LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
sdrvsy_rook.f
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1 *> \brief \b SDRVSY_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 SDRVSY_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 * REAL THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER IWORK( * ), NVAL( * )
23 * REAL A( * ), AFAC( * ), AINV( * ), B( * ),
24 * $ RWORK( * ), WORK( * ), X( * ), XACT( * )
25 * ..
26 *
27 *
28 *> \par Purpose:
29 * =============
30 *>
31 *> \verbatim
32 *>
33 *> SDRVSY_ROOK tests the driver routines SSYSV_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 REAL array, dimension (NMAX*NMAX)
90 *> \endverbatim
91 *>
92 *> \param[out] AFAC
93 *> \verbatim
94 *> AFAC is REAL array, dimension (NMAX*NMAX)
95 *> \endverbatim
96 *>
97 *> \param[out] AINV
98 *> \verbatim
99 *> AINV is REAL array, dimension (NMAX*NMAX)
100 *> \endverbatim
101 *>
102 *> \param[out] B
103 *> \verbatim
104 *> B is REAL array, dimension (NMAX*NRHS)
105 *> \endverbatim
106 *>
107 *> \param[out] X
108 *> \verbatim
109 *> X is REAL array, dimension (NMAX*NRHS)
110 *> \endverbatim
111 *>
112 *> \param[out] XACT
113 *> \verbatim
114 *> XACT is REAL array, dimension (NMAX*NRHS)
115 *> \endverbatim
116 *>
117 *> \param[out] WORK
118 *> \verbatim
119 *> WORK is REAL array, dimension
120 *> (NMAX*max(2,NRHS))
121 *> \endverbatim
122 *>
123 *> \param[out] RWORK
124 *> \verbatim
125 *> RWORK is REAL array, dimension (NMAX+2*NRHS)
126 *> \endverbatim
127 *>
128 *> \param[out] IWORK
129 *> \verbatim
130 *> IWORK is INTEGER array, dimension (2*NMAX)
131 *> \endverbatim
132 *>
133 *> \param[in] NOUT
134 *> \verbatim
135 *> NOUT is INTEGER
136 *> The unit number for output.
137 *> \endverbatim
138 *
139 * Authors:
140 * ========
141 *
142 *> \author Univ. of Tennessee
143 *> \author Univ. of California Berkeley
144 *> \author Univ. of Colorado Denver
145 *> \author NAG Ltd.
146 *
147 *> \ingroup double_lin
148 *
149 * =====================================================================
150  SUBROUTINE sdrvsy_rook( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
151  $ NMAX, A, AFAC, AINV, B, X, XACT, WORK,
152  $ RWORK, IWORK, NOUT )
153 *
154 * -- LAPACK test routine --
155 * -- LAPACK is a software package provided by Univ. of Tennessee, --
156 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
157 *
158 * .. Scalar Arguments ..
159  LOGICAL TSTERR
160  INTEGER NMAX, NN, NOUT, NRHS
161  REAL THRESH
162 * ..
163 * .. Array Arguments ..
164  LOGICAL DOTYPE( * )
165  INTEGER IWORK( * ), NVAL( * )
166  REAL A( * ), AFAC( * ), AINV( * ), B( * ),
167  $ rwork( * ), work( * ), x( * ), xact( * )
168 * ..
169 *
170 * =====================================================================
171 *
172 * .. Parameters ..
173  REAL ONE, ZERO
174  PARAMETER ( ONE = 1.0e+0, zero = 0.0e+0 )
175  INTEGER NTYPES, NTESTS
176  parameter( ntypes = 10, ntests = 3 )
177  INTEGER NFACT
178  parameter( nfact = 2 )
179 * ..
180 * .. Local Scalars ..
181  LOGICAL ZEROT
182  CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
183  CHARACTER*3 PATH, MATPATH
184  INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
185  $ izero, j, k, kl, ku, lda, lwork, mode, n,
186  $ nb, nbmin, nerrs, nfail, nimat, nrun, nt
187  REAL AINVNM, ANORM, CNDNUM, RCONDC
188 * ..
189 * .. Local Arrays ..
190  CHARACTER FACTS( NFACT ), UPLOS( 2 )
191  INTEGER ISEED( 4 ), ISEEDY( 4 )
192  REAL RESULT( NTESTS )
193 * ..
194 * .. External Functions ..
195  REAL SLANSY
196  EXTERNAL SLANSY
197 * ..
198 * .. External Subroutines ..
199  EXTERNAL aladhd, alaerh, alasvm, serrvx, sget04, slacpy,
202  $ ssytri_rook,
203  $ xlaenv
204 * ..
205 * .. Scalars in Common ..
206  LOGICAL LERR, OK
207  CHARACTER*32 SRNAMT
208  INTEGER INFOT, NUNIT
209 * ..
210 * .. Common blocks ..
211  COMMON / infoc / infot, nunit, ok, lerr
212  COMMON / srnamc / srnamt
213 * ..
214 * .. Intrinsic Functions ..
215  INTRINSIC max, min
216 * ..
217 * .. Data statements ..
218  DATA iseedy / 1988, 1989, 1990, 1991 /
219  DATA uplos / 'U', 'L' / , facts / 'F', 'N' /
220 * ..
221 * .. Executable Statements ..
222 *
223 * Initialize constants and the random number seed.
224 *
225 * Test path
226 *
227  path( 1: 1 ) = 'Single precision'
228  path( 2: 3 ) = 'SR'
229 *
230 * Path to generate matrices
231 *
232  matpath( 1: 1 ) = 'Single precision'
233  matpath( 2: 3 ) = 'SY'
234 *
235  nrun = 0
236  nfail = 0
237  nerrs = 0
238  DO 10 i = 1, 4
239  iseed( i ) = iseedy( i )
240  10 CONTINUE
241  lwork = max( 2*nmax, nmax*nrhs )
242 *
243 * Test the error exits
244 *
245  IF( tsterr )
246  $ CALL serrvx( path, nout )
247  infot = 0
248 *
249 * Set the block size and minimum block size for which the block
250 * routine should be used, which will be later returned by ILAENV.
251 *
252  nb = 1
253  nbmin = 2
254  CALL xlaenv( 1, nb )
255  CALL xlaenv( 2, nbmin )
256 *
257 * Do for each value of N in NVAL
258 *
259  DO 180 in = 1, nn
260  n = nval( in )
261  lda = max( n, 1 )
262  xtype = 'N'
263  nimat = ntypes
264  IF( n.LE.0 )
265  $ nimat = 1
266 *
267  DO 170 imat = 1, nimat
268 *
269 * Do the tests only if DOTYPE( IMAT ) is true.
270 *
271  IF( .NOT.dotype( imat ) )
272  $ GO TO 170
273 *
274 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
275 *
276  zerot = imat.GE.3 .AND. imat.LE.6
277  IF( zerot .AND. n.LT.imat-2 )
278  $ GO TO 170
279 *
280 * Do first for UPLO = 'U', then for UPLO = 'L'
281 *
282  DO 160 iuplo = 1, 2
283  uplo = uplos( iuplo )
284 *
285 * Begin generate the test matrix A.
286 *
287 * Set up parameters with SLATB4 for the matrix generator
288 * based on the type of matrix to be generated.
289 *
290  CALL slatb4( matpath, imat, n, n, TYPE, kl, ku, anorm,
291  $ mode, cndnum, dist )
292 *
293 * Generate a matrix with SLATMS.
294 *
295  srnamt = 'SLATMS'
296  CALL slatms( n, n, dist, iseed, TYPE, rwork, mode,
297  $ cndnum, anorm, kl, ku, uplo, a, lda, work,
298  $ info )
299 *
300 * Check error code from SLATMS and handle error.
301 *
302  IF( info.NE.0 ) THEN
303  CALL alaerh( path, 'SLATMS', info, 0, uplo, n, n, -1,
304  $ -1, -1, imat, nfail, nerrs, nout )
305 *
306 * Skip all tests for this generated matrix
307 *
308  GO TO 160
309  END IF
310 *
311 * For types 3-6, zero one or more rows and columns of the
312 * matrix to test that INFO is returned correctly.
313 *
314  IF( zerot ) THEN
315  IF( imat.EQ.3 ) THEN
316  izero = 1
317  ELSE IF( imat.EQ.4 ) THEN
318  izero = n
319  ELSE
320  izero = n / 2 + 1
321  END IF
322 *
323  IF( imat.LT.6 ) THEN
324 *
325 * Set row and column IZERO to zero.
326 *
327  IF( iuplo.EQ.1 ) THEN
328  ioff = ( izero-1 )*lda
329  DO 20 i = 1, izero - 1
330  a( ioff+i ) = zero
331  20 CONTINUE
332  ioff = ioff + izero
333  DO 30 i = izero, n
334  a( ioff ) = zero
335  ioff = ioff + lda
336  30 CONTINUE
337  ELSE
338  ioff = izero
339  DO 40 i = 1, izero - 1
340  a( ioff ) = zero
341  ioff = ioff + lda
342  40 CONTINUE
343  ioff = ioff - izero
344  DO 50 i = izero, n
345  a( ioff+i ) = zero
346  50 CONTINUE
347  END IF
348  ELSE
349  ioff = 0
350  IF( iuplo.EQ.1 ) THEN
351 *
352 * Set the first IZERO rows and columns to zero.
353 *
354  DO 70 j = 1, n
355  i2 = min( j, izero )
356  DO 60 i = 1, i2
357  a( ioff+i ) = zero
358  60 CONTINUE
359  ioff = ioff + lda
360  70 CONTINUE
361  ELSE
362 *
363 * Set the last IZERO rows and columns to zero.
364 *
365  DO 90 j = 1, n
366  i1 = max( j, izero )
367  DO 80 i = i1, n
368  a( ioff+i ) = zero
369  80 CONTINUE
370  ioff = ioff + lda
371  90 CONTINUE
372  END IF
373  END IF
374  ELSE
375  izero = 0
376  END IF
377 *
378 * End generate the test matrix A.
379 *
380  DO 150 ifact = 1, nfact
381 *
382 * Do first for FACT = 'F', then for other values.
383 *
384  fact = facts( ifact )
385 *
386 * Compute the condition number for comparison with
387 * the value returned by DSYSVX_ROOK.
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 = slansy( '1', uplo, n, a, lda, rwork )
399 *
400 * Factor the matrix A.
401 *
402  CALL slacpy( uplo, n, n, a, lda, afac, lda )
403  CALL ssytrf_rook( uplo, n, afac, lda, iwork, work,
404  $ lwork, info )
405 *
406 * Compute inv(A) and take its norm.
407 *
408  CALL slacpy( uplo, n, n, afac, lda, ainv, lda )
409  lwork = (n+nb+1)*(nb+3)
410  CALL ssytri_rook( uplo, n, ainv, lda, iwork,
411  $ work, info )
412  ainvnm = slansy( '1', uplo, n, ainv, lda, rwork )
413 *
414 * Compute the 1-norm condition number of A.
415 *
416  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
417  rcondc = one
418  ELSE
419  rcondc = ( one / anorm ) / ainvnm
420  END IF
421  END IF
422 *
423 * Form an exact solution and set the right hand side.
424 *
425  srnamt = 'SLARHS'
426  CALL slarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
427  $ nrhs, a, lda, xact, lda, b, lda, iseed,
428  $ info )
429  xtype = 'C'
430 *
431 * --- Test SSYSV_ROOK ---
432 *
433  IF( ifact.EQ.2 ) THEN
434  CALL slacpy( uplo, n, n, a, lda, afac, lda )
435  CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
436 *
437 * Factor the matrix and solve the system using
438 * SSYSV_ROOK.
439 *
440  srnamt = 'SSYSV_ROOK'
441  CALL ssysv_rook( uplo, n, nrhs, afac, lda, iwork,
442  $ x, lda, work, lwork, info )
443 *
444 * Adjust the expected value of INFO to account for
445 * pivoting.
446 *
447  k = izero
448  IF( k.GT.0 ) THEN
449  100 CONTINUE
450  IF( iwork( k ).LT.0 ) THEN
451  IF( iwork( k ).NE.-k ) THEN
452  k = -iwork( k )
453  GO TO 100
454  END IF
455  ELSE IF( iwork( k ).NE.k ) THEN
456  k = iwork( k )
457  GO TO 100
458  END IF
459  END IF
460 *
461 * Check error code from SSYSV_ROOK and handle error.
462 *
463  IF( info.NE.k ) THEN
464  CALL alaerh( path, 'SSYSV_ROOK', info, k, uplo,
465  $ n, n, -1, -1, nrhs, imat, nfail,
466  $ nerrs, nout )
467  GO TO 120
468  ELSE IF( info.NE.0 ) THEN
469  GO TO 120
470  END IF
471 *
472 *+ TEST 1 Reconstruct matrix from factors and compute
473 * residual.
474 *
475  CALL ssyt01_rook( uplo, n, a, lda, afac, lda,
476  $ iwork, ainv, lda, rwork,
477  $ result( 1 ) )
478 *
479 *+ TEST 2 Compute residual of the computed solution.
480 *
481  CALL slacpy( 'Full', n, nrhs, b, lda, work, lda )
482  CALL spot02( uplo, n, nrhs, a, lda, x, lda, work,
483  $ lda, rwork, result( 2 ) )
484 *
485 *+ TEST 3
486 * Check solution from generated exact solution.
487 *
488  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
489  $ result( 3 ) )
490  nt = 3
491 *
492 * Print information about the tests that did not pass
493 * the threshold.
494 *
495  DO 110 k = 1, nt
496  IF( result( k ).GE.thresh ) THEN
497  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
498  $ CALL aladhd( nout, path )
499  WRITE( nout, fmt = 9999 )'SSYSV_ROOK', uplo,
500  $ n, imat, k, result( k )
501  nfail = nfail + 1
502  END IF
503  110 CONTINUE
504  nrun = nrun + nt
505  120 CONTINUE
506  END IF
507 *
508  150 CONTINUE
509 *
510  160 CONTINUE
511  170 CONTINUE
512  180 CONTINUE
513 *
514 * Print a summary of the results.
515 *
516  CALL alasvm( path, nout, nfail, nrun, nerrs )
517 *
518  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
519  $ ', test ', i2, ', ratio =', g12.5 )
520  RETURN
521 *
522 * End of SDRVSY_ROOK
523 *
524  END
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
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 sdrvsy_rook(DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
SDRVSY_ROOK
Definition: sdrvsy_rook.f:153
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:321
subroutine ssytri_rook(UPLO, N, A, LDA, IPIV, WORK, INFO)
SSYTRI_ROOK
Definition: ssytri_rook.f:129
subroutine ssytrf_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
SSYTRF_ROOK
Definition: ssytrf_rook.f:208
subroutine ssysv_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
SSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices
Definition: ssysv_rook.f:204
subroutine slarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
SLARHS
Definition: slarhs.f:205
subroutine slatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
SLATB4
Definition: slatb4.f:120
subroutine spot05(UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
SPOT05
Definition: spot05.f:164
subroutine serrvx(PATH, NUNIT)
SERRVX
Definition: serrvx.f:55
subroutine sget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
SGET04
Definition: sget04.f:102
subroutine spot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
SPOT02
Definition: spot02.f:127
subroutine ssyt01_rook(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
SSYT01_ROOK
Definition: ssyt01_rook.f:124