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
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
|
SUBROUTINE ZDRVHE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
$ A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
$ NOUT )
*
* -- LAPACK test routine (version 3.2.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* April 2009
*
* .. Scalar Arguments ..
LOGICAL TSTERR
INTEGER NMAX, NN, NOUT, NRHS
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER IWORK( * ), NVAL( * )
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
$ WORK( * ), X( * ), XACT( * )
* ..
*
* Purpose
* =======
*
* ZDRVHE tests the driver routines ZHESV, -SVX, and -SVXX.
*
* Note that this file is used only when the XBLAS are available,
* otherwise zdrvhe.f defines this subroutine.
*
* Arguments
* =========
*
* DOTYPE (input) 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.
*
* NN (input) INTEGER
* The number of values of N contained in the vector NVAL.
*
* NVAL (input) INTEGER array, dimension (NN)
* The values of the matrix dimension N.
*
* NRHS (input) INTEGER
* The number of right hand side vectors to be generated for
* each linear system.
*
* THRESH (input) 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.
*
* TSTERR (input) LOGICAL
* Flag that indicates whether error exits are to be tested.
*
* NMAX (input) INTEGER
* The maximum value permitted for N, used in dimensioning the
* work arrays.
*
* A (workspace) COMPLEX*16 array, dimension (NMAX*NMAX)
*
* AFAC (workspace) COMPLEX*16 array, dimension (NMAX*NMAX)
*
* AINV (workspace) COMPLEX*16 array, dimension (NMAX*NMAX)
*
* B (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
*
* X (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
*
* XACT (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
*
* WORK (workspace) COMPLEX*16 array, dimension
* (NMAX*max(2,NRHS))
*
* RWORK (workspace) DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
*
* IWORK (workspace) INTEGER array, dimension (NMAX)
*
* NOUT (input) INTEGER
* The unit number for output.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
INTEGER NTYPES, NTESTS
PARAMETER ( NTYPES = 10, NTESTS = 6 )
INTEGER NFACT
PARAMETER ( NFACT = 2 )
* ..
* .. Local Scalars ..
LOGICAL ZEROT
CHARACTER DIST, EQUED, FACT, TYPE, UPLO, XTYPE
CHARACTER*3 PATH
INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
$ IZERO, J, K, K1, KL, KU, LDA, LWORK, MODE, N,
$ NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT,
$ N_ERR_BNDS
DOUBLE PRECISION AINVNM, ANORM, CNDNUM, RCOND, RCONDC,
$ RPVGRW_SVXX
* ..
* .. Local Arrays ..
CHARACTER FACTS( NFACT ), UPLOS( 2 )
INTEGER ISEED( 4 ), ISEEDY( 4 )
DOUBLE PRECISION RESULT( NTESTS ), BERR( NRHS ),
$ ERRBNDS_N( NRHS, 3 ), ERRBNDS_C( NRHS, 3 )
* ..
* .. External Functions ..
DOUBLE PRECISION DGET06, ZLANHE
EXTERNAL DGET06, ZLANHE
* ..
* .. External Subroutines ..
EXTERNAL ALADHD, ALAERH, ALASVM, XLAENV, ZERRVX, ZGET04,
$ ZHESV, ZHESVX, ZHET01, ZHETRF, ZHETRI2, ZLACPY,
$ ZLAIPD, ZLARHS, ZLASET, ZLATB4, ZLATMS, ZPOT02,
$ ZPOT05, ZHESVXX
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
CHARACTER*32 SRNAMT
INTEGER INFOT, NUNIT
* ..
* .. Common blocks ..
COMMON / INFOC / INFOT, NUNIT, OK, LERR
COMMON / SRNAMC / SRNAMT
* ..
* .. Intrinsic Functions ..
INTRINSIC DCMPLX, MAX, MIN
* ..
* .. Data statements ..
DATA ISEEDY / 1988, 1989, 1990, 1991 /
DATA UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 1 ) = 'Z'
PATH( 2: 3 ) = 'HE'
NRUN = 0
NFAIL = 0
NERRS = 0
DO 10 I = 1, 4
ISEED( I ) = ISEEDY( I )
10 CONTINUE
LWORK = MAX( 2*NMAX, NMAX*NRHS )
*
* Test the error exits
*
IF( TSTERR )
$ CALL ZERRVX( PATH, NOUT )
INFOT = 0
*
* Set the block size and minimum block size for testing.
*
NB = 1
NBMIN = 2
CALL XLAENV( 1, NB )
CALL XLAENV( 2, NBMIN )
*
* Do for each value of N in NVAL
*
DO 180 IN = 1, NN
N = NVAL( IN )
LDA = MAX( N, 1 )
XTYPE = 'N'
NIMAT = NTYPES
IF( N.LE.0 )
$ NIMAT = 1
*
DO 170 IMAT = 1, NIMAT
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 170
*
* Skip types 3, 4, 5, or 6 if the matrix size is too small.
*
ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
IF( ZEROT .AND. N.LT.IMAT-2 )
$ GO TO 170
*
* Do first for UPLO = 'U', then for UPLO = 'L'
*
DO 160 IUPLO = 1, 2
UPLO = UPLOS( IUPLO )
*
* Set up parameters with ZLATB4 and generate a test matrix
* with ZLATMS.
*
CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
$ CNDNUM, DIST )
*
SRNAMT = 'ZLATMS'
CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
$ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
$ INFO )
*
* Check error code from ZLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N, -1,
$ -1, -1, IMAT, NFAIL, NERRS, NOUT )
GO TO 160
END IF
*
* For types 3-6, zero one or more rows and columns of the
* matrix to test that INFO is returned correctly.
*
IF( ZEROT ) THEN
IF( IMAT.EQ.3 ) THEN
IZERO = 1
ELSE IF( IMAT.EQ.4 ) THEN
IZERO = N
ELSE
IZERO = N / 2 + 1
END IF
*
IF( IMAT.LT.6 ) THEN
*
* Set row and column IZERO to zero.
*
IF( IUPLO.EQ.1 ) THEN
IOFF = ( IZERO-1 )*LDA
DO 20 I = 1, IZERO - 1
A( IOFF+I ) = ZERO
20 CONTINUE
IOFF = IOFF + IZERO
DO 30 I = IZERO, N
A( IOFF ) = ZERO
IOFF = IOFF + LDA
30 CONTINUE
ELSE
IOFF = IZERO
DO 40 I = 1, IZERO - 1
A( IOFF ) = ZERO
IOFF = IOFF + LDA
40 CONTINUE
IOFF = IOFF - IZERO
DO 50 I = IZERO, N
A( IOFF+I ) = ZERO
50 CONTINUE
END IF
ELSE
IOFF = 0
IF( IUPLO.EQ.1 ) THEN
*
* Set the first IZERO rows and columns to zero.
*
DO 70 J = 1, N
I2 = MIN( J, IZERO )
DO 60 I = 1, I2
A( IOFF+I ) = ZERO
60 CONTINUE
IOFF = IOFF + LDA
70 CONTINUE
ELSE
*
* Set the last IZERO rows and columns to zero.
*
DO 90 J = 1, N
I1 = MAX( J, IZERO )
DO 80 I = I1, N
A( IOFF+I ) = ZERO
80 CONTINUE
IOFF = IOFF + LDA
90 CONTINUE
END IF
END IF
ELSE
IZERO = 0
END IF
*
* Set the imaginary part of the diagonals.
*
CALL ZLAIPD( N, A, LDA+1, 0 )
*
DO 150 IFACT = 1, NFACT
*
* Do first for FACT = 'F', then for other values.
*
FACT = FACTS( IFACT )
*
* Compute the condition number for comparison with
* the value returned by ZHESVX.
*
IF( ZEROT ) THEN
IF( IFACT.EQ.1 )
$ GO TO 150
RCONDC = ZERO
*
ELSE IF( IFACT.EQ.1 ) THEN
*
* Compute the 1-norm of A.
*
ANORM = ZLANHE( '1', UPLO, N, A, LDA, RWORK )
*
* Factor the matrix A.
*
CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
CALL ZHETRF( UPLO, N, AFAC, LDA, IWORK, WORK,
$ LWORK, INFO )
*
* Compute inv(A) and take its norm.
*
CALL ZLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
LWORK = (N+NB+1)*(NB+3)
CALL ZHETRI2( UPLO, N, AINV, LDA, IWORK, WORK,
$ LWORK, INFO )
AINVNM = ZLANHE( '1', UPLO, N, AINV, LDA, RWORK )
*
* 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
*
* Form an exact solution and set the right hand side.
*
SRNAMT = 'ZLARHS'
CALL ZLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
$ NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
$ INFO )
XTYPE = 'C'
*
* --- Test ZHESV ---
*
IF( IFACT.EQ.2 ) THEN
CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
*
* Factor the matrix and solve the system using ZHESV.
*
SRNAMT = 'ZHESV '
CALL ZHESV( UPLO, N, NRHS, AFAC, LDA, IWORK, X,
$ LDA, WORK, LWORK, INFO )
*
* Adjust the expected value of INFO to account for
* pivoting.
*
K = IZERO
IF( K.GT.0 ) THEN
100 CONTINUE
IF( IWORK( K ).LT.0 ) THEN
IF( IWORK( K ).NE.-K ) THEN
K = -IWORK( K )
GO TO 100
END IF
ELSE IF( IWORK( K ).NE.K ) THEN
K = IWORK( K )
GO TO 100
END IF
END IF
*
* Check error code from ZHESV .
*
IF( INFO.NE.K ) THEN
CALL ALAERH( PATH, 'ZHESV ', INFO, K, UPLO, N,
$ N, -1, -1, NRHS, IMAT, NFAIL,
$ NERRS, NOUT )
GO TO 120
ELSE IF( INFO.NE.0 ) THEN
GO TO 120
END IF
*
* Reconstruct matrix from factors and compute
* residual.
*
CALL ZHET01( UPLO, N, A, LDA, AFAC, LDA, IWORK,
$ AINV, LDA, RWORK, RESULT( 1 ) )
*
* Compute residual of the computed solution.
*
CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
CALL ZPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
$ LDA, RWORK, RESULT( 2 ) )
*
* Check solution from generated exact solution.
*
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 3 ) )
NT = 3
*
* Print information about the tests that did not pass
* the threshold.
*
DO 110 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 )'ZHESV ', UPLO, N,
$ IMAT, K, RESULT( K )
NFAIL = NFAIL + 1
END IF
110 CONTINUE
NRUN = NRUN + NT
120 CONTINUE
END IF
*
* --- Test ZHESVX ---
*
IF( IFACT.EQ.2 )
$ CALL ZLASET( UPLO, N, N, DCMPLX( ZERO ),
$ DCMPLX( ZERO ), AFAC, LDA )
CALL ZLASET( 'Full', N, NRHS, DCMPLX( ZERO ),
$ DCMPLX( ZERO ), X, LDA )
*
* Solve the system and compute the condition number and
* error bounds using ZHESVX.
*
SRNAMT = 'ZHESVX'
CALL ZHESVX( FACT, UPLO, N, NRHS, A, LDA, AFAC, LDA,
$ IWORK, B, LDA, X, LDA, RCOND, RWORK,
$ RWORK( NRHS+1 ), WORK, LWORK,
$ RWORK( 2*NRHS+1 ), INFO )
*
* Adjust the expected value of INFO to account for
* pivoting.
*
K = IZERO
IF( K.GT.0 ) THEN
130 CONTINUE
IF( IWORK( K ).LT.0 ) THEN
IF( IWORK( K ).NE.-K ) THEN
K = -IWORK( K )
GO TO 130
END IF
ELSE IF( IWORK( K ).NE.K ) THEN
K = IWORK( K )
GO TO 130
END IF
END IF
*
* Check the error code from ZHESVX.
*
IF( INFO.NE.K ) THEN
CALL ALAERH( PATH, 'ZHESVX', INFO, K, FACT // UPLO,
$ N, N, -1, -1, NRHS, IMAT, NFAIL,
$ NERRS, NOUT )
GO TO 150
END IF
*
IF( INFO.EQ.0 ) THEN
IF( IFACT.GE.2 ) THEN
*
* Reconstruct matrix from factors and compute
* residual.
*
CALL ZHET01( UPLO, N, A, LDA, AFAC, LDA, IWORK,
$ AINV, LDA, RWORK( 2*NRHS+1 ),
$ RESULT( 1 ) )
K1 = 1
ELSE
K1 = 2
END IF
*
* Compute residual of the computed solution.
*
CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
CALL ZPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
$ LDA, RWORK( 2*NRHS+1 ), RESULT( 2 ) )
*
* Check solution from generated exact solution.
*
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 3 ) )
*
* Check the error bounds from iterative refinement.
*
CALL ZPOT05( UPLO, N, NRHS, A, LDA, B, LDA, X, LDA,
$ XACT, LDA, RWORK, RWORK( NRHS+1 ),
$ RESULT( 4 ) )
ELSE
K1 = 6
END IF
*
* Compare RCOND from ZHESVX with the computed value
* in RCONDC.
*
RESULT( 6 ) = DGET06( RCOND, RCONDC )
*
* Print information about the tests that did not pass
* the threshold.
*
DO 140 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 )'ZHESVX', FACT, UPLO,
$ N, IMAT, K, RESULT( K )
NFAIL = NFAIL + 1
END IF
140 CONTINUE
NRUN = NRUN + 7 - K1
*
* --- Test ZHESVXX ---
*
* Restore the matrices A and B.
*
IF( IFACT.EQ.2 )
$ CALL ZLASET( UPLO, N, N, CMPLX( ZERO ),
$ CMPLX( ZERO ), AFAC, LDA )
CALL ZLASET( 'Full', N, NRHS, CMPLX( ZERO ),
$ CMPLX( ZERO ), X, LDA )
*
* Solve the system and compute the condition number
* and error bounds using ZHESVXX.
*
SRNAMT = 'ZHESVXX'
N_ERR_BNDS = 3
EQUED = 'N'
CALL ZHESVXX( FACT, UPLO, N, NRHS, A, LDA, AFAC,
$ LDA, IWORK, EQUED, WORK( N+1 ), B, LDA, X,
$ LDA, RCOND, RPVGRW_SVXX, BERR, N_ERR_BNDS,
$ ERRBNDS_N, ERRBNDS_C, 0, ZERO, WORK,
$ IWORK( N+1 ), INFO )
*
* Adjust the expected value of INFO to account for
* pivoting.
*
K = IZERO
IF( K.GT.0 ) THEN
135 CONTINUE
IF( IWORK( K ).LT.0 ) THEN
IF( IWORK( K ).NE.-K ) THEN
K = -IWORK( K )
GO TO 135
END IF
ELSE IF( IWORK( K ).NE.K ) THEN
K = IWORK( K )
GO TO 135
END IF
END IF
*
* Check the error code from ZHESVXX.
*
IF( INFO.NE.K ) THEN
CALL ALAERH( PATH, 'ZHESVXX', INFO, K,
$ FACT // UPLO, N, N, -1, -1, NRHS, IMAT, NFAIL,
$ NERRS, NOUT )
GO TO 150
END IF
*
IF( INFO.EQ.0 ) THEN
IF( IFACT.GE.2 ) THEN
*
* Reconstruct matrix from factors and compute
* residual.
*
CALL ZHET01( UPLO, N, A, LDA, AFAC, LDA, IWORK,
$ AINV, LDA, RWORK(2*NRHS+1),
$ RESULT( 1 ) )
K1 = 1
ELSE
K1 = 2
END IF
*
* Compute residual of the computed solution.
*
CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
CALL ZPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
$ LDA, RWORK( 2*NRHS+1 ), RESULT( 2 ) )
RESULT( 2 ) = 0.0
*
* Check solution from generated exact solution.
*
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 3 ) )
*
* Check the error bounds from iterative refinement.
*
CALL ZPOT05( UPLO, N, NRHS, A, LDA, B, LDA, X, LDA,
$ XACT, LDA, RWORK, RWORK( NRHS+1 ),
$ RESULT( 4 ) )
ELSE
K1 = 6
END IF
*
* Compare RCOND from ZHESVXX with the computed value
* in RCONDC.
*
RESULT( 6 ) = DGET06( RCOND, RCONDC )
*
* Print information about the tests that did not pass
* the threshold.
*
DO 85 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 )'ZHESVXX',
$ FACT, UPLO, N, IMAT, K,
$ RESULT( K )
NFAIL = NFAIL + 1
END IF
85 CONTINUE
NRUN = NRUN + 7 - K1
*
150 CONTINUE
*
160 CONTINUE
170 CONTINUE
180 CONTINUE
*
* Print a summary of the results.
*
CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
* Test Error Bounds from ZHESVXX
CALL ZEBCHVXX(THRESH, PATH)
9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
$ ', test ', I2, ', ratio =', G12.5 )
9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N =', I5,
$ ', type ', I2, ', test ', I2, ', ratio =', G12.5 )
RETURN
*
* End of ZDRVHE
*
END
|
