LAPACK  3.9.0
LAPACK: Linear Algebra PACKage
cdrvsy_rk.f
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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 *> \endverbatim
102 *>
103 *> \param[out] AINV
104 *> \verbatim
105 *> AINV is COMPLEX array, dimension (NMAX*NMAX)
106 *> \endverbatim
107 *>
108 *> \param[out] B
109 *> \verbatim
110 *> B is COMPLEX array, dimension (NMAX*NRHS)
111 *> \endverbatim
112 *>
113 *> \param[out] X
114 *> \verbatim
115 *> X is COMPLEX array, dimension (NMAX*NRHS)
116 *> \endverbatim
117 *>
118 *> \param[out] XACT
119 *> \verbatim
120 *> XACT is COMPLEX array, dimension (NMAX*NRHS)
121 *> \endverbatim
122 *>
123 *> \param[out] WORK
124 *> \verbatim
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 cdrvsy_rk( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
157  $ NMAX, A, AFAC, E, AINV, B, X, XACT, WORK,
158  $ RWORK, IWORK, 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( * ), E( * ),
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 = 11, ntests = 3 )
185  INTEGER NFACT
186  parameter( nfact = 2 )
187 * ..
188 * .. Local Scalars ..
189  LOGICAL ZEROT
190  CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
191  CHARACTER*3 MATPATH, PATH
192  INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
193  $ izero, j, k, kl, ku, lda, lwork, mode, n,
194  $ nb, nbmin, nerrs, nfail, nimat, nrun, nt
195  REAL AINVNM, ANORM, CNDNUM, RCONDC
196 * ..
197 * .. Local Arrays ..
198  CHARACTER FACTS( NFACT ), UPLOS( 2 )
199  INTEGER ISEED( 4 ), ISEEDY( 4 )
200  REAL RESULT( NTESTS )
201 
202 * ..
203 * .. External Functions ..
204  REAL CLANSY
205  EXTERNAL CLANSY
206 * ..
207 * .. External Subroutines ..
208  EXTERNAL aladhd, alaerh, alasvm, xlaenv, cerrvx, cget04,
209  $ clacpy, clarhs, clatb4, clatms, clatsy,
210  $ csysv_rk, csyt01_3, csyt02, csytrf_rk, csytri_3
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 max, min
223 * ..
224 * .. Data statements ..
225  DATA iseedy / 1988, 1989, 1990, 1991 /
226  DATA uplos / 'U', 'L' / , facts / 'F', 'N' /
227 * ..
228 * .. Executable Statements ..
229 *
230 * Initialize constants and the random number seed.
231 *
232 * Test path
233 *
234  path( 1: 1 ) = 'Complex precision'
235  path( 2: 3 ) = 'SK'
236 *
237 * Path to generate matrices
238 *
239  matpath( 1: 1 ) = 'Complex precision'
240  matpath( 2: 3 ) = 'SY'
241 *
242  nrun = 0
243  nfail = 0
244  nerrs = 0
245  DO 10 i = 1, 4
246  iseed( i ) = iseedy( i )
247  10 CONTINUE
248  lwork = max( 2*nmax, nmax*nrhs )
249 *
250 * Test the error exits
251 *
252  IF( tsterr )
253  $ CALL cerrvx( path, nout )
254  infot = 0
255 *
256 * Set the block size and minimum block size for which the block
257 * routine should be used, which will be later returned by ILAENV.
258 *
259  nb = 1
260  nbmin = 2
261  CALL xlaenv( 1, nb )
262  CALL xlaenv( 2, nbmin )
263 *
264 * Do for each value of N in NVAL
265 *
266  DO 180 in = 1, nn
267  n = nval( in )
268  lda = max( n, 1 )
269  xtype = 'N'
270  nimat = ntypes
271  IF( n.LE.0 )
272  $ nimat = 1
273 *
274  DO 170 imat = 1, nimat
275 *
276 * Do the tests only if DOTYPE( IMAT ) is true.
277 *
278  IF( .NOT.dotype( imat ) )
279  $ GO TO 170
280 *
281 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
282 *
283  zerot = imat.GE.3 .AND. imat.LE.6
284  IF( zerot .AND. n.LT.imat-2 )
285  $ GO TO 170
286 *
287 * Do first for UPLO = 'U', then for UPLO = 'L'
288 *
289  DO 160 iuplo = 1, 2
290  uplo = uplos( iuplo )
291 *
292  IF( imat.NE.ntypes ) THEN
293 *
294 * Begin generate the test matrix A.
295 *
296 * Set up parameters with CLATB4 for the matrix generator
297 * based on the type of matrix to be generated.
298 *
299  CALL clatb4( matpath, imat, n, n, TYPE, kl, ku, anorm,
300  $ mode, cndnum, dist )
301 *
302 * Generate a matrix with CLATMS.
303 *
304  srnamt = 'CLATMS'
305  CALL clatms( n, n, dist, iseed, TYPE, rwork, mode,
306  $ cndnum, anorm, kl, ku, uplo, a, lda,
307  $ work, info )
308 *
309 * Check error code from CLATMS and handle error.
310 *
311  IF( info.NE.0 ) THEN
312  CALL alaerh( path, 'CLATMS', info, 0, uplo, n, n,
313  $ -1, -1, -1, imat, nfail, nerrs, nout )
314  GO TO 160
315  END IF
316 *
317 * For types 3-6, zero one or more rows and columns of
318 * the matrix to test that INFO is returned correctly.
319 *
320  IF( zerot ) THEN
321  IF( imat.EQ.3 ) THEN
322  izero = 1
323  ELSE IF( imat.EQ.4 ) THEN
324  izero = n
325  ELSE
326  izero = n / 2 + 1
327  END IF
328 *
329  IF( imat.LT.6 ) THEN
330 *
331 * Set row and column IZERO to zero.
332 *
333  IF( iuplo.EQ.1 ) THEN
334  ioff = ( izero-1 )*lda
335  DO 20 i = 1, izero - 1
336  a( ioff+i ) = zero
337  20 CONTINUE
338  ioff = ioff + izero
339  DO 30 i = izero, n
340  a( ioff ) = zero
341  ioff = ioff + lda
342  30 CONTINUE
343  ELSE
344  ioff = izero
345  DO 40 i = 1, izero - 1
346  a( ioff ) = zero
347  ioff = ioff + lda
348  40 CONTINUE
349  ioff = ioff - izero
350  DO 50 i = izero, n
351  a( ioff+i ) = zero
352  50 CONTINUE
353  END IF
354  ELSE
355  IF( iuplo.EQ.1 ) THEN
356 *
357 * Set the first IZERO rows and columns to zero.
358 *
359  ioff = 0
360  DO 70 j = 1, n
361  i2 = min( j, izero )
362  DO 60 i = 1, i2
363  a( ioff+i ) = zero
364  60 CONTINUE
365  ioff = ioff + lda
366  70 CONTINUE
367  ELSE
368 *
369 * Set the first IZERO rows and columns to zero.
370 *
371  ioff = 0
372  DO 90 j = 1, n
373  i1 = max( j, izero )
374  DO 80 i = i1, n
375  a( ioff+i ) = zero
376  80 CONTINUE
377  ioff = ioff + lda
378  90 CONTINUE
379  END IF
380  END IF
381  ELSE
382  izero = 0
383  END IF
384 *
385 * End generate the test matrix A.
386 *
387  ELSE
388 *
389 * IMAT = NTYPES: Use a special block diagonal matrix to
390 * test alternate code for the 2-by-2 blocks.
391 *
392  CALL clatsy( uplo, n, a, lda, iseed )
393  END IF
394 *
395  DO 150 ifact = 1, nfact
396 *
397 * Do first for FACT = 'F', then for other values.
398 *
399  fact = facts( ifact )
400 *
401 * Compute the condition number
402 *
403  IF( zerot ) THEN
404  IF( ifact.EQ.1 )
405  $ GO TO 150
406  rcondc = zero
407 *
408  ELSE IF( ifact.EQ.1 ) THEN
409 *
410 * Compute the 1-norm of A.
411 *
412  anorm = clansy( '1', uplo, n, a, lda, rwork )
413 *
414 * Factor the matrix A.
415 *
416 
417  CALL clacpy( uplo, n, n, a, lda, afac, lda )
418  CALL csytrf_rk( uplo, n, afac, lda, e, iwork, work,
419  $ lwork, info )
420 *
421 * Compute inv(A) and take its norm.
422 *
423  CALL clacpy( uplo, n, n, afac, lda, ainv, lda )
424  lwork = (n+nb+1)*(nb+3)
425 *
426 * We need to copute the invesrse to compute
427 * RCONDC that is used later in TEST3.
428 *
429  CALL csytri_3( uplo, n, ainv, lda, e, iwork,
430  $ work, lwork, info )
431  ainvnm = clansy( '1', uplo, n, ainv, lda, rwork )
432 *
433 * Compute the 1-norm condition number of A.
434 *
435  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
436  rcondc = one
437  ELSE
438  rcondc = ( one / anorm ) / ainvnm
439  END IF
440  END IF
441 *
442 * Form an exact solution and set the right hand side.
443 *
444  srnamt = 'CLARHS'
445  CALL clarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
446  $ nrhs, a, lda, xact, lda, b, lda, iseed,
447  $ info )
448  xtype = 'C'
449 *
450 * --- Test CSYSV_RK ---
451 *
452  IF( ifact.EQ.2 ) THEN
453  CALL clacpy( uplo, n, n, a, lda, afac, lda )
454  CALL clacpy( 'Full', n, nrhs, b, lda, x, lda )
455 *
456 * Factor the matrix and solve the system using
457 * CSYSV_RK.
458 *
459  srnamt = 'CSYSV_RK'
460  CALL csysv_rk( uplo, n, nrhs, afac, lda, e, iwork,
461  $ x, lda, work, lwork, info )
462 *
463 * Adjust the expected value of INFO to account for
464 * pivoting.
465 *
466  k = izero
467  IF( k.GT.0 ) THEN
468  100 CONTINUE
469  IF( iwork( k ).LT.0 ) THEN
470  IF( iwork( k ).NE.-k ) THEN
471  k = -iwork( k )
472  GO TO 100
473  END IF
474  ELSE IF( iwork( k ).NE.k ) THEN
475  k = iwork( k )
476  GO TO 100
477  END IF
478  END IF
479 *
480 * Check error code from CSYSV_RK and handle error.
481 *
482  IF( info.NE.k ) THEN
483  CALL alaerh( path, 'CSYSV_RK', info, k, uplo,
484  $ n, n, -1, -1, nrhs, imat, nfail,
485  $ nerrs, nout )
486  GO TO 120
487  ELSE IF( info.NE.0 ) THEN
488  GO TO 120
489  END IF
490 *
491 *+ TEST 1 Reconstruct matrix from factors and compute
492 * residual.
493 *
494  CALL csyt01_3( uplo, n, a, lda, afac, lda, e,
495  $ iwork, ainv, lda, rwork,
496  $ result( 1 ) )
497 *
498 *+ TEST 2 Compute residual of the computed solution.
499 *
500  CALL clacpy( 'Full', n, nrhs, b, lda, work, lda )
501  CALL csyt02( uplo, n, nrhs, a, lda, x, lda, work,
502  $ lda, rwork, result( 2 ) )
503 *
504 *+ TEST 3
505 * Check solution from generated exact solution.
506 *
507  CALL cget04( n, nrhs, x, lda, xact, lda, rcondc,
508  $ result( 3 ) )
509  nt = 3
510 *
511 * Print information about the tests that did not pass
512 * the threshold.
513 *
514  DO 110 k = 1, nt
515  IF( result( k ).GE.thresh ) THEN
516  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
517  $ CALL aladhd( nout, path )
518  WRITE( nout, fmt = 9999 )'CSYSV_RK', uplo,
519  $ n, imat, k, result( k )
520  nfail = nfail + 1
521  END IF
522  110 CONTINUE
523  nrun = nrun + nt
524  120 CONTINUE
525  END IF
526 *
527  150 CONTINUE
528 *
529  160 CONTINUE
530  170 CONTINUE
531  180 CONTINUE
532 *
533 * Print a summary of the results.
534 *
535  CALL alasvm( path, nout, nfail, nrun, nerrs )
536 *
537  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
538  $ ', test ', i2, ', ratio =', g12.5 )
539  RETURN
540 *
541 * End of CDRVSY_RK
542 *
543  END
csyt02
subroutine csyt02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
CSYT02
Definition: csyt02.f:129
csysv_rk
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
alasvm
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:75
cerrvx
subroutine cerrvx(PATH, NUNIT)
CERRVX
Definition: cerrvx.f:57
cdrvsy_rk
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:159
cget04
subroutine cget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
CGET04
Definition: cget04.f:104
csyt01_3
subroutine csyt01_3(UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C, LDC, RWORK, RESID)
CSYT01_3
Definition: csyt01_3.f:143
clacpy
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
clatsy
subroutine clatsy(UPLO, N, X, LDX, ISEED)
CLATSY
Definition: clatsy.f:91
csytrf_rk
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
csytri_3
subroutine csytri_3(UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
CSYTRI_3
Definition: csytri_3.f:172
clatms
subroutine clatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
CLATMS
Definition: clatms.f:334
aladhd
subroutine aladhd(IOUNIT, PATH)
ALADHD
Definition: aladhd.f:92
alaerh
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
clarhs
subroutine clarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
CLARHS
Definition: clarhs.f:211
clatb4
subroutine clatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
CLATB4
Definition: clatb4.f:123
xlaenv
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83