Annotation of rpl/lapack/lapack/zla_gerfsx_extended.f, revision 1.9
1.5 bertrand 1: *> \brief \b ZLA_GERFSX_EXTENDED
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZLA_GERFSX_EXTENDED + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_gerfsx_extended.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_gerfsx_extended.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gerfsx_extended.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLA_GERFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, NRHS, A,
22: * LDA, AF, LDAF, IPIV, COLEQU, C, B,
23: * LDB, Y, LDY, BERR_OUT, N_NORMS,
24: * ERRS_N, ERRS_C, RES, AYB, DY,
25: * Y_TAIL, RCOND, ITHRESH, RTHRESH,
26: * DZ_UB, IGNORE_CWISE, INFO )
27: *
28: * .. Scalar Arguments ..
29: * INTEGER INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
30: * $ TRANS_TYPE, N_NORMS
31: * LOGICAL COLEQU, IGNORE_CWISE
32: * INTEGER ITHRESH
33: * DOUBLE PRECISION RTHRESH, DZ_UB
34: * ..
35: * .. Array Arguments
36: * INTEGER IPIV( * )
37: * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
38: * $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
39: * DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ),
40: * $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * )
41: * ..
42: *
43: *
44: *> \par Purpose:
45: * =============
46: *>
47: *> \verbatim
48: *>
49: *> ZLA_GERFSX_EXTENDED improves the computed solution to a system of
50: *> linear equations by performing extra-precise iterative refinement
51: *> and provides error bounds and backward error estimates for the solution.
52: *> This subroutine is called by ZGERFSX to perform iterative refinement.
53: *> In addition to normwise error bound, the code provides maximum
54: *> componentwise error bound if possible. See comments for ERRS_N
55: *> and ERRS_C for details of the error bounds. Note that this
56: *> subroutine is only resonsible for setting the second fields of
57: *> ERRS_N and ERRS_C.
58: *> \endverbatim
59: *
60: * Arguments:
61: * ==========
62: *
63: *> \param[in] PREC_TYPE
64: *> \verbatim
65: *> PREC_TYPE is INTEGER
66: *> Specifies the intermediate precision to be used in refinement.
67: *> The value is defined by ILAPREC(P) where P is a CHARACTER and
68: *> P = 'S': Single
69: *> = 'D': Double
70: *> = 'I': Indigenous
71: *> = 'X', 'E': Extra
72: *> \endverbatim
73: *>
74: *> \param[in] TRANS_TYPE
75: *> \verbatim
76: *> TRANS_TYPE is INTEGER
77: *> Specifies the transposition operation on A.
78: *> The value is defined by ILATRANS(T) where T is a CHARACTER and
79: *> T = 'N': No transpose
80: *> = 'T': Transpose
81: *> = 'C': Conjugate transpose
82: *> \endverbatim
83: *>
84: *> \param[in] N
85: *> \verbatim
86: *> N is INTEGER
87: *> The number of linear equations, i.e., the order of the
88: *> matrix A. N >= 0.
89: *> \endverbatim
90: *>
91: *> \param[in] NRHS
92: *> \verbatim
93: *> NRHS is INTEGER
94: *> The number of right-hand-sides, i.e., the number of columns of the
95: *> matrix B.
96: *> \endverbatim
97: *>
98: *> \param[in] A
99: *> \verbatim
100: *> A is COMPLEX*16 array, dimension (LDA,N)
101: *> On entry, the N-by-N matrix A.
102: *> \endverbatim
103: *>
104: *> \param[in] LDA
105: *> \verbatim
106: *> LDA is INTEGER
107: *> The leading dimension of the array A. LDA >= max(1,N).
108: *> \endverbatim
109: *>
110: *> \param[in] AF
111: *> \verbatim
112: *> AF is COMPLEX*16 array, dimension (LDAF,N)
113: *> The factors L and U from the factorization
114: *> A = P*L*U as computed by ZGETRF.
115: *> \endverbatim
116: *>
117: *> \param[in] LDAF
118: *> \verbatim
119: *> LDAF is INTEGER
120: *> The leading dimension of the array AF. LDAF >= max(1,N).
121: *> \endverbatim
122: *>
123: *> \param[in] IPIV
124: *> \verbatim
125: *> IPIV is INTEGER array, dimension (N)
126: *> The pivot indices from the factorization A = P*L*U
127: *> as computed by ZGETRF; row i of the matrix was interchanged
128: *> with row IPIV(i).
129: *> \endverbatim
130: *>
131: *> \param[in] COLEQU
132: *> \verbatim
133: *> COLEQU is LOGICAL
134: *> If .TRUE. then column equilibration was done to A before calling
135: *> this routine. This is needed to compute the solution and error
136: *> bounds correctly.
137: *> \endverbatim
138: *>
139: *> \param[in] C
140: *> \verbatim
141: *> C is DOUBLE PRECISION array, dimension (N)
142: *> The column scale factors for A. If COLEQU = .FALSE., C
143: *> is not accessed. If C is input, each element of C should be a power
144: *> of the radix to ensure a reliable solution and error estimates.
145: *> Scaling by powers of the radix does not cause rounding errors unless
146: *> the result underflows or overflows. Rounding errors during scaling
147: *> lead to refining with a matrix that is not equivalent to the
148: *> input matrix, producing error estimates that may not be
149: *> reliable.
150: *> \endverbatim
151: *>
152: *> \param[in] B
153: *> \verbatim
154: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
155: *> The right-hand-side matrix B.
156: *> \endverbatim
157: *>
158: *> \param[in] LDB
159: *> \verbatim
160: *> LDB is INTEGER
161: *> The leading dimension of the array B. LDB >= max(1,N).
162: *> \endverbatim
163: *>
164: *> \param[in,out] Y
165: *> \verbatim
166: *> Y is COMPLEX*16 array, dimension (LDY,NRHS)
167: *> On entry, the solution matrix X, as computed by ZGETRS.
168: *> On exit, the improved solution matrix Y.
169: *> \endverbatim
170: *>
171: *> \param[in] LDY
172: *> \verbatim
173: *> LDY is INTEGER
174: *> The leading dimension of the array Y. LDY >= max(1,N).
175: *> \endverbatim
176: *>
177: *> \param[out] BERR_OUT
178: *> \verbatim
179: *> BERR_OUT is DOUBLE PRECISION array, dimension (NRHS)
180: *> On exit, BERR_OUT(j) contains the componentwise relative backward
181: *> error for right-hand-side j from the formula
182: *> max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
183: *> where abs(Z) is the componentwise absolute value of the matrix
184: *> or vector Z. This is computed by ZLA_LIN_BERR.
185: *> \endverbatim
186: *>
187: *> \param[in] N_NORMS
188: *> \verbatim
189: *> N_NORMS is INTEGER
190: *> Determines which error bounds to return (see ERRS_N
191: *> and ERRS_C).
192: *> If N_NORMS >= 1 return normwise error bounds.
193: *> If N_NORMS >= 2 return componentwise error bounds.
194: *> \endverbatim
195: *>
196: *> \param[in,out] ERRS_N
197: *> \verbatim
198: *> ERRS_N is DOUBLE PRECISION array, dimension
199: *> (NRHS, N_ERR_BNDS)
200: *> For each right-hand side, this array contains information about
201: *> various error bounds and condition numbers corresponding to the
202: *> normwise relative error, which is defined as follows:
203: *>
204: *> Normwise relative error in the ith solution vector:
205: *> max_j (abs(XTRUE(j,i) - X(j,i)))
206: *> ------------------------------
207: *> max_j abs(X(j,i))
208: *>
209: *> The array is indexed by the type of error information as described
210: *> below. There currently are up to three pieces of information
211: *> returned.
212: *>
213: *> The first index in ERRS_N(i,:) corresponds to the ith
214: *> right-hand side.
215: *>
216: *> The second index in ERRS_N(:,err) contains the following
217: *> three fields:
218: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
219: *> reciprocal condition number is less than the threshold
220: *> sqrt(n) * slamch('Epsilon').
221: *>
222: *> err = 2 "Guaranteed" error bound: The estimated forward error,
223: *> almost certainly within a factor of 10 of the true error
224: *> so long as the next entry is greater than the threshold
225: *> sqrt(n) * slamch('Epsilon'). This error bound should only
226: *> be trusted if the previous boolean is true.
227: *>
228: *> err = 3 Reciprocal condition number: Estimated normwise
229: *> reciprocal condition number. Compared with the threshold
230: *> sqrt(n) * slamch('Epsilon') to determine if the error
231: *> estimate is "guaranteed". These reciprocal condition
232: *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
233: *> appropriately scaled matrix Z.
234: *> Let Z = S*A, where S scales each row by a power of the
235: *> radix so all absolute row sums of Z are approximately 1.
236: *>
237: *> This subroutine is only responsible for setting the second field
238: *> above.
239: *> See Lapack Working Note 165 for further details and extra
240: *> cautions.
241: *> \endverbatim
242: *>
243: *> \param[in,out] ERRS_C
244: *> \verbatim
245: *> ERRS_C is DOUBLE PRECISION array, dimension
246: *> (NRHS, N_ERR_BNDS)
247: *> For each right-hand side, this array contains information about
248: *> various error bounds and condition numbers corresponding to the
249: *> componentwise relative error, which is defined as follows:
250: *>
251: *> Componentwise relative error in the ith solution vector:
252: *> abs(XTRUE(j,i) - X(j,i))
253: *> max_j ----------------------
254: *> abs(X(j,i))
255: *>
256: *> The array is indexed by the right-hand side i (on which the
257: *> componentwise relative error depends), and the type of error
258: *> information as described below. There currently are up to three
259: *> pieces of information returned for each right-hand side. If
260: *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
261: *> ERRS_C is not accessed. If N_ERR_BNDS .LT. 3, then at most
262: *> the first (:,N_ERR_BNDS) entries are returned.
263: *>
264: *> The first index in ERRS_C(i,:) corresponds to the ith
265: *> right-hand side.
266: *>
267: *> The second index in ERRS_C(:,err) contains the following
268: *> three fields:
269: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
270: *> reciprocal condition number is less than the threshold
271: *> sqrt(n) * slamch('Epsilon').
272: *>
273: *> err = 2 "Guaranteed" error bound: The estimated forward error,
274: *> almost certainly within a factor of 10 of the true error
275: *> so long as the next entry is greater than the threshold
276: *> sqrt(n) * slamch('Epsilon'). This error bound should only
277: *> be trusted if the previous boolean is true.
278: *>
279: *> err = 3 Reciprocal condition number: Estimated componentwise
280: *> reciprocal condition number. Compared with the threshold
281: *> sqrt(n) * slamch('Epsilon') to determine if the error
282: *> estimate is "guaranteed". These reciprocal condition
283: *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
284: *> appropriately scaled matrix Z.
285: *> Let Z = S*(A*diag(x)), where x is the solution for the
286: *> current right-hand side and S scales each row of
287: *> A*diag(x) by a power of the radix so all absolute row
288: *> sums of Z are approximately 1.
289: *>
290: *> This subroutine is only responsible for setting the second field
291: *> above.
292: *> See Lapack Working Note 165 for further details and extra
293: *> cautions.
294: *> \endverbatim
295: *>
296: *> \param[in] RES
297: *> \verbatim
298: *> RES is COMPLEX*16 array, dimension (N)
299: *> Workspace to hold the intermediate residual.
300: *> \endverbatim
301: *>
302: *> \param[in] AYB
303: *> \verbatim
304: *> AYB is DOUBLE PRECISION array, dimension (N)
305: *> Workspace.
306: *> \endverbatim
307: *>
308: *> \param[in] DY
309: *> \verbatim
310: *> DY is COMPLEX*16 array, dimension (N)
311: *> Workspace to hold the intermediate solution.
312: *> \endverbatim
313: *>
314: *> \param[in] Y_TAIL
315: *> \verbatim
316: *> Y_TAIL is COMPLEX*16 array, dimension (N)
317: *> Workspace to hold the trailing bits of the intermediate solution.
318: *> \endverbatim
319: *>
320: *> \param[in] RCOND
321: *> \verbatim
322: *> RCOND is DOUBLE PRECISION
323: *> Reciprocal scaled condition number. This is an estimate of the
324: *> reciprocal Skeel condition number of the matrix A after
325: *> equilibration (if done). If this is less than the machine
326: *> precision (in particular, if it is zero), the matrix is singular
327: *> to working precision. Note that the error may still be small even
328: *> if this number is very small and the matrix appears ill-
329: *> conditioned.
330: *> \endverbatim
331: *>
332: *> \param[in] ITHRESH
333: *> \verbatim
334: *> ITHRESH is INTEGER
335: *> The maximum number of residual computations allowed for
336: *> refinement. The default is 10. For 'aggressive' set to 100 to
337: *> permit convergence using approximate factorizations or
338: *> factorizations other than LU. If the factorization uses a
339: *> technique other than Gaussian elimination, the guarantees in
340: *> ERRS_N and ERRS_C may no longer be trustworthy.
341: *> \endverbatim
342: *>
343: *> \param[in] RTHRESH
344: *> \verbatim
345: *> RTHRESH is DOUBLE PRECISION
346: *> Determines when to stop refinement if the error estimate stops
347: *> decreasing. Refinement will stop when the next solution no longer
348: *> satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is
349: *> the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The
350: *> default value is 0.5. For 'aggressive' set to 0.9 to permit
351: *> convergence on extremely ill-conditioned matrices. See LAWN 165
352: *> for more details.
353: *> \endverbatim
354: *>
355: *> \param[in] DZ_UB
356: *> \verbatim
357: *> DZ_UB is DOUBLE PRECISION
358: *> Determines when to start considering componentwise convergence.
359: *> Componentwise convergence is only considered after each component
360: *> of the solution Y is stable, which we definte as the relative
361: *> change in each component being less than DZ_UB. The default value
362: *> is 0.25, requiring the first bit to be stable. See LAWN 165 for
363: *> more details.
364: *> \endverbatim
365: *>
366: *> \param[in] IGNORE_CWISE
367: *> \verbatim
368: *> IGNORE_CWISE is LOGICAL
369: *> If .TRUE. then ignore componentwise convergence. Default value
370: *> is .FALSE..
371: *> \endverbatim
372: *>
373: *> \param[out] INFO
374: *> \verbatim
375: *> INFO is INTEGER
376: *> = 0: Successful exit.
377: *> < 0: if INFO = -i, the ith argument to ZGETRS had an illegal
378: *> value
379: *> \endverbatim
380: *
381: * Authors:
382: * ========
383: *
384: *> \author Univ. of Tennessee
385: *> \author Univ. of California Berkeley
386: *> \author Univ. of Colorado Denver
387: *> \author NAG Ltd.
388: *
389: *> \date November 2011
390: *
391: *> \ingroup complex16GEcomputational
392: *
393: * =====================================================================
1.1 bertrand 394: SUBROUTINE ZLA_GERFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, NRHS, A,
395: $ LDA, AF, LDAF, IPIV, COLEQU, C, B,
396: $ LDB, Y, LDY, BERR_OUT, N_NORMS,
397: $ ERRS_N, ERRS_C, RES, AYB, DY,
398: $ Y_TAIL, RCOND, ITHRESH, RTHRESH,
399: $ DZ_UB, IGNORE_CWISE, INFO )
400: *
1.5 bertrand 401: * -- LAPACK computational routine (version 3.4.0) --
402: * -- LAPACK is a software package provided by Univ. of Tennessee, --
403: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
404: * November 2011
1.1 bertrand 405: *
406: * .. Scalar Arguments ..
407: INTEGER INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
408: $ TRANS_TYPE, N_NORMS
409: LOGICAL COLEQU, IGNORE_CWISE
410: INTEGER ITHRESH
411: DOUBLE PRECISION RTHRESH, DZ_UB
412: * ..
413: * .. Array Arguments
414: INTEGER IPIV( * )
415: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
416: $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
417: DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ),
418: $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * )
419: * ..
420: *
421: * =====================================================================
422: *
423: * .. Local Scalars ..
424: CHARACTER TRANS
425: INTEGER CNT, I, J, X_STATE, Z_STATE, Y_PREC_STATE
426: DOUBLE PRECISION YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT,
427: $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX,
428: $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z,
429: $ EPS, HUGEVAL, INCR_THRESH
430: LOGICAL INCR_PREC
431: COMPLEX*16 ZDUM
432: * ..
433: * .. Parameters ..
434: INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE,
435: $ NOPROG_STATE, BASE_RESIDUAL, EXTRA_RESIDUAL,
436: $ EXTRA_Y
437: PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1,
438: $ CONV_STATE = 2,
439: $ NOPROG_STATE = 3 )
440: PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1,
441: $ EXTRA_Y = 2 )
442: INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
443: INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
444: INTEGER CMP_ERR_I, PIV_GROWTH_I
445: PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2,
446: $ BERR_I = 3 )
447: PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 )
448: PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8,
449: $ PIV_GROWTH_I = 9 )
450: INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
451: $ LA_LINRX_CWISE_I
452: PARAMETER ( LA_LINRX_ITREF_I = 1,
453: $ LA_LINRX_ITHRESH_I = 2 )
454: PARAMETER ( LA_LINRX_CWISE_I = 3 )
455: INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
456: $ LA_LINRX_RCOND_I
457: PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
458: PARAMETER ( LA_LINRX_RCOND_I = 3 )
459: * ..
460: * .. External Subroutines ..
461: EXTERNAL ZAXPY, ZCOPY, ZGETRS, ZGEMV, BLAS_ZGEMV_X,
462: $ BLAS_ZGEMV2_X, ZLA_GEAMV, ZLA_WWADDW, DLAMCH,
463: $ CHLA_TRANSTYPE, ZLA_LIN_BERR
464: DOUBLE PRECISION DLAMCH
465: CHARACTER CHLA_TRANSTYPE
466: * ..
467: * .. Intrinsic Functions ..
468: INTRINSIC ABS, MAX, MIN
469: * ..
470: * .. Statement Functions ..
471: DOUBLE PRECISION CABS1
472: * ..
473: * .. Statement Function Definitions ..
474: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
475: * ..
476: * .. Executable Statements ..
477: *
478: IF ( INFO.NE.0 ) RETURN
479: TRANS = CHLA_TRANSTYPE(TRANS_TYPE)
480: EPS = DLAMCH( 'Epsilon' )
481: HUGEVAL = DLAMCH( 'Overflow' )
482: * Force HUGEVAL to Inf
483: HUGEVAL = HUGEVAL * HUGEVAL
484: * Using HUGEVAL may lead to spurious underflows.
485: INCR_THRESH = DBLE( N ) * EPS
486: *
487: DO J = 1, NRHS
488: Y_PREC_STATE = EXTRA_RESIDUAL
489: IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN
490: DO I = 1, N
491: Y_TAIL( I ) = 0.0D+0
492: END DO
493: END IF
494:
495: DXRAT = 0.0D+0
496: DXRATMAX = 0.0D+0
497: DZRAT = 0.0D+0
498: DZRATMAX = 0.0D+0
499: FINAL_DX_X = HUGEVAL
500: FINAL_DZ_Z = HUGEVAL
501: PREVNORMDX = HUGEVAL
502: PREV_DZ_Z = HUGEVAL
503: DZ_Z = HUGEVAL
504: DX_X = HUGEVAL
505:
506: X_STATE = WORKING_STATE
507: Z_STATE = UNSTABLE_STATE
508: INCR_PREC = .FALSE.
509:
510: DO CNT = 1, ITHRESH
511: *
512: * Compute residual RES = B_s - op(A_s) * Y,
513: * op(A) = A, A**T, or A**H depending on TRANS (and type).
514: *
515: CALL ZCOPY( N, B( 1, J ), 1, RES, 1 )
516: IF ( Y_PREC_STATE .EQ. BASE_RESIDUAL ) THEN
517: CALL ZGEMV( TRANS, N, N, (-1.0D+0,0.0D+0), A, LDA,
518: $ Y( 1, J ), 1, (1.0D+0,0.0D+0), RES, 1)
519: ELSE IF (Y_PREC_STATE .EQ. EXTRA_RESIDUAL) THEN
520: CALL BLAS_ZGEMV_X( TRANS_TYPE, N, N, (-1.0D+0,0.0D+0), A,
521: $ LDA, Y( 1, J ), 1, (1.0D+0,0.0D+0),
522: $ RES, 1, PREC_TYPE )
523: ELSE
524: CALL BLAS_ZGEMV2_X( TRANS_TYPE, N, N, (-1.0D+0,0.0D+0),
525: $ A, LDA, Y(1, J), Y_TAIL, 1, (1.0D+0,0.0D+0), RES, 1,
526: $ PREC_TYPE)
527: END IF
528:
529: ! XXX: RES is no longer needed.
530: CALL ZCOPY( N, RES, 1, DY, 1 )
531: CALL ZGETRS( TRANS, N, 1, AF, LDAF, IPIV, DY, N, INFO )
532: *
533: * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
534: *
535: NORMX = 0.0D+0
536: NORMY = 0.0D+0
537: NORMDX = 0.0D+0
538: DZ_Z = 0.0D+0
539: YMIN = HUGEVAL
540: *
541: DO I = 1, N
542: YK = CABS1( Y( I, J ) )
543: DYK = CABS1( DY( I ) )
544:
545: IF ( YK .NE. 0.0D+0 ) THEN
546: DZ_Z = MAX( DZ_Z, DYK / YK )
547: ELSE IF ( DYK .NE. 0.0D+0 ) THEN
548: DZ_Z = HUGEVAL
549: END IF
550:
551: YMIN = MIN( YMIN, YK )
552:
553: NORMY = MAX( NORMY, YK )
554:
555: IF ( COLEQU ) THEN
556: NORMX = MAX( NORMX, YK * C( I ) )
557: NORMDX = MAX( NORMDX, DYK * C( I ) )
558: ELSE
559: NORMX = NORMY
560: NORMDX = MAX(NORMDX, DYK)
561: END IF
562: END DO
563:
564: IF ( NORMX .NE. 0.0D+0 ) THEN
565: DX_X = NORMDX / NORMX
566: ELSE IF ( NORMDX .EQ. 0.0D+0 ) THEN
567: DX_X = 0.0D+0
568: ELSE
569: DX_X = HUGEVAL
570: END IF
571:
572: DXRAT = NORMDX / PREVNORMDX
573: DZRAT = DZ_Z / PREV_DZ_Z
574: *
575: * Check termination criteria
576: *
577: IF (.NOT.IGNORE_CWISE
578: $ .AND. YMIN*RCOND .LT. INCR_THRESH*NORMY
579: $ .AND. Y_PREC_STATE .LT. EXTRA_Y )
580: $ INCR_PREC = .TRUE.
581:
582: IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH )
583: $ X_STATE = WORKING_STATE
584: IF ( X_STATE .EQ. WORKING_STATE ) THEN
585: IF (DX_X .LE. EPS) THEN
586: X_STATE = CONV_STATE
587: ELSE IF ( DXRAT .GT. RTHRESH ) THEN
588: IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
589: INCR_PREC = .TRUE.
590: ELSE
591: X_STATE = NOPROG_STATE
592: END IF
593: ELSE
594: IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT
595: END IF
596: IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X
597: END IF
598:
599: IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB )
600: $ Z_STATE = WORKING_STATE
601: IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH )
602: $ Z_STATE = WORKING_STATE
603: IF ( Z_STATE .EQ. WORKING_STATE ) THEN
604: IF ( DZ_Z .LE. EPS ) THEN
605: Z_STATE = CONV_STATE
606: ELSE IF ( DZ_Z .GT. DZ_UB ) THEN
607: Z_STATE = UNSTABLE_STATE
608: DZRATMAX = 0.0D+0
609: FINAL_DZ_Z = HUGEVAL
610: ELSE IF ( DZRAT .GT. RTHRESH ) THEN
611: IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
612: INCR_PREC = .TRUE.
613: ELSE
614: Z_STATE = NOPROG_STATE
615: END IF
616: ELSE
617: IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT
618: END IF
619: IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
620: END IF
621: *
622: * Exit if both normwise and componentwise stopped working,
623: * but if componentwise is unstable, let it go at least two
624: * iterations.
625: *
626: IF ( X_STATE.NE.WORKING_STATE ) THEN
627: IF ( IGNORE_CWISE ) GOTO 666
628: IF ( Z_STATE.EQ.NOPROG_STATE .OR. Z_STATE.EQ.CONV_STATE )
629: $ GOTO 666
630: IF ( Z_STATE.EQ.UNSTABLE_STATE .AND. CNT.GT.1 ) GOTO 666
631: END IF
632:
633: IF ( INCR_PREC ) THEN
634: INCR_PREC = .FALSE.
635: Y_PREC_STATE = Y_PREC_STATE + 1
636: DO I = 1, N
637: Y_TAIL( I ) = 0.0D+0
638: END DO
639: END IF
640:
641: PREVNORMDX = NORMDX
642: PREV_DZ_Z = DZ_Z
643: *
644: * Update soluton.
645: *
646: IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
647: CALL ZAXPY( N, (1.0D+0,0.0D+0), DY, 1, Y(1,J), 1 )
648: ELSE
649: CALL ZLA_WWADDW( N, Y( 1, J ), Y_TAIL, DY )
650: END IF
651:
652: END DO
653: * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT.
654: 666 CONTINUE
655: *
656: * Set final_* when cnt hits ithresh
657: *
658: IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X
659: IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
660: *
661: * Compute error bounds
662: *
663: IF (N_NORMS .GE. 1) THEN
664: ERRS_N( J, LA_LINRX_ERR_I ) = FINAL_DX_X / (1 - DXRATMAX)
665:
666: END IF
667: IF ( N_NORMS .GE. 2 ) THEN
668: ERRS_C( J, LA_LINRX_ERR_I ) = FINAL_DZ_Z / (1 - DZRATMAX)
669: END IF
670: *
671: * Compute componentwise relative backward error from formula
672: * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
673: * where abs(Z) is the componentwise absolute value of the matrix
674: * or vector Z.
675: *
676: * Compute residual RES = B_s - op(A_s) * Y,
677: * op(A) = A, A**T, or A**H depending on TRANS (and type).
678: *
679: CALL ZCOPY( N, B( 1, J ), 1, RES, 1 )
680: CALL ZGEMV( TRANS, N, N, (-1.0D+0,0.0D+0), A, LDA, Y(1,J), 1,
681: $ (1.0D+0,0.0D+0), RES, 1 )
682:
683: DO I = 1, N
684: AYB( I ) = CABS1( B( I, J ) )
685: END DO
686: *
687: * Compute abs(op(A_s))*abs(Y) + abs(B_s).
688: *
689: CALL ZLA_GEAMV ( TRANS_TYPE, N, N, 1.0D+0,
690: $ A, LDA, Y(1, J), 1, 1.0D+0, AYB, 1 )
691:
692: CALL ZLA_LIN_BERR ( N, N, 1, RES, AYB, BERR_OUT( J ) )
693: *
694: * End of loop for each RHS.
695: *
696: END DO
697: *
698: RETURN
699: END
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