LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
schkpt.f
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1 *> \brief \b SCHKPT
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 SCHKPT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
12 * A, D, E, B, X, XACT, WORK, RWORK, NOUT )
13 *
14 * .. Scalar Arguments ..
15 * LOGICAL TSTERR
16 * INTEGER NN, NNS, NOUT
17 * REAL THRESH
18 * ..
19 * .. Array Arguments ..
20 * LOGICAL DOTYPE( * )
21 * INTEGER NSVAL( * ), NVAL( * )
22 * REAL A( * ), B( * ), D( * ), E( * ), RWORK( * ),
23 * \$ WORK( * ), X( * ), XACT( * )
24 * ..
25 *
26 *
27 *> \par Purpose:
28 * =============
29 *>
30 *> \verbatim
31 *>
32 *> SCHKPT tests SPTTRF, -TRS, -RFS, and -CON
33 *> \endverbatim
34 *
35 * Arguments:
36 * ==========
37 *
38 *> \param[in] DOTYPE
39 *> \verbatim
40 *> DOTYPE is LOGICAL array, dimension (NTYPES)
41 *> The matrix types to be used for testing. Matrices of type j
42 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
43 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
44 *> \endverbatim
45 *>
46 *> \param[in] NN
47 *> \verbatim
48 *> NN is INTEGER
49 *> The number of values of N contained in the vector NVAL.
50 *> \endverbatim
51 *>
52 *> \param[in] NVAL
53 *> \verbatim
54 *> NVAL is INTEGER array, dimension (NN)
55 *> The values of the matrix dimension N.
56 *> \endverbatim
57 *>
58 *> \param[in] NNS
59 *> \verbatim
60 *> NNS is INTEGER
61 *> The number of values of NRHS contained in the vector NSVAL.
62 *> \endverbatim
63 *>
64 *> \param[in] NSVAL
65 *> \verbatim
66 *> NSVAL is INTEGER array, dimension (NNS)
67 *> The values of the number of right hand sides NRHS.
68 *> \endverbatim
69 *>
70 *> \param[in] THRESH
71 *> \verbatim
72 *> THRESH is REAL
73 *> The threshold value for the test ratios. A result is
74 *> included in the output file if RESULT >= THRESH. To have
75 *> every test ratio printed, use THRESH = 0.
76 *> \endverbatim
77 *>
78 *> \param[in] TSTERR
79 *> \verbatim
80 *> TSTERR is LOGICAL
81 *> Flag that indicates whether error exits are to be tested.
82 *> \endverbatim
83 *>
84 *> \param[out] A
85 *> \verbatim
86 *> A is REAL array, dimension (NMAX*2)
87 *> \endverbatim
88 *>
89 *> \param[out] D
90 *> \verbatim
91 *> D is REAL array, dimension (NMAX*2)
92 *> \endverbatim
93 *>
94 *> \param[out] E
95 *> \verbatim
96 *> E is REAL array, dimension (NMAX*2)
97 *> \endverbatim
98 *>
99 *> \param[out] B
100 *> \verbatim
101 *> B is REAL array, dimension (NMAX*NSMAX)
102 *> where NSMAX is the largest entry in NSVAL.
103 *> \endverbatim
104 *>
105 *> \param[out] X
106 *> \verbatim
107 *> X is REAL array, dimension (NMAX*NSMAX)
108 *> \endverbatim
109 *>
110 *> \param[out] XACT
111 *> \verbatim
112 *> XACT is REAL array, dimension (NMAX*NSMAX)
113 *> \endverbatim
114 *>
115 *> \param[out] WORK
116 *> \verbatim
117 *> WORK is REAL array, dimension
118 *> (NMAX*max(3,NSMAX))
119 *> \endverbatim
120 *>
121 *> \param[out] RWORK
122 *> \verbatim
123 *> RWORK is REAL array, dimension
124 *> (max(NMAX,2*NSMAX))
125 *> \endverbatim
126 *>
127 *> \param[in] NOUT
128 *> \verbatim
129 *> NOUT is INTEGER
130 *> The unit number for output.
131 *> \endverbatim
132 *
133 * Authors:
134 * ========
135 *
136 *> \author Univ. of Tennessee
137 *> \author Univ. of California Berkeley
138 *> \author Univ. of Colorado Denver
139 *> \author NAG Ltd.
140 *
141 *> \date December 2016
142 *
143 *> \ingroup single_lin
144 *
145 * =====================================================================
146  SUBROUTINE schkpt( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
147  \$ A, D, E, B, X, XACT, WORK, RWORK, NOUT )
148 *
149 * -- LAPACK test routine (version 3.7.0) --
150 * -- LAPACK is a software package provided by Univ. of Tennessee, --
151 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
152 * December 2016
153 *
154 * .. Scalar Arguments ..
155  LOGICAL TSTERR
156  INTEGER NN, NNS, NOUT
157  REAL THRESH
158 * ..
159 * .. Array Arguments ..
160  LOGICAL DOTYPE( * )
161  INTEGER NSVAL( * ), NVAL( * )
162  REAL A( * ), B( * ), D( * ), E( * ), RWORK( * ),
163  \$ work( * ), x( * ), xact( * )
164 * ..
165 *
166 * =====================================================================
167 *
168 * .. Parameters ..
169  REAL ONE, ZERO
170  parameter( one = 1.0e+0, zero = 0.0e+0 )
171  INTEGER NTYPES
172  parameter( ntypes = 12 )
173  INTEGER NTESTS
174  parameter( ntests = 7 )
175 * ..
176 * .. Local Scalars ..
177  LOGICAL ZEROT
178  CHARACTER DIST, TYPE
179  CHARACTER*3 PATH
180  INTEGER I, IA, IMAT, IN, INFO, IRHS, IX, IZERO, J, K,
181  \$ kl, ku, lda, mode, n, nerrs, nfail, nimat,
182  \$ nrhs, nrun
183  REAL AINVNM, ANORM, COND, DMAX, RCOND, RCONDC
184 * ..
185 * .. Local Arrays ..
186  INTEGER ISEED( 4 ), ISEEDY( 4 )
187  REAL RESULT( ntests ), Z( 3 )
188 * ..
189 * .. External Functions ..
190  INTEGER ISAMAX
191  REAL SASUM, SGET06, SLANST
192  EXTERNAL isamax, sasum, sget06, slanst
193 * ..
194 * .. External Subroutines ..
195  EXTERNAL alaerh, alahd, alasum, scopy, serrgt, sget04,
198  \$ sscal
199 * ..
200 * .. Intrinsic Functions ..
201  INTRINSIC abs, max
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 / 0, 0, 0, 1 /
214 * ..
215 * .. Executable Statements ..
216 *
217  path( 1: 1 ) = 'Single precision'
218  path( 2: 3 ) = 'PT'
219  nrun = 0
220  nfail = 0
221  nerrs = 0
222  DO 10 i = 1, 4
223  iseed( i ) = iseedy( i )
224  10 CONTINUE
225 *
226 * Test the error exits
227 *
228  IF( tsterr )
229  \$ CALL serrgt( path, nout )
230  infot = 0
231 *
232  DO 110 in = 1, nn
233 *
234 * Do for each value of N in NVAL.
235 *
236  n = nval( in )
237  lda = max( 1, n )
238  nimat = ntypes
239  IF( n.LE.0 )
240  \$ nimat = 1
241 *
242  DO 100 imat = 1, nimat
243 *
244 * Do the tests only if DOTYPE( IMAT ) is true.
245 *
246  IF( n.GT.0 .AND. .NOT.dotype( imat ) )
247  \$ GO TO 100
248 *
249 * Set up parameters with SLATB4.
250 *
251  CALL slatb4( path, imat, n, n, TYPE, KL, KU, ANORM, MODE,
252  \$ cond, dist )
253 *
254  zerot = imat.GE.8 .AND. imat.LE.10
255  IF( imat.LE.6 ) THEN
256 *
257 * Type 1-6: generate a symmetric tridiagonal matrix of
258 * known condition number in lower triangular band storage.
259 *
260  srnamt = 'SLATMS'
261  CALL slatms( n, n, dist, iseed, TYPE, RWORK, MODE, COND,
262  \$ anorm, kl, ku, 'B', a, 2, work, info )
263 *
264 * Check the error code from SLATMS.
265 *
266  IF( info.NE.0 ) THEN
267  CALL alaerh( path, 'SLATMS', info, 0, ' ', n, n, kl,
268  \$ ku, -1, imat, nfail, nerrs, nout )
269  GO TO 100
270  END IF
271  izero = 0
272 *
273 * Copy the matrix to D and E.
274 *
275  ia = 1
276  DO 20 i = 1, n - 1
277  d( i ) = a( ia )
278  e( i ) = a( ia+1 )
279  ia = ia + 2
280  20 CONTINUE
281  IF( n.GT.0 )
282  \$ d( n ) = a( ia )
283  ELSE
284 *
285 * Type 7-12: generate a diagonally dominant matrix with
286 * unknown condition number in the vectors D and E.
287 *
288  IF( .NOT.zerot .OR. .NOT.dotype( 7 ) ) THEN
289 *
290 * Let D and E have values from [-1,1].
291 *
292  CALL slarnv( 2, iseed, n, d )
293  CALL slarnv( 2, iseed, n-1, e )
294 *
295 * Make the tridiagonal matrix diagonally dominant.
296 *
297  IF( n.EQ.1 ) THEN
298  d( 1 ) = abs( d( 1 ) )
299  ELSE
300  d( 1 ) = abs( d( 1 ) ) + abs( e( 1 ) )
301  d( n ) = abs( d( n ) ) + abs( e( n-1 ) )
302  DO 30 i = 2, n - 1
303  d( i ) = abs( d( i ) ) + abs( e( i ) ) +
304  \$ abs( e( i-1 ) )
305  30 CONTINUE
306  END IF
307 *
308 * Scale D and E so the maximum element is ANORM.
309 *
310  ix = isamax( n, d, 1 )
311  dmax = d( ix )
312  CALL sscal( n, anorm / dmax, d, 1 )
313  CALL sscal( n-1, anorm / dmax, e, 1 )
314 *
315  ELSE IF( izero.GT.0 ) THEN
316 *
317 * Reuse the last matrix by copying back the zeroed out
318 * elements.
319 *
320  IF( izero.EQ.1 ) THEN
321  d( 1 ) = z( 2 )
322  IF( n.GT.1 )
323  \$ e( 1 ) = z( 3 )
324  ELSE IF( izero.EQ.n ) THEN
325  e( n-1 ) = z( 1 )
326  d( n ) = z( 2 )
327  ELSE
328  e( izero-1 ) = z( 1 )
329  d( izero ) = z( 2 )
330  e( izero ) = z( 3 )
331  END IF
332  END IF
333 *
334 * For types 8-10, set one row and column of the matrix to
335 * zero.
336 *
337  izero = 0
338  IF( imat.EQ.8 ) THEN
339  izero = 1
340  z( 2 ) = d( 1 )
341  d( 1 ) = zero
342  IF( n.GT.1 ) THEN
343  z( 3 ) = e( 1 )
344  e( 1 ) = zero
345  END IF
346  ELSE IF( imat.EQ.9 ) THEN
347  izero = n
348  IF( n.GT.1 ) THEN
349  z( 1 ) = e( n-1 )
350  e( n-1 ) = zero
351  END IF
352  z( 2 ) = d( n )
353  d( n ) = zero
354  ELSE IF( imat.EQ.10 ) THEN
355  izero = ( n+1 ) / 2
356  IF( izero.GT.1 ) THEN
357  z( 1 ) = e( izero-1 )
358  e( izero-1 ) = zero
359  z( 3 ) = e( izero )
360  e( izero ) = zero
361  END IF
362  z( 2 ) = d( izero )
363  d( izero ) = zero
364  END IF
365  END IF
366 *
367  CALL scopy( n, d, 1, d( n+1 ), 1 )
368  IF( n.GT.1 )
369  \$ CALL scopy( n-1, e, 1, e( n+1 ), 1 )
370 *
371 *+ TEST 1
372 * Factor A as L*D*L' and compute the ratio
373 * norm(L*D*L' - A) / (n * norm(A) * EPS )
374 *
375  CALL spttrf( n, d( n+1 ), e( n+1 ), info )
376 *
377 * Check error code from SPTTRF.
378 *
379  IF( info.NE.izero ) THEN
380  CALL alaerh( path, 'SPTTRF', info, izero, ' ', n, n, -1,
381  \$ -1, -1, imat, nfail, nerrs, nout )
382  GO TO 100
383  END IF
384 *
385  IF( info.GT.0 ) THEN
386  rcondc = zero
387  GO TO 90
388  END IF
389 *
390  CALL sptt01( n, d, e, d( n+1 ), e( n+1 ), work,
391  \$ result( 1 ) )
392 *
393 * Print the test ratio if greater than or equal to THRESH.
394 *
395  IF( result( 1 ).GE.thresh ) THEN
396  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
397  \$ CALL alahd( nout, path )
398  WRITE( nout, fmt = 9999 )n, imat, 1, result( 1 )
399  nfail = nfail + 1
400  END IF
401  nrun = nrun + 1
402 *
403 * Compute RCONDC = 1 / (norm(A) * norm(inv(A))
404 *
405 * Compute norm(A).
406 *
407  anorm = slanst( '1', n, d, e )
408 *
409 * Use SPTTRS to solve for one column at a time of inv(A),
410 * computing the maximum column sum as we go.
411 *
412  ainvnm = zero
413  DO 50 i = 1, n
414  DO 40 j = 1, n
415  x( j ) = zero
416  40 CONTINUE
417  x( i ) = one
418  CALL spttrs( n, 1, d( n+1 ), e( n+1 ), x, lda, info )
419  ainvnm = max( ainvnm, sasum( n, x, 1 ) )
420  50 CONTINUE
421  rcondc = one / max( one, anorm*ainvnm )
422 *
423  DO 80 irhs = 1, nns
424  nrhs = nsval( irhs )
425 *
426 * Generate NRHS random solution vectors.
427 *
428  ix = 1
429  DO 60 j = 1, nrhs
430  CALL slarnv( 2, iseed, n, xact( ix ) )
431  ix = ix + lda
432  60 CONTINUE
433 *
434 * Set the right hand side.
435 *
436  CALL slaptm( n, nrhs, one, d, e, xact, lda, zero, b,
437  \$ lda )
438 *
439 *+ TEST 2
440 * Solve A*x = b and compute the residual.
441 *
442  CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
443  CALL spttrs( n, nrhs, d( n+1 ), e( n+1 ), x, lda, info )
444 *
445 * Check error code from SPTTRS.
446 *
447  IF( info.NE.0 )
448  \$ CALL alaerh( path, 'SPTTRS', info, 0, ' ', n, n, -1,
449  \$ -1, nrhs, imat, nfail, nerrs, nout )
450 *
451  CALL slacpy( 'Full', n, nrhs, b, lda, work, lda )
452  CALL sptt02( n, nrhs, d, e, x, lda, work, lda,
453  \$ result( 2 ) )
454 *
455 *+ TEST 3
456 * Check solution from generated exact solution.
457 *
458  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
459  \$ result( 3 ) )
460 *
461 *+ TESTS 4, 5, and 6
462 * Use iterative refinement to improve the solution.
463 *
464  srnamt = 'SPTRFS'
465  CALL sptrfs( n, nrhs, d, e, d( n+1 ), e( n+1 ), b, lda,
466  \$ x, lda, rwork, rwork( nrhs+1 ), work, info )
467 *
468 * Check error code from SPTRFS.
469 *
470  IF( info.NE.0 )
471  \$ CALL alaerh( path, 'SPTRFS', info, 0, ' ', n, n, -1,
472  \$ -1, nrhs, imat, nfail, nerrs, nout )
473 *
474  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
475  \$ result( 4 ) )
476  CALL sptt05( n, nrhs, d, e, b, lda, x, lda, xact, lda,
477  \$ rwork, rwork( nrhs+1 ), result( 5 ) )
478 *
479 * Print information about the tests that did not pass the
480 * threshold.
481 *
482  DO 70 k = 2, 6
483  IF( result( k ).GE.thresh ) THEN
484  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
485  \$ CALL alahd( nout, path )
486  WRITE( nout, fmt = 9998 )n, nrhs, imat, k,
487  \$ result( k )
488  nfail = nfail + 1
489  END IF
490  70 CONTINUE
491  nrun = nrun + 5
492  80 CONTINUE
493 *
494 *+ TEST 7
495 * Estimate the reciprocal of the condition number of the
496 * matrix.
497 *
498  90 CONTINUE
499  srnamt = 'SPTCON'
500  CALL sptcon( n, d( n+1 ), e( n+1 ), anorm, rcond, rwork,
501  \$ info )
502 *
503 * Check error code from SPTCON.
504 *
505  IF( info.NE.0 )
506  \$ CALL alaerh( path, 'SPTCON', info, 0, ' ', n, n, -1, -1,
507  \$ -1, imat, nfail, nerrs, nout )
508 *
509  result( 7 ) = sget06( rcond, rcondc )
510 *
511 * Print the test ratio if greater than or equal to THRESH.
512 *
513  IF( result( 7 ).GE.thresh ) THEN
514  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
515  \$ CALL alahd( nout, path )
516  WRITE( nout, fmt = 9999 )n, imat, 7, result( 7 )
517  nfail = nfail + 1
518  END IF
519  nrun = nrun + 1
520  100 CONTINUE
521  110 CONTINUE
522 *
523 * Print a summary of the results.
524 *
525  CALL alasum( path, nout, nfail, nrun, nerrs )
526 *
527  9999 FORMAT( ' N =', i5, ', type ', i2, ', test ', i2, ', ratio = ',
528  \$ g12.5 )
529  9998 FORMAT( ' N =', i5, ', NRHS=', i3, ', type ', i2, ', test(', i2,
530  \$ ') = ', g12.5 )
531  RETURN
532 *
533 * End of SCHKPT
534 *
535  END
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:107
subroutine sptt01(N, D, E, DF, EF, WORK, RESID)
SPTT01
Definition: sptt01.f:93
subroutine sptt05(N, NRHS, D, E, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
SPTT05
Definition: sptt05.f:152
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
subroutine sptcon(N, D, E, ANORM, RCOND, WORK, INFO)
SPTCON
Definition: sptcon.f:120
subroutine slatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
SLATB4
Definition: slatb4.f:122
subroutine serrgt(PATH, NUNIT)
SERRGT
Definition: serrgt.f:57
subroutine sptt02(N, NRHS, D, E, X, LDX, B, LDB, RESID)
SPTT02
Definition: sptt02.f:106
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:323
subroutine sget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
SGET04
Definition: sget04.f:104
subroutine slarnv(IDIST, ISEED, N, X)
SLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: slarnv.f:99
subroutine sptrfs(N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, INFO)
SPTRFS
Definition: sptrfs.f:165
subroutine slaptm(N, NRHS, ALPHA, D, E, X, LDX, BETA, B, LDB)
SLAPTM
Definition: slaptm.f:118
subroutine spttrf(N, D, E, INFO)
SPTTRF
Definition: spttrf.f:93
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:81
subroutine schkpt(DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, A, D, E, B, X, XACT, WORK, RWORK, NOUT)
SCHKPT
Definition: schkpt.f:148
subroutine spttrs(N, NRHS, D, E, B, LDB, INFO)
SPTTRS
Definition: spttrs.f:111
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
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:84
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:75