LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
sdrvsx.f
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1 *> \brief \b SDRVSX
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 SDRVSX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
12 * NIUNIT, NOUNIT, A, LDA, H, HT, WR, WI, WRT,
13 * WIT, WRTMP, WITMP, VS, LDVS, VS1, RESULT, WORK,
14 * LWORK, IWORK, BWORK, INFO )
15 *
16 * .. Scalar Arguments ..
17 * INTEGER INFO, LDA, LDVS, LWORK, NIUNIT, NOUNIT, NSIZES,
18 * $ NTYPES
19 * REAL THRESH
20 * ..
21 * .. Array Arguments ..
22 * LOGICAL BWORK( * ), DOTYPE( * )
23 * INTEGER ISEED( 4 ), IWORK( * ), NN( * )
24 * REAL A( LDA, * ), H( LDA, * ), HT( LDA, * ),
25 * $ RESULT( 17 ), VS( LDVS, * ), VS1( LDVS, * ),
26 * $ WI( * ), WIT( * ), WITMP( * ), WORK( * ),
27 * $ WR( * ), WRT( * ), WRTMP( * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> SDRVSX checks the nonsymmetric eigenvalue (Schur form) problem
37 *> expert driver SGEESX.
38 *>
39 *> SDRVSX uses both test matrices generated randomly depending on
40 *> data supplied in the calling sequence, as well as on data
41 *> read from an input file and including precomputed condition
42 *> numbers to which it compares the ones it computes.
43 *>
44 *> When SDRVSX is called, a number of matrix "sizes" ("n's") and a
45 *> number of matrix "types" are specified. For each size ("n")
46 *> and each type of matrix, one matrix will be generated and used
47 *> to test the nonsymmetric eigenroutines. For each matrix, 15
48 *> tests will be performed:
49 *>
50 *> (1) 0 if T is in Schur form, 1/ulp otherwise
51 *> (no sorting of eigenvalues)
52 *>
53 *> (2) | A - VS T VS' | / ( n |A| ulp )
54 *>
55 *> Here VS is the matrix of Schur eigenvectors, and T is in Schur
56 *> form (no sorting of eigenvalues).
57 *>
58 *> (3) | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).
59 *>
60 *> (4) 0 if WR+sqrt(-1)*WI are eigenvalues of T
61 *> 1/ulp otherwise
62 *> (no sorting of eigenvalues)
63 *>
64 *> (5) 0 if T(with VS) = T(without VS),
65 *> 1/ulp otherwise
66 *> (no sorting of eigenvalues)
67 *>
68 *> (6) 0 if eigenvalues(with VS) = eigenvalues(without VS),
69 *> 1/ulp otherwise
70 *> (no sorting of eigenvalues)
71 *>
72 *> (7) 0 if T is in Schur form, 1/ulp otherwise
73 *> (with sorting of eigenvalues)
74 *>
75 *> (8) | A - VS T VS' | / ( n |A| ulp )
76 *>
77 *> Here VS is the matrix of Schur eigenvectors, and T is in Schur
78 *> form (with sorting of eigenvalues).
79 *>
80 *> (9) | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).
81 *>
82 *> (10) 0 if WR+sqrt(-1)*WI are eigenvalues of T
83 *> 1/ulp otherwise
84 *> If workspace sufficient, also compare WR, WI with and
85 *> without reciprocal condition numbers
86 *> (with sorting of eigenvalues)
87 *>
88 *> (11) 0 if T(with VS) = T(without VS),
89 *> 1/ulp otherwise
90 *> If workspace sufficient, also compare T with and without
91 *> reciprocal condition numbers
92 *> (with sorting of eigenvalues)
93 *>
94 *> (12) 0 if eigenvalues(with VS) = eigenvalues(without VS),
95 *> 1/ulp otherwise
96 *> If workspace sufficient, also compare VS with and without
97 *> reciprocal condition numbers
98 *> (with sorting of eigenvalues)
99 *>
100 *> (13) if sorting worked and SDIM is the number of
101 *> eigenvalues which were SELECTed
102 *> If workspace sufficient, also compare SDIM with and
103 *> without reciprocal condition numbers
104 *>
105 *> (14) if RCONDE the same no matter if VS and/or RCONDV computed
106 *>
107 *> (15) if RCONDV the same no matter if VS and/or RCONDE computed
108 *>
109 *> The "sizes" are specified by an array NN(1:NSIZES); the value of
110 *> each element NN(j) specifies one size.
111 *> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
112 *> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
113 *> Currently, the list of possible types is:
114 *>
115 *> (1) The zero matrix.
116 *> (2) The identity matrix.
117 *> (3) A (transposed) Jordan block, with 1's on the diagonal.
118 *>
119 *> (4) A diagonal matrix with evenly spaced entries
120 *> 1, ..., ULP and random signs.
121 *> (ULP = (first number larger than 1) - 1 )
122 *> (5) A diagonal matrix with geometrically spaced entries
123 *> 1, ..., ULP and random signs.
124 *> (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
125 *> and random signs.
126 *>
127 *> (7) Same as (4), but multiplied by a constant near
128 *> the overflow threshold
129 *> (8) Same as (4), but multiplied by a constant near
130 *> the underflow threshold
131 *>
132 *> (9) A matrix of the form U' T U, where U is orthogonal and
133 *> T has evenly spaced entries 1, ..., ULP with random signs
134 *> on the diagonal and random O(1) entries in the upper
135 *> triangle.
136 *>
137 *> (10) A matrix of the form U' T U, where U is orthogonal and
138 *> T has geometrically spaced entries 1, ..., ULP with random
139 *> signs on the diagonal and random O(1) entries in the upper
140 *> triangle.
141 *>
142 *> (11) A matrix of the form U' T U, where U is orthogonal and
143 *> T has "clustered" entries 1, ULP,..., ULP with random
144 *> signs on the diagonal and random O(1) entries in the upper
145 *> triangle.
146 *>
147 *> (12) A matrix of the form U' T U, where U is orthogonal and
148 *> T has real or complex conjugate paired eigenvalues randomly
149 *> chosen from ( ULP, 1 ) and random O(1) entries in the upper
150 *> triangle.
151 *>
152 *> (13) A matrix of the form X' T X, where X has condition
153 *> SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
154 *> with random signs on the diagonal and random O(1) entries
155 *> in the upper triangle.
156 *>
157 *> (14) A matrix of the form X' T X, where X has condition
158 *> SQRT( ULP ) and T has geometrically spaced entries
159 *> 1, ..., ULP with random signs on the diagonal and random
160 *> O(1) entries in the upper triangle.
161 *>
162 *> (15) A matrix of the form X' T X, where X has condition
163 *> SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
164 *> with random signs on the diagonal and random O(1) entries
165 *> in the upper triangle.
166 *>
167 *> (16) A matrix of the form X' T X, where X has condition
168 *> SQRT( ULP ) and T has real or complex conjugate paired
169 *> eigenvalues randomly chosen from ( ULP, 1 ) and random
170 *> O(1) entries in the upper triangle.
171 *>
172 *> (17) Same as (16), but multiplied by a constant
173 *> near the overflow threshold
174 *> (18) Same as (16), but multiplied by a constant
175 *> near the underflow threshold
176 *>
177 *> (19) Nonsymmetric matrix with random entries chosen from (-1,1).
178 *> If N is at least 4, all entries in first two rows and last
179 *> row, and first column and last two columns are zero.
180 *> (20) Same as (19), but multiplied by a constant
181 *> near the overflow threshold
182 *> (21) Same as (19), but multiplied by a constant
183 *> near the underflow threshold
184 *>
185 *> In addition, an input file will be read from logical unit number
186 *> NIUNIT. The file contains matrices along with precomputed
187 *> eigenvalues and reciprocal condition numbers for the eigenvalue
188 *> average and right invariant subspace. For these matrices, in
189 *> addition to tests (1) to (15) we will compute the following two
190 *> tests:
191 *>
192 *> (16) |RCONDE - RCDEIN| / cond(RCONDE)
193 *>
194 *> RCONDE is the reciprocal average eigenvalue condition number
195 *> computed by SGEESX and RCDEIN (the precomputed true value)
196 *> is supplied as input. cond(RCONDE) is the condition number
197 *> of RCONDE, and takes errors in computing RCONDE into account,
198 *> so that the resulting quantity should be O(ULP). cond(RCONDE)
199 *> is essentially given by norm(A)/RCONDV.
200 *>
201 *> (17) |RCONDV - RCDVIN| / cond(RCONDV)
202 *>
203 *> RCONDV is the reciprocal right invariant subspace condition
204 *> number computed by SGEESX and RCDVIN (the precomputed true
205 *> value) is supplied as input. cond(RCONDV) is the condition
206 *> number of RCONDV, and takes errors in computing RCONDV into
207 *> account, so that the resulting quantity should be O(ULP).
208 *> cond(RCONDV) is essentially given by norm(A)/RCONDE.
209 *> \endverbatim
210 *
211 * Arguments:
212 * ==========
213 *
214 *> \param[in] NSIZES
215 *> \verbatim
216 *> NSIZES is INTEGER
217 *> The number of sizes of matrices to use. NSIZES must be at
218 *> least zero. If it is zero, no randomly generated matrices
219 *> are tested, but any test matrices read from NIUNIT will be
220 *> tested.
221 *> \endverbatim
222 *>
223 *> \param[in] NN
224 *> \verbatim
225 *> NN is INTEGER array, dimension (NSIZES)
226 *> An array containing the sizes to be used for the matrices.
227 *> Zero values will be skipped. The values must be at least
228 *> zero.
229 *> \endverbatim
230 *>
231 *> \param[in] NTYPES
232 *> \verbatim
233 *> NTYPES is INTEGER
234 *> The number of elements in DOTYPE. NTYPES must be at least
235 *> zero. If it is zero, no randomly generated test matrices
236 *> are tested, but and test matrices read from NIUNIT will be
237 *> tested. If it is MAXTYP+1 and NSIZES is 1, then an
238 *> additional type, MAXTYP+1 is defined, which is to use
239 *> whatever matrix is in A. This is only useful if
240 *> DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. .
241 *> \endverbatim
242 *>
243 *> \param[in] DOTYPE
244 *> \verbatim
245 *> DOTYPE is LOGICAL array, dimension (NTYPES)
246 *> If DOTYPE(j) is .TRUE., then for each size in NN a
247 *> matrix of that size and of type j will be generated.
248 *> If NTYPES is smaller than the maximum number of types
249 *> defined (PARAMETER MAXTYP), then types NTYPES+1 through
250 *> MAXTYP will not be generated. If NTYPES is larger
251 *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
252 *> will be ignored.
253 *> \endverbatim
254 *>
255 *> \param[in,out] ISEED
256 *> \verbatim
257 *> ISEED is INTEGER array, dimension (4)
258 *> On entry ISEED specifies the seed of the random number
259 *> generator. The array elements should be between 0 and 4095;
260 *> if not they will be reduced mod 4096. Also, ISEED(4) must
261 *> be odd. The random number generator uses a linear
262 *> congruential sequence limited to small integers, and so
263 *> should produce machine independent random numbers. The
264 *> values of ISEED are changed on exit, and can be used in the
265 *> next call to SDRVSX to continue the same random number
266 *> sequence.
267 *> \endverbatim
268 *>
269 *> \param[in] THRESH
270 *> \verbatim
271 *> THRESH is REAL
272 *> A test will count as "failed" if the "error", computed as
273 *> described above, exceeds THRESH. Note that the error
274 *> is scaled to be O(1), so THRESH should be a reasonably
275 *> small multiple of 1, e.g., 10 or 100. In particular,
276 *> it should not depend on the precision (single vs. double)
277 *> or the size of the matrix. It must be at least zero.
278 *> \endverbatim
279 *>
280 *> \param[in] NIUNIT
281 *> \verbatim
282 *> NIUNIT is INTEGER
283 *> The FORTRAN unit number for reading in the data file of
284 *> problems to solve.
285 *> \endverbatim
286 *>
287 *> \param[in] NOUNIT
288 *> \verbatim
289 *> NOUNIT is INTEGER
290 *> The FORTRAN unit number for printing out error messages
291 *> (e.g., if a routine returns INFO not equal to 0.)
292 *> \endverbatim
293 *>
294 *> \param[out] A
295 *> \verbatim
296 *> A is REAL array, dimension (LDA, max(NN))
297 *> Used to hold the matrix whose eigenvalues are to be
298 *> computed. On exit, A contains the last matrix actually used.
299 *> \endverbatim
300 *>
301 *> \param[in] LDA
302 *> \verbatim
303 *> LDA is INTEGER
304 *> The leading dimension of A, and H. LDA must be at
305 *> least 1 and at least max( NN ).
306 *> \endverbatim
307 *>
308 *> \param[out] H
309 *> \verbatim
310 *> H is REAL array, dimension (LDA, max(NN))
311 *> Another copy of the test matrix A, modified by SGEESX.
312 *> \endverbatim
313 *>
314 *> \param[out] HT
315 *> \verbatim
316 *> HT is REAL array, dimension (LDA, max(NN))
317 *> Yet another copy of the test matrix A, modified by SGEESX.
318 *> \endverbatim
319 *>
320 *> \param[out] WR
321 *> \verbatim
322 *> WR is REAL array, dimension (max(NN))
323 *> \endverbatim
324 *>
325 *> \param[out] WI
326 *> \verbatim
327 *> WI is REAL array, dimension (max(NN))
328 *>
329 *> The real and imaginary parts of the eigenvalues of A.
330 *> On exit, WR + WI*i are the eigenvalues of the matrix in A.
331 *> \endverbatim
332 *>
333 *> \param[out] WRT
334 *> \verbatim
335 *> WRT is REAL array, dimension (max(NN))
336 *> \endverbatim
337 *>
338 *> \param[out] WIT
339 *> \verbatim
340 *> WIT is REAL array, dimension (max(NN))
341 *>
342 *> Like WR, WI, these arrays contain the eigenvalues of A,
343 *> but those computed when SGEESX only computes a partial
344 *> eigendecomposition, i.e. not Schur vectors
345 *> \endverbatim
346 *>
347 *> \param[out] WRTMP
348 *> \verbatim
349 *> WRTMP is REAL array, dimension (max(NN))
350 *> \endverbatim
351 *>
352 *> \param[out] WITMP
353 *> \verbatim
354 *> WITMP is REAL array, dimension (max(NN))
355 *>
356 *> More temporary storage for eigenvalues.
357 *> \endverbatim
358 *>
359 *> \param[out] VS
360 *> \verbatim
361 *> VS is REAL array, dimension (LDVS, max(NN))
362 *> VS holds the computed Schur vectors.
363 *> \endverbatim
364 *>
365 *> \param[in] LDVS
366 *> \verbatim
367 *> LDVS is INTEGER
368 *> Leading dimension of VS. Must be at least max(1,max(NN)).
369 *> \endverbatim
370 *>
371 *> \param[out] VS1
372 *> \verbatim
373 *> VS1 is REAL array, dimension (LDVS, max(NN))
374 *> VS1 holds another copy of the computed Schur vectors.
375 *> \endverbatim
376 *>
377 *> \param[out] RESULT
378 *> \verbatim
379 *> RESULT is REAL array, dimension (17)
380 *> The values computed by the 17 tests described above.
381 *> The values are currently limited to 1/ulp, to avoid overflow.
382 *> \endverbatim
383 *>
384 *> \param[out] WORK
385 *> \verbatim
386 *> WORK is REAL array, dimension (LWORK)
387 *> \endverbatim
388 *>
389 *> \param[in] LWORK
390 *> \verbatim
391 *> LWORK is INTEGER
392 *> The number of entries in WORK. This must be at least
393 *> max(3*NN(j),2*NN(j)**2) for all j.
394 *> \endverbatim
395 *>
396 *> \param[out] IWORK
397 *> \verbatim
398 *> IWORK is INTEGER array, dimension (max(NN)*max(NN))
399 *> \endverbatim
400 *>
401 *> \param[out] BWORK
402 *> \verbatim
403 *> BWORK is LOGICAL array, dimension (max(NN))
404 *> \endverbatim
405 *>
406 *> \param[out] INFO
407 *> \verbatim
408 *> INFO is INTEGER
409 *> If 0, successful exit.
410 *> <0, input parameter -INFO is incorrect
411 *> >0, SLATMR, SLATMS, SLATME or SGET24 returned an error
412 *> code and INFO is its absolute value
413 *>
414 *>-----------------------------------------------------------------------
415 *>
416 *> Some Local Variables and Parameters:
417 *> ---- ----- --------- --- ----------
418 *> ZERO, ONE Real 0 and 1.
419 *> MAXTYP The number of types defined.
420 *> NMAX Largest value in NN.
421 *> NERRS The number of tests which have exceeded THRESH
422 *> COND, CONDS,
423 *> IMODE Values to be passed to the matrix generators.
424 *> ANORM Norm of A; passed to matrix generators.
425 *>
426 *> OVFL, UNFL Overflow and underflow thresholds.
427 *> ULP, ULPINV Finest relative precision and its inverse.
428 *> RTULP, RTULPI Square roots of the previous 4 values.
429 *> The following four arrays decode JTYPE:
430 *> KTYPE(j) The general type (1-10) for type "j".
431 *> KMODE(j) The MODE value to be passed to the matrix
432 *> generator for type "j".
433 *> KMAGN(j) The order of magnitude ( O(1),
434 *> O(overflow^(1/2) ), O(underflow^(1/2) )
435 *> KCONDS(j) Selectw whether CONDS is to be 1 or
436 *> 1/sqrt(ulp). (0 means irrelevant.)
437 *> \endverbatim
438 *
439 * Authors:
440 * ========
441 *
442 *> \author Univ. of Tennessee
443 *> \author Univ. of California Berkeley
444 *> \author Univ. of Colorado Denver
445 *> \author NAG Ltd.
446 *
447 *> \ingroup single_eig
448 *
449 * =====================================================================
450  SUBROUTINE sdrvsx( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
451  $ NIUNIT, NOUNIT, A, LDA, H, HT, WR, WI, WRT,
452  $ WIT, WRTMP, WITMP, VS, LDVS, VS1, RESULT, WORK,
453  $ LWORK, IWORK, BWORK, INFO )
454 *
455 * -- LAPACK test routine --
456 * -- LAPACK is a software package provided by Univ. of Tennessee, --
457 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
458 *
459 * .. Scalar Arguments ..
460  INTEGER INFO, LDA, LDVS, LWORK, NIUNIT, NOUNIT, NSIZES,
461  $ NTYPES
462  REAL THRESH
463 * ..
464 * .. Array Arguments ..
465  LOGICAL BWORK( * ), DOTYPE( * )
466  INTEGER ISEED( 4 ), IWORK( * ), NN( * )
467  REAL A( LDA, * ), H( LDA, * ), HT( LDA, * ),
468  $ result( 17 ), vs( ldvs, * ), vs1( ldvs, * ),
469  $ wi( * ), wit( * ), witmp( * ), work( * ),
470  $ wr( * ), wrt( * ), wrtmp( * )
471 * ..
472 *
473 * =====================================================================
474 *
475 * .. Parameters ..
476  REAL ZERO, ONE
477  PARAMETER ( ZERO = 0.0e0, one = 1.0e0 )
478  INTEGER MAXTYP
479  parameter( maxtyp = 21 )
480 * ..
481 * .. Local Scalars ..
482  LOGICAL BADNN
483  CHARACTER*3 PATH
484  INTEGER I, IINFO, IMODE, ITYPE, IWK, J, JCOL, JSIZE,
485  $ jtype, mtypes, n, nerrs, nfail, nmax,
486  $ nnwork, nslct, ntest, ntestf, ntestt
487  REAL ANORM, COND, CONDS, OVFL, RCDEIN, RCDVIN,
488  $ RTULP, RTULPI, ULP, ULPINV, UNFL
489 * ..
490 * .. Local Arrays ..
491  CHARACTER ADUMMA( 1 )
492  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), ISLCT( 20 ),
493  $ KCONDS( MAXTYP ), KMAGN( MAXTYP ),
494  $ kmode( maxtyp ), ktype( maxtyp )
495 * ..
496 * .. Arrays in Common ..
497  LOGICAL SELVAL( 20 )
498  REAL SELWI( 20 ), SELWR( 20 )
499 * ..
500 * .. Scalars in Common ..
501  INTEGER SELDIM, SELOPT
502 * ..
503 * .. Common blocks ..
504  COMMON / sslct / selopt, seldim, selval, selwr, selwi
505 * ..
506 * .. External Functions ..
507  REAL SLAMCH
508  EXTERNAL SLAMCH
509 * ..
510 * .. External Subroutines ..
511  EXTERNAL sget24, slabad, slasum, slatme, slatmr, slatms,
512  $ slaset, xerbla
513 * ..
514 * .. Intrinsic Functions ..
515  INTRINSIC abs, max, min, sqrt
516 * ..
517 * .. Data statements ..
518  DATA ktype / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
519  DATA kmagn / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
520  $ 3, 1, 2, 3 /
521  DATA kmode / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
522  $ 1, 5, 5, 5, 4, 3, 1 /
523  DATA kconds / 3*0, 5*0, 4*1, 6*2, 3*0 /
524 * ..
525 * .. Executable Statements ..
526 *
527  path( 1: 1 ) = 'Single precision'
528  path( 2: 3 ) = 'SX'
529 *
530 * Check for errors
531 *
532  ntestt = 0
533  ntestf = 0
534  info = 0
535 *
536 * Important constants
537 *
538  badnn = .false.
539 *
540 * 12 is the largest dimension in the input file of precomputed
541 * problems
542 *
543  nmax = 12
544  DO 10 j = 1, nsizes
545  nmax = max( nmax, nn( j ) )
546  IF( nn( j ).LT.0 )
547  $ badnn = .true.
548  10 CONTINUE
549 *
550 * Check for errors
551 *
552  IF( nsizes.LT.0 ) THEN
553  info = -1
554  ELSE IF( badnn ) THEN
555  info = -2
556  ELSE IF( ntypes.LT.0 ) THEN
557  info = -3
558  ELSE IF( thresh.LT.zero ) THEN
559  info = -6
560  ELSE IF( niunit.LE.0 ) THEN
561  info = -7
562  ELSE IF( nounit.LE.0 ) THEN
563  info = -8
564  ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
565  info = -10
566  ELSE IF( ldvs.LT.1 .OR. ldvs.LT.nmax ) THEN
567  info = -20
568  ELSE IF( max( 3*nmax, 2*nmax**2 ).GT.lwork ) THEN
569  info = -24
570  END IF
571 *
572  IF( info.NE.0 ) THEN
573  CALL xerbla( 'SDRVSX', -info )
574  RETURN
575  END IF
576 *
577 * If nothing to do check on NIUNIT
578 *
579  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
580  $ GO TO 150
581 *
582 * More Important constants
583 *
584  unfl = slamch( 'Safe minimum' )
585  ovfl = one / unfl
586  CALL slabad( unfl, ovfl )
587  ulp = slamch( 'Precision' )
588  ulpinv = one / ulp
589  rtulp = sqrt( ulp )
590  rtulpi = one / rtulp
591 *
592 * Loop over sizes, types
593 *
594  nerrs = 0
595 *
596  DO 140 jsize = 1, nsizes
597  n = nn( jsize )
598  IF( nsizes.NE.1 ) THEN
599  mtypes = min( maxtyp, ntypes )
600  ELSE
601  mtypes = min( maxtyp+1, ntypes )
602  END IF
603 *
604  DO 130 jtype = 1, mtypes
605  IF( .NOT.dotype( jtype ) )
606  $ GO TO 130
607 *
608 * Save ISEED in case of an error.
609 *
610  DO 20 j = 1, 4
611  ioldsd( j ) = iseed( j )
612  20 CONTINUE
613 *
614 * Compute "A"
615 *
616 * Control parameters:
617 *
618 * KMAGN KCONDS KMODE KTYPE
619 * =1 O(1) 1 clustered 1 zero
620 * =2 large large clustered 2 identity
621 * =3 small exponential Jordan
622 * =4 arithmetic diagonal, (w/ eigenvalues)
623 * =5 random log symmetric, w/ eigenvalues
624 * =6 random general, w/ eigenvalues
625 * =7 random diagonal
626 * =8 random symmetric
627 * =9 random general
628 * =10 random triangular
629 *
630  IF( mtypes.GT.maxtyp )
631  $ GO TO 90
632 *
633  itype = ktype( jtype )
634  imode = kmode( jtype )
635 *
636 * Compute norm
637 *
638  GO TO ( 30, 40, 50 )kmagn( jtype )
639 *
640  30 CONTINUE
641  anorm = one
642  GO TO 60
643 *
644  40 CONTINUE
645  anorm = ovfl*ulp
646  GO TO 60
647 *
648  50 CONTINUE
649  anorm = unfl*ulpinv
650  GO TO 60
651 *
652  60 CONTINUE
653 *
654  CALL slaset( 'Full', lda, n, zero, zero, a, lda )
655  iinfo = 0
656  cond = ulpinv
657 *
658 * Special Matrices -- Identity & Jordan block
659 *
660 * Zero
661 *
662  IF( itype.EQ.1 ) THEN
663  iinfo = 0
664 *
665  ELSE IF( itype.EQ.2 ) THEN
666 *
667 * Identity
668 *
669  DO 70 jcol = 1, n
670  a( jcol, jcol ) = anorm
671  70 CONTINUE
672 *
673  ELSE IF( itype.EQ.3 ) THEN
674 *
675 * Jordan Block
676 *
677  DO 80 jcol = 1, n
678  a( jcol, jcol ) = anorm
679  IF( jcol.GT.1 )
680  $ a( jcol, jcol-1 ) = one
681  80 CONTINUE
682 *
683  ELSE IF( itype.EQ.4 ) THEN
684 *
685 * Diagonal Matrix, [Eigen]values Specified
686 *
687  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
688  $ anorm, 0, 0, 'N', a, lda, work( n+1 ),
689  $ iinfo )
690 *
691  ELSE IF( itype.EQ.5 ) THEN
692 *
693 * Symmetric, eigenvalues specified
694 *
695  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
696  $ anorm, n, n, 'N', a, lda, work( n+1 ),
697  $ iinfo )
698 *
699  ELSE IF( itype.EQ.6 ) THEN
700 *
701 * General, eigenvalues specified
702 *
703  IF( kconds( jtype ).EQ.1 ) THEN
704  conds = one
705  ELSE IF( kconds( jtype ).EQ.2 ) THEN
706  conds = rtulpi
707  ELSE
708  conds = zero
709  END IF
710 *
711  adumma( 1 ) = ' '
712  CALL slatme( n, 'S', iseed, work, imode, cond, one,
713  $ adumma, 'T', 'T', 'T', work( n+1 ), 4,
714  $ conds, n, n, anorm, a, lda, work( 2*n+1 ),
715  $ iinfo )
716 *
717  ELSE IF( itype.EQ.7 ) THEN
718 *
719 * Diagonal, random eigenvalues
720 *
721  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
722  $ 'T', 'N', work( n+1 ), 1, one,
723  $ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
724  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
725 *
726  ELSE IF( itype.EQ.8 ) THEN
727 *
728 * Symmetric, random eigenvalues
729 *
730  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
731  $ 'T', 'N', work( n+1 ), 1, one,
732  $ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
733  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
734 *
735  ELSE IF( itype.EQ.9 ) THEN
736 *
737 * General, random eigenvalues
738 *
739  CALL slatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
740  $ 'T', 'N', work( n+1 ), 1, one,
741  $ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
742  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
743  IF( n.GE.4 ) THEN
744  CALL slaset( 'Full', 2, n, zero, zero, a, lda )
745  CALL slaset( 'Full', n-3, 1, zero, zero, a( 3, 1 ),
746  $ lda )
747  CALL slaset( 'Full', n-3, 2, zero, zero, a( 3, n-1 ),
748  $ lda )
749  CALL slaset( 'Full', 1, n, zero, zero, a( n, 1 ),
750  $ lda )
751  END IF
752 *
753  ELSE IF( itype.EQ.10 ) THEN
754 *
755 * Triangular, random eigenvalues
756 *
757  CALL slatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
758  $ 'T', 'N', work( n+1 ), 1, one,
759  $ work( 2*n+1 ), 1, one, 'N', idumma, n, 0,
760  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
761 *
762  ELSE
763 *
764  iinfo = 1
765  END IF
766 *
767  IF( iinfo.NE.0 ) THEN
768  WRITE( nounit, fmt = 9991 )'Generator', iinfo, n, jtype,
769  $ ioldsd
770  info = abs( iinfo )
771  RETURN
772  END IF
773 *
774  90 CONTINUE
775 *
776 * Test for minimal and generous workspace
777 *
778  DO 120 iwk = 1, 2
779  IF( iwk.EQ.1 ) THEN
780  nnwork = 3*n
781  ELSE
782  nnwork = max( 3*n, 2*n*n )
783  END IF
784  nnwork = max( nnwork, 1 )
785 *
786  CALL sget24( .false., jtype, thresh, ioldsd, nounit, n,
787  $ a, lda, h, ht, wr, wi, wrt, wit, wrtmp,
788  $ witmp, vs, ldvs, vs1, rcdein, rcdvin, nslct,
789  $ islct, result, work, nnwork, iwork, bwork,
790  $ info )
791 *
792 * Check for RESULT(j) > THRESH
793 *
794  ntest = 0
795  nfail = 0
796  DO 100 j = 1, 15
797  IF( result( j ).GE.zero )
798  $ ntest = ntest + 1
799  IF( result( j ).GE.thresh )
800  $ nfail = nfail + 1
801  100 CONTINUE
802 *
803  IF( nfail.GT.0 )
804  $ ntestf = ntestf + 1
805  IF( ntestf.EQ.1 ) THEN
806  WRITE( nounit, fmt = 9999 )path
807  WRITE( nounit, fmt = 9998 )
808  WRITE( nounit, fmt = 9997 )
809  WRITE( nounit, fmt = 9996 )
810  WRITE( nounit, fmt = 9995 )thresh
811  WRITE( nounit, fmt = 9994 )
812  ntestf = 2
813  END IF
814 *
815  DO 110 j = 1, 15
816  IF( result( j ).GE.thresh ) THEN
817  WRITE( nounit, fmt = 9993 )n, iwk, ioldsd, jtype,
818  $ j, result( j )
819  END IF
820  110 CONTINUE
821 *
822  nerrs = nerrs + nfail
823  ntestt = ntestt + ntest
824 *
825  120 CONTINUE
826  130 CONTINUE
827  140 CONTINUE
828 *
829  150 CONTINUE
830 *
831 * Read in data from file to check accuracy of condition estimation
832 * Read input data until N=0
833 *
834  jtype = 0
835  160 CONTINUE
836  READ( niunit, fmt = *, END = 200 )N, nslct
837  IF( n.EQ.0 )
838  $ GO TO 200
839  jtype = jtype + 1
840  iseed( 1 ) = jtype
841  IF( nslct.GT.0 )
842  $ READ( niunit, fmt = * )( islct( i ), i = 1, nslct )
843  DO 170 i = 1, n
844  READ( niunit, fmt = * )( a( i, j ), j = 1, n )
845  170 CONTINUE
846  READ( niunit, fmt = * )rcdein, rcdvin
847 *
848  CALL sget24( .true., 22, thresh, iseed, nounit, n, a, lda, h, ht,
849  $ wr, wi, wrt, wit, wrtmp, witmp, vs, ldvs, vs1,
850  $ rcdein, rcdvin, nslct, islct, result, work, lwork,
851  $ iwork, bwork, info )
852 *
853 * Check for RESULT(j) > THRESH
854 *
855  ntest = 0
856  nfail = 0
857  DO 180 j = 1, 17
858  IF( result( j ).GE.zero )
859  $ ntest = ntest + 1
860  IF( result( j ).GE.thresh )
861  $ nfail = nfail + 1
862  180 CONTINUE
863 *
864  IF( nfail.GT.0 )
865  $ ntestf = ntestf + 1
866  IF( ntestf.EQ.1 ) THEN
867  WRITE( nounit, fmt = 9999 )path
868  WRITE( nounit, fmt = 9998 )
869  WRITE( nounit, fmt = 9997 )
870  WRITE( nounit, fmt = 9996 )
871  WRITE( nounit, fmt = 9995 )thresh
872  WRITE( nounit, fmt = 9994 )
873  ntestf = 2
874  END IF
875  DO 190 j = 1, 17
876  IF( result( j ).GE.thresh ) THEN
877  WRITE( nounit, fmt = 9992 )n, jtype, j, result( j )
878  END IF
879  190 CONTINUE
880 *
881  nerrs = nerrs + nfail
882  ntestt = ntestt + ntest
883  GO TO 160
884  200 CONTINUE
885 *
886 * Summary
887 *
888  CALL slasum( path, nounit, nerrs, ntestt )
889 *
890  9999 FORMAT( / 1x, a3, ' -- Real Schur Form Decomposition Expert ',
891  $ 'Driver', / ' Matrix types (see SDRVSX for details):' )
892 *
893  9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
894  $ ' ', ' 5=Diagonal: geometr. spaced entries.',
895  $ / ' 2=Identity matrix. ', ' 6=Diagona',
896  $ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
897  $ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
898  $ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
899  $ 'mall, evenly spaced.' )
900  9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
901  $ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
902  $ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
903  $ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
904  $ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
905  $ 'lex ', / ' 12=Well-cond., random complex ', ' ',
906  $ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
907  $ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
908  $ ' complx ' )
909  9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
910  $ 'with small random entries.', / ' 20=Matrix with large ran',
911  $ 'dom entries. ', / )
912  9995 FORMAT( ' Tests performed with test threshold =', f8.2,
913  $ / ' ( A denotes A on input and T denotes A on output)',
914  $ / / ' 1 = 0 if T in Schur form (no sort), ',
915  $ ' 1/ulp otherwise', /
916  $ ' 2 = | A - VS T transpose(VS) | / ( n |A| ulp ) (no sort)',
917  $ / ' 3 = | I - VS transpose(VS) | / ( n ulp ) (no sort) ', /
918  $ ' 4 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (no sort),',
919  $ ' 1/ulp otherwise', /
920  $ ' 5 = 0 if T same no matter if VS computed (no sort),',
921  $ ' 1/ulp otherwise', /
922  $ ' 6 = 0 if WR, WI same no matter if VS computed (no sort)',
923  $ ', 1/ulp otherwise' )
924  9994 FORMAT( ' 7 = 0 if T in Schur form (sort), ', ' 1/ulp otherwise',
925  $ / ' 8 = | A - VS T transpose(VS) | / ( n |A| ulp ) (sort)',
926  $ / ' 9 = | I - VS transpose(VS) | / ( n ulp ) (sort) ',
927  $ / ' 10 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (sort),',
928  $ ' 1/ulp otherwise', /
929  $ ' 11 = 0 if T same no matter what else computed (sort),',
930  $ ' 1/ulp otherwise', /
931  $ ' 12 = 0 if WR, WI same no matter what else computed ',
932  $ '(sort), 1/ulp otherwise', /
933  $ ' 13 = 0 if sorting successful, 1/ulp otherwise',
934  $ / ' 14 = 0 if RCONDE same no matter what else computed,',
935  $ ' 1/ulp otherwise', /
936  $ ' 15 = 0 if RCONDv same no matter what else computed,',
937  $ ' 1/ulp otherwise', /
938  $ ' 16 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),',
939  $ / ' 17 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),' )
940  9993 FORMAT( ' N=', i5, ', IWK=', i2, ', seed=', 4( i4, ',' ),
941  $ ' type ', i2, ', test(', i2, ')=', g10.3 )
942  9992 FORMAT( ' N=', i5, ', input example =', i3, ', test(', i2, ')=',
943  $ g10.3 )
944  9991 FORMAT( ' SDRVSX: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
945  $ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
946 *
947  RETURN
948 *
949 * End of SDRVSX
950 *
951  END
subroutine slabad(SMALL, LARGE)
SLABAD
Definition: slabad.f:74
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 xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:321
subroutine slatme(N, DIST, ISEED, D, MODE, COND, DMAX, EI, RSIGN, UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, A, LDA, WORK, INFO)
SLATME
Definition: slatme.f:332
subroutine slatmr(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, PACK, A, LDA, IWORK, INFO)
SLATMR
Definition: slatmr.f:471
subroutine sget24(COMP, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA, H, HT, WR, WI, WRT, WIT, WRTMP, WITMP, VS, LDVS, VS1, RCDEIN, RCDVIN, NSLCT, ISLCT, RESULT, WORK, LWORK, IWORK, BWORK, INFO)
SGET24
Definition: sget24.f:343
subroutine sdrvsx(NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, NIUNIT, NOUNIT, A, LDA, H, HT, WR, WI, WRT, WIT, WRTMP, WITMP, VS, LDVS, VS1, RESULT, WORK, LWORK, IWORK, BWORK, INFO)
SDRVSX
Definition: sdrvsx.f:454
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:41