LAPACK  3.9.0
LAPACK: Linear Algebra PACKage
sdrvsy_rook.f
Go to the documentation of this file.
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 *> \date November 2013
148 *
149 *> \ingroup double_lin
150 *
151 * =====================================================================
152  SUBROUTINE sdrvsy_rook( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
153  $ NMAX, A, AFAC, AINV, B, X, XACT, WORK,
154  $ RWORK, IWORK, NOUT )
155 *
156 * -- LAPACK test routine (version 3.5.0) --
157 * -- LAPACK is a software package provided by Univ. of Tennessee, --
158 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
159 * November 2013
160 *
161 * .. Scalar Arguments ..
162  LOGICAL tsterr
163  INTEGER nmax, nn, nout, nrhs
164  REAL thresh
165 * ..
166 * .. Array Arguments ..
167  LOGICAL dotype( * )
168  INTEGER IWORK( * ), NVAL( * )
169  REAL A( * ), AFAC( * ), AINV( * ), B( * ),
170  $ rwork( * ), work( * ), x( * ), xact( * )
171 * ..
172 *
173 * =====================================================================
174 *
175 * .. Parameters ..
176  REAL ONE, ZERO
177  PARAMETER ( ONE = 1.0e+0, zero = 0.0e+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  REAL AINVNM, ANORM, CNDNUM, RCONDC
191 * ..
192 * .. Local Arrays ..
193  CHARACTER FACTS( NFACT ), UPLOS( 2 )
194  INTEGER ISEED( 4 ), ISEEDY( 4 )
195  REAL RESULT( NTESTS )
196 * ..
197 * .. External Functions ..
198  REAL SLANSY
199  EXTERNAL SLANSY
200 * ..
201 * .. External Subroutines ..
202  EXTERNAL aladhd, alaerh, alasvm, serrvx, sget04, slacpy,
203  $ slarhs, slaset, slatb4, slatms, spot02, spot05,
204  $ ssysv_rook, ssyt01_rook, ssytrf_rook,
205  $ ssytri_rook,
206  $ xlaenv
207 * ..
208 * .. Scalars in Common ..
209  LOGICAL LERR, OK
210  CHARACTER*32 SRNAMT
211  INTEGER INFOT, NUNIT
212 * ..
213 * .. Common blocks ..
214  COMMON / infoc / infot, nunit, ok, lerr
215  COMMON / srnamc / srnamt
216 * ..
217 * .. Intrinsic Functions ..
218  INTRINSIC max, min
219 * ..
220 * .. Data statements ..
221  DATA iseedy / 1988, 1989, 1990, 1991 /
222  DATA uplos / 'U', 'L' / , facts / 'F', 'N' /
223 * ..
224 * .. Executable Statements ..
225 *
226 * Initialize constants and the random number seed.
227 *
228 * Test path
229 *
230  path( 1: 1 ) = 'Single precision'
231  path( 2: 3 ) = 'SR'
232 *
233 * Path to generate matrices
234 *
235  matpath( 1: 1 ) = 'Single precision'
236  matpath( 2: 3 ) = 'SY'
237 *
238  nrun = 0
239  nfail = 0
240  nerrs = 0
241  DO 10 i = 1, 4
242  iseed( i ) = iseedy( i )
243  10 CONTINUE
244  lwork = max( 2*nmax, nmax*nrhs )
245 *
246 * Test the error exits
247 *
248  IF( tsterr )
249  $ CALL serrvx( path, nout )
250  infot = 0
251 *
252 * Set the block size and minimum block size for which the block
253 * routine should be used, which will be later returned by ILAENV.
254 *
255  nb = 1
256  nbmin = 2
257  CALL xlaenv( 1, nb )
258  CALL xlaenv( 2, nbmin )
259 *
260 * Do for each value of N in NVAL
261 *
262  DO 180 in = 1, nn
263  n = nval( in )
264  lda = max( n, 1 )
265  xtype = 'N'
266  nimat = ntypes
267  IF( n.LE.0 )
268  $ nimat = 1
269 *
270  DO 170 imat = 1, nimat
271 *
272 * Do the tests only if DOTYPE( IMAT ) is true.
273 *
274  IF( .NOT.dotype( imat ) )
275  $ GO TO 170
276 *
277 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
278 *
279  zerot = imat.GE.3 .AND. imat.LE.6
280  IF( zerot .AND. n.LT.imat-2 )
281  $ GO TO 170
282 *
283 * Do first for UPLO = 'U', then for UPLO = 'L'
284 *
285  DO 160 iuplo = 1, 2
286  uplo = uplos( iuplo )
287 *
288 * Begin generate the test matrix A.
289 *
290 * Set up parameters with SLATB4 for the matrix generator
291 * based on the type of matrix to be generated.
292 *
293  CALL slatb4( matpath, imat, n, n, TYPE, kl, ku, anorm,
294  $ mode, cndnum, dist )
295 *
296 * Generate a matrix with SLATMS.
297 *
298  srnamt = 'SLATMS'
299  CALL slatms( n, n, dist, iseed, TYPE, rwork, mode,
300  $ cndnum, anorm, kl, ku, uplo, a, lda, work,
301  $ info )
302 *
303 * Check error code from SLATMS and handle error.
304 *
305  IF( info.NE.0 ) THEN
306  CALL alaerh( path, 'SLATMS', info, 0, uplo, n, n, -1,
307  $ -1, -1, imat, nfail, nerrs, nout )
308 *
309 * Skip all tests for this generated matrix
310 *
311  GO TO 160
312  END IF
313 *
314 * For types 3-6, zero one or more rows and columns of the
315 * matrix to test that INFO is returned correctly.
316 *
317  IF( zerot ) THEN
318  IF( imat.EQ.3 ) THEN
319  izero = 1
320  ELSE IF( imat.EQ.4 ) THEN
321  izero = n
322  ELSE
323  izero = n / 2 + 1
324  END IF
325 *
326  IF( imat.LT.6 ) THEN
327 *
328 * Set row and column IZERO to zero.
329 *
330  IF( iuplo.EQ.1 ) THEN
331  ioff = ( izero-1 )*lda
332  DO 20 i = 1, izero - 1
333  a( ioff+i ) = zero
334  20 CONTINUE
335  ioff = ioff + izero
336  DO 30 i = izero, n
337  a( ioff ) = zero
338  ioff = ioff + lda
339  30 CONTINUE
340  ELSE
341  ioff = izero
342  DO 40 i = 1, izero - 1
343  a( ioff ) = zero
344  ioff = ioff + lda
345  40 CONTINUE
346  ioff = ioff - izero
347  DO 50 i = izero, n
348  a( ioff+i ) = zero
349  50 CONTINUE
350  END IF
351  ELSE
352  ioff = 0
353  IF( iuplo.EQ.1 ) THEN
354 *
355 * Set the first IZERO rows and columns to zero.
356 *
357  DO 70 j = 1, n
358  i2 = min( j, izero )
359  DO 60 i = 1, i2
360  a( ioff+i ) = zero
361  60 CONTINUE
362  ioff = ioff + lda
363  70 CONTINUE
364  ELSE
365 *
366 * Set the last IZERO rows and columns to zero.
367 *
368  DO 90 j = 1, n
369  i1 = max( j, izero )
370  DO 80 i = i1, n
371  a( ioff+i ) = zero
372  80 CONTINUE
373  ioff = ioff + lda
374  90 CONTINUE
375  END IF
376  END IF
377  ELSE
378  izero = 0
379  END IF
380 *
381 * End generate the test matrix A.
382 *
383  DO 150 ifact = 1, nfact
384 *
385 * Do first for FACT = 'F', then for other values.
386 *
387  fact = facts( ifact )
388 *
389 * Compute the condition number for comparison with
390 * the value returned by DSYSVX_ROOK.
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 = slansy( '1', uplo, n, a, lda, rwork )
402 *
403 * Factor the matrix A.
404 *
405  CALL slacpy( uplo, n, n, a, lda, afac, lda )
406  CALL ssytrf_rook( uplo, n, afac, lda, iwork, work,
407  $ lwork, info )
408 *
409 * Compute inv(A) and take its norm.
410 *
411  CALL slacpy( uplo, n, n, afac, lda, ainv, lda )
412  lwork = (n+nb+1)*(nb+3)
413  CALL ssytri_rook( uplo, n, ainv, lda, iwork,
414  $ work, info )
415  ainvnm = slansy( '1', uplo, n, ainv, lda, rwork )
416 *
417 * Compute the 1-norm condition number of A.
418 *
419  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
420  rcondc = one
421  ELSE
422  rcondc = ( one / anorm ) / ainvnm
423  END IF
424  END IF
425 *
426 * Form an exact solution and set the right hand side.
427 *
428  srnamt = 'SLARHS'
429  CALL slarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
430  $ nrhs, a, lda, xact, lda, b, lda, iseed,
431  $ info )
432  xtype = 'C'
433 *
434 * --- Test SSYSV_ROOK ---
435 *
436  IF( ifact.EQ.2 ) THEN
437  CALL slacpy( uplo, n, n, a, lda, afac, lda )
438  CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
439 *
440 * Factor the matrix and solve the system using
441 * SSYSV_ROOK.
442 *
443  srnamt = 'SSYSV_ROOK'
444  CALL ssysv_rook( uplo, n, nrhs, afac, lda, iwork,
445  $ x, lda, work, lwork, info )
446 *
447 * Adjust the expected value of INFO to account for
448 * pivoting.
449 *
450  k = izero
451  IF( k.GT.0 ) THEN
452  100 CONTINUE
453  IF( iwork( k ).LT.0 ) THEN
454  IF( iwork( k ).NE.-k ) THEN
455  k = -iwork( k )
456  GO TO 100
457  END IF
458  ELSE IF( iwork( k ).NE.k ) THEN
459  k = iwork( k )
460  GO TO 100
461  END IF
462  END IF
463 *
464 * Check error code from SSYSV_ROOK and handle error.
465 *
466  IF( info.NE.k ) THEN
467  CALL alaerh( path, 'SSYSV_ROOK', info, k, uplo,
468  $ n, n, -1, -1, nrhs, imat, nfail,
469  $ nerrs, nout )
470  GO TO 120
471  ELSE IF( info.NE.0 ) THEN
472  GO TO 120
473  END IF
474 *
475 *+ TEST 1 Reconstruct matrix from factors and compute
476 * residual.
477 *
478  CALL ssyt01_rook( uplo, n, a, lda, afac, lda,
479  $ iwork, ainv, lda, rwork,
480  $ result( 1 ) )
481 *
482 *+ TEST 2 Compute residual of the computed solution.
483 *
484  CALL slacpy( 'Full', n, nrhs, b, lda, work, lda )
485  CALL spot02( uplo, n, nrhs, a, lda, x, lda, work,
486  $ lda, rwork, result( 2 ) )
487 *
488 *+ TEST 3
489 * Check solution from generated exact solution.
490 *
491  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
492  $ result( 3 ) )
493  nt = 3
494 *
495 * Print information about the tests that did not pass
496 * the threshold.
497 *
498  DO 110 k = 1, nt
499  IF( result( k ).GE.thresh ) THEN
500  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
501  $ CALL aladhd( nout, path )
502  WRITE( nout, fmt = 9999 )'SSYSV_ROOK', uplo,
503  $ n, imat, k, result( k )
504  nfail = nfail + 1
505  END IF
506  110 CONTINUE
507  nrun = nrun + nt
508  120 CONTINUE
509  END IF
510 *
511  150 CONTINUE
512 *
513  160 CONTINUE
514  170 CONTINUE
515  180 CONTINUE
516 *
517 * Print a summary of the results.
518 *
519  CALL alasvm( path, nout, nfail, nrun, nerrs )
520 *
521  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
522  $ ', test ', i2, ', ratio =', g12.5 )
523  RETURN
524 *
525 * End of SDRVSY_ROOK
526 *
527  END
ssytri_rook
subroutine ssytri_rook(UPLO, N, A, LDA, IPIV, WORK, INFO)
SSYTRI_ROOK
Definition: ssytri_rook.f:131
slarhs
subroutine slarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
SLARHS
Definition: slarhs.f:206
alasvm
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:75
spot02
subroutine spot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
SPOT02
Definition: spot02.f:129
ssytrf_rook
subroutine ssytrf_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
SSYTRF_ROOK
Definition: ssytrf_rook.f:210
ssyt01_rook
subroutine ssyt01_rook(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
SSYT01_ROOK
Definition: ssyt01_rook.f:126
slacpy
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:105
sdrvsy_rook
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:155
ssysv_rook
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:206
aladhd
subroutine aladhd(IOUNIT, PATH)
ALADHD
Definition: aladhd.f:92
slaset
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:112
sget04
subroutine sget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
SGET04
Definition: sget04.f:104
alaerh
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
slatms
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:323
slatb4
subroutine slatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
SLATB4
Definition: slatb4.f:122
spot05
subroutine spot05(UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
SPOT05
Definition: spot05.f:166
xlaenv
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
serrvx
subroutine serrvx(PATH, NUNIT)
SERRVX
Definition: serrvx.f:57