Annotation of rpl/lapack/lapack/zporfsx.f, revision 1.7
1.5 bertrand 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
1.7 ! bertrand 136: *> S is DOUBLE PRECISION array, dimension (N)
1.5 bertrand 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
1.7 ! bertrand 307: *> PARAMS is DOUBLE PRECISION array, dimension NPARAMS
1.5 bertrand 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: *
1.7 ! bertrand 386: *> \date April 2012
1.5 bertrand 387: *
388: *> \ingroup complex16POcomputational
389: *
390: * =====================================================================
1.1 bertrand 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: *
1.7 ! bertrand 396: * -- LAPACK computational routine (version 3.4.1) --
1.5 bertrand 397: * -- LAPACK is a software package provided by Univ. of Tennessee, --
398: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.7 ! bertrand 399: * April 2012
1.1 bertrand 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: *
1.5 bertrand 415: * ==================================================================
1.1 bertrand 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 ..
450: EXTERNAL XERBLA, ZPOCON, ZLA_PORFSX_EXTENDED
451: * ..
452: * .. Intrinsic Functions ..
453: INTRINSIC MAX, SQRT, TRANSFER
454: * ..
455: * .. External Functions ..
456: EXTERNAL LSAME, BLAS_FPINFO_X, ILATRANS, ILAPREC
457: EXTERNAL DLAMCH, ZLANHE, ZLA_PORCOND_X, ZLA_PORCOND_C
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
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