1: *> \brief \b DPORFSX
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DPORFSX + dependencies
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11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dporfsx.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dporfsx.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DPORFSX( 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, IWORK, 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: * INTEGER IWORK( * )
34: * DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
35: * $ X( LDX, * ), WORK( * )
36: * DOUBLE PRECISION S( * ), PARAMS( * ), BERR( * ),
37: * $ ERR_BNDS_NORM( NRHS, * ),
38: * $ ERR_BNDS_COMP( NRHS, * )
39: * ..
40: *
41: *
42: *> \par Purpose:
43: * =============
44: *>
45: *> \verbatim
46: *>
47: *> DPORFSX improves the computed solution to a system of linear
48: *> equations when the coefficient matrix is symmetric positive
49: *> definite, and provides error bounds and backward error estimates
50: *> for the solution. In addition to normwise error bound, the code
51: *> provides maximum componentwise error bound if possible. See
52: *> comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the
53: *> error bounds.
54: *>
55: *> The original system of linear equations may have been equilibrated
56: *> before calling this routine, as described by arguments EQUED and S
57: *> below. In this case, the solution and error bounds returned are
58: *> for the original unequilibrated system.
59: *> \endverbatim
60: *
61: * Arguments:
62: * ==========
63: *
64: *> \verbatim
65: *> Some optional parameters are bundled in the PARAMS array. These
66: *> settings determine how refinement is performed, but often the
67: *> defaults are acceptable. If the defaults are acceptable, users
68: *> can pass NPARAMS = 0 which prevents the source code from accessing
69: *> the PARAMS argument.
70: *> \endverbatim
71: *>
72: *> \param[in] UPLO
73: *> \verbatim
74: *> UPLO is CHARACTER*1
75: *> = 'U': Upper triangle of A is stored;
76: *> = 'L': Lower triangle of A is stored.
77: *> \endverbatim
78: *>
79: *> \param[in] EQUED
80: *> \verbatim
81: *> EQUED is CHARACTER*1
82: *> Specifies the form of equilibration that was done to A
83: *> before calling this routine. This is needed to compute
84: *> the solution and error bounds correctly.
85: *> = 'N': No equilibration
86: *> = 'Y': Both row and column equilibration, i.e., A has been
87: *> replaced by diag(S) * A * diag(S).
88: *> The right hand side B has been changed accordingly.
89: *> \endverbatim
90: *>
91: *> \param[in] N
92: *> \verbatim
93: *> N is INTEGER
94: *> The order of the matrix A. N >= 0.
95: *> \endverbatim
96: *>
97: *> \param[in] NRHS
98: *> \verbatim
99: *> NRHS is INTEGER
100: *> The number of right hand sides, i.e., the number of columns
101: *> of the matrices B and X. NRHS >= 0.
102: *> \endverbatim
103: *>
104: *> \param[in] A
105: *> \verbatim
106: *> A is DOUBLE PRECISION array, dimension (LDA,N)
107: *> The symmetric matrix A. If UPLO = 'U', the leading N-by-N
108: *> upper triangular part of A contains the upper triangular part
109: *> of the matrix A, and the strictly lower triangular part of A
110: *> is not referenced. If UPLO = 'L', the leading N-by-N lower
111: *> triangular part of A contains the lower triangular part of
112: *> the matrix A, and the strictly upper triangular part of A is
113: *> not referenced.
114: *> \endverbatim
115: *>
116: *> \param[in] LDA
117: *> \verbatim
118: *> LDA is INTEGER
119: *> The leading dimension of the array A. LDA >= max(1,N).
120: *> \endverbatim
121: *>
122: *> \param[in] AF
123: *> \verbatim
124: *> AF is DOUBLE PRECISION array, dimension (LDAF,N)
125: *> The triangular factor U or L from the Cholesky factorization
126: *> A = U**T*U or A = L*L**T, as computed by DPOTRF.
127: *> \endverbatim
128: *>
129: *> \param[in] LDAF
130: *> \verbatim
131: *> LDAF is INTEGER
132: *> The leading dimension of the array AF. LDAF >= max(1,N).
133: *> \endverbatim
134: *>
135: *> \param[in,out] S
136: *> \verbatim
137: *> S is DOUBLE PRECISION array, dimension (N)
138: *> The scale factors for A. If EQUED = 'Y', A is multiplied on
139: *> the left and right by diag(S). S is an input argument if FACT =
140: *> 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED
141: *> = 'Y', each element of S must be positive. If S is output, each
142: *> element of S is a power of the radix. If S is input, each element
143: *> of S should be a power of the radix to ensure a reliable solution
144: *> and error estimates. Scaling by powers of the radix does not cause
145: *> rounding errors unless the result underflows or overflows.
146: *> Rounding errors during scaling lead to refining with a matrix that
147: *> is not equivalent to the input matrix, producing error estimates
148: *> that may not be reliable.
149: *> \endverbatim
150: *>
151: *> \param[in] B
152: *> \verbatim
153: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
154: *> The right hand side matrix B.
155: *> \endverbatim
156: *>
157: *> \param[in] LDB
158: *> \verbatim
159: *> LDB is INTEGER
160: *> The leading dimension of the array B. LDB >= max(1,N).
161: *> \endverbatim
162: *>
163: *> \param[in,out] X
164: *> \verbatim
165: *> X is DOUBLE PRECISION array, dimension (LDX,NRHS)
166: *> On entry, the solution matrix X, as computed by DGETRS.
167: *> On exit, the improved solution matrix X.
168: *> \endverbatim
169: *>
170: *> \param[in] LDX
171: *> \verbatim
172: *> LDX is INTEGER
173: *> The leading dimension of the array X. LDX >= max(1,N).
174: *> \endverbatim
175: *>
176: *> \param[out] RCOND
177: *> \verbatim
178: *> RCOND is DOUBLE PRECISION
179: *> Reciprocal scaled condition number. This is an estimate of the
180: *> reciprocal Skeel condition number of the matrix A after
181: *> equilibration (if done). If this is less than the machine
182: *> precision (in particular, if it is zero), the matrix is singular
183: *> to working precision. Note that the error may still be small even
184: *> if this number is very small and the matrix appears ill-
185: *> conditioned.
186: *> \endverbatim
187: *>
188: *> \param[out] BERR
189: *> \verbatim
190: *> BERR is DOUBLE PRECISION array, dimension (NRHS)
191: *> Componentwise relative backward error. This is the
192: *> componentwise relative backward error of each solution vector X(j)
193: *> (i.e., the smallest relative change in any element of A or B that
194: *> makes X(j) an exact solution).
195: *> \endverbatim
196: *>
197: *> \param[in] N_ERR_BNDS
198: *> \verbatim
199: *> N_ERR_BNDS is INTEGER
200: *> Number of error bounds to return for each right hand side
201: *> and each type (normwise or componentwise). See ERR_BNDS_NORM and
202: *> ERR_BNDS_COMP below.
203: *> \endverbatim
204: *>
205: *> \param[out] ERR_BNDS_NORM
206: *> \verbatim
207: *> ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
208: *> For each right-hand side, this array contains information about
209: *> various error bounds and condition numbers corresponding to the
210: *> normwise relative error, which is defined as follows:
211: *>
212: *> Normwise relative error in the ith solution vector:
213: *> max_j (abs(XTRUE(j,i) - X(j,i)))
214: *> ------------------------------
215: *> max_j abs(X(j,i))
216: *>
217: *> The array is indexed by the type of error information as described
218: *> below. There currently are up to three pieces of information
219: *> returned.
220: *>
221: *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
222: *> right-hand side.
223: *>
224: *> The second index in ERR_BNDS_NORM(:,err) contains the following
225: *> three fields:
226: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
227: *> reciprocal condition number is less than the threshold
228: *> sqrt(n) * dlamch('Epsilon').
229: *>
230: *> err = 2 "Guaranteed" error bound: The estimated forward error,
231: *> almost certainly within a factor of 10 of the true error
232: *> so long as the next entry is greater than the threshold
233: *> sqrt(n) * dlamch('Epsilon'). This error bound should only
234: *> be trusted if the previous boolean is true.
235: *>
236: *> err = 3 Reciprocal condition number: Estimated normwise
237: *> reciprocal condition number. Compared with the threshold
238: *> sqrt(n) * dlamch('Epsilon') to determine if the error
239: *> estimate is "guaranteed". These reciprocal condition
240: *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
241: *> appropriately scaled matrix Z.
242: *> Let Z = S*A, where S scales each row by a power of the
243: *> radix so all absolute row sums of Z are approximately 1.
244: *>
245: *> See Lapack Working Note 165 for further details and extra
246: *> cautions.
247: *> \endverbatim
248: *>
249: *> \param[out] ERR_BNDS_COMP
250: *> \verbatim
251: *> ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
252: *> For each right-hand side, this array contains information about
253: *> various error bounds and condition numbers corresponding to the
254: *> componentwise relative error, which is defined as follows:
255: *>
256: *> Componentwise relative error in the ith solution vector:
257: *> abs(XTRUE(j,i) - X(j,i))
258: *> max_j ----------------------
259: *> abs(X(j,i))
260: *>
261: *> The array is indexed by the right-hand side i (on which the
262: *> componentwise relative error depends), and the type of error
263: *> information as described below. There currently are up to three
264: *> pieces of information returned for each right-hand side. If
265: *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
266: *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most
267: *> the first (:,N_ERR_BNDS) entries are returned.
268: *>
269: *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
270: *> right-hand side.
271: *>
272: *> The second index in ERR_BNDS_COMP(:,err) contains the following
273: *> three fields:
274: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
275: *> reciprocal condition number is less than the threshold
276: *> sqrt(n) * dlamch('Epsilon').
277: *>
278: *> err = 2 "Guaranteed" error bound: The estimated forward error,
279: *> almost certainly within a factor of 10 of the true error
280: *> so long as the next entry is greater than the threshold
281: *> sqrt(n) * dlamch('Epsilon'). This error bound should only
282: *> be trusted if the previous boolean is true.
283: *>
284: *> err = 3 Reciprocal condition number: Estimated componentwise
285: *> reciprocal condition number. Compared with the threshold
286: *> sqrt(n) * dlamch('Epsilon') to determine if the error
287: *> estimate is "guaranteed". These reciprocal condition
288: *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
289: *> appropriately scaled matrix Z.
290: *> Let Z = S*(A*diag(x)), where x is the solution for the
291: *> current right-hand side and S scales each row of
292: *> A*diag(x) by a power of the radix so all absolute row
293: *> sums of Z are approximately 1.
294: *>
295: *> See Lapack Working Note 165 for further details and extra
296: *> cautions.
297: *> \endverbatim
298: *>
299: *> \param[in] NPARAMS
300: *> \verbatim
301: *> NPARAMS is INTEGER
302: *> Specifies the number of parameters set in PARAMS. If <= 0, the
303: *> PARAMS array is never referenced and default values are used.
304: *> \endverbatim
305: *>
306: *> \param[in,out] PARAMS
307: *> \verbatim
308: *> PARAMS is DOUBLE PRECISION array, dimension (NPARAMS)
309: *> Specifies algorithm parameters. If an entry is < 0.0, then
310: *> that entry will be filled with default value used for that
311: *> parameter. Only positions up to NPARAMS are accessed; defaults
312: *> are used for higher-numbered parameters.
313: *>
314: *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
315: *> refinement or not.
316: *> Default: 1.0D+0
317: *> = 0.0: No refinement is performed, and no error bounds are
318: *> computed.
319: *> = 1.0: Use the double-precision refinement algorithm,
320: *> possibly with doubled-single computations if the
321: *> compilation environment does not support DOUBLE
322: *> PRECISION.
323: *> (other values are reserved for future use)
324: *>
325: *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
326: *> computations allowed for refinement.
327: *> Default: 10
328: *> Aggressive: Set to 100 to permit convergence using approximate
329: *> factorizations or factorizations other than LU. If
330: *> the factorization uses a technique other than
331: *> Gaussian elimination, the guarantees in
332: *> err_bnds_norm and err_bnds_comp may no longer be
333: *> trustworthy.
334: *>
335: *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
336: *> will attempt to find a solution with small componentwise
337: *> relative error in the double-precision algorithm. Positive
338: *> is true, 0.0 is false.
339: *> Default: 1.0 (attempt componentwise convergence)
340: *> \endverbatim
341: *>
342: *> \param[out] WORK
343: *> \verbatim
344: *> WORK is DOUBLE PRECISION array, dimension (4*N)
345: *> \endverbatim
346: *>
347: *> \param[out] IWORK
348: *> \verbatim
349: *> IWORK is INTEGER array, dimension (N)
350: *> \endverbatim
351: *>
352: *> \param[out] INFO
353: *> \verbatim
354: *> INFO is INTEGER
355: *> = 0: Successful exit. The solution to every right-hand side is
356: *> guaranteed.
357: *> < 0: If INFO = -i, the i-th argument had an illegal value
358: *> > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization
359: *> has been completed, but the factor U is exactly singular, so
360: *> the solution and error bounds could not be computed. RCOND = 0
361: *> is returned.
362: *> = N+J: The solution corresponding to the Jth right-hand side is
363: *> not guaranteed. The solutions corresponding to other right-
364: *> hand sides K with K > J may not be guaranteed as well, but
365: *> only the first such right-hand side is reported. If a small
366: *> componentwise error is not requested (PARAMS(3) = 0.0) then
367: *> the Jth right-hand side is the first with a normwise error
368: *> bound that is not guaranteed (the smallest J such
369: *> that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
370: *> the Jth right-hand side is the first with either a normwise or
371: *> componentwise error bound that is not guaranteed (the smallest
372: *> J such that either ERR_BNDS_NORM(J,1) = 0.0 or
373: *> ERR_BNDS_COMP(J,1) = 0.0). See the definition of
374: *> ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
375: *> about all of the right-hand sides check ERR_BNDS_NORM or
376: *> ERR_BNDS_COMP.
377: *> \endverbatim
378: *
379: * Authors:
380: * ========
381: *
382: *> \author Univ. of Tennessee
383: *> \author Univ. of California Berkeley
384: *> \author Univ. of Colorado Denver
385: *> \author NAG Ltd.
386: *
387: *> \ingroup doublePOcomputational
388: *
389: * =====================================================================
390: SUBROUTINE DPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B,
391: $ LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
392: $ ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
393: $ WORK, IWORK, INFO )
394: *
395: * -- LAPACK computational routine --
396: * -- LAPACK is a software package provided by Univ. of Tennessee, --
397: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
398: *
399: * .. Scalar Arguments ..
400: CHARACTER UPLO, EQUED
401: INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
402: $ N_ERR_BNDS
403: DOUBLE PRECISION RCOND
404: * ..
405: * .. Array Arguments ..
406: INTEGER IWORK( * )
407: DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
408: $ X( LDX, * ), WORK( * )
409: DOUBLE PRECISION S( * ), PARAMS( * ), BERR( * ),
410: $ ERR_BNDS_NORM( NRHS, * ),
411: $ ERR_BNDS_COMP( NRHS, * )
412: * ..
413: *
414: * ==================================================================
415: *
416: * .. Parameters ..
417: DOUBLE PRECISION ZERO, ONE
418: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
419: DOUBLE PRECISION ITREF_DEFAULT, ITHRESH_DEFAULT
420: DOUBLE PRECISION COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT
421: DOUBLE PRECISION DZTHRESH_DEFAULT
422: PARAMETER ( ITREF_DEFAULT = 1.0D+0 )
423: PARAMETER ( ITHRESH_DEFAULT = 10.0D+0 )
424: PARAMETER ( COMPONENTWISE_DEFAULT = 1.0D+0 )
425: PARAMETER ( RTHRESH_DEFAULT = 0.5D+0 )
426: PARAMETER ( DZTHRESH_DEFAULT = 0.25D+0 )
427: INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
428: $ LA_LINRX_CWISE_I
429: PARAMETER ( LA_LINRX_ITREF_I = 1,
430: $ LA_LINRX_ITHRESH_I = 2 )
431: PARAMETER ( LA_LINRX_CWISE_I = 3 )
432: INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
433: $ LA_LINRX_RCOND_I
434: PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
435: PARAMETER ( LA_LINRX_RCOND_I = 3 )
436: * ..
437: * .. Local Scalars ..
438: CHARACTER(1) NORM
439: LOGICAL RCEQU
440: INTEGER J, PREC_TYPE, REF_TYPE
441: INTEGER N_NORMS
442: DOUBLE PRECISION ANORM, RCOND_TMP
443: DOUBLE PRECISION ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
444: LOGICAL IGNORE_CWISE
445: INTEGER ITHRESH
446: DOUBLE PRECISION RTHRESH, UNSTABLE_THRESH
447: * ..
448: * .. External Subroutines ..
449: EXTERNAL XERBLA, DPOCON, DLA_PORFSX_EXTENDED
450: * ..
451: * .. Intrinsic Functions ..
452: INTRINSIC MAX, SQRT
453: * ..
454: * .. External Functions ..
455: EXTERNAL LSAME, ILAPREC
456: EXTERNAL DLAMCH, DLANSY, DLA_PORCOND
457: DOUBLE PRECISION DLAMCH, DLANSY, DLA_PORCOND
458: LOGICAL LSAME
459: INTEGER ILAPREC
460: * ..
461: * .. Executable Statements ..
462: *
463: * Check the input parameters.
464: *
465: INFO = 0
466: REF_TYPE = INT( ITREF_DEFAULT )
467: IF ( NPARAMS .GE. LA_LINRX_ITREF_I ) THEN
468: IF ( PARAMS( LA_LINRX_ITREF_I ) .LT. 0.0D+0 ) THEN
469: PARAMS( LA_LINRX_ITREF_I ) = ITREF_DEFAULT
470: ELSE
471: REF_TYPE = PARAMS( LA_LINRX_ITREF_I )
472: END IF
473: END IF
474: *
475: * Set default parameters.
476: *
477: ILLRCOND_THRESH = DBLE( N ) * DLAMCH( 'Epsilon' )
478: ITHRESH = INT( ITHRESH_DEFAULT )
479: RTHRESH = RTHRESH_DEFAULT
480: UNSTABLE_THRESH = DZTHRESH_DEFAULT
481: IGNORE_CWISE = COMPONENTWISE_DEFAULT .EQ. 0.0D+0
482: *
483: IF ( NPARAMS.GE.LA_LINRX_ITHRESH_I ) THEN
484: IF ( PARAMS( LA_LINRX_ITHRESH_I ).LT.0.0D+0 ) THEN
485: PARAMS( LA_LINRX_ITHRESH_I ) = ITHRESH
486: ELSE
487: ITHRESH = INT( PARAMS( LA_LINRX_ITHRESH_I ) )
488: END IF
489: END IF
490: IF ( NPARAMS.GE.LA_LINRX_CWISE_I ) THEN
491: IF ( PARAMS( LA_LINRX_CWISE_I ).LT.0.0D+0 ) THEN
492: IF ( IGNORE_CWISE ) THEN
493: PARAMS( LA_LINRX_CWISE_I ) = 0.0D+0
494: ELSE
495: PARAMS( LA_LINRX_CWISE_I ) = 1.0D+0
496: END IF
497: ELSE
498: IGNORE_CWISE = PARAMS( LA_LINRX_CWISE_I ) .EQ. 0.0D+0
499: END IF
500: END IF
501: IF ( REF_TYPE .EQ. 0 .OR. N_ERR_BNDS .EQ. 0 ) THEN
502: N_NORMS = 0
503: ELSE IF ( IGNORE_CWISE ) THEN
504: N_NORMS = 1
505: ELSE
506: N_NORMS = 2
507: END IF
508: *
509: RCEQU = LSAME( EQUED, 'Y' )
510: *
511: * Test input parameters.
512: *
513: IF (.NOT.LSAME(UPLO, 'U') .AND. .NOT.LSAME(UPLO, 'L')) THEN
514: INFO = -1
515: ELSE IF( .NOT.RCEQU .AND. .NOT.LSAME( EQUED, 'N' ) ) THEN
516: INFO = -2
517: ELSE IF( N.LT.0 ) THEN
518: INFO = -3
519: ELSE IF( NRHS.LT.0 ) THEN
520: INFO = -4
521: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
522: INFO = -6
523: ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
524: INFO = -8
525: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
526: INFO = -11
527: ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
528: INFO = -13
529: END IF
530: IF( INFO.NE.0 ) THEN
531: CALL XERBLA( 'DPORFSX', -INFO )
532: RETURN
533: END IF
534: *
535: * Quick return if possible.
536: *
537: IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN
538: RCOND = 1.0D+0
539: DO J = 1, NRHS
540: BERR( J ) = 0.0D+0
541: IF ( N_ERR_BNDS .GE. 1 ) THEN
542: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
543: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
544: END IF
545: IF ( N_ERR_BNDS .GE. 2 ) THEN
546: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 0.0D+0
547: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 0.0D+0
548: END IF
549: IF ( N_ERR_BNDS .GE. 3 ) THEN
550: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 1.0D+0
551: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 1.0D+0
552: END IF
553: END DO
554: RETURN
555: END IF
556: *
557: * Default to failure.
558: *
559: RCOND = 0.0D+0
560: DO J = 1, NRHS
561: BERR( J ) = 1.0D+0
562: IF ( N_ERR_BNDS .GE. 1 ) THEN
563: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
564: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
565: END IF
566: IF ( N_ERR_BNDS .GE. 2 ) THEN
567: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
568: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
569: END IF
570: IF ( N_ERR_BNDS .GE. 3 ) THEN
571: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 0.0D+0
572: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 0.0D+0
573: END IF
574: END DO
575: *
576: * Compute the norm of A and the reciprocal of the condition
577: * number of A.
578: *
579: NORM = 'I'
580: ANORM = DLANSY( NORM, UPLO, N, A, LDA, WORK )
581: CALL DPOCON( UPLO, N, AF, LDAF, ANORM, RCOND, WORK,
582: $ IWORK, INFO )
583: *
584: * Perform refinement on each right-hand side
585: *
586: IF ( REF_TYPE .NE. 0 ) THEN
587:
588: PREC_TYPE = ILAPREC( 'E' )
589:
590: CALL DLA_PORFSX_EXTENDED( PREC_TYPE, UPLO, N,
591: $ NRHS, A, LDA, AF, LDAF, RCEQU, S, B,
592: $ LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM, ERR_BNDS_COMP,
593: $ WORK( N+1 ), WORK( 1 ), WORK( 2*N+1 ), WORK( 1 ), RCOND,
594: $ ITHRESH, RTHRESH, UNSTABLE_THRESH, IGNORE_CWISE,
595: $ INFO )
596: END IF
597:
598: ERR_LBND = MAX( 10.0D+0, SQRT( DBLE( N ) ) ) * DLAMCH( 'Epsilon' )
599: IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 1 ) THEN
600: *
601: * Compute scaled normwise condition number cond(A*C).
602: *
603: IF ( RCEQU ) THEN
604: RCOND_TMP = DLA_PORCOND( UPLO, N, A, LDA, AF, LDAF,
605: $ -1, S, INFO, WORK, IWORK )
606: ELSE
607: RCOND_TMP = DLA_PORCOND( UPLO, N, A, LDA, AF, LDAF,
608: $ 0, S, INFO, WORK, IWORK )
609: END IF
610: DO J = 1, NRHS
611: *
612: * Cap the error at 1.0.
613: *
614: IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
615: $ .AND. ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 )
616: $ ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
617: *
618: * Threshold the error (see LAWN).
619: *
620: IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN
621: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
622: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 0.0D+0
623: IF ( INFO .LE. N ) INFO = N + J
624: ELSE IF ( ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .LT. ERR_LBND )
625: $ THEN
626: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = ERR_LBND
627: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
628: END IF
629: *
630: * Save the condition number.
631: *
632: IF (N_ERR_BNDS .GE. LA_LINRX_RCOND_I) THEN
633: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = RCOND_TMP
634: END IF
635: END DO
636: END IF
637:
638: IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 2 ) THEN
639: *
640: * Compute componentwise condition number cond(A*diag(Y(:,J))) for
641: * each right-hand side using the current solution as an estimate of
642: * the true solution. If the componentwise error estimate is too
643: * large, then the solution is a lousy estimate of truth and the
644: * estimated RCOND may be too optimistic. To avoid misleading users,
645: * the inverse condition number is set to 0.0 when the estimated
646: * cwise error is at least CWISE_WRONG.
647: *
648: CWISE_WRONG = SQRT( DLAMCH( 'Epsilon' ) )
649: DO J = 1, NRHS
650: IF (ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .LT. CWISE_WRONG )
651: $ THEN
652: RCOND_TMP = DLA_PORCOND( UPLO, N, A, LDA, AF, LDAF, 1,
653: $ X( 1, J ), INFO, WORK, IWORK )
654: ELSE
655: RCOND_TMP = 0.0D+0
656: END IF
657: *
658: * Cap the error at 1.0.
659: *
660: IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
661: $ .AND. ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 )
662: $ ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
663: *
664: * Threshold the error (see LAWN).
665: *
666: IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN
667: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
668: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 0.0D+0
669: IF ( PARAMS( LA_LINRX_CWISE_I ) .EQ. 1.0D+0
670: $ .AND. INFO.LT.N + J ) INFO = N + J
671: ELSE IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I )
672: $ .LT. ERR_LBND ) THEN
673: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = ERR_LBND
674: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
675: END IF
676: *
677: * Save the condition number.
678: *
679: IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
680: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = RCOND_TMP
681: END IF
682:
683: END DO
684: END IF
685: *
686: RETURN
687: *
688: * End of DPORFSX
689: *
690: END
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