LAPACK  3.10.1
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 *> \ingroup double_lin
147 *
148 * =====================================================================
149  SUBROUTINE ddrvsy_rook( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
150  $ NMAX, A, AFAC, AINV, B, X, XACT, WORK,
151  $ RWORK, IWORK, NOUT )
152 *
153 * -- LAPACK test routine --
154 * -- LAPACK is a software package provided by Univ. of Tennessee, --
155 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
156 *
157 * .. Scalar Arguments ..
158  LOGICAL TSTERR
159  INTEGER NMAX, NN, NOUT, NRHS
160  DOUBLE PRECISION THRESH
161 * ..
162 * .. Array Arguments ..
163  LOGICAL DOTYPE( * )
164  INTEGER IWORK( * ), NVAL( * )
165  DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ),
166  $ rwork( * ), work( * ), x( * ), xact( * )
167 * ..
168 *
169 * =====================================================================
170 *
171 * .. Parameters ..
172  DOUBLE PRECISION ONE, ZERO
173  PARAMETER ( ONE = 1.0d+0, zero = 0.0d+0 )
174  INTEGER NTYPES, NTESTS
175  parameter( ntypes = 10, ntests = 3 )
176  INTEGER NFACT
177  parameter( nfact = 2 )
178 * ..
179 * .. Local Scalars ..
180  LOGICAL ZEROT
181  CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
182  CHARACTER*3 PATH, MATPATH
183  INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
184  $ izero, j, k, kl, ku, lda, lwork, mode, n,
185  $ nb, nbmin, nerrs, nfail, nimat, nrun, nt
186  DOUBLE PRECISION AINVNM, ANORM, CNDNUM, RCONDC
187 * ..
188 * .. Local Arrays ..
189  CHARACTER FACTS( NFACT ), UPLOS( 2 )
190  INTEGER ISEED( 4 ), ISEEDY( 4 )
191  DOUBLE PRECISION RESULT( NTESTS )
192 * ..
193 * .. External Functions ..
194  DOUBLE PRECISION DLANSY
195  EXTERNAL DLANSY
196 * ..
197 * .. External Subroutines ..
198  EXTERNAL aladhd, alaerh, alasvm, derrvx, dget04, dlacpy,
201  $ dsytri_rook,
202  $ xlaenv
203 * ..
204 * .. Scalars in Common ..
205  LOGICAL LERR, OK
206  CHARACTER*32 SRNAMT
207  INTEGER INFOT, NUNIT
208 * ..
209 * .. Common blocks ..
210  COMMON / infoc / infot, nunit, ok, lerr
211  COMMON / srnamc / srnamt
212 * ..
213 * .. Intrinsic Functions ..
214  INTRINSIC max, min
215 * ..
216 * .. Data statements ..
217  DATA iseedy / 1988, 1989, 1990, 1991 /
218  DATA uplos / 'U', 'L' / , facts / 'F', 'N' /
219 * ..
220 * .. Executable Statements ..
221 *
222 * Initialize constants and the random number seed.
223 *
224 * Test path
225 *
226  path( 1: 1 ) = 'Double precision'
227  path( 2: 3 ) = 'SR'
228 *
229 * Path to generate matrices
230 *
231  matpath( 1: 1 ) = 'Double precision'
232  matpath( 2: 3 ) = 'SY'
233 *
234  nrun = 0
235  nfail = 0
236  nerrs = 0
237  DO 10 i = 1, 4
238  iseed( i ) = iseedy( i )
239  10 CONTINUE
240  lwork = max( 2*nmax, nmax*nrhs )
241 *
242 * Test the error exits
243 *
244  IF( tsterr )
245  $ CALL derrvx( path, nout )
246  infot = 0
247 *
248 * Set the block size and minimum block size for which the block
249 * routine should be used, which will be later returned by ILAENV.
250 *
251  nb = 1
252  nbmin = 2
253  CALL xlaenv( 1, nb )
254  CALL xlaenv( 2, nbmin )
255 *
256 * Do for each value of N in NVAL
257 *
258  DO 180 in = 1, nn
259  n = nval( in )
260  lda = max( n, 1 )
261  xtype = 'N'
262  nimat = ntypes
263  IF( n.LE.0 )
264  $ nimat = 1
265 *
266  DO 170 imat = 1, nimat
267 *
268 * Do the tests only if DOTYPE( IMAT ) is true.
269 *
270  IF( .NOT.dotype( imat ) )
271  $ GO TO 170
272 *
273 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
274 *
275  zerot = imat.GE.3 .AND. imat.LE.6
276  IF( zerot .AND. n.LT.imat-2 )
277  $ GO TO 170
278 *
279 * Do first for UPLO = 'U', then for UPLO = 'L'
280 *
281  DO 160 iuplo = 1, 2
282  uplo = uplos( iuplo )
283 *
284 * Begin generate the test matrix A.
285 *
286 * Set up parameters with DLATB4 for the matrix generator
287 * based on the type of matrix to be generated.
288 *
289  CALL dlatb4( matpath, imat, n, n, TYPE, kl, ku, anorm,
290  $ mode, cndnum, dist )
291 *
292 * Generate a matrix with DLATMS.
293 *
294  srnamt = 'DLATMS'
295  CALL dlatms( n, n, dist, iseed, TYPE, rwork, mode,
296  $ cndnum, anorm, kl, ku, uplo, a, lda, work,
297  $ info )
298 *
299 * Check error code from DLATMS and handle error.
300 *
301  IF( info.NE.0 ) THEN
302  CALL alaerh( path, 'DLATMS', info, 0, uplo, n, n, -1,
303  $ -1, -1, imat, nfail, nerrs, nout )
304 *
305 * Skip all tests for this generated matrix
306 *
307  GO TO 160
308  END IF
309 *
310 * For types 3-6, zero one or more rows and columns of the
311 * matrix to test that INFO is returned correctly.
312 *
313  IF( zerot ) THEN
314  IF( imat.EQ.3 ) THEN
315  izero = 1
316  ELSE IF( imat.EQ.4 ) THEN
317  izero = n
318  ELSE
319  izero = n / 2 + 1
320  END IF
321 *
322  IF( imat.LT.6 ) THEN
323 *
324 * Set row and column IZERO to zero.
325 *
326  IF( iuplo.EQ.1 ) THEN
327  ioff = ( izero-1 )*lda
328  DO 20 i = 1, izero - 1
329  a( ioff+i ) = zero
330  20 CONTINUE
331  ioff = ioff + izero
332  DO 30 i = izero, n
333  a( ioff ) = zero
334  ioff = ioff + lda
335  30 CONTINUE
336  ELSE
337  ioff = izero
338  DO 40 i = 1, izero - 1
339  a( ioff ) = zero
340  ioff = ioff + lda
341  40 CONTINUE
342  ioff = ioff - izero
343  DO 50 i = izero, n
344  a( ioff+i ) = zero
345  50 CONTINUE
346  END IF
347  ELSE
348  ioff = 0
349  IF( iuplo.EQ.1 ) THEN
350 *
351 * Set the first IZERO rows and columns to zero.
352 *
353  DO 70 j = 1, n
354  i2 = min( j, izero )
355  DO 60 i = 1, i2
356  a( ioff+i ) = zero
357  60 CONTINUE
358  ioff = ioff + lda
359  70 CONTINUE
360  ELSE
361 *
362 * Set the last IZERO rows and columns to zero.
363 *
364  DO 90 j = 1, n
365  i1 = max( j, izero )
366  DO 80 i = i1, n
367  a( ioff+i ) = zero
368  80 CONTINUE
369  ioff = ioff + lda
370  90 CONTINUE
371  END IF
372  END IF
373  ELSE
374  izero = 0
375  END IF
376 *
377 * End generate the test matrix A.
378 *
379  DO 150 ifact = 1, nfact
380 *
381 * Do first for FACT = 'F', then for other values.
382 *
383  fact = facts( ifact )
384 *
385 * Compute the condition number for comparison with
386 * the value returned by DSYSVX_ROOK.
387 *
388  IF( zerot ) THEN
389  IF( ifact.EQ.1 )
390  $ GO TO 150
391  rcondc = zero
392 *
393  ELSE IF( ifact.EQ.1 ) THEN
394 *
395 * Compute the 1-norm of A.
396 *
397  anorm = dlansy( '1', uplo, n, a, lda, rwork )
398 *
399 * Factor the matrix A.
400 *
401  CALL dlacpy( uplo, n, n, a, lda, afac, lda )
402  CALL dsytrf_rook( uplo, n, afac, lda, iwork, work,
403  $ lwork, info )
404 *
405 * Compute inv(A) and take its norm.
406 *
407  CALL dlacpy( uplo, n, n, afac, lda, ainv, lda )
408  lwork = (n+nb+1)*(nb+3)
409  CALL dsytri_rook( uplo, n, ainv, lda, iwork,
410  $ work, info )
411  ainvnm = dlansy( '1', uplo, n, ainv, lda, rwork )
412 *
413 * Compute the 1-norm condition number of A.
414 *
415  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
416  rcondc = one
417  ELSE
418  rcondc = ( one / anorm ) / ainvnm
419  END IF
420  END IF
421 *
422 * Form an exact solution and set the right hand side.
423 *
424  srnamt = 'DLARHS'
425  CALL dlarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
426  $ nrhs, a, lda, xact, lda, b, lda, iseed,
427  $ info )
428  xtype = 'C'
429 *
430 * --- Test DSYSV_ROOK ---
431 *
432  IF( ifact.EQ.2 ) THEN
433  CALL dlacpy( uplo, n, n, a, lda, afac, lda )
434  CALL dlacpy( 'Full', n, nrhs, b, lda, x, lda )
435 *
436 * Factor the matrix and solve the system using
437 * DSYSV_ROOK.
438 *
439  srnamt = 'DSYSV_ROOK'
440  CALL dsysv_rook( uplo, n, nrhs, afac, lda, iwork,
441  $ x, lda, work, lwork, info )
442 *
443 * Adjust the expected value of INFO to account for
444 * pivoting.
445 *
446  k = izero
447  IF( k.GT.0 ) THEN
448  100 CONTINUE
449  IF( iwork( k ).LT.0 ) THEN
450  IF( iwork( k ).NE.-k ) THEN
451  k = -iwork( k )
452  GO TO 100
453  END IF
454  ELSE IF( iwork( k ).NE.k ) THEN
455  k = iwork( k )
456  GO TO 100
457  END IF
458  END IF
459 *
460 * Check error code from DSYSV_ROOK and handle error.
461 *
462  IF( info.NE.k ) THEN
463  CALL alaerh( path, 'DSYSV_ROOK', info, k, uplo,
464  $ n, n, -1, -1, nrhs, imat, nfail,
465  $ nerrs, nout )
466  GO TO 120
467  ELSE IF( info.NE.0 ) THEN
468  GO TO 120
469  END IF
470 *
471 *+ TEST 1 Reconstruct matrix from factors and compute
472 * residual.
473 *
474  CALL dsyt01_rook( uplo, n, a, lda, afac, lda,
475  $ iwork, ainv, lda, rwork,
476  $ result( 1 ) )
477 *
478 *+ TEST 2 Compute residual of the computed solution.
479 *
480  CALL dlacpy( 'Full', n, nrhs, b, lda, work, lda )
481  CALL dpot02( uplo, n, nrhs, a, lda, x, lda, work,
482  $ lda, rwork, result( 2 ) )
483 *
484 *+ TEST 3
485 * Check solution from generated exact solution.
486 *
487  CALL dget04( n, nrhs, x, lda, xact, lda, rcondc,
488  $ result( 3 ) )
489  nt = 3
490 *
491 * Print information about the tests that did not pass
492 * the threshold.
493 *
494  DO 110 k = 1, nt
495  IF( result( k ).GE.thresh ) THEN
496  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
497  $ CALL aladhd( nout, path )
498  WRITE( nout, fmt = 9999 )'DSYSV_ROOK', uplo,
499  $ n, imat, k, result( k )
500  nfail = nfail + 1
501  END IF
502  110 CONTINUE
503  nrun = nrun + nt
504  120 CONTINUE
505  END IF
506 *
507  150 CONTINUE
508 *
509  160 CONTINUE
510  170 CONTINUE
511  180 CONTINUE
512 *
513 * Print a summary of the results.
514 *
515  CALL alasvm( path, nout, nfail, nrun, nerrs )
516 *
517  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
518  $ ', test ', i2, ', ratio =', g12.5 )
519  RETURN
520 *
521 * End of DDRVSY_ROOK
522 *
523  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 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:110
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:73
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:81
subroutine aladhd(IOUNIT, PATH)
ALADHD
Definition: aladhd.f:90
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 dsyt01_rook(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
DSYT01_ROOK
Definition: dsyt01_rook.f:124
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 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:152
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 dpot05(UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
DPOT05
Definition: dpot05.f:164
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_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
DSYTRF_ROOK
Definition: dsytrf_rook.f:208
subroutine dsytri_rook(UPLO, N, A, LDA, IPIV, WORK, INFO)
DSYTRI_ROOK
Definition: dsytri_rook.f:129
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:204