LAPACK  3.8.0
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 *> \date December 2016
151 *
152 *> \ingroup double_lin
153 *
154 * =====================================================================
155  SUBROUTINE ddrvsy_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  DOUBLE PRECISION THRESH
168 * ..
169 * .. Array Arguments ..
170  LOGICAL DOTYPE( * )
171  INTEGER IWORK( * ), NVAL( * )
172  DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ), E( * ),
173  $ rwork( * ), work( * ), x( * ), xact( * )
174 * ..
175 *
176 * =====================================================================
177 *
178 * .. Parameters ..
179  DOUBLE PRECISION ONE, ZERO
180  parameter( one = 1.0d+0, zero = 0.0d+0 )
181  INTEGER NTYPES, NTESTS
182  parameter( ntypes = 10, ntests = 3 )
183  INTEGER NFACT
184  parameter( nfact = 2 )
185 * ..
186 * .. Local Scalars ..
187  LOGICAL ZEROT
188  CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
189  CHARACTER*3 PATH, MATPATH
190  INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
191  $ izero, j, k, kl, ku, lda, lwork, mode, n,
192  $ nb, nbmin, nerrs, nfail, nimat, nrun, nt
193  DOUBLE PRECISION AINVNM, ANORM, CNDNUM, RCONDC
194 * ..
195 * .. Local Arrays ..
196  CHARACTER FACTS( nfact ), UPLOS( 2 )
197  INTEGER ISEED( 4 ), ISEEDY( 4 )
198  DOUBLE PRECISION RESULT( ntests )
199 * ..
200 * .. External Functions ..
201  DOUBLE PRECISION DLANSY
202  EXTERNAL dlansy
203 * ..
204 * .. External Subroutines ..
205  EXTERNAL aladhd, alaerh, alasvm, derrvx, dget04, dlacpy,
208 * ..
209 * .. Scalars in Common ..
210  LOGICAL LERR, OK
211  CHARACTER*32 SRNAMT
212  INTEGER INFOT, NUNIT
213 * ..
214 * .. Common blocks ..
215  COMMON / infoc / infot, nunit, ok, lerr
216  COMMON / srnamc / srnamt
217 * ..
218 * .. Intrinsic Functions ..
219  INTRINSIC max, min
220 * ..
221 * .. Data statements ..
222  DATA iseedy / 1988, 1989, 1990, 1991 /
223  DATA uplos / 'U', 'L' / , facts / 'F', 'N' /
224 * ..
225 * .. Executable Statements ..
226 *
227 * Initialize constants and the random number seed.
228 *
229 * Test path
230 *
231  path( 1: 1 ) = 'Double precision'
232  path( 2: 3 ) = 'SK'
233 *
234 * Path to generate matrices
235 *
236  matpath( 1: 1 ) = 'Double precision'
237  matpath( 2: 3 ) = 'SY'
238 *
239  nrun = 0
240  nfail = 0
241  nerrs = 0
242  DO 10 i = 1, 4
243  iseed( i ) = iseedy( i )
244  10 CONTINUE
245  lwork = max( 2*nmax, nmax*nrhs )
246 *
247 * Test the error exits
248 *
249  IF( tsterr )
250  $ CALL derrvx( path, nout )
251  infot = 0
252 *
253 * Set the block size and minimum block size for which the block
254 * routine should be used, which will be later returned by ILAENV.
255 *
256  nb = 1
257  nbmin = 2
258  CALL xlaenv( 1, nb )
259  CALL xlaenv( 2, nbmin )
260 *
261 * Do for each value of N in NVAL
262 *
263  DO 180 in = 1, nn
264  n = nval( in )
265  lda = max( n, 1 )
266  xtype = 'N'
267  nimat = ntypes
268  IF( n.LE.0 )
269  $ nimat = 1
270 *
271  DO 170 imat = 1, nimat
272 *
273 * Do the tests only if DOTYPE( IMAT ) is true.
274 *
275  IF( .NOT.dotype( imat ) )
276  $ GO TO 170
277 *
278 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
279 *
280  zerot = imat.GE.3 .AND. imat.LE.6
281  IF( zerot .AND. n.LT.imat-2 )
282  $ GO TO 170
283 *
284 * Do first for UPLO = 'U', then for UPLO = 'L'
285 *
286  DO 160 iuplo = 1, 2
287  uplo = uplos( iuplo )
288 *
289 * Begin generate the test matrix A.
290 *
291 * Set up parameters with DLATB4 for the matrix generator
292 * based on the type of matrix to be generated.
293 *
294  CALL dlatb4( matpath, imat, n, n, TYPE, KL, KU, ANORM,
295  $ mode, cndnum, dist )
296 *
297 * Generate a matrix with DLATMS.
298 *
299  srnamt = 'DLATMS'
300  CALL dlatms( n, n, dist, iseed, TYPE, RWORK, MODE,
301  $ cndnum, anorm, kl, ku, uplo, a, lda, work,
302  $ info )
303 *
304 * Check error code from DLATMS and handle error.
305 *
306  IF( info.NE.0 ) THEN
307  CALL alaerh( path, 'DLATMS', info, 0, uplo, n, n, -1,
308  $ -1, -1, imat, nfail, nerrs, nout )
309 *
310 * Skip all tests for this generated matrix
311 *
312  GO TO 160
313  END IF
314 *
315 * For types 3-6, zero one or more rows and columns of the
316 * matrix to test that INFO is returned correctly.
317 *
318  IF( zerot ) THEN
319  IF( imat.EQ.3 ) THEN
320  izero = 1
321  ELSE IF( imat.EQ.4 ) THEN
322  izero = n
323  ELSE
324  izero = n / 2 + 1
325  END IF
326 *
327  IF( imat.LT.6 ) THEN
328 *
329 * Set row and column IZERO to zero.
330 *
331  IF( iuplo.EQ.1 ) THEN
332  ioff = ( izero-1 )*lda
333  DO 20 i = 1, izero - 1
334  a( ioff+i ) = zero
335  20 CONTINUE
336  ioff = ioff + izero
337  DO 30 i = izero, n
338  a( ioff ) = zero
339  ioff = ioff + lda
340  30 CONTINUE
341  ELSE
342  ioff = izero
343  DO 40 i = 1, izero - 1
344  a( ioff ) = zero
345  ioff = ioff + lda
346  40 CONTINUE
347  ioff = ioff - izero
348  DO 50 i = izero, n
349  a( ioff+i ) = zero
350  50 CONTINUE
351  END IF
352  ELSE
353  ioff = 0
354  IF( iuplo.EQ.1 ) THEN
355 *
356 * Set the first IZERO rows and columns to zero.
357 *
358  DO 70 j = 1, n
359  i2 = min( j, izero )
360  DO 60 i = 1, i2
361  a( ioff+i ) = zero
362  60 CONTINUE
363  ioff = ioff + lda
364  70 CONTINUE
365  ELSE
366 *
367 * Set the last IZERO rows and columns to zero.
368 *
369  DO 90 j = 1, n
370  i1 = max( j, izero )
371  DO 80 i = i1, n
372  a( ioff+i ) = zero
373  80 CONTINUE
374  ioff = ioff + lda
375  90 CONTINUE
376  END IF
377  END IF
378  ELSE
379  izero = 0
380  END IF
381 *
382 * End generate the test matrix A.
383 *
384  DO 150 ifact = 1, nfact
385 *
386 * Do first for FACT = 'F', then for other values.
387 *
388  fact = facts( ifact )
389 *
390 * Compute the condition number
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 = dlansy( '1', uplo, n, a, lda, rwork )
402 *
403 * Factor the matrix A.
404 *
405  CALL dlacpy( uplo, n, n, a, lda, afac, lda )
406  CALL dsytrf_rk( uplo, n, afac, lda, e, iwork, work,
407  $ lwork, info )
408 *
409 * Compute inv(A) and take its norm.
410 *
411  CALL dlacpy( uplo, n, n, afac, lda, ainv, lda )
412  lwork = (n+nb+1)*(nb+3)
413 *
414 * We need to copute the invesrse to compute
415 * RCONDC that is used later in TEST3.
416 *
417  CALL dsytri_3( uplo, n, ainv, lda, e, iwork,
418  $ work, lwork, info )
419  ainvnm = dlansy( '1', uplo, n, ainv, lda, rwork )
420 *
421 * Compute the 1-norm condition number of A.
422 *
423  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
424  rcondc = one
425  ELSE
426  rcondc = ( one / anorm ) / ainvnm
427  END IF
428  END IF
429 *
430 * Form an exact solution and set the right hand side.
431 *
432  srnamt = 'DLARHS'
433  CALL dlarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
434  $ nrhs, a, lda, xact, lda, b, lda, iseed,
435  $ info )
436  xtype = 'C'
437 *
438 * --- Test DSYSV_RK ---
439 *
440  IF( ifact.EQ.2 ) THEN
441  CALL dlacpy( uplo, n, n, a, lda, afac, lda )
442  CALL dlacpy( 'Full', n, nrhs, b, lda, x, lda )
443 *
444 * Factor the matrix and solve the system using
445 * DSYSV_RK.
446 *
447  srnamt = 'DSYSV_RK'
448  CALL dsysv_rk( uplo, n, nrhs, afac, lda, e, iwork,
449  $ x, lda, work, lwork, info )
450 *
451 * Adjust the expected value of INFO to account for
452 * pivoting.
453 *
454  k = izero
455  IF( k.GT.0 ) THEN
456  100 CONTINUE
457  IF( iwork( k ).LT.0 ) THEN
458  IF( iwork( k ).NE.-k ) THEN
459  k = -iwork( k )
460  GO TO 100
461  END IF
462  ELSE IF( iwork( k ).NE.k ) THEN
463  k = iwork( k )
464  GO TO 100
465  END IF
466  END IF
467 *
468 * Check error code from DSYSV_RK and handle error.
469 *
470  IF( info.NE.k ) THEN
471  CALL alaerh( path, 'DSYSV_RK', info, k, uplo,
472  $ n, n, -1, -1, nrhs, imat, nfail,
473  $ nerrs, nout )
474  GO TO 120
475  ELSE IF( info.NE.0 ) THEN
476  GO TO 120
477  END IF
478 *
479 *+ TEST 1 Reconstruct matrix from factors and compute
480 * residual.
481 *
482  CALL dsyt01_3( uplo, n, a, lda, afac, lda, e,
483  $ iwork, ainv, lda, rwork,
484  $ result( 1 ) )
485 *
486 *+ TEST 2 Compute residual of the computed solution.
487 *
488  CALL dlacpy( 'Full', n, nrhs, b, lda, work, lda )
489  CALL dpot02( uplo, n, nrhs, a, lda, x, lda, work,
490  $ lda, rwork, result( 2 ) )
491 *
492 *+ TEST 3
493 * Check solution from generated exact solution.
494 *
495  CALL dget04( n, nrhs, x, lda, xact, lda, rcondc,
496  $ result( 3 ) )
497  nt = 3
498 *
499 * Print information about the tests that did not pass
500 * the threshold.
501 *
502  DO 110 k = 1, nt
503  IF( result( k ).GE.thresh ) THEN
504  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
505  $ CALL aladhd( nout, path )
506  WRITE( nout, fmt = 9999 )'DSYSV_RK', uplo,
507  $ n, imat, k, result( k )
508  nfail = nfail + 1
509  END IF
510  110 CONTINUE
511  nrun = nrun + nt
512  120 CONTINUE
513  END IF
514 *
515  150 CONTINUE
516 *
517  160 CONTINUE
518  170 CONTINUE
519  180 CONTINUE
520 *
521 * Print a summary of the results.
522 *
523  CALL alasvm( path, nout, nfail, nrun, nerrs )
524 *
525  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
526  $ ', test ', i2, ', ratio =', g12.5 )
527  RETURN
528 *
529 * End of DDRVSY_RK
530 *
531  END
subroutine dlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
DLATMS
Definition: dlatms.f:323
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
subroutine dsytri_3(UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
DSYTRI_3
Definition: dsytri_3.f:172
subroutine aladhd(IOUNIT, PATH)
ALADHD
Definition: aladhd.f:92
subroutine derrvx(PATH, NUNIT)
DERRVX
Definition: derrvx.f:57
subroutine dget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
DGET04
Definition: dget04.f:104
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:261
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:75
subroutine dlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
DLATB4
Definition: dlatb4.f:122
subroutine dlarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
DLARHS
Definition: dlarhs.f:206
subroutine dsyt01_3(UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C, LDC, RWORK, RESID)
DSYT01_3
Definition: dsyt01_3.f:142
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:105
subroutine dpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
DPOT02
Definition: dpot02.f:129
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:230
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:158