LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
ddrvvx.f
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1 *> \brief \b DDRVVX
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 DDRVVX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
12 * NIUNIT, NOUNIT, A, LDA, H, WR, WI, WR1, WI1,
13 * VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, RCNDV1,
14 * RCDVIN, RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1,
15 * RESULT, WORK, NWORK, IWORK, INFO )
16 *
17 * .. Scalar Arguments ..
18 * INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NIUNIT, NOUNIT,
19 * \$ NSIZES, NTYPES, NWORK
20 * DOUBLE PRECISION THRESH
21 * ..
22 * .. Array Arguments ..
23 * LOGICAL DOTYPE( * )
24 * INTEGER ISEED( 4 ), IWORK( * ), NN( * )
25 * DOUBLE PRECISION A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
26 * \$ RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
27 * \$ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
28 * \$ RESULT( 11 ), SCALE( * ), SCALE1( * ),
29 * \$ VL( LDVL, * ), VR( LDVR, * ), WI( * ),
30 * \$ WI1( * ), WORK( * ), WR( * ), WR1( * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> DDRVVX checks the nonsymmetric eigenvalue problem expert driver
40 *> DGEEVX.
41 *>
42 *> DDRVVX uses both test matrices generated randomly depending on
43 *> data supplied in the calling sequence, as well as on data
44 *> read from an input file and including precomputed condition
45 *> numbers to which it compares the ones it computes.
46 *>
47 *> When DDRVVX is called, a number of matrix "sizes" ("n's") and a
48 *> number of matrix "types" are specified in the calling sequence.
49 *> For each size ("n") and each type of matrix, one matrix will be
50 *> generated and used to test the nonsymmetric eigenroutines. For
51 *> each matrix, 9 tests will be performed:
52 *>
53 *> (1) | A * VR - VR * W | / ( n |A| ulp )
54 *>
55 *> Here VR is the matrix of unit right eigenvectors.
56 *> W is a block diagonal matrix, with a 1x1 block for each
57 *> real eigenvalue and a 2x2 block for each complex conjugate
58 *> pair. If eigenvalues j and j+1 are a complex conjugate pair,
59 *> so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the
60 *> 2 x 2 block corresponding to the pair will be:
61 *>
62 *> ( wr wi )
63 *> ( -wi wr )
64 *>
65 *> Such a block multiplying an n x 2 matrix ( ur ui ) on the
66 *> right will be the same as multiplying ur + i*ui by wr + i*wi.
67 *>
68 *> (2) | A**H * VL - VL * W**H | / ( n |A| ulp )
69 *>
70 *> Here VL is the matrix of unit left eigenvectors, A**H is the
71 *> conjugate transpose of A, and W is as above.
72 *>
73 *> (3) | |VR(i)| - 1 | / ulp and largest component real
74 *>
75 *> VR(i) denotes the i-th column of VR.
76 *>
77 *> (4) | |VL(i)| - 1 | / ulp and largest component real
78 *>
79 *> VL(i) denotes the i-th column of VL.
80 *>
81 *> (5) W(full) = W(partial)
82 *>
83 *> W(full) denotes the eigenvalues computed when VR, VL, RCONDV
84 *> and RCONDE are also computed, and W(partial) denotes the
85 *> eigenvalues computed when only some of VR, VL, RCONDV, and
86 *> RCONDE are computed.
87 *>
88 *> (6) VR(full) = VR(partial)
89 *>
90 *> VR(full) denotes the right eigenvectors computed when VL, RCONDV
91 *> and RCONDE are computed, and VR(partial) denotes the result
92 *> when only some of VL and RCONDV are computed.
93 *>
94 *> (7) VL(full) = VL(partial)
95 *>
96 *> VL(full) denotes the left eigenvectors computed when VR, RCONDV
97 *> and RCONDE are computed, and VL(partial) denotes the result
98 *> when only some of VR and RCONDV are computed.
99 *>
100 *> (8) 0 if SCALE, ILO, IHI, ABNRM (full) =
101 *> SCALE, ILO, IHI, ABNRM (partial)
102 *> 1/ulp otherwise
103 *>
104 *> SCALE, ILO, IHI and ABNRM describe how the matrix is balanced.
105 *> (full) is when VR, VL, RCONDE and RCONDV are also computed, and
106 *> (partial) is when some are not computed.
107 *>
108 *> (9) RCONDV(full) = RCONDV(partial)
109 *>
110 *> RCONDV(full) denotes the reciprocal condition numbers of the
111 *> right eigenvectors computed when VR, VL and RCONDE are also
112 *> computed. RCONDV(partial) denotes the reciprocal condition
113 *> numbers when only some of VR, VL and RCONDE are computed.
114 *>
115 *> The "sizes" are specified by an array NN(1:NSIZES); the value of
116 *> each element NN(j) specifies one size.
117 *> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
118 *> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
119 *> Currently, the list of possible types is:
120 *>
121 *> (1) The zero matrix.
122 *> (2) The identity matrix.
123 *> (3) A (transposed) Jordan block, with 1's on the diagonal.
124 *>
125 *> (4) A diagonal matrix with evenly spaced entries
126 *> 1, ..., ULP and random signs.
127 *> (ULP = (first number larger than 1) - 1 )
128 *> (5) A diagonal matrix with geometrically spaced entries
129 *> 1, ..., ULP and random signs.
130 *> (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
131 *> and random signs.
132 *>
133 *> (7) Same as (4), but multiplied by a constant near
134 *> the overflow threshold
135 *> (8) Same as (4), but multiplied by a constant near
136 *> the underflow threshold
137 *>
138 *> (9) A matrix of the form U' T U, where U is orthogonal and
139 *> T has evenly spaced entries 1, ..., ULP with random signs
140 *> on the diagonal and random O(1) entries in the upper
141 *> triangle.
142 *>
143 *> (10) A matrix of the form U' T U, where U is orthogonal and
144 *> T has geometrically spaced entries 1, ..., ULP with random
145 *> signs on the diagonal and random O(1) entries in the upper
146 *> triangle.
147 *>
148 *> (11) A matrix of the form U' T U, where U is orthogonal and
149 *> T has "clustered" entries 1, ULP,..., ULP with random
150 *> signs on the diagonal and random O(1) entries in the upper
151 *> triangle.
152 *>
153 *> (12) A matrix of the form U' T U, where U is orthogonal and
154 *> T has real or complex conjugate paired eigenvalues randomly
155 *> chosen from ( ULP, 1 ) and random O(1) entries in the upper
156 *> triangle.
157 *>
158 *> (13) A matrix of the form X' T X, where X has condition
159 *> SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
160 *> with random signs on the diagonal and random O(1) entries
161 *> in the upper triangle.
162 *>
163 *> (14) A matrix of the form X' T X, where X has condition
164 *> SQRT( ULP ) and T has geometrically spaced entries
165 *> 1, ..., ULP with random signs on the diagonal and random
166 *> O(1) entries in the upper triangle.
167 *>
168 *> (15) A matrix of the form X' T X, where X has condition
169 *> SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
170 *> with random signs on the diagonal and random O(1) entries
171 *> in the upper triangle.
172 *>
173 *> (16) A matrix of the form X' T X, where X has condition
174 *> SQRT( ULP ) and T has real or complex conjugate paired
175 *> eigenvalues randomly chosen from ( ULP, 1 ) and random
176 *> O(1) entries in the upper triangle.
177 *>
178 *> (17) Same as (16), but multiplied by a constant
179 *> near the overflow threshold
180 *> (18) Same as (16), but multiplied by a constant
181 *> near the underflow threshold
182 *>
183 *> (19) Nonsymmetric matrix with random entries chosen from (-1,1).
184 *> If N is at least 4, all entries in first two rows and last
185 *> row, and first column and last two columns are zero.
186 *> (20) Same as (19), but multiplied by a constant
187 *> near the overflow threshold
188 *> (21) Same as (19), but multiplied by a constant
189 *> near the underflow threshold
190 *>
191 *> In addition, an input file will be read from logical unit number
192 *> NIUNIT. The file contains matrices along with precomputed
193 *> eigenvalues and reciprocal condition numbers for the eigenvalues
194 *> and right eigenvectors. For these matrices, in addition to tests
195 *> (1) to (9) we will compute the following two tests:
196 *>
197 *> (10) |RCONDV - RCDVIN| / cond(RCONDV)
198 *>
199 *> RCONDV is the reciprocal right eigenvector condition number
200 *> computed by DGEEVX and RCDVIN (the precomputed true value)
201 *> is supplied as input. cond(RCONDV) is the condition number of
202 *> RCONDV, and takes errors in computing RCONDV into account, so
203 *> that the resulting quantity should be O(ULP). cond(RCONDV) is
204 *> essentially given by norm(A)/RCONDE.
205 *>
206 *> (11) |RCONDE - RCDEIN| / cond(RCONDE)
207 *>
208 *> RCONDE is the reciprocal eigenvalue condition number
209 *> computed by DGEEVX and RCDEIN (the precomputed true value)
210 *> is supplied as input. cond(RCONDE) is the condition number
211 *> of RCONDE, and takes errors in computing RCONDE into account,
212 *> so that the resulting quantity should be O(ULP). cond(RCONDE)
213 *> is essentially given by norm(A)/RCONDV.
214 *> \endverbatim
215 *
216 * Arguments:
217 * ==========
218 *
219 *> \param[in] NSIZES
220 *> \verbatim
221 *> NSIZES is INTEGER
222 *> The number of sizes of matrices to use. NSIZES must be at
223 *> least zero. If it is zero, no randomly generated matrices
224 *> are tested, but any test matrices read from NIUNIT will be
225 *> tested.
226 *> \endverbatim
227 *>
228 *> \param[in] NN
229 *> \verbatim
230 *> NN is INTEGER array, dimension (NSIZES)
231 *> An array containing the sizes to be used for the matrices.
232 *> Zero values will be skipped. The values must be at least
233 *> zero.
234 *> \endverbatim
235 *>
236 *> \param[in] NTYPES
237 *> \verbatim
238 *> NTYPES is INTEGER
239 *> The number of elements in DOTYPE. NTYPES must be at least
240 *> zero. If it is zero, no randomly generated test matrices
241 *> are tested, but and test matrices read from NIUNIT will be
242 *> tested. If it is MAXTYP+1 and NSIZES is 1, then an
243 *> additional type, MAXTYP+1 is defined, which is to use
244 *> whatever matrix is in A. This is only useful if
245 *> DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. .
246 *> \endverbatim
247 *>
248 *> \param[in] DOTYPE
249 *> \verbatim
250 *> DOTYPE is LOGICAL array, dimension (NTYPES)
251 *> If DOTYPE(j) is .TRUE., then for each size in NN a
252 *> matrix of that size and of type j will be generated.
253 *> If NTYPES is smaller than the maximum number of types
254 *> defined (PARAMETER MAXTYP), then types NTYPES+1 through
255 *> MAXTYP will not be generated. If NTYPES is larger
256 *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
257 *> will be ignored.
258 *> \endverbatim
259 *>
260 *> \param[in,out] ISEED
261 *> \verbatim
262 *> ISEED is INTEGER array, dimension (4)
263 *> On entry ISEED specifies the seed of the random number
264 *> generator. The array elements should be between 0 and 4095;
265 *> if not they will be reduced mod 4096. Also, ISEED(4) must
266 *> be odd. The random number generator uses a linear
267 *> congruential sequence limited to small integers, and so
268 *> should produce machine independent random numbers. The
269 *> values of ISEED are changed on exit, and can be used in the
270 *> next call to DDRVVX to continue the same random number
271 *> sequence.
272 *> \endverbatim
273 *>
274 *> \param[in] THRESH
275 *> \verbatim
276 *> THRESH is DOUBLE PRECISION
277 *> A test will count as "failed" if the "error", computed as
278 *> described above, exceeds THRESH. Note that the error
279 *> is scaled to be O(1), so THRESH should be a reasonably
280 *> small multiple of 1, e.g., 10 or 100. In particular,
281 *> it should not depend on the precision (single vs. double)
282 *> or the size of the matrix. It must be at least zero.
283 *> \endverbatim
284 *>
285 *> \param[in] NIUNIT
286 *> \verbatim
287 *> NIUNIT is INTEGER
288 *> The FORTRAN unit number for reading in the data file of
289 *> problems to solve.
290 *> \endverbatim
291 *>
292 *> \param[in] NOUNIT
293 *> \verbatim
294 *> NOUNIT is INTEGER
295 *> The FORTRAN unit number for printing out error messages
296 *> (e.g., if a routine returns INFO not equal to 0.)
297 *> \endverbatim
298 *>
299 *> \param[out] A
300 *> \verbatim
301 *> A is DOUBLE PRECISION array, dimension
302 *> (LDA, max(NN,12))
303 *> Used to hold the matrix whose eigenvalues are to be
304 *> computed. On exit, A contains the last matrix actually used.
305 *> \endverbatim
306 *>
307 *> \param[in] LDA
308 *> \verbatim
309 *> LDA is INTEGER
310 *> The leading dimension of the arrays A and H.
311 *> LDA >= max(NN,12), since 12 is the dimension of the largest
312 *> matrix in the precomputed input file.
313 *> \endverbatim
314 *>
315 *> \param[out] H
316 *> \verbatim
317 *> H is DOUBLE PRECISION array, dimension
318 *> (LDA, max(NN,12))
319 *> Another copy of the test matrix A, modified by DGEEVX.
320 *> \endverbatim
321 *>
322 *> \param[out] WR
323 *> \verbatim
324 *> WR is DOUBLE PRECISION array, dimension (max(NN))
325 *> \endverbatim
326 *>
327 *> \param[out] WI
328 *> \verbatim
329 *> WI is DOUBLE PRECISION array, dimension (max(NN))
330 *>
331 *> The real and imaginary parts of the eigenvalues of A.
332 *> On exit, WR + WI*i are the eigenvalues of the matrix in A.
333 *> \endverbatim
334 *>
335 *> \param[out] WR1
336 *> \verbatim
337 *> WR1 is DOUBLE PRECISION array, dimension (max(NN,12))
338 *> \endverbatim
339 *>
340 *> \param[out] WI1
341 *> \verbatim
342 *> WI1 is DOUBLE PRECISION array, dimension (max(NN,12))
343 *>
344 *> Like WR, WI, these arrays contain the eigenvalues of A,
345 *> but those computed when DGEEVX only computes a partial
346 *> eigendecomposition, i.e. not the eigenvalues and left
347 *> and right eigenvectors.
348 *> \endverbatim
349 *>
350 *> \param[out] VL
351 *> \verbatim
352 *> VL is DOUBLE PRECISION array, dimension
353 *> (LDVL, max(NN,12))
354 *> VL holds the computed left eigenvectors.
355 *> \endverbatim
356 *>
357 *> \param[in] LDVL
358 *> \verbatim
359 *> LDVL is INTEGER
360 *> Leading dimension of VL. Must be at least max(1,max(NN,12)).
361 *> \endverbatim
362 *>
363 *> \param[out] VR
364 *> \verbatim
365 *> VR is DOUBLE PRECISION array, dimension
366 *> (LDVR, max(NN,12))
367 *> VR holds the computed right eigenvectors.
368 *> \endverbatim
369 *>
370 *> \param[in] LDVR
371 *> \verbatim
372 *> LDVR is INTEGER
373 *> Leading dimension of VR. Must be at least max(1,max(NN,12)).
374 *> \endverbatim
375 *>
376 *> \param[out] LRE
377 *> \verbatim
378 *> LRE is DOUBLE PRECISION array, dimension
379 *> (LDLRE, max(NN,12))
380 *> LRE holds the computed right or left eigenvectors.
381 *> \endverbatim
382 *>
383 *> \param[in] LDLRE
384 *> \verbatim
385 *> LDLRE is INTEGER
386 *> Leading dimension of LRE. Must be at least max(1,max(NN,12))
387 *> \endverbatim
388 *>
389 *> \param[out] RCONDV
390 *> \verbatim
391 *> RCONDV is DOUBLE PRECISION array, dimension (N)
392 *> RCONDV holds the computed reciprocal condition numbers
393 *> for eigenvectors.
394 *> \endverbatim
395 *>
396 *> \param[out] RCNDV1
397 *> \verbatim
398 *> RCNDV1 is DOUBLE PRECISION array, dimension (N)
399 *> RCNDV1 holds more computed reciprocal condition numbers
400 *> for eigenvectors.
401 *> \endverbatim
402 *>
403 *> \param[out] RCDVIN
404 *> \verbatim
405 *> RCDVIN is DOUBLE PRECISION array, dimension (N)
406 *> When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
407 *> condition numbers for eigenvectors to be compared with
408 *> RCONDV.
409 *> \endverbatim
410 *>
411 *> \param[out] RCONDE
412 *> \verbatim
413 *> RCONDE is DOUBLE PRECISION array, dimension (N)
414 *> RCONDE holds the computed reciprocal condition numbers
415 *> for eigenvalues.
416 *> \endverbatim
417 *>
418 *> \param[out] RCNDE1
419 *> \verbatim
420 *> RCNDE1 is DOUBLE PRECISION array, dimension (N)
421 *> RCNDE1 holds more computed reciprocal condition numbers
422 *> for eigenvalues.
423 *> \endverbatim
424 *>
425 *> \param[out] RCDEIN
426 *> \verbatim
427 *> RCDEIN is DOUBLE PRECISION array, dimension (N)
428 *> When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
429 *> condition numbers for eigenvalues to be compared with
430 *> RCONDE.
431 *> \endverbatim
432 *>
433 *> \param[out] SCALE
434 *> \verbatim
435 *> SCALE is DOUBLE PRECISION array, dimension (N)
436 *> Holds information describing balancing of matrix.
437 *> \endverbatim
438 *>
439 *> \param[out] SCALE1
440 *> \verbatim
441 *> SCALE1 is DOUBLE PRECISION array, dimension (N)
442 *> Holds information describing balancing of matrix.
443 *> \endverbatim
444 *>
445 *> \param[out] RESULT
446 *> \verbatim
447 *> RESULT is DOUBLE PRECISION array, dimension (11)
448 *> The values computed by the seven tests described above.
449 *> The values are currently limited to 1/ulp, to avoid overflow.
450 *> \endverbatim
451 *>
452 *> \param[out] WORK
453 *> \verbatim
454 *> WORK is DOUBLE PRECISION array, dimension (NWORK)
455 *> \endverbatim
456 *>
457 *> \param[in] NWORK
458 *> \verbatim
459 *> NWORK is INTEGER
460 *> The number of entries in WORK. This must be at least
461 *> max(6*12+2*12**2,6*NN(j)+2*NN(j)**2) =
462 *> max( 360 ,6*NN(j)+2*NN(j)**2) for all j.
463 *> \endverbatim
464 *>
465 *> \param[out] IWORK
466 *> \verbatim
467 *> IWORK is INTEGER array, dimension (2*max(NN,12))
468 *> \endverbatim
469 *>
470 *> \param[out] INFO
471 *> \verbatim
472 *> INFO is INTEGER
473 *> If 0, then successful exit.
474 *> If <0, then input paramter -INFO is incorrect.
475 *> If >0, DLATMR, SLATMS, SLATME or DGET23 returned an error
476 *> code, and INFO is its absolute value.
477 *>
478 *>-----------------------------------------------------------------------
479 *>
480 *> Some Local Variables and Parameters:
481 *> ---- ----- --------- --- ----------
482 *>
483 *> ZERO, ONE Real 0 and 1.
484 *> MAXTYP The number of types defined.
485 *> NMAX Largest value in NN or 12.
486 *> NERRS The number of tests which have exceeded THRESH
487 *> COND, CONDS,
488 *> IMODE Values to be passed to the matrix generators.
489 *> ANORM Norm of A; passed to matrix generators.
490 *>
491 *> OVFL, UNFL Overflow and underflow thresholds.
492 *> ULP, ULPINV Finest relative precision and its inverse.
493 *> RTULP, RTULPI Square roots of the previous 4 values.
494 *>
495 *> The following four arrays decode JTYPE:
496 *> KTYPE(j) The general type (1-10) for type "j".
497 *> KMODE(j) The MODE value to be passed to the matrix
498 *> generator for type "j".
499 *> KMAGN(j) The order of magnitude ( O(1),
500 *> O(overflow^(1/2) ), O(underflow^(1/2) )
501 *> KCONDS(j) Selectw whether CONDS is to be 1 or
502 *> 1/sqrt(ulp). (0 means irrelevant.)
503 *> \endverbatim
504 *
505 * Authors:
506 * ========
507 *
508 *> \author Univ. of Tennessee
509 *> \author Univ. of California Berkeley
510 *> \author Univ. of Colorado Denver
511 *> \author NAG Ltd.
512 *
513 *> \date November 2011
514 *
515 *> \ingroup double_eig
516 *
517 * =====================================================================
518  SUBROUTINE ddrvvx( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
519  \$ niunit, nounit, a, lda, h, wr, wi, wr1, wi1,
520  \$ vl, ldvl, vr, ldvr, lre, ldlre, rcondv, rcndv1,
521  \$ rcdvin, rconde, rcnde1, rcdein, scale, scale1,
522  \$ result, work, nwork, iwork, info )
523 *
524 * -- LAPACK test routine (version 3.4.0) --
525 * -- LAPACK is a software package provided by Univ. of Tennessee, --
526 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
527 * November 2011
528 *
529 * .. Scalar Arguments ..
530  INTEGER info, lda, ldlre, ldvl, ldvr, niunit, nounit,
531  \$ nsizes, ntypes, nwork
532  DOUBLE PRECISION thresh
533 * ..
534 * .. Array Arguments ..
535  LOGICAL dotype( * )
536  INTEGER iseed( 4 ), iwork( * ), nn( * )
537  DOUBLE PRECISION a( lda, * ), h( lda, * ), lre( ldlre, * ),
538  \$ rcdein( * ), rcdvin( * ), rcnde1( * ),
539  \$ rcndv1( * ), rconde( * ), rcondv( * ),
540  \$ result( 11 ), scale( * ), scale1( * ),
541  \$ vl( ldvl, * ), vr( ldvr, * ), wi( * ),
542  \$ wi1( * ), work( * ), wr( * ), wr1( * )
543 * ..
544 *
545 * =====================================================================
546 *
547 * .. Parameters ..
548  DOUBLE PRECISION zero, one
549  parameter( zero = 0.0d0, one = 1.0d0 )
550  INTEGER maxtyp
551  parameter( maxtyp = 21 )
552 * ..
553 * .. Local Scalars ..
555  CHARACTER balanc
556  CHARACTER*3 path
557  INTEGER i, ibal, iinfo, imode, itype, iwk, j, jcol,
558  \$ jsize, jtype, mtypes, n, nerrs, nfail, nmax,
559  \$ nnwork, ntest, ntestf, ntestt
560  DOUBLE PRECISION anorm, cond, conds, ovfl, rtulp, rtulpi, ulp,
561  \$ ulpinv, unfl
562 * ..
563 * .. Local Arrays ..
564  CHARACTER adumma( 1 ), bal( 4 )
565  INTEGER idumma( 1 ), ioldsd( 4 ), kconds( maxtyp ),
566  \$ kmagn( maxtyp ), kmode( maxtyp ),
567  \$ ktype( maxtyp )
568 * ..
569 * .. External Functions ..
570  DOUBLE PRECISION dlamch
571  EXTERNAL dlamch
572 * ..
573 * .. External Subroutines ..
574  EXTERNAL dget23, dlabad, dlaset, dlasum, dlatme, dlatmr,
575  \$ dlatms, xerbla
576 * ..
577 * .. Intrinsic Functions ..
578  INTRINSIC abs, max, min, sqrt
579 * ..
580 * .. Data statements ..
581  DATA ktype / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
582  DATA kmagn / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
583  \$ 3, 1, 2, 3 /
584  DATA kmode / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
585  \$ 1, 5, 5, 5, 4, 3, 1 /
586  DATA kconds / 3*0, 5*0, 4*1, 6*2, 3*0 /
587  DATA bal / 'N', 'P', 'S', 'B' /
588 * ..
589 * .. Executable Statements ..
590 *
591  path( 1: 1 ) = 'Double precision'
592  path( 2: 3 ) = 'VX'
593 *
594 * Check for errors
595 *
596  ntestt = 0
597  ntestf = 0
598  info = 0
599 *
600 * Important constants
601 *
603 *
604 * 12 is the largest dimension in the input file of precomputed
605 * problems
606 *
607  nmax = 12
608  DO 10 j = 1, nsizes
609  nmax = max( nmax, nn( j ) )
610  IF( nn( j ).LT.0 )
612  10 continue
613 *
614 * Check for errors
615 *
616  IF( nsizes.LT.0 ) THEN
617  info = -1
618  ELSE IF( badnn ) THEN
619  info = -2
620  ELSE IF( ntypes.LT.0 ) THEN
621  info = -3
622  ELSE IF( thresh.LT.zero ) THEN
623  info = -6
624  ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
625  info = -10
626  ELSE IF( ldvl.LT.1 .OR. ldvl.LT.nmax ) THEN
627  info = -17
628  ELSE IF( ldvr.LT.1 .OR. ldvr.LT.nmax ) THEN
629  info = -19
630  ELSE IF( ldlre.LT.1 .OR. ldlre.LT.nmax ) THEN
631  info = -21
632  ELSE IF( 6*nmax+2*nmax**2.GT.nwork ) THEN
633  info = -32
634  END IF
635 *
636  IF( info.NE.0 ) THEN
637  CALL xerbla( 'DDRVVX', -info )
638  return
639  END IF
640 *
641 * If nothing to do check on NIUNIT
642 *
643  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
644  \$ go to 160
645 *
646 * More Important constants
647 *
648  unfl = dlamch( 'Safe minimum' )
649  ovfl = one / unfl
650  CALL dlabad( unfl, ovfl )
651  ulp = dlamch( 'Precision' )
652  ulpinv = one / ulp
653  rtulp = sqrt( ulp )
654  rtulpi = one / rtulp
655 *
656 * Loop over sizes, types
657 *
658  nerrs = 0
659 *
660  DO 150 jsize = 1, nsizes
661  n = nn( jsize )
662  IF( nsizes.NE.1 ) THEN
663  mtypes = min( maxtyp, ntypes )
664  ELSE
665  mtypes = min( maxtyp+1, ntypes )
666  END IF
667 *
668  DO 140 jtype = 1, mtypes
669  IF( .NOT.dotype( jtype ) )
670  \$ go to 140
671 *
672 * Save ISEED in case of an error.
673 *
674  DO 20 j = 1, 4
675  ioldsd( j ) = iseed( j )
676  20 continue
677 *
678 * Compute "A"
679 *
680 * Control parameters:
681 *
682 * KMAGN KCONDS KMODE KTYPE
683 * =1 O(1) 1 clustered 1 zero
684 * =2 large large clustered 2 identity
685 * =3 small exponential Jordan
686 * =4 arithmetic diagonal, (w/ eigenvalues)
687 * =5 random log symmetric, w/ eigenvalues
688 * =6 random general, w/ eigenvalues
689 * =7 random diagonal
690 * =8 random symmetric
691 * =9 random general
692 * =10 random triangular
693 *
694  IF( mtypes.GT.maxtyp )
695  \$ go to 90
696 *
697  itype = ktype( jtype )
698  imode = kmode( jtype )
699 *
700 * Compute norm
701 *
702  go to( 30, 40, 50 )kmagn( jtype )
703 *
704  30 continue
705  anorm = one
706  go to 60
707 *
708  40 continue
709  anorm = ovfl*ulp
710  go to 60
711 *
712  50 continue
713  anorm = unfl*ulpinv
714  go to 60
715 *
716  60 continue
717 *
718  CALL dlaset( 'Full', lda, n, zero, zero, a, lda )
719  iinfo = 0
720  cond = ulpinv
721 *
722 * Special Matrices -- Identity & Jordan block
723 *
724 * Zero
725 *
726  IF( itype.EQ.1 ) THEN
727  iinfo = 0
728 *
729  ELSE IF( itype.EQ.2 ) THEN
730 *
731 * Identity
732 *
733  DO 70 jcol = 1, n
734  a( jcol, jcol ) = anorm
735  70 continue
736 *
737  ELSE IF( itype.EQ.3 ) THEN
738 *
739 * Jordan Block
740 *
741  DO 80 jcol = 1, n
742  a( jcol, jcol ) = anorm
743  IF( jcol.GT.1 )
744  \$ a( jcol, jcol-1 ) = one
745  80 continue
746 *
747  ELSE IF( itype.EQ.4 ) THEN
748 *
749 * Diagonal Matrix, [Eigen]values Specified
750 *
751  CALL dlatms( n, n, 'S', iseed, 'S', work, imode, cond,
752  \$ anorm, 0, 0, 'N', a, lda, work( n+1 ),
753  \$ iinfo )
754 *
755  ELSE IF( itype.EQ.5 ) THEN
756 *
757 * Symmetric, eigenvalues specified
758 *
759  CALL dlatms( n, n, 'S', iseed, 'S', work, imode, cond,
760  \$ anorm, n, n, 'N', a, lda, work( n+1 ),
761  \$ iinfo )
762 *
763  ELSE IF( itype.EQ.6 ) THEN
764 *
765 * General, eigenvalues specified
766 *
767  IF( kconds( jtype ).EQ.1 ) THEN
768  conds = one
769  ELSE IF( kconds( jtype ).EQ.2 ) THEN
770  conds = rtulpi
771  ELSE
772  conds = zero
773  END IF
774 *
775  adumma( 1 ) = ' '
776  CALL dlatme( n, 'S', iseed, work, imode, cond, one,
777  \$ adumma, 'T', 'T', 'T', work( n+1 ), 4,
778  \$ conds, n, n, anorm, a, lda, work( 2*n+1 ),
779  \$ iinfo )
780 *
781  ELSE IF( itype.EQ.7 ) THEN
782 *
783 * Diagonal, random eigenvalues
784 *
785  CALL dlatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
786  \$ 'T', 'N', work( n+1 ), 1, one,
787  \$ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
788  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
789 *
790  ELSE IF( itype.EQ.8 ) THEN
791 *
792 * Symmetric, random eigenvalues
793 *
794  CALL dlatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
795  \$ 'T', 'N', work( n+1 ), 1, one,
796  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
797  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
798 *
799  ELSE IF( itype.EQ.9 ) THEN
800 *
801 * General, random eigenvalues
802 *
803  CALL dlatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
804  \$ 'T', 'N', work( n+1 ), 1, one,
805  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
806  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
807  IF( n.GE.4 ) THEN
808  CALL dlaset( 'Full', 2, n, zero, zero, a, lda )
809  CALL dlaset( 'Full', n-3, 1, zero, zero, a( 3, 1 ),
810  \$ lda )
811  CALL dlaset( 'Full', n-3, 2, zero, zero, a( 3, n-1 ),
812  \$ lda )
813  CALL dlaset( 'Full', 1, n, zero, zero, a( n, 1 ),
814  \$ lda )
815  END IF
816 *
817  ELSE IF( itype.EQ.10 ) THEN
818 *
819 * Triangular, random eigenvalues
820 *
821  CALL dlatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
822  \$ 'T', 'N', work( n+1 ), 1, one,
823  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, 0,
824  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
825 *
826  ELSE
827 *
828  iinfo = 1
829  END IF
830 *
831  IF( iinfo.NE.0 ) THEN
832  WRITE( nounit, fmt = 9992 )'Generator', iinfo, n, jtype,
833  \$ ioldsd
834  info = abs( iinfo )
835  return
836  END IF
837 *
838  90 continue
839 *
840 * Test for minimal and generous workspace
841 *
842  DO 130 iwk = 1, 3
843  IF( iwk.EQ.1 ) THEN
844  nnwork = 3*n
845  ELSE IF( iwk.EQ.2 ) THEN
846  nnwork = 6*n + n**2
847  ELSE
848  nnwork = 6*n + 2*n**2
849  END IF
850  nnwork = max( nnwork, 1 )
851 *
852 * Test for all balancing options
853 *
854  DO 120 ibal = 1, 4
855  balanc = bal( ibal )
856 *
857 * Perform tests
858 *
859  CALL dget23( .false., balanc, jtype, thresh, ioldsd,
860  \$ nounit, n, a, lda, h, wr, wi, wr1, wi1,
861  \$ vl, ldvl, vr, ldvr, lre, ldlre, rcondv,
862  \$ rcndv1, rcdvin, rconde, rcnde1, rcdein,
863  \$ scale, scale1, result, work, nnwork,
864  \$ iwork, info )
865 *
866 * Check for RESULT(j) > THRESH
867 *
868  ntest = 0
869  nfail = 0
870  DO 100 j = 1, 9
871  IF( result( j ).GE.zero )
872  \$ ntest = ntest + 1
873  IF( result( j ).GE.thresh )
874  \$ nfail = nfail + 1
875  100 continue
876 *
877  IF( nfail.GT.0 )
878  \$ ntestf = ntestf + 1
879  IF( ntestf.EQ.1 ) THEN
880  WRITE( nounit, fmt = 9999 )path
881  WRITE( nounit, fmt = 9998 )
882  WRITE( nounit, fmt = 9997 )
883  WRITE( nounit, fmt = 9996 )
884  WRITE( nounit, fmt = 9995 )thresh
885  ntestf = 2
886  END IF
887 *
888  DO 110 j = 1, 9
889  IF( result( j ).GE.thresh ) THEN
890  WRITE( nounit, fmt = 9994 )balanc, n, iwk,
891  \$ ioldsd, jtype, j, result( j )
892  END IF
893  110 continue
894 *
895  nerrs = nerrs + nfail
896  ntestt = ntestt + ntest
897 *
898  120 continue
899  130 continue
900  140 continue
901  150 continue
902 *
903  160 continue
904 *
905 * Read in data from file to check accuracy of condition estimation.
906 * Assume input eigenvalues are sorted lexicographically (increasing
907 * by real part, then decreasing by imaginary part)
908 *
909  jtype = 0
910  170 continue
911  READ( niunit, fmt = *, END = 220 )n
912 *
913 * Read input data until N=0
914 *
915  IF( n.EQ.0 )
916  \$ go to 220
917  jtype = jtype + 1
918  iseed( 1 ) = jtype
919  DO 180 i = 1, n
920  READ( niunit, fmt = * )( a( i, j ), j = 1, n )
921  180 continue
922  DO 190 i = 1, n
923  READ( niunit, fmt = * )wr1( i ), wi1( i ), rcdein( i ),
924  \$ rcdvin( i )
925  190 continue
926  CALL dget23( .true., 'N', 22, thresh, iseed, nounit, n, a, lda, h,
927  \$ wr, wi, wr1, wi1, vl, ldvl, vr, ldvr, lre, ldlre,
928  \$ rcondv, rcndv1, rcdvin, rconde, rcnde1, rcdein,
929  \$ scale, scale1, result, work, 6*n+2*n**2, iwork,
930  \$ info )
931 *
932 * Check for RESULT(j) > THRESH
933 *
934  ntest = 0
935  nfail = 0
936  DO 200 j = 1, 11
937  IF( result( j ).GE.zero )
938  \$ ntest = ntest + 1
939  IF( result( j ).GE.thresh )
940  \$ nfail = nfail + 1
941  200 continue
942 *
943  IF( nfail.GT.0 )
944  \$ ntestf = ntestf + 1
945  IF( ntestf.EQ.1 ) THEN
946  WRITE( nounit, fmt = 9999 )path
947  WRITE( nounit, fmt = 9998 )
948  WRITE( nounit, fmt = 9997 )
949  WRITE( nounit, fmt = 9996 )
950  WRITE( nounit, fmt = 9995 )thresh
951  ntestf = 2
952  END IF
953 *
954  DO 210 j = 1, 11
955  IF( result( j ).GE.thresh ) THEN
956  WRITE( nounit, fmt = 9993 )n, jtype, j, result( j )
957  END IF
958  210 continue
959 *
960  nerrs = nerrs + nfail
961  ntestt = ntestt + ntest
962  go to 170
963  220 continue
964 *
965 * Summary
966 *
967  CALL dlasum( path, nounit, nerrs, ntestt )
968 *
969  9999 format( / 1x, a3, ' -- Real Eigenvalue-Eigenvector Decomposition',
970  \$ ' Expert Driver', /
971  \$ ' Matrix types (see DDRVVX for details): ' )
972 *
973  9998 format( / ' Special Matrices:', / ' 1=Zero matrix. ',
974  \$ ' ', ' 5=Diagonal: geometr. spaced entries.',
975  \$ / ' 2=Identity matrix. ', ' 6=Diagona',
976  \$ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
977  \$ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
978  \$ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
979  \$ 'mall, evenly spaced.' )
980  9997 format( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
981  \$ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
982  \$ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
983  \$ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
984  \$ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
985  \$ 'lex ', / ' 12=Well-cond., random complex ', ' ',
986  \$ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
987  \$ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
988  \$ ' complx ' )
989  9996 format( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
990  \$ 'with small random entries.', / ' 20=Matrix with large ran',
991  \$ 'dom entries. ', ' 22=Matrix read from input file', / )
992  9995 format( ' Tests performed with test threshold =', f8.2,
993  \$ / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ',
994  \$ / ' 2 = | transpose(A) VL - VL W | / ( n |A| ulp ) ',
995  \$ / ' 3 = | |VR(i)| - 1 | / ulp ',
996  \$ / ' 4 = | |VL(i)| - 1 | / ulp ',
997  \$ / ' 5 = 0 if W same no matter if VR or VL computed,',
998  \$ ' 1/ulp otherwise', /
999  \$ ' 6 = 0 if VR same no matter what else computed,',
1000  \$ ' 1/ulp otherwise', /
1001  \$ ' 7 = 0 if VL same no matter what else computed,',
1002  \$ ' 1/ulp otherwise', /
1003  \$ ' 8 = 0 if RCONDV same no matter what else computed,',
1004  \$ ' 1/ulp otherwise', /
1005  \$ ' 9 = 0 if SCALE, ILO, IHI, ABNRM same no matter what else',
1006  \$ ' computed, 1/ulp otherwise',
1007  \$ / ' 10 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),',
1008  \$ / ' 11 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),' )
1009  9994 format( ' BALANC=''', a1, ''',N=', i4, ',IWK=', i1, ', seed=',
1010  \$ 4( i4, ',' ), ' type ', i2, ', test(', i2, ')=', g10.3 )
1011  9993 format( ' N=', i5, ', input example =', i3, ', test(', i2, ')=',
1012  \$ g10.3 )
1013  9992 format( ' DDRVVX: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
1014  \$ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
1015 *
1016  return
1017 *
1018 * End of DDRVVX
1019 *
1020  END