LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
cdrvhp.f
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1 *> \brief \b CDRVHP
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 CDRVHP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
12 * A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
13 * NOUT )
14 *
15 * .. Scalar Arguments ..
16 * LOGICAL TSTERR
17 * INTEGER NMAX, NN, NOUT, NRHS
18 * REAL THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER IWORK( * ), NVAL( * )
23 * REAL RWORK( * )
24 * COMPLEX A( * ), AFAC( * ), AINV( * ), B( * ),
25 * $ WORK( * ), X( * ), XACT( * )
26 * ..
27 *
28 *
29 *> \par Purpose:
30 * =============
31 *>
32 *> \verbatim
33 *>
34 *> CDRVHP tests the driver routines CHPSV and -SVX.
35 *> \endverbatim
36 *
37 * Arguments:
38 * ==========
39 *
40 *> \param[in] DOTYPE
41 *> \verbatim
42 *> DOTYPE is LOGICAL array, dimension (NTYPES)
43 *> The matrix types to be used for testing. Matrices of type j
44 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
45 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
46 *> \endverbatim
47 *>
48 *> \param[in] NN
49 *> \verbatim
50 *> NN is INTEGER
51 *> The number of values of N contained in the vector NVAL.
52 *> \endverbatim
53 *>
54 *> \param[in] NVAL
55 *> \verbatim
56 *> NVAL is INTEGER array, dimension (NN)
57 *> The values of the matrix dimension N.
58 *> \endverbatim
59 *>
60 *> \param[in] NRHS
61 *> \verbatim
62 *> NRHS is INTEGER
63 *> The number of right hand side vectors to be generated for
64 *> each linear system.
65 *> \endverbatim
66 *>
67 *> \param[in] THRESH
68 *> \verbatim
69 *> THRESH is REAL
70 *> The threshold value for the test ratios. A result is
71 *> included in the output file if RESULT >= THRESH. To have
72 *> every test ratio printed, use THRESH = 0.
73 *> \endverbatim
74 *>
75 *> \param[in] TSTERR
76 *> \verbatim
77 *> TSTERR is LOGICAL
78 *> Flag that indicates whether error exits are to be tested.
79 *> \endverbatim
80 *>
81 *> \param[in] NMAX
82 *> \verbatim
83 *> NMAX is INTEGER
84 *> The maximum value permitted for N, used in dimensioning the
85 *> work arrays.
86 *> \endverbatim
87 *>
88 *> \param[out] A
89 *> \verbatim
90 *> A is COMPLEX array, dimension
91 *> (NMAX*(NMAX+1)/2)
92 *> \endverbatim
93 *>
94 *> \param[out] AFAC
95 *> \verbatim
96 *> AFAC is COMPLEX array, dimension
97 *> (NMAX*(NMAX+1)/2)
98 *> \endverbatim
99 *>
100 *> \param[out] AINV
101 *> \verbatim
102 *> AINV is COMPLEX array, dimension
103 *> (NMAX*(NMAX+1)/2)
104 *> \endverbatim
105 *>
106 *> \param[out] B
107 *> \verbatim
108 *> B is COMPLEX array, dimension (NMAX*NRHS)
109 *> \endverbatim
110 *>
111 *> \param[out] X
112 *> \verbatim
113 *> X is COMPLEX array, dimension (NMAX*NRHS)
114 *> \endverbatim
115 *>
116 *> \param[out] XACT
117 *> \verbatim
118 *> XACT is COMPLEX array, dimension (NMAX*NRHS)
119 *> \endverbatim
120 *>
121 *> \param[out] WORK
122 *> \verbatim
123 *> WORK is COMPLEX array, dimension
124 *> (NMAX*max(2,NRHS))
125 *> \endverbatim
126 *>
127 *> \param[out] RWORK
128 *> \verbatim
129 *> RWORK is REAL array, dimension (NMAX+2*NRHS)
130 *> \endverbatim
131 *>
132 *> \param[out] IWORK
133 *> \verbatim
134 *> IWORK is INTEGER array, dimension (NMAX)
135 *> \endverbatim
136 *>
137 *> \param[in] NOUT
138 *> \verbatim
139 *> NOUT is INTEGER
140 *> The unit number for output.
141 *> \endverbatim
142 *
143 * Authors:
144 * ========
145 *
146 *> \author Univ. of Tennessee
147 *> \author Univ. of California Berkeley
148 *> \author Univ. of Colorado Denver
149 *> \author NAG Ltd.
150 *
151 *> \date December 2016
152 *
153 *> \ingroup complex_lin
154 *
155 * =====================================================================
156  SUBROUTINE cdrvhp( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
157  $ A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
158  $ NOUT )
159 *
160 * -- LAPACK test routine (version 3.7.0) --
161 * -- LAPACK is a software package provided by Univ. of Tennessee, --
162 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163 * December 2016
164 *
165 * .. Scalar Arguments ..
166  LOGICAL TSTERR
167  INTEGER NMAX, NN, NOUT, NRHS
168  REAL THRESH
169 * ..
170 * .. Array Arguments ..
171  LOGICAL DOTYPE( * )
172  INTEGER IWORK( * ), NVAL( * )
173  REAL RWORK( * )
174  COMPLEX A( * ), AFAC( * ), AINV( * ), B( * ),
175  $ work( * ), x( * ), xact( * )
176 * ..
177 *
178 * =====================================================================
179 *
180 * .. Parameters ..
181  REAL ONE, ZERO
182  parameter( one = 1.0e+0, zero = 0.0e+0 )
183  INTEGER NTYPES, NTESTS
184  parameter( ntypes = 10, ntests = 6 )
185  INTEGER NFACT
186  parameter( nfact = 2 )
187 * ..
188 * .. Local Scalars ..
189  LOGICAL ZEROT
190  CHARACTER DIST, FACT, PACKIT, TYPE, UPLO, XTYPE
191  CHARACTER*3 PATH
192  INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
193  $ izero, j, k, k1, kl, ku, lda, mode, n, nb,
194  $ nbmin, nerrs, nfail, nimat, npp, nrun, nt
195  REAL AINVNM, ANORM, CNDNUM, RCOND, RCONDC
196 * ..
197 * .. Local Arrays ..
198  CHARACTER FACTS( nfact )
199  INTEGER ISEED( 4 ), ISEEDY( 4 )
200  REAL RESULT( ntests )
201 * ..
202 * .. External Functions ..
203  REAL CLANHP, SGET06
204  EXTERNAL clanhp, sget06
205 * ..
206 * .. External Subroutines ..
207  EXTERNAL aladhd, alaerh, alasvm, ccopy, cerrvx, cget04,
210  $ cppt05, xlaenv
211 * ..
212 * .. Scalars in Common ..
213  LOGICAL LERR, OK
214  CHARACTER*32 SRNAMT
215  INTEGER INFOT, NUNIT
216 * ..
217 * .. Common blocks ..
218  COMMON / infoc / infot, nunit, ok, lerr
219  COMMON / srnamc / srnamt
220 * ..
221 * .. Intrinsic Functions ..
222  INTRINSIC cmplx, max, min
223 * ..
224 * .. Data statements ..
225  DATA iseedy / 1988, 1989, 1990, 1991 /
226  DATA facts / 'F', 'N' /
227 * ..
228 * .. Executable Statements ..
229 *
230 * Initialize constants and the random number seed.
231 *
232  path( 1: 1 ) = 'C'
233  path( 2: 3 ) = 'HP'
234  nrun = 0
235  nfail = 0
236  nerrs = 0
237  DO 10 i = 1, 4
238  iseed( i ) = iseedy( i )
239  10 CONTINUE
240 *
241 * Test the error exits
242 *
243  IF( tsterr )
244  $ CALL cerrvx( path, nout )
245  infot = 0
246 *
247 * Set the block size and minimum block size for testing.
248 *
249  nb = 1
250  nbmin = 2
251  CALL xlaenv( 1, nb )
252  CALL xlaenv( 2, nbmin )
253 *
254 * Do for each value of N in NVAL
255 *
256  DO 180 in = 1, nn
257  n = nval( in )
258  lda = max( n, 1 )
259  npp = n*( n+1 ) / 2
260  xtype = 'N'
261  nimat = ntypes
262  IF( n.LE.0 )
263  $ nimat = 1
264 *
265  DO 170 imat = 1, nimat
266 *
267 * Do the tests only if DOTYPE( IMAT ) is true.
268 *
269  IF( .NOT.dotype( imat ) )
270  $ GO TO 170
271 *
272 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
273 *
274  zerot = imat.GE.3 .AND. imat.LE.6
275  IF( zerot .AND. n.LT.imat-2 )
276  $ GO TO 170
277 *
278 * Do first for UPLO = 'U', then for UPLO = 'L'
279 *
280  DO 160 iuplo = 1, 2
281  IF( iuplo.EQ.1 ) THEN
282  uplo = 'U'
283  packit = 'C'
284  ELSE
285  uplo = 'L'
286  packit = 'R'
287  END IF
288 *
289 * Set up parameters with CLATB4 and generate a test matrix
290 * with CLATMS.
291 *
292  CALL clatb4( path, imat, n, n, TYPE, KL, KU, ANORM, MODE,
293  $ cndnum, dist )
294 *
295  srnamt = 'CLATMS'
296  CALL clatms( n, n, dist, iseed, TYPE, RWORK, MODE,
297  $ cndnum, anorm, kl, ku, packit, a, lda, work,
298  $ info )
299 *
300 * Check error code from CLATMS.
301 *
302  IF( info.NE.0 ) THEN
303  CALL alaerh( path, 'CLATMS', info, 0, uplo, n, n, -1,
304  $ -1, -1, imat, nfail, nerrs, nout )
305  GO TO 160
306  END IF
307 *
308 * For types 3-6, zero one or more rows and columns of the
309 * matrix to test that INFO is returned correctly.
310 *
311  IF( zerot ) THEN
312  IF( imat.EQ.3 ) THEN
313  izero = 1
314  ELSE IF( imat.EQ.4 ) THEN
315  izero = n
316  ELSE
317  izero = n / 2 + 1
318  END IF
319 *
320  IF( imat.LT.6 ) THEN
321 *
322 * Set row and column IZERO to zero.
323 *
324  IF( iuplo.EQ.1 ) THEN
325  ioff = ( izero-1 )*izero / 2
326  DO 20 i = 1, izero - 1
327  a( ioff+i ) = zero
328  20 CONTINUE
329  ioff = ioff + izero
330  DO 30 i = izero, n
331  a( ioff ) = zero
332  ioff = ioff + i
333  30 CONTINUE
334  ELSE
335  ioff = izero
336  DO 40 i = 1, izero - 1
337  a( ioff ) = zero
338  ioff = ioff + n - i
339  40 CONTINUE
340  ioff = ioff - izero
341  DO 50 i = izero, n
342  a( ioff+i ) = zero
343  50 CONTINUE
344  END IF
345  ELSE
346  ioff = 0
347  IF( iuplo.EQ.1 ) THEN
348 *
349 * Set the first IZERO rows and columns to zero.
350 *
351  DO 70 j = 1, n
352  i2 = min( j, izero )
353  DO 60 i = 1, i2
354  a( ioff+i ) = zero
355  60 CONTINUE
356  ioff = ioff + j
357  70 CONTINUE
358  ELSE
359 *
360 * Set the last IZERO rows and columns to zero.
361 *
362  DO 90 j = 1, n
363  i1 = max( j, izero )
364  DO 80 i = i1, n
365  a( ioff+i ) = zero
366  80 CONTINUE
367  ioff = ioff + n - j
368  90 CONTINUE
369  END IF
370  END IF
371  ELSE
372  izero = 0
373  END IF
374 *
375 * Set the imaginary part of the diagonals.
376 *
377  IF( iuplo.EQ.1 ) THEN
378  CALL claipd( n, a, 2, 1 )
379  ELSE
380  CALL claipd( n, a, n, -1 )
381  END IF
382 *
383  DO 150 ifact = 1, nfact
384 *
385 * Do first for FACT = 'F', then for other values.
386 *
387  fact = facts( ifact )
388 *
389 * Compute the condition number for comparison with
390 * the value returned by CHPSVX.
391 *
392  IF( zerot ) THEN
393  IF( ifact.EQ.1 )
394  $ GO TO 150
395  rcondc = zero
396 *
397  ELSE IF( ifact.EQ.1 ) THEN
398 *
399 * Compute the 1-norm of A.
400 *
401  anorm = clanhp( '1', uplo, n, a, rwork )
402 *
403 * Factor the matrix A.
404 *
405  CALL ccopy( npp, a, 1, afac, 1 )
406  CALL chptrf( uplo, n, afac, iwork, info )
407 *
408 * Compute inv(A) and take its norm.
409 *
410  CALL ccopy( npp, afac, 1, ainv, 1 )
411  CALL chptri( uplo, n, ainv, iwork, work, info )
412  ainvnm = clanhp( '1', uplo, n, ainv, rwork )
413 *
414 * Compute the 1-norm condition number of A.
415 *
416  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
417  rcondc = one
418  ELSE
419  rcondc = ( one / anorm ) / ainvnm
420  END IF
421  END IF
422 *
423 * Form an exact solution and set the right hand side.
424 *
425  srnamt = 'CLARHS'
426  CALL clarhs( path, xtype, uplo, ' ', n, n, kl, ku,
427  $ nrhs, a, lda, xact, lda, b, lda, iseed,
428  $ info )
429  xtype = 'C'
430 *
431 * --- Test CHPSV ---
432 *
433  IF( ifact.EQ.2 ) THEN
434  CALL ccopy( npp, a, 1, afac, 1 )
435  CALL clacpy( 'Full', n, nrhs, b, lda, x, lda )
436 *
437 * Factor the matrix and solve the system using CHPSV.
438 *
439  srnamt = 'CHPSV '
440  CALL chpsv( uplo, n, nrhs, afac, iwork, x, lda,
441  $ info )
442 *
443 * Adjust the expected value of INFO to account for
444 * pivoting.
445 *
446  k = izero
447  IF( k.GT.0 ) THEN
448  100 CONTINUE
449  IF( iwork( k ).LT.0 ) THEN
450  IF( iwork( k ).NE.-k ) THEN
451  k = -iwork( k )
452  GO TO 100
453  END IF
454  ELSE IF( iwork( k ).NE.k ) THEN
455  k = iwork( k )
456  GO TO 100
457  END IF
458  END IF
459 *
460 * Check error code from CHPSV .
461 *
462  IF( info.NE.k ) THEN
463  CALL alaerh( path, 'CHPSV ', info, k, uplo, n,
464  $ n, -1, -1, nrhs, imat, nfail,
465  $ nerrs, nout )
466  GO TO 120
467  ELSE IF( info.NE.0 ) THEN
468  GO TO 120
469  END IF
470 *
471 * Reconstruct matrix from factors and compute
472 * residual.
473 *
474  CALL chpt01( uplo, n, a, afac, iwork, ainv, lda,
475  $ rwork, result( 1 ) )
476 *
477 * Compute residual of the computed solution.
478 *
479  CALL clacpy( 'Full', n, nrhs, b, lda, work, lda )
480  CALL cppt02( uplo, n, nrhs, a, x, lda, work, lda,
481  $ rwork, result( 2 ) )
482 *
483 * Check solution from generated exact solution.
484 *
485  CALL cget04( n, nrhs, x, lda, xact, lda, rcondc,
486  $ result( 3 ) )
487  nt = 3
488 *
489 * Print information about the tests that did not pass
490 * the threshold.
491 *
492  DO 110 k = 1, nt
493  IF( result( k ).GE.thresh ) THEN
494  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
495  $ CALL aladhd( nout, path )
496  WRITE( nout, fmt = 9999 )'CHPSV ', uplo, n,
497  $ imat, k, result( k )
498  nfail = nfail + 1
499  END IF
500  110 CONTINUE
501  nrun = nrun + nt
502  120 CONTINUE
503  END IF
504 *
505 * --- Test CHPSVX ---
506 *
507  IF( ifact.EQ.2 .AND. npp.GT.0 )
508  $ CALL claset( 'Full', npp, 1, cmplx( zero ),
509  $ cmplx( zero ), afac, npp )
510  CALL claset( 'Full', n, nrhs, cmplx( zero ),
511  $ cmplx( zero ), x, lda )
512 *
513 * Solve the system and compute the condition number and
514 * error bounds using CHPSVX.
515 *
516  srnamt = 'CHPSVX'
517  CALL chpsvx( fact, uplo, n, nrhs, a, afac, iwork, b,
518  $ lda, x, lda, rcond, rwork,
519  $ rwork( nrhs+1 ), work, rwork( 2*nrhs+1 ),
520  $ info )
521 *
522 * Adjust the expected value of INFO to account for
523 * pivoting.
524 *
525  k = izero
526  IF( k.GT.0 ) THEN
527  130 CONTINUE
528  IF( iwork( k ).LT.0 ) THEN
529  IF( iwork( k ).NE.-k ) THEN
530  k = -iwork( k )
531  GO TO 130
532  END IF
533  ELSE IF( iwork( k ).NE.k ) THEN
534  k = iwork( k )
535  GO TO 130
536  END IF
537  END IF
538 *
539 * Check the error code from CHPSVX.
540 *
541  IF( info.NE.k ) THEN
542  CALL alaerh( path, 'CHPSVX', info, k, fact // uplo,
543  $ n, n, -1, -1, nrhs, imat, nfail,
544  $ nerrs, nout )
545  GO TO 150
546  END IF
547 *
548  IF( info.EQ.0 ) THEN
549  IF( ifact.GE.2 ) THEN
550 *
551 * Reconstruct matrix from factors and compute
552 * residual.
553 *
554  CALL chpt01( uplo, n, a, afac, iwork, ainv, lda,
555  $ rwork( 2*nrhs+1 ), result( 1 ) )
556  k1 = 1
557  ELSE
558  k1 = 2
559  END IF
560 *
561 * Compute residual of the computed solution.
562 *
563  CALL clacpy( 'Full', n, nrhs, b, lda, work, lda )
564  CALL cppt02( uplo, n, nrhs, a, x, lda, work, lda,
565  $ rwork( 2*nrhs+1 ), result( 2 ) )
566 *
567 * Check solution from generated exact solution.
568 *
569  CALL cget04( n, nrhs, x, lda, xact, lda, rcondc,
570  $ result( 3 ) )
571 *
572 * Check the error bounds from iterative refinement.
573 *
574  CALL cppt05( uplo, n, nrhs, a, b, lda, x, lda,
575  $ xact, lda, rwork, rwork( nrhs+1 ),
576  $ result( 4 ) )
577  ELSE
578  k1 = 6
579  END IF
580 *
581 * Compare RCOND from CHPSVX with the computed value
582 * in RCONDC.
583 *
584  result( 6 ) = sget06( rcond, rcondc )
585 *
586 * Print information about the tests that did not pass
587 * the threshold.
588 *
589  DO 140 k = k1, 6
590  IF( result( k ).GE.thresh ) THEN
591  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
592  $ CALL aladhd( nout, path )
593  WRITE( nout, fmt = 9998 )'CHPSVX', fact, uplo,
594  $ n, imat, k, result( k )
595  nfail = nfail + 1
596  END IF
597  140 CONTINUE
598  nrun = nrun + 7 - k1
599 *
600  150 CONTINUE
601 *
602  160 CONTINUE
603  170 CONTINUE
604  180 CONTINUE
605 *
606 * Print a summary of the results.
607 *
608  CALL alasvm( path, nout, nfail, nrun, nerrs )
609 *
610  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
611  $ ', test ', i2, ', ratio =', g12.5 )
612  9998 FORMAT( 1x, a, ', FACT=''', a1, ''', UPLO=''', a1, ''', N =', i5,
613  $ ', type ', i2, ', test ', i2, ', ratio =', g12.5 )
614  RETURN
615 *
616 * End of CDRVHP
617 *
618  END
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:75
subroutine cppt02(UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
CPPT02
Definition: cppt02.f:125
subroutine claipd(N, A, INDA, VINDA)
CLAIPD
Definition: claipd.f:85
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
subroutine chptrf(UPLO, N, AP, IPIV, INFO)
CHPTRF
Definition: chptrf.f:161
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: claset.f:108
subroutine cppt05(UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
CPPT05
Definition: cppt05.f:159
subroutine cerrvx(PATH, NUNIT)
CERRVX
Definition: cerrvx.f:57
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
subroutine chptri(UPLO, N, AP, IPIV, WORK, INFO)
CHPTRI
Definition: chptri.f:111
subroutine cdrvhp(DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CDRVHP
Definition: cdrvhp.f:159
subroutine aladhd(IOUNIT, PATH)
ALADHD
Definition: aladhd.f:92
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:105
subroutine clatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
CLATMS
Definition: clatms.f:334
subroutine ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:83
subroutine chpsvx(FACT, UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, RWORK, INFO)
CHPSVX computes the solution to system of linear equations A * X = B for OTHER matrices ...
Definition: chpsvx.f:279
subroutine chpsv(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
CHPSV computes the solution to system of linear equations A * X = B for OTHER matrices ...
Definition: chpsv.f:164
subroutine chpt01(UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
CHPT01
Definition: chpt01.f:115
subroutine clarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
CLARHS
Definition: clarhs.f:211
subroutine cget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
CGET04
Definition: cget04.f:104
subroutine clatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
CLATB4
Definition: clatb4.f:123