LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
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 parameter -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 *> \ingroup single_eig
513 *
514 * =====================================================================
515  SUBROUTINE sdrvvx( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
516  $ NIUNIT, NOUNIT, A, LDA, H, WR, WI, WR1, WI1,
517  $ VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, RCNDV1,
518  $ RCDVIN, RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1,
519  $ RESULT, WORK, NWORK, IWORK, INFO )
520 *
521 * -- LAPACK test routine --
522 * -- LAPACK is a software package provided by Univ. of Tennessee, --
523 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
524 *
525 * .. Scalar Arguments ..
526  INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NIUNIT, NOUNIT,
527  $ NSIZES, NTYPES, NWORK
528  REAL THRESH
529 * ..
530 * .. Array Arguments ..
531  LOGICAL DOTYPE( * )
532  INTEGER ISEED( 4 ), IWORK( * ), NN( * )
533  REAL A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
534  $ RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
535  $ rcndv1( * ), rconde( * ), rcondv( * ),
536  $ result( 11 ), scale( * ), scale1( * ),
537  $ vl( ldvl, * ), vr( ldvr, * ), wi( * ),
538  $ wi1( * ), work( * ), wr( * ), wr1( * )
539 * ..
540 *
541 * =====================================================================
542 *
543 * .. Parameters ..
544  REAL ZERO, ONE
545  PARAMETER ( ZERO = 0.0e0, one = 1.0e0 )
546  INTEGER MAXTYP
547  PARAMETER ( MAXTYP = 21 )
548 * ..
549 * .. Local Scalars ..
550  LOGICAL BADNN
551  CHARACTER BALANC
552  CHARACTER*3 PATH
553  INTEGER I, IBAL, IINFO, IMODE, ITYPE, IWK, J, JCOL,
554  $ jsize, jtype, mtypes, n, nerrs, nfail,
555  $ nmax, nnwork, ntest, ntestf, ntestt
556  REAL ANORM, COND, CONDS, OVFL, RTULP, RTULPI, ULP,
557  $ ulpinv, unfl
558 * ..
559 * .. Local Arrays ..
560  CHARACTER ADUMMA( 1 ), BAL( 4 )
561  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
562  $ KMAGN( MAXTYP ), KMODE( MAXTYP ),
563  $ KTYPE( MAXTYP )
564 * ..
565 * .. External Functions ..
566  REAL SLAMCH
567  EXTERNAL SLAMCH
568 * ..
569 * .. External Subroutines ..
570  EXTERNAL sget23, slabad, slasum, slatme, slatmr, slatms,
571  $ slaset, xerbla
572 * ..
573 * .. Intrinsic Functions ..
574  INTRINSIC abs, max, min, sqrt
575 * ..
576 * .. Data statements ..
577  DATA ktype / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
578  DATA kmagn / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
579  $ 3, 1, 2, 3 /
580  DATA kmode / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
581  $ 1, 5, 5, 5, 4, 3, 1 /
582  DATA kconds / 3*0, 5*0, 4*1, 6*2, 3*0 /
583  DATA bal / 'N', 'P', 'S', 'B' /
584 * ..
585 * .. Executable Statements ..
586 *
587  path( 1: 1 ) = 'Single precision'
588  path( 2: 3 ) = 'VX'
589 *
590 * Check for errors
591 *
592  ntestt = 0
593  ntestf = 0
594  info = 0
595 *
596 * Important constants
597 *
598  badnn = .false.
599 *
600 * 12 is the largest dimension in the input file of precomputed
601 * problems
602 *
603  nmax = 12
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 * Check for errors
611 *
612  IF( nsizes.LT.0 ) THEN
613  info = -1
614  ELSE IF( badnn ) THEN
615  info = -2
616  ELSE IF( ntypes.LT.0 ) THEN
617  info = -3
618  ELSE IF( thresh.LT.zero ) THEN
619  info = -6
620  ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
621  info = -10
622  ELSE IF( ldvl.LT.1 .OR. ldvl.LT.nmax ) THEN
623  info = -17
624  ELSE IF( ldvr.LT.1 .OR. ldvr.LT.nmax ) THEN
625  info = -19
626  ELSE IF( ldlre.LT.1 .OR. ldlre.LT.nmax ) THEN
627  info = -21
628  ELSE IF( 6*nmax+2*nmax**2.GT.nwork ) THEN
629  info = -32
630  END IF
631 *
632  IF( info.NE.0 ) THEN
633  CALL xerbla( 'SDRVVX', -info )
634  RETURN
635  END IF
636 *
637 * If nothing to do check on NIUNIT
638 *
639  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
640  $ GO TO 160
641 *
642 * More Important constants
643 *
644  unfl = slamch( 'Safe minimum' )
645  ovfl = one / unfl
646  CALL slabad( unfl, ovfl )
647  ulp = slamch( 'Precision' )
648  ulpinv = one / ulp
649  rtulp = sqrt( ulp )
650  rtulpi = one / rtulp
651 *
652 * Loop over sizes, types
653 *
654  nerrs = 0
655 *
656  DO 150 jsize = 1, nsizes
657  n = nn( jsize )
658  IF( nsizes.NE.1 ) THEN
659  mtypes = min( maxtyp, ntypes )
660  ELSE
661  mtypes = min( maxtyp+1, ntypes )
662  END IF
663 *
664  DO 140 jtype = 1, mtypes
665  IF( .NOT.dotype( jtype ) )
666  $ GO TO 140
667 *
668 * Save ISEED in case of an error.
669 *
670  DO 20 j = 1, 4
671  ioldsd( j ) = iseed( j )
672  20 CONTINUE
673 *
674 * Compute "A"
675 *
676 * Control parameters:
677 *
678 * KMAGN KCONDS KMODE KTYPE
679 * =1 O(1) 1 clustered 1 zero
680 * =2 large large clustered 2 identity
681 * =3 small exponential Jordan
682 * =4 arithmetic diagonal, (w/ eigenvalues)
683 * =5 random log symmetric, w/ eigenvalues
684 * =6 random general, w/ eigenvalues
685 * =7 random diagonal
686 * =8 random symmetric
687 * =9 random general
688 * =10 random triangular
689 *
690  IF( mtypes.GT.maxtyp )
691  $ GO TO 90
692 *
693  itype = ktype( jtype )
694  imode = kmode( jtype )
695 *
696 * Compute norm
697 *
698  GO TO ( 30, 40, 50 )kmagn( jtype )
699 *
700  30 CONTINUE
701  anorm = one
702  GO TO 60
703 *
704  40 CONTINUE
705  anorm = ovfl*ulp
706  GO TO 60
707 *
708  50 CONTINUE
709  anorm = unfl*ulpinv
710  GO TO 60
711 *
712  60 CONTINUE
713 *
714  CALL slaset( 'Full', lda, n, zero, zero, a, lda )
715  iinfo = 0
716  cond = ulpinv
717 *
718 * Special Matrices -- Identity & Jordan block
719 *
720 * Zero
721 *
722  IF( itype.EQ.1 ) THEN
723  iinfo = 0
724 *
725  ELSE IF( itype.EQ.2 ) THEN
726 *
727 * Identity
728 *
729  DO 70 jcol = 1, n
730  a( jcol, jcol ) = anorm
731  70 CONTINUE
732 *
733  ELSE IF( itype.EQ.3 ) THEN
734 *
735 * Jordan Block
736 *
737  DO 80 jcol = 1, n
738  a( jcol, jcol ) = anorm
739  IF( jcol.GT.1 )
740  $ a( jcol, jcol-1 ) = one
741  80 CONTINUE
742 *
743  ELSE IF( itype.EQ.4 ) THEN
744 *
745 * Diagonal Matrix, [Eigen]values Specified
746 *
747  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
748  $ anorm, 0, 0, 'N', a, lda, work( n+1 ),
749  $ iinfo )
750 *
751  ELSE IF( itype.EQ.5 ) THEN
752 *
753 * Symmetric, eigenvalues specified
754 *
755  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
756  $ anorm, n, n, 'N', a, lda, work( n+1 ),
757  $ iinfo )
758 *
759  ELSE IF( itype.EQ.6 ) THEN
760 *
761 * General, eigenvalues specified
762 *
763  IF( kconds( jtype ).EQ.1 ) THEN
764  conds = one
765  ELSE IF( kconds( jtype ).EQ.2 ) THEN
766  conds = rtulpi
767  ELSE
768  conds = zero
769  END IF
770 *
771  adumma( 1 ) = ' '
772  CALL slatme( n, 'S', iseed, work, imode, cond, one,
773  $ adumma, 'T', 'T', 'T', work( n+1 ), 4,
774  $ conds, n, n, anorm, a, lda, work( 2*n+1 ),
775  $ iinfo )
776 *
777  ELSE IF( itype.EQ.7 ) THEN
778 *
779 * Diagonal, random eigenvalues
780 *
781  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
782  $ 'T', 'N', work( n+1 ), 1, one,
783  $ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
784  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
785 *
786  ELSE IF( itype.EQ.8 ) THEN
787 *
788 * Symmetric, random eigenvalues
789 *
790  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
791  $ 'T', 'N', work( n+1 ), 1, one,
792  $ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
793  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
794 *
795  ELSE IF( itype.EQ.9 ) THEN
796 *
797 * General, random eigenvalues
798 *
799  CALL slatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
800  $ 'T', 'N', work( n+1 ), 1, one,
801  $ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
802  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
803  IF( n.GE.4 ) THEN
804  CALL slaset( 'Full', 2, n, zero, zero, a, lda )
805  CALL slaset( 'Full', n-3, 1, zero, zero, a( 3, 1 ),
806  $ lda )
807  CALL slaset( 'Full', n-3, 2, zero, zero, a( 3, n-1 ),
808  $ lda )
809  CALL slaset( 'Full', 1, n, zero, zero, a( n, 1 ),
810  $ lda )
811  END IF
812 *
813  ELSE IF( itype.EQ.10 ) THEN
814 *
815 * Triangular, random eigenvalues
816 *
817  CALL slatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
818  $ 'T', 'N', work( n+1 ), 1, one,
819  $ work( 2*n+1 ), 1, one, 'N', idumma, n, 0,
820  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
821 *
822  ELSE
823 *
824  iinfo = 1
825  END IF
826 *
827  IF( iinfo.NE.0 ) THEN
828  WRITE( nounit, fmt = 9992 )'Generator', iinfo, n, jtype,
829  $ ioldsd
830  info = abs( iinfo )
831  RETURN
832  END IF
833 *
834  90 CONTINUE
835 *
836 * Test for minimal and generous workspace
837 *
838  DO 130 iwk = 1, 3
839  IF( iwk.EQ.1 ) THEN
840  nnwork = 3*n
841  ELSE IF( iwk.EQ.2 ) THEN
842  nnwork = 6*n + n**2
843  ELSE
844  nnwork = 6*n + 2*n**2
845  END IF
846  nnwork = max( nnwork, 1 )
847 *
848 * Test for all balancing options
849 *
850  DO 120 ibal = 1, 4
851  balanc = bal( ibal )
852 *
853 * Perform tests
854 *
855  CALL sget23( .false., balanc, jtype, thresh, ioldsd,
856  $ nounit, n, a, lda, h, wr, wi, wr1, wi1,
857  $ vl, ldvl, vr, ldvr, lre, ldlre, rcondv,
858  $ rcndv1, rcdvin, rconde, rcnde1, rcdein,
859  $ scale, scale1, result, work, nnwork,
860  $ iwork, info )
861 *
862 * Check for RESULT(j) > THRESH
863 *
864  ntest = 0
865  nfail = 0
866  DO 100 j = 1, 9
867  IF( result( j ).GE.zero )
868  $ ntest = ntest + 1
869  IF( result( j ).GE.thresh )
870  $ nfail = nfail + 1
871  100 CONTINUE
872 *
873  IF( nfail.GT.0 )
874  $ ntestf = ntestf + 1
875  IF( ntestf.EQ.1 ) THEN
876  WRITE( nounit, fmt = 9999 )path
877  WRITE( nounit, fmt = 9998 )
878  WRITE( nounit, fmt = 9997 )
879  WRITE( nounit, fmt = 9996 )
880  WRITE( nounit, fmt = 9995 )thresh
881  ntestf = 2
882  END IF
883 *
884  DO 110 j = 1, 9
885  IF( result( j ).GE.thresh ) THEN
886  WRITE( nounit, fmt = 9994 )balanc, n, iwk,
887  $ ioldsd, jtype, j, result( j )
888  END IF
889  110 CONTINUE
890 *
891  nerrs = nerrs + nfail
892  ntestt = ntestt + ntest
893 *
894  120 CONTINUE
895  130 CONTINUE
896  140 CONTINUE
897  150 CONTINUE
898 *
899  160 CONTINUE
900 *
901 * Read in data from file to check accuracy of condition estimation.
902 * Assume input eigenvalues are sorted lexicographically (increasing
903 * by real part, then decreasing by imaginary part)
904 *
905  jtype = 0
906  170 CONTINUE
907  READ( niunit, fmt = *, END = 220 )n
908 *
909 * Read input data until N=0
910 *
911  IF( n.EQ.0 )
912  $ GO TO 220
913  jtype = jtype + 1
914  iseed( 1 ) = jtype
915  DO 180 i = 1, n
916  READ( niunit, fmt = * )( a( i, j ), j = 1, n )
917  180 CONTINUE
918  DO 190 i = 1, n
919  READ( niunit, fmt = * )wr1( i ), wi1( i ), rcdein( i ),
920  $ rcdvin( i )
921  190 CONTINUE
922  CALL sget23( .true., 'N', 22, thresh, iseed, nounit, n, a, lda, h,
923  $ wr, wi, wr1, wi1, vl, ldvl, vr, ldvr, lre, ldlre,
924  $ rcondv, rcndv1, rcdvin, rconde, rcnde1, rcdein,
925  $ scale, scale1, result, work, 6*n+2*n**2, iwork,
926  $ info )
927 *
928 * Check for RESULT(j) > THRESH
929 *
930  ntest = 0
931  nfail = 0
932  DO 200 j = 1, 11
933  IF( result( j ).GE.zero )
934  $ ntest = ntest + 1
935  IF( result( j ).GE.thresh )
936  $ nfail = nfail + 1
937  200 CONTINUE
938 *
939  IF( nfail.GT.0 )
940  $ ntestf = ntestf + 1
941  IF( ntestf.EQ.1 ) THEN
942  WRITE( nounit, fmt = 9999 )path
943  WRITE( nounit, fmt = 9998 )
944  WRITE( nounit, fmt = 9997 )
945  WRITE( nounit, fmt = 9996 )
946  WRITE( nounit, fmt = 9995 )thresh
947  ntestf = 2
948  END IF
949 *
950  DO 210 j = 1, 11
951  IF( result( j ).GE.thresh ) THEN
952  WRITE( nounit, fmt = 9993 )n, jtype, j, result( j )
953  END IF
954  210 CONTINUE
955 *
956  nerrs = nerrs + nfail
957  ntestt = ntestt + ntest
958  GO TO 170
959  220 CONTINUE
960 *
961 * Summary
962 *
963  CALL slasum( path, nounit, nerrs, ntestt )
964 *
965  9999 FORMAT( / 1x, a3, ' -- Real Eigenvalue-Eigenvector Decomposition',
966  $ ' Expert Driver', /
967  $ ' Matrix types (see SDRVVX for details): ' )
968 *
969  9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
970  $ ' ', ' 5=Diagonal: geometr. spaced entries.',
971  $ / ' 2=Identity matrix. ', ' 6=Diagona',
972  $ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
973  $ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
974  $ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
975  $ 'mall, evenly spaced.' )
976  9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
977  $ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
978  $ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
979  $ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
980  $ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
981  $ 'lex ', / ' 12=Well-cond., random complex ', ' ',
982  $ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
983  $ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
984  $ ' complx ' )
985  9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
986  $ 'with small random entries.', / ' 20=Matrix with large ran',
987  $ 'dom entries. ', ' 22=Matrix read from input file', / )
988  9995 FORMAT( ' Tests performed with test threshold =', f8.2,
989  $ / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ',
990  $ / ' 2 = | transpose(A) VL - VL W | / ( n |A| ulp ) ',
991  $ / ' 3 = | |VR(i)| - 1 | / ulp ',
992  $ / ' 4 = | |VL(i)| - 1 | / ulp ',
993  $ / ' 5 = 0 if W same no matter if VR or VL computed,',
994  $ ' 1/ulp otherwise', /
995  $ ' 6 = 0 if VR same no matter what else computed,',
996  $ ' 1/ulp otherwise', /
997  $ ' 7 = 0 if VL same no matter what else computed,',
998  $ ' 1/ulp otherwise', /
999  $ ' 8 = 0 if RCONDV same no matter what else computed,',
1000  $ ' 1/ulp otherwise', /
1001  $ ' 9 = 0 if SCALE, ILO, IHI, ABNRM same no matter what else',
1002  $ ' computed, 1/ulp otherwise',
1003  $ / ' 10 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),',
1004  $ / ' 11 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),' )
1005  9994 FORMAT( ' BALANC=''', a1, ''',N=', i4, ',IWK=', i1, ', seed=',
1006  $ 4( i4, ',' ), ' type ', i2, ', test(', i2, ')=', g10.3 )
1007  9993 FORMAT( ' N=', i5, ', input example =', i3, ', test(', i2, ')=',
1008  $ g10.3 )
1009  9992 FORMAT( ' SDRVVX: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
1010  $ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
1011 *
1012  RETURN
1013 *
1014 * End of SDRVVX
1015 *
1016  END
subroutine slabad(SMALL, LARGE)
SLABAD
Definition: slabad.f:74
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:321
subroutine slatme(N, DIST, ISEED, D, MODE, COND, DMAX, EI, RSIGN, UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, A, LDA, WORK, INFO)
SLATME
Definition: slatme.f:332
subroutine slatmr(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, PACK, A, LDA, IWORK, INFO)
SLATMR
Definition: slatmr.f:471
subroutine sdrvvx(NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, NIUNIT, NOUNIT, A, LDA, H, WR, WI, WR1, WI1, VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN, RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT, WORK, NWORK, IWORK, INFO)
SDRVVX
Definition: sdrvvx.f:520
subroutine sget23(COMP, BALANC, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA, H, WR, WI, WR1, WI1, VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN, RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT, WORK, LWORK, IWORK, INFO)
SGET23
Definition: sget23.f:378
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:41