
72 *> \verbatim
73 *> UPLO is CHARACTER*1
74 *> = 'U': Upper triangle of A is stored;
75 *> = 'L': Lower triangle of A is stored.
76 *> \endverbatim
77 *>
78 *> \param[in] EQUED
79 *> \verbatim
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.
88 *> \endverbatim
89 *>
90 *> \param[in] N
91 *> \verbatim
92 *> N is INTEGER
93 *> The order of the matrix A. N >= 0.
94 *> \endverbatim
95 *>
96 *> \param[in] NRHS
97 *> \verbatim
98 *> NRHS is INTEGER
99 *> The number of right hand sides, i.e., the number of columns
100 *> of the matrices B and X. NRHS >= 0.
101 *> \endverbatim
102 *>
103 *> \param[in] A
104 *> \verbatim
105 *> A is COMPLEX*16 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 part
108 *> of the matrix A, and the strictly lower triangular part of A
109 *> is not referenced. If UPLO = 'L', the leading N-by-N lower
110 *> triangular part of A contains the lower triangular part of
111 *> the matrix A, and the strictly upper triangular part of A is
112 *> not referenced.
113 *> \endverbatim
114 *>
115 *> \param[in] LDA
116 *> \verbatim
117 *> LDA is INTEGER
118 *> The leading dimension of the array A. LDA >= max(1,N).
119 *> \endverbatim
120 *>
121 *> \param[in] AF
122 *> \verbatim
123 *> AF is COMPLEX*16 array, dimension (LDAF,N)
124 *> The triangular factor U or L from the Cholesky factorization
125 *> A = U**T*U or A = L*L**T, as computed by DPOTRF.
126 *> \endverbatim
127 *>
128 *> \param[in] LDAF
129 *> \verbatim
130 *> LDAF is INTEGER
131 *> The leading dimension of the array AF. LDAF >= max(1,N).
132 *> \endverbatim
133 *>
134 *> \param[in,out] S
135 *> \verbatim
136 *> S is DOUBLE PRECISION array, dimension (N)
137 *> The row scale factors for A. If EQUED = 'Y', A is multiplied on
138 *> the left and right by diag(S). S is an input argument if FACT =
139 *> 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED
140 *> = 'Y', each element of S must be positive. If S is output, each
141 *> element of S is a power of the radix. If S is input, each element
142 *> of S should be a power of the radix to ensure a reliable solution
143 *> and error estimates. Scaling by powers of the radix does not cause
144 *> rounding errors unless the result underflows or overflows.
145 *> Rounding errors during scaling lead to refining with a matrix that
146 *> is not equivalent to the input matrix, producing error estimates
147 *> that may not be reliable.
148 *> \endverbatim
149 *>
150 *> \param[in] B
151 *> \verbatim
152 *> B is COMPLEX*16 array, dimension (LDB,NRHS)
153 *> The right hand side matrix B.
154 *> \endverbatim
155 *>
156 *> \param[in] LDB
157 *> \verbatim
158 *> LDB is INTEGER
159 *> The leading dimension of the array B. LDB >= max(1,N).
160 *> \endverbatim
161 *>
162 *> \param[in,out] X
163 *> \verbatim
164 *> X is COMPLEX*16 array, dimension (LDX,NRHS)
165 *> On entry, the solution matrix X, as computed by DGETRS.
166 *> On exit, the improved solution matrix X.
167 *> \endverbatim
168 *>
169 *> \param[in] LDX
170 *> \verbatim
171 *> LDX is INTEGER
172 *> The leading dimension of the array X. LDX >= max(1,N).
173 *> \endverbatim
174 *>
175 *> \param[out] RCOND
176 *> \verbatim
177 *> RCOND is DOUBLE PRECISION
178 *> Reciprocal scaled condition number. This is an estimate of the
179 *> reciprocal Skeel condition number of the matrix A after
180 *> equilibration (if done). If this is less than the machine
181 *> precision (in particular, if it is zero), the matrix is singular
182 *> to working precision. Note that the error may still be small even
183 *> if this number is very small and the matrix appears ill-
184 *> conditioned.
185 *> \endverbatim
186 *>
187 *> \param[out] BERR
188 *> \verbatim
189 *> BERR is DOUBLE PRECISION array, dimension (NRHS)
190 *> Componentwise relative backward error. This is the
191 *> componentwise relative backward error of each solution vector X(j)
192 *> (i.e., the smallest relative change in any element of A or B that
193 *> makes X(j) an exact solution).
194 *> \endverbatim
195 *>
196 *> \param[in] N_ERR_BNDS
197 *> \verbatim
198 *> N_ERR_BNDS is INTEGER
199 *> Number of error bounds to return for each right hand side
200 *> and each type (normwise or componentwise). See ERR_BNDS_NORM and
201 *> ERR_BNDS_COMP below.
202 *> \endverbatim
203 *>
204 *> \param[out] ERR_BNDS_NORM
205 *> \verbatim
206 *> ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
207 *> For each right-hand side, this array contains information about
208 *> various error bounds and condition numbers corresponding to the
209 *> normwise relative error, which is defined as follows:
210 *>
211 *> Normwise relative error in the ith solution vector:
212 *> max_j (abs(XTRUE(j,i) - X(j,i)))
213 *> ------------------------------
214 *> max_j abs(X(j,i))
215 *>
216 *> The array is indexed by the type of error information as described
217 *> below. There currently are up to three pieces of information
218 *> returned.
219 *>
220 *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
221 *> right-hand side.
222 *>
223 *> The second index in ERR_BNDS_NORM(:,err) contains the following
224 *> three fields:
225 *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
226 *> reciprocal condition number is less than the threshold
227 *> sqrt(n) * dlamch('Epsilon').
228 *>
229 *> err = 2 "Guaranteed" error bound: The estimated forward error,
230 *> almost certainly within a factor of 10 of the true error
231 *> so long as the next entry is greater than the threshold
232 *> sqrt(n) * dlamch('Epsilon'). This error bound should only
233 *> be trusted if the previous boolean is true.
234 *>
235 *> err = 3 Reciprocal condition number: Estimated normwise
236 *> reciprocal condition number. Compared with the threshold
237 *> sqrt(n) * dlamch('Epsilon') to determine if the error
238 *> estimate is "guaranteed". These reciprocal condition
239 *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
240 *> appropriately scaled matrix Z.
241 *> Let Z = S*A, where S scales each row by a power of the
242 *> radix so all absolute row sums of Z are approximately 1.
243 *>
244 *> See Lapack Working Note 165 for further details and extra
245 *> cautions.
246 *> \endverbatim
247 *>
248 *> \param[out] ERR_BNDS_COMP
249 *> \verbatim
250 *> ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
251 *> For each right-hand side, this array contains information about
252 *> various error bounds and condition numbers corresponding to the
253 *> componentwise relative error, which is defined as follows:
254 *>
255 *> Componentwise relative error in the ith solution vector:
256 *> abs(XTRUE(j,i) - X(j,i))
257 *> max_j ----------------------
258 *> abs(X(j,i))
259 *>
260 *> The array is indexed by the right-hand side i (on which the
261 *> componentwise relative error depends), and the type of error
262 *> information as described below. There currently are up to three
263 *> pieces of information returned for each right-hand side. If
264 *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
265 *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
266 *> the first (:,N_ERR_BNDS) entries are returned.
267 *>
268 *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
269 *> right-hand side.
270 *>
271 *> The second index in ERR_BNDS_COMP(:,err) contains the following
272 *> three fields:
273 *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
274 *> reciprocal condition number is less than the threshold
275 *> sqrt(n) * dlamch('Epsilon').
276 *>
277 *> err = 2 "Guaranteed" error bound: The estimated forward error,
278 *> almost certainly within a factor of 10 of the true error
279 *> so long as the next entry is greater than the threshold
280 *> sqrt(n) * dlamch('Epsilon'). This error bound should only
281 *> be trusted if the previous boolean is true.
282 *>
283 *> err = 3 Reciprocal condition number: Estimated componentwise
284 *> reciprocal condition number. Compared with the threshold
285 *> sqrt(n) * dlamch('Epsilon') to determine if the error
286 *> estimate is "guaranteed". These reciprocal condition
287 *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
288 *> appropriately scaled matrix Z.
289 *> Let Z = S*(A*diag(x)), where x is the solution for the
290 *> current right-hand side and S scales each row of
291 *> A*diag(x) by a power of the radix so all absolute row
292 *> sums of Z are approximately 1.
293 *>
294 *> See Lapack Working Note 165 for further details and extra
295 *> cautions.
296 *> \endverbatim
297 *>
298 *> \param[in] NPARAMS
299 *> \verbatim
300 *> NPARAMS is INTEGER
301 *> Specifies the number of parameters set in PARAMS. If .LE. 0, the
302 *> PARAMS array is never referenced and default values are used.
303 *> \endverbatim
304 *>
305 *> \param[in,out] PARAMS
306 *> \verbatim
307 *> PARAMS is DOUBLE PRECISION array, dimension NPARAMS
308 *> Specifies algorithm parameters. If an entry is .LT. 0.0, then
309 *> that entry will be filled with default value used for that
310 *> parameter. Only positions up to NPARAMS are accessed; defaults
311 *> are used for higher-numbered parameters.
312 *>
313 *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
314 *> refinement or not.
315 *> Default: 1.0D+0
316 *> = 0.0 : No refinement is performed, and no error bounds are
317 *> computed.
318 *> = 1.0 : Use the double-precision refinement algorithm,
319 *> possibly with doubled-single computations if the
320 *> compilation environment does not support DOUBLE
321 *> PRECISION.
322 *> (other values are reserved for future use)
323 *>
324 *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
325 *> computations allowed for refinement.
326 *> Default: 10
327 *> Aggressive: Set to 100 to permit convergence using approximate
328 *> factorizations or factorizations other than LU. If
329 *> the factorization uses a technique other than
330 *> Gaussian elimination, the guarantees in
331 *> err_bnds_norm and err_bnds_comp may no longer be
332 *> trustworthy.
333 *>
334 *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
335 *> will attempt to find a solution with small componentwise
336 *> relative error in the double-precision algorithm. Positive
337 *> is true, 0.0 is false.
338 *> Default: 1.0 (attempt componentwise convergence)
339 *> \endverbatim
340 *>
341 *> \param[out] WORK
342 *> \verbatim
343 *> WORK is COMPLEX*16 array, dimension (2*N)
344 *> \endverbatim
345 *>
346 *> \param[out] RWORK
347 *> \verbatim
348 *> RWORK is DOUBLE PRECISION array, dimension (2*N)
349 *> \endverbatim
350 *>
351 *> \param[out] INFO
352 *> \verbatim
353 *> INFO is INTEGER
354 *> = 0: Successful exit. The solution to every right-hand side is
355 *> guaranteed.
356 *> < 0: If INFO = -i, the i-th argument had an illegal value
357 *> > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization
358 *> has been completed, but the factor U is exactly singular, so
359 *> the solution and error bounds could not be computed. RCOND = 0
360 *> is returned.
361 *> = N+J: The solution corresponding to the Jth right-hand side is
362 *> not guaranteed. The solutions corresponding to other right-
363 *> hand sides K with K > J may not be guaranteed as well, but
364 *> only the first such right-hand side is reported. If a small
365 *> componentwise error is not requested (PARAMS(3) = 0.0) then
366 *> the Jth right-hand side is the first with a normwise error
367 *> bound that is not guaranteed (the smallest J such
368 *> that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
369 *> the Jth right-hand side is the first with either a normwise or
370 *> componentwise error bound that is not guaranteed (the smallest
371 *> J such that either ERR_BNDS_NORM(J,1) = 0.0 or
372 *> ERR_BNDS_COMP(J,1) = 0.0). See the definition of
373 *> ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
374 *> about all of the right-hand sides check ERR_BNDS_NORM or
375 *> ERR_BNDS_COMP.
376 *> \endverbatim
377 *
378 * Authors:
379 * ========
380 *
381 *> \author Univ. of Tennessee
382 *> \author Univ. of California Berkeley
383 *> \author Univ. of Colorado Denver
384 *> \author NAG Ltd.
385 *
386 *> \date April 2012
387 *
388 *> \ingroup complex16POcomputational
389 *
390 * =====================================================================
391  SUBROUTINE zporfsx( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B,
392  $ ldb, x, ldx, rcond, berr, n_err_bnds,
393  $ err_bnds_norm, err_bnds_comp, nparams, params,
394  $ work, rwork, info )
395 *
396 * -- LAPACK computational routine (version 3.4.1) --
397 * -- LAPACK is a software package provided by Univ. of Tennessee, --
398 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
399 * April 2012
400 *
401 * .. Scalar Arguments ..
402  CHARACTER uplo, equed
403  INTEGER info, lda, ldaf, ldb, ldx, n, nrhs, nparams,
404  $ n_err_bnds
405  DOUBLE PRECISION rcond
406 * ..
407 * .. Array Arguments ..
408  COMPLEX*16 a( lda, * ), af( ldaf, * ), b( ldb, * ),
409  $ x( ldx, * ), work( * )
410  DOUBLE PRECISION rwork( * ), s( * ), params(*), berr( * ),
411  $ err_bnds_norm( nrhs, * ),
412  $ err_bnds_comp( nrhs, * )
413 * ..
414 *
415 * ==================================================================
416 *
417 * .. Parameters ..
418  DOUBLE PRECISION zero, one
419  parameter( zero = 0.0d+0, one = 1.0d+0 )
420  DOUBLE PRECISION itref_default, ithresh_default
421  DOUBLE PRECISION componentwise_default, rthresh_default
422  DOUBLE PRECISION dzthresh_default
423  parameter( itref_default = 1.0d+0 )
424  parameter( ithresh_default = 10.0d+0 )
425  parameter( componentwise_default = 1.0d+0 )
426  parameter( rthresh_default = 0.5d+0 )
427  parameter( dzthresh_default = 0.25d+0 )
428  INTEGER la_linrx_itref_i, la_linrx_ithresh_i,
429  $ la_linrx_cwise_i
430  parameter( la_linrx_itref_i = 1,
431  $ la_linrx_ithresh_i = 2 )
432  parameter( la_linrx_cwise_i = 3 )
433  INTEGER la_linrx_trust_i, la_linrx_err_i,
434  $ la_linrx_rcond_i
435  parameter( la_linrx_trust_i = 1, la_linrx_err_i = 2 )
436  parameter( la_linrx_rcond_i = 3 )
437 * ..
438 * .. Local Scalars ..
439  CHARACTER(1) norm
440  LOGICAL rcequ
441  INTEGER j, prec_type, ref_type
442  INTEGER n_norms
443  DOUBLE PRECISION anorm, rcond_tmp
444  DOUBLE PRECISION illrcond_thresh, err_lbnd, cwise_wrong
445  LOGICAL ignore_cwise
446  INTEGER ithresh
447  DOUBLE PRECISION rthresh, unstable_thresh
448 * ..
449 * .. External Subroutines ..
451 * ..
452 * .. Intrinsic Functions ..
453  INTRINSIC max, sqrt, transfer
454 * ..
455 * .. External Functions ..
456  EXTERNAL lsame, blas_fpinfo_x, ilatrans, ilaprec
458  DOUBLE PRECISION dlamch, zlanhe, zla_porcond_x, zla_porcond_c
459  LOGICAL lsame
460  INTEGER blas_fpinfo_x
461  INTEGER ilatrans, ilaprec
462 * ..
463 * .. Executable Statements ..
464 *
465 * Check the input parameters.
466 *
467  info = 0
468  ref_type = int( itref_default )
469  IF ( nparams .GE. la_linrx_itref_i ) THEN
470  IF ( params( la_linrx_itref_i ) .LT. 0.0d+0 ) THEN
471  params( la_linrx_itref_i ) = itref_default
472  ELSE
473  ref_type = params( la_linrx_itref_i )
474  END IF
475  END IF
476 *
477 * Set default parameters.
478 *
479  illrcond_thresh = dble( n ) * dlamch( 'Epsilon' )
480  ithresh = int( ithresh_default )
481  rthresh = rthresh_default
482  unstable_thresh = dzthresh_default
483  ignore_cwise = componentwise_default .EQ. 0.0d+0
484 *
485  IF ( nparams.GE.la_linrx_ithresh_i ) THEN
486  IF ( params(la_linrx_ithresh_i ).LT.0.0d+0 ) THEN
487  params( la_linrx_ithresh_i ) = ithresh
488  ELSE
489  ithresh = int( params( la_linrx_ithresh_i ) )
490  END IF
491  END IF
492  IF ( nparams.GE.la_linrx_cwise_i ) THEN
493  IF ( params(la_linrx_cwise_i ).LT.0.0d+0 ) THEN
494  IF ( ignore_cwise ) THEN
495  params( la_linrx_cwise_i ) = 0.0d+0
496  ELSE
497  params( la_linrx_cwise_i ) = 1.0d+0
498  END IF
499  ELSE
500  ignore_cwise = params( la_linrx_cwise_i ) .EQ. 0.0d+0
501  END IF
502  END IF
503  IF ( ref_type .EQ. 0 .OR. n_err_bnds .EQ. 0 ) THEN
504  n_norms = 0
505  ELSE IF ( ignore_cwise ) THEN
506  n_norms = 1
507  ELSE
508  n_norms = 2
509  END IF
510 *
511  rcequ = lsame( equed, 'Y' )
512 *
513 * Test input parameters.
514 *
515  IF (.NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
516  info = -1
517  ELSE IF( .NOT.rcequ .AND. .NOT.lsame( equed, 'N' ) ) THEN
518  info = -2
519  ELSE IF( n.LT.0 ) THEN
520  info = -3
521  ELSE IF( nrhs.LT.0 ) THEN
522  info = -4
523  ELSE IF( lda.LT.max( 1, n ) ) THEN
524  info = -6
525  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
526  info = -8
527  ELSE IF( ldb.LT.max( 1, n ) ) THEN
528  info = -11
529  ELSE IF( ldx.LT.max( 1, n ) ) THEN
530  info = -13
531  END IF
532  IF( info.NE.0 ) THEN
533  CALL xerbla( 'ZPORFSX', -info )
534  RETURN
535  END IF
536 *
537 * Quick return if possible.
538 *
539  IF( n.EQ.0 .OR. nrhs.EQ.0 ) THEN
540  rcond = 1.0d+0
541  DO j = 1, nrhs
542  berr( j ) = 0.0d+0
543  IF ( n_err_bnds .GE. 1 ) THEN
544  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
545  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
546  END IF
547  IF ( n_err_bnds .GE. 2 ) THEN
548  err_bnds_norm( j, la_linrx_err_i ) = 0.0d+0
549  err_bnds_comp( j, la_linrx_err_i ) = 0.0d+0
550  END IF
551  IF ( n_err_bnds .GE. 3 ) THEN
552  err_bnds_norm( j, la_linrx_rcond_i ) = 1.0d+0
553  err_bnds_comp( j, la_linrx_rcond_i ) = 1.0d+0
554  END IF
555  END DO
556  RETURN
557  END IF
558 *
559 * Default to failure.
560 *
561  rcond = 0.0d+0
562  DO j = 1, nrhs
563  berr( j ) = 1.0d+0
564  IF ( n_err_bnds .GE. 1 ) THEN
565  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
566  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
567  END IF
568  IF ( n_err_bnds .GE. 2 ) THEN
569  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
570  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
571  END IF
572  IF ( n_err_bnds .GE. 3 ) THEN
573  err_bnds_norm( j, la_linrx_rcond_i ) = 0.0d+0
574  err_bnds_comp( j, la_linrx_rcond_i ) = 0.0d+0
575  END IF
576  END DO
577 *
578 * Compute the norm of A and the reciprocal of the condition
579 * number of A.
580 *
581  norm = 'I'
582  anorm = zlanhe( norm, uplo, n, a, lda, rwork )
583  CALL zpocon( uplo, n, af, ldaf, anorm, rcond, work, rwork,
584  $ info )
585 *
586 * Perform refinement on each right-hand side
587 *
588  IF ( ref_type .NE. 0 ) THEN
589 
590  prec_type = ilaprec( 'E' )
591 
592  CALL zla_porfsx_extended( prec_type, uplo, n,
593  $ nrhs, a, lda, af, ldaf, rcequ, s, b,
594  $ ldb, x, ldx, berr, n_norms, err_bnds_norm, err_bnds_comp,
595  $ work, rwork, work(n+1),
596  $ transfer(rwork(1:2*n), (/ (zero, zero) /), n), rcond,
597  $ ithresh, rthresh, unstable_thresh, ignore_cwise,
598  $ info )
599  END IF
600 
601  err_lbnd = max( 10.0d+0, sqrt( dble( n ) ) ) * dlamch( 'Epsilon' )
602  IF ( n_err_bnds .GE. 1 .AND. n_norms .GE. 1 ) THEN
603 *
604 * Compute scaled normwise condition number cond(A*C).
605 *
606  IF ( rcequ ) THEN
607  rcond_tmp = zla_porcond_c( uplo, n, a, lda, af, ldaf,
608  $ s, .true., info, work, rwork )
609  ELSE
610  rcond_tmp = zla_porcond_c( uplo, n, a, lda, af, ldaf,
611  $ s, .false., info, work, rwork )
612  END IF
613  DO j = 1, nrhs
614 *
615 * Cap the error at 1.0.
616 *
617  IF ( n_err_bnds .GE. la_linrx_err_i
618  $ .AND. err_bnds_norm( j, la_linrx_err_i ) .GT. 1.0d+0 )
619  $ err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
620 *
621 * Threshold the error (see LAWN).
622 *
623  IF ( rcond_tmp .LT. illrcond_thresh ) THEN
624  err_bnds_norm( j, la_linrx_err_i ) = 1.0d+0
625  err_bnds_norm( j, la_linrx_trust_i ) = 0.0d+0
626  IF ( info .LE. n ) info = n + j
627  ELSE IF ( err_bnds_norm( j, la_linrx_err_i ) .LT. err_lbnd )
628  $ THEN
629  err_bnds_norm( j, la_linrx_err_i ) = err_lbnd
630  err_bnds_norm( j, la_linrx_trust_i ) = 1.0d+0
631  END IF
632 *
633 * Save the condition number.
634 *
635  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
636  err_bnds_norm( j, la_linrx_rcond_i ) = rcond_tmp
637  END IF
638 
639  END DO
640  END IF
641 
642  IF (n_err_bnds .GE. 1 .AND. n_norms .GE. 2) THEN
643 *
644 * Compute componentwise condition number cond(A*diag(Y(:,J))) for
645 * each right-hand side using the current solution as an estimate of
646 * the true solution. If the componentwise error estimate is too
647 * large, then the solution is a lousy estimate of truth and the
648 * estimated RCOND may be too optimistic. To avoid misleading users,
649 * the inverse condition number is set to 0.0 when the estimated
650 * cwise error is at least CWISE_WRONG.
651 *
652  cwise_wrong = sqrt( dlamch( 'Epsilon' ) )
653  DO j = 1, nrhs
654  IF (err_bnds_comp( j, la_linrx_err_i ) .LT. cwise_wrong )
655  $ THEN
656  rcond_tmp = zla_porcond_x( uplo, n, a, lda, af, ldaf,
657  $ x(1,j), info, work, rwork )
658  ELSE
659  rcond_tmp = 0.0d+0
660  END IF
661 *
662 * Cap the error at 1.0.
663 *
664  IF ( n_err_bnds .GE. la_linrx_err_i
665  $ .AND. err_bnds_comp( j, la_linrx_err_i ) .GT. 1.0d+0 )
666  $ err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
667 *
668 * Threshold the error (see LAWN).
669 *
670  IF (rcond_tmp .LT. illrcond_thresh) THEN
671  err_bnds_comp( j, la_linrx_err_i ) = 1.0d+0
672  err_bnds_comp( j, la_linrx_trust_i ) = 0.0d+0
673  IF ( params( la_linrx_cwise_i ) .EQ. 1.0d+0
674  $ .AND. info.LT.n + j ) info = n + j
675  ELSE IF ( err_bnds_comp( j, la_linrx_err_i )
676  $ .LT. err_lbnd ) THEN
677  err_bnds_comp( j, la_linrx_err_i ) = err_lbnd
678  err_bnds_comp( j, la_linrx_trust_i ) = 1.0d+0
679  END IF
680 *
681 * Save the condition number.
682 *
683  IF ( n_err_bnds .GE. la_linrx_rcond_i ) THEN
684  err_bnds_comp( j, la_linrx_rcond_i ) = rcond_tmp
685  END IF
686 
687  END DO
688  END IF
689 *
690  RETURN
691 *
692 * End of ZPORFSX
693 *
694  END