LAPACK  3.7.0 LAPACK: Linear Algebra PACKage
sdrvvx.f
Go to the documentation of this file.
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 *> \date June 2016
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 3.7.0) --
524 * -- LAPACK is a software package provided by Univ. of Tennessee, --
525 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
526 * June 2016
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 ..
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 *
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 )
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
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:522
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:380
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:473
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:323
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:334
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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:112