LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
cdrvsx.f
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1 *> \brief \b CDRVSX
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 CDRVSX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
12 * NIUNIT, NOUNIT, A, LDA, H, HT, W, WT, WTMP, VS,
13 * LDVS, VS1, RESULT, WORK, LWORK, RWORK, BWORK,
14 * 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 ), NN( * )
24 * REAL RESULT( 17 ), RWORK( * )
25 * COMPLEX A( LDA, * ), H( LDA, * ), HT( LDA, * ),
26 * \$ VS( LDVS, * ), VS1( LDVS, * ), W( * ),
27 * \$ WORK( * ), WT( * ), WTMP( * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> CDRVSX checks the nonsymmetric eigenvalue (Schur form) problem
37 *> expert driver CGEESX.
38 *>
39 *> CDRVSX 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 CDRVSX 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 W 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 W are eigenvalues of T
83 *> 1/ulp otherwise
84 *> If workspace sufficient, also compare W 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 complex angles.
121 *> (ULP = (first number larger than 1) - 1 )
122 *> (5) A diagonal matrix with geometrically spaced entries
123 *> 1, ..., ULP and random complex angles.
124 *> (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
125 *> and random complex angles.
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 unitary and
133 *> T has evenly spaced entries 1, ..., ULP with random
134 *> complex angles on the diagonal and random O(1) entries in
135 *> the upper triangle.
136 *>
137 *> (10) A matrix of the form U' T U, where U is unitary and
138 *> T has geometrically spaced entries 1, ..., ULP with random
139 *> complex angles on the diagonal and random O(1) entries in
140 *> the upper 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 *> complex angles on the diagonal and random O(1) entries in
145 *> the upper triangle.
146 *>
147 *> (12) A matrix of the form U' T U, where U is unitary and
148 *> T has complex eigenvalues randomly chosen from
149 *> ULP < |z| < 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 complex angles on the diagonal and random O(1)
155 *> entries 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 complex angles on the diagonal
160 *> and random 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 complex angles on the diagonal and random O(1)
165 *> entries 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 complex eigenvalues randomly chosen
169 *> from ULP < |z| < 1 and random O(1) entries in the upper
170 *> 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 CGEESX 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 CGEESX 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 CDRVSX 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 COMPLEX 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 COMPLEX array, dimension (LDA, max(NN))
311 *> Another copy of the test matrix A, modified by CGEESX.
312 *> \endverbatim
313 *>
314 *> \param[out] HT
315 *> \verbatim
316 *> HT is COMPLEX array, dimension (LDA, max(NN))
317 *> Yet another copy of the test matrix A, modified by CGEESX.
318 *> \endverbatim
319 *>
320 *> \param[out] W
321 *> \verbatim
322 *> W is COMPLEX array, dimension (max(NN))
323 *> The computed eigenvalues of A.
324 *> \endverbatim
325 *>
326 *> \param[out] WT
327 *> \verbatim
328 *> WT is COMPLEX array, dimension (max(NN))
329 *> Like W, this array contains the eigenvalues of A,
330 *> but those computed when CGEESX only computes a partial
331 *> eigendecomposition, i.e. not Schur vectors
332 *> \endverbatim
333 *>
334 *> \param[out] WTMP
335 *> \verbatim
336 *> WTMP is COMPLEX array, dimension (max(NN))
337 *> More temporary storage for eigenvalues.
338 *> \endverbatim
339 *>
340 *> \param[out] VS
341 *> \verbatim
342 *> VS is COMPLEX array, dimension (LDVS, max(NN))
343 *> VS holds the computed Schur vectors.
344 *> \endverbatim
345 *>
346 *> \param[in] LDVS
347 *> \verbatim
348 *> LDVS is INTEGER
349 *> Leading dimension of VS. Must be at least max(1,max(NN)).
350 *> \endverbatim
351 *>
352 *> \param[out] VS1
353 *> \verbatim
354 *> VS1 is COMPLEX array, dimension (LDVS, max(NN))
355 *> VS1 holds another copy of the computed Schur vectors.
356 *> \endverbatim
357 *>
358 *> \param[out] RESULT
359 *> \verbatim
360 *> RESULT is REAL array, dimension (17)
361 *> The values computed by the 17 tests described above.
362 *> The values are currently limited to 1/ulp, to avoid overflow.
363 *> \endverbatim
364 *>
365 *> \param[out] WORK
366 *> \verbatim
367 *> WORK is COMPLEX array, dimension (LWORK)
368 *> \endverbatim
369 *>
370 *> \param[in] LWORK
371 *> \verbatim
372 *> LWORK is INTEGER
373 *> The number of entries in WORK. This must be at least
374 *> max(1,2*NN(j)**2) for all j.
375 *> \endverbatim
376 *>
377 *> \param[out] RWORK
378 *> \verbatim
379 *> RWORK is REAL array, dimension (max(NN))
380 *> \endverbatim
381 *>
382 *> \param[out] BWORK
383 *> \verbatim
384 *> BWORK is LOGICAL array, dimension (max(NN))
385 *> \endverbatim
386 *>
387 *> \param[out] INFO
388 *> \verbatim
389 *> INFO is INTEGER
390 *> If 0, successful exit.
391 *> <0, input parameter -INFO is incorrect
392 *> >0, CLATMR, CLATMS, CLATME or CGET24 returned an error
393 *> code and INFO is its absolute value
394 *>
395 *>-----------------------------------------------------------------------
396 *>
397 *> Some Local Variables and Parameters:
398 *> ---- ----- --------- --- ----------
399 *> ZERO, ONE Real 0 and 1.
400 *> MAXTYP The number of types defined.
401 *> NMAX Largest value in NN.
402 *> NERRS The number of tests which have exceeded THRESH
403 *> COND, CONDS,
404 *> IMODE Values to be passed to the matrix generators.
405 *> ANORM Norm of A; passed to matrix generators.
406 *>
407 *> OVFL, UNFL Overflow and underflow thresholds.
408 *> ULP, ULPINV Finest relative precision and its inverse.
409 *> RTULP, RTULPI Square roots of the previous 4 values.
410 *> The following four arrays decode JTYPE:
411 *> KTYPE(j) The general type (1-10) for type "j".
412 *> KMODE(j) The MODE value to be passed to the matrix
413 *> generator for type "j".
414 *> KMAGN(j) The order of magnitude ( O(1),
415 *> O(overflow^(1/2) ), O(underflow^(1/2) )
416 *> KCONDS(j) Selectw whether CONDS is to be 1 or
417 *> 1/sqrt(ulp). (0 means irrelevant.)
418 *> \endverbatim
419 *
420 * Authors:
421 * ========
422 *
423 *> \author Univ. of Tennessee
424 *> \author Univ. of California Berkeley
425 *> \author Univ. of Colorado Denver
426 *> \author NAG Ltd.
427 *
428 *> \date June 2016
429 *
430 *> \ingroup complex_eig
431 *
432 * =====================================================================
433  SUBROUTINE cdrvsx( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
434  \$ NIUNIT, NOUNIT, A, LDA, H, HT, W, WT, WTMP, VS,
435  \$ LDVS, VS1, RESULT, WORK, LWORK, RWORK, BWORK,
436  \$ INFO )
437 *
438 * -- LAPACK test routine (version 3.7.0) --
439 * -- LAPACK is a software package provided by Univ. of Tennessee, --
440 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
441 * June 2016
442 *
443 * .. Scalar Arguments ..
444  INTEGER INFO, LDA, LDVS, LWORK, NIUNIT, NOUNIT, NSIZES,
445  \$ ntypes
446  REAL THRESH
447 * ..
448 * .. Array Arguments ..
449  LOGICAL BWORK( * ), DOTYPE( * )
450  INTEGER ISEED( 4 ), NN( * )
451  REAL RESULT( 17 ), RWORK( * )
452  COMPLEX A( lda, * ), H( lda, * ), HT( lda, * ),
453  \$ vs( ldvs, * ), vs1( ldvs, * ), w( * ),
454  \$ work( * ), wt( * ), wtmp( * )
455 * ..
456 *
457 * =====================================================================
458 *
459 * .. Parameters ..
460  COMPLEX CZERO
461  parameter( czero = ( 0.0e+0, 0.0e+0 ) )
462  COMPLEX CONE
463  parameter( cone = ( 1.0e+0, 0.0e+0 ) )
464  REAL ZERO, ONE
465  parameter( zero = 0.0e+0, one = 1.0e+0 )
466  INTEGER MAXTYP
467  parameter( maxtyp = 21 )
468 * ..
469 * .. Local Scalars ..
471  CHARACTER*3 PATH
472  INTEGER I, IINFO, IMODE, ISRT, ITYPE, IWK, J, JCOL,
473  \$ jsize, jtype, mtypes, n, nerrs, nfail,
474  \$ nmax, nnwork, nslct, ntest, ntestf, ntestt
475  REAL ANORM, COND, CONDS, OVFL, RCDEIN, RCDVIN,
476  \$ rtulp, rtulpi, ulp, ulpinv, unfl
477 * ..
478 * .. Local Arrays ..
479  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), ISLCT( 20 ),
480  \$ kconds( maxtyp ), kmagn( maxtyp ),
481  \$ kmode( maxtyp ), ktype( maxtyp )
482 * ..
483 * .. Arrays in Common ..
484  LOGICAL SELVAL( 20 )
485  REAL SELWI( 20 ), SELWR( 20 )
486 * ..
487 * .. Scalars in Common ..
488  INTEGER SELDIM, SELOPT
489 * ..
490 * .. Common blocks ..
491  COMMON / sslct / selopt, seldim, selval, selwr, selwi
492 * ..
493 * .. External Functions ..
494  REAL SLAMCH
495  EXTERNAL slamch
496 * ..
497 * .. External Subroutines ..
498  EXTERNAL cget24, clatme, clatmr, clatms, claset, slabad,
499  \$ slasum, xerbla
500 * ..
501 * .. Intrinsic Functions ..
502  INTRINSIC abs, max, min, sqrt
503 * ..
504 * .. Data statements ..
505  DATA ktype / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
506  DATA kmagn / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
507  \$ 3, 1, 2, 3 /
508  DATA kmode / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
509  \$ 1, 5, 5, 5, 4, 3, 1 /
510  DATA kconds / 3*0, 5*0, 4*1, 6*2, 3*0 /
511 * ..
512 * .. Executable Statements ..
513 *
514  path( 1: 1 ) = 'Complex precision'
515  path( 2: 3 ) = 'SX'
516 *
517 * Check for errors
518 *
519  ntestt = 0
520  ntestf = 0
521  info = 0
522 *
523 * Important constants
524 *
526 *
527 * 8 is the largest dimension in the input file of precomputed
528 * problems
529 *
530  nmax = 8
531  DO 10 j = 1, nsizes
532  nmax = max( nmax, nn( j ) )
533  IF( nn( j ).LT.0 )
535  10 CONTINUE
536 *
537 * Check for errors
538 *
539  IF( nsizes.LT.0 ) THEN
540  info = -1
541  ELSE IF( badnn ) THEN
542  info = -2
543  ELSE IF( ntypes.LT.0 ) THEN
544  info = -3
545  ELSE IF( thresh.LT.zero ) THEN
546  info = -6
547  ELSE IF( niunit.LE.0 ) THEN
548  info = -7
549  ELSE IF( nounit.LE.0 ) THEN
550  info = -8
551  ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
552  info = -10
553  ELSE IF( ldvs.LT.1 .OR. ldvs.LT.nmax ) THEN
554  info = -20
555  ELSE IF( max( 3*nmax, 2*nmax**2 ).GT.lwork ) THEN
556  info = -24
557  END IF
558 *
559  IF( info.NE.0 ) THEN
560  CALL xerbla( 'CDRVSX', -info )
561  RETURN
562  END IF
563 *
564 * If nothing to do check on NIUNIT
565 *
566  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
567  \$ GO TO 150
568 *
569 * More Important constants
570 *
571  unfl = slamch( 'Safe minimum' )
572  ovfl = one / unfl
573  CALL slabad( unfl, ovfl )
574  ulp = slamch( 'Precision' )
575  ulpinv = one / ulp
576  rtulp = sqrt( ulp )
577  rtulpi = one / rtulp
578 *
579 * Loop over sizes, types
580 *
581  nerrs = 0
582 *
583  DO 140 jsize = 1, nsizes
584  n = nn( jsize )
585  IF( nsizes.NE.1 ) THEN
586  mtypes = min( maxtyp, ntypes )
587  ELSE
588  mtypes = min( maxtyp+1, ntypes )
589  END IF
590 *
591  DO 130 jtype = 1, mtypes
592  IF( .NOT.dotype( jtype ) )
593  \$ GO TO 130
594 *
595 * Save ISEED in case of an error.
596 *
597  DO 20 j = 1, 4
598  ioldsd( j ) = iseed( j )
599  20 CONTINUE
600 *
601 * Compute "A"
602 *
603 * Control parameters:
604 *
605 * KMAGN KCONDS KMODE KTYPE
606 * =1 O(1) 1 clustered 1 zero
607 * =2 large large clustered 2 identity
608 * =3 small exponential Jordan
609 * =4 arithmetic diagonal, (w/ eigenvalues)
610 * =5 random log symmetric, w/ eigenvalues
611 * =6 random general, w/ eigenvalues
612 * =7 random diagonal
613 * =8 random symmetric
614 * =9 random general
615 * =10 random triangular
616 *
617  IF( mtypes.GT.maxtyp )
618  \$ GO TO 90
619 *
620  itype = ktype( jtype )
621  imode = kmode( jtype )
622 *
623 * Compute norm
624 *
625  GO TO ( 30, 40, 50 )kmagn( jtype )
626 *
627  30 CONTINUE
628  anorm = one
629  GO TO 60
630 *
631  40 CONTINUE
632  anorm = ovfl*ulp
633  GO TO 60
634 *
635  50 CONTINUE
636  anorm = unfl*ulpinv
637  GO TO 60
638 *
639  60 CONTINUE
640 *
641  CALL claset( 'Full', lda, n, czero, czero, a, lda )
642  iinfo = 0
643  cond = ulpinv
644 *
645 * Special Matrices -- Identity & Jordan block
646 *
647  IF( itype.EQ.1 ) THEN
648 *
649 * Zero
650 *
651  iinfo = 0
652 *
653  ELSE IF( itype.EQ.2 ) THEN
654 *
655 * Identity
656 *
657  DO 70 jcol = 1, n
658  a( jcol, jcol ) = anorm
659  70 CONTINUE
660 *
661  ELSE IF( itype.EQ.3 ) THEN
662 *
663 * Jordan Block
664 *
665  DO 80 jcol = 1, n
666  a( jcol, jcol ) = anorm
667  IF( jcol.GT.1 )
668  \$ a( jcol, jcol-1 ) = cone
669  80 CONTINUE
670 *
671  ELSE IF( itype.EQ.4 ) THEN
672 *
673 * Diagonal Matrix, [Eigen]values Specified
674 *
675  CALL clatms( n, n, 'S', iseed, 'H', rwork, imode, cond,
676  \$ anorm, 0, 0, 'N', a, lda, work( n+1 ),
677  \$ iinfo )
678 *
679  ELSE IF( itype.EQ.5 ) THEN
680 *
681 * Symmetric, eigenvalues specified
682 *
683  CALL clatms( n, n, 'S', iseed, 'H', rwork, imode, cond,
684  \$ anorm, n, n, 'N', a, lda, work( n+1 ),
685  \$ iinfo )
686 *
687  ELSE IF( itype.EQ.6 ) THEN
688 *
689 * General, eigenvalues specified
690 *
691  IF( kconds( jtype ).EQ.1 ) THEN
692  conds = one
693  ELSE IF( kconds( jtype ).EQ.2 ) THEN
694  conds = rtulpi
695  ELSE
696  conds = zero
697  END IF
698 *
699  CALL clatme( n, 'D', iseed, work, imode, cond, cone,
700  \$ 'T', 'T', 'T', rwork, 4, conds, n, n, anorm,
701  \$ a, lda, work( 2*n+1 ), iinfo )
702 *
703  ELSE IF( itype.EQ.7 ) THEN
704 *
705 * Diagonal, random eigenvalues
706 *
707  CALL clatmr( n, n, 'D', iseed, 'N', work, 6, one, cone,
708  \$ 'T', 'N', work( n+1 ), 1, one,
709  \$ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
710  \$ zero, anorm, 'NO', a, lda, idumma, iinfo )
711 *
712  ELSE IF( itype.EQ.8 ) THEN
713 *
714 * Symmetric, random eigenvalues
715 *
716  CALL clatmr( n, n, 'D', iseed, 'H', work, 6, one, cone,
717  \$ 'T', 'N', work( n+1 ), 1, one,
718  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
719  \$ zero, anorm, 'NO', a, lda, idumma, iinfo )
720 *
721  ELSE IF( itype.EQ.9 ) THEN
722 *
723 * General, random eigenvalues
724 *
725  CALL clatmr( n, n, 'D', iseed, 'N', work, 6, one, cone,
726  \$ 'T', 'N', work( n+1 ), 1, one,
727  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
728  \$ zero, anorm, 'NO', a, lda, idumma, iinfo )
729  IF( n.GE.4 ) THEN
730  CALL claset( 'Full', 2, n, czero, czero, a, lda )
731  CALL claset( 'Full', n-3, 1, czero, czero, a( 3, 1 ),
732  \$ lda )
733  CALL claset( 'Full', n-3, 2, czero, czero,
734  \$ a( 3, n-1 ), lda )
735  CALL claset( 'Full', 1, n, czero, czero, a( n, 1 ),
736  \$ lda )
737  END IF
738 *
739  ELSE IF( itype.EQ.10 ) THEN
740 *
741 * Triangular, random eigenvalues
742 *
743  CALL clatmr( n, n, 'D', iseed, 'N', work, 6, one, cone,
744  \$ 'T', 'N', work( n+1 ), 1, one,
745  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, 0,
746  \$ zero, anorm, 'NO', a, lda, idumma, iinfo )
747 *
748  ELSE
749 *
750  iinfo = 1
751  END IF
752 *
753  IF( iinfo.NE.0 ) THEN
754  WRITE( nounit, fmt = 9991 )'Generator', iinfo, n, jtype,
755  \$ ioldsd
756  info = abs( iinfo )
757  RETURN
758  END IF
759 *
760  90 CONTINUE
761 *
762 * Test for minimal and generous workspace
763 *
764  DO 120 iwk = 1, 2
765  IF( iwk.EQ.1 ) THEN
766  nnwork = 2*n
767  ELSE
768  nnwork = max( 2*n, n*( n+1 ) / 2 )
769  END IF
770  nnwork = max( nnwork, 1 )
771 *
772  CALL cget24( .false., jtype, thresh, ioldsd, nounit, n,
773  \$ a, lda, h, ht, w, wt, wtmp, vs, ldvs, vs1,
774  \$ rcdein, rcdvin, nslct, islct, 0, result,
775  \$ work, nnwork, rwork, bwork, info )
776 *
777 * Check for RESULT(j) > THRESH
778 *
779  ntest = 0
780  nfail = 0
781  DO 100 j = 1, 15
782  IF( result( j ).GE.zero )
783  \$ ntest = ntest + 1
784  IF( result( j ).GE.thresh )
785  \$ nfail = nfail + 1
786  100 CONTINUE
787 *
788  IF( nfail.GT.0 )
789  \$ ntestf = ntestf + 1
790  IF( ntestf.EQ.1 ) THEN
791  WRITE( nounit, fmt = 9999 )path
792  WRITE( nounit, fmt = 9998 )
793  WRITE( nounit, fmt = 9997 )
794  WRITE( nounit, fmt = 9996 )
795  WRITE( nounit, fmt = 9995 )thresh
796  WRITE( nounit, fmt = 9994 )
797  ntestf = 2
798  END IF
799 *
800  DO 110 j = 1, 15
801  IF( result( j ).GE.thresh ) THEN
802  WRITE( nounit, fmt = 9993 )n, iwk, ioldsd, jtype,
803  \$ j, result( j )
804  END IF
805  110 CONTINUE
806 *
807  nerrs = nerrs + nfail
808  ntestt = ntestt + ntest
809 *
810  120 CONTINUE
811  130 CONTINUE
812  140 CONTINUE
813 *
814  150 CONTINUE
815 *
816 * Read in data from file to check accuracy of condition estimation
817 * Read input data until N=0
818 *
819  jtype = 0
820  160 CONTINUE
821  READ( niunit, fmt = *, end = 200 )n, nslct, isrt
822  IF( n.EQ.0 )
823  \$ GO TO 200
824  jtype = jtype + 1
825  iseed( 1 ) = jtype
826  READ( niunit, fmt = * )( islct( i ), i = 1, nslct )
827  DO 170 i = 1, n
828  READ( niunit, fmt = * )( a( i, j ), j = 1, n )
829  170 CONTINUE
830  READ( niunit, fmt = * )rcdein, rcdvin
831 *
832  CALL cget24( .true., 22, thresh, iseed, nounit, n, a, lda, h, ht,
833  \$ w, wt, wtmp, vs, ldvs, vs1, rcdein, rcdvin, nslct,
834  \$ islct, isrt, result, work, lwork, rwork, bwork,
835  \$ info )
836 *
837 * Check for RESULT(j) > THRESH
838 *
839  ntest = 0
840  nfail = 0
841  DO 180 j = 1, 17
842  IF( result( j ).GE.zero )
843  \$ ntest = ntest + 1
844  IF( result( j ).GE.thresh )
845  \$ nfail = nfail + 1
846  180 CONTINUE
847 *
848  IF( nfail.GT.0 )
849  \$ ntestf = ntestf + 1
850  IF( ntestf.EQ.1 ) THEN
851  WRITE( nounit, fmt = 9999 )path
852  WRITE( nounit, fmt = 9998 )
853  WRITE( nounit, fmt = 9997 )
854  WRITE( nounit, fmt = 9996 )
855  WRITE( nounit, fmt = 9995 )thresh
856  WRITE( nounit, fmt = 9994 )
857  ntestf = 2
858  END IF
859  DO 190 j = 1, 17
860  IF( result( j ).GE.thresh ) THEN
861  WRITE( nounit, fmt = 9992 )n, jtype, j, result( j )
862  END IF
863  190 CONTINUE
864 *
865  nerrs = nerrs + nfail
866  ntestt = ntestt + ntest
867  GO TO 160
868  200 CONTINUE
869 *
870 * Summary
871 *
872  CALL slasum( path, nounit, nerrs, ntestt )
873 *
874  9999 FORMAT( / 1x, a3, ' -- Complex Schur Form Decomposition Expert ',
875  \$ 'Driver', / ' Matrix types (see CDRVSX for details): ' )
876 *
877  9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
878  \$ ' ', ' 5=Diagonal: geometr. spaced entries.',
879  \$ / ' 2=Identity matrix. ', ' 6=Diagona',
880  \$ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
881  \$ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
882  \$ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
883  \$ 'mall, evenly spaced.' )
884  9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
885  \$ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
886  \$ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
887  \$ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
888  \$ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
889  \$ 'lex ', / ' 12=Well-cond., random complex ', ' ',
890  \$ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
891  \$ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
892  \$ ' complx ' )
893  9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
894  \$ 'with small random entries.', / ' 20=Matrix with large ran',
895  \$ 'dom entries. ', / )
896  9995 FORMAT( ' Tests performed with test threshold =', f8.2,
897  \$ / ' ( A denotes A on input and T denotes A on output)',
898  \$ / / ' 1 = 0 if T in Schur form (no sort), ',
899  \$ ' 1/ulp otherwise', /
900  \$ ' 2 = | A - VS T transpose(VS) | / ( n |A| ulp ) (no sort)',
901  \$ / ' 3 = | I - VS transpose(VS) | / ( n ulp ) (no sort) ',
902  \$ / ' 4 = 0 if W are eigenvalues of T (no sort),',
903  \$ ' 1/ulp otherwise', /
904  \$ ' 5 = 0 if T same no matter if VS computed (no sort),',
905  \$ ' 1/ulp otherwise', /
906  \$ ' 6 = 0 if W same no matter if VS computed (no sort)',
907  \$ ', 1/ulp otherwise' )
908  9994 FORMAT( ' 7 = 0 if T in Schur form (sort), ', ' 1/ulp otherwise',
909  \$ / ' 8 = | A - VS T transpose(VS) | / ( n |A| ulp ) (sort)',
910  \$ / ' 9 = | I - VS transpose(VS) | / ( n ulp ) (sort) ',
911  \$ / ' 10 = 0 if W are eigenvalues of T (sort),',
912  \$ ' 1/ulp otherwise', /
913  \$ ' 11 = 0 if T same no matter what else computed (sort),',
914  \$ ' 1/ulp otherwise', /
915  \$ ' 12 = 0 if W same no matter what else computed ',
916  \$ '(sort), 1/ulp otherwise', /
917  \$ ' 13 = 0 if sorting successful, 1/ulp otherwise',
918  \$ / ' 14 = 0 if RCONDE same no matter what else computed,',
919  \$ ' 1/ulp otherwise', /
920  \$ ' 15 = 0 if RCONDv same no matter what else computed,',
921  \$ ' 1/ulp otherwise', /
922  \$ ' 16 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),',
923  \$ / ' 17 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),' )
924  9993 FORMAT( ' N=', i5, ', IWK=', i2, ', seed=', 4( i4, ',' ),
925  \$ ' type ', i2, ', test(', i2, ')=', g10.3 )
926  9992 FORMAT( ' N=', i5, ', input example =', i3, ', test(', i2, ')=',
927  \$ g10.3 )
928  9991 FORMAT( ' CDRVSX: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
929  \$ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
930 *
931  RETURN
932 *
933 * End of CDRVSX
934 *
935  END
subroutine clatme(N, DIST, ISEED, D, MODE, COND, DMAX, RSIGN, UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, A, LDA, WORK, INFO)
CLATME
Definition: clatme.f:303
subroutine clatmr(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)
CLATMR
Definition: clatmr.f:492
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: claset.f:108
subroutine cdrvsx(NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, NIUNIT, NOUNIT, A, LDA, H, HT, W, WT, WTMP, VS, LDVS, VS1, RESULT, WORK, LWORK, RWORK, BWORK, INFO)
CDRVSX
Definition: cdrvsx.f:437
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine cget24(COMP, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA, H, HT, W, WT, WTMP, VS, LDVS, VS1, RCDEIN, RCDVIN, NSLCT, ISLCT, ISRT, RESULT, WORK, LWORK, RWORK, BWORK, INFO)
CGET24
Definition: cget24.f:337