1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
|
*> \brief \b ZDRVPT
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZDRVPT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D,
* E, B, X, XACT, WORK, RWORK, NOUT )
*
* .. Scalar Arguments ..
* LOGICAL TSTERR
* INTEGER NN, NOUT, NRHS
* DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * )
* INTEGER NVAL( * )
* DOUBLE PRECISION D( * ), RWORK( * )
* COMPLEX*16 A( * ), B( * ), E( * ), WORK( * ), X( * ),
* $ XACT( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZDRVPT tests ZPTSV and -SVX.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> DOTYPE is LOGICAL array, dimension (NTYPES)
*> The matrix types to be used for testing. Matrices of type j
*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
*> \endverbatim
*>
*> \param[in] NN
*> \verbatim
*> NN is INTEGER
*> The number of values of N contained in the vector NVAL.
*> \endverbatim
*>
*> \param[in] NVAL
*> \verbatim
*> NVAL is INTEGER array, dimension (NN)
*> The values of the matrix dimension N.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of right hand side vectors to be generated for
*> each linear system.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*> THRESH is DOUBLE PRECISION
*> The threshold value for the test ratios. A result is
*> included in the output file if RESULT >= THRESH. To have
*> every test ratio printed, use THRESH = 0.
*> \endverbatim
*>
*> \param[in] TSTERR
*> \verbatim
*> TSTERR is LOGICAL
*> Flag that indicates whether error exits are to be tested.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (NMAX*2)
*> \endverbatim
*>
*> \param[out] D
*> \verbatim
*> D is DOUBLE PRECISION array, dimension (NMAX*2)
*> \endverbatim
*>
*> \param[out] E
*> \verbatim
*> E is COMPLEX*16 array, dimension (NMAX*2)
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*> B is COMPLEX*16 array, dimension (NMAX*NRHS)
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*> X is COMPLEX*16 array, dimension (NMAX*NRHS)
*> \endverbatim
*>
*> \param[out] XACT
*> \verbatim
*> XACT is COMPLEX*16 array, dimension (NMAX*NRHS)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension
*> (NMAX*max(3,NRHS))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
*> \endverbatim
*>
*> \param[in] NOUT
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16_lin
*
* =====================================================================
SUBROUTINE ZDRVPT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D,
$ E, B, X, XACT, WORK, RWORK, NOUT )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
LOGICAL TSTERR
INTEGER NN, NOUT, NRHS
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER NVAL( * )
DOUBLE PRECISION D( * ), RWORK( * )
COMPLEX*16 A( * ), B( * ), E( * ), WORK( * ), X( * ),
$ XACT( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
INTEGER NTYPES
PARAMETER ( NTYPES = 12 )
INTEGER NTESTS
PARAMETER ( NTESTS = 6 )
* ..
* .. Local Scalars ..
LOGICAL ZEROT
CHARACTER DIST, FACT, TYPE
CHARACTER*3 PATH
INTEGER I, IA, IFACT, IMAT, IN, INFO, IX, IZERO, J, K,
$ K1, KL, KU, LDA, MODE, N, NERRS, NFAIL, NIMAT,
$ NRUN, NT
DOUBLE PRECISION AINVNM, ANORM, COND, DMAX, RCOND, RCONDC
* ..
* .. Local Arrays ..
INTEGER ISEED( 4 ), ISEEDY( 4 )
DOUBLE PRECISION RESULT( NTESTS ), Z( 3 )
* ..
* .. External Functions ..
INTEGER IDAMAX
DOUBLE PRECISION DGET06, DZASUM, ZLANHT
EXTERNAL IDAMAX, DGET06, DZASUM, ZLANHT
* ..
* .. External Subroutines ..
EXTERNAL ALADHD, ALAERH, ALASVM, DCOPY, DLARNV, DSCAL,
$ ZCOPY, ZDSCAL, ZERRVX, ZGET04, ZLACPY, ZLAPTM,
$ ZLARNV, ZLASET, ZLATB4, ZLATMS, ZPTSV, ZPTSVX,
$ ZPTT01, ZPTT02, ZPTT05, ZPTTRF, ZPTTRS
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DCMPLX, MAX
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
CHARACTER*32 SRNAMT
INTEGER INFOT, NUNIT
* ..
* .. Common blocks ..
COMMON / INFOC / INFOT, NUNIT, OK, LERR
COMMON / SRNAMC / SRNAMT
* ..
* .. Data statements ..
DATA ISEEDY / 0, 0, 0, 1 /
* ..
* .. Executable Statements ..
*
PATH( 1: 1 ) = 'Zomplex precision'
PATH( 2: 3 ) = 'PT'
NRUN = 0
NFAIL = 0
NERRS = 0
DO 10 I = 1, 4
ISEED( I ) = ISEEDY( I )
10 CONTINUE
*
* Test the error exits
*
IF( TSTERR )
$ CALL ZERRVX( PATH, NOUT )
INFOT = 0
*
DO 120 IN = 1, NN
*
* Do for each value of N in NVAL.
*
N = NVAL( IN )
LDA = MAX( 1, N )
NIMAT = NTYPES
IF( N.LE.0 )
$ NIMAT = 1
*
DO 110 IMAT = 1, NIMAT
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( N.GT.0 .AND. .NOT.DOTYPE( IMAT ) )
$ GO TO 110
*
* Set up parameters with ZLATB4.
*
CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
$ COND, DIST )
*
ZEROT = IMAT.GE.8 .AND. IMAT.LE.10
IF( IMAT.LE.6 ) THEN
*
* Type 1-6: generate a symmetric tridiagonal matrix of
* known condition number in lower triangular band storage.
*
SRNAMT = 'ZLATMS'
CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, COND,
$ ANORM, KL, KU, 'B', A, 2, WORK, INFO )
*
* Check the error code from ZLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'ZLATMS', INFO, 0, ' ', N, N, KL,
$ KU, -1, IMAT, NFAIL, NERRS, NOUT )
GO TO 110
END IF
IZERO = 0
*
* Copy the matrix to D and E.
*
IA = 1
DO 20 I = 1, N - 1
D( I ) = A( IA )
E( I ) = A( IA+1 )
IA = IA + 2
20 CONTINUE
IF( N.GT.0 )
$ D( N ) = A( IA )
ELSE
*
* Type 7-12: generate a diagonally dominant matrix with
* unknown condition number in the vectors D and E.
*
IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 7 ) ) THEN
*
* Let D and E have values from [-1,1].
*
CALL DLARNV( 2, ISEED, N, D )
CALL ZLARNV( 2, ISEED, N-1, E )
*
* Make the tridiagonal matrix diagonally dominant.
*
IF( N.EQ.1 ) THEN
D( 1 ) = ABS( D( 1 ) )
ELSE
D( 1 ) = ABS( D( 1 ) ) + ABS( E( 1 ) )
D( N ) = ABS( D( N ) ) + ABS( E( N-1 ) )
DO 30 I = 2, N - 1
D( I ) = ABS( D( I ) ) + ABS( E( I ) ) +
$ ABS( E( I-1 ) )
30 CONTINUE
END IF
*
* Scale D and E so the maximum element is ANORM.
*
IX = IDAMAX( N, D, 1 )
DMAX = D( IX )
CALL DSCAL( N, ANORM / DMAX, D, 1 )
IF( N.GT.1 )
$ CALL ZDSCAL( N-1, ANORM / DMAX, E, 1 )
*
ELSE IF( IZERO.GT.0 ) THEN
*
* Reuse the last matrix by copying back the zeroed out
* elements.
*
IF( IZERO.EQ.1 ) THEN
D( 1 ) = Z( 2 )
IF( N.GT.1 )
$ E( 1 ) = Z( 3 )
ELSE IF( IZERO.EQ.N ) THEN
E( N-1 ) = Z( 1 )
D( N ) = Z( 2 )
ELSE
E( IZERO-1 ) = Z( 1 )
D( IZERO ) = Z( 2 )
E( IZERO ) = Z( 3 )
END IF
END IF
*
* For types 8-10, set one row and column of the matrix to
* zero.
*
IZERO = 0
IF( IMAT.EQ.8 ) THEN
IZERO = 1
Z( 2 ) = D( 1 )
D( 1 ) = ZERO
IF( N.GT.1 ) THEN
Z( 3 ) = E( 1 )
E( 1 ) = ZERO
END IF
ELSE IF( IMAT.EQ.9 ) THEN
IZERO = N
IF( N.GT.1 ) THEN
Z( 1 ) = E( N-1 )
E( N-1 ) = ZERO
END IF
Z( 2 ) = D( N )
D( N ) = ZERO
ELSE IF( IMAT.EQ.10 ) THEN
IZERO = ( N+1 ) / 2
IF( IZERO.GT.1 ) THEN
Z( 1 ) = E( IZERO-1 )
E( IZERO-1 ) = ZERO
Z( 3 ) = E( IZERO )
E( IZERO ) = ZERO
END IF
Z( 2 ) = D( IZERO )
D( IZERO ) = ZERO
END IF
END IF
*
* Generate NRHS random solution vectors.
*
IX = 1
DO 40 J = 1, NRHS
CALL ZLARNV( 2, ISEED, N, XACT( IX ) )
IX = IX + LDA
40 CONTINUE
*
* Set the right hand side.
*
CALL ZLAPTM( 'Lower', N, NRHS, ONE, D, E, XACT, LDA, ZERO,
$ B, LDA )
*
DO 100 IFACT = 1, 2
IF( IFACT.EQ.1 ) THEN
FACT = 'F'
ELSE
FACT = 'N'
END IF
*
* Compute the condition number for comparison with
* the value returned by ZPTSVX.
*
IF( ZEROT ) THEN
IF( IFACT.EQ.1 )
$ GO TO 100
RCONDC = ZERO
*
ELSE IF( IFACT.EQ.1 ) THEN
*
* Compute the 1-norm of A.
*
ANORM = ZLANHT( '1', N, D, E )
*
CALL DCOPY( N, D, 1, D( N+1 ), 1 )
IF( N.GT.1 )
$ CALL ZCOPY( N-1, E, 1, E( N+1 ), 1 )
*
* Factor the matrix A.
*
CALL ZPTTRF( N, D( N+1 ), E( N+1 ), INFO )
*
* Use ZPTTRS to solve for one column at a time of
* inv(A), computing the maximum column sum as we go.
*
AINVNM = ZERO
DO 60 I = 1, N
DO 50 J = 1, N
X( J ) = ZERO
50 CONTINUE
X( I ) = ONE
CALL ZPTTRS( 'Lower', N, 1, D( N+1 ), E( N+1 ), X,
$ LDA, INFO )
AINVNM = MAX( AINVNM, DZASUM( N, X, 1 ) )
60 CONTINUE
*
* Compute the 1-norm condition number of A.
*
IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDC = ONE
ELSE
RCONDC = ( ONE / ANORM ) / AINVNM
END IF
END IF
*
IF( IFACT.EQ.2 ) THEN
*
* --- Test ZPTSV --
*
CALL DCOPY( N, D, 1, D( N+1 ), 1 )
IF( N.GT.1 )
$ CALL ZCOPY( N-1, E, 1, E( N+1 ), 1 )
CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
*
* Factor A as L*D*L' and solve the system A*X = B.
*
SRNAMT = 'ZPTSV '
CALL ZPTSV( N, NRHS, D( N+1 ), E( N+1 ), X, LDA,
$ INFO )
*
* Check error code from ZPTSV .
*
IF( INFO.NE.IZERO )
$ CALL ALAERH( PATH, 'ZPTSV ', INFO, IZERO, ' ', N,
$ N, 1, 1, NRHS, IMAT, NFAIL, NERRS,
$ NOUT )
NT = 0
IF( IZERO.EQ.0 ) THEN
*
* Check the factorization by computing the ratio
* norm(L*D*L' - A) / (n * norm(A) * EPS )
*
CALL ZPTT01( N, D, E, D( N+1 ), E( N+1 ), WORK,
$ RESULT( 1 ) )
*
* Compute the residual in the solution.
*
CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
CALL ZPTT02( 'Lower', N, NRHS, D, E, X, LDA, WORK,
$ LDA, RESULT( 2 ) )
*
* Check solution from generated exact solution.
*
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 3 ) )
NT = 3
END IF
*
* Print information about the tests that did not pass
* the threshold.
*
DO 70 K = 1, NT
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 )'ZPTSV ', N, IMAT, K,
$ RESULT( K )
NFAIL = NFAIL + 1
END IF
70 CONTINUE
NRUN = NRUN + NT
END IF
*
* --- Test ZPTSVX ---
*
IF( IFACT.GT.1 ) THEN
*
* Initialize D( N+1:2*N ) and E( N+1:2*N ) to zero.
*
DO 80 I = 1, N - 1
D( N+I ) = ZERO
E( N+I ) = ZERO
80 CONTINUE
IF( N.GT.0 )
$ D( N+N ) = ZERO
END IF
*
CALL ZLASET( 'Full', N, NRHS, DCMPLX( ZERO ),
$ DCMPLX( ZERO ), X, LDA )
*
* Solve the system and compute the condition number and
* error bounds using ZPTSVX.
*
SRNAMT = 'ZPTSVX'
CALL ZPTSVX( FACT, N, NRHS, D, E, D( N+1 ), E( N+1 ), B,
$ LDA, X, LDA, RCOND, RWORK, RWORK( NRHS+1 ),
$ WORK, RWORK( 2*NRHS+1 ), INFO )
*
* Check the error code from ZPTSVX.
*
IF( INFO.NE.IZERO )
$ CALL ALAERH( PATH, 'ZPTSVX', INFO, IZERO, FACT, N, N,
$ 1, 1, NRHS, IMAT, NFAIL, NERRS, NOUT )
IF( IZERO.EQ.0 ) THEN
IF( IFACT.EQ.2 ) THEN
*
* Check the factorization by computing the ratio
* norm(L*D*L' - A) / (n * norm(A) * EPS )
*
K1 = 1
CALL ZPTT01( N, D, E, D( N+1 ), E( N+1 ), WORK,
$ RESULT( 1 ) )
ELSE
K1 = 2
END IF
*
* Compute the residual in the solution.
*
CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
CALL ZPTT02( 'Lower', N, NRHS, D, E, X, LDA, WORK,
$ LDA, RESULT( 2 ) )
*
* Check solution from generated exact solution.
*
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 3 ) )
*
* Check error bounds from iterative refinement.
*
CALL ZPTT05( N, NRHS, D, E, B, LDA, X, LDA, XACT, LDA,
$ RWORK, RWORK( NRHS+1 ), RESULT( 4 ) )
ELSE
K1 = 6
END IF
*
* Check the reciprocal of the condition number.
*
RESULT( 6 ) = DGET06( RCOND, RCONDC )
*
* Print information about the tests that did not pass
* the threshold.
*
DO 90 K = K1, 6
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALADHD( NOUT, PATH )
WRITE( NOUT, FMT = 9998 )'ZPTSVX', FACT, N, IMAT,
$ K, RESULT( K )
NFAIL = NFAIL + 1
END IF
90 CONTINUE
NRUN = NRUN + 7 - K1
100 CONTINUE
110 CONTINUE
120 CONTINUE
*
* Print a summary of the results.
*
CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
9999 FORMAT( 1X, A, ', N =', I5, ', type ', I2, ', test ', I2,
$ ', ratio = ', G12.5 )
9998 FORMAT( 1X, A, ', FACT=''', A1, ''', N =', I5, ', type ', I2,
$ ', test ', I2, ', ratio = ', G12.5 )
RETURN
*
* End of ZDRVPT
*
END
|