Annotation of rpl/lapack/lapack/zporfsx.f, revision 1.2
1.1 bertrand 1: SUBROUTINE ZPORFSX( 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, RWORK, 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: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
24: $ X( LDX, * ), WORK( * )
25: DOUBLE PRECISION RWORK( * ), S( * ), PARAMS(*), BERR( * ),
26: $ ERR_BNDS_NORM( NRHS, * ),
27: $ ERR_BNDS_COMP( NRHS, * )
28: * ..
29: *
30: * Purpose
31: * =======
32: *
33: * ZPORFSX improves the computed solution to a system of linear
34: * equations when the coefficient matrix is symmetric positive
35: * definite, and provides error bounds and backward error estimates
36: * for the solution. In addition to normwise error bound, the code
37: * provides maximum componentwise error bound if possible. See
38: * comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the
39: * error bounds.
40: *
41: * The original system of linear equations may have been equilibrated
42: * before calling this routine, as described by arguments EQUED and S
43: * below. In this case, the solution and error bounds returned are
44: * for the original unequilibrated system.
45: *
46: * Arguments
47: * =========
48: *
49: * Some optional parameters are bundled in the PARAMS array. These
50: * settings determine how refinement is performed, but often the
51: * defaults are acceptable. If the defaults are acceptable, users
52: * can pass NPARAMS = 0 which prevents the source code from accessing
53: * the PARAMS argument.
54: *
55: * UPLO (input) CHARACTER*1
56: * = 'U': Upper triangle of A is stored;
57: * = 'L': Lower triangle of A is stored.
58: *
59: * EQUED (input) CHARACTER*1
60: * Specifies the form of equilibration that was done to A
61: * before calling this routine. This is needed to compute
62: * the solution and error bounds correctly.
63: * = 'N': No equilibration
64: * = 'Y': Both row and column equilibration, i.e., A has been
65: * replaced by diag(S) * A * diag(S).
66: * The right hand side B has been changed accordingly.
67: *
68: * N (input) INTEGER
69: * The order of the matrix A. N >= 0.
70: *
71: * NRHS (input) INTEGER
72: * The number of right hand sides, i.e., the number of columns
73: * of the matrices B and X. NRHS >= 0.
74: *
75: * A (input) COMPLEX*16 array, dimension (LDA,N)
76: * The symmetric matrix A. If UPLO = 'U', the leading N-by-N
77: * upper triangular part of A contains the upper triangular part
78: * of the matrix A, and the strictly lower triangular part of A
79: * is not referenced. If UPLO = 'L', the leading N-by-N lower
80: * triangular part of A contains the lower triangular part of
81: * the matrix A, and the strictly upper triangular part of A is
82: * not referenced.
83: *
84: * LDA (input) INTEGER
85: * The leading dimension of the array A. LDA >= max(1,N).
86: *
87: * AF (input) COMPLEX*16 array, dimension (LDAF,N)
88: * The triangular factor U or L from the Cholesky factorization
89: * A = U**T*U or A = L*L**T, as computed by DPOTRF.
90: *
91: * LDAF (input) INTEGER
92: * The leading dimension of the array AF. LDAF >= max(1,N).
93: *
94: * S (input or output) DOUBLE PRECISION array, dimension (N)
95: * The row scale factors for A. If EQUED = 'Y', A is multiplied on
96: * the left and right by diag(S). S is an input argument if FACT =
97: * 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED
98: * = 'Y', each element of S must be positive. If S is output, each
99: * element of S is a power of the radix. If S is input, each element
100: * of S should be a power of the radix to ensure a reliable solution
101: * and error estimates. Scaling by powers of the radix does not cause
102: * rounding errors unless the result underflows or overflows.
103: * Rounding errors during scaling lead to refining with a matrix that
104: * is not equivalent to the input matrix, producing error estimates
105: * that may not be reliable.
106: *
107: * B (input) COMPLEX*16 array, dimension (LDB,NRHS)
108: * The right hand side matrix B.
109: *
110: * LDB (input) INTEGER
111: * The leading dimension of the array B. LDB >= max(1,N).
112: *
113: * X (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
114: * On entry, the solution matrix X, as computed by DGETRS.
115: * On exit, the improved solution matrix X.
116: *
117: * LDX (input) INTEGER
118: * The leading dimension of the array X. LDX >= max(1,N).
119: *
120: * RCOND (output) DOUBLE PRECISION
121: * Reciprocal scaled condition number. This is an estimate of the
122: * reciprocal Skeel condition number of the matrix A after
123: * equilibration (if done). If this is less than the machine
124: * precision (in particular, if it is zero), the matrix is singular
125: * to working precision. Note that the error may still be small even
126: * if this number is very small and the matrix appears ill-
127: * conditioned.
128: *
129: * BERR (output) DOUBLE PRECISION array, dimension (NRHS)
130: * Componentwise relative backward error. This is the
131: * componentwise relative backward error of each solution vector X(j)
132: * (i.e., the smallest relative change in any element of A or B that
133: * makes X(j) an exact solution).
134: *
135: * N_ERR_BNDS (input) INTEGER
136: * Number of error bounds to return for each right hand side
137: * and each type (normwise or componentwise). See ERR_BNDS_NORM and
138: * ERR_BNDS_COMP below.
139: *
140: * ERR_BNDS_NORM (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
141: * For each right-hand side, this array contains information about
142: * various error bounds and condition numbers corresponding to the
143: * normwise relative error, which is defined as follows:
144: *
145: * Normwise relative error in the ith solution vector:
146: * max_j (abs(XTRUE(j,i) - X(j,i)))
147: * ------------------------------
148: * max_j abs(X(j,i))
149: *
150: * The array is indexed by the type of error information as described
151: * below. There currently are up to three pieces of information
152: * returned.
153: *
154: * The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
155: * right-hand side.
156: *
157: * The second index in ERR_BNDS_NORM(:,err) contains the following
158: * three fields:
159: * err = 1 "Trust/don't trust" boolean. Trust the answer if the
160: * reciprocal condition number is less than the threshold
161: * sqrt(n) * dlamch('Epsilon').
162: *
163: * err = 2 "Guaranteed" error bound: The estimated forward error,
164: * almost certainly within a factor of 10 of the true error
165: * so long as the next entry is greater than the threshold
166: * sqrt(n) * dlamch('Epsilon'). This error bound should only
167: * be trusted if the previous boolean is true.
168: *
169: * err = 3 Reciprocal condition number: Estimated normwise
170: * reciprocal condition number. Compared with the threshold
171: * sqrt(n) * dlamch('Epsilon') to determine if the error
172: * estimate is "guaranteed". These reciprocal condition
173: * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
174: * appropriately scaled matrix Z.
175: * Let Z = S*A, where S scales each row by a power of the
176: * radix so all absolute row sums of Z are approximately 1.
177: *
178: * See Lapack Working Note 165 for further details and extra
179: * cautions.
180: *
181: * ERR_BNDS_COMP (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
182: * For each right-hand side, this array contains information about
183: * various error bounds and condition numbers corresponding to the
184: * componentwise relative error, which is defined as follows:
185: *
186: * Componentwise relative error in the ith solution vector:
187: * abs(XTRUE(j,i) - X(j,i))
188: * max_j ----------------------
189: * abs(X(j,i))
190: *
191: * The array is indexed by the right-hand side i (on which the
192: * componentwise relative error depends), and the type of error
193: * information as described below. There currently are up to three
194: * pieces of information returned for each right-hand side. If
195: * componentwise accuracy is not requested (PARAMS(3) = 0.0), then
196: * ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
197: * the first (:,N_ERR_BNDS) entries are returned.
198: *
199: * The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
200: * right-hand side.
201: *
202: * The second index in ERR_BNDS_COMP(:,err) contains the following
203: * three fields:
204: * err = 1 "Trust/don't trust" boolean. Trust the answer if the
205: * reciprocal condition number is less than the threshold
206: * sqrt(n) * dlamch('Epsilon').
207: *
208: * err = 2 "Guaranteed" error bound: The estimated forward error,
209: * almost certainly within a factor of 10 of the true error
210: * so long as the next entry is greater than the threshold
211: * sqrt(n) * dlamch('Epsilon'). This error bound should only
212: * be trusted if the previous boolean is true.
213: *
214: * err = 3 Reciprocal condition number: Estimated componentwise
215: * reciprocal condition number. Compared with the threshold
216: * sqrt(n) * dlamch('Epsilon') to determine if the error
217: * estimate is "guaranteed". These reciprocal condition
218: * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
219: * appropriately scaled matrix Z.
220: * Let Z = S*(A*diag(x)), where x is the solution for the
221: * current right-hand side and S scales each row of
222: * A*diag(x) by a power of the radix so all absolute row
223: * sums of Z are approximately 1.
224: *
225: * See Lapack Working Note 165 for further details and extra
226: * cautions.
227: *
228: * NPARAMS (input) INTEGER
229: * Specifies the number of parameters set in PARAMS. If .LE. 0, the
230: * PARAMS array is never referenced and default values are used.
231: *
232: * PARAMS (input / output) DOUBLE PRECISION array, dimension NPARAMS
233: * Specifies algorithm parameters. If an entry is .LT. 0.0, then
234: * that entry will be filled with default value used for that
235: * parameter. Only positions up to NPARAMS are accessed; defaults
236: * are used for higher-numbered parameters.
237: *
238: * PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
239: * refinement or not.
240: * Default: 1.0D+0
241: * = 0.0 : No refinement is performed, and no error bounds are
242: * computed.
243: * = 1.0 : Use the double-precision refinement algorithm,
244: * possibly with doubled-single computations if the
245: * compilation environment does not support DOUBLE
246: * PRECISION.
247: * (other values are reserved for future use)
248: *
249: * PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
250: * computations allowed for refinement.
251: * Default: 10
252: * Aggressive: Set to 100 to permit convergence using approximate
253: * factorizations or factorizations other than LU. If
254: * the factorization uses a technique other than
255: * Gaussian elimination, the guarantees in
256: * err_bnds_norm and err_bnds_comp may no longer be
257: * trustworthy.
258: *
259: * PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
260: * will attempt to find a solution with small componentwise
261: * relative error in the double-precision algorithm. Positive
262: * is true, 0.0 is false.
263: * Default: 1.0 (attempt componentwise convergence)
264: *
265: * WORK (workspace) COMPLEX*16 array, dimension (2*N)
266: *
267: * RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
268: *
269: * INFO (output) INTEGER
270: * = 0: Successful exit. The solution to every right-hand side is
271: * guaranteed.
272: * < 0: If INFO = -i, the i-th argument had an illegal value
273: * > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization
274: * has been completed, but the factor U is exactly singular, so
275: * the solution and error bounds could not be computed. RCOND = 0
276: * is returned.
277: * = N+J: The solution corresponding to the Jth right-hand side is
278: * not guaranteed. The solutions corresponding to other right-
279: * hand sides K with K > J may not be guaranteed as well, but
280: * only the first such right-hand side is reported. If a small
281: * componentwise error is not requested (PARAMS(3) = 0.0) then
282: * the Jth right-hand side is the first with a normwise error
283: * bound that is not guaranteed (the smallest J such
284: * that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
285: * the Jth right-hand side is the first with either a normwise or
286: * componentwise error bound that is not guaranteed (the smallest
287: * J such that either ERR_BNDS_NORM(J,1) = 0.0 or
288: * ERR_BNDS_COMP(J,1) = 0.0). See the definition of
289: * ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
290: * about all of the right-hand sides check ERR_BNDS_NORM or
291: * ERR_BNDS_COMP.
292: *
293: * ==================================================================
294: *
295: * .. Parameters ..
296: DOUBLE PRECISION ZERO, ONE
297: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
298: DOUBLE PRECISION ITREF_DEFAULT, ITHRESH_DEFAULT
299: DOUBLE PRECISION COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT
300: DOUBLE PRECISION DZTHRESH_DEFAULT
301: PARAMETER ( ITREF_DEFAULT = 1.0D+0 )
302: PARAMETER ( ITHRESH_DEFAULT = 10.0D+0 )
303: PARAMETER ( COMPONENTWISE_DEFAULT = 1.0D+0 )
304: PARAMETER ( RTHRESH_DEFAULT = 0.5D+0 )
305: PARAMETER ( DZTHRESH_DEFAULT = 0.25D+0 )
306: INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
307: $ LA_LINRX_CWISE_I
308: PARAMETER ( LA_LINRX_ITREF_I = 1,
309: $ LA_LINRX_ITHRESH_I = 2 )
310: PARAMETER ( LA_LINRX_CWISE_I = 3 )
311: INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
312: $ LA_LINRX_RCOND_I
313: PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
314: PARAMETER ( LA_LINRX_RCOND_I = 3 )
315: * ..
316: * .. Local Scalars ..
317: CHARACTER(1) NORM
318: LOGICAL RCEQU
319: INTEGER J, PREC_TYPE, REF_TYPE
320: INTEGER N_NORMS
321: DOUBLE PRECISION ANORM, RCOND_TMP
322: DOUBLE PRECISION ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
323: LOGICAL IGNORE_CWISE
324: INTEGER ITHRESH
325: DOUBLE PRECISION RTHRESH, UNSTABLE_THRESH
326: * ..
327: * .. External Subroutines ..
328: EXTERNAL XERBLA, ZPOCON, ZLA_PORFSX_EXTENDED
329: * ..
330: * .. Intrinsic Functions ..
331: INTRINSIC MAX, SQRT, TRANSFER
332: * ..
333: * .. External Functions ..
334: EXTERNAL LSAME, BLAS_FPINFO_X, ILATRANS, ILAPREC
335: EXTERNAL DLAMCH, ZLANHE, ZLA_PORCOND_X, ZLA_PORCOND_C
336: DOUBLE PRECISION DLAMCH, ZLANHE, ZLA_PORCOND_X, ZLA_PORCOND_C
337: LOGICAL LSAME
338: INTEGER BLAS_FPINFO_X
339: INTEGER ILATRANS, ILAPREC
340: * ..
341: * .. Executable Statements ..
342: *
343: * Check the input parameters.
344: *
345: INFO = 0
346: REF_TYPE = INT( ITREF_DEFAULT )
347: IF ( NPARAMS .GE. LA_LINRX_ITREF_I ) THEN
348: IF ( PARAMS( LA_LINRX_ITREF_I ) .LT. 0.0D+0 ) THEN
349: PARAMS( LA_LINRX_ITREF_I ) = ITREF_DEFAULT
350: ELSE
351: REF_TYPE = PARAMS( LA_LINRX_ITREF_I )
352: END IF
353: END IF
354: *
355: * Set default parameters.
356: *
357: ILLRCOND_THRESH = DBLE( N ) * DLAMCH( 'Epsilon' )
358: ITHRESH = INT( ITHRESH_DEFAULT )
359: RTHRESH = RTHRESH_DEFAULT
360: UNSTABLE_THRESH = DZTHRESH_DEFAULT
361: IGNORE_CWISE = COMPONENTWISE_DEFAULT .EQ. 0.0D+0
362: *
363: IF ( NPARAMS.GE.LA_LINRX_ITHRESH_I ) THEN
364: IF ( PARAMS(LA_LINRX_ITHRESH_I ).LT.0.0D+0 ) THEN
365: PARAMS( LA_LINRX_ITHRESH_I ) = ITHRESH
366: ELSE
367: ITHRESH = INT( PARAMS( LA_LINRX_ITHRESH_I ) )
368: END IF
369: END IF
370: IF ( NPARAMS.GE.LA_LINRX_CWISE_I ) THEN
371: IF ( PARAMS(LA_LINRX_CWISE_I ).LT.0.0D+0 ) THEN
372: IF ( IGNORE_CWISE ) THEN
373: PARAMS( LA_LINRX_CWISE_I ) = 0.0D+0
374: ELSE
375: PARAMS( LA_LINRX_CWISE_I ) = 1.0D+0
376: END IF
377: ELSE
378: IGNORE_CWISE = PARAMS( LA_LINRX_CWISE_I ) .EQ. 0.0D+0
379: END IF
380: END IF
381: IF ( REF_TYPE .EQ. 0 .OR. N_ERR_BNDS .EQ. 0 ) THEN
382: N_NORMS = 0
383: ELSE IF ( IGNORE_CWISE ) THEN
384: N_NORMS = 1
385: ELSE
386: N_NORMS = 2
387: END IF
388: *
389: RCEQU = LSAME( EQUED, 'Y' )
390: *
391: * Test input parameters.
392: *
393: IF (.NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
394: INFO = -1
395: ELSE IF( .NOT.RCEQU .AND. .NOT.LSAME( EQUED, 'N' ) ) THEN
396: INFO = -2
397: ELSE IF( N.LT.0 ) THEN
398: INFO = -3
399: ELSE IF( NRHS.LT.0 ) THEN
400: INFO = -4
401: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
402: INFO = -6
403: ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
404: INFO = -8
405: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
406: INFO = -11
407: ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
408: INFO = -13
409: END IF
410: IF( INFO.NE.0 ) THEN
411: CALL XERBLA( 'ZPORFSX', -INFO )
412: RETURN
413: END IF
414: *
415: * Quick return if possible.
416: *
417: IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN
418: RCOND = 1.0D+0
419: DO J = 1, NRHS
420: BERR( J ) = 0.0D+0
421: IF ( N_ERR_BNDS .GE. 1 ) THEN
422: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
423: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
424: END IF
425: IF ( N_ERR_BNDS .GE. 2 ) THEN
426: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 0.0D+0
427: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 0.0D+0
428: END IF
429: IF ( N_ERR_BNDS .GE. 3 ) THEN
430: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 1.0D+0
431: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 1.0D+0
432: END IF
433: END DO
434: RETURN
435: END IF
436: *
437: * Default to failure.
438: *
439: RCOND = 0.0D+0
440: DO J = 1, NRHS
441: BERR( J ) = 1.0D+0
442: IF ( N_ERR_BNDS .GE. 1 ) THEN
443: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
444: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
445: END IF
446: IF ( N_ERR_BNDS .GE. 2 ) THEN
447: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
448: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
449: END IF
450: IF ( N_ERR_BNDS .GE. 3 ) THEN
451: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 0.0D+0
452: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 0.0D+0
453: END IF
454: END DO
455: *
456: * Compute the norm of A and the reciprocal of the condition
457: * number of A.
458: *
459: NORM = 'I'
460: ANORM = ZLANHE( NORM, UPLO, N, A, LDA, RWORK )
461: CALL ZPOCON( UPLO, N, AF, LDAF, ANORM, RCOND, WORK, RWORK,
462: $ INFO )
463: *
464: * Perform refinement on each right-hand side
465: *
466: IF ( REF_TYPE .NE. 0 ) THEN
467:
468: PREC_TYPE = ILAPREC( 'E' )
469:
470: CALL ZLA_PORFSX_EXTENDED( PREC_TYPE, UPLO, N,
471: $ NRHS, A, LDA, AF, LDAF, RCEQU, S, B,
472: $ LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM, ERR_BNDS_COMP,
473: $ WORK, RWORK, WORK(N+1),
474: $ TRANSFER (RWORK(1:2*N), (/ (ZERO, ZERO) /), N), 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 = ZLA_PORCOND_C( UPLO, N, A, LDA, AF, LDAF,
486: $ S, .TRUE., INFO, WORK, RWORK )
487: ELSE
488: RCOND_TMP = ZLA_PORCOND_C( UPLO, N, A, LDA, AF, LDAF,
489: $ S, .FALSE., INFO, WORK, RWORK )
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:
517: END DO
518: END IF
519:
520: IF (N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 2) THEN
521: *
522: * Compute componentwise condition number cond(A*diag(Y(:,J))) for
523: * each right-hand side using the current solution as an estimate of
524: * the true solution. If the componentwise error estimate is too
525: * large, then the solution is a lousy estimate of truth and the
526: * estimated RCOND may be too optimistic. To avoid misleading users,
527: * the inverse condition number is set to 0.0 when the estimated
528: * cwise error is at least CWISE_WRONG.
529: *
530: CWISE_WRONG = SQRT( DLAMCH( 'Epsilon' ) )
531: DO J = 1, NRHS
532: IF (ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .LT. CWISE_WRONG )
533: $ THEN
534: RCOND_TMP = ZLA_PORCOND_X( UPLO, N, A, LDA, AF, LDAF,
535: $ X(1,J), INFO, WORK, RWORK )
536: ELSE
537: RCOND_TMP = 0.0D+0
538: END IF
539: *
540: * Cap the error at 1.0.
541: *
542: IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
543: $ .AND. ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 )
544: $ ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
545: *
546: * Threshold the error (see LAWN).
547: *
548: IF (RCOND_TMP .LT. ILLRCOND_THRESH) THEN
549: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
550: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 0.0D+0
551: IF ( PARAMS( LA_LINRX_CWISE_I ) .EQ. 1.0D+0
552: $ .AND. INFO.LT.N + J ) INFO = N + J
553: ELSE IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I )
554: $ .LT. ERR_LBND ) THEN
555: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = ERR_LBND
556: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
557: END IF
558: *
559: * Save the condition number.
560: *
561: IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
562: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = RCOND_TMP
563: END IF
564:
565: END DO
566: END IF
567: *
568: RETURN
569: *
570: * End of ZPORFSX
571: *
572: END
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