LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
ddrvac.f
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1 *> \brief \b DDRVAC
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 DDRVAC( DOTYPE, NM, MVAL, NNS, NSVAL, THRESH, NMAX,
12 * A, AFAC, B, X, WORK,
13 * RWORK, SWORK, NOUT )
14 *
15 * .. Scalar Arguments ..
16 * INTEGER NMAX, NM, NNS, NOUT
17 * DOUBLE PRECISION THRESH
18 * ..
19 * .. Array Arguments ..
20 * LOGICAL DOTYPE( * )
21 * INTEGER MVAL( * ), NSVAL( * )
22 * REAL SWORK(*)
23 * DOUBLE PRECISION A( * ), AFAC( * ), B( * ),
24 * $ RWORK( * ), WORK( * ), X( * )
25 * ..
26 *
27 *
28 *> \par Purpose:
29 * =============
30 *>
31 *> \verbatim
32 *>
33 *> DDRVAC tests DSPOSV.
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] NM
48 *> \verbatim
49 *> NM is INTEGER
50 *> The number of values of N contained in the vector MVAL.
51 *> \endverbatim
52 *>
53 *> \param[in] MVAL
54 *> \verbatim
55 *> MVAL is INTEGER array, dimension (NM)
56 *> The values of the matrix dimension N.
57 *> \endverbatim
58 *>
59 *> \param[in] NNS
60 *> \verbatim
61 *> NNS is INTEGER
62 *> The number of values of NRHS contained in the vector NSVAL.
63 *> \endverbatim
64 *>
65 *> \param[in] NSVAL
66 *> \verbatim
67 *> NSVAL is INTEGER array, dimension (NNS)
68 *> The values of the number of right hand sides NRHS.
69 *> \endverbatim
70 *>
71 *> \param[in] THRESH
72 *> \verbatim
73 *> THRESH is DOUBLE PRECISION
74 *> The threshold value for the test ratios. A result is
75 *> included in the output file if RESULT >= THRESH. To have
76 *> every test ratio printed, use THRESH = 0.
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] B
97 *> \verbatim
98 *> B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
99 *> \endverbatim
100 *>
101 *> \param[out] X
102 *> \verbatim
103 *> X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
104 *> \endverbatim
105 *>
106 *> \param[out] WORK
107 *> \verbatim
108 *> WORK is DOUBLE PRECISION array, dimension
109 *> (NMAX*max(3,NSMAX))
110 *> \endverbatim
111 *>
112 *> \param[out] RWORK
113 *> \verbatim
114 *> RWORK is DOUBLE PRECISION array, dimension
115 *> (max(2*NMAX,2*NSMAX+NWORK))
116 *> \endverbatim
117 *>
118 *> \param[out] SWORK
119 *> \verbatim
120 *> SWORK is REAL array, dimension
121 *> (NMAX*(NSMAX+NMAX))
122 *> \endverbatim
123 *>
124 *> \param[in] NOUT
125 *> \verbatim
126 *> NOUT is INTEGER
127 *> The unit number for output.
128 *> \endverbatim
129 *
130 * Authors:
131 * ========
132 *
133 *> \author Univ. of Tennessee
134 *> \author Univ. of California Berkeley
135 *> \author Univ. of Colorado Denver
136 *> \author NAG Ltd.
137 *
138 *> \date December 2016
139 *
140 *> \ingroup double_lin
141 *
142 * =====================================================================
143  SUBROUTINE ddrvac( DOTYPE, NM, MVAL, NNS, NSVAL, THRESH, NMAX,
144  $ A, AFAC, B, X, WORK,
145  $ RWORK, SWORK, NOUT )
146 *
147 * -- LAPACK test routine (version 3.7.0) --
148 * -- LAPACK is a software package provided by Univ. of Tennessee, --
149 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
150 * December 2016
151 *
152 * .. Scalar Arguments ..
153  INTEGER NMAX, NM, NNS, NOUT
154  DOUBLE PRECISION THRESH
155 * ..
156 * .. Array Arguments ..
157  LOGICAL DOTYPE( * )
158  INTEGER MVAL( * ), NSVAL( * )
159  REAL SWORK(*)
160  DOUBLE PRECISION A( * ), AFAC( * ), B( * ),
161  $ rwork( * ), work( * ), x( * )
162 * ..
163 *
164 * =====================================================================
165 *
166 * .. Parameters ..
167  DOUBLE PRECISION ZERO
168  parameter( zero = 0.0d+0 )
169  INTEGER NTYPES
170  parameter( ntypes = 9 )
171  INTEGER NTESTS
172  parameter( ntests = 1 )
173 * ..
174 * .. Local Scalars ..
175  LOGICAL ZEROT
176  CHARACTER DIST, TYPE, UPLO, XTYPE
177  CHARACTER*3 PATH
178  INTEGER I, IM, IMAT, INFO, IOFF, IRHS, IUPLO,
179  $ izero, kl, ku, lda, mode, n,
180  $ nerrs, nfail, nimat, nrhs, nrun
181  DOUBLE PRECISION ANORM, CNDNUM
182 * ..
183 * .. Local Arrays ..
184  CHARACTER UPLOS( 2 )
185  INTEGER ISEED( 4 ), ISEEDY( 4 )
186  DOUBLE PRECISION RESULT( ntests )
187 * ..
188 * .. Local Variables ..
189  INTEGER ITER, KASE
190 * ..
191 * .. External Functions ..
192  LOGICAL LSAME
193  EXTERNAL lsame
194 * ..
195 * .. External Subroutines ..
196  EXTERNAL alaerh, dlacpy,
197  $ dlarhs, dlaset, dlatb4, dlatms,
198  $ dpot06, dsposv
199 * ..
200 * .. Intrinsic Functions ..
201  INTRINSIC dble, max, sqrt
202 * ..
203 * .. Scalars in Common ..
204  LOGICAL LERR, OK
205  CHARACTER*32 SRNAMT
206  INTEGER INFOT, NUNIT
207 * ..
208 * .. Common blocks ..
209  COMMON / infoc / infot, nunit, ok, lerr
210  COMMON / srnamc / srnamt
211 * ..
212 * .. Data statements ..
213  DATA iseedy / 1988, 1989, 1990, 1991 /
214  DATA uplos / 'U', 'L' /
215 * ..
216 * .. Executable Statements ..
217 *
218 * Initialize constants and the random number seed.
219 *
220  kase = 0
221  path( 1: 1 ) = 'Double precision'
222  path( 2: 3 ) = 'PO'
223  nrun = 0
224  nfail = 0
225  nerrs = 0
226  DO 10 i = 1, 4
227  iseed( i ) = iseedy( i )
228  10 CONTINUE
229 *
230  infot = 0
231 *
232 * Do for each value of N in MVAL
233 *
234  DO 120 im = 1, nm
235  n = mval( im )
236  lda = max( n, 1 )
237  nimat = ntypes
238  IF( n.LE.0 )
239  $ nimat = 1
240 *
241  DO 110 imat = 1, nimat
242 *
243 * Do the tests only if DOTYPE( IMAT ) is true.
244 *
245  IF( .NOT.dotype( imat ) )
246  $ GO TO 110
247 *
248 * Skip types 3, 4, or 5 if the matrix size is too small.
249 *
250  zerot = imat.GE.3 .AND. imat.LE.5
251  IF( zerot .AND. n.LT.imat-2 )
252  $ GO TO 110
253 *
254 * Do first for UPLO = 'U', then for UPLO = 'L'
255 *
256  DO 100 iuplo = 1, 2
257  uplo = uplos( iuplo )
258 *
259 * Set up parameters with DLATB4 and generate a test matrix
260 * with DLATMS.
261 *
262  CALL dlatb4( path, imat, n, n, TYPE, KL, KU, ANORM, MODE,
263  $ cndnum, dist )
264 *
265  srnamt = 'DLATMS'
266  CALL dlatms( n, n, dist, iseed, TYPE, RWORK, MODE,
267  $ cndnum, anorm, kl, ku, uplo, a, lda, work,
268  $ info )
269 *
270 * Check error code from DLATMS.
271 *
272  IF( info.NE.0 ) THEN
273  CALL alaerh( path, 'DLATMS', info, 0, uplo, n, n, -1,
274  $ -1, -1, imat, nfail, nerrs, nout )
275  GO TO 100
276  END IF
277 *
278 * For types 3-5, zero one row and column of the matrix to
279 * test that INFO is returned correctly.
280 *
281  IF( zerot ) THEN
282  IF( imat.EQ.3 ) THEN
283  izero = 1
284  ELSE IF( imat.EQ.4 ) THEN
285  izero = n
286  ELSE
287  izero = n / 2 + 1
288  END IF
289  ioff = ( izero-1 )*lda
290 *
291 * Set row and column IZERO of A to 0.
292 *
293  IF( iuplo.EQ.1 ) THEN
294  DO 20 i = 1, izero - 1
295  a( ioff+i ) = zero
296  20 CONTINUE
297  ioff = ioff + izero
298  DO 30 i = izero, n
299  a( ioff ) = zero
300  ioff = ioff + lda
301  30 CONTINUE
302  ELSE
303  ioff = izero
304  DO 40 i = 1, izero - 1
305  a( ioff ) = zero
306  ioff = ioff + lda
307  40 CONTINUE
308  ioff = ioff - izero
309  DO 50 i = izero, n
310  a( ioff+i ) = zero
311  50 CONTINUE
312  END IF
313  ELSE
314  izero = 0
315  END IF
316 *
317  DO 60 irhs = 1, nns
318  nrhs = nsval( irhs )
319  xtype = 'N'
320 *
321 * Form an exact solution and set the right hand side.
322 *
323  srnamt = 'DLARHS'
324  CALL dlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
325  $ nrhs, a, lda, x, lda, b, lda,
326  $ iseed, info )
327 *
328 * Compute the L*L' or U'*U factorization of the
329 * matrix and solve the system.
330 *
331  srnamt = 'DSPOSV '
332  kase = kase + 1
333 *
334  CALL dlacpy( 'All', n, n, a, lda, afac, lda)
335 *
336  CALL dsposv( uplo, n, nrhs, afac, lda, b, lda, x, lda,
337  $ work, swork, iter, info )
338 
339  IF (iter.LT.0) THEN
340  CALL dlacpy( 'All', n, n, a, lda, afac, lda )
341  ENDIF
342 *
343 * Check error code from DSPOSV .
344 *
345  IF( info.NE.izero ) THEN
346 *
347  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
348  $ CALL alahd( nout, path )
349  nerrs = nerrs + 1
350 *
351  IF( info.NE.izero .AND. izero.NE.0 ) THEN
352  WRITE( nout, fmt = 9988 )'DSPOSV',info,izero,n,
353  $ imat
354  ELSE
355  WRITE( nout, fmt = 9975 )'DSPOSV',info,n,imat
356  END IF
357  END IF
358 *
359 * Skip the remaining test if the matrix is singular.
360 *
361  IF( info.NE.0 )
362  $ GO TO 110
363 *
364 * Check the quality of the solution
365 *
366  CALL dlacpy( 'All', n, nrhs, b, lda, work, lda )
367 *
368  CALL dpot06( uplo, n, nrhs, a, lda, x, lda, work,
369  $ lda, rwork, result( 1 ) )
370 *
371 * Check if the test passes the tesing.
372 * Print information about the tests that did not
373 * pass the testing.
374 *
375 * If iterative refinement has been used and claimed to
376 * be successful (ITER>0), we want
377 * NORM1(B - A*X)/(NORM1(A)*NORM1(X)*EPS*SRQT(N)) < 1
378 *
379 * If double precision has been used (ITER<0), we want
380 * NORM1(B - A*X)/(NORM1(A)*NORM1(X)*EPS) < THRES
381 * (Cf. the linear solver testing routines)
382 *
383  IF ((thresh.LE.0.0e+00)
384  $ .OR.((iter.GE.0).AND.(n.GT.0)
385  $ .AND.(result(1).GE.sqrt(dble(n))))
386  $ .OR.((iter.LT.0).AND.(result(1).GE.thresh))) THEN
387 *
388  IF( nfail.EQ.0 .AND. nerrs.EQ.0 ) THEN
389  WRITE( nout, fmt = 8999 )'DPO'
390  WRITE( nout, fmt = '( '' Matrix types:'' )' )
391  WRITE( nout, fmt = 8979 )
392  WRITE( nout, fmt = '( '' Test ratios:'' )' )
393  WRITE( nout, fmt = 8960 )1
394  WRITE( nout, fmt = '( '' Messages:'' )' )
395  END IF
396 *
397  WRITE( nout, fmt = 9998 )uplo, n, nrhs, imat, 1,
398  $ result( 1 )
399 *
400  nfail = nfail + 1
401 *
402  END IF
403 *
404  nrun = nrun + 1
405 *
406  60 CONTINUE
407  100 CONTINUE
408  110 CONTINUE
409  120 CONTINUE
410 *
411 * Print a summary of the results.
412 *
413  IF( nfail.GT.0 ) THEN
414  WRITE( nout, fmt = 9996 )'DSPOSV', nfail, nrun
415  ELSE
416  WRITE( nout, fmt = 9995 )'DSPOSV', nrun
417  END IF
418  IF( nerrs.GT.0 ) THEN
419  WRITE( nout, fmt = 9994 )nerrs
420  END IF
421 *
422  9998 FORMAT( ' UPLO=''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
423  $ i2, ', test(', i2, ') =', g12.5 )
424  9996 FORMAT( 1x, a6, ': ', i6, ' out of ', i6,
425  $ ' tests failed to pass the threshold' )
426  9995 FORMAT( /1x, 'All tests for ', a6,
427  $ ' routines passed the threshold ( ', i6, ' tests run)' )
428  9994 FORMAT( 6x, i6, ' error messages recorded' )
429 *
430 * SUBNAM, INFO, INFOE, N, IMAT
431 *
432  9988 FORMAT( ' *** ', a6, ' returned with INFO =', i5, ' instead of ',
433  $ i5, / ' ==> N =', i5, ', type ',
434  $ i2 )
435 *
436 * SUBNAM, INFO, N, IMAT
437 *
438  9975 FORMAT( ' *** Error code from ', a6, '=', i5, ' for M=', i5,
439  $ ', type ', i2 )
440  8999 FORMAT( / 1x, a3, ': positive definite dense matrices' )
441  8979 FORMAT( 4x, '1. Diagonal', 24x, '7. Last n/2 columns zero', / 4x,
442  $ '2. Upper triangular', 16x,
443  $ '8. Random, CNDNUM = sqrt(0.1/EPS)', / 4x,
444  $ '3. Lower triangular', 16x, '9. Random, CNDNUM = 0.1/EPS',
445  $ / 4x, '4. Random, CNDNUM = 2', 13x,
446  $ '10. Scaled near underflow', / 4x, '5. First column zero',
447  $ 14x, '11. Scaled near overflow', / 4x,
448  $ '6. Last column zero' )
449  8960 FORMAT( 3x, i2, ': norm_1( B - A * X ) / ',
450  $ '( norm_1(A) * norm_1(X) * EPS * SQRT(N) ) > 1 if ITERREF',
451  $ / 4x, 'or norm_1( B - A * X ) / ',
452  $ '( norm_1(A) * norm_1(X) * EPS ) > THRES if DPOTRF' )
453 
454  RETURN
455 *
456 * End of DDRVAC
457 *
458  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 alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:107
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 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 ddrvac(DOTYPE, NM, MVAL, NNS, NSVAL, THRESH, NMAX, A, AFAC, B, X, WORK, RWORK, SWORK, NOUT)
DDRVAC
Definition: ddrvac.f:146
subroutine dpot06(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
DPOT06
Definition: dpot06.f:129
subroutine dsposv(UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK, SWORK, ITER, INFO)
DSPOSV computes the solution to system of linear equations A * X = B for PO matrices ...
Definition: dsposv.f:201