LAPACK  3.6.0
LAPACK: Linear Algebra PACKage
dchkgg.f
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1 *> \brief \b DCHKGG
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 DCHKGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
12 * TSTDIF, THRSHN, NOUNIT, A, LDA, B, H, T, S1,
13 * S2, P1, P2, U, LDU, V, Q, Z, ALPHR1, ALPHI1,
14 * BETA1, ALPHR3, ALPHI3, BETA3, EVECTL, EVECTR,
15 * WORK, LWORK, LLWORK, RESULT, INFO )
16 *
17 * .. Scalar Arguments ..
18 * LOGICAL TSTDIF
19 * INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES
20 * DOUBLE PRECISION THRESH, THRSHN
21 * ..
22 * .. Array Arguments ..
23 * LOGICAL DOTYPE( * ), LLWORK( * )
24 * INTEGER ISEED( 4 ), NN( * )
25 * DOUBLE PRECISION A( LDA, * ), ALPHI1( * ), ALPHI3( * ),
26 * $ ALPHR1( * ), ALPHR3( * ), B( LDA, * ),
27 * $ BETA1( * ), BETA3( * ), EVECTL( LDU, * ),
28 * $ EVECTR( LDU, * ), H( LDA, * ), P1( LDA, * ),
29 * $ P2( LDA, * ), Q( LDU, * ), RESULT( 15 ),
30 * $ S1( LDA, * ), S2( LDA, * ), T( LDA, * ),
31 * $ U( LDU, * ), V( LDU, * ), WORK( * ),
32 * $ Z( LDU, * )
33 * ..
34 *
35 *
36 *> \par Purpose:
37 * =============
38 *>
39 *> \verbatim
40 *>
41 *> DCHKGG checks the nonsymmetric generalized eigenvalue problem
42 *> routines.
43 *> T T T
44 *> DGGHRD factors A and B as U H V and U T V , where means
45 *> transpose, H is hessenberg, T is triangular and U and V are
46 *> orthogonal.
47 *> T T
48 *> DHGEQZ factors H and T as Q S Z and Q P Z , where P is upper
49 *> triangular, S is in generalized Schur form (block upper triangular,
50 *> with 1x1 and 2x2 blocks on the diagonal, the 2x2 blocks
51 *> corresponding to complex conjugate pairs of generalized
52 *> eigenvalues), and Q and Z are orthogonal. It also computes the
53 *> generalized eigenvalues (alpha(1),beta(1)),...,(alpha(n),beta(n)),
54 *> where alpha(j)=S(j,j) and beta(j)=P(j,j) -- thus,
55 *> w(j) = alpha(j)/beta(j) is a root of the generalized eigenvalue
56 *> problem
57 *>
58 *> det( A - w(j) B ) = 0
59 *>
60 *> and m(j) = beta(j)/alpha(j) is a root of the essentially equivalent
61 *> problem
62 *>
63 *> det( m(j) A - B ) = 0
64 *>
65 *> DTGEVC computes the matrix L of left eigenvectors and the matrix R
66 *> of right eigenvectors for the matrix pair ( S, P ). In the
67 *> description below, l and r are left and right eigenvectors
68 *> corresponding to the generalized eigenvalues (alpha,beta).
69 *>
70 *> When DCHKGG is called, a number of matrix "sizes" ("n's") and a
71 *> number of matrix "types" are specified. For each size ("n")
72 *> and each type of matrix, one matrix will be generated and used
73 *> to test the nonsymmetric eigenroutines. For each matrix, 15
74 *> tests will be performed. The first twelve "test ratios" should be
75 *> small -- O(1). They will be compared with the threshhold THRESH:
76 *>
77 *> T
78 *> (1) | A - U H V | / ( |A| n ulp )
79 *>
80 *> T
81 *> (2) | B - U T V | / ( |B| n ulp )
82 *>
83 *> T
84 *> (3) | I - UU | / ( n ulp )
85 *>
86 *> T
87 *> (4) | I - VV | / ( n ulp )
88 *>
89 *> T
90 *> (5) | H - Q S Z | / ( |H| n ulp )
91 *>
92 *> T
93 *> (6) | T - Q P Z | / ( |T| n ulp )
94 *>
95 *> T
96 *> (7) | I - QQ | / ( n ulp )
97 *>
98 *> T
99 *> (8) | I - ZZ | / ( n ulp )
100 *>
101 *> (9) max over all left eigenvalue/-vector pairs (beta/alpha,l) of
102 *>
103 *> | l**H * (beta S - alpha P) | / ( ulp max( |beta S|, |alpha P| ) )
104 *>
105 *> (10) max over all left eigenvalue/-vector pairs (beta/alpha,l') of
106 *> T
107 *> | l'**H * (beta H - alpha T) | / ( ulp max( |beta H|, |alpha T| ) )
108 *>
109 *> where the eigenvectors l' are the result of passing Q to
110 *> DTGEVC and back transforming (HOWMNY='B').
111 *>
112 *> (11) max over all right eigenvalue/-vector pairs (beta/alpha,r) of
113 *>
114 *> | (beta S - alpha T) r | / ( ulp max( |beta S|, |alpha T| ) )
115 *>
116 *> (12) max over all right eigenvalue/-vector pairs (beta/alpha,r') of
117 *>
118 *> | (beta H - alpha T) r' | / ( ulp max( |beta H|, |alpha T| ) )
119 *>
120 *> where the eigenvectors r' are the result of passing Z to
121 *> DTGEVC and back transforming (HOWMNY='B').
122 *>
123 *> The last three test ratios will usually be small, but there is no
124 *> mathematical requirement that they be so. They are therefore
125 *> compared with THRESH only if TSTDIF is .TRUE.
126 *>
127 *> (13) | S(Q,Z computed) - S(Q,Z not computed) | / ( |S| ulp )
128 *>
129 *> (14) | P(Q,Z computed) - P(Q,Z not computed) | / ( |P| ulp )
130 *>
131 *> (15) max( |alpha(Q,Z computed) - alpha(Q,Z not computed)|/|S| ,
132 *> |beta(Q,Z computed) - beta(Q,Z not computed)|/|P| ) / ulp
133 *>
134 *> In addition, the normalization of L and R are checked, and compared
135 *> with the threshhold THRSHN.
136 *>
137 *> Test Matrices
138 *> ---- --------
139 *>
140 *> The sizes of the test matrices are specified by an array
141 *> NN(1:NSIZES); the value of each element NN(j) specifies one size.
142 *> The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if
143 *> DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
144 *> Currently, the list of possible types is:
145 *>
146 *> (1) ( 0, 0 ) (a pair of zero matrices)
147 *>
148 *> (2) ( I, 0 ) (an identity and a zero matrix)
149 *>
150 *> (3) ( 0, I ) (an identity and a zero matrix)
151 *>
152 *> (4) ( I, I ) (a pair of identity matrices)
153 *>
154 *> t t
155 *> (5) ( J , J ) (a pair of transposed Jordan blocks)
156 *>
157 *> t ( I 0 )
158 *> (6) ( X, Y ) where X = ( J 0 ) and Y = ( t )
159 *> ( 0 I ) ( 0 J )
160 *> and I is a k x k identity and J a (k+1)x(k+1)
161 *> Jordan block; k=(N-1)/2
162 *>
163 *> (7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal
164 *> matrix with those diagonal entries.)
165 *> (8) ( I, D )
166 *>
167 *> (9) ( big*D, small*I ) where "big" is near overflow and small=1/big
168 *>
169 *> (10) ( small*D, big*I )
170 *>
171 *> (11) ( big*I, small*D )
172 *>
173 *> (12) ( small*I, big*D )
174 *>
175 *> (13) ( big*D, big*I )
176 *>
177 *> (14) ( small*D, small*I )
178 *>
179 *> (15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and
180 *> D2 is diag( 0, N-3, N-4,..., 1, 0, 0 )
181 *> t t
182 *> (16) U ( J , J ) V where U and V are random orthogonal matrices.
183 *>
184 *> (17) U ( T1, T2 ) V where T1 and T2 are upper triangular matrices
185 *> with random O(1) entries above the diagonal
186 *> and diagonal entries diag(T1) =
187 *> ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) =
188 *> ( 0, N-3, N-4,..., 1, 0, 0 )
189 *>
190 *> (18) U ( T1, T2 ) V diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 )
191 *> diag(T2) = ( 0, 1, 0, 1,..., 1, 0 )
192 *> s = machine precision.
193 *>
194 *> (19) U ( T1, T2 ) V diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 )
195 *> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 )
196 *>
197 *> N-5
198 *> (20) U ( T1, T2 ) V diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 )
199 *> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
200 *>
201 *> (21) U ( T1, T2 ) V diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 )
202 *> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
203 *> where r1,..., r(N-4) are random.
204 *>
205 *> (22) U ( big*T1, small*T2 ) V diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
206 *> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
207 *>
208 *> (23) U ( small*T1, big*T2 ) V diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
209 *> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
210 *>
211 *> (24) U ( small*T1, small*T2 ) V diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
212 *> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
213 *>
214 *> (25) U ( big*T1, big*T2 ) V diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
215 *> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
216 *>
217 *> (26) U ( T1, T2 ) V where T1 and T2 are random upper-triangular
218 *> matrices.
219 *> \endverbatim
220 *
221 * Arguments:
222 * ==========
223 *
224 *> \param[in] NSIZES
225 *> \verbatim
226 *> NSIZES is INTEGER
227 *> The number of sizes of matrices to use. If it is zero,
228 *> DCHKGG does nothing. It must be at least zero.
229 *> \endverbatim
230 *>
231 *> \param[in] NN
232 *> \verbatim
233 *> NN is INTEGER array, dimension (NSIZES)
234 *> An array containing the sizes to be used for the matrices.
235 *> Zero values will be skipped. The values must be at least
236 *> zero.
237 *> \endverbatim
238 *>
239 *> \param[in] NTYPES
240 *> \verbatim
241 *> NTYPES is INTEGER
242 *> The number of elements in DOTYPE. If it is zero, DCHKGG
243 *> does nothing. It must be at least zero. If it is MAXTYP+1
244 *> and NSIZES is 1, then an additional type, MAXTYP+1 is
245 *> defined, which is to use whatever matrix is in A. This
246 *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
247 *> DOTYPE(MAXTYP+1) is .TRUE. .
248 *> \endverbatim
249 *>
250 *> \param[in] DOTYPE
251 *> \verbatim
252 *> DOTYPE is LOGICAL array, dimension (NTYPES)
253 *> If DOTYPE(j) is .TRUE., then for each size in NN a
254 *> matrix of that size and of type j will be generated.
255 *> If NTYPES is smaller than the maximum number of types
256 *> defined (PARAMETER MAXTYP), then types NTYPES+1 through
257 *> MAXTYP will not be generated. If NTYPES is larger
258 *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
259 *> will be ignored.
260 *> \endverbatim
261 *>
262 *> \param[in,out] ISEED
263 *> \verbatim
264 *> ISEED is INTEGER array, dimension (4)
265 *> On entry ISEED specifies the seed of the random number
266 *> generator. The array elements should be between 0 and 4095;
267 *> if not they will be reduced mod 4096. Also, ISEED(4) must
268 *> be odd. The random number generator uses a linear
269 *> congruential sequence limited to small integers, and so
270 *> should produce machine independent random numbers. The
271 *> values of ISEED are changed on exit, and can be used in the
272 *> next call to DCHKGG to continue the same random number
273 *> sequence.
274 *> \endverbatim
275 *>
276 *> \param[in] THRESH
277 *> \verbatim
278 *> THRESH is DOUBLE PRECISION
279 *> A test will count as "failed" if the "error", computed as
280 *> described above, exceeds THRESH. Note that the error is
281 *> scaled to be O(1), so THRESH should be a reasonably small
282 *> multiple of 1, e.g., 10 or 100. In particular, it should
283 *> not depend on the precision (single vs. double) or the size
284 *> of the matrix. It must be at least zero.
285 *> \endverbatim
286 *>
287 *> \param[in] TSTDIF
288 *> \verbatim
289 *> TSTDIF is LOGICAL
290 *> Specifies whether test ratios 13-15 will be computed and
291 *> compared with THRESH.
292 *> = .FALSE.: Only test ratios 1-12 will be computed and tested.
293 *> Ratios 13-15 will be set to zero.
294 *> = .TRUE.: All the test ratios 1-15 will be computed and
295 *> tested.
296 *> \endverbatim
297 *>
298 *> \param[in] THRSHN
299 *> \verbatim
300 *> THRSHN is DOUBLE PRECISION
301 *> Threshhold for reporting eigenvector normalization error.
302 *> If the normalization of any eigenvector differs from 1 by
303 *> more than THRSHN*ulp, then a special error message will be
304 *> printed. (This is handled separately from the other tests,
305 *> since only a compiler or programming error should cause an
306 *> error message, at least if THRSHN is at least 5--10.)
307 *> \endverbatim
308 *>
309 *> \param[in] NOUNIT
310 *> \verbatim
311 *> NOUNIT is INTEGER
312 *> The FORTRAN unit number for printing out error messages
313 *> (e.g., if a routine returns IINFO not equal to 0.)
314 *> \endverbatim
315 *>
316 *> \param[in,out] A
317 *> \verbatim
318 *> A is DOUBLE PRECISION array, dimension
319 *> (LDA, max(NN))
320 *> Used to hold the original A matrix. Used as input only
321 *> if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
322 *> DOTYPE(MAXTYP+1)=.TRUE.
323 *> \endverbatim
324 *>
325 *> \param[in] LDA
326 *> \verbatim
327 *> LDA is INTEGER
328 *> The leading dimension of A, B, H, T, S1, P1, S2, and P2.
329 *> It must be at least 1 and at least max( NN ).
330 *> \endverbatim
331 *>
332 *> \param[in,out] B
333 *> \verbatim
334 *> B is DOUBLE PRECISION array, dimension
335 *> (LDA, max(NN))
336 *> Used to hold the original B matrix. Used as input only
337 *> if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
338 *> DOTYPE(MAXTYP+1)=.TRUE.
339 *> \endverbatim
340 *>
341 *> \param[out] H
342 *> \verbatim
343 *> H is DOUBLE PRECISION array, dimension (LDA, max(NN))
344 *> The upper Hessenberg matrix computed from A by DGGHRD.
345 *> \endverbatim
346 *>
347 *> \param[out] T
348 *> \verbatim
349 *> T is DOUBLE PRECISION array, dimension (LDA, max(NN))
350 *> The upper triangular matrix computed from B by DGGHRD.
351 *> \endverbatim
352 *>
353 *> \param[out] S1
354 *> \verbatim
355 *> S1 is DOUBLE PRECISION array, dimension (LDA, max(NN))
356 *> The Schur (block upper triangular) matrix computed from H by
357 *> DHGEQZ when Q and Z are also computed.
358 *> \endverbatim
359 *>
360 *> \param[out] S2
361 *> \verbatim
362 *> S2 is DOUBLE PRECISION array, dimension (LDA, max(NN))
363 *> The Schur (block upper triangular) matrix computed from H by
364 *> DHGEQZ when Q and Z are not computed.
365 *> \endverbatim
366 *>
367 *> \param[out] P1
368 *> \verbatim
369 *> P1 is DOUBLE PRECISION array, dimension (LDA, max(NN))
370 *> The upper triangular matrix computed from T by DHGEQZ
371 *> when Q and Z are also computed.
372 *> \endverbatim
373 *>
374 *> \param[out] P2
375 *> \verbatim
376 *> P2 is DOUBLE PRECISION array, dimension (LDA, max(NN))
377 *> The upper triangular matrix computed from T by DHGEQZ
378 *> when Q and Z are not computed.
379 *> \endverbatim
380 *>
381 *> \param[out] U
382 *> \verbatim
383 *> U is DOUBLE PRECISION array, dimension (LDU, max(NN))
384 *> The (left) orthogonal matrix computed by DGGHRD.
385 *> \endverbatim
386 *>
387 *> \param[in] LDU
388 *> \verbatim
389 *> LDU is INTEGER
390 *> The leading dimension of U, V, Q, Z, EVECTL, and EVEZTR. It
391 *> must be at least 1 and at least max( NN ).
392 *> \endverbatim
393 *>
394 *> \param[out] V
395 *> \verbatim
396 *> V is DOUBLE PRECISION array, dimension (LDU, max(NN))
397 *> The (right) orthogonal matrix computed by DGGHRD.
398 *> \endverbatim
399 *>
400 *> \param[out] Q
401 *> \verbatim
402 *> Q is DOUBLE PRECISION array, dimension (LDU, max(NN))
403 *> The (left) orthogonal matrix computed by DHGEQZ.
404 *> \endverbatim
405 *>
406 *> \param[out] Z
407 *> \verbatim
408 *> Z is DOUBLE PRECISION array, dimension (LDU, max(NN))
409 *> The (left) orthogonal matrix computed by DHGEQZ.
410 *> \endverbatim
411 *>
412 *> \param[out] ALPHR1
413 *> \verbatim
414 *> ALPHR1 is DOUBLE PRECISION array, dimension (max(NN))
415 *> \endverbatim
416 *>
417 *> \param[out] ALPHI1
418 *> \verbatim
419 *> ALPHI1 is DOUBLE PRECISION array, dimension (max(NN))
420 *> \endverbatim
421 *>
422 *> \param[out] BETA1
423 *> \verbatim
424 *> BETA1 is DOUBLE PRECISION array, dimension (max(NN))
425 *>
426 *> The generalized eigenvalues of (A,B) computed by DHGEQZ
427 *> when Q, Z, and the full Schur matrices are computed.
428 *> On exit, ( ALPHR1(k)+ALPHI1(k)*i ) / BETA1(k) is the k-th
429 *> generalized eigenvalue of the matrices in A and B.
430 *> \endverbatim
431 *>
432 *> \param[out] ALPHR3
433 *> \verbatim
434 *> ALPHR3 is DOUBLE PRECISION array, dimension (max(NN))
435 *> \endverbatim
436 *>
437 *> \param[out] ALPHI3
438 *> \verbatim
439 *> ALPHI3 is DOUBLE PRECISION array, dimension (max(NN))
440 *> \endverbatim
441 *>
442 *> \param[out] BETA3
443 *> \verbatim
444 *> BETA3 is DOUBLE PRECISION array, dimension (max(NN))
445 *> \endverbatim
446 *>
447 *> \param[out] EVECTL
448 *> \verbatim
449 *> EVECTL is DOUBLE PRECISION array, dimension (LDU, max(NN))
450 *> The (block lower triangular) left eigenvector matrix for
451 *> the matrices in S1 and P1. (See DTGEVC for the format.)
452 *> \endverbatim
453 *>
454 *> \param[out] EVECTR
455 *> \verbatim
456 *> EVECTR is DOUBLE PRECISION array, dimension (LDU, max(NN))
457 *> The (block upper triangular) right eigenvector matrix for
458 *> the matrices in S1 and P1. (See DTGEVC for the format.)
459 *> \endverbatim
460 *>
461 *> \param[out] WORK
462 *> \verbatim
463 *> WORK is DOUBLE PRECISION array, dimension (LWORK)
464 *> \endverbatim
465 *>
466 *> \param[in] LWORK
467 *> \verbatim
468 *> LWORK is INTEGER
469 *> The number of entries in WORK. This must be at least
470 *> max( 2 * N**2, 6*N, 1 ), for all N=NN(j).
471 *> \endverbatim
472 *>
473 *> \param[out] LLWORK
474 *> \verbatim
475 *> LLWORK is LOGICAL array, dimension (max(NN))
476 *> \endverbatim
477 *>
478 *> \param[out] RESULT
479 *> \verbatim
480 *> RESULT is DOUBLE PRECISION array, dimension (15)
481 *> The values computed by the tests described above.
482 *> The values are currently limited to 1/ulp, to avoid
483 *> overflow.
484 *> \endverbatim
485 *>
486 *> \param[out] INFO
487 *> \verbatim
488 *> INFO is INTEGER
489 *> = 0: successful exit
490 *> < 0: if INFO = -i, the i-th argument had an illegal value
491 *> > 0: A routine returned an error code. INFO is the
492 *> absolute value of the INFO value returned.
493 *> \endverbatim
494 *
495 * Authors:
496 * ========
497 *
498 *> \author Univ. of Tennessee
499 *> \author Univ. of California Berkeley
500 *> \author Univ. of Colorado Denver
501 *> \author NAG Ltd.
502 *
503 *> \date November 2011
504 *
505 *> \ingroup double_eig
506 *
507 * =====================================================================
508  SUBROUTINE dchkgg( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
509  $ tstdif, thrshn, nounit, a, lda, b, h, t, s1,
510  $ s2, p1, p2, u, ldu, v, q, z, alphr1, alphi1,
511  $ beta1, alphr3, alphi3, beta3, evectl, evectr,
512  $ work, lwork, llwork, result, info )
513 *
514 * -- LAPACK test routine (version 3.4.0) --
515 * -- LAPACK is a software package provided by Univ. of Tennessee, --
516 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
517 * November 2011
518 *
519 * .. Scalar Arguments ..
520  LOGICAL TSTDIF
521  INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES
522  DOUBLE PRECISION THRESH, THRSHN
523 * ..
524 * .. Array Arguments ..
525  LOGICAL DOTYPE( * ), LLWORK( * )
526  INTEGER ISEED( 4 ), NN( * )
527  DOUBLE PRECISION A( lda, * ), ALPHI1( * ), ALPHI3( * ),
528  $ alphr1( * ), alphr3( * ), b( lda, * ),
529  $ beta1( * ), beta3( * ), evectl( ldu, * ),
530  $ evectr( ldu, * ), h( lda, * ), p1( lda, * ),
531  $ p2( lda, * ), q( ldu, * ), result( 15 ),
532  $ s1( lda, * ), s2( lda, * ), t( lda, * ),
533  $ u( ldu, * ), v( ldu, * ), work( * ),
534  $ z( ldu, * )
535 * ..
536 *
537 * =====================================================================
538 *
539 * .. Parameters ..
540  DOUBLE PRECISION ZERO, ONE
541  parameter( zero = 0.0d0, one = 1.0d0 )
542  INTEGER MAXTYP
543  parameter( maxtyp = 26 )
544 * ..
545 * .. Local Scalars ..
546  LOGICAL BADNN
547  INTEGER I1, IADD, IINFO, IN, J, JC, JR, JSIZE, JTYPE,
548  $ lwkopt, mtypes, n, n1, nerrs, nmats, nmax,
549  $ ntest, ntestt
550  DOUBLE PRECISION ANORM, BNORM, SAFMAX, SAFMIN, TEMP1, TEMP2,
551  $ ulp, ulpinv
552 * ..
553 * .. Local Arrays ..
554  INTEGER IASIGN( maxtyp ), IBSIGN( maxtyp ),
555  $ ioldsd( 4 ), kadd( 6 ), kamagn( maxtyp ),
556  $ katype( maxtyp ), kazero( maxtyp ),
557  $ kbmagn( maxtyp ), kbtype( maxtyp ),
558  $ kbzero( maxtyp ), kclass( maxtyp ),
559  $ ktrian( maxtyp ), kz1( 6 ), kz2( 6 )
560  DOUBLE PRECISION DUMMA( 4 ), RMAGN( 0: 3 )
561 * ..
562 * .. External Functions ..
563  DOUBLE PRECISION DLAMCH, DLANGE, DLARND
564  EXTERNAL dlamch, dlange, dlarnd
565 * ..
566 * .. External Subroutines ..
567  EXTERNAL dgeqr2, dget51, dget52, dgghrd, dhgeqz, dlabad,
569  $ dtgevc, xerbla
570 * ..
571 * .. Intrinsic Functions ..
572  INTRINSIC abs, dble, max, min, sign
573 * ..
574 * .. Data statements ..
575  DATA kclass / 15*1, 10*2, 1*3 /
576  DATA kz1 / 0, 1, 2, 1, 3, 3 /
577  DATA kz2 / 0, 0, 1, 2, 1, 1 /
578  DATA kadd / 0, 0, 0, 0, 3, 2 /
579  DATA katype / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4,
580  $ 4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 /
581  DATA kbtype / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4,
582  $ 1, 1, -4, 2, -4, 8*8, 0 /
583  DATA kazero / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3,
584  $ 4*5, 4*3, 1 /
585  DATA kbzero / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4,
586  $ 4*6, 4*4, 1 /
587  DATA kamagn / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3,
588  $ 2, 1 /
589  DATA kbmagn / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3,
590  $ 2, 1 /
591  DATA ktrian / 16*0, 10*1 /
592  DATA iasign / 6*0, 2, 0, 2*2, 2*0, 3*2, 0, 2, 3*0,
593  $ 5*2, 0 /
594  DATA ibsign / 7*0, 2, 2*0, 2*2, 2*0, 2, 0, 2, 9*0 /
595 * ..
596 * .. Executable Statements ..
597 *
598 * Check for errors
599 *
600  info = 0
601 *
602  badnn = .false.
603  nmax = 1
604  DO 10 j = 1, nsizes
605  nmax = max( nmax, nn( j ) )
606  IF( nn( j ).LT.0 )
607  $ badnn = .true.
608  10 CONTINUE
609 *
610 * Maximum blocksize and shift -- we assume that blocksize and number
611 * of shifts are monotone increasing functions of N.
612 *
613  lwkopt = max( 6*nmax, 2*nmax*nmax, 1 )
614 *
615 * Check for errors
616 *
617  IF( nsizes.LT.0 ) THEN
618  info = -1
619  ELSE IF( badnn ) THEN
620  info = -2
621  ELSE IF( ntypes.LT.0 ) THEN
622  info = -3
623  ELSE IF( thresh.LT.zero ) THEN
624  info = -6
625  ELSE IF( lda.LE.1 .OR. lda.LT.nmax ) THEN
626  info = -10
627  ELSE IF( ldu.LE.1 .OR. ldu.LT.nmax ) THEN
628  info = -19
629  ELSE IF( lwkopt.GT.lwork ) THEN
630  info = -30
631  END IF
632 *
633  IF( info.NE.0 ) THEN
634  CALL xerbla( 'DCHKGG', -info )
635  RETURN
636  END IF
637 *
638 * Quick return if possible
639 *
640  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
641  $ RETURN
642 *
643  safmin = dlamch( 'Safe minimum' )
644  ulp = dlamch( 'Epsilon' )*dlamch( 'Base' )
645  safmin = safmin / ulp
646  safmax = one / safmin
647  CALL dlabad( safmin, safmax )
648  ulpinv = one / ulp
649 *
650 * The values RMAGN(2:3) depend on N, see below.
651 *
652  rmagn( 0 ) = zero
653  rmagn( 1 ) = one
654 *
655 * Loop over sizes, types
656 *
657  ntestt = 0
658  nerrs = 0
659  nmats = 0
660 *
661  DO 240 jsize = 1, nsizes
662  n = nn( jsize )
663  n1 = max( 1, n )
664  rmagn( 2 ) = safmax*ulp / dble( n1 )
665  rmagn( 3 ) = safmin*ulpinv*n1
666 *
667  IF( nsizes.NE.1 ) THEN
668  mtypes = min( maxtyp, ntypes )
669  ELSE
670  mtypes = min( maxtyp+1, ntypes )
671  END IF
672 *
673  DO 230 jtype = 1, mtypes
674  IF( .NOT.dotype( jtype ) )
675  $ GO TO 230
676  nmats = nmats + 1
677  ntest = 0
678 *
679 * Save ISEED in case of an error.
680 *
681  DO 20 j = 1, 4
682  ioldsd( j ) = iseed( j )
683  20 CONTINUE
684 *
685 * Initialize RESULT
686 *
687  DO 30 j = 1, 15
688  result( j ) = zero
689  30 CONTINUE
690 *
691 * Compute A and B
692 *
693 * Description of control parameters:
694 *
695 * KZLASS: =1 means w/o rotation, =2 means w/ rotation,
696 * =3 means random.
697 * KATYPE: the "type" to be passed to DLATM4 for computing A.
698 * KAZERO: the pattern of zeros on the diagonal for A:
699 * =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
700 * =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
701 * =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of
702 * non-zero entries.)
703 * KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
704 * =2: large, =3: small.
705 * IASIGN: 1 if the diagonal elements of A are to be
706 * multiplied by a random magnitude 1 number, =2 if
707 * randomly chosen diagonal blocks are to be rotated
708 * to form 2x2 blocks.
709 * KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B.
710 * KTRIAN: =0: don't fill in the upper triangle, =1: do.
711 * KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
712 * RMAGN: used to implement KAMAGN and KBMAGN.
713 *
714  IF( mtypes.GT.maxtyp )
715  $ GO TO 110
716  iinfo = 0
717  IF( kclass( jtype ).LT.3 ) THEN
718 *
719 * Generate A (w/o rotation)
720 *
721  IF( abs( katype( jtype ) ).EQ.3 ) THEN
722  in = 2*( ( n-1 ) / 2 ) + 1
723  IF( in.NE.n )
724  $ CALL dlaset( 'Full', n, n, zero, zero, a, lda )
725  ELSE
726  in = n
727  END IF
728  CALL dlatm4( katype( jtype ), in, kz1( kazero( jtype ) ),
729  $ kz2( kazero( jtype ) ), iasign( jtype ),
730  $ rmagn( kamagn( jtype ) ), ulp,
731  $ rmagn( ktrian( jtype )*kamagn( jtype ) ), 2,
732  $ iseed, a, lda )
733  iadd = kadd( kazero( jtype ) )
734  IF( iadd.GT.0 .AND. iadd.LE.n )
735  $ a( iadd, iadd ) = rmagn( kamagn( jtype ) )
736 *
737 * Generate B (w/o rotation)
738 *
739  IF( abs( kbtype( jtype ) ).EQ.3 ) THEN
740  in = 2*( ( n-1 ) / 2 ) + 1
741  IF( in.NE.n )
742  $ CALL dlaset( 'Full', n, n, zero, zero, b, lda )
743  ELSE
744  in = n
745  END IF
746  CALL dlatm4( kbtype( jtype ), in, kz1( kbzero( jtype ) ),
747  $ kz2( kbzero( jtype ) ), ibsign( jtype ),
748  $ rmagn( kbmagn( jtype ) ), one,
749  $ rmagn( ktrian( jtype )*kbmagn( jtype ) ), 2,
750  $ iseed, b, lda )
751  iadd = kadd( kbzero( jtype ) )
752  IF( iadd.NE.0 .AND. iadd.LE.n )
753  $ b( iadd, iadd ) = rmagn( kbmagn( jtype ) )
754 *
755  IF( kclass( jtype ).EQ.2 .AND. n.GT.0 ) THEN
756 *
757 * Include rotations
758 *
759 * Generate U, V as Householder transformations times
760 * a diagonal matrix.
761 *
762  DO 50 jc = 1, n - 1
763  DO 40 jr = jc, n
764  u( jr, jc ) = dlarnd( 3, iseed )
765  v( jr, jc ) = dlarnd( 3, iseed )
766  40 CONTINUE
767  CALL dlarfg( n+1-jc, u( jc, jc ), u( jc+1, jc ), 1,
768  $ work( jc ) )
769  work( 2*n+jc ) = sign( one, u( jc, jc ) )
770  u( jc, jc ) = one
771  CALL dlarfg( n+1-jc, v( jc, jc ), v( jc+1, jc ), 1,
772  $ work( n+jc ) )
773  work( 3*n+jc ) = sign( one, v( jc, jc ) )
774  v( jc, jc ) = one
775  50 CONTINUE
776  u( n, n ) = one
777  work( n ) = zero
778  work( 3*n ) = sign( one, dlarnd( 2, iseed ) )
779  v( n, n ) = one
780  work( 2*n ) = zero
781  work( 4*n ) = sign( one, dlarnd( 2, iseed ) )
782 *
783 * Apply the diagonal matrices
784 *
785  DO 70 jc = 1, n
786  DO 60 jr = 1, n
787  a( jr, jc ) = work( 2*n+jr )*work( 3*n+jc )*
788  $ a( jr, jc )
789  b( jr, jc ) = work( 2*n+jr )*work( 3*n+jc )*
790  $ b( jr, jc )
791  60 CONTINUE
792  70 CONTINUE
793  CALL dorm2r( 'L', 'N', n, n, n-1, u, ldu, work, a,
794  $ lda, work( 2*n+1 ), iinfo )
795  IF( iinfo.NE.0 )
796  $ GO TO 100
797  CALL dorm2r( 'R', 'T', n, n, n-1, v, ldu, work( n+1 ),
798  $ a, lda, work( 2*n+1 ), iinfo )
799  IF( iinfo.NE.0 )
800  $ GO TO 100
801  CALL dorm2r( 'L', 'N', n, n, n-1, u, ldu, work, b,
802  $ lda, work( 2*n+1 ), iinfo )
803  IF( iinfo.NE.0 )
804  $ GO TO 100
805  CALL dorm2r( 'R', 'T', n, n, n-1, v, ldu, work( n+1 ),
806  $ b, lda, work( 2*n+1 ), iinfo )
807  IF( iinfo.NE.0 )
808  $ GO TO 100
809  END IF
810  ELSE
811 *
812 * Random matrices
813 *
814  DO 90 jc = 1, n
815  DO 80 jr = 1, n
816  a( jr, jc ) = rmagn( kamagn( jtype ) )*
817  $ dlarnd( 2, iseed )
818  b( jr, jc ) = rmagn( kbmagn( jtype ) )*
819  $ dlarnd( 2, iseed )
820  80 CONTINUE
821  90 CONTINUE
822  END IF
823 *
824  anorm = dlange( '1', n, n, a, lda, work )
825  bnorm = dlange( '1', n, n, b, lda, work )
826 *
827  100 CONTINUE
828 *
829  IF( iinfo.NE.0 ) THEN
830  WRITE( nounit, fmt = 9999 )'Generator', iinfo, n, jtype,
831  $ ioldsd
832  info = abs( iinfo )
833  RETURN
834  END IF
835 *
836  110 CONTINUE
837 *
838 * Call DGEQR2, DORM2R, and DGGHRD to compute H, T, U, and V
839 *
840  CALL dlacpy( ' ', n, n, a, lda, h, lda )
841  CALL dlacpy( ' ', n, n, b, lda, t, lda )
842  ntest = 1
843  result( 1 ) = ulpinv
844 *
845  CALL dgeqr2( n, n, t, lda, work, work( n+1 ), iinfo )
846  IF( iinfo.NE.0 ) THEN
847  WRITE( nounit, fmt = 9999 )'DGEQR2', iinfo, n, jtype,
848  $ ioldsd
849  info = abs( iinfo )
850  GO TO 210
851  END IF
852 *
853  CALL dorm2r( 'L', 'T', n, n, n, t, lda, work, h, lda,
854  $ work( n+1 ), iinfo )
855  IF( iinfo.NE.0 ) THEN
856  WRITE( nounit, fmt = 9999 )'DORM2R', iinfo, n, jtype,
857  $ ioldsd
858  info = abs( iinfo )
859  GO TO 210
860  END IF
861 *
862  CALL dlaset( 'Full', n, n, zero, one, u, ldu )
863  CALL dorm2r( 'R', 'N', n, n, n, t, lda, work, u, ldu,
864  $ work( n+1 ), iinfo )
865  IF( iinfo.NE.0 ) THEN
866  WRITE( nounit, fmt = 9999 )'DORM2R', iinfo, n, jtype,
867  $ ioldsd
868  info = abs( iinfo )
869  GO TO 210
870  END IF
871 *
872  CALL dgghrd( 'V', 'I', n, 1, n, h, lda, t, lda, u, ldu, v,
873  $ ldu, iinfo )
874  IF( iinfo.NE.0 ) THEN
875  WRITE( nounit, fmt = 9999 )'DGGHRD', iinfo, n, jtype,
876  $ ioldsd
877  info = abs( iinfo )
878  GO TO 210
879  END IF
880  ntest = 4
881 *
882 * Do tests 1--4
883 *
884  CALL dget51( 1, n, a, lda, h, lda, u, ldu, v, ldu, work,
885  $ result( 1 ) )
886  CALL dget51( 1, n, b, lda, t, lda, u, ldu, v, ldu, work,
887  $ result( 2 ) )
888  CALL dget51( 3, n, b, lda, t, lda, u, ldu, u, ldu, work,
889  $ result( 3 ) )
890  CALL dget51( 3, n, b, lda, t, lda, v, ldu, v, ldu, work,
891  $ result( 4 ) )
892 *
893 * Call DHGEQZ to compute S1, P1, S2, P2, Q, and Z, do tests.
894 *
895 * Compute T1 and UZ
896 *
897 * Eigenvalues only
898 *
899  CALL dlacpy( ' ', n, n, h, lda, s2, lda )
900  CALL dlacpy( ' ', n, n, t, lda, p2, lda )
901  ntest = 5
902  result( 5 ) = ulpinv
903 *
904  CALL dhgeqz( 'E', 'N', 'N', n, 1, n, s2, lda, p2, lda,
905  $ alphr3, alphi3, beta3, q, ldu, z, ldu, work,
906  $ lwork, iinfo )
907  IF( iinfo.NE.0 ) THEN
908  WRITE( nounit, fmt = 9999 )'DHGEQZ(E)', iinfo, n, jtype,
909  $ ioldsd
910  info = abs( iinfo )
911  GO TO 210
912  END IF
913 *
914 * Eigenvalues and Full Schur Form
915 *
916  CALL dlacpy( ' ', n, n, h, lda, s2, lda )
917  CALL dlacpy( ' ', n, n, t, lda, p2, lda )
918 *
919  CALL dhgeqz( 'S', 'N', 'N', n, 1, n, s2, lda, p2, lda,
920  $ alphr1, alphi1, beta1, q, ldu, z, ldu, work,
921  $ lwork, iinfo )
922  IF( iinfo.NE.0 ) THEN
923  WRITE( nounit, fmt = 9999 )'DHGEQZ(S)', iinfo, n, jtype,
924  $ ioldsd
925  info = abs( iinfo )
926  GO TO 210
927  END IF
928 *
929 * Eigenvalues, Schur Form, and Schur Vectors
930 *
931  CALL dlacpy( ' ', n, n, h, lda, s1, lda )
932  CALL dlacpy( ' ', n, n, t, lda, p1, lda )
933 *
934  CALL dhgeqz( 'S', 'I', 'I', n, 1, n, s1, lda, p1, lda,
935  $ alphr1, alphi1, beta1, q, ldu, z, ldu, work,
936  $ lwork, iinfo )
937  IF( iinfo.NE.0 ) THEN
938  WRITE( nounit, fmt = 9999 )'DHGEQZ(V)', iinfo, n, jtype,
939  $ ioldsd
940  info = abs( iinfo )
941  GO TO 210
942  END IF
943 *
944  ntest = 8
945 *
946 * Do Tests 5--8
947 *
948  CALL dget51( 1, n, h, lda, s1, lda, q, ldu, z, ldu, work,
949  $ result( 5 ) )
950  CALL dget51( 1, n, t, lda, p1, lda, q, ldu, z, ldu, work,
951  $ result( 6 ) )
952  CALL dget51( 3, n, t, lda, p1, lda, q, ldu, q, ldu, work,
953  $ result( 7 ) )
954  CALL dget51( 3, n, t, lda, p1, lda, z, ldu, z, ldu, work,
955  $ result( 8 ) )
956 *
957 * Compute the Left and Right Eigenvectors of (S1,P1)
958 *
959 * 9: Compute the left eigenvector Matrix without
960 * back transforming:
961 *
962  ntest = 9
963  result( 9 ) = ulpinv
964 *
965 * To test "SELECT" option, compute half of the eigenvectors
966 * in one call, and half in another
967 *
968  i1 = n / 2
969  DO 120 j = 1, i1
970  llwork( j ) = .true.
971  120 CONTINUE
972  DO 130 j = i1 + 1, n
973  llwork( j ) = .false.
974  130 CONTINUE
975 *
976  CALL dtgevc( 'L', 'S', llwork, n, s1, lda, p1, lda, evectl,
977  $ ldu, dumma, ldu, n, in, work, iinfo )
978  IF( iinfo.NE.0 ) THEN
979  WRITE( nounit, fmt = 9999 )'DTGEVC(L,S1)', iinfo, n,
980  $ jtype, ioldsd
981  info = abs( iinfo )
982  GO TO 210
983  END IF
984 *
985  i1 = in
986  DO 140 j = 1, i1
987  llwork( j ) = .false.
988  140 CONTINUE
989  DO 150 j = i1 + 1, n
990  llwork( j ) = .true.
991  150 CONTINUE
992 *
993  CALL dtgevc( 'L', 'S', llwork, n, s1, lda, p1, lda,
994  $ evectl( 1, i1+1 ), ldu, dumma, ldu, n, in,
995  $ work, iinfo )
996  IF( iinfo.NE.0 ) THEN
997  WRITE( nounit, fmt = 9999 )'DTGEVC(L,S2)', iinfo, n,
998  $ jtype, ioldsd
999  info = abs( iinfo )
1000  GO TO 210
1001  END IF
1002 *
1003  CALL dget52( .true., n, s1, lda, p1, lda, evectl, ldu,
1004  $ alphr1, alphi1, beta1, work, dumma( 1 ) )
1005  result( 9 ) = dumma( 1 )
1006  IF( dumma( 2 ).GT.thrshn ) THEN
1007  WRITE( nounit, fmt = 9998 )'Left', 'DTGEVC(HOWMNY=S)',
1008  $ dumma( 2 ), n, jtype, ioldsd
1009  END IF
1010 *
1011 * 10: Compute the left eigenvector Matrix with
1012 * back transforming:
1013 *
1014  ntest = 10
1015  result( 10 ) = ulpinv
1016  CALL dlacpy( 'F', n, n, q, ldu, evectl, ldu )
1017  CALL dtgevc( 'L', 'B', llwork, n, s1, lda, p1, lda, evectl,
1018  $ ldu, dumma, ldu, n, in, work, iinfo )
1019  IF( iinfo.NE.0 ) THEN
1020  WRITE( nounit, fmt = 9999 )'DTGEVC(L,B)', iinfo, n,
1021  $ jtype, ioldsd
1022  info = abs( iinfo )
1023  GO TO 210
1024  END IF
1025 *
1026  CALL dget52( .true., n, h, lda, t, lda, evectl, ldu, alphr1,
1027  $ alphi1, beta1, work, dumma( 1 ) )
1028  result( 10 ) = dumma( 1 )
1029  IF( dumma( 2 ).GT.thrshn ) THEN
1030  WRITE( nounit, fmt = 9998 )'Left', 'DTGEVC(HOWMNY=B)',
1031  $ dumma( 2 ), n, jtype, ioldsd
1032  END IF
1033 *
1034 * 11: Compute the right eigenvector Matrix without
1035 * back transforming:
1036 *
1037  ntest = 11
1038  result( 11 ) = ulpinv
1039 *
1040 * To test "SELECT" option, compute half of the eigenvectors
1041 * in one call, and half in another
1042 *
1043  i1 = n / 2
1044  DO 160 j = 1, i1
1045  llwork( j ) = .true.
1046  160 CONTINUE
1047  DO 170 j = i1 + 1, n
1048  llwork( j ) = .false.
1049  170 CONTINUE
1050 *
1051  CALL dtgevc( 'R', 'S', llwork, n, s1, lda, p1, lda, dumma,
1052  $ ldu, evectr, ldu, n, in, work, iinfo )
1053  IF( iinfo.NE.0 ) THEN
1054  WRITE( nounit, fmt = 9999 )'DTGEVC(R,S1)', iinfo, n,
1055  $ jtype, ioldsd
1056  info = abs( iinfo )
1057  GO TO 210
1058  END IF
1059 *
1060  i1 = in
1061  DO 180 j = 1, i1
1062  llwork( j ) = .false.
1063  180 CONTINUE
1064  DO 190 j = i1 + 1, n
1065  llwork( j ) = .true.
1066  190 CONTINUE
1067 *
1068  CALL dtgevc( 'R', 'S', llwork, n, s1, lda, p1, lda, dumma,
1069  $ ldu, evectr( 1, i1+1 ), ldu, n, in, work,
1070  $ iinfo )
1071  IF( iinfo.NE.0 ) THEN
1072  WRITE( nounit, fmt = 9999 )'DTGEVC(R,S2)', iinfo, n,
1073  $ jtype, ioldsd
1074  info = abs( iinfo )
1075  GO TO 210
1076  END IF
1077 *
1078  CALL dget52( .false., n, s1, lda, p1, lda, evectr, ldu,
1079  $ alphr1, alphi1, beta1, work, dumma( 1 ) )
1080  result( 11 ) = dumma( 1 )
1081  IF( dumma( 2 ).GT.thresh ) THEN
1082  WRITE( nounit, fmt = 9998 )'Right', 'DTGEVC(HOWMNY=S)',
1083  $ dumma( 2 ), n, jtype, ioldsd
1084  END IF
1085 *
1086 * 12: Compute the right eigenvector Matrix with
1087 * back transforming:
1088 *
1089  ntest = 12
1090  result( 12 ) = ulpinv
1091  CALL dlacpy( 'F', n, n, z, ldu, evectr, ldu )
1092  CALL dtgevc( 'R', 'B', llwork, n, s1, lda, p1, lda, dumma,
1093  $ ldu, evectr, ldu, n, in, work, iinfo )
1094  IF( iinfo.NE.0 ) THEN
1095  WRITE( nounit, fmt = 9999 )'DTGEVC(R,B)', iinfo, n,
1096  $ jtype, ioldsd
1097  info = abs( iinfo )
1098  GO TO 210
1099  END IF
1100 *
1101  CALL dget52( .false., n, h, lda, t, lda, evectr, ldu,
1102  $ alphr1, alphi1, beta1, work, dumma( 1 ) )
1103  result( 12 ) = dumma( 1 )
1104  IF( dumma( 2 ).GT.thresh ) THEN
1105  WRITE( nounit, fmt = 9998 )'Right', 'DTGEVC(HOWMNY=B)',
1106  $ dumma( 2 ), n, jtype, ioldsd
1107  END IF
1108 *
1109 * Tests 13--15 are done only on request
1110 *
1111  IF( tstdif ) THEN
1112 *
1113 * Do Tests 13--14
1114 *
1115  CALL dget51( 2, n, s1, lda, s2, lda, q, ldu, z, ldu,
1116  $ work, result( 13 ) )
1117  CALL dget51( 2, n, p1, lda, p2, lda, q, ldu, z, ldu,
1118  $ work, result( 14 ) )
1119 *
1120 * Do Test 15
1121 *
1122  temp1 = zero
1123  temp2 = zero
1124  DO 200 j = 1, n
1125  temp1 = max( temp1, abs( alphr1( j )-alphr3( j ) )+
1126  $ abs( alphi1( j )-alphi3( j ) ) )
1127  temp2 = max( temp2, abs( beta1( j )-beta3( j ) ) )
1128  200 CONTINUE
1129 *
1130  temp1 = temp1 / max( safmin, ulp*max( temp1, anorm ) )
1131  temp2 = temp2 / max( safmin, ulp*max( temp2, bnorm ) )
1132  result( 15 ) = max( temp1, temp2 )
1133  ntest = 15
1134  ELSE
1135  result( 13 ) = zero
1136  result( 14 ) = zero
1137  result( 15 ) = zero
1138  ntest = 12
1139  END IF
1140 *
1141 * End of Loop -- Check for RESULT(j) > THRESH
1142 *
1143  210 CONTINUE
1144 *
1145  ntestt = ntestt + ntest
1146 *
1147 * Print out tests which fail.
1148 *
1149  DO 220 jr = 1, ntest
1150  IF( result( jr ).GE.thresh ) THEN
1151 *
1152 * If this is the first test to fail,
1153 * print a header to the data file.
1154 *
1155  IF( nerrs.EQ.0 ) THEN
1156  WRITE( nounit, fmt = 9997 )'DGG'
1157 *
1158 * Matrix types
1159 *
1160  WRITE( nounit, fmt = 9996 )
1161  WRITE( nounit, fmt = 9995 )
1162  WRITE( nounit, fmt = 9994 )'Orthogonal'
1163 *
1164 * Tests performed
1165 *
1166  WRITE( nounit, fmt = 9993 )'orthogonal', '''',
1167  $ 'transpose', ( '''', j = 1, 10 )
1168 *
1169  END IF
1170  nerrs = nerrs + 1
1171  IF( result( jr ).LT.10000.0d0 ) THEN
1172  WRITE( nounit, fmt = 9992 )n, jtype, ioldsd, jr,
1173  $ result( jr )
1174  ELSE
1175  WRITE( nounit, fmt = 9991 )n, jtype, ioldsd, jr,
1176  $ result( jr )
1177  END IF
1178  END IF
1179  220 CONTINUE
1180 *
1181  230 CONTINUE
1182  240 CONTINUE
1183 *
1184 * Summary
1185 *
1186  CALL dlasum( 'DGG', nounit, nerrs, ntestt )
1187  RETURN
1188 *
1189  9999 FORMAT( ' DCHKGG: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
1190  $ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
1191 *
1192  9998 FORMAT( ' DCHKGG: ', a, ' Eigenvectors from ', a, ' incorrectly ',
1193  $ 'normalized.', / ' Bits of error=', 0p, g10.3, ',', 9x,
1194  $ 'N=', i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5,
1195  $ ')' )
1196 *
1197  9997 FORMAT( / 1x, a3, ' -- Real Generalized eigenvalue problem' )
1198 *
1199  9996 FORMAT( ' Matrix types (see DCHKGG for details): ' )
1200 *
1201  9995 FORMAT( ' Special Matrices:', 23x,
1202  $ '(J''=transposed Jordan block)',
1203  $ / ' 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I) 5=(J'',J'') ',
1204  $ '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices: ( ',
1205  $ 'D=diag(0,1,2,...) )', / ' 7=(D,I) 9=(large*D, small*I',
1206  $ ') 11=(large*I, small*D) 13=(large*D, large*I)', /
1207  $ ' 8=(I,D) 10=(small*D, large*I) 12=(small*I, large*D) ',
1208  $ ' 14=(small*D, small*I)', / ' 15=(D, reversed D)' )
1209  9994 FORMAT( ' Matrices Rotated by Random ', a, ' Matrices U, V:',
1210  $ / ' 16=Transposed Jordan Blocks 19=geometric ',
1211  $ 'alpha, beta=0,1', / ' 17=arithm. alpha&beta ',
1212  $ ' 20=arithmetic alpha, beta=0,1', / ' 18=clustered ',
1213  $ 'alpha, beta=0,1 21=random alpha, beta=0,1',
1214  $ / ' Large & Small Matrices:', / ' 22=(large, small) ',
1215  $ '23=(small,large) 24=(small,small) 25=(large,large)',
1216  $ / ' 26=random O(1) matrices.' )
1217 *
1218  9993 FORMAT( / ' Tests performed: (H is Hessenberg, S is Schur, B, ',
1219  $ 'T, P are triangular,', / 20x, 'U, V, Q, and Z are ', a,
1220  $ ', l and r are the', / 20x,
1221  $ 'appropriate left and right eigenvectors, resp., a is',
1222  $ / 20x, 'alpha, b is beta, and ', a, ' means ', a, '.)',
1223  $ / ' 1 = | A - U H V', a,
1224  $ ' | / ( |A| n ulp ) 2 = | B - U T V', a,
1225  $ ' | / ( |B| n ulp )', / ' 3 = | I - UU', a,
1226  $ ' | / ( n ulp ) 4 = | I - VV', a,
1227  $ ' | / ( n ulp )', / ' 5 = | H - Q S Z', a,
1228  $ ' | / ( |H| n ulp )', 6x, '6 = | T - Q P Z', a,
1229  $ ' | / ( |T| n ulp )', / ' 7 = | I - QQ', a,
1230  $ ' | / ( n ulp ) 8 = | I - ZZ', a,
1231  $ ' | / ( n ulp )', / ' 9 = max | ( b S - a P )', a,
1232  $ ' l | / const. 10 = max | ( b H - a T )', a,
1233  $ ' l | / const.', /
1234  $ ' 11= max | ( b S - a P ) r | / const. 12 = max | ( b H',
1235  $ ' - a T ) r | / const.', / 1x )
1236 *
1237  9992 FORMAT( ' Matrix order=', i5, ', type=', i2, ', seed=',
1238  $ 4( i4, ',' ), ' result ', i2, ' is', 0p, f8.2 )
1239  9991 FORMAT( ' Matrix order=', i5, ', type=', i2, ', seed=',
1240  $ 4( i4, ',' ), ' result ', i2, ' is', 1p, d10.3 )
1241 *
1242 * End of DCHKGG
1243 *
1244  END
subroutine dchkgg(NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, TSTDIF, THRSHN, NOUNIT, A, LDA, B, H, T, S1, S2, P1, P2, U, LDU, V, Q, Z, ALPHR1, ALPHI1, BETA1, ALPHR3, ALPHI3, BETA3, EVECTL, EVECTR, WORK, LWORK, LLWORK, RESULT, INFO)
DCHKGG
Definition: dchkgg.f:513
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: dlaset.f:112
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:105
subroutine dlarfg(N, ALPHA, X, INCX, TAU)
DLARFG generates an elementary reflector (Householder matrix).
Definition: dlarfg.f:108
subroutine dlabad(SMALL, LARGE)
DLABAD
Definition: dlabad.f:76
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dgghrd(COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, INFO)
DGGHRD
Definition: dgghrd.f:209
subroutine dhgeqz(JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT, ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, WORK, LWORK, INFO)
DHGEQZ
Definition: dhgeqz.f:306
subroutine dget52(LEFT, N, A, LDA, B, LDB, E, LDE, ALPHAR, ALPHAI, BETA, WORK, RESULT)
DGET52
Definition: dget52.f:201
subroutine dget51(ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK, RESULT)
DGET51
Definition: dget51.f:151
subroutine dtgevc(SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, LDVL, VR, LDVR, MM, M, WORK, INFO)
DTGEVC
Definition: dtgevc.f:297
subroutine dlatm4(ITYPE, N, NZ1, NZ2, ISIGN, AMAGN, RCOND, TRIANG, IDIST, ISEED, A, LDA)
DLATM4
Definition: dlatm4.f:177
subroutine dgeqr2(M, N, A, LDA, TAU, WORK, INFO)
DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm...
Definition: dgeqr2.f:123
subroutine dlasum(TYPE, IOUNIT, IE, NRUN)
DLASUM
Definition: dlasum.f:45
subroutine dorm2r(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sge...
Definition: dorm2r.f:161