LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
ddrvsy_rk.f
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1 *> \brief \b DDRVSY_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 DDRVSY_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 * DOUBLE PRECISION THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER IWORK( * ), NVAL( * )
23 * DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ), E( * ),
24 * \$ RWORK( * ), WORK( * ), X( * ), XACT( * )
25 * ..
26 *
27 *
28 *> \par Purpose:
29 * =============
30 *>
31 *> \verbatim
32 *> DDRVSY_RK tests the driver routines DSYSV_RK.
33 *> \endverbatim
34 *
35 * Arguments:
36 * ==========
37 *
38 *> \param[in] DOTYPE
39 *> \verbatim
40 *> DOTYPE is LOGICAL array, dimension (NTYPES)
41 *> The matrix types to be used for testing. Matrices of type j
42 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
43 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
44 *> \endverbatim
45 *>
46 *> \param[in] NN
47 *> \verbatim
48 *> NN is INTEGER
49 *> The number of values of N contained in the vector NVAL.
50 *> \endverbatim
51 *>
52 *> \param[in] NVAL
53 *> \verbatim
54 *> NVAL is INTEGER array, dimension (NN)
55 *> The values of the matrix dimension N.
56 *> \endverbatim
57 *>
58 *> \param[in] NRHS
59 *> \verbatim
60 *> NRHS is INTEGER
61 *> The number of right hand side vectors to be generated for
62 *> each linear system.
63 *> \endverbatim
64 *>
65 *> \param[in] THRESH
66 *> \verbatim
67 *> THRESH is DOUBLE PRECISION
68 *> The threshold value for the test ratios. A result is
69 *> included in the output file if RESULT >= THRESH. To have
70 *> every test ratio printed, use THRESH = 0.
71 *> \endverbatim
72 *>
73 *> \param[in] TSTERR
74 *> \verbatim
75 *> TSTERR is LOGICAL
76 *> Flag that indicates whether error exits are to be tested.
77 *> \endverbatim
78 *>
79 *> \param[in] NMAX
80 *> \verbatim
81 *> NMAX is INTEGER
82 *> The maximum value permitted for N, used in dimensioning the
83 *> work arrays.
84 *> \endverbatim
85 *>
86 *> \param[out] A
87 *> \verbatim
88 *> A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
89 *> \endverbatim
90 *>
91 *> \param[out] AFAC
92 *> \verbatim
93 *> AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
94 *> \endverbatim
95 *>
96 *> \param[out] E
97 *> \verbatim
98 *> E is DOUBLE PRECISION array, dimension (NMAX)
99 *> \endverbatim
100 *>
101 *> \param[out] AINV
102 *> \verbatim
103 *> AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
104 *> \endverbatim
105 *>
106 *> \param[out] B
107 *> \verbatim
108 *> B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
109 *> \endverbatim
110 *>
111 *> \param[out] X
112 *> \verbatim
113 *> X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
114 *> \endverbatim
115 *>
116 *> \param[out] XACT
117 *> \verbatim
118 *> XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
119 *> \endverbatim
120 *>
121 *> \param[out] WORK
122 *> \verbatim
123 *> WORK is DOUBLE PRECISION array, dimension (NMAX*max(2,NRHS))
124 *> \endverbatim
125 *>
126 *> \param[out] RWORK
127 *> \verbatim
128 *> RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
129 *> \endverbatim
130 *>
131 *> \param[out] IWORK
132 *> \verbatim
133 *> IWORK is INTEGER array, dimension (2*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 *> \ingroup double_lin
151 *
152 * =====================================================================
153  SUBROUTINE ddrvsy_rk( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
154  \$ NMAX, A, AFAC, E, AINV, B, X, XACT, WORK,
155  \$ RWORK, IWORK, NOUT )
156 *
157 * -- LAPACK test routine --
158 * -- LAPACK is a software package provided by Univ. of Tennessee, --
159 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
160 *
161 * .. Scalar Arguments ..
162  LOGICAL TSTERR
163  INTEGER NMAX, NN, NOUT, NRHS
164  DOUBLE PRECISION THRESH
165 * ..
166 * .. Array Arguments ..
167  LOGICAL DOTYPE( * )
168  INTEGER IWORK( * ), NVAL( * )
169  DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ), E( * ),
170  \$ rwork( * ), work( * ), x( * ), xact( * )
171 * ..
172 *
173 * =====================================================================
174 *
175 * .. Parameters ..
176  DOUBLE PRECISION ONE, ZERO
177  PARAMETER ( ONE = 1.0d+0, zero = 0.0d+0 )
178  INTEGER NTYPES, NTESTS
179  parameter( ntypes = 10, ntests = 3 )
180  INTEGER NFACT
181  parameter( nfact = 2 )
182 * ..
183 * .. Local Scalars ..
184  LOGICAL ZEROT
185  CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
186  CHARACTER*3 PATH, MATPATH
187  INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
188  \$ izero, j, k, kl, ku, lda, lwork, mode, n,
189  \$ nb, nbmin, nerrs, nfail, nimat, nrun, nt
190  DOUBLE PRECISION AINVNM, ANORM, CNDNUM, RCONDC
191 * ..
192 * .. Local Arrays ..
193  CHARACTER FACTS( NFACT ), UPLOS( 2 )
194  INTEGER ISEED( 4 ), ISEEDY( 4 )
195  DOUBLE PRECISION RESULT( NTESTS )
196 * ..
197 * .. External Functions ..
198  DOUBLE PRECISION DLANSY
199  EXTERNAL DLANSY
200 * ..
201 * .. External Subroutines ..
202  EXTERNAL aladhd, alaerh, alasvm, derrvx, dget04, dlacpy,
205 * ..
206 * .. Scalars in Common ..
207  LOGICAL LERR, OK
208  CHARACTER*32 SRNAMT
209  INTEGER INFOT, NUNIT
210 * ..
211 * .. Common blocks ..
212  COMMON / infoc / infot, nunit, ok, lerr
213  COMMON / srnamc / srnamt
214 * ..
215 * .. Intrinsic Functions ..
216  INTRINSIC max, min
217 * ..
218 * .. Data statements ..
219  DATA iseedy / 1988, 1989, 1990, 1991 /
220  DATA uplos / 'U', 'L' / , facts / 'F', 'N' /
221 * ..
222 * .. Executable Statements ..
223 *
224 * Initialize constants and the random number seed.
225 *
226 * Test path
227 *
228  path( 1: 1 ) = 'Double precision'
229  path( 2: 3 ) = 'SK'
230 *
231 * Path to generate matrices
232 *
233  matpath( 1: 1 ) = 'Double precision'
234  matpath( 2: 3 ) = 'SY'
235 *
236  nrun = 0
237  nfail = 0
238  nerrs = 0
239  DO 10 i = 1, 4
240  iseed( i ) = iseedy( i )
241  10 CONTINUE
242  lwork = max( 2*nmax, nmax*nrhs )
243 *
244 * Test the error exits
245 *
246  IF( tsterr )
247  \$ CALL derrvx( path, nout )
248  infot = 0
249 *
250 * Set the block size and minimum block size for which the block
251 * routine should be used, which will be later returned by ILAENV.
252 *
253  nb = 1
254  nbmin = 2
255  CALL xlaenv( 1, nb )
256  CALL xlaenv( 2, nbmin )
257 *
258 * Do for each value of N in NVAL
259 *
260  DO 180 in = 1, nn
261  n = nval( in )
262  lda = max( n, 1 )
263  xtype = 'N'
264  nimat = ntypes
265  IF( n.LE.0 )
266  \$ nimat = 1
267 *
268  DO 170 imat = 1, nimat
269 *
270 * Do the tests only if DOTYPE( IMAT ) is true.
271 *
272  IF( .NOT.dotype( imat ) )
273  \$ GO TO 170
274 *
275 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
276 *
277  zerot = imat.GE.3 .AND. imat.LE.6
278  IF( zerot .AND. n.LT.imat-2 )
279  \$ GO TO 170
280 *
281 * Do first for UPLO = 'U', then for UPLO = 'L'
282 *
283  DO 160 iuplo = 1, 2
284  uplo = uplos( iuplo )
285 *
286 * Begin generate the test matrix A.
287 *
288 * Set up parameters with DLATB4 for the matrix generator
289 * based on the type of matrix to be generated.
290 *
291  CALL dlatb4( matpath, imat, n, n, TYPE, kl, ku, anorm,
292  \$ mode, cndnum, dist )
293 *
294 * Generate a matrix with DLATMS.
295 *
296  srnamt = 'DLATMS'
297  CALL dlatms( n, n, dist, iseed, TYPE, rwork, mode,
298  \$ cndnum, anorm, kl, ku, uplo, a, lda, work,
299  \$ info )
300 *
301 * Check error code from DLATMS and handle error.
302 *
303  IF( info.NE.0 ) THEN
304  CALL alaerh( path, 'DLATMS', info, 0, uplo, n, n, -1,
305  \$ -1, -1, imat, nfail, nerrs, nout )
306 *
307 * Skip all tests for this generated matrix
308 *
309  GO TO 160
310  END IF
311 *
312 * For types 3-6, zero one or more rows and columns of the
313 * matrix to test that INFO is returned correctly.
314 *
315  IF( zerot ) THEN
316  IF( imat.EQ.3 ) THEN
317  izero = 1
318  ELSE IF( imat.EQ.4 ) THEN
319  izero = n
320  ELSE
321  izero = n / 2 + 1
322  END IF
323 *
324  IF( imat.LT.6 ) THEN
325 *
326 * Set row and column IZERO to zero.
327 *
328  IF( iuplo.EQ.1 ) THEN
329  ioff = ( izero-1 )*lda
330  DO 20 i = 1, izero - 1
331  a( ioff+i ) = zero
332  20 CONTINUE
333  ioff = ioff + izero
334  DO 30 i = izero, n
335  a( ioff ) = zero
336  ioff = ioff + lda
337  30 CONTINUE
338  ELSE
339  ioff = izero
340  DO 40 i = 1, izero - 1
341  a( ioff ) = zero
342  ioff = ioff + lda
343  40 CONTINUE
344  ioff = ioff - izero
345  DO 50 i = izero, n
346  a( ioff+i ) = zero
347  50 CONTINUE
348  END IF
349  ELSE
350  ioff = 0
351  IF( iuplo.EQ.1 ) THEN
352 *
353 * Set the first IZERO rows and columns to zero.
354 *
355  DO 70 j = 1, n
356  i2 = min( j, izero )
357  DO 60 i = 1, i2
358  a( ioff+i ) = zero
359  60 CONTINUE
360  ioff = ioff + lda
361  70 CONTINUE
362  ELSE
363 *
364 * Set the last IZERO rows and columns to zero.
365 *
366  DO 90 j = 1, n
367  i1 = max( j, izero )
368  DO 80 i = i1, n
369  a( ioff+i ) = zero
370  80 CONTINUE
371  ioff = ioff + lda
372  90 CONTINUE
373  END IF
374  END IF
375  ELSE
376  izero = 0
377  END IF
378 *
379 * End generate the test matrix A.
380 *
381  DO 150 ifact = 1, nfact
382 *
383 * Do first for FACT = 'F', then for other values.
384 *
385  fact = facts( ifact )
386 *
387 * Compute the condition number
388 *
389  IF( zerot ) THEN
390  IF( ifact.EQ.1 )
391  \$ GO TO 150
392  rcondc = zero
393 *
394  ELSE IF( ifact.EQ.1 ) THEN
395 *
396 * Compute the 1-norm of A.
397 *
398  anorm = dlansy( '1', uplo, n, a, lda, rwork )
399 *
400 * Factor the matrix A.
401 *
402  CALL dlacpy( uplo, n, n, a, lda, afac, lda )
403  CALL dsytrf_rk( uplo, n, afac, lda, e, iwork, work,
404  \$ lwork, info )
405 *
406 * Compute inv(A) and take its norm.
407 *
408  CALL dlacpy( uplo, n, n, afac, lda, ainv, lda )
409  lwork = (n+nb+1)*(nb+3)
410 *
411 * We need to compute the inverse to compute
412 * RCONDC that is used later in TEST3.
413 *
414  CALL dsytri_3( uplo, n, ainv, lda, e, iwork,
415  \$ work, lwork, info )
416  ainvnm = dlansy( '1', uplo, n, ainv, lda, rwork )
417 *
418 * Compute the 1-norm condition number of A.
419 *
420  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
421  rcondc = one
422  ELSE
423  rcondc = ( one / anorm ) / ainvnm
424  END IF
425  END IF
426 *
427 * Form an exact solution and set the right hand side.
428 *
429  srnamt = 'DLARHS'
430  CALL dlarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
431  \$ nrhs, a, lda, xact, lda, b, lda, iseed,
432  \$ info )
433  xtype = 'C'
434 *
435 * --- Test DSYSV_RK ---
436 *
437  IF( ifact.EQ.2 ) THEN
438  CALL dlacpy( uplo, n, n, a, lda, afac, lda )
439  CALL dlacpy( 'Full', n, nrhs, b, lda, x, lda )
440 *
441 * Factor the matrix and solve the system using
442 * DSYSV_RK.
443 *
444  srnamt = 'DSYSV_RK'
445  CALL dsysv_rk( uplo, n, nrhs, afac, lda, e, iwork,
446  \$ x, lda, work, lwork, info )
447 *
448 * Adjust the expected value of INFO to account for
449 * pivoting.
450 *
451  k = izero
452  IF( k.GT.0 ) THEN
453  100 CONTINUE
454  IF( iwork( k ).LT.0 ) THEN
455  IF( iwork( k ).NE.-k ) THEN
456  k = -iwork( k )
457  GO TO 100
458  END IF
459  ELSE IF( iwork( k ).NE.k ) THEN
460  k = iwork( k )
461  GO TO 100
462  END IF
463  END IF
464 *
465 * Check error code from DSYSV_RK and handle error.
466 *
467  IF( info.NE.k ) THEN
468  CALL alaerh( path, 'DSYSV_RK', info, k, uplo,
469  \$ n, n, -1, -1, nrhs, imat, nfail,
470  \$ nerrs, nout )
471  GO TO 120
472  ELSE IF( info.NE.0 ) THEN
473  GO TO 120
474  END IF
475 *
476 *+ TEST 1 Reconstruct matrix from factors and compute
477 * residual.
478 *
479  CALL dsyt01_3( uplo, n, a, lda, afac, lda, e,
480  \$ iwork, ainv, lda, rwork,
481  \$ result( 1 ) )
482 *
483 *+ TEST 2 Compute residual of the computed solution.
484 *
485  CALL dlacpy( 'Full', n, nrhs, b, lda, work, lda )
486  CALL dpot02( uplo, n, nrhs, a, lda, x, lda, work,
487  \$ lda, rwork, result( 2 ) )
488 *
489 *+ TEST 3
490 * Check solution from generated exact solution.
491 *
492  CALL dget04( n, nrhs, x, lda, xact, lda, rcondc,
493  \$ result( 3 ) )
494  nt = 3
495 *
496 * Print information about the tests that did not pass
497 * the threshold.
498 *
499  DO 110 k = 1, nt
500  IF( result( k ).GE.thresh ) THEN
501  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
502  \$ CALL aladhd( nout, path )
503  WRITE( nout, fmt = 9999 )'DSYSV_RK', uplo,
504  \$ n, imat, k, result( k )
505  nfail = nfail + 1
506  END IF
507  110 CONTINUE
508  nrun = nrun + nt
509  120 CONTINUE
510  END IF
511 *
512  150 CONTINUE
513 *
514  160 CONTINUE
515  170 CONTINUE
516  180 CONTINUE
517 *
518 * Print a summary of the results.
519 *
520  CALL alasvm( path, nout, nfail, nrun, nerrs )
521 *
522  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
523  \$ ', test ', i2, ', ratio =', g12.5 )
524  RETURN
525 *
526 * End of DDRVSY_RK
527 *
528  END
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:103
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:73
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:81
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:147
subroutine dlarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
DLARHS
Definition: dlarhs.f:205
subroutine ddrvsy_rk(DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, E, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
DDRVSY_RK
Definition: ddrvsy_rk.f:156
subroutine dsyt01_3(UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C, LDC, RWORK, RESID)
DSYT01_3
Definition: dsyt01_3.f:140
subroutine dget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
DGET04
Definition: dget04.f:102
subroutine dpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
DPOT02
Definition: dpot02.f:127
subroutine dlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
DLATB4
Definition: dlatb4.f:120
subroutine derrvx(PATH, NUNIT)
DERRVX
Definition: derrvx.f:55
subroutine dlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
DLATMS
Definition: dlatms.f:321
subroutine dsytrf_rk(UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
DSYTRF_RK computes the factorization of a real symmetric indefinite matrix using the bounded Bunch-Ka...
Definition: dsytrf_rk.f:259
subroutine dsytri_3(UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
DSYTRI_3
Definition: dsytri_3.f:170
subroutine dsysv_rk(UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, WORK, LWORK, INFO)
DSYSV_RK computes the solution to system of linear equations A * X = B for SY matrices
Definition: dsysv_rk.f:228