Annotation of rpl/lapack/lapack/dporfsx.f, revision 1.3
1.1 bertrand 1: SUBROUTINE DPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B,
2: $ LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
3: $ ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
4: $ WORK, IWORK, INFO )
5: *
6: * -- LAPACK routine (version 3.2.2) --
7: * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
8: * -- Jason Riedy of Univ. of California Berkeley. --
9: * -- June 2010 --
10: *
11: * -- LAPACK is a software package provided by Univ. of Tennessee, --
12: * -- Univ. of California Berkeley and NAG Ltd. --
13: *
14: IMPLICIT NONE
15: * ..
16: * .. Scalar Arguments ..
17: CHARACTER UPLO, EQUED
18: INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
19: $ N_ERR_BNDS
20: DOUBLE PRECISION RCOND
21: * ..
22: * .. Array Arguments ..
23: INTEGER IWORK( * )
24: DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
25: $ X( LDX, * ), WORK( * )
26: DOUBLE PRECISION S( * ), PARAMS( * ), BERR( * ),
27: $ ERR_BNDS_NORM( NRHS, * ),
28: $ ERR_BNDS_COMP( NRHS, * )
29: * ..
30: *
31: * Purpose
32: * =======
33: *
34: * DPORFSX improves the computed solution to a system of linear
35: * equations when the coefficient matrix is symmetric positive
36: * definite, and provides error bounds and backward error estimates
37: * for the solution. In addition to normwise error bound, the code
38: * provides maximum componentwise error bound if possible. See
39: * comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the
40: * error bounds.
41: *
42: * The original system of linear equations may have been equilibrated
43: * before calling this routine, as described by arguments EQUED and S
44: * below. In this case, the solution and error bounds returned are
45: * for the original unequilibrated system.
46: *
47: * Arguments
48: * =========
49: *
50: * Some optional parameters are bundled in the PARAMS array. These
51: * settings determine how refinement is performed, but often the
52: * defaults are acceptable. If the defaults are acceptable, users
53: * can pass NPARAMS = 0 which prevents the source code from accessing
54: * the PARAMS argument.
55: *
56: * UPLO (input) CHARACTER*1
57: * = 'U': Upper triangle of A is stored;
58: * = 'L': Lower triangle of A is stored.
59: *
60: * EQUED (input) CHARACTER*1
61: * Specifies the form of equilibration that was done to A
62: * before calling this routine. This is needed to compute
63: * the solution and error bounds correctly.
64: * = 'N': No equilibration
65: * = 'Y': Both row and column equilibration, i.e., A has been
66: * replaced by diag(S) * A * diag(S).
67: * The right hand side B has been changed accordingly.
68: *
69: * N (input) INTEGER
70: * The order of the matrix A. N >= 0.
71: *
72: * NRHS (input) INTEGER
73: * The number of right hand sides, i.e., the number of columns
74: * of the matrices B and X. NRHS >= 0.
75: *
76: * A (input) DOUBLE PRECISION array, dimension (LDA,N)
77: * The symmetric matrix A. If UPLO = 'U', the leading N-by-N
78: * upper triangular part of A contains the upper triangular part
79: * of the matrix A, and the strictly lower triangular part of A
80: * is not referenced. If UPLO = 'L', the leading N-by-N lower
81: * triangular part of A contains the lower triangular part of
82: * the matrix A, and the strictly upper triangular part of A is
83: * not referenced.
84: *
85: * LDA (input) INTEGER
86: * The leading dimension of the array A. LDA >= max(1,N).
87: *
88: * AF (input) DOUBLE PRECISION array, dimension (LDAF,N)
89: * The triangular factor U or L from the Cholesky factorization
90: * A = U**T*U or A = L*L**T, as computed by DPOTRF.
91: *
92: * LDAF (input) INTEGER
93: * The leading dimension of the array AF. LDAF >= max(1,N).
94: *
95: * S (input or output) DOUBLE PRECISION array, dimension (N)
96: * The row scale factors for A. If EQUED = 'Y', A is multiplied on
97: * the left and right by diag(S). S is an input argument if FACT =
98: * 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED
99: * = 'Y', each element of S must be positive. If S is output, each
100: * element of S is a power of the radix. If S is input, each element
101: * of S should be a power of the radix to ensure a reliable solution
102: * and error estimates. Scaling by powers of the radix does not cause
103: * rounding errors unless the result underflows or overflows.
104: * Rounding errors during scaling lead to refining with a matrix that
105: * is not equivalent to the input matrix, producing error estimates
106: * that may not be reliable.
107: *
108: * B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
109: * The right hand side matrix B.
110: *
111: * LDB (input) INTEGER
112: * The leading dimension of the array B. LDB >= max(1,N).
113: *
114: * X (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
115: * On entry, the solution matrix X, as computed by DGETRS.
116: * On exit, the improved solution matrix X.
117: *
118: * LDX (input) INTEGER
119: * The leading dimension of the array X. LDX >= max(1,N).
120: *
121: * RCOND (output) DOUBLE PRECISION
122: * Reciprocal scaled condition number. This is an estimate of the
123: * reciprocal Skeel condition number of the matrix A after
124: * equilibration (if done). If this is less than the machine
125: * precision (in particular, if it is zero), the matrix is singular
126: * to working precision. Note that the error may still be small even
127: * if this number is very small and the matrix appears ill-
128: * conditioned.
129: *
130: * BERR (output) DOUBLE PRECISION array, dimension (NRHS)
131: * Componentwise relative backward error. This is the
132: * componentwise relative backward error of each solution vector X(j)
133: * (i.e., the smallest relative change in any element of A or B that
134: * makes X(j) an exact solution).
135: *
136: * N_ERR_BNDS (input) INTEGER
137: * Number of error bounds to return for each right hand side
138: * and each type (normwise or componentwise). See ERR_BNDS_NORM and
139: * ERR_BNDS_COMP below.
140: *
141: * ERR_BNDS_NORM (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
142: * For each right-hand side, this array contains information about
143: * various error bounds and condition numbers corresponding to the
144: * normwise relative error, which is defined as follows:
145: *
146: * Normwise relative error in the ith solution vector:
147: * max_j (abs(XTRUE(j,i) - X(j,i)))
148: * ------------------------------
149: * max_j abs(X(j,i))
150: *
151: * The array is indexed by the type of error information as described
152: * below. There currently are up to three pieces of information
153: * returned.
154: *
155: * The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
156: * right-hand side.
157: *
158: * The second index in ERR_BNDS_NORM(:,err) contains the following
159: * three fields:
160: * err = 1 "Trust/don't trust" boolean. Trust the answer if the
161: * reciprocal condition number is less than the threshold
162: * sqrt(n) * dlamch('Epsilon').
163: *
164: * err = 2 "Guaranteed" error bound: The estimated forward error,
165: * almost certainly within a factor of 10 of the true error
166: * so long as the next entry is greater than the threshold
167: * sqrt(n) * dlamch('Epsilon'). This error bound should only
168: * be trusted if the previous boolean is true.
169: *
170: * err = 3 Reciprocal condition number: Estimated normwise
171: * reciprocal condition number. Compared with the threshold
172: * sqrt(n) * dlamch('Epsilon') to determine if the error
173: * estimate is "guaranteed". These reciprocal condition
174: * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
175: * appropriately scaled matrix Z.
176: * Let Z = S*A, where S scales each row by a power of the
177: * radix so all absolute row sums of Z are approximately 1.
178: *
179: * See Lapack Working Note 165 for further details and extra
180: * cautions.
181: *
182: * ERR_BNDS_COMP (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
183: * For each right-hand side, this array contains information about
184: * various error bounds and condition numbers corresponding to the
185: * componentwise relative error, which is defined as follows:
186: *
187: * Componentwise relative error in the ith solution vector:
188: * abs(XTRUE(j,i) - X(j,i))
189: * max_j ----------------------
190: * abs(X(j,i))
191: *
192: * The array is indexed by the right-hand side i (on which the
193: * componentwise relative error depends), and the type of error
194: * information as described below. There currently are up to three
195: * pieces of information returned for each right-hand side. If
196: * componentwise accuracy is not requested (PARAMS(3) = 0.0), then
197: * ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
198: * the first (:,N_ERR_BNDS) entries are returned.
199: *
200: * The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
201: * right-hand side.
202: *
203: * The second index in ERR_BNDS_COMP(:,err) contains the following
204: * three fields:
205: * err = 1 "Trust/don't trust" boolean. Trust the answer if the
206: * reciprocal condition number is less than the threshold
207: * sqrt(n) * dlamch('Epsilon').
208: *
209: * err = 2 "Guaranteed" error bound: The estimated forward error,
210: * almost certainly within a factor of 10 of the true error
211: * so long as the next entry is greater than the threshold
212: * sqrt(n) * dlamch('Epsilon'). This error bound should only
213: * be trusted if the previous boolean is true.
214: *
215: * err = 3 Reciprocal condition number: Estimated componentwise
216: * reciprocal condition number. Compared with the threshold
217: * sqrt(n) * dlamch('Epsilon') to determine if the error
218: * estimate is "guaranteed". These reciprocal condition
219: * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
220: * appropriately scaled matrix Z.
221: * Let Z = S*(A*diag(x)), where x is the solution for the
222: * current right-hand side and S scales each row of
223: * A*diag(x) by a power of the radix so all absolute row
224: * sums of Z are approximately 1.
225: *
226: * See Lapack Working Note 165 for further details and extra
227: * cautions.
228: *
229: * NPARAMS (input) INTEGER
230: * Specifies the number of parameters set in PARAMS. If .LE. 0, the
231: * PARAMS array is never referenced and default values are used.
232: *
233: * PARAMS (input / output) DOUBLE PRECISION array, dimension (NPARAMS)
234: * Specifies algorithm parameters. If an entry is .LT. 0.0, then
235: * that entry will be filled with default value used for that
236: * parameter. Only positions up to NPARAMS are accessed; defaults
237: * are used for higher-numbered parameters.
238: *
239: * PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
240: * refinement or not.
241: * Default: 1.0D+0
242: * = 0.0 : No refinement is performed, and no error bounds are
243: * computed.
244: * = 1.0 : Use the double-precision refinement algorithm,
245: * possibly with doubled-single computations if the
246: * compilation environment does not support DOUBLE
247: * PRECISION.
248: * (other values are reserved for future use)
249: *
250: * PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
251: * computations allowed for refinement.
252: * Default: 10
253: * Aggressive: Set to 100 to permit convergence using approximate
254: * factorizations or factorizations other than LU. If
255: * the factorization uses a technique other than
256: * Gaussian elimination, the guarantees in
257: * err_bnds_norm and err_bnds_comp may no longer be
258: * trustworthy.
259: *
260: * PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
261: * will attempt to find a solution with small componentwise
262: * relative error in the double-precision algorithm. Positive
263: * is true, 0.0 is false.
264: * Default: 1.0 (attempt componentwise convergence)
265: *
266: * WORK (workspace) DOUBLE PRECISION array, dimension (4*N)
267: *
268: * IWORK (workspace) INTEGER array, dimension (N)
269: *
270: * INFO (output) INTEGER
271: * = 0: Successful exit. The solution to every right-hand side is
272: * guaranteed.
273: * < 0: If INFO = -i, the i-th argument had an illegal value
274: * > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization
275: * has been completed, but the factor U is exactly singular, so
276: * the solution and error bounds could not be computed. RCOND = 0
277: * is returned.
278: * = N+J: The solution corresponding to the Jth right-hand side is
279: * not guaranteed. The solutions corresponding to other right-
280: * hand sides K with K > J may not be guaranteed as well, but
281: * only the first such right-hand side is reported. If a small
282: * componentwise error is not requested (PARAMS(3) = 0.0) then
283: * the Jth right-hand side is the first with a normwise error
284: * bound that is not guaranteed (the smallest J such
285: * that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
286: * the Jth right-hand side is the first with either a normwise or
287: * componentwise error bound that is not guaranteed (the smallest
288: * J such that either ERR_BNDS_NORM(J,1) = 0.0 or
289: * ERR_BNDS_COMP(J,1) = 0.0). See the definition of
290: * ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
291: * about all of the right-hand sides check ERR_BNDS_NORM or
292: * ERR_BNDS_COMP.
293: *
294: * ==================================================================
295: *
296: * .. Parameters ..
297: DOUBLE PRECISION ZERO, ONE
298: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
299: DOUBLE PRECISION ITREF_DEFAULT, ITHRESH_DEFAULT
300: DOUBLE PRECISION COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT
301: DOUBLE PRECISION DZTHRESH_DEFAULT
302: PARAMETER ( ITREF_DEFAULT = 1.0D+0 )
303: PARAMETER ( ITHRESH_DEFAULT = 10.0D+0 )
304: PARAMETER ( COMPONENTWISE_DEFAULT = 1.0D+0 )
305: PARAMETER ( RTHRESH_DEFAULT = 0.5D+0 )
306: PARAMETER ( DZTHRESH_DEFAULT = 0.25D+0 )
307: INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
308: $ LA_LINRX_CWISE_I
309: PARAMETER ( LA_LINRX_ITREF_I = 1,
310: $ LA_LINRX_ITHRESH_I = 2 )
311: PARAMETER ( LA_LINRX_CWISE_I = 3 )
312: INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
313: $ LA_LINRX_RCOND_I
314: PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
315: PARAMETER ( LA_LINRX_RCOND_I = 3 )
316: * ..
317: * .. Local Scalars ..
318: CHARACTER(1) NORM
319: LOGICAL RCEQU
320: INTEGER J, PREC_TYPE, REF_TYPE
321: INTEGER N_NORMS
322: DOUBLE PRECISION ANORM, RCOND_TMP
323: DOUBLE PRECISION ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
324: LOGICAL IGNORE_CWISE
325: INTEGER ITHRESH
326: DOUBLE PRECISION RTHRESH, UNSTABLE_THRESH
327: * ..
328: * .. External Subroutines ..
329: EXTERNAL XERBLA, DPOCON, DLA_PORFSX_EXTENDED
330: * ..
331: * .. Intrinsic Functions ..
332: INTRINSIC MAX, SQRT
333: * ..
334: * .. External Functions ..
335: EXTERNAL LSAME, BLAS_FPINFO_X, ILATRANS, ILAPREC
336: EXTERNAL DLAMCH, DLANSY, DLA_PORCOND
337: DOUBLE PRECISION DLAMCH, DLANSY, DLA_PORCOND
338: LOGICAL LSAME
339: INTEGER BLAS_FPINFO_X
340: INTEGER ILATRANS, ILAPREC
341: * ..
342: * .. Executable Statements ..
343: *
344: * Check the input parameters.
345: *
346: INFO = 0
347: REF_TYPE = INT( ITREF_DEFAULT )
348: IF ( NPARAMS .GE. LA_LINRX_ITREF_I ) THEN
349: IF ( PARAMS( LA_LINRX_ITREF_I ) .LT. 0.0D+0 ) THEN
350: PARAMS( LA_LINRX_ITREF_I ) = ITREF_DEFAULT
351: ELSE
352: REF_TYPE = PARAMS( LA_LINRX_ITREF_I )
353: END IF
354: END IF
355: *
356: * Set default parameters.
357: *
358: ILLRCOND_THRESH = DBLE( N ) * DLAMCH( 'Epsilon' )
359: ITHRESH = INT( ITHRESH_DEFAULT )
360: RTHRESH = RTHRESH_DEFAULT
361: UNSTABLE_THRESH = DZTHRESH_DEFAULT
362: IGNORE_CWISE = COMPONENTWISE_DEFAULT .EQ. 0.0D+0
363: *
364: IF ( NPARAMS.GE.LA_LINRX_ITHRESH_I ) THEN
365: IF ( PARAMS( LA_LINRX_ITHRESH_I ).LT.0.0D+0 ) THEN
366: PARAMS( LA_LINRX_ITHRESH_I ) = ITHRESH
367: ELSE
368: ITHRESH = INT( PARAMS( LA_LINRX_ITHRESH_I ) )
369: END IF
370: END IF
371: IF ( NPARAMS.GE.LA_LINRX_CWISE_I ) THEN
372: IF ( PARAMS( LA_LINRX_CWISE_I ).LT.0.0D+0 ) THEN
373: IF ( IGNORE_CWISE ) THEN
374: PARAMS( LA_LINRX_CWISE_I ) = 0.0D+0
375: ELSE
376: PARAMS( LA_LINRX_CWISE_I ) = 1.0D+0
377: END IF
378: ELSE
379: IGNORE_CWISE = PARAMS( LA_LINRX_CWISE_I ) .EQ. 0.0D+0
380: END IF
381: END IF
382: IF ( REF_TYPE .EQ. 0 .OR. N_ERR_BNDS .EQ. 0 ) THEN
383: N_NORMS = 0
384: ELSE IF ( IGNORE_CWISE ) THEN
385: N_NORMS = 1
386: ELSE
387: N_NORMS = 2
388: END IF
389: *
390: RCEQU = LSAME( EQUED, 'Y' )
391: *
392: * Test input parameters.
393: *
394: IF (.NOT.LSAME(UPLO, 'U') .AND. .NOT.LSAME(UPLO, 'L')) THEN
395: INFO = -1
396: ELSE IF( .NOT.RCEQU .AND. .NOT.LSAME( EQUED, 'N' ) ) THEN
397: INFO = -2
398: ELSE IF( N.LT.0 ) THEN
399: INFO = -3
400: ELSE IF( NRHS.LT.0 ) THEN
401: INFO = -4
402: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
403: INFO = -6
404: ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
405: INFO = -8
406: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
407: INFO = -11
408: ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
409: INFO = -13
410: END IF
411: IF( INFO.NE.0 ) THEN
412: CALL XERBLA( 'DPORFSX', -INFO )
413: RETURN
414: END IF
415: *
416: * Quick return if possible.
417: *
418: IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN
419: RCOND = 1.0D+0
420: DO J = 1, NRHS
421: BERR( J ) = 0.0D+0
422: IF ( N_ERR_BNDS .GE. 1 ) THEN
423: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
424: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
425: END IF
426: IF ( N_ERR_BNDS .GE. 2 ) THEN
427: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 0.0D+0
428: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 0.0D+0
429: END IF
430: IF ( N_ERR_BNDS .GE. 3 ) THEN
431: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 1.0D+0
432: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 1.0D+0
433: END IF
434: END DO
435: RETURN
436: END IF
437: *
438: * Default to failure.
439: *
440: RCOND = 0.0D+0
441: DO J = 1, NRHS
442: BERR( J ) = 1.0D+0
443: IF ( N_ERR_BNDS .GE. 1 ) THEN
444: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
445: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
446: END IF
447: IF ( N_ERR_BNDS .GE. 2 ) THEN
448: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
449: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
450: END IF
451: IF ( N_ERR_BNDS .GE. 3 ) THEN
452: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 0.0D+0
453: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 0.0D+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 = DLANSY( NORM, UPLO, N, A, LDA, WORK )
462: CALL DPOCON( UPLO, N, AF, LDAF, ANORM, RCOND, WORK,
463: $ IWORK, INFO )
464: *
465: * Perform refinement on each right-hand side
466: *
467: IF ( REF_TYPE .NE. 0 ) THEN
468:
469: PREC_TYPE = ILAPREC( 'E' )
470:
471: CALL DLA_PORFSX_EXTENDED( PREC_TYPE, UPLO, N,
472: $ NRHS, A, LDA, AF, LDAF, RCEQU, S, B,
473: $ LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM, ERR_BNDS_COMP,
474: $ WORK( N+1 ), WORK( 1 ), WORK( 2*N+1 ), WORK( 1 ), RCOND,
475: $ ITHRESH, RTHRESH, UNSTABLE_THRESH, IGNORE_CWISE,
476: $ INFO )
477: END IF
478:
479: ERR_LBND = MAX( 10.0D+0, SQRT( DBLE( N ) ) ) * DLAMCH( 'Epsilon' )
480: IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 1 ) THEN
481: *
482: * Compute scaled normwise condition number cond(A*C).
483: *
484: IF ( RCEQU ) THEN
485: RCOND_TMP = DLA_PORCOND( UPLO, N, A, LDA, AF, LDAF,
486: $ -1, S, INFO, WORK, IWORK )
487: ELSE
488: RCOND_TMP = DLA_PORCOND( UPLO, N, A, LDA, AF, LDAF,
489: $ 0, S, INFO, WORK, IWORK )
490: END IF
491: DO J = 1, NRHS
492: *
493: * Cap the error at 1.0.
494: *
495: IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
496: $ .AND. ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 )
497: $ ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
498: *
499: * Threshold the error (see LAWN).
500: *
501: IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN
502: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
503: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 0.0D+0
504: IF ( INFO .LE. N ) INFO = N + J
505: ELSE IF ( ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .LT. ERR_LBND )
506: $ THEN
507: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = ERR_LBND
508: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
509: END IF
510: *
511: * Save the condition number.
512: *
513: IF (N_ERR_BNDS .GE. LA_LINRX_RCOND_I) THEN
514: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = RCOND_TMP
515: END IF
516: END DO
517: END IF
518:
519: IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 2 ) THEN
520: *
521: * Compute componentwise condition number cond(A*diag(Y(:,J))) for
522: * each right-hand side using the current solution as an estimate of
523: * the true solution. If the componentwise error estimate is too
524: * large, then the solution is a lousy estimate of truth and the
525: * estimated RCOND may be too optimistic. To avoid misleading users,
526: * the inverse condition number is set to 0.0 when the estimated
527: * cwise error is at least CWISE_WRONG.
528: *
529: CWISE_WRONG = SQRT( DLAMCH( 'Epsilon' ) )
530: DO J = 1, NRHS
531: IF (ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .LT. CWISE_WRONG )
532: $ THEN
533: RCOND_TMP = DLA_PORCOND( UPLO, N, A, LDA, AF, LDAF, 1,
534: $ X( 1, J ), INFO, WORK, IWORK )
535: ELSE
536: RCOND_TMP = 0.0D+0
537: END IF
538: *
539: * Cap the error at 1.0.
540: *
541: IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
542: $ .AND. ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 )
543: $ ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
544: *
545: * Threshold the error (see LAWN).
546: *
547: IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN
548: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
549: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 0.0D+0
550: IF ( PARAMS( LA_LINRX_CWISE_I ) .EQ. 1.0D+0
551: $ .AND. INFO.LT.N + J ) INFO = N + J
552: ELSE IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I )
553: $ .LT. ERR_LBND ) THEN
554: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = ERR_LBND
555: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
556: END IF
557: *
558: * Save the condition number.
559: *
560: IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
561: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = RCOND_TMP
562: END IF
563:
564: END DO
565: END IF
566: *
567: RETURN
568: *
569: * End of DPORFSX
570: *
571: END
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