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
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11: *> [TGZ]</a>
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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 responsible 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 P
68: *> = 'S': Single
69: *> = 'D': Double
70: *> = 'I': Indigenous
71: *> = 'X' or '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 T
79: *> = '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 (NRHS, N_ERR_BNDS)
199: *> For each right-hand side, this array contains information about
200: *> various error bounds and condition numbers corresponding to the
201: *> normwise relative error, which is defined as follows:
202: *>
203: *> Normwise relative error in the ith solution vector:
204: *> max_j (abs(XTRUE(j,i) - X(j,i)))
205: *> ------------------------------
206: *> max_j abs(X(j,i))
207: *>
208: *> The array is indexed by the type of error information as described
209: *> below. There currently are up to three pieces of information
210: *> returned.
211: *>
212: *> The first index in ERRS_N(i,:) corresponds to the ith
213: *> right-hand side.
214: *>
215: *> The second index in ERRS_N(:,err) contains the following
216: *> three fields:
217: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
218: *> reciprocal condition number is less than the threshold
219: *> sqrt(n) * slamch('Epsilon').
220: *>
221: *> err = 2 "Guaranteed" error bound: The estimated forward error,
222: *> almost certainly within a factor of 10 of the true error
223: *> so long as the next entry is greater than the threshold
224: *> sqrt(n) * slamch('Epsilon'). This error bound should only
225: *> be trusted if the previous boolean is true.
226: *>
227: *> err = 3 Reciprocal condition number: Estimated normwise
228: *> reciprocal condition number. Compared with the threshold
229: *> sqrt(n) * slamch('Epsilon') to determine if the error
230: *> estimate is "guaranteed". These reciprocal condition
231: *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
232: *> appropriately scaled matrix Z.
233: *> Let Z = S*A, where S scales each row by a power of the
234: *> radix so all absolute row sums of Z are approximately 1.
235: *>
236: *> This subroutine is only responsible for setting the second field
237: *> above.
238: *> See Lapack Working Note 165 for further details and extra
239: *> cautions.
240: *> \endverbatim
241: *>
242: *> \param[in,out] ERRS_C
243: *> \verbatim
244: *> ERRS_C is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
245: *> For each right-hand side, this array contains information about
246: *> various error bounds and condition numbers corresponding to the
247: *> componentwise relative error, which is defined as follows:
248: *>
249: *> Componentwise relative error in the ith solution vector:
250: *> abs(XTRUE(j,i) - X(j,i))
251: *> max_j ----------------------
252: *> abs(X(j,i))
253: *>
254: *> The array is indexed by the right-hand side i (on which the
255: *> componentwise relative error depends), and the type of error
256: *> information as described below. There currently are up to three
257: *> pieces of information returned for each right-hand side. If
258: *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
259: *> ERRS_C is not accessed. If N_ERR_BNDS < 3, then at most
260: *> the first (:,N_ERR_BNDS) entries are returned.
261: *>
262: *> The first index in ERRS_C(i,:) corresponds to the ith
263: *> right-hand side.
264: *>
265: *> The second index in ERRS_C(:,err) contains the following
266: *> three fields:
267: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
268: *> reciprocal condition number is less than the threshold
269: *> sqrt(n) * slamch('Epsilon').
270: *>
271: *> err = 2 "Guaranteed" error bound: The estimated forward error,
272: *> almost certainly within a factor of 10 of the true error
273: *> so long as the next entry is greater than the threshold
274: *> sqrt(n) * slamch('Epsilon'). This error bound should only
275: *> be trusted if the previous boolean is true.
276: *>
277: *> err = 3 Reciprocal condition number: Estimated componentwise
278: *> reciprocal condition number. Compared with the threshold
279: *> sqrt(n) * slamch('Epsilon') to determine if the error
280: *> estimate is "guaranteed". These reciprocal condition
281: *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
282: *> appropriately scaled matrix Z.
283: *> Let Z = S*(A*diag(x)), where x is the solution for the
284: *> current right-hand side and S scales each row of
285: *> A*diag(x) by a power of the radix so all absolute row
286: *> sums of Z are approximately 1.
287: *>
288: *> This subroutine is only responsible for setting the second field
289: *> above.
290: *> See Lapack Working Note 165 for further details and extra
291: *> cautions.
292: *> \endverbatim
293: *>
294: *> \param[in] RES
295: *> \verbatim
296: *> RES is COMPLEX*16 array, dimension (N)
297: *> Workspace to hold the intermediate residual.
298: *> \endverbatim
299: *>
300: *> \param[in] AYB
301: *> \verbatim
302: *> AYB is DOUBLE PRECISION array, dimension (N)
303: *> Workspace.
304: *> \endverbatim
305: *>
306: *> \param[in] DY
307: *> \verbatim
308: *> DY is COMPLEX*16 array, dimension (N)
309: *> Workspace to hold the intermediate solution.
310: *> \endverbatim
311: *>
312: *> \param[in] Y_TAIL
313: *> \verbatim
314: *> Y_TAIL is COMPLEX*16 array, dimension (N)
315: *> Workspace to hold the trailing bits of the intermediate solution.
316: *> \endverbatim
317: *>
318: *> \param[in] RCOND
319: *> \verbatim
320: *> RCOND is DOUBLE PRECISION
321: *> Reciprocal scaled condition number. This is an estimate of the
322: *> reciprocal Skeel condition number of the matrix A after
323: *> equilibration (if done). If this is less than the machine
324: *> precision (in particular, if it is zero), the matrix is singular
325: *> to working precision. Note that the error may still be small even
326: *> if this number is very small and the matrix appears ill-
327: *> conditioned.
328: *> \endverbatim
329: *>
330: *> \param[in] ITHRESH
331: *> \verbatim
332: *> ITHRESH is INTEGER
333: *> The maximum number of residual computations allowed for
334: *> refinement. The default is 10. For 'aggressive' set to 100 to
335: *> permit convergence using approximate factorizations or
336: *> factorizations other than LU. If the factorization uses a
337: *> technique other than Gaussian elimination, the guarantees in
338: *> ERRS_N and ERRS_C may no longer be trustworthy.
339: *> \endverbatim
340: *>
341: *> \param[in] RTHRESH
342: *> \verbatim
343: *> RTHRESH is DOUBLE PRECISION
344: *> Determines when to stop refinement if the error estimate stops
345: *> decreasing. Refinement will stop when the next solution no longer
346: *> satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is
347: *> the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The
348: *> default value is 0.5. For 'aggressive' set to 0.9 to permit
349: *> convergence on extremely ill-conditioned matrices. See LAWN 165
350: *> for more details.
351: *> \endverbatim
352: *>
353: *> \param[in] DZ_UB
354: *> \verbatim
355: *> DZ_UB is DOUBLE PRECISION
356: *> Determines when to start considering componentwise convergence.
357: *> Componentwise convergence is only considered after each component
358: *> of the solution Y is stable, which we define as the relative
359: *> change in each component being less than DZ_UB. The default value
360: *> is 0.25, requiring the first bit to be stable. See LAWN 165 for
361: *> more details.
362: *> \endverbatim
363: *>
364: *> \param[in] IGNORE_CWISE
365: *> \verbatim
366: *> IGNORE_CWISE is LOGICAL
367: *> If .TRUE. then ignore componentwise convergence. Default value
368: *> is .FALSE..
369: *> \endverbatim
370: *>
371: *> \param[out] INFO
372: *> \verbatim
373: *> INFO is INTEGER
374: *> = 0: Successful exit.
375: *> < 0: if INFO = -i, the ith argument to ZGETRS had an illegal
376: *> value
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 complex16GEcomputational
388: *
389: * =====================================================================
390: SUBROUTINE ZLA_GERFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, NRHS, A,
391: $ LDA, AF, LDAF, IPIV, COLEQU, C, B,
392: $ LDB, Y, LDY, BERR_OUT, N_NORMS,
393: $ ERRS_N, ERRS_C, RES, AYB, DY,
394: $ Y_TAIL, RCOND, ITHRESH, RTHRESH,
395: $ DZ_UB, IGNORE_CWISE, INFO )
396: *
397: * -- LAPACK computational routine --
398: * -- LAPACK is a software package provided by Univ. of Tennessee, --
399: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
400: *
401: * .. Scalar Arguments ..
402: INTEGER INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
403: $ TRANS_TYPE, N_NORMS
404: LOGICAL COLEQU, IGNORE_CWISE
405: INTEGER ITHRESH
406: DOUBLE PRECISION RTHRESH, DZ_UB
407: * ..
408: * .. Array Arguments
409: INTEGER IPIV( * )
410: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
411: $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
412: DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ),
413: $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * )
414: * ..
415: *
416: * =====================================================================
417: *
418: * .. Local Scalars ..
419: CHARACTER TRANS
420: INTEGER CNT, I, J, X_STATE, Z_STATE, Y_PREC_STATE
421: DOUBLE PRECISION YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT,
422: $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX,
423: $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z,
424: $ EPS, HUGEVAL, INCR_THRESH
425: LOGICAL INCR_PREC
426: COMPLEX*16 ZDUM
427: * ..
428: * .. Parameters ..
429: INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE,
430: $ NOPROG_STATE, BASE_RESIDUAL, EXTRA_RESIDUAL,
431: $ EXTRA_Y
432: PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1,
433: $ CONV_STATE = 2,
434: $ NOPROG_STATE = 3 )
435: PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1,
436: $ EXTRA_Y = 2 )
437: INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
438: INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
439: INTEGER CMP_ERR_I, PIV_GROWTH_I
440: PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2,
441: $ BERR_I = 3 )
442: PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 )
443: PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8,
444: $ PIV_GROWTH_I = 9 )
445: INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
446: $ LA_LINRX_CWISE_I
447: PARAMETER ( LA_LINRX_ITREF_I = 1,
448: $ LA_LINRX_ITHRESH_I = 2 )
449: PARAMETER ( LA_LINRX_CWISE_I = 3 )
450: INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
451: $ LA_LINRX_RCOND_I
452: PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
453: PARAMETER ( LA_LINRX_RCOND_I = 3 )
454: * ..
455: * .. External Subroutines ..
456: EXTERNAL ZAXPY, ZCOPY, ZGETRS, ZGEMV, BLAS_ZGEMV_X,
457: $ BLAS_ZGEMV2_X, ZLA_GEAMV, ZLA_WWADDW, DLAMCH,
458: $ CHLA_TRANSTYPE, ZLA_LIN_BERR
459: DOUBLE PRECISION DLAMCH
460: CHARACTER CHLA_TRANSTYPE
461: * ..
462: * .. Intrinsic Functions ..
463: INTRINSIC ABS, MAX, MIN
464: * ..
465: * .. Statement Functions ..
466: DOUBLE PRECISION CABS1
467: * ..
468: * .. Statement Function Definitions ..
469: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
470: * ..
471: * .. Executable Statements ..
472: *
473: IF ( INFO.NE.0 ) RETURN
474: TRANS = CHLA_TRANSTYPE(TRANS_TYPE)
475: EPS = DLAMCH( 'Epsilon' )
476: HUGEVAL = DLAMCH( 'Overflow' )
477: * Force HUGEVAL to Inf
478: HUGEVAL = HUGEVAL * HUGEVAL
479: * Using HUGEVAL may lead to spurious underflows.
480: INCR_THRESH = DBLE( N ) * EPS
481: *
482: DO J = 1, NRHS
483: Y_PREC_STATE = EXTRA_RESIDUAL
484: IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN
485: DO I = 1, N
486: Y_TAIL( I ) = 0.0D+0
487: END DO
488: END IF
489:
490: DXRAT = 0.0D+0
491: DXRATMAX = 0.0D+0
492: DZRAT = 0.0D+0
493: DZRATMAX = 0.0D+0
494: FINAL_DX_X = HUGEVAL
495: FINAL_DZ_Z = HUGEVAL
496: PREVNORMDX = HUGEVAL
497: PREV_DZ_Z = HUGEVAL
498: DZ_Z = HUGEVAL
499: DX_X = HUGEVAL
500:
501: X_STATE = WORKING_STATE
502: Z_STATE = UNSTABLE_STATE
503: INCR_PREC = .FALSE.
504:
505: DO CNT = 1, ITHRESH
506: *
507: * Compute residual RES = B_s - op(A_s) * Y,
508: * op(A) = A, A**T, or A**H depending on TRANS (and type).
509: *
510: CALL ZCOPY( N, B( 1, J ), 1, RES, 1 )
511: IF ( Y_PREC_STATE .EQ. BASE_RESIDUAL ) THEN
512: CALL ZGEMV( TRANS, N, N, (-1.0D+0,0.0D+0), A, LDA,
513: $ Y( 1, J ), 1, (1.0D+0,0.0D+0), RES, 1)
514: ELSE IF (Y_PREC_STATE .EQ. EXTRA_RESIDUAL) THEN
515: CALL BLAS_ZGEMV_X( TRANS_TYPE, N, N, (-1.0D+0,0.0D+0), A,
516: $ LDA, Y( 1, J ), 1, (1.0D+0,0.0D+0),
517: $ RES, 1, PREC_TYPE )
518: ELSE
519: CALL BLAS_ZGEMV2_X( TRANS_TYPE, N, N, (-1.0D+0,0.0D+0),
520: $ A, LDA, Y(1, J), Y_TAIL, 1, (1.0D+0,0.0D+0), RES, 1,
521: $ PREC_TYPE)
522: END IF
523:
524: ! XXX: RES is no longer needed.
525: CALL ZCOPY( N, RES, 1, DY, 1 )
526: CALL ZGETRS( TRANS, N, 1, AF, LDAF, IPIV, DY, N, INFO )
527: *
528: * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
529: *
530: NORMX = 0.0D+0
531: NORMY = 0.0D+0
532: NORMDX = 0.0D+0
533: DZ_Z = 0.0D+0
534: YMIN = HUGEVAL
535: *
536: DO I = 1, N
537: YK = CABS1( Y( I, J ) )
538: DYK = CABS1( DY( I ) )
539:
540: IF ( YK .NE. 0.0D+0 ) THEN
541: DZ_Z = MAX( DZ_Z, DYK / YK )
542: ELSE IF ( DYK .NE. 0.0D+0 ) THEN
543: DZ_Z = HUGEVAL
544: END IF
545:
546: YMIN = MIN( YMIN, YK )
547:
548: NORMY = MAX( NORMY, YK )
549:
550: IF ( COLEQU ) THEN
551: NORMX = MAX( NORMX, YK * C( I ) )
552: NORMDX = MAX( NORMDX, DYK * C( I ) )
553: ELSE
554: NORMX = NORMY
555: NORMDX = MAX(NORMDX, DYK)
556: END IF
557: END DO
558:
559: IF ( NORMX .NE. 0.0D+0 ) THEN
560: DX_X = NORMDX / NORMX
561: ELSE IF ( NORMDX .EQ. 0.0D+0 ) THEN
562: DX_X = 0.0D+0
563: ELSE
564: DX_X = HUGEVAL
565: END IF
566:
567: DXRAT = NORMDX / PREVNORMDX
568: DZRAT = DZ_Z / PREV_DZ_Z
569: *
570: * Check termination criteria
571: *
572: IF (.NOT.IGNORE_CWISE
573: $ .AND. YMIN*RCOND .LT. INCR_THRESH*NORMY
574: $ .AND. Y_PREC_STATE .LT. EXTRA_Y )
575: $ INCR_PREC = .TRUE.
576:
577: IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH )
578: $ X_STATE = WORKING_STATE
579: IF ( X_STATE .EQ. WORKING_STATE ) THEN
580: IF (DX_X .LE. EPS) THEN
581: X_STATE = CONV_STATE
582: ELSE IF ( DXRAT .GT. RTHRESH ) THEN
583: IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
584: INCR_PREC = .TRUE.
585: ELSE
586: X_STATE = NOPROG_STATE
587: END IF
588: ELSE
589: IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT
590: END IF
591: IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X
592: END IF
593:
594: IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB )
595: $ Z_STATE = WORKING_STATE
596: IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH )
597: $ Z_STATE = WORKING_STATE
598: IF ( Z_STATE .EQ. WORKING_STATE ) THEN
599: IF ( DZ_Z .LE. EPS ) THEN
600: Z_STATE = CONV_STATE
601: ELSE IF ( DZ_Z .GT. DZ_UB ) THEN
602: Z_STATE = UNSTABLE_STATE
603: DZRATMAX = 0.0D+0
604: FINAL_DZ_Z = HUGEVAL
605: ELSE IF ( DZRAT .GT. RTHRESH ) THEN
606: IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
607: INCR_PREC = .TRUE.
608: ELSE
609: Z_STATE = NOPROG_STATE
610: END IF
611: ELSE
612: IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT
613: END IF
614: IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
615: END IF
616: *
617: * Exit if both normwise and componentwise stopped working,
618: * but if componentwise is unstable, let it go at least two
619: * iterations.
620: *
621: IF ( X_STATE.NE.WORKING_STATE ) THEN
622: IF ( IGNORE_CWISE ) GOTO 666
623: IF ( Z_STATE.EQ.NOPROG_STATE .OR. Z_STATE.EQ.CONV_STATE )
624: $ GOTO 666
625: IF ( Z_STATE.EQ.UNSTABLE_STATE .AND. CNT.GT.1 ) GOTO 666
626: END IF
627:
628: IF ( INCR_PREC ) THEN
629: INCR_PREC = .FALSE.
630: Y_PREC_STATE = Y_PREC_STATE + 1
631: DO I = 1, N
632: Y_TAIL( I ) = 0.0D+0
633: END DO
634: END IF
635:
636: PREVNORMDX = NORMDX
637: PREV_DZ_Z = DZ_Z
638: *
639: * Update soluton.
640: *
641: IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
642: CALL ZAXPY( N, (1.0D+0,0.0D+0), DY, 1, Y(1,J), 1 )
643: ELSE
644: CALL ZLA_WWADDW( N, Y( 1, J ), Y_TAIL, DY )
645: END IF
646:
647: END DO
648: * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT.
649: 666 CONTINUE
650: *
651: * Set final_* when cnt hits ithresh
652: *
653: IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X
654: IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
655: *
656: * Compute error bounds
657: *
658: IF (N_NORMS .GE. 1) THEN
659: ERRS_N( J, LA_LINRX_ERR_I ) = FINAL_DX_X / (1 - DXRATMAX)
660:
661: END IF
662: IF ( N_NORMS .GE. 2 ) THEN
663: ERRS_C( J, LA_LINRX_ERR_I ) = FINAL_DZ_Z / (1 - DZRATMAX)
664: END IF
665: *
666: * Compute componentwise relative backward error from formula
667: * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
668: * where abs(Z) is the componentwise absolute value of the matrix
669: * or vector Z.
670: *
671: * Compute residual RES = B_s - op(A_s) * Y,
672: * op(A) = A, A**T, or A**H depending on TRANS (and type).
673: *
674: CALL ZCOPY( N, B( 1, J ), 1, RES, 1 )
675: CALL ZGEMV( TRANS, N, N, (-1.0D+0,0.0D+0), A, LDA, Y(1,J), 1,
676: $ (1.0D+0,0.0D+0), RES, 1 )
677:
678: DO I = 1, N
679: AYB( I ) = CABS1( B( I, J ) )
680: END DO
681: *
682: * Compute abs(op(A_s))*abs(Y) + abs(B_s).
683: *
684: CALL ZLA_GEAMV ( TRANS_TYPE, N, N, 1.0D+0,
685: $ A, LDA, Y(1, J), 1, 1.0D+0, AYB, 1 )
686:
687: CALL ZLA_LIN_BERR ( N, N, 1, RES, AYB, BERR_OUT( J ) )
688: *
689: * End of loop for each RHS.
690: *
691: END DO
692: *
693: RETURN
694: *
695: * End of ZLA_GERFSX_EXTENDED
696: *
697: END
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