LAPACK  3.7.0
LAPACK: Linear Algebra PACKage
zchkhe_rk.f
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1 *> \brief \b ZCHKHE_RK
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_RK( 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( * ), E( * ),
25 * $ WORK( * ), X( * ), XACT( * )
26 * ..
27 *
28 *
29 *> \par Purpose:
30 * =============
31 *>
32 *> \verbatim
33 *>
34 *> ZCHKHE_RK tests ZHETRF_RK, -TRI_3, -TRS_3,
35 *> and -CON_3.
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] E
117 *> \verbatim
118 *> E is COMPLEX*16 array, dimension (NMAX)
119 *> \endverbatim
120 *>
121 *> \param[out] AINV
122 *> \verbatim
123 *> AINV is COMPLEX*16 array, dimension (NMAX*NMAX)
124 *> \endverbatim
125 *>
126 *> \param[out] B
127 *> \verbatim
128 *> B is CCOMPLEX*16 array, dimension (NMAX*NSMAX)
129 *> where NSMAX is the largest entry in NSVAL.
130 *> \endverbatim
131 *>
132 *> \param[out] X
133 *> \verbatim
134 *> X is COMPLEX*16 array, dimension (NMAX*NSMAX)
135 *> \endverbatim
136 *>
137 *> \param[out] XACT
138 *> \verbatim
139 *> XACT is COMPLEX*16 array, dimension (NMAX*NSMAX)
140 *> \endverbatim
141 *>
142 *> \param[out] WORK
143 *> \verbatim
144 *> WORK is COMPLEX*16 array, dimension (NMAX*max(3,NSMAX))
145 *> \endverbatim
146 *>
147 *> \param[out] RWORK
148 *> \verbatim
149 *> RWORK is DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX)
150 *> \endverbatim
151 *>
152 *> \param[out] IWORK
153 *> \verbatim
154 *> IWORK is INTEGER array, dimension (2*NMAX)
155 *> \endverbatim
156 *>
157 *> \param[in] NOUT
158 *> \verbatim
159 *> NOUT is INTEGER
160 *> The unit number for output.
161 *> \endverbatim
162 *
163 * Authors:
164 * ========
165 *
166 *> \author Univ. of Tennessee
167 *> \author Univ. of California Berkeley
168 *> \author Univ. of Colorado Denver
169 *> \author NAG Ltd.
170 *
171 *> \date December 2016
172 *
173 *> \ingroup complex16_lin
174 *
175 * =====================================================================
176  SUBROUTINE zchkhe_rk( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
177  $ thresh, tsterr, nmax, a, afac, e, ainv, b,
178  $ x, xact, work, rwork, iwork, nout )
179 *
180 * -- LAPACK test routine (version 3.7.0) --
181 * -- LAPACK is a software package provided by Univ. of Tennessee, --
182 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
183 * December 2016
184 *
185 * .. Scalar Arguments ..
186  LOGICAL TSTERR
187  INTEGER NMAX, NN, NNB, NNS, NOUT
188  DOUBLE PRECISION THRESH
189 * ..
190 * .. Array Arguments ..
191  LOGICAL DOTYPE( * )
192  INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
193  DOUBLE PRECISION RWORK( * )
194  COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ), E( * ),
195  $ work( * ), x( * ), xact( * )
196 * ..
197 *
198 * =====================================================================
199 *
200 * .. Parameters ..
201  DOUBLE PRECISION ZERO, ONE
202  parameter ( zero = 0.0d+0, one = 1.0d+0 )
203  DOUBLE PRECISION ONEHALF
204  parameter ( onehalf = 0.5d+0 )
205  DOUBLE PRECISION EIGHT, SEVTEN
206  parameter ( eight = 8.0d+0, sevten = 17.0d+0 )
207  COMPLEX*16 CZERO
208  parameter ( czero = ( 0.0d+0, 0.0d+0 ) )
209  INTEGER NTYPES
210  parameter ( ntypes = 10 )
211  INTEGER NTESTS
212  parameter ( ntests = 7 )
213 * ..
214 * .. Local Scalars ..
215  LOGICAL TRFCON, ZEROT
216  CHARACTER DIST, TYPE, UPLO, XTYPE
217  CHARACTER*3 PATH, MATPATH
218  INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
219  $ itemp, itemp2, iuplo, izero, j, k, kl, ku, lda,
220  $ lwork, mode, n, nb, nerrs, nfail, nimat, nrhs,
221  $ nrun, nt
222  DOUBLE PRECISION ALPHA, ANORM, CNDNUM, CONST, SING_MAX,
223  $ sing_min, rcond, rcondc, dtemp
224 * ..
225 * .. Local Arrays ..
226  CHARACTER UPLOS( 2 )
227  INTEGER ISEED( 4 ), ISEEDY( 4 ), IDUMMY( 1 )
228  DOUBLE PRECISION RESULT( ntests )
229  COMPLEX*16 BLOCK( 2, 2 ), ZDUMMY( 1 )
230 * ..
231 * .. External Functions ..
232  DOUBLE PRECISION DGET06, ZLANGE, ZLANHE
233  EXTERNAL dget06, zlange, zlanhe
234 * ..
235 * .. External Subroutines ..
236  EXTERNAL alaerh, alahd, alasum, zerrhe, zgesvd, zget04,
237  $ zlacpy, zlarhs, zlatb4, zlatms, zpot02, zpot03,
238  $ zhecon_3, zhet01_3, zhetrf_rk, zhetri_3,
239  $ zhetrs_3, xlaenv
240 * ..
241 * .. Intrinsic Functions ..
242  INTRINSIC dconjg, max, min, sqrt
243 * ..
244 * .. Scalars in Common ..
245  LOGICAL LERR, OK
246  CHARACTER*32 SRNAMT
247  INTEGER INFOT, NUNIT
248 * ..
249 * .. Common blocks ..
250  COMMON / infoc / infot, nunit, ok, lerr
251  COMMON / srnamc / srnamt
252 * ..
253 * .. Data statements ..
254  DATA iseedy / 1988, 1989, 1990, 1991 /
255  DATA uplos / 'U', 'L' /
256 * ..
257 * .. Executable Statements ..
258 *
259 * Initialize constants and the random number seed.
260 *
261  alpha = ( one+sqrt( sevten ) ) / eight
262 *
263 * Test path
264 *
265  path( 1: 1 ) = 'Zomplex precision'
266  path( 2: 3 ) = 'HK'
267 *
268 * Path to generate matrices
269 *
270  matpath( 1: 1 ) = 'Zomplex precision'
271  matpath( 2: 3 ) = 'HE'
272 *
273  nrun = 0
274  nfail = 0
275  nerrs = 0
276  DO 10 i = 1, 4
277  iseed( i ) = iseedy( i )
278  10 CONTINUE
279 *
280 * Test the error exits
281 *
282  IF( tsterr )
283  $ CALL zerrhe( path, nout )
284  infot = 0
285 *
286 * Set the minimum block size for which the block routine should
287 * be used, which will be later returned by ILAENV
288 *
289  CALL xlaenv( 2, 2 )
290 *
291 * Do for each value of N in NVAL
292 *
293  DO 270 in = 1, nn
294  n = nval( in )
295  lda = max( n, 1 )
296  xtype = 'N'
297  nimat = ntypes
298  IF( n.LE.0 )
299  $ nimat = 1
300 *
301  izero = 0
302 *
303 * Do for each value of matrix type IMAT
304 *
305  DO 260 imat = 1, nimat
306 *
307 * Do the tests only if DOTYPE( IMAT ) is true.
308 *
309  IF( .NOT.dotype( imat ) )
310  $ GO TO 260
311 *
312 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
313 *
314  zerot = imat.GE.3 .AND. imat.LE.6
315  IF( zerot .AND. n.LT.imat-2 )
316  $ GO TO 260
317 *
318 * Do first for UPLO = 'U', then for UPLO = 'L'
319 *
320  DO 250 iuplo = 1, 2
321  uplo = uplos( iuplo )
322 *
323 * Begin generate the test matrix A.
324 *
325 * Set up parameters with ZLATB4 for the matrix generator
326 * based on the type of matrix to be generated.
327 *
328  CALL zlatb4( matpath, imat, n, n, TYPE, KL, KU, ANORM,
329  $ mode, cndnum, dist )
330 *
331 * Generate a matrix with ZLATMS.
332 *
333  srnamt = 'ZLATMS'
334  CALL zlatms( n, n, dist, iseed, TYPE, RWORK, MODE,
335  $ cndnum, anorm, kl, ku, uplo, a, lda,
336  $ work, info )
337 *
338 * Check error code from ZLATMS and handle error.
339 *
340  IF( info.NE.0 ) THEN
341  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n,
342  $ -1, -1, -1, imat, nfail, nerrs, nout )
343 *
344 * Skip all tests for this generated matrix
345 *
346  GO TO 250
347  END IF
348 *
349 * For matrix types 3-6, zero one or more rows and
350 * columns of the matrix to test that INFO is returned
351 * correctly.
352 *
353  IF( zerot ) THEN
354  IF( imat.EQ.3 ) THEN
355  izero = 1
356  ELSE IF( imat.EQ.4 ) THEN
357  izero = n
358  ELSE
359  izero = n / 2 + 1
360  END IF
361 *
362  IF( imat.LT.6 ) THEN
363 *
364 * Set row and column IZERO to zero.
365 *
366  IF( iuplo.EQ.1 ) THEN
367  ioff = ( izero-1 )*lda
368  DO 20 i = 1, izero - 1
369  a( ioff+i ) = czero
370  20 CONTINUE
371  ioff = ioff + izero
372  DO 30 i = izero, n
373  a( ioff ) = czero
374  ioff = ioff + lda
375  30 CONTINUE
376  ELSE
377  ioff = izero
378  DO 40 i = 1, izero - 1
379  a( ioff ) = czero
380  ioff = ioff + lda
381  40 CONTINUE
382  ioff = ioff - izero
383  DO 50 i = izero, n
384  a( ioff+i ) = czero
385  50 CONTINUE
386  END IF
387  ELSE
388  IF( iuplo.EQ.1 ) THEN
389 *
390 * Set the first IZERO rows and columns to zero.
391 *
392  ioff = 0
393  DO 70 j = 1, n
394  i2 = min( j, izero )
395  DO 60 i = 1, i2
396  a( ioff+i ) = czero
397  60 CONTINUE
398  ioff = ioff + lda
399  70 CONTINUE
400  ELSE
401 *
402 * Set the last IZERO rows and columns to zero.
403 *
404  ioff = 0
405  DO 90 j = 1, n
406  i1 = max( j, izero )
407  DO 80 i = i1, n
408  a( ioff+i ) = czero
409  80 CONTINUE
410  ioff = ioff + lda
411  90 CONTINUE
412  END IF
413  END IF
414  ELSE
415  izero = 0
416  END IF
417 *
418 * End generate the test matrix A.
419 *
420 *
421 * Do for each value of NB in NBVAL
422 *
423  DO 240 inb = 1, nnb
424 *
425 * Set the optimal blocksize, which will be later
426 * returned by ILAENV.
427 *
428  nb = nbval( inb )
429  CALL xlaenv( 1, nb )
430 *
431 * Copy the test matrix A into matrix AFAC which
432 * will be factorized in place. This is needed to
433 * preserve the test matrix A for subsequent tests.
434 *
435  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
436 *
437 * Compute the L*D*L**T or U*D*U**T factorization of the
438 * matrix. IWORK stores details of the interchanges and
439 * the block structure of D. AINV is a work array for
440 * block factorization, LWORK is the length of AINV.
441 *
442  lwork = max( 2, nb )*lda
443  srnamt = 'ZHETRF_RK'
444  CALL zhetrf_rk( uplo, n, afac, lda, e, iwork, ainv,
445  $ lwork, info )
446 *
447 * Adjust the expected value of INFO to account for
448 * pivoting.
449 *
450  k = izero
451  IF( k.GT.0 ) THEN
452  100 CONTINUE
453  IF( iwork( k ).LT.0 ) THEN
454  IF( iwork( k ).NE.-k ) THEN
455  k = -iwork( k )
456  GO TO 100
457  END IF
458  ELSE IF( iwork( k ).NE.k ) THEN
459  k = iwork( k )
460  GO TO 100
461  END IF
462  END IF
463 *
464 * Check error code from ZHETRF_RK and handle error.
465 *
466  IF( info.NE.k)
467  $ CALL alaerh( path, 'ZHETRF_RK', info, k,
468  $ uplo, n, n, -1, -1, nb, imat,
469  $ nfail, nerrs, nout )
470 *
471 * Set the condition estimate flag if the INFO is not 0.
472 *
473  IF( info.NE.0 ) THEN
474  trfcon = .true.
475  ELSE
476  trfcon = .false.
477  END IF
478 *
479 *+ TEST 1
480 * Reconstruct matrix from factors and compute residual.
481 *
482  CALL zhet01_3( uplo, n, a, lda, afac, lda, e, iwork,
483  $ ainv, lda, rwork, result( 1 ) )
484  nt = 1
485 *
486 *+ TEST 2
487 * Form the inverse and compute the residual,
488 * if the factorization was competed without INFO > 0
489 * (i.e. there is no zero rows and columns).
490 * Do it only for the first block size.
491 *
492  IF( inb.EQ.1 .AND. .NOT.trfcon ) THEN
493  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
494  srnamt = 'ZHETRI_3'
495 *
496 * Another reason that we need to compute the invesrse
497 * is that ZPOT03 produces RCONDC which is used later
498 * in TEST6 and TEST7.
499 *
500  lwork = (n+nb+1)*(nb+3)
501  CALL zhetri_3( uplo, n, ainv, lda, e, iwork, work,
502  $ lwork, info )
503 *
504 * Check error code from ZHETRI_3 and handle error.
505 *
506  IF( info.NE.0 )
507  $ CALL alaerh( path, 'ZHETRI_3', info, -1,
508  $ uplo, n, n, -1, -1, -1, imat,
509  $ nfail, nerrs, nout )
510 *
511 * Compute the residual for a Hermitian matrix times
512 * its inverse.
513 *
514  CALL zpot03( uplo, n, a, lda, ainv, lda, work, lda,
515  $ rwork, rcondc, result( 2 ) )
516  nt = 2
517  END IF
518 *
519 * Print information about the tests that did not pass
520 * the threshold.
521 *
522  DO 110 k = 1, nt
523  IF( result( k ).GE.thresh ) THEN
524  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
525  $ CALL alahd( nout, path )
526  WRITE( nout, fmt = 9999 )uplo, n, nb, imat, k,
527  $ result( k )
528  nfail = nfail + 1
529  END IF
530  110 CONTINUE
531  nrun = nrun + nt
532 *
533 *+ TEST 3
534 * Compute largest element in U or L
535 *
536  result( 3 ) = zero
537  dtemp = zero
538 *
539  const = ( ( alpha**2-one ) / ( alpha**2-onehalf ) ) /
540  $ ( one-alpha )
541 *
542  IF( iuplo.EQ.1 ) THEN
543 *
544 * Compute largest element in U
545 *
546  k = n
547  120 CONTINUE
548  IF( k.LE.1 )
549  $ GO TO 130
550 *
551  IF( iwork( k ).GT.zero ) THEN
552 *
553 * Get max absolute value from elements
554 * in column k in U
555 *
556  dtemp = zlange( 'M', k-1, 1,
557  $ afac( ( k-1 )*lda+1 ), lda, rwork )
558  ELSE
559 *
560 * Get max absolute value from elements
561 * in columns k and k-1 in U
562 *
563  dtemp = zlange( 'M', k-2, 2,
564  $ afac( ( k-2 )*lda+1 ), lda, rwork )
565  k = k - 1
566 *
567  END IF
568 *
569 * DTEMP should be bounded by CONST
570 *
571  dtemp = dtemp - const + thresh
572  IF( dtemp.GT.result( 3 ) )
573  $ result( 3 ) = dtemp
574 *
575  k = k - 1
576 *
577  GO TO 120
578  130 CONTINUE
579 *
580  ELSE
581 *
582 * Compute largest element in L
583 *
584  k = 1
585  140 CONTINUE
586  IF( k.GE.n )
587  $ GO TO 150
588 *
589  IF( iwork( k ).GT.zero ) THEN
590 *
591 * Get max absolute value from elements
592 * in column k in L
593 *
594  dtemp = zlange( 'M', n-k, 1,
595  $ afac( ( k-1 )*lda+k+1 ), lda, rwork )
596  ELSE
597 *
598 * Get max absolute value from elements
599 * in columns k and k+1 in L
600 *
601  dtemp = zlange( 'M', n-k-1, 2,
602  $ afac( ( k-1 )*lda+k+2 ), lda, rwork )
603  k = k + 1
604 *
605  END IF
606 *
607 * DTEMP should be bounded by CONST
608 *
609  dtemp = dtemp - const + thresh
610  IF( dtemp.GT.result( 3 ) )
611  $ result( 3 ) = dtemp
612 *
613  k = k + 1
614 *
615  GO TO 140
616  150 CONTINUE
617  END IF
618 *
619 *
620 *+ TEST 4
621 * Compute largest 2-Norm (condition number)
622 * of 2-by-2 diag blocks
623 *
624  result( 4 ) = zero
625  dtemp = zero
626 *
627  const = ( ( alpha**2-one ) / ( alpha**2-onehalf ) )*
628  $ ( ( one + alpha ) / ( one - alpha ) )
629  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
630 *
631  IF( iuplo.EQ.1 ) THEN
632 *
633 * Loop backward for UPLO = 'U'
634 *
635  k = n
636  160 CONTINUE
637  IF( k.LE.1 )
638  $ GO TO 170
639 *
640  IF( iwork( k ).LT.zero ) THEN
641 *
642 * Get the two singular values
643 * (real and non-negative) of a 2-by-2 block,
644 * store them in RWORK array
645 *
646  block( 1, 1 ) = afac( ( k-2 )*lda+k-1 )
647  block( 1, 2 ) = e( k )
648  block( 2, 1 ) = dconjg( block( 1, 2 ) )
649  block( 2, 2 ) = afac( (k-1)*lda+k )
650 *
651  CALL zgesvd( 'N', 'N', 2, 2, block, 2, rwork,
652  $ zdummy, 1, zdummy, 1,
653  $ work, 6, rwork( 3 ), info )
654 *
655 *
656  sing_max = rwork( 1 )
657  sing_min = rwork( 2 )
658 *
659  dtemp = sing_max / sing_min
660 *
661 * DTEMP should be bounded by CONST
662 *
663  dtemp = dtemp - const + thresh
664  IF( dtemp.GT.result( 4 ) )
665  $ result( 4 ) = dtemp
666  k = k - 1
667 *
668  END IF
669 *
670  k = k - 1
671 *
672  GO TO 160
673  170 CONTINUE
674 *
675  ELSE
676 *
677 * Loop forward for UPLO = 'L'
678 *
679  k = 1
680  180 CONTINUE
681  IF( k.GE.n )
682  $ GO TO 190
683 *
684  IF( iwork( k ).LT.zero ) THEN
685 *
686 * Get the two singular values
687 * (real and non-negative) of a 2-by-2 block,
688 * store them in RWORK array
689 *
690  block( 1, 1 ) = afac( ( k-1 )*lda+k )
691  block( 2, 1 ) = e( k )
692  block( 1, 2 ) = dconjg( block( 2, 1 ) )
693  block( 2, 2 ) = afac( k*lda+k+1 )
694 *
695  CALL zgesvd( 'N', 'N', 2, 2, block, 2, rwork,
696  $ zdummy, 1, zdummy, 1,
697  $ work, 6, rwork(3), info )
698 *
699  sing_max = rwork( 1 )
700  sing_min = rwork( 2 )
701 *
702  dtemp = sing_max / sing_min
703 *
704 * DTEMP should be bounded by CONST
705 *
706  dtemp = dtemp - const + thresh
707  IF( dtemp.GT.result( 4 ) )
708  $ result( 4 ) = dtemp
709  k = k + 1
710 *
711  END IF
712 *
713  k = k + 1
714 *
715  GO TO 180
716  190 CONTINUE
717  END IF
718 *
719 * Print information about the tests that did not pass
720 * the threshold.
721 *
722  DO 200 k = 3, 4
723  IF( result( k ).GE.thresh ) THEN
724  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
725  $ CALL alahd( nout, path )
726  WRITE( nout, fmt = 9999 )uplo, n, nb, imat, k,
727  $ result( k )
728  nfail = nfail + 1
729  END IF
730  200 CONTINUE
731  nrun = nrun + 2
732 *
733 * Skip the other tests if this is not the first block
734 * size.
735 *
736  IF( inb.GT.1 )
737  $ GO TO 240
738 *
739 * Do only the condition estimate if INFO is not 0.
740 *
741  IF( trfcon ) THEN
742  rcondc = zero
743  GO TO 230
744  END IF
745 *
746 * Do for each value of NRHS in NSVAL.
747 *
748  DO 220 irhs = 1, nns
749  nrhs = nsval( irhs )
750 *
751 * Begin loop over NRHS values
752 *
753 *
754 *+ TEST 5 ( Using TRS_3)
755 * Solve and compute residual for A * X = B.
756 *
757 * Choose a set of NRHS random solution vectors
758 * stored in XACT and set up the right hand side B
759 *
760  srnamt = 'ZLARHS'
761  CALL zlarhs( matpath, xtype, uplo, ' ', n, n,
762  $ kl, ku, nrhs, a, lda, xact, lda,
763  $ b, lda, iseed, info )
764  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
765 *
766  srnamt = 'ZHETRS_3'
767  CALL zhetrs_3( uplo, n, nrhs, afac, lda, e, iwork,
768  $ x, lda, info )
769 *
770 * Check error code from ZHETRS_3 and handle error.
771 *
772  IF( info.NE.0 )
773  $ CALL alaerh( path, 'ZHETRS_3', info, 0,
774  $ uplo, n, n, -1, -1, nrhs, imat,
775  $ nfail, nerrs, nout )
776 *
777  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
778 *
779 * Compute the residual for the solution
780 *
781  CALL zpot02( uplo, n, nrhs, a, lda, x, lda, work,
782  $ lda, rwork, result( 5 ) )
783 *
784 *+ TEST 6
785 * Check solution from generated exact solution.
786 *
787  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
788  $ result( 6 ) )
789 *
790 * Print information about the tests that did not pass
791 * the threshold.
792 *
793  DO 210 k = 5, 6
794  IF( result( k ).GE.thresh ) THEN
795  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
796  $ CALL alahd( nout, path )
797  WRITE( nout, fmt = 9998 )uplo, n, nrhs,
798  $ imat, k, result( k )
799  nfail = nfail + 1
800  END IF
801  210 CONTINUE
802  nrun = nrun + 2
803 *
804 * End do for each value of NRHS in NSVAL.
805 *
806  220 CONTINUE
807 *
808 *+ TEST 7
809 * Get an estimate of RCOND = 1/CNDNUM.
810 *
811  230 CONTINUE
812  anorm = zlanhe( '1', uplo, n, a, lda, rwork )
813  srnamt = 'ZHECON_3'
814  CALL zhecon_3( uplo, n, afac, lda, e, iwork, anorm,
815  $ rcond, work, info )
816 *
817 * Check error code from ZHECON_3 and handle error.
818 *
819  IF( info.NE.0 )
820  $ CALL alaerh( path, 'ZHECON_3', info, 0,
821  $ uplo, n, n, -1, -1, -1, imat,
822  $ nfail, nerrs, nout )
823 *
824 * Compute the test ratio to compare values of RCOND
825 *
826  result( 7 ) = dget06( rcond, rcondc )
827 *
828 * Print information about the tests that did not pass
829 * the threshold.
830 *
831  IF( result( 7 ).GE.thresh ) THEN
832  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
833  $ CALL alahd( nout, path )
834  WRITE( nout, fmt = 9997 )uplo, n, imat, 7,
835  $ result( 7 )
836  nfail = nfail + 1
837  END IF
838  nrun = nrun + 1
839  240 CONTINUE
840 *
841  250 CONTINUE
842  260 CONTINUE
843  270 CONTINUE
844 *
845 * Print a summary of the results.
846 *
847  CALL alasum( path, nout, nfail, nrun, nerrs )
848 *
849  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NB =', i4, ', type ',
850  $ i2, ', test ', i2, ', ratio =', g12.5 )
851  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
852  $ i2, ', test ', i2, ', ratio =', g12.5 )
853  9997 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ',', 10x, ' type ', i2,
854  $ ', test ', i2, ', ratio =', g12.5 )
855  RETURN
856 *
857 * End of ZCHKHE_RK
858 *
859  END
alahd
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:107
alaerh
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
zhetrf_rk
subroutine zhetrf_rk(UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
ZHETRF_RK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch...
Definition: zhetrf_rk.f:261
zget04
subroutine zget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
ZGET04
Definition: zget04.f:104
zhet01_3
subroutine zhet01_3(UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C, LDC, RWORK, RESID)
ZHET01_3
Definition: zhet01_3.f:143
zerrhe
subroutine zerrhe(PATH, NUNIT)
ZERRHE
Definition: zerrhe.f:57
zpot02
subroutine zpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZPOT02
Definition: zpot02.f:129
zlarhs
subroutine zlarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
ZLARHS
Definition: zlarhs.f:211
zhetrs_3
subroutine zhetrs_3(UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, INFO)
ZHETRS_3
Definition: zhetrs_3.f:167
zlacpy
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
xlaenv
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
zpot03
subroutine zpot03(UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
ZPOT03
Definition: zpot03.f:128
zlatb4
subroutine zlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
ZLATB4
Definition: zlatb4.f:123
zhetri_3
subroutine zhetri_3(UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
ZHETRI_3
Definition: zhetri_3.f:172
zgesvd
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
zhecon_3
subroutine zhecon_3(UPLO, N, A, LDA, E, IPIV, ANORM, RCOND, WORK, INFO)
ZHECON_3
Definition: zhecon_3.f:173
zchkhe_rk
subroutine zchkhe_rk(DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, E, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
ZCHKHE_RK
Definition: zchkhe_rk.f:179
zlatms
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:334
alasum
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:75