LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
cdrvsy_rk.f
Go to the documentation of this file.
1 *> \brief \b CDRVSY_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 CDRVSY_RK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
12 * NMAX, A, AFAC, E, AINV, B, X, XACT, WORK,
13 * RWORK, IWORK, 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( * ), E( * ),
25 * \$ WORK( * ), X( * ), XACT( * )
26 * ..
27 *
28 *
29 *> \par Purpose:
30 * =============
31 *>
32 *> \verbatim
33 *>
34 *> CDRVSY_RK tests the driver routines CSYSV_RK.
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 (NMAX*NMAX)
91 *> \endverbatim
92 *>
93 *> \param[out] AFAC
94 *> \verbatim
95 *> AFAC is COMPLEX array, dimension (NMAX*NMAX)
96 *> \endverbatim
97 *>
98 *> \param[out] E
99 *> \verbatim
100 *> E is COMPLEX array, dimension (NMAX)
101 *> \param[out] AINV
102 *>
103 *> \verbatim
104 *> AINV is COMPLEX array, dimension (NMAX*NMAX)
105 *> \endverbatim
106 *>
107 *> \param[out] B
108 *> \verbatim
109 *> B is COMPLEX array, dimension (NMAX*NRHS)
110 *> \endverbatim
111 *>
112 *> \param[out] X
113 *> \verbatim
114 *> X is COMPLEX array, dimension (NMAX*NRHS)
115 *> \endverbatim
116 *>
117 *> \param[out] XACT
118 *> \verbatim
119 *> XACT is COMPLEX array, dimension (NMAX*NRHS)
120 *> \endverbatim
121 *>
122 *> \param[out] WORK
123 *> \verbatim
124 *> \endverbatim
125 *>
126 *> \param[out] RWORK
127 *> \verbatim
128 *> RWORK is REAL array, dimension (NMAX+2*NRHS)
129 *> \endverbatim
130 *>
131 *> \param[out] IWORK
132 *> \verbatim
133 *> IWORK is INTEGER array, dimension (NMAX)
134 *> \endverbatim
135 *>
136 *> \param[in] NOUT
137 *> \verbatim
138 *> NOUT is INTEGER
139 *> The unit number for output.
140 *> \endverbatim
141 *
142 * Authors:
143 * ========
144 *
145 *> \author Univ. of Tennessee
146 *> \author Univ. of California Berkeley
147 *> \author Univ. of Colorado Denver
148 *> \author NAG Ltd.
149 *
150 *> \date December 2016
151 *
152 *> \ingroup complex_lin
153 *
154 * =====================================================================
155  SUBROUTINE cdrvsy_rk( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
156  \$ NMAX, A, AFAC, E, AINV, B, X, XACT, WORK,
157  \$ RWORK, IWORK, NOUT )
158 *
159 * -- LAPACK test routine (version 3.7.0) --
160 * -- LAPACK is a software package provided by Univ. of Tennessee, --
161 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
162 * December 2016
163 *
164 * .. Scalar Arguments ..
165  LOGICAL TSTERR
166  INTEGER NMAX, NN, NOUT, NRHS
167  REAL THRESH
168 * ..
169 * .. Array Arguments ..
170  LOGICAL DOTYPE( * )
171  INTEGER IWORK( * ), NVAL( * )
172  REAL RWORK( * )
173  COMPLEX A( * ), AFAC( * ), AINV( * ), B( * ), E( * ),
174  \$ work( * ), x( * ), xact( * )
175 * ..
176 *
177 * =====================================================================
178 *
179 * .. Parameters ..
180  REAL ONE, ZERO
181  parameter( one = 1.0e+0, zero = 0.0e+0 )
182  INTEGER NTYPES, NTESTS
183  parameter( ntypes = 11, ntests = 3 )
184  INTEGER NFACT
185  parameter( nfact = 2 )
186 * ..
187 * .. Local Scalars ..
188  LOGICAL ZEROT
189  CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
190  CHARACTER*3 MATPATH, PATH
191  INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
192  \$ izero, j, k, kl, ku, lda, lwork, mode, n,
193  \$ nb, nbmin, nerrs, nfail, nimat, nrun, nt
194  REAL AINVNM, ANORM, CNDNUM, RCONDC
195 * ..
196 * .. Local Arrays ..
197  CHARACTER FACTS( nfact ), UPLOS( 2 )
198  INTEGER ISEED( 4 ), ISEEDY( 4 )
199  REAL RESULT( ntests )
200
201 * ..
202 * .. External Functions ..
203  REAL CLANSY
204  EXTERNAL clansy
205 * ..
206 * .. External Subroutines ..
207  EXTERNAL aladhd, alaerh, alasvm, xlaenv, cerrvx, cget04,
210 * ..
211 * .. Scalars in Common ..
212  LOGICAL LERR, OK
213  CHARACTER*32 SRNAMT
214  INTEGER INFOT, NUNIT
215 * ..
216 * .. Common blocks ..
217  COMMON / infoc / infot, nunit, ok, lerr
218  COMMON / srnamc / srnamt
219 * ..
220 * .. Intrinsic Functions ..
221  INTRINSIC max, min
222 * ..
223 * .. Data statements ..
224  DATA iseedy / 1988, 1989, 1990, 1991 /
225  DATA uplos / 'U', 'L' / , facts / 'F', 'N' /
226 * ..
227 * .. Executable Statements ..
228 *
229 * Initialize constants and the random number seed.
230 *
231 * Test path
232 *
233  path( 1: 1 ) = 'Complex precision'
234  path( 2: 3 ) = 'SK'
235 *
236 * Path to generate matrices
237 *
238  matpath( 1: 1 ) = 'Complex precision'
239  matpath( 2: 3 ) = 'SY'
240 *
241  nrun = 0
242  nfail = 0
243  nerrs = 0
244  DO 10 i = 1, 4
245  iseed( i ) = iseedy( i )
246  10 CONTINUE
247  lwork = max( 2*nmax, nmax*nrhs )
248 *
249 * Test the error exits
250 *
251  IF( tsterr )
252  \$ CALL cerrvx( path, nout )
253  infot = 0
254 *
255 * Set the block size and minimum block size for which the block
256 * routine should be used, which will be later returned by ILAENV.
257 *
258  nb = 1
259  nbmin = 2
260  CALL xlaenv( 1, nb )
261  CALL xlaenv( 2, nbmin )
262 *
263 * Do for each value of N in NVAL
264 *
265  DO 180 in = 1, nn
266  n = nval( in )
267  lda = max( n, 1 )
268  xtype = 'N'
269  nimat = ntypes
270  IF( n.LE.0 )
271  \$ nimat = 1
272 *
273  DO 170 imat = 1, nimat
274 *
275 * Do the tests only if DOTYPE( IMAT ) is true.
276 *
277  IF( .NOT.dotype( imat ) )
278  \$ GO TO 170
279 *
280 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
281 *
282  zerot = imat.GE.3 .AND. imat.LE.6
283  IF( zerot .AND. n.LT.imat-2 )
284  \$ GO TO 170
285 *
286 * Do first for UPLO = 'U', then for UPLO = 'L'
287 *
288  DO 160 iuplo = 1, 2
289  uplo = uplos( iuplo )
290 *
291  IF( imat.NE.ntypes ) THEN
292 *
293 * Begin generate the test matrix A.
294 *
295 * Set up parameters with CLATB4 for the matrix generator
296 * based on the type of matrix to be generated.
297 *
298  CALL clatb4( matpath, imat, n, n, TYPE, KL, KU, ANORM,
299  \$ mode, cndnum, dist )
300 *
301 * Generate a matrix with CLATMS.
302 *
303  srnamt = 'CLATMS'
304  CALL clatms( n, n, dist, iseed, TYPE, RWORK, MODE,
305  \$ cndnum, anorm, kl, ku, uplo, a, lda,
306  \$ work, info )
307 *
308 * Check error code from CLATMS and handle error.
309 *
310  IF( info.NE.0 ) THEN
311  CALL alaerh( path, 'CLATMS', info, 0, uplo, n, n,
312  \$ -1, -1, -1, imat, nfail, nerrs, nout )
313  GO TO 160
314  END IF
315 *
316 * For types 3-6, zero one or more rows and columns of
317 * the matrix to test that INFO is returned correctly.
318 *
319  IF( zerot ) THEN
320  IF( imat.EQ.3 ) THEN
321  izero = 1
322  ELSE IF( imat.EQ.4 ) THEN
323  izero = n
324  ELSE
325  izero = n / 2 + 1
326  END IF
327 *
328  IF( imat.LT.6 ) THEN
329 *
330 * Set row and column IZERO to zero.
331 *
332  IF( iuplo.EQ.1 ) THEN
333  ioff = ( izero-1 )*lda
334  DO 20 i = 1, izero - 1
335  a( ioff+i ) = zero
336  20 CONTINUE
337  ioff = ioff + izero
338  DO 30 i = izero, n
339  a( ioff ) = zero
340  ioff = ioff + lda
341  30 CONTINUE
342  ELSE
343  ioff = izero
344  DO 40 i = 1, izero - 1
345  a( ioff ) = zero
346  ioff = ioff + lda
347  40 CONTINUE
348  ioff = ioff - izero
349  DO 50 i = izero, n
350  a( ioff+i ) = zero
351  50 CONTINUE
352  END IF
353  ELSE
354  IF( iuplo.EQ.1 ) THEN
355 *
356 * Set the first IZERO rows and columns to zero.
357 *
358  ioff = 0
359  DO 70 j = 1, n
360  i2 = min( j, izero )
361  DO 60 i = 1, i2
362  a( ioff+i ) = zero
363  60 CONTINUE
364  ioff = ioff + lda
365  70 CONTINUE
366  ELSE
367 *
368 * Set the first IZERO rows and columns to zero.
369 *
370  ioff = 0
371  DO 90 j = 1, n
372  i1 = max( j, izero )
373  DO 80 i = i1, n
374  a( ioff+i ) = zero
375  80 CONTINUE
376  ioff = ioff + lda
377  90 CONTINUE
378  END IF
379  END IF
380  ELSE
381  izero = 0
382  END IF
383 *
384 * End generate the test matrix A.
385 *
386  ELSE
387 *
388 * IMAT = NTYPES: Use a special block diagonal matrix to
389 * test alternate code for the 2-by-2 blocks.
390 *
391  CALL clatsy( uplo, n, a, lda, iseed )
392  END IF
393 *
394  DO 150 ifact = 1, nfact
395 *
396 * Do first for FACT = 'F', then for other values.
397 *
398  fact = facts( ifact )
399 *
400 * Compute the condition number
401 *
402  IF( zerot ) THEN
403  IF( ifact.EQ.1 )
404  \$ GO TO 150
405  rcondc = zero
406 *
407  ELSE IF( ifact.EQ.1 ) THEN
408 *
409 * Compute the 1-norm of A.
410 *
411  anorm = clansy( '1', uplo, n, a, lda, rwork )
412 *
413 * Factor the matrix A.
414 *
415
416  CALL clacpy( uplo, n, n, a, lda, afac, lda )
417  CALL csytrf_rk( uplo, n, afac, lda, e, iwork, work,
418  \$ lwork, info )
419 *
420 * Compute inv(A) and take its norm.
421 *
422  CALL clacpy( uplo, n, n, afac, lda, ainv, lda )
423  lwork = (n+nb+1)*(nb+3)
424 *
425 * We need to copute the invesrse to compute
426 * RCONDC that is used later in TEST3.
427 *
428  CALL csytri_3( uplo, n, ainv, lda, e, iwork,
429  \$ work, lwork, info )
430  ainvnm = clansy( '1', uplo, n, ainv, lda, rwork )
431 *
432 * Compute the 1-norm condition number of A.
433 *
434  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
435  rcondc = one
436  ELSE
437  rcondc = ( one / anorm ) / ainvnm
438  END IF
439  END IF
440 *
441 * Form an exact solution and set the right hand side.
442 *
443  srnamt = 'CLARHS'
444  CALL clarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
445  \$ nrhs, a, lda, xact, lda, b, lda, iseed,
446  \$ info )
447  xtype = 'C'
448 *
449 * --- Test CSYSV_RK ---
450 *
451  IF( ifact.EQ.2 ) THEN
452  CALL clacpy( uplo, n, n, a, lda, afac, lda )
453  CALL clacpy( 'Full', n, nrhs, b, lda, x, lda )
454 *
455 * Factor the matrix and solve the system using
456 * CSYSV_RK.
457 *
458  srnamt = 'CSYSV_RK'
459  CALL csysv_rk( uplo, n, nrhs, afac, lda, e, iwork,
460  \$ x, lda, work, lwork, info )
461 *
462 * Adjust the expected value of INFO to account for
463 * pivoting.
464 *
465  k = izero
466  IF( k.GT.0 ) THEN
467  100 CONTINUE
468  IF( iwork( k ).LT.0 ) THEN
469  IF( iwork( k ).NE.-k ) THEN
470  k = -iwork( k )
471  GO TO 100
472  END IF
473  ELSE IF( iwork( k ).NE.k ) THEN
474  k = iwork( k )
475  GO TO 100
476  END IF
477  END IF
478 *
479 * Check error code from CSYSV_RK and handle error.
480 *
481  IF( info.NE.k ) THEN
482  CALL alaerh( path, 'CSYSV_RK', info, k, uplo,
483  \$ n, n, -1, -1, nrhs, imat, nfail,
484  \$ nerrs, nout )
485  GO TO 120
486  ELSE IF( info.NE.0 ) THEN
487  GO TO 120
488  END IF
489 *
490 *+ TEST 1 Reconstruct matrix from factors and compute
491 * residual.
492 *
493  CALL csyt01_3( uplo, n, a, lda, afac, lda, e,
494  \$ iwork, ainv, lda, rwork,
495  \$ result( 1 ) )
496 *
497 *+ TEST 2 Compute residual of the computed solution.
498 *
499  CALL clacpy( 'Full', n, nrhs, b, lda, work, lda )
500  CALL csyt02( uplo, n, nrhs, a, lda, x, lda, work,
501  \$ lda, rwork, result( 2 ) )
502 *
503 *+ TEST 3
504 * Check solution from generated exact solution.
505 *
506  CALL cget04( n, nrhs, x, lda, xact, lda, rcondc,
507  \$ result( 3 ) )
508  nt = 3
509 *
510 * Print information about the tests that did not pass
511 * the threshold.
512 *
513  DO 110 k = 1, nt
514  IF( result( k ).GE.thresh ) THEN
515  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
516  \$ CALL aladhd( nout, path )
517  WRITE( nout, fmt = 9999 )'CSYSV_RK', uplo,
518  \$ n, imat, k, result( k )
519  nfail = nfail + 1
520  END IF
521  110 CONTINUE
522  nrun = nrun + nt
523  120 CONTINUE
524  END IF
525 *
526  150 CONTINUE
527 *
528  160 CONTINUE
529  170 CONTINUE
530  180 CONTINUE
531 *
532 * Print a summary of the results.
533 *
534  CALL alasvm( path, nout, nfail, nrun, nerrs )
535 *
536  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
537  \$ ', test ', i2, ', ratio =', g12.5 )
538  RETURN
539 *
540 * End of CDRVSY_RK
541 *
542  END
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
subroutine csyt02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
CSYT02
Definition: csyt02.f:129
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 alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:75
subroutine cdrvsy_rk(DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, E, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CDRVSY_RK
Definition: cdrvsy_rk.f:158
subroutine cget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
CGET04
Definition: cget04.f:104
subroutine cerrvx(PATH, NUNIT)
CERRVX
Definition: cerrvx.f:57
subroutine clatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
CLATB4
Definition: clatb4.f:123
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
subroutine csytri_3(UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
CSYTRI_3
Definition: csytri_3.f:172
subroutine csyt01_3(UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C, LDC, RWORK, RESID)
CSYT01_3
Definition: csyt01_3.f:143
subroutine clatsy(UPLO, N, X, LDX, ISEED)
CLATSY
Definition: clatsy.f:91
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 csytrf_rk(UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
CSYTRF_RK computes the factorization of a complex symmetric indefinite matrix using the bounded Bunch...
Definition: csytrf_rk.f:261
subroutine csysv_rk(UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, WORK, LWORK, INFO)
CSYSV_RK computes the solution to system of linear equations A * X = B for SY matrices ...
Definition: csysv_rk.f:230