LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
zchkhe_rook.f
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1 *> \brief \b ZCHKHE_ROOK
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE ZCHKHE_ROOK( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
12 * THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
13 * XACT, WORK, RWORK, IWORK, NOUT )
14 *
15 * .. Scalar Arguments ..
16 * LOGICAL TSTERR
17 * INTEGER NMAX, NN, NNB, NNS, NOUT
18 * DOUBLE PRECISION THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
23 * DOUBLE PRECISION RWORK( * )
24 * COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
25 * $ WORK( * ), X( * ), XACT( * )
26 * ..
27 *
28 *
29 *> \par Purpose:
30 * =============
31 *>
32 *> \verbatim
33 *>
34 *> ZCHKHE_ROOK tests ZHETRF_ROOK, -TRI_ROOK, -TRS_ROOK,
35 *> and -CON_ROOK.
36 *> \endverbatim
37 *
38 * Arguments:
39 * ==========
40 *
41 *> \param[in] DOTYPE
42 *> \verbatim
43 *> DOTYPE is LOGICAL array, dimension (NTYPES)
44 *> The matrix types to be used for testing. Matrices of type j
45 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
46 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
47 *> \endverbatim
48 *>
49 *> \param[in] NN
50 *> \verbatim
51 *> NN is INTEGER
52 *> The number of values of N contained in the vector NVAL.
53 *> \endverbatim
54 *>
55 *> \param[in] NVAL
56 *> \verbatim
57 *> NVAL is INTEGER array, dimension (NN)
58 *> The values of the matrix dimension N.
59 *> \endverbatim
60 *>
61 *> \param[in] NNB
62 *> \verbatim
63 *> NNB is INTEGER
64 *> The number of values of NB contained in the vector NBVAL.
65 *> \endverbatim
66 *>
67 *> \param[in] NBVAL
68 *> \verbatim
69 *> NBVAL is INTEGER array, dimension (NBVAL)
70 *> The values of the blocksize NB.
71 *> \endverbatim
72 *>
73 *> \param[in] NNS
74 *> \verbatim
75 *> NNS is INTEGER
76 *> The number of values of NRHS contained in the vector NSVAL.
77 *> \endverbatim
78 *>
79 *> \param[in] NSVAL
80 *> \verbatim
81 *> NSVAL is INTEGER array, dimension (NNS)
82 *> The values of the number of right hand sides NRHS.
83 *> \endverbatim
84 *>
85 *> \param[in] THRESH
86 *> \verbatim
87 *> THRESH is DOUBLE PRECISION
88 *> The threshold value for the test ratios. A result is
89 *> included in the output file if RESULT >= THRESH. To have
90 *> every test ratio printed, use THRESH = 0.
91 *> \endverbatim
92 *>
93 *> \param[in] TSTERR
94 *> \verbatim
95 *> TSTERR is LOGICAL
96 *> Flag that indicates whether error exits are to be tested.
97 *> \endverbatim
98 *>
99 *> \param[in] NMAX
100 *> \verbatim
101 *> NMAX is INTEGER
102 *> The maximum value permitted for N, used in dimensioning the
103 *> work arrays.
104 *> \endverbatim
105 *>
106 *> \param[out] A
107 *> \verbatim
108 *> A is CCOMPLEX*16 array, dimension (NMAX*NMAX)
109 *> \endverbatim
110 *>
111 *> \param[out] AFAC
112 *> \verbatim
113 *> AFAC is COMPLEX*16 array, dimension (NMAX*NMAX)
114 *> \endverbatim
115 *>
116 *> \param[out] AINV
117 *> \verbatim
118 *> AINV is COMPLEX*16 array, dimension (NMAX*NMAX)
119 *> \endverbatim
120 *>
121 *> \param[out] B
122 *> \verbatim
123 *> B is CCOMPLEX*16 array, dimension (NMAX*NSMAX)
124 *> where NSMAX is the largest entry in NSVAL.
125 *> \endverbatim
126 *>
127 *> \param[out] X
128 *> \verbatim
129 *> X is COMPLEX*16 array, dimension (NMAX*NSMAX)
130 *> \endverbatim
131 *>
132 *> \param[out] XACT
133 *> \verbatim
134 *> XACT is COMPLEX*16 array, dimension (NMAX*NSMAX)
135 *> \endverbatim
136 *>
137 *> \param[out] WORK
138 *> \verbatim
139 *> WORK is COMPLEX*16 array, dimension (NMAX*max(3,NSMAX))
140 *> \endverbatim
141 *>
142 *> \param[out] RWORK
143 *> \verbatim
144 *> RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX)
145 *> \endverbatim
146 *>
147 *> \param[out] IWORK
148 *> \verbatim
149 *> IWORK is INTEGER array, dimension (2*NMAX)
150 *> \endverbatim
151 *>
152 *> \param[in] NOUT
153 *> \verbatim
154 *> NOUT is INTEGER
155 *> The unit number for output.
156 *> \endverbatim
157 *
158 * Authors:
159 * ========
160 *
161 *> \author Univ. of Tennessee
162 *> \author Univ. of California Berkeley
163 *> \author Univ. of Colorado Denver
164 *> \author NAG Ltd.
165 *
166 *> \date December 2016
167 *
168 *> \ingroup complex16_lin
169 *
170 * =====================================================================
171  SUBROUTINE zchkhe_rook( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
172  $ THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
173  $ XACT, WORK, RWORK, IWORK, NOUT )
174 *
175 * -- LAPACK test routine (version 3.7.0) --
176 * -- LAPACK is a software package provided by Univ. of Tennessee, --
177 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
178 * December 2016
179 *
180 * .. Scalar Arguments ..
181  LOGICAL TSTERR
182  INTEGER NMAX, NN, NNB, NNS, NOUT
183  DOUBLE PRECISION THRESH
184 * ..
185 * .. Array Arguments ..
186  LOGICAL DOTYPE( * )
187  INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
188  DOUBLE PRECISION RWORK( * )
189  COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
190  $ work( * ), x( * ), xact( * )
191 * ..
192 *
193 * =====================================================================
194 *
195 * .. Parameters ..
196  DOUBLE PRECISION ZERO, ONE
197  parameter( zero = 0.0d+0, one = 1.0d+0 )
198  DOUBLE PRECISION ONEHALF
199  parameter( onehalf = 0.5d+0 )
200  DOUBLE PRECISION EIGHT, SEVTEN
201  parameter( eight = 8.0d+0, sevten = 17.0d+0 )
202  COMPLEX*16 CZERO
203  parameter( czero = ( 0.0d+0, 0.0d+0 ) )
204  INTEGER NTYPES
205  parameter( ntypes = 10 )
206  INTEGER NTESTS
207  parameter( ntests = 7 )
208 * ..
209 * .. Local Scalars ..
210  LOGICAL TRFCON, ZEROT
211  CHARACTER DIST, TYPE, UPLO, XTYPE
212  CHARACTER*3 PATH, MATPATH
213  INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
214  $ iuplo, izero, j, k, kl, ku, lda, lwork, mode,
215  $ n, nb, nerrs, nfail, nimat, nrhs, nrun, nt
216  DOUBLE PRECISION ALPHA, ANORM, CNDNUM, CONST, SING_MAX,
217  $ sing_min, rcond, rcondc, dtemp
218 * ..
219 * .. Local Arrays ..
220  CHARACTER UPLOS( 2 )
221  INTEGER ISEED( 4 ), ISEEDY( 4 )
222  DOUBLE PRECISION RESULT( ntests )
223  COMPLEX*16 BLOCK( 2, 2 ), ZDUMMY( 1 )
224 * ..
225 * .. External Functions ..
226  DOUBLE PRECISION ZLANGE, ZLANHE, DGET06
227  EXTERNAL zlange, zlanhe, dget06
228 * ..
229 * .. External Subroutines ..
230  EXTERNAL alaerh, alahd, alasum, zerrhe, zgesvd, zget04,
234 * ..
235 * .. Intrinsic Functions ..
236  INTRINSIC conjg, max, min, sqrt
237 * ..
238 * .. Scalars in Common ..
239  LOGICAL LERR, OK
240  CHARACTER*32 SRNAMT
241  INTEGER INFOT, NUNIT
242 * ..
243 * .. Common blocks ..
244  COMMON / infoc / infot, nunit, ok, lerr
245  COMMON / srnamc / srnamt
246 * ..
247 * .. Data statements ..
248  DATA iseedy / 1988, 1989, 1990, 1991 /
249  DATA uplos / 'U', 'L' /
250 * ..
251 * .. Executable Statements ..
252 *
253 * Initialize constants and the random number seed.
254 *
255  alpha = ( one+sqrt( sevten ) ) / eight
256 *
257 * Test path
258 *
259  path( 1: 1 ) = 'Zomplex precision'
260  path( 2: 3 ) = 'HR'
261 *
262 * Path to generate matrices
263 *
264  matpath( 1: 1 ) = 'Zomplex precision'
265  matpath( 2: 3 ) = 'HE'
266 *
267  nrun = 0
268  nfail = 0
269  nerrs = 0
270  DO 10 i = 1, 4
271  iseed( i ) = iseedy( i )
272  10 CONTINUE
273 *
274 * Test the error exits
275 *
276  IF( tsterr )
277  $ CALL zerrhe( path, nout )
278  infot = 0
279 *
280 * Set the minimum block size for which the block routine should
281 * be used, which will be later returned by ILAENV
282 *
283  CALL xlaenv( 2, 2 )
284 *
285 * Do for each value of N in NVAL
286 *
287  DO 270 in = 1, nn
288  n = nval( in )
289  lda = max( n, 1 )
290  xtype = 'N'
291  nimat = ntypes
292  IF( n.LE.0 )
293  $ nimat = 1
294 *
295  izero = 0
296 *
297 * Do for each value of matrix type IMAT
298 *
299  DO 260 imat = 1, nimat
300 *
301 * Do the tests only if DOTYPE( IMAT ) is true.
302 *
303  IF( .NOT.dotype( imat ) )
304  $ GO TO 260
305 *
306 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
307 *
308  zerot = imat.GE.3 .AND. imat.LE.6
309  IF( zerot .AND. n.LT.imat-2 )
310  $ GO TO 260
311 *
312 * Do first for UPLO = 'U', then for UPLO = 'L'
313 *
314  DO 250 iuplo = 1, 2
315  uplo = uplos( iuplo )
316 *
317 * Begin generate the test matrix A.
318 *
319 * Set up parameters with ZLATB4 for the matrix generator
320 * based on the type of matrix to be generated.
321 *
322  CALL zlatb4( matpath, imat, n, n, TYPE, KL, KU, ANORM,
323  $ mode, cndnum, dist )
324 *
325 * Generate a matrix with ZLATMS.
326 *
327  srnamt = 'ZLATMS'
328  CALL zlatms( n, n, dist, iseed, TYPE, RWORK, MODE,
329  $ cndnum, anorm, kl, ku, uplo, a, lda,
330  $ work, info )
331 *
332 * Check error code from ZLATMS and handle error.
333 *
334  IF( info.NE.0 ) THEN
335  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n,
336  $ -1, -1, -1, imat, nfail, nerrs, nout )
337 *
338 * Skip all tests for this generated matrix
339 *
340  GO TO 250
341  END IF
342 *
343 * For matrix types 3-6, zero one or more rows and
344 * columns of the matrix to test that INFO is returned
345 * correctly.
346 *
347  IF( zerot ) THEN
348  IF( imat.EQ.3 ) THEN
349  izero = 1
350  ELSE IF( imat.EQ.4 ) THEN
351  izero = n
352  ELSE
353  izero = n / 2 + 1
354  END IF
355 *
356  IF( imat.LT.6 ) THEN
357 *
358 * Set row and column IZERO to zero.
359 *
360  IF( iuplo.EQ.1 ) THEN
361  ioff = ( izero-1 )*lda
362  DO 20 i = 1, izero - 1
363  a( ioff+i ) = czero
364  20 CONTINUE
365  ioff = ioff + izero
366  DO 30 i = izero, n
367  a( ioff ) = czero
368  ioff = ioff + lda
369  30 CONTINUE
370  ELSE
371  ioff = izero
372  DO 40 i = 1, izero - 1
373  a( ioff ) = czero
374  ioff = ioff + lda
375  40 CONTINUE
376  ioff = ioff - izero
377  DO 50 i = izero, n
378  a( ioff+i ) = czero
379  50 CONTINUE
380  END IF
381  ELSE
382  IF( iuplo.EQ.1 ) THEN
383 *
384 * Set the first IZERO rows and columns to zero.
385 *
386  ioff = 0
387  DO 70 j = 1, n
388  i2 = min( j, izero )
389  DO 60 i = 1, i2
390  a( ioff+i ) = czero
391  60 CONTINUE
392  ioff = ioff + lda
393  70 CONTINUE
394  ELSE
395 *
396 * Set the last IZERO rows and columns to zero.
397 *
398  ioff = 0
399  DO 90 j = 1, n
400  i1 = max( j, izero )
401  DO 80 i = i1, n
402  a( ioff+i ) = czero
403  80 CONTINUE
404  ioff = ioff + lda
405  90 CONTINUE
406  END IF
407  END IF
408  ELSE
409  izero = 0
410  END IF
411 *
412 * End generate the test matrix A.
413 *
414 *
415 * Do for each value of NB in NBVAL
416 *
417  DO 240 inb = 1, nnb
418 *
419 * Set the optimal blocksize, which will be later
420 * returned by ILAENV.
421 *
422  nb = nbval( inb )
423  CALL xlaenv( 1, nb )
424 *
425 * Copy the test matrix A into matrix AFAC which
426 * will be factorized in place. This is needed to
427 * preserve the test matrix A for subsequent tests.
428 *
429  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
430 *
431 * Compute the L*D*L**T or U*D*U**T factorization of the
432 * matrix. IWORK stores details of the interchanges and
433 * the block structure of D. AINV is a work array for
434 * block factorization, LWORK is the length of AINV.
435 *
436  lwork = max( 2, nb )*lda
437  srnamt = 'ZHETRF_ROOK'
438  CALL zhetrf_rook( uplo, n, afac, lda, iwork, ainv,
439  $ lwork, info )
440 *
441 * Adjust the expected value of INFO to account for
442 * pivoting.
443 *
444  k = izero
445  IF( k.GT.0 ) THEN
446  100 CONTINUE
447  IF( iwork( k ).LT.0 ) THEN
448  IF( iwork( k ).NE.-k ) THEN
449  k = -iwork( k )
450  GO TO 100
451  END IF
452  ELSE IF( iwork( k ).NE.k ) THEN
453  k = iwork( k )
454  GO TO 100
455  END IF
456  END IF
457 *
458 * Check error code from ZHETRF_ROOK and handle error.
459 *
460  IF( info.NE.k)
461  $ CALL alaerh( path, 'ZHETRF_ROOK', info, k,
462  $ uplo, n, n, -1, -1, nb, imat,
463  $ nfail, nerrs, nout )
464 *
465 * Set the condition estimate flag if the INFO is not 0.
466 *
467  IF( info.NE.0 ) THEN
468  trfcon = .true.
469  ELSE
470  trfcon = .false.
471  END IF
472 *
473 *+ TEST 1
474 * Reconstruct matrix from factors and compute residual.
475 *
476  CALL zhet01_rook( uplo, n, a, lda, afac, lda, iwork,
477  $ ainv, lda, rwork, result( 1 ) )
478  nt = 1
479 *
480 *+ TEST 2
481 * Form the inverse and compute the residual,
482 * if the factorization was competed without INFO > 0
483 * (i.e. there is no zero rows and columns).
484 * Do it only for the first block size.
485 *
486  IF( inb.EQ.1 .AND. .NOT.trfcon ) THEN
487  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
488  srnamt = 'ZHETRI_ROOK'
489  CALL zhetri_rook( uplo, n, ainv, lda, iwork, work,
490  $ info )
491 *
492 * Check error code from ZHETRI_ROOK and handle error.
493 *
494  IF( info.NE.0 )
495  $ CALL alaerh( path, 'ZHETRI_ROOK', info, -1,
496  $ uplo, n, n, -1, -1, -1, imat,
497  $ nfail, nerrs, nout )
498 *
499 * Compute the residual for a Hermitian matrix times
500 * its inverse.
501 *
502  CALL zpot03( uplo, n, a, lda, ainv, lda, work, lda,
503  $ rwork, rcondc, result( 2 ) )
504  nt = 2
505  END IF
506 *
507 * Print information about the tests that did not pass
508 * the threshold.
509 *
510  DO 110 k = 1, nt
511  IF( result( k ).GE.thresh ) THEN
512  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
513  $ CALL alahd( nout, path )
514  WRITE( nout, fmt = 9999 )uplo, n, nb, imat, k,
515  $ result( k )
516  nfail = nfail + 1
517  END IF
518  110 CONTINUE
519  nrun = nrun + nt
520 *
521 *+ TEST 3
522 * Compute largest element in U or L
523 *
524  result( 3 ) = zero
525  dtemp = zero
526 *
527  const = ( ( alpha**2-one ) / ( alpha**2-onehalf ) ) /
528  $ ( one-alpha )
529 *
530  IF( iuplo.EQ.1 ) THEN
531 *
532 * Compute largest element in U
533 *
534  k = n
535  120 CONTINUE
536  IF( k.LE.1 )
537  $ GO TO 130
538 *
539  IF( iwork( k ).GT.zero ) THEN
540 *
541 * Get max absolute value from elements
542 * in column k in U
543 *
544  dtemp = zlange( 'M', k-1, 1,
545  $ afac( ( k-1 )*lda+1 ), lda, rwork )
546  ELSE
547 *
548 * Get max absolute value from elements
549 * in columns k and k-1 in U
550 *
551  dtemp = zlange( 'M', k-2, 2,
552  $ afac( ( k-2 )*lda+1 ), lda, rwork )
553  k = k - 1
554 *
555  END IF
556 *
557 * DTEMP should be bounded by CONST
558 *
559  dtemp = dtemp - const + thresh
560  IF( dtemp.GT.result( 3 ) )
561  $ result( 3 ) = dtemp
562 *
563  k = k - 1
564 *
565  GO TO 120
566  130 CONTINUE
567 *
568  ELSE
569 *
570 * Compute largest element in L
571 *
572  k = 1
573  140 CONTINUE
574  IF( k.GE.n )
575  $ GO TO 150
576 *
577  IF( iwork( k ).GT.zero ) THEN
578 *
579 * Get max absolute value from elements
580 * in column k in L
581 *
582  dtemp = zlange( 'M', n-k, 1,
583  $ afac( ( k-1 )*lda+k+1 ), lda, rwork )
584  ELSE
585 *
586 * Get max absolute value from elements
587 * in columns k and k+1 in L
588 *
589  dtemp = zlange( 'M', n-k-1, 2,
590  $ afac( ( k-1 )*lda+k+2 ), lda, rwork )
591  k = k + 1
592 *
593  END IF
594 *
595 * DTEMP should be bounded by CONST
596 *
597  dtemp = dtemp - const + thresh
598  IF( dtemp.GT.result( 3 ) )
599  $ result( 3 ) = dtemp
600 *
601  k = k + 1
602 *
603  GO TO 140
604  150 CONTINUE
605  END IF
606 *
607 *
608 *+ TEST 4
609 * Compute largest 2-Norm (condition number)
610 * of 2-by-2 diag blocks
611 *
612  result( 4 ) = zero
613  dtemp = zero
614 *
615  const = ( ( alpha**2-one ) / ( alpha**2-onehalf ) )*
616  $ ( ( one + alpha ) / ( one - alpha ) )
617  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
618 *
619  IF( iuplo.EQ.1 ) THEN
620 *
621 * Loop backward for UPLO = 'U'
622 *
623  k = n
624  160 CONTINUE
625  IF( k.LE.1 )
626  $ GO TO 170
627 *
628  IF( iwork( k ).LT.zero ) THEN
629 *
630 * Get the two singular values
631 * (real and non-negative) of a 2-by-2 block,
632 * store them in RWORK array
633 *
634  block( 1, 1 ) = afac( ( k-2 )*lda+k-1 )
635  block( 1, 2 ) = afac( (k-1)*lda+k-1 )
636  block( 2, 1 ) = conjg( block( 1, 2 ) )
637  block( 2, 2 ) = afac( (k-1)*lda+k )
638 *
639  CALL zgesvd( 'N', 'N', 2, 2, block, 2, rwork,
640  $ zdummy, 1, zdummy, 1,
641  $ work, 6, rwork( 3 ), info )
642 *
643 *
644  sing_max = rwork( 1 )
645  sing_min = rwork( 2 )
646 *
647  dtemp = sing_max / sing_min
648 *
649 * DTEMP should be bounded by CONST
650 *
651  dtemp = dtemp - const + thresh
652  IF( dtemp.GT.result( 4 ) )
653  $ result( 4 ) = dtemp
654  k = k - 1
655 *
656  END IF
657 *
658  k = k - 1
659 *
660  GO TO 160
661  170 CONTINUE
662 *
663  ELSE
664 *
665 * Loop forward for UPLO = 'L'
666 *
667  k = 1
668  180 CONTINUE
669  IF( k.GE.n )
670  $ GO TO 190
671 *
672  IF( iwork( k ).LT.zero ) THEN
673 *
674 * Get the two singular values
675 * (real and non-negative) of a 2-by-2 block,
676 * store them in RWORK array
677 *
678  block( 1, 1 ) = afac( ( k-1 )*lda+k )
679  block( 2, 1 ) = afac( ( k-1 )*lda+k+1 )
680  block( 1, 2 ) = conjg( block( 2, 1 ) )
681  block( 2, 2 ) = afac( k*lda+k+1 )
682 *
683  CALL zgesvd( 'N', 'N', 2, 2, block, 2, rwork,
684  $ zdummy, 1, zdummy, 1,
685  $ work, 6, rwork(3), info )
686 *
687  sing_max = rwork( 1 )
688  sing_min = rwork( 2 )
689 *
690  dtemp = sing_max / sing_min
691 *
692 * DTEMP should be bounded by CONST
693 *
694  dtemp = dtemp - const + thresh
695  IF( dtemp.GT.result( 4 ) )
696  $ result( 4 ) = dtemp
697  k = k + 1
698 *
699  END IF
700 *
701  k = k + 1
702 *
703  GO TO 180
704  190 CONTINUE
705  END IF
706 *
707 * Print information about the tests that did not pass
708 * the threshold.
709 *
710  DO 200 k = 3, 4
711  IF( result( k ).GE.thresh ) THEN
712  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
713  $ CALL alahd( nout, path )
714  WRITE( nout, fmt = 9999 )uplo, n, nb, imat, k,
715  $ result( k )
716  nfail = nfail + 1
717  END IF
718  200 CONTINUE
719  nrun = nrun + 2
720 *
721 * Skip the other tests if this is not the first block
722 * size.
723 *
724  IF( inb.GT.1 )
725  $ GO TO 240
726 *
727 * Do only the condition estimate if INFO is not 0.
728 *
729  IF( trfcon ) THEN
730  rcondc = zero
731  GO TO 230
732  END IF
733 *
734 * Do for each value of NRHS in NSVAL.
735 *
736  DO 220 irhs = 1, nns
737  nrhs = nsval( irhs )
738 *
739 * Begin loop over NRHS values
740 *
741 *
742 *+ TEST 5 ( Using TRS_ROOK)
743 * Solve and compute residual for A * X = B.
744 *
745 * Choose a set of NRHS random solution vectors
746 * stored in XACT and set up the right hand side B
747 *
748  srnamt = 'ZLARHS'
749  CALL zlarhs( matpath, xtype, uplo, ' ', n, n,
750  $ kl, ku, nrhs, a, lda, xact, lda,
751  $ b, lda, iseed, info )
752  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
753 *
754  srnamt = 'ZHETRS_ROOK'
755  CALL zhetrs_rook( uplo, n, nrhs, afac, lda, iwork,
756  $ x, lda, info )
757 *
758 * Check error code from ZHETRS_ROOK and handle error.
759 *
760  IF( info.NE.0 )
761  $ CALL alaerh( path, 'ZHETRS_ROOK', info, 0,
762  $ uplo, n, n, -1, -1, nrhs, imat,
763  $ nfail, nerrs, nout )
764 *
765  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
766 *
767 * Compute the residual for the solution
768 *
769  CALL zpot02( uplo, n, nrhs, a, lda, x, lda, work,
770  $ lda, rwork, result( 5 ) )
771 *
772 *+ TEST 6
773 * Check solution from generated exact solution.
774 *
775  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
776  $ result( 6 ) )
777 *
778 * Print information about the tests that did not pass
779 * the threshold.
780 *
781  DO 210 k = 5, 6
782  IF( result( k ).GE.thresh ) THEN
783  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
784  $ CALL alahd( nout, path )
785  WRITE( nout, fmt = 9998 )uplo, n, nrhs,
786  $ imat, k, result( k )
787  nfail = nfail + 1
788  END IF
789  210 CONTINUE
790  nrun = nrun + 2
791 *
792 * End do for each value of NRHS in NSVAL.
793 *
794  220 CONTINUE
795 *
796 *+ TEST 7
797 * Get an estimate of RCOND = 1/CNDNUM.
798 *
799  230 CONTINUE
800  anorm = zlanhe( '1', uplo, n, a, lda, rwork )
801  srnamt = 'ZHECON_ROOK'
802  CALL zhecon_rook( uplo, n, afac, lda, iwork, anorm,
803  $ rcond, work, info )
804 *
805 * Check error code from ZHECON_ROOK and handle error.
806 *
807  IF( info.NE.0 )
808  $ CALL alaerh( path, 'ZHECON_ROOK', info, 0,
809  $ uplo, n, n, -1, -1, -1, imat,
810  $ nfail, nerrs, nout )
811 *
812 * Compute the test ratio to compare values of RCOND
813 *
814  result( 7 ) = dget06( rcond, rcondc )
815 *
816 * Print information about the tests that did not pass
817 * the threshold.
818 *
819  IF( result( 7 ).GE.thresh ) THEN
820  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
821  $ CALL alahd( nout, path )
822  WRITE( nout, fmt = 9997 )uplo, n, imat, 7,
823  $ result( 7 )
824  nfail = nfail + 1
825  END IF
826  nrun = nrun + 1
827  240 CONTINUE
828 *
829  250 CONTINUE
830  260 CONTINUE
831  270 CONTINUE
832 *
833 * Print a summary of the results.
834 *
835  CALL alasum( path, nout, nfail, nrun, nerrs )
836 *
837  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NB =', i4, ', type ',
838  $ i2, ', test ', i2, ', ratio =', g12.5 )
839  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
840  $ i2, ', test ', i2, ', ratio =', g12.5 )
841  9997 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ',', 10x, ' type ', i2,
842  $ ', test ', i2, ', ratio =', g12.5 )
843  RETURN
844 *
845 * End of ZCHKHE_ROOK
846 *
847  END
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:107
subroutine zpot03(UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
ZPOT03
Definition: zpot03.f:128
subroutine zget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
ZGET04
Definition: zget04.f:104
subroutine zchkhe_rook(DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
ZCHKHE_ROOK
Definition: zchkhe_rook.f:174
subroutine zerrhe(PATH, NUNIT)
ZERRHE
Definition: zerrhe.f:57
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
subroutine zhetrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZHETRS_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using fac...
Definition: zhetrs_rook.f:138
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
subroutine zhet01_rook(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
ZHET01_ROOK
Definition: zhet01_rook.f:127
subroutine zgesvd(JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, INFO)
ZGESVD computes the singular value decomposition (SVD) for GE matrices
Definition: zgesvd.f:216
subroutine zlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
ZLATB4
Definition: zlatb4.f:123
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
subroutine zhetrf_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bun...
Definition: zhetrf_rook.f:214
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:334
subroutine zhetri_rook(UPLO, N, A, LDA, IPIV, WORK, INFO)
ZHETRI_ROOK computes the inverse of HE matrix using the factorization obtained with the bounded Bunch...
Definition: zhetri_rook.f:130
subroutine zlarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
ZLARHS
Definition: zlarhs.f:211
subroutine zpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZPOT02
Definition: zpot02.f:129
subroutine zhecon_rook(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO)
ZHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization ob...
Definition: zhecon_rook.f:141
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:75