LAPACK  3.9.0
LAPACK: Linear Algebra PACKage
sdrvsp.f
Go to the documentation of this file.
1 *> \brief \b SDRVSP
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 SDRVSP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
12 * A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
13 * 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 *> SDRVSP tests the driver routines SSPSV and -SVX.
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 REAL
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
90 *> (NMAX*(NMAX+1)/2)
91 *> \endverbatim
92 *>
93 *> \param[out] AFAC
94 *> \verbatim
95 *> AFAC is REAL array, dimension
96 *> (NMAX*(NMAX+1)/2)
97 *> \endverbatim
98 *>
99 *> \param[out] AINV
100 *> \verbatim
101 *> AINV is REAL array, dimension
102 *> (NMAX*(NMAX+1)/2)
103 *> \endverbatim
104 *>
105 *> \param[out] B
106 *> \verbatim
107 *> B is REAL array, dimension (NMAX*NRHS)
108 *> \endverbatim
109 *>
110 *> \param[out] X
111 *> \verbatim
112 *> X is REAL array, dimension (NMAX*NRHS)
113 *> \endverbatim
114 *>
115 *> \param[out] XACT
116 *> \verbatim
117 *> XACT is REAL array, dimension (NMAX*NRHS)
118 *> \endverbatim
119 *>
120 *> \param[out] WORK
121 *> \verbatim
122 *> WORK is REAL array, dimension
123 *> (NMAX*max(2,NRHS))
124 *> \endverbatim
125 *>
126 *> \param[out] RWORK
127 *> \verbatim
128 *> RWORK is REAL array, dimension (NMAX+2*NRHS)
129 *> \endverbatim
130 *>
131 *> \param[out] IWORK
132 *> \verbatim
133 *> IWORK is INTEGER array, dimension (2*NMAX)
134 *> \endverbatim
135 *>
136 *> \param[in] NOUT
137 *> \verbatim
138 *> NOUT is INTEGER
139 *> The unit number for output.
140 *> \endverbatim
141 *
142 * Authors:
143 * ========
144 *
145 *> \author Univ. of Tennessee
146 *> \author Univ. of California Berkeley
147 *> \author Univ. of Colorado Denver
148 *> \author NAG Ltd.
149 *
150 *> \date December 2016
151 *
152 *> \ingroup single_lin
153 *
154 * =====================================================================
155  SUBROUTINE sdrvsp( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
156  $ A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
157  $ NOUT )
158 *
159 * -- LAPACK test routine (version 3.7.0) --
160 * -- LAPACK is a software package provided by Univ. of Tennessee, --
161 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
162 * December 2016
163 *
164 * .. Scalar Arguments ..
165  LOGICAL TSTERR
166  INTEGER NMAX, NN, NOUT, NRHS
167  REAL THRESH
168 * ..
169 * .. Array Arguments ..
170  LOGICAL DOTYPE( * )
171  INTEGER IWORK( * ), NVAL( * )
172  REAL A( * ), AFAC( * ), AINV( * ), B( * ),
173  $ rwork( * ), work( * ), x( * ), xact( * )
174 * ..
175 *
176 * =====================================================================
177 *
178 * .. Parameters ..
179  REAL ONE, ZERO
180  PARAMETER ( ONE = 1.0e+0, zero = 0.0e+0 )
181  INTEGER NTYPES, NTESTS
182  parameter( ntypes = 10, ntests = 6 )
183  INTEGER NFACT
184  parameter( nfact = 2 )
185 * ..
186 * .. Local Scalars ..
187  LOGICAL ZEROT
188  CHARACTER DIST, FACT, PACKIT, TYPE, UPLO, XTYPE
189  CHARACTER*3 PATH
190  INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
191  $ izero, j, k, k1, kl, ku, lda, lwork, mode, n,
192  $ nerrs, nfail, nimat, npp, nrun, nt
193  REAL AINVNM, ANORM, CNDNUM, RCOND, RCONDC
194 * ..
195 * .. Local Arrays ..
196  CHARACTER FACTS( NFACT )
197  INTEGER ISEED( 4 ), ISEEDY( 4 )
198  REAL RESULT( NTESTS )
199 * ..
200 * .. External Functions ..
201  REAL SGET06, SLANSP
202  EXTERNAL SGET06, SLANSP
203 * ..
204 * .. External Subroutines ..
205  EXTERNAL aladhd, alaerh, alasvm, scopy, serrvx, sget04,
206  $ slacpy, slarhs, slaset, slatb4, slatms, sppt02,
207  $ sppt05, sspsv, sspsvx, sspt01, ssptrf, ssptri
208 * ..
209 * .. Scalars in Common ..
210  LOGICAL LERR, OK
211  CHARACTER*32 SRNAMT
212  INTEGER INFOT, NUNIT
213 * ..
214 * .. Common blocks ..
215  COMMON / infoc / infot, nunit, ok, lerr
216  COMMON / srnamc / srnamt
217 * ..
218 * .. Intrinsic Functions ..
219  INTRINSIC max, min
220 * ..
221 * .. Data statements ..
222  DATA iseedy / 1988, 1989, 1990, 1991 /
223  DATA facts / 'F', 'N' /
224 * ..
225 * .. Executable Statements ..
226 *
227 * Initialize constants and the random number seed.
228 *
229  path( 1: 1 ) = 'Single precision'
230  path( 2: 3 ) = 'SP'
231  nrun = 0
232  nfail = 0
233  nerrs = 0
234  DO 10 i = 1, 4
235  iseed( i ) = iseedy( i )
236  10 CONTINUE
237  lwork = max( 2*nmax, nmax*nrhs )
238 *
239 * Test the error exits
240 *
241  IF( tsterr )
242  $ CALL serrvx( path, nout )
243  infot = 0
244 *
245 * Do for each value of N in NVAL
246 *
247  DO 180 in = 1, nn
248  n = nval( in )
249  lda = max( n, 1 )
250  npp = n*( n+1 ) / 2
251  xtype = 'N'
252  nimat = ntypes
253  IF( n.LE.0 )
254  $ nimat = 1
255 *
256  DO 170 imat = 1, nimat
257 *
258 * Do the tests only if DOTYPE( IMAT ) is true.
259 *
260  IF( .NOT.dotype( imat ) )
261  $ GO TO 170
262 *
263 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
264 *
265  zerot = imat.GE.3 .AND. imat.LE.6
266  IF( zerot .AND. n.LT.imat-2 )
267  $ GO TO 170
268 *
269 * Do first for UPLO = 'U', then for UPLO = 'L'
270 *
271  DO 160 iuplo = 1, 2
272  IF( iuplo.EQ.1 ) THEN
273  uplo = 'U'
274  packit = 'C'
275  ELSE
276  uplo = 'L'
277  packit = 'R'
278  END IF
279 *
280 * Set up parameters with SLATB4 and generate a test matrix
281 * with SLATMS.
282 *
283  CALL slatb4( path, imat, n, n, TYPE, kl, ku, anorm, mode,
284  $ cndnum, dist )
285 *
286  srnamt = 'SLATMS'
287  CALL slatms( n, n, dist, iseed, TYPE, rwork, mode,
288  $ cndnum, anorm, kl, ku, packit, a, lda, work,
289  $ info )
290 *
291 * Check error code from SLATMS.
292 *
293  IF( info.NE.0 ) THEN
294  CALL alaerh( path, 'SLATMS', info, 0, uplo, n, n, -1,
295  $ -1, -1, imat, nfail, nerrs, nout )
296  GO TO 160
297  END IF
298 *
299 * For types 3-6, zero one or more rows and columns of the
300 * matrix to test that INFO is returned correctly.
301 *
302  IF( zerot ) THEN
303  IF( imat.EQ.3 ) THEN
304  izero = 1
305  ELSE IF( imat.EQ.4 ) THEN
306  izero = n
307  ELSE
308  izero = n / 2 + 1
309  END IF
310 *
311  IF( imat.LT.6 ) THEN
312 *
313 * Set row and column IZERO to zero.
314 *
315  IF( iuplo.EQ.1 ) THEN
316  ioff = ( izero-1 )*izero / 2
317  DO 20 i = 1, izero - 1
318  a( ioff+i ) = zero
319  20 CONTINUE
320  ioff = ioff + izero
321  DO 30 i = izero, n
322  a( ioff ) = zero
323  ioff = ioff + i
324  30 CONTINUE
325  ELSE
326  ioff = izero
327  DO 40 i = 1, izero - 1
328  a( ioff ) = zero
329  ioff = ioff + n - i
330  40 CONTINUE
331  ioff = ioff - izero
332  DO 50 i = izero, n
333  a( ioff+i ) = zero
334  50 CONTINUE
335  END IF
336  ELSE
337  ioff = 0
338  IF( iuplo.EQ.1 ) THEN
339 *
340 * Set the first IZERO rows and columns to zero.
341 *
342  DO 70 j = 1, n
343  i2 = min( j, izero )
344  DO 60 i = 1, i2
345  a( ioff+i ) = zero
346  60 CONTINUE
347  ioff = ioff + j
348  70 CONTINUE
349  ELSE
350 *
351 * Set the last IZERO rows and columns to zero.
352 *
353  DO 90 j = 1, n
354  i1 = max( j, izero )
355  DO 80 i = i1, n
356  a( ioff+i ) = zero
357  80 CONTINUE
358  ioff = ioff + n - j
359  90 CONTINUE
360  END IF
361  END IF
362  ELSE
363  izero = 0
364  END IF
365 *
366  DO 150 ifact = 1, nfact
367 *
368 * Do first for FACT = 'F', then for other values.
369 *
370  fact = facts( ifact )
371 *
372 * Compute the condition number for comparison with
373 * the value returned by SSPSVX.
374 *
375  IF( zerot ) THEN
376  IF( ifact.EQ.1 )
377  $ GO TO 150
378  rcondc = zero
379 *
380  ELSE IF( ifact.EQ.1 ) THEN
381 *
382 * Compute the 1-norm of A.
383 *
384  anorm = slansp( '1', uplo, n, a, rwork )
385 *
386 * Factor the matrix A.
387 *
388  CALL scopy( npp, a, 1, afac, 1 )
389  CALL ssptrf( uplo, n, afac, iwork, info )
390 *
391 * Compute inv(A) and take its norm.
392 *
393  CALL scopy( npp, afac, 1, ainv, 1 )
394  CALL ssptri( uplo, n, ainv, iwork, work, info )
395  ainvnm = slansp( '1', uplo, n, ainv, rwork )
396 *
397 * Compute the 1-norm condition number of A.
398 *
399  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
400  rcondc = one
401  ELSE
402  rcondc = ( one / anorm ) / ainvnm
403  END IF
404  END IF
405 *
406 * Form an exact solution and set the right hand side.
407 *
408  srnamt = 'SLARHS'
409  CALL slarhs( path, xtype, uplo, ' ', n, n, kl, ku,
410  $ nrhs, a, lda, xact, lda, b, lda, iseed,
411  $ info )
412  xtype = 'C'
413 *
414 * --- Test SSPSV ---
415 *
416  IF( ifact.EQ.2 ) THEN
417  CALL scopy( npp, a, 1, afac, 1 )
418  CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
419 *
420 * Factor the matrix and solve the system using SSPSV.
421 *
422  srnamt = 'SSPSV '
423  CALL sspsv( uplo, n, nrhs, afac, iwork, x, lda,
424  $ info )
425 *
426 * Adjust the expected value of INFO to account for
427 * pivoting.
428 *
429  k = izero
430  IF( k.GT.0 ) THEN
431  100 CONTINUE
432  IF( iwork( k ).LT.0 ) THEN
433  IF( iwork( k ).NE.-k ) THEN
434  k = -iwork( k )
435  GO TO 100
436  END IF
437  ELSE IF( iwork( k ).NE.k ) THEN
438  k = iwork( k )
439  GO TO 100
440  END IF
441  END IF
442 *
443 * Check error code from SSPSV .
444 *
445  IF( info.NE.k ) THEN
446  CALL alaerh( path, 'SSPSV ', info, k, uplo, n,
447  $ n, -1, -1, nrhs, imat, nfail,
448  $ nerrs, nout )
449  GO TO 120
450  ELSE IF( info.NE.0 ) THEN
451  GO TO 120
452  END IF
453 *
454 * Reconstruct matrix from factors and compute
455 * residual.
456 *
457  CALL sspt01( uplo, n, a, afac, iwork, ainv, lda,
458  $ rwork, result( 1 ) )
459 *
460 * Compute residual of the computed solution.
461 *
462  CALL slacpy( 'Full', n, nrhs, b, lda, work, lda )
463  CALL sppt02( uplo, n, nrhs, a, x, lda, work, lda,
464  $ rwork, result( 2 ) )
465 *
466 * Check solution from generated exact solution.
467 *
468  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
469  $ result( 3 ) )
470  nt = 3
471 *
472 * Print information about the tests that did not pass
473 * the threshold.
474 *
475  DO 110 k = 1, nt
476  IF( result( k ).GE.thresh ) THEN
477  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
478  $ CALL aladhd( nout, path )
479  WRITE( nout, fmt = 9999 )'SSPSV ', uplo, n,
480  $ imat, k, result( k )
481  nfail = nfail + 1
482  END IF
483  110 CONTINUE
484  nrun = nrun + nt
485  120 CONTINUE
486  END IF
487 *
488 * --- Test SSPSVX ---
489 *
490  IF( ifact.EQ.2 .AND. npp.GT.0 )
491  $ CALL slaset( 'Full', npp, 1, zero, zero, afac,
492  $ npp )
493  CALL slaset( 'Full', n, nrhs, zero, zero, x, lda )
494 *
495 * Solve the system and compute the condition number and
496 * error bounds using SSPSVX.
497 *
498  srnamt = 'SSPSVX'
499  CALL sspsvx( fact, uplo, n, nrhs, a, afac, iwork, b,
500  $ lda, x, lda, rcond, rwork,
501  $ rwork( nrhs+1 ), work, iwork( n+1 ),
502  $ info )
503 *
504 * Adjust the expected value of INFO to account for
505 * pivoting.
506 *
507  k = izero
508  IF( k.GT.0 ) THEN
509  130 CONTINUE
510  IF( iwork( k ).LT.0 ) THEN
511  IF( iwork( k ).NE.-k ) THEN
512  k = -iwork( k )
513  GO TO 130
514  END IF
515  ELSE IF( iwork( k ).NE.k ) THEN
516  k = iwork( k )
517  GO TO 130
518  END IF
519  END IF
520 *
521 * Check the error code from SSPSVX.
522 *
523  IF( info.NE.k ) THEN
524  CALL alaerh( path, 'SSPSVX', info, k, fact // uplo,
525  $ n, n, -1, -1, nrhs, imat, nfail,
526  $ nerrs, nout )
527  GO TO 150
528  END IF
529 *
530  IF( info.EQ.0 ) THEN
531  IF( ifact.GE.2 ) THEN
532 *
533 * Reconstruct matrix from factors and compute
534 * residual.
535 *
536  CALL sspt01( uplo, n, a, afac, iwork, ainv, lda,
537  $ rwork( 2*nrhs+1 ), result( 1 ) )
538  k1 = 1
539  ELSE
540  k1 = 2
541  END IF
542 *
543 * Compute residual of the computed solution.
544 *
545  CALL slacpy( 'Full', n, nrhs, b, lda, work, lda )
546  CALL sppt02( uplo, n, nrhs, a, x, lda, work, lda,
547  $ rwork( 2*nrhs+1 ), result( 2 ) )
548 *
549 * Check solution from generated exact solution.
550 *
551  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
552  $ result( 3 ) )
553 *
554 * Check the error bounds from iterative refinement.
555 *
556  CALL sppt05( uplo, n, nrhs, a, b, lda, x, lda,
557  $ xact, lda, rwork, rwork( nrhs+1 ),
558  $ result( 4 ) )
559  ELSE
560  k1 = 6
561  END IF
562 *
563 * Compare RCOND from SSPSVX with the computed value
564 * in RCONDC.
565 *
566  result( 6 ) = sget06( rcond, rcondc )
567 *
568 * Print information about the tests that did not pass
569 * the threshold.
570 *
571  DO 140 k = k1, 6
572  IF( result( k ).GE.thresh ) THEN
573  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
574  $ CALL aladhd( nout, path )
575  WRITE( nout, fmt = 9998 )'SSPSVX', fact, uplo,
576  $ n, imat, k, result( k )
577  nfail = nfail + 1
578  END IF
579  140 CONTINUE
580  nrun = nrun + 7 - k1
581 *
582  150 CONTINUE
583 *
584  160 CONTINUE
585  170 CONTINUE
586  180 CONTINUE
587 *
588 * Print a summary of the results.
589 *
590  CALL alasvm( path, nout, nfail, nrun, nerrs )
591 *
592  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
593  $ ', test ', i2, ', ratio =', g12.5 )
594  9998 FORMAT( 1x, a, ', FACT=''', a1, ''', UPLO=''', a1, ''', N =', i5,
595  $ ', type ', i2, ', test ', i2, ', ratio =', g12.5 )
596  RETURN
597 *
598 * End of SDRVSP
599 *
600  END
sspsvx
subroutine sspsvx(FACT, UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, IWORK, INFO)
SSPSVX computes the solution to system of linear equations A * X = B for OTHER matrices
Definition: sspsvx.f:278
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
sspsv
subroutine sspsv(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
SSPSV computes the solution to system of linear equations A * X = B for OTHER matrices
Definition: sspsv.f:164
sppt02
subroutine sppt02(UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
SPPT02
Definition: sppt02.f:124
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
scopy
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:84
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
sspt01
subroutine sspt01(UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
SSPT01
Definition: sspt01.f:112
slatb4
subroutine slatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
SLATB4
Definition: slatb4.f:122
ssptrf
subroutine ssptrf(UPLO, N, AP, IPIV, INFO)
SSPTRF
Definition: ssptrf.f:159
sdrvsp
subroutine sdrvsp(DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
SDRVSP
Definition: sdrvsp.f:158
ssptri
subroutine ssptri(UPLO, N, AP, IPIV, WORK, INFO)
SSPTRI
Definition: ssptri.f:111
serrvx
subroutine serrvx(PATH, NUNIT)
SERRVX
Definition: serrvx.f:57
sppt05
subroutine sppt05(UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
SPPT05
Definition: sppt05.f:158