LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
ddrvsy_rook.f
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1 *> \brief \b DDRVSY_ROOK
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_ROOK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
12 * $ NMAX, A, AFAC, 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( * ),
24 * $ RWORK( * ), WORK( * ), X( * ), XACT( * )
25 * ..
26 *
27 *
28 *> \par Purpose:
29 * =============
30 *>
31 *> \verbatim
32 *>
33 *> DDRVSY_ROOK tests the driver routines DSYSV_ROOK.
34 *> \endverbatim
35 *
36 * Arguments:
37 * ==========
38 *
39 *> \param[in] DOTYPE
40 *> \verbatim
41 *> DOTYPE is LOGICAL array, dimension (NTYPES)
42 *> The matrix types to be used for testing. Matrices of type j
43 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
44 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
45 *> \endverbatim
46 *>
47 *> \param[in] NN
48 *> \verbatim
49 *> NN is INTEGER
50 *> The number of values of N contained in the vector NVAL.
51 *> \endverbatim
52 *>
53 *> \param[in] NVAL
54 *> \verbatim
55 *> NVAL is INTEGER array, dimension (NN)
56 *> The values of the matrix dimension N.
57 *> \endverbatim
58 *>
59 *> \param[in] NRHS
60 *> \verbatim
61 *> NRHS is INTEGER
62 *> The number of right hand side vectors to be generated for
63 *> each linear system.
64 *> \endverbatim
65 *>
66 *> \param[in] THRESH
67 *> \verbatim
68 *> THRESH is DOUBLE PRECISION
69 *> The threshold value for the test ratios. A result is
70 *> included in the output file if RESULT >= THRESH. To have
71 *> every test ratio printed, use THRESH = 0.
72 *> \endverbatim
73 *>
74 *> \param[in] TSTERR
75 *> \verbatim
76 *> TSTERR is LOGICAL
77 *> Flag that indicates whether error exits are to be tested.
78 *> \endverbatim
79 *>
80 *> \param[in] NMAX
81 *> \verbatim
82 *> NMAX is INTEGER
83 *> The maximum value permitted for N, used in dimensioning the
84 *> work arrays.
85 *> \endverbatim
86 *>
87 *> \param[out] A
88 *> \verbatim
89 *> A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
90 *> \endverbatim
91 *>
92 *> \param[out] AFAC
93 *> \verbatim
94 *> AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
95 *> \endverbatim
96 *>
97 *> \param[out] AINV
98 *> \verbatim
99 *> AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
100 *> \endverbatim
101 *>
102 *> \param[out] B
103 *> \verbatim
104 *> B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
105 *> \endverbatim
106 *>
107 *> \param[out] X
108 *> \verbatim
109 *> X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
110 *> \endverbatim
111 *>
112 *> \param[out] XACT
113 *> \verbatim
114 *> XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
115 *> \endverbatim
116 *>
117 *> \param[out] WORK
118 *> \verbatim
119 *> WORK is DOUBLE PRECISION array, dimension (NMAX*max(2,NRHS))
120 *> \endverbatim
121 *>
122 *> \param[out] RWORK
123 *> \verbatim
124 *> RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
125 *> \endverbatim
126 *>
127 *> \param[out] IWORK
128 *> \verbatim
129 *> IWORK is INTEGER array, dimension (2*NMAX)
130 *> \endverbatim
131 *>
132 *> \param[in] NOUT
133 *> \verbatim
134 *> NOUT is INTEGER
135 *> The unit number for output.
136 *> \endverbatim
137 *
138 * Authors:
139 * ========
140 *
141 *> \author Univ. of Tennessee
142 *> \author Univ. of California Berkeley
143 *> \author Univ. of Colorado Denver
144 *> \author NAG Ltd.
145 *
146 *> \date November 2013
147 *
148 *> \ingroup double_lin
149 *
150 * =====================================================================
151  SUBROUTINE ddrvsy_rook( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
152  $ NMAX, A, AFAC, AINV, B, X, XACT, WORK,
153  $ RWORK, IWORK, NOUT )
154 *
155 * -- LAPACK test routine (version 3.5.0) --
156 * -- LAPACK is a software package provided by Univ. of Tennessee, --
157 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
158 * November 2013
159 *
160 * .. Scalar Arguments ..
161  LOGICAL TSTERR
162  INTEGER NMAX, NN, NOUT, NRHS
163  DOUBLE PRECISION THRESH
164 * ..
165 * .. Array Arguments ..
166  LOGICAL DOTYPE( * )
167  INTEGER IWORK( * ), NVAL( * )
168  DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ),
169  $ rwork( * ), work( * ), x( * ), xact( * )
170 * ..
171 *
172 * =====================================================================
173 *
174 * .. Parameters ..
175  DOUBLE PRECISION ONE, ZERO
176  parameter( one = 1.0d+0, zero = 0.0d+0 )
177  INTEGER NTYPES, NTESTS
178  parameter( ntypes = 10, ntests = 3 )
179  INTEGER NFACT
180  parameter( nfact = 2 )
181 * ..
182 * .. Local Scalars ..
183  LOGICAL ZEROT
184  CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
185  CHARACTER*3 PATH, MATPATH
186  INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
187  $ izero, j, k, kl, ku, lda, lwork, mode, n,
188  $ nb, nbmin, nerrs, nfail, nimat, nrun, nt
189  DOUBLE PRECISION AINVNM, ANORM, CNDNUM, RCONDC
190 * ..
191 * .. Local Arrays ..
192  CHARACTER FACTS( nfact ), UPLOS( 2 )
193  INTEGER ISEED( 4 ), ISEEDY( 4 )
194  DOUBLE PRECISION RESULT( ntests )
195 * ..
196 * .. External Functions ..
197  DOUBLE PRECISION DLANSY
198  EXTERNAL dlansy
199 * ..
200 * .. External Subroutines ..
201  EXTERNAL aladhd, alaerh, alasvm, derrvx, dget04, dlacpy,
204  $ dsytri_rook,
205  $ xlaenv
206 * ..
207 * .. Scalars in Common ..
208  LOGICAL LERR, OK
209  CHARACTER*32 SRNAMT
210  INTEGER INFOT, NUNIT
211 * ..
212 * .. Common blocks ..
213  COMMON / infoc / infot, nunit, ok, lerr
214  COMMON / srnamc / srnamt
215 * ..
216 * .. Intrinsic Functions ..
217  INTRINSIC max, min
218 * ..
219 * .. Data statements ..
220  DATA iseedy / 1988, 1989, 1990, 1991 /
221  DATA uplos / 'U', 'L' / , facts / 'F', 'N' /
222 * ..
223 * .. Executable Statements ..
224 *
225 * Initialize constants and the random number seed.
226 *
227 * Test path
228 *
229  path( 1: 1 ) = 'Double precision'
230  path( 2: 3 ) = 'SR'
231 *
232 * Path to generate matrices
233 *
234  matpath( 1: 1 ) = 'Double precision'
235  matpath( 2: 3 ) = 'SY'
236 *
237  nrun = 0
238  nfail = 0
239  nerrs = 0
240  DO 10 i = 1, 4
241  iseed( i ) = iseedy( i )
242  10 CONTINUE
243  lwork = max( 2*nmax, nmax*nrhs )
244 *
245 * Test the error exits
246 *
247  IF( tsterr )
248  $ CALL derrvx( path, nout )
249  infot = 0
250 *
251 * Set the block size and minimum block size for which the block
252 * routine should be used, which will be later returned by ILAENV.
253 *
254  nb = 1
255  nbmin = 2
256  CALL xlaenv( 1, nb )
257  CALL xlaenv( 2, nbmin )
258 *
259 * Do for each value of N in NVAL
260 *
261  DO 180 in = 1, nn
262  n = nval( in )
263  lda = max( n, 1 )
264  xtype = 'N'
265  nimat = ntypes
266  IF( n.LE.0 )
267  $ nimat = 1
268 *
269  DO 170 imat = 1, nimat
270 *
271 * Do the tests only if DOTYPE( IMAT ) is true.
272 *
273  IF( .NOT.dotype( imat ) )
274  $ GO TO 170
275 *
276 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
277 *
278  zerot = imat.GE.3 .AND. imat.LE.6
279  IF( zerot .AND. n.LT.imat-2 )
280  $ GO TO 170
281 *
282 * Do first for UPLO = 'U', then for UPLO = 'L'
283 *
284  DO 160 iuplo = 1, 2
285  uplo = uplos( iuplo )
286 *
287 * Begin generate the test matrix A.
288 *
289 * Set up parameters with DLATB4 for the matrix generator
290 * based on the type of matrix to be generated.
291 *
292  CALL dlatb4( matpath, imat, n, n, TYPE, KL, KU, ANORM,
293  $ mode, cndnum, dist )
294 *
295 * Generate a matrix with DLATMS.
296 *
297  srnamt = 'DLATMS'
298  CALL dlatms( n, n, dist, iseed, TYPE, RWORK, MODE,
299  $ cndnum, anorm, kl, ku, uplo, a, lda, work,
300  $ info )
301 *
302 * Check error code from DLATMS and handle error.
303 *
304  IF( info.NE.0 ) THEN
305  CALL alaerh( path, 'DLATMS', info, 0, uplo, n, n, -1,
306  $ -1, -1, imat, nfail, nerrs, nout )
307 *
308 * Skip all tests for this generated matrix
309 *
310  GO TO 160
311  END IF
312 *
313 * For types 3-6, zero one or more rows and columns of the
314 * matrix to test that INFO is returned correctly.
315 *
316  IF( zerot ) THEN
317  IF( imat.EQ.3 ) THEN
318  izero = 1
319  ELSE IF( imat.EQ.4 ) THEN
320  izero = n
321  ELSE
322  izero = n / 2 + 1
323  END IF
324 *
325  IF( imat.LT.6 ) THEN
326 *
327 * Set row and column IZERO to zero.
328 *
329  IF( iuplo.EQ.1 ) THEN
330  ioff = ( izero-1 )*lda
331  DO 20 i = 1, izero - 1
332  a( ioff+i ) = zero
333  20 CONTINUE
334  ioff = ioff + izero
335  DO 30 i = izero, n
336  a( ioff ) = zero
337  ioff = ioff + lda
338  30 CONTINUE
339  ELSE
340  ioff = izero
341  DO 40 i = 1, izero - 1
342  a( ioff ) = zero
343  ioff = ioff + lda
344  40 CONTINUE
345  ioff = ioff - izero
346  DO 50 i = izero, n
347  a( ioff+i ) = zero
348  50 CONTINUE
349  END IF
350  ELSE
351  ioff = 0
352  IF( iuplo.EQ.1 ) THEN
353 *
354 * Set the first IZERO rows and columns to zero.
355 *
356  DO 70 j = 1, n
357  i2 = min( j, izero )
358  DO 60 i = 1, i2
359  a( ioff+i ) = zero
360  60 CONTINUE
361  ioff = ioff + lda
362  70 CONTINUE
363  ELSE
364 *
365 * Set the last IZERO rows and columns to zero.
366 *
367  DO 90 j = 1, n
368  i1 = max( j, izero )
369  DO 80 i = i1, n
370  a( ioff+i ) = zero
371  80 CONTINUE
372  ioff = ioff + lda
373  90 CONTINUE
374  END IF
375  END IF
376  ELSE
377  izero = 0
378  END IF
379 *
380 * End generate the test matrix A.
381 *
382  DO 150 ifact = 1, nfact
383 *
384 * Do first for FACT = 'F', then for other values.
385 *
386  fact = facts( ifact )
387 *
388 * Compute the condition number for comparison with
389 * the value returned by DSYSVX_ROOK.
390 *
391  IF( zerot ) THEN
392  IF( ifact.EQ.1 )
393  $ GO TO 150
394  rcondc = zero
395 *
396  ELSE IF( ifact.EQ.1 ) THEN
397 *
398 * Compute the 1-norm of A.
399 *
400  anorm = dlansy( '1', uplo, n, a, lda, rwork )
401 *
402 * Factor the matrix A.
403 *
404  CALL dlacpy( uplo, n, n, a, lda, afac, lda )
405  CALL dsytrf_rook( uplo, n, afac, lda, iwork, work,
406  $ lwork, info )
407 *
408 * Compute inv(A) and take its norm.
409 *
410  CALL dlacpy( uplo, n, n, afac, lda, ainv, lda )
411  lwork = (n+nb+1)*(nb+3)
412  CALL dsytri_rook( uplo, n, ainv, lda, iwork,
413  $ work, info )
414  ainvnm = dlansy( '1', uplo, n, ainv, lda, rwork )
415 *
416 * Compute the 1-norm condition number of A.
417 *
418  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
419  rcondc = one
420  ELSE
421  rcondc = ( one / anorm ) / ainvnm
422  END IF
423  END IF
424 *
425 * Form an exact solution and set the right hand side.
426 *
427  srnamt = 'DLARHS'
428  CALL dlarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
429  $ nrhs, a, lda, xact, lda, b, lda, iseed,
430  $ info )
431  xtype = 'C'
432 *
433 * --- Test DSYSV_ROOK ---
434 *
435  IF( ifact.EQ.2 ) THEN
436  CALL dlacpy( uplo, n, n, a, lda, afac, lda )
437  CALL dlacpy( 'Full', n, nrhs, b, lda, x, lda )
438 *
439 * Factor the matrix and solve the system using
440 * DSYSV_ROOK.
441 *
442  srnamt = 'DSYSV_ROOK'
443  CALL dsysv_rook( uplo, n, nrhs, afac, lda, iwork,
444  $ x, lda, work, lwork, info )
445 *
446 * Adjust the expected value of INFO to account for
447 * pivoting.
448 *
449  k = izero
450  IF( k.GT.0 ) THEN
451  100 CONTINUE
452  IF( iwork( k ).LT.0 ) THEN
453  IF( iwork( k ).NE.-k ) THEN
454  k = -iwork( k )
455  GO TO 100
456  END IF
457  ELSE IF( iwork( k ).NE.k ) THEN
458  k = iwork( k )
459  GO TO 100
460  END IF
461  END IF
462 *
463 * Check error code from DSYSV_ROOK and handle error.
464 *
465  IF( info.NE.k ) THEN
466  CALL alaerh( path, 'DSYSV_ROOK', info, k, uplo,
467  $ n, n, -1, -1, nrhs, imat, nfail,
468  $ nerrs, nout )
469  GO TO 120
470  ELSE IF( info.NE.0 ) THEN
471  GO TO 120
472  END IF
473 *
474 *+ TEST 1 Reconstruct matrix from factors and compute
475 * residual.
476 *
477  CALL dsyt01_rook( uplo, n, a, lda, afac, lda,
478  $ iwork, ainv, lda, rwork,
479  $ result( 1 ) )
480 *
481 *+ TEST 2 Compute residual of the computed solution.
482 *
483  CALL dlacpy( 'Full', n, nrhs, b, lda, work, lda )
484  CALL dpot02( uplo, n, nrhs, a, lda, x, lda, work,
485  $ lda, rwork, result( 2 ) )
486 *
487 *+ TEST 3
488 * Check solution from generated exact solution.
489 *
490  CALL dget04( n, nrhs, x, lda, xact, lda, rcondc,
491  $ result( 3 ) )
492  nt = 3
493 *
494 * Print information about the tests that did not pass
495 * the threshold.
496 *
497  DO 110 k = 1, nt
498  IF( result( k ).GE.thresh ) THEN
499  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
500  $ CALL aladhd( nout, path )
501  WRITE( nout, fmt = 9999 )'DSYSV_ROOK', uplo,
502  $ n, imat, k, result( k )
503  nfail = nfail + 1
504  END IF
505  110 CONTINUE
506  nrun = nrun + nt
507  120 CONTINUE
508  END IF
509 *
510  150 CONTINUE
511 *
512  160 CONTINUE
513  170 CONTINUE
514  180 CONTINUE
515 *
516 * Print a summary of the results.
517 *
518  CALL alasvm( path, nout, nfail, nrun, nerrs )
519 *
520  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
521  $ ', test ', i2, ', ratio =', g12.5 )
522  RETURN
523 *
524 * End of DDRVSY_ROOK
525 *
526  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:105
subroutine dlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
DLATB4
Definition: dlatb4.f:122
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:75
subroutine ddrvsy_rook(DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
DDRVSY_ROOK
Definition: ddrvsy_rook.f:154
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
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 dlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
DLATMS
Definition: dlatms.f:323
subroutine dpot05(UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
DPOT05
Definition: dpot05.f:166
subroutine dsytri_rook(UPLO, N, A, LDA, IPIV, WORK, INFO)
DSYTRI_ROOK
Definition: dsytri_rook.f:131
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: dlaset.f:112
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
subroutine dget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
DGET04
Definition: dget04.f:104
subroutine dsyt01_rook(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
DSYT01_ROOK
Definition: dsyt01_rook.f:126
subroutine aladhd(IOUNIT, PATH)
ALADHD
Definition: aladhd.f:92
subroutine derrvx(PATH, NUNIT)
DERRVX
Definition: derrvx.f:57
subroutine dsysv_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
DSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices ...
Definition: dsysv_rook.f:206
subroutine dsytrf_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
DSYTRF_ROOK
Definition: dsytrf_rook.f:210
subroutine dpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
DPOT02
Definition: dpot02.f:129