LAPACK  3.5.0
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sdrvvx.f
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1 *> \brief \b SDRVVX
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 SDRVVX( 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 * REAL THRESH
21 * ..
22 * .. Array Arguments ..
23 * LOGICAL DOTYPE( * )
24 * INTEGER ISEED( 4 ), IWORK( * ), NN( * )
25 * REAL 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 *> SDRVVX checks the nonsymmetric eigenvalue problem expert driver
40 *> SGEEVX.
41 *>
42 *> SDRVVX 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 SDRVVX 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 SGEEVX 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 SGEEVX 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 SDRVVX to continue the same random number
271 *> sequence.
272 *> \endverbatim
273 *>
274 *> \param[in] THRESH
275 *> \verbatim
276 *> THRESH is REAL
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 REAL 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 REAL array, dimension
318 *> (LDA, max(NN,12))
319 *> Another copy of the test matrix A, modified by SGEEVX.
320 *> \endverbatim
321 *>
322 *> \param[out] WR
323 *> \verbatim
324 *> WR is REAL array, dimension (max(NN))
325 *> \endverbatim
326 *>
327 *> \param[out] WI
328 *> \verbatim
329 *> WI is REAL array, dimension (max(NN))
330 *> The real and imaginary parts of the eigenvalues of A.
331 *> On exit, WR + WI*i are the eigenvalues of the matrix in A.
332 *> \endverbatim
333 *>
334 *> \param[out] WR1
335 *> \verbatim
336 *> WR1 is REAL array, dimension (max(NN,12))
337 *> \endverbatim
338 *>
339 *> \param[out] WI1
340 *> \verbatim
341 *> WI1 is REAL array, dimension (max(NN,12))
342 *>
343 *> Like WR, WI, these arrays contain the eigenvalues of A,
344 *> but those computed when SGEEVX only computes a partial
345 *> eigendecomposition, i.e. not the eigenvalues and left
346 *> and right eigenvectors.
347 *> \endverbatim
348 *>
349 *> \param[out] VL
350 *> \verbatim
351 *> VL is REAL array, dimension
352 *> (LDVL, max(NN,12))
353 *> VL holds the computed left eigenvectors.
354 *> \endverbatim
355 *>
356 *> \param[in] LDVL
357 *> \verbatim
358 *> LDVL is INTEGER
359 *> Leading dimension of VL. Must be at least max(1,max(NN,12)).
360 *> \endverbatim
361 *>
362 *> \param[out] VR
363 *> \verbatim
364 *> VR is REAL array, dimension
365 *> (LDVR, max(NN,12))
366 *> VR holds the computed right eigenvectors.
367 *> \endverbatim
368 *>
369 *> \param[in] LDVR
370 *> \verbatim
371 *> LDVR is INTEGER
372 *> Leading dimension of VR. Must be at least max(1,max(NN,12)).
373 *> \endverbatim
374 *>
375 *> \param[out] LRE
376 *> \verbatim
377 *> LRE is REAL array, dimension
378 *> (LDLRE, max(NN,12))
379 *> LRE holds the computed right or left eigenvectors.
380 *> \endverbatim
381 *>
382 *> \param[in] LDLRE
383 *> \verbatim
384 *> LDLRE is INTEGER
385 *> Leading dimension of LRE. Must be at least max(1,max(NN,12))
386 *> \endverbatim
387 *>
388 *> \param[out] RCONDV
389 *> \verbatim
390 *> RCONDV is REAL array, dimension (N)
391 *> RCONDV holds the computed reciprocal condition numbers
392 *> for eigenvectors.
393 *> \endverbatim
394 *>
395 *> \param[out] RCNDV1
396 *> \verbatim
397 *> RCNDV1 is REAL array, dimension (N)
398 *> RCNDV1 holds more computed reciprocal condition numbers
399 *> for eigenvectors.
400 *> \endverbatim
401 *>
402 *> \param[out] RCDVIN
403 *> \verbatim
404 *> RCDVIN is REAL array, dimension (N)
405 *> When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
406 *> condition numbers for eigenvectors to be compared with
407 *> RCONDV.
408 *> \endverbatim
409 *>
410 *> \param[out] RCONDE
411 *> \verbatim
412 *> RCONDE is REAL array, dimension (N)
413 *> RCONDE holds the computed reciprocal condition numbers
414 *> for eigenvalues.
415 *> \endverbatim
416 *>
417 *> \param[out] RCNDE1
418 *> \verbatim
419 *> RCNDE1 is REAL array, dimension (N)
420 *> RCNDE1 holds more computed reciprocal condition numbers
421 *> for eigenvalues.
422 *> \endverbatim
423 *>
424 *> \param[out] RCDEIN
425 *> \verbatim
426 *> RCDEIN is REAL array, dimension (N)
427 *> When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
428 *> condition numbers for eigenvalues to be compared with
429 *> RCONDE.
430 *> \endverbatim
431 *>
432 *> \param[out] SCALE
433 *> \verbatim
434 *> SCALE is REAL array, dimension (N)
435 *> Holds information describing balancing of matrix.
436 *> \endverbatim
437 *>
438 *> \param[out] SCALE1
439 *> \verbatim
440 *> SCALE1 is REAL array, dimension (N)
441 *> Holds information describing balancing of matrix.
442 *> \endverbatim
443 *>
444 *> \param[out] RESULT
445 *> \verbatim
446 *> RESULT is REAL array, dimension (11)
447 *> The values computed by the seven tests described above.
448 *> The values are currently limited to 1/ulp, to avoid overflow.
449 *> \endverbatim
450 *>
451 *> \param[out] WORK
452 *> \verbatim
453 *> WORK is REAL array, dimension (NWORK)
454 *> \endverbatim
455 *>
456 *> \param[in] NWORK
457 *> \verbatim
458 *> NWORK is INTEGER
459 *> The number of entries in WORK. This must be at least
460 *> max(6*12+2*12**2,6*NN(j)+2*NN(j)**2) =
461 *> max( 360 ,6*NN(j)+2*NN(j)**2) for all j.
462 *> \endverbatim
463 *>
464 *> \param[out] IWORK
465 *> \verbatim
466 *> IWORK is INTEGER array, dimension (2*max(NN,12))
467 *> \endverbatim
468 *>
469 *> \param[out] INFO
470 *> \verbatim
471 *> INFO is INTEGER
472 *> If 0, then successful exit.
473 *> If <0, then input paramter -INFO is incorrect.
474 *> If >0, SLATMR, SLATMS, SLATME or SGET23 returned an error
475 *> code, and INFO is its absolute value.
476 *>
477 *>-----------------------------------------------------------------------
478 *>
479 *> Some Local Variables and Parameters:
480 *> ---- ----- --------- --- ----------
481 *>
482 *> ZERO, ONE Real 0 and 1.
483 *> MAXTYP The number of types defined.
484 *> NMAX Largest value in NN or 12.
485 *> NERRS The number of tests which have exceeded THRESH
486 *> COND, CONDS,
487 *> IMODE Values to be passed to the matrix generators.
488 *> ANORM Norm of A; passed to matrix generators.
489 *>
490 *> OVFL, UNFL Overflow and underflow thresholds.
491 *> ULP, ULPINV Finest relative precision and its inverse.
492 *> RTULP, RTULPI Square roots of the previous 4 values.
493 *>
494 *> The following four arrays decode JTYPE:
495 *> KTYPE(j) The general type (1-10) for type "j".
496 *> KMODE(j) The MODE value to be passed to the matrix
497 *> generator for type "j".
498 *> KMAGN(j) The order of magnitude ( O(1),
499 *> O(overflow^(1/2) ), O(underflow^(1/2) )
500 *> KCONDS(j) Selectw whether CONDS is to be 1 or
501 *> 1/sqrt(ulp). (0 means irrelevant.)
502 *> \endverbatim
503 *
504 * Authors:
505 * ========
506 *
507 *> \author Univ. of Tennessee
508 *> \author Univ. of California Berkeley
509 *> \author Univ. of Colorado Denver
510 *> \author NAG Ltd.
511 *
512 *> \date November 2011
513 *
514 *> \ingroup single_eig
515 *
516 * =====================================================================
517  SUBROUTINE sdrvvx( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
518  $ niunit, nounit, a, lda, h, wr, wi, wr1, wi1,
519  $ vl, ldvl, vr, ldvr, lre, ldlre, rcondv, rcndv1,
520  $ rcdvin, rconde, rcnde1, rcdein, scale, scale1,
521  $ result, work, nwork, iwork, info )
522 *
523 * -- LAPACK test routine (version 3.4.0) --
524 * -- LAPACK is a software package provided by Univ. of Tennessee, --
525 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
526 * November 2011
527 *
528 * .. Scalar Arguments ..
529  INTEGER info, lda, ldlre, ldvl, ldvr, niunit, nounit,
530  $ nsizes, ntypes, nwork
531  REAL thresh
532 * ..
533 * .. Array Arguments ..
534  LOGICAL dotype( * )
535  INTEGER iseed( 4 ), iwork( * ), nn( * )
536  REAL a( lda, * ), h( lda, * ), lre( ldlre, * ),
537  $ rcdein( * ), rcdvin( * ), rcnde1( * ),
538  $ rcndv1( * ), rconde( * ), rcondv( * ),
539  $ result( 11 ), scale( * ), scale1( * ),
540  $ vl( ldvl, * ), vr( ldvr, * ), wi( * ),
541  $ wi1( * ), work( * ), wr( * ), wr1( * )
542 * ..
543 *
544 * =====================================================================
545 *
546 * .. Parameters ..
547  REAL zero, one
548  parameter( zero = 0.0e0, one = 1.0e0 )
549  INTEGER maxtyp
550  parameter( maxtyp = 21 )
551 * ..
552 * .. Local Scalars ..
553  LOGICAL badnn
554  CHARACTER balanc
555  CHARACTER*3 path
556  INTEGER i, ibal, iinfo, imode, itype, iwk, j, jcol,
557  $ jsize, jtype, mtypes, n, nerrs, nfail,
558  $ nmax, nnwork, ntest, ntestf, ntestt
559  REAL anorm, cond, conds, ovfl, rtulp, rtulpi, ulp,
560  $ ulpinv, unfl
561 * ..
562 * .. Local Arrays ..
563  CHARACTER adumma( 1 ), bal( 4 )
564  INTEGER idumma( 1 ), ioldsd( 4 ), kconds( maxtyp ),
565  $ kmagn( maxtyp ), kmode( maxtyp ),
566  $ ktype( maxtyp )
567 * ..
568 * .. External Functions ..
569  REAL slamch
570  EXTERNAL slamch
571 * ..
572 * .. External Subroutines ..
573  EXTERNAL sget23, slabad, slasum, slatme, slatmr, slatms,
574  $ slaset, xerbla
575 * ..
576 * .. Intrinsic Functions ..
577  INTRINSIC abs, max, min, sqrt
578 * ..
579 * .. Data statements ..
580  DATA ktype / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
581  DATA kmagn / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
582  $ 3, 1, 2, 3 /
583  DATA kmode / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
584  $ 1, 5, 5, 5, 4, 3, 1 /
585  DATA kconds / 3*0, 5*0, 4*1, 6*2, 3*0 /
586  DATA bal / 'N', 'P', 'S', 'B' /
587 * ..
588 * .. Executable Statements ..
589 *
590  path( 1: 1 ) = 'Single precision'
591  path( 2: 3 ) = 'VX'
592 *
593 * Check for errors
594 *
595  ntestt = 0
596  ntestf = 0
597  info = 0
598 *
599 * Important constants
600 *
601  badnn = .false.
602 *
603 * 12 is the largest dimension in the input file of precomputed
604 * problems
605 *
606  nmax = 12
607  DO 10 j = 1, nsizes
608  nmax = max( nmax, nn( j ) )
609  IF( nn( j ).LT.0 )
610  $ badnn = .true.
611  10 CONTINUE
612 *
613 * Check for errors
614 *
615  IF( nsizes.LT.0 ) THEN
616  info = -1
617  ELSE IF( badnn ) THEN
618  info = -2
619  ELSE IF( ntypes.LT.0 ) THEN
620  info = -3
621  ELSE IF( thresh.LT.zero ) THEN
622  info = -6
623  ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
624  info = -10
625  ELSE IF( ldvl.LT.1 .OR. ldvl.LT.nmax ) THEN
626  info = -17
627  ELSE IF( ldvr.LT.1 .OR. ldvr.LT.nmax ) THEN
628  info = -19
629  ELSE IF( ldlre.LT.1 .OR. ldlre.LT.nmax ) THEN
630  info = -21
631  ELSE IF( 6*nmax+2*nmax**2.GT.nwork ) THEN
632  info = -32
633  END IF
634 *
635  IF( info.NE.0 ) THEN
636  CALL xerbla( 'SDRVVX', -info )
637  RETURN
638  END IF
639 *
640 * If nothing to do check on NIUNIT
641 *
642  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
643  $ go to 160
644 *
645 * More Important constants
646 *
647  unfl = slamch( 'Safe minimum' )
648  ovfl = one / unfl
649  CALL slabad( unfl, ovfl )
650  ulp = slamch( 'Precision' )
651  ulpinv = one / ulp
652  rtulp = sqrt( ulp )
653  rtulpi = one / rtulp
654 *
655 * Loop over sizes, types
656 *
657  nerrs = 0
658 *
659  DO 150 jsize = 1, nsizes
660  n = nn( jsize )
661  IF( nsizes.NE.1 ) THEN
662  mtypes = min( maxtyp, ntypes )
663  ELSE
664  mtypes = min( maxtyp+1, ntypes )
665  END IF
666 *
667  DO 140 jtype = 1, mtypes
668  IF( .NOT.dotype( jtype ) )
669  $ go to 140
670 *
671 * Save ISEED in case of an error.
672 *
673  DO 20 j = 1, 4
674  ioldsd( j ) = iseed( j )
675  20 CONTINUE
676 *
677 * Compute "A"
678 *
679 * Control parameters:
680 *
681 * KMAGN KCONDS KMODE KTYPE
682 * =1 O(1) 1 clustered 1 zero
683 * =2 large large clustered 2 identity
684 * =3 small exponential Jordan
685 * =4 arithmetic diagonal, (w/ eigenvalues)
686 * =5 random log symmetric, w/ eigenvalues
687 * =6 random general, w/ eigenvalues
688 * =7 random diagonal
689 * =8 random symmetric
690 * =9 random general
691 * =10 random triangular
692 *
693  IF( mtypes.GT.maxtyp )
694  $ go to 90
695 *
696  itype = ktype( jtype )
697  imode = kmode( jtype )
698 *
699 * Compute norm
700 *
701  go to( 30, 40, 50 )kmagn( jtype )
702 *
703  30 CONTINUE
704  anorm = one
705  go to 60
706 *
707  40 CONTINUE
708  anorm = ovfl*ulp
709  go to 60
710 *
711  50 CONTINUE
712  anorm = unfl*ulpinv
713  go to 60
714 *
715  60 CONTINUE
716 *
717  CALL slaset( 'Full', lda, n, zero, zero, a, lda )
718  iinfo = 0
719  cond = ulpinv
720 *
721 * Special Matrices -- Identity & Jordan block
722 *
723 * Zero
724 *
725  IF( itype.EQ.1 ) THEN
726  iinfo = 0
727 *
728  ELSE IF( itype.EQ.2 ) THEN
729 *
730 * Identity
731 *
732  DO 70 jcol = 1, n
733  a( jcol, jcol ) = anorm
734  70 CONTINUE
735 *
736  ELSE IF( itype.EQ.3 ) THEN
737 *
738 * Jordan Block
739 *
740  DO 80 jcol = 1, n
741  a( jcol, jcol ) = anorm
742  IF( jcol.GT.1 )
743  $ a( jcol, jcol-1 ) = one
744  80 CONTINUE
745 *
746  ELSE IF( itype.EQ.4 ) THEN
747 *
748 * Diagonal Matrix, [Eigen]values Specified
749 *
750  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
751  $ anorm, 0, 0, 'N', a, lda, work( n+1 ),
752  $ iinfo )
753 *
754  ELSE IF( itype.EQ.5 ) THEN
755 *
756 * Symmetric, eigenvalues specified
757 *
758  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
759  $ anorm, n, n, 'N', a, lda, work( n+1 ),
760  $ iinfo )
761 *
762  ELSE IF( itype.EQ.6 ) THEN
763 *
764 * General, eigenvalues specified
765 *
766  IF( kconds( jtype ).EQ.1 ) THEN
767  conds = one
768  ELSE IF( kconds( jtype ).EQ.2 ) THEN
769  conds = rtulpi
770  ELSE
771  conds = zero
772  END IF
773 *
774  adumma( 1 ) = ' '
775  CALL slatme( n, 'S', iseed, work, imode, cond, one,
776  $ adumma, 'T', 'T', 'T', work( n+1 ), 4,
777  $ conds, n, n, anorm, a, lda, work( 2*n+1 ),
778  $ iinfo )
779 *
780  ELSE IF( itype.EQ.7 ) THEN
781 *
782 * Diagonal, random eigenvalues
783 *
784  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
785  $ 'T', 'N', work( n+1 ), 1, one,
786  $ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
787  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
788 *
789  ELSE IF( itype.EQ.8 ) THEN
790 *
791 * Symmetric, random eigenvalues
792 *
793  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
794  $ 'T', 'N', work( n+1 ), 1, one,
795  $ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
796  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
797 *
798  ELSE IF( itype.EQ.9 ) THEN
799 *
800 * General, random eigenvalues
801 *
802  CALL slatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
803  $ 'T', 'N', work( n+1 ), 1, one,
804  $ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
805  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
806  IF( n.GE.4 ) THEN
807  CALL slaset( 'Full', 2, n, zero, zero, a, lda )
808  CALL slaset( 'Full', n-3, 1, zero, zero, a( 3, 1 ),
809  $ lda )
810  CALL slaset( 'Full', n-3, 2, zero, zero, a( 3, n-1 ),
811  $ lda )
812  CALL slaset( 'Full', 1, n, zero, zero, a( n, 1 ),
813  $ lda )
814  END IF
815 *
816  ELSE IF( itype.EQ.10 ) THEN
817 *
818 * Triangular, random eigenvalues
819 *
820  CALL slatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
821  $ 'T', 'N', work( n+1 ), 1, one,
822  $ work( 2*n+1 ), 1, one, 'N', idumma, n, 0,
823  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
824 *
825  ELSE
826 *
827  iinfo = 1
828  END IF
829 *
830  IF( iinfo.NE.0 ) THEN
831  WRITE( nounit, fmt = 9992 )'Generator', iinfo, n, jtype,
832  $ ioldsd
833  info = abs( iinfo )
834  RETURN
835  END IF
836 *
837  90 CONTINUE
838 *
839 * Test for minimal and generous workspace
840 *
841  DO 130 iwk = 1, 3
842  IF( iwk.EQ.1 ) THEN
843  nnwork = 3*n
844  ELSE IF( iwk.EQ.2 ) THEN
845  nnwork = 6*n + n**2
846  ELSE
847  nnwork = 6*n + 2*n**2
848  END IF
849  nnwork = max( nnwork, 1 )
850 *
851 * Test for all balancing options
852 *
853  DO 120 ibal = 1, 4
854  balanc = bal( ibal )
855 *
856 * Perform tests
857 *
858  CALL sget23( .false., balanc, jtype, thresh, ioldsd,
859  $ nounit, n, a, lda, h, wr, wi, wr1, wi1,
860  $ vl, ldvl, vr, ldvr, lre, ldlre, rcondv,
861  $ rcndv1, rcdvin, rconde, rcnde1, rcdein,
862  $ scale, scale1, result, work, nnwork,
863  $ iwork, info )
864 *
865 * Check for RESULT(j) > THRESH
866 *
867  ntest = 0
868  nfail = 0
869  DO 100 j = 1, 9
870  IF( result( j ).GE.zero )
871  $ ntest = ntest + 1
872  IF( result( j ).GE.thresh )
873  $ nfail = nfail + 1
874  100 CONTINUE
875 *
876  IF( nfail.GT.0 )
877  $ ntestf = ntestf + 1
878  IF( ntestf.EQ.1 ) THEN
879  WRITE( nounit, fmt = 9999 )path
880  WRITE( nounit, fmt = 9998 )
881  WRITE( nounit, fmt = 9997 )
882  WRITE( nounit, fmt = 9996 )
883  WRITE( nounit, fmt = 9995 )thresh
884  ntestf = 2
885  END IF
886 *
887  DO 110 j = 1, 9
888  IF( result( j ).GE.thresh ) THEN
889  WRITE( nounit, fmt = 9994 )balanc, n, iwk,
890  $ ioldsd, jtype, j, result( j )
891  END IF
892  110 CONTINUE
893 *
894  nerrs = nerrs + nfail
895  ntestt = ntestt + ntest
896 *
897  120 CONTINUE
898  130 CONTINUE
899  140 CONTINUE
900  150 CONTINUE
901 *
902  160 CONTINUE
903 *
904 * Read in data from file to check accuracy of condition estimation.
905 * Assume input eigenvalues are sorted lexicographically (increasing
906 * by real part, then decreasing by imaginary part)
907 *
908  jtype = 0
909  170 CONTINUE
910  READ( niunit, fmt = *, END = 220 )n
911 *
912 * Read input data until N=0
913 *
914  IF( n.EQ.0 )
915  $ go to 220
916  jtype = jtype + 1
917  iseed( 1 ) = jtype
918  DO 180 i = 1, n
919  READ( niunit, fmt = * )( a( i, j ), j = 1, n )
920  180 CONTINUE
921  DO 190 i = 1, n
922  READ( niunit, fmt = * )wr1( i ), wi1( i ), rcdein( i ),
923  $ rcdvin( i )
924  190 CONTINUE
925  CALL sget23( .true., 'N', 22, thresh, iseed, nounit, n, a, lda, h,
926  $ wr, wi, wr1, wi1, vl, ldvl, vr, ldvr, lre, ldlre,
927  $ rcondv, rcndv1, rcdvin, rconde, rcnde1, rcdein,
928  $ scale, scale1, result, work, 6*n+2*n**2, iwork,
929  $ info )
930 *
931 * Check for RESULT(j) > THRESH
932 *
933  ntest = 0
934  nfail = 0
935  DO 200 j = 1, 11
936  IF( result( j ).GE.zero )
937  $ ntest = ntest + 1
938  IF( result( j ).GE.thresh )
939  $ nfail = nfail + 1
940  200 CONTINUE
941 *
942  IF( nfail.GT.0 )
943  $ ntestf = ntestf + 1
944  IF( ntestf.EQ.1 ) THEN
945  WRITE( nounit, fmt = 9999 )path
946  WRITE( nounit, fmt = 9998 )
947  WRITE( nounit, fmt = 9997 )
948  WRITE( nounit, fmt = 9996 )
949  WRITE( nounit, fmt = 9995 )thresh
950  ntestf = 2
951  END IF
952 *
953  DO 210 j = 1, 11
954  IF( result( j ).GE.thresh ) THEN
955  WRITE( nounit, fmt = 9993 )n, jtype, j, result( j )
956  END IF
957  210 CONTINUE
958 *
959  nerrs = nerrs + nfail
960  ntestt = ntestt + ntest
961  go to 170
962  220 CONTINUE
963 *
964 * Summary
965 *
966  CALL slasum( path, nounit, nerrs, ntestt )
967 *
968  9999 FORMAT( / 1x, a3, ' -- Real Eigenvalue-Eigenvector Decomposition',
969  $ ' Expert Driver', /
970  $ ' Matrix types (see SDRVVX for details): ' )
971 *
972  9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
973  $ ' ', ' 5=Diagonal: geometr. spaced entries.',
974  $ / ' 2=Identity matrix. ', ' 6=Diagona',
975  $ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
976  $ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
977  $ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
978  $ 'mall, evenly spaced.' )
979  9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
980  $ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
981  $ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
982  $ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
983  $ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
984  $ 'lex ', / ' 12=Well-cond., random complex ', ' ',
985  $ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
986  $ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
987  $ ' complx ' )
988  9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
989  $ 'with small random entries.', / ' 20=Matrix with large ran',
990  $ 'dom entries. ', ' 22=Matrix read from input file', / )
991  9995 FORMAT( ' Tests performed with test threshold =', f8.2,
992  $ / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ',
993  $ / ' 2 = | transpose(A) VL - VL W | / ( n |A| ulp ) ',
994  $ / ' 3 = | |VR(i)| - 1 | / ulp ',
995  $ / ' 4 = | |VL(i)| - 1 | / ulp ',
996  $ / ' 5 = 0 if W same no matter if VR or VL computed,',
997  $ ' 1/ulp otherwise', /
998  $ ' 6 = 0 if VR same no matter what else computed,',
999  $ ' 1/ulp otherwise', /
1000  $ ' 7 = 0 if VL same no matter what else computed,',
1001  $ ' 1/ulp otherwise', /
1002  $ ' 8 = 0 if RCONDV same no matter what else computed,',
1003  $ ' 1/ulp otherwise', /
1004  $ ' 9 = 0 if SCALE, ILO, IHI, ABNRM same no matter what else',
1005  $ ' computed, 1/ulp otherwise',
1006  $ / ' 10 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),',
1007  $ / ' 11 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),' )
1008  9994 FORMAT( ' BALANC=''', a1, ''',N=', i4, ',IWK=', i1, ', seed=',
1009  $ 4( i4, ',' ), ' type ', i2, ', test(', i2, ')=', g10.3 )
1010  9993 FORMAT( ' N=', i5, ', input example =', i3, ', test(', i2, ')=',
1011  $ g10.3 )
1012  9992 FORMAT( ' SDRVVX: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
1013  $ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
1014 *
1015  RETURN
1016 *
1017 * End of SDRVVX
1018 *
1019  END