LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
sdrvsx.f
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1 *> \brief \b SDRVSX
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 SDRVSX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
12 * NIUNIT, NOUNIT, A, LDA, H, HT, WR, WI, WRT,
13 * WIT, WRTMP, WITMP, VS, LDVS, VS1, RESULT, WORK,
14 * LWORK, IWORK, BWORK, INFO )
15 *
16 * .. Scalar Arguments ..
17 * INTEGER INFO, LDA, LDVS, LWORK, NIUNIT, NOUNIT, NSIZES,
18 * \$ NTYPES
19 * REAL THRESH
20 * ..
21 * .. Array Arguments ..
22 * LOGICAL BWORK( * ), DOTYPE( * )
23 * INTEGER ISEED( 4 ), IWORK( * ), NN( * )
24 * REAL A( LDA, * ), H( LDA, * ), HT( LDA, * ),
25 * \$ RESULT( 17 ), VS( LDVS, * ), VS1( LDVS, * ),
26 * \$ WI( * ), WIT( * ), WITMP( * ), WORK( * ),
27 * \$ WR( * ), WRT( * ), WRTMP( * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> SDRVSX checks the nonsymmetric eigenvalue (Schur form) problem
37 *> expert driver SGEESX.
38 *>
39 *> SDRVSX uses both test matrices generated randomly depending on
40 *> data supplied in the calling sequence, as well as on data
41 *> read from an input file and including precomputed condition
42 *> numbers to which it compares the ones it computes.
43 *>
44 *> When SDRVSX is called, a number of matrix "sizes" ("n's") and a
45 *> number of matrix "types" are specified. For each size ("n")
46 *> and each type of matrix, one matrix will be generated and used
47 *> to test the nonsymmetric eigenroutines. For each matrix, 15
48 *> tests will be performed:
49 *>
50 *> (1) 0 if T is in Schur form, 1/ulp otherwise
51 *> (no sorting of eigenvalues)
52 *>
53 *> (2) | A - VS T VS' | / ( n |A| ulp )
54 *>
55 *> Here VS is the matrix of Schur eigenvectors, and T is in Schur
56 *> form (no sorting of eigenvalues).
57 *>
58 *> (3) | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).
59 *>
60 *> (4) 0 if WR+sqrt(-1)*WI are eigenvalues of T
61 *> 1/ulp otherwise
62 *> (no sorting of eigenvalues)
63 *>
64 *> (5) 0 if T(with VS) = T(without VS),
65 *> 1/ulp otherwise
66 *> (no sorting of eigenvalues)
67 *>
68 *> (6) 0 if eigenvalues(with VS) = eigenvalues(without VS),
69 *> 1/ulp otherwise
70 *> (no sorting of eigenvalues)
71 *>
72 *> (7) 0 if T is in Schur form, 1/ulp otherwise
73 *> (with sorting of eigenvalues)
74 *>
75 *> (8) | A - VS T VS' | / ( n |A| ulp )
76 *>
77 *> Here VS is the matrix of Schur eigenvectors, and T is in Schur
78 *> form (with sorting of eigenvalues).
79 *>
80 *> (9) | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).
81 *>
82 *> (10) 0 if WR+sqrt(-1)*WI are eigenvalues of T
83 *> 1/ulp otherwise
84 *> If workspace sufficient, also compare WR, WI with and
85 *> without reciprocal condition numbers
86 *> (with sorting of eigenvalues)
87 *>
88 *> (11) 0 if T(with VS) = T(without VS),
89 *> 1/ulp otherwise
90 *> If workspace sufficient, also compare T with and without
91 *> reciprocal condition numbers
92 *> (with sorting of eigenvalues)
93 *>
94 *> (12) 0 if eigenvalues(with VS) = eigenvalues(without VS),
95 *> 1/ulp otherwise
96 *> If workspace sufficient, also compare VS with and without
97 *> reciprocal condition numbers
98 *> (with sorting of eigenvalues)
99 *>
100 *> (13) if sorting worked and SDIM is the number of
101 *> eigenvalues which were SELECTed
102 *> If workspace sufficient, also compare SDIM with and
103 *> without reciprocal condition numbers
104 *>
105 *> (14) if RCONDE the same no matter if VS and/or RCONDV computed
106 *>
107 *> (15) if RCONDV the same no matter if VS and/or RCONDE computed
108 *>
109 *> The "sizes" are specified by an array NN(1:NSIZES); the value of
110 *> each element NN(j) specifies one size.
111 *> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
112 *> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
113 *> Currently, the list of possible types is:
114 *>
115 *> (1) The zero matrix.
116 *> (2) The identity matrix.
117 *> (3) A (transposed) Jordan block, with 1's on the diagonal.
118 *>
119 *> (4) A diagonal matrix with evenly spaced entries
120 *> 1, ..., ULP and random signs.
121 *> (ULP = (first number larger than 1) - 1 )
122 *> (5) A diagonal matrix with geometrically spaced entries
123 *> 1, ..., ULP and random signs.
124 *> (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
125 *> and random signs.
126 *>
127 *> (7) Same as (4), but multiplied by a constant near
128 *> the overflow threshold
129 *> (8) Same as (4), but multiplied by a constant near
130 *> the underflow threshold
131 *>
132 *> (9) A matrix of the form U' T U, where U is orthogonal and
133 *> T has evenly spaced entries 1, ..., ULP with random signs
134 *> on the diagonal and random O(1) entries in the upper
135 *> triangle.
136 *>
137 *> (10) A matrix of the form U' T U, where U is orthogonal and
138 *> T has geometrically spaced entries 1, ..., ULP with random
139 *> signs on the diagonal and random O(1) entries in the upper
140 *> triangle.
141 *>
142 *> (11) A matrix of the form U' T U, where U is orthogonal and
143 *> T has "clustered" entries 1, ULP,..., ULP with random
144 *> signs on the diagonal and random O(1) entries in the upper
145 *> triangle.
146 *>
147 *> (12) A matrix of the form U' T U, where U is orthogonal and
148 *> T has real or complex conjugate paired eigenvalues randomly
149 *> chosen from ( ULP, 1 ) and random O(1) entries in the upper
150 *> triangle.
151 *>
152 *> (13) A matrix of the form X' T X, where X has condition
153 *> SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
154 *> with random signs on the diagonal and random O(1) entries
155 *> in the upper triangle.
156 *>
157 *> (14) A matrix of the form X' T X, where X has condition
158 *> SQRT( ULP ) and T has geometrically spaced entries
159 *> 1, ..., ULP with random signs on the diagonal and random
160 *> O(1) entries in the upper triangle.
161 *>
162 *> (15) A matrix of the form X' T X, where X has condition
163 *> SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
164 *> with random signs on the diagonal and random O(1) entries
165 *> in the upper triangle.
166 *>
167 *> (16) A matrix of the form X' T X, where X has condition
168 *> SQRT( ULP ) and T has real or complex conjugate paired
169 *> eigenvalues randomly chosen from ( ULP, 1 ) and random
170 *> O(1) entries in the upper triangle.
171 *>
172 *> (17) Same as (16), but multiplied by a constant
173 *> near the overflow threshold
174 *> (18) Same as (16), but multiplied by a constant
175 *> near the underflow threshold
176 *>
177 *> (19) Nonsymmetric matrix with random entries chosen from (-1,1).
178 *> If N is at least 4, all entries in first two rows and last
179 *> row, and first column and last two columns are zero.
180 *> (20) Same as (19), but multiplied by a constant
181 *> near the overflow threshold
182 *> (21) Same as (19), but multiplied by a constant
183 *> near the underflow threshold
184 *>
185 *> In addition, an input file will be read from logical unit number
186 *> NIUNIT. The file contains matrices along with precomputed
187 *> eigenvalues and reciprocal condition numbers for the eigenvalue
188 *> average and right invariant subspace. For these matrices, in
189 *> addition to tests (1) to (15) we will compute the following two
190 *> tests:
191 *>
192 *> (16) |RCONDE - RCDEIN| / cond(RCONDE)
193 *>
194 *> RCONDE is the reciprocal average eigenvalue condition number
195 *> computed by SGEESX and RCDEIN (the precomputed true value)
196 *> is supplied as input. cond(RCONDE) is the condition number
197 *> of RCONDE, and takes errors in computing RCONDE into account,
198 *> so that the resulting quantity should be O(ULP). cond(RCONDE)
199 *> is essentially given by norm(A)/RCONDV.
200 *>
201 *> (17) |RCONDV - RCDVIN| / cond(RCONDV)
202 *>
203 *> RCONDV is the reciprocal right invariant subspace condition
204 *> number computed by SGEESX and RCDVIN (the precomputed true
205 *> value) is supplied as input. cond(RCONDV) is the condition
206 *> number of RCONDV, and takes errors in computing RCONDV into
207 *> account, so that the resulting quantity should be O(ULP).
208 *> cond(RCONDV) is essentially given by norm(A)/RCONDE.
209 *> \endverbatim
210 *
211 * Arguments:
212 * ==========
213 *
214 *> \param[in] NSIZES
215 *> \verbatim
216 *> NSIZES is INTEGER
217 *> The number of sizes of matrices to use. NSIZES must be at
218 *> least zero. If it is zero, no randomly generated matrices
219 *> are tested, but any test matrices read from NIUNIT will be
220 *> tested.
221 *> \endverbatim
222 *>
223 *> \param[in] NN
224 *> \verbatim
225 *> NN is INTEGER array, dimension (NSIZES)
226 *> An array containing the sizes to be used for the matrices.
227 *> Zero values will be skipped. The values must be at least
228 *> zero.
229 *> \endverbatim
230 *>
231 *> \param[in] NTYPES
232 *> \verbatim
233 *> NTYPES is INTEGER
234 *> The number of elements in DOTYPE. NTYPES must be at least
235 *> zero. If it is zero, no randomly generated test matrices
236 *> are tested, but and test matrices read from NIUNIT will be
237 *> tested. If it is MAXTYP+1 and NSIZES is 1, then an
238 *> additional type, MAXTYP+1 is defined, which is to use
239 *> whatever matrix is in A. This is only useful if
240 *> DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. .
241 *> \endverbatim
242 *>
243 *> \param[in] DOTYPE
244 *> \verbatim
245 *> DOTYPE is LOGICAL array, dimension (NTYPES)
246 *> If DOTYPE(j) is .TRUE., then for each size in NN a
247 *> matrix of that size and of type j will be generated.
248 *> If NTYPES is smaller than the maximum number of types
249 *> defined (PARAMETER MAXTYP), then types NTYPES+1 through
250 *> MAXTYP will not be generated. If NTYPES is larger
251 *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
252 *> will be ignored.
253 *> \endverbatim
254 *>
255 *> \param[in,out] ISEED
256 *> \verbatim
257 *> ISEED is INTEGER array, dimension (4)
258 *> On entry ISEED specifies the seed of the random number
259 *> generator. The array elements should be between 0 and 4095;
260 *> if not they will be reduced mod 4096. Also, ISEED(4) must
261 *> be odd. The random number generator uses a linear
262 *> congruential sequence limited to small integers, and so
263 *> should produce machine independent random numbers. The
264 *> values of ISEED are changed on exit, and can be used in the
265 *> next call to SDRVSX to continue the same random number
266 *> sequence.
267 *> \endverbatim
268 *>
269 *> \param[in] THRESH
270 *> \verbatim
271 *> THRESH is REAL
272 *> A test will count as "failed" if the "error", computed as
273 *> described above, exceeds THRESH. Note that the error
274 *> is scaled to be O(1), so THRESH should be a reasonably
275 *> small multiple of 1, e.g., 10 or 100. In particular,
276 *> it should not depend on the precision (single vs. double)
277 *> or the size of the matrix. It must be at least zero.
278 *> \endverbatim
279 *>
280 *> \param[in] NIUNIT
281 *> \verbatim
282 *> NIUNIT is INTEGER
283 *> The FORTRAN unit number for reading in the data file of
284 *> problems to solve.
285 *> \endverbatim
286 *>
287 *> \param[in] NOUNIT
288 *> \verbatim
289 *> NOUNIT is INTEGER
290 *> The FORTRAN unit number for printing out error messages
291 *> (e.g., if a routine returns INFO not equal to 0.)
292 *> \endverbatim
293 *>
294 *> \param[out] A
295 *> \verbatim
296 *> A is REAL array, dimension (LDA, max(NN))
297 *> Used to hold the matrix whose eigenvalues are to be
298 *> computed. On exit, A contains the last matrix actually used.
299 *> \endverbatim
300 *>
301 *> \param[in] LDA
302 *> \verbatim
303 *> LDA is INTEGER
304 *> The leading dimension of A, and H. LDA must be at
305 *> least 1 and at least max( NN ).
306 *> \endverbatim
307 *>
308 *> \param[out] H
309 *> \verbatim
310 *> H is REAL array, dimension (LDA, max(NN))
311 *> Another copy of the test matrix A, modified by SGEESX.
312 *> \endverbatim
313 *>
314 *> \param[out] HT
315 *> \verbatim
316 *> HT is REAL array, dimension (LDA, max(NN))
317 *> Yet another copy of the test matrix A, modified by SGEESX.
318 *> \endverbatim
319 *>
320 *> \param[out] WR
321 *> \verbatim
322 *> WR is REAL array, dimension (max(NN))
323 *> \endverbatim
324 *>
325 *> \param[out] WI
326 *> \verbatim
327 *> WI is REAL array, dimension (max(NN))
328 *>
329 *> The real and imaginary parts of the eigenvalues of A.
330 *> On exit, WR + WI*i are the eigenvalues of the matrix in A.
331 *> \endverbatim
332 *>
333 *> \param[out] WRT
334 *> \verbatim
335 *> WRT is REAL array, dimension (max(NN))
336 *> \endverbatim
337 *>
338 *> \param[out] WIT
339 *> \verbatim
340 *> WIT is REAL array, dimension (max(NN))
341 *>
342 *> Like WR, WI, these arrays contain the eigenvalues of A,
343 *> but those computed when SGEESX only computes a partial
344 *> eigendecomposition, i.e. not Schur vectors
345 *> \endverbatim
346 *>
347 *> \param[out] WRTMP
348 *> \verbatim
349 *> WRTMP is REAL array, dimension (max(NN))
350 *> \endverbatim
351 *>
352 *> \param[out] WITMP
353 *> \verbatim
354 *> WITMP is REAL array, dimension (max(NN))
355 *>
356 *> More temporary storage for eigenvalues.
357 *> \endverbatim
358 *>
359 *> \param[out] VS
360 *> \verbatim
361 *> VS is REAL array, dimension (LDVS, max(NN))
362 *> VS holds the computed Schur vectors.
363 *> \endverbatim
364 *>
365 *> \param[in] LDVS
366 *> \verbatim
367 *> LDVS is INTEGER
368 *> Leading dimension of VS. Must be at least max(1,max(NN)).
369 *> \endverbatim
370 *>
371 *> \param[out] VS1
372 *> \verbatim
373 *> VS1 is REAL array, dimension (LDVS, max(NN))
374 *> VS1 holds another copy of the computed Schur vectors.
375 *> \endverbatim
376 *>
377 *> \param[out] RESULT
378 *> \verbatim
379 *> RESULT is REAL array, dimension (17)
380 *> The values computed by the 17 tests described above.
381 *> The values are currently limited to 1/ulp, to avoid overflow.
382 *> \endverbatim
383 *>
384 *> \param[out] WORK
385 *> \verbatim
386 *> WORK is REAL array, dimension (LWORK)
387 *> \endverbatim
388 *>
389 *> \param[in] LWORK
390 *> \verbatim
391 *> LWORK is INTEGER
392 *> The number of entries in WORK. This must be at least
393 *> max(3*NN(j),2*NN(j)**2) for all j.
394 *> \endverbatim
395 *>
396 *> \param[out] IWORK
397 *> \verbatim
398 *> IWORK is INTEGER array, dimension (max(NN)*max(NN))
399 *> \endverbatim
400 *>
401 *> \param[out] BWORK
402 *> \verbatim
403 *> BWORK is LOGICAL array, dimension (max(NN))
404 *> \endverbatim
405 *>
406 *> \param[out] INFO
407 *> \verbatim
408 *> INFO is INTEGER
409 *> If 0, successful exit.
410 *> <0, input parameter -INFO is incorrect
411 *> >0, SLATMR, SLATMS, SLATME or SGET24 returned an error
412 *> code and INFO is its absolute value
413 *>
414 *>-----------------------------------------------------------------------
415 *>
416 *> Some Local Variables and Parameters:
417 *> ---- ----- --------- --- ----------
418 *> ZERO, ONE Real 0 and 1.
419 *> MAXTYP The number of types defined.
420 *> NMAX Largest value in NN.
421 *> NERRS The number of tests which have exceeded THRESH
422 *> COND, CONDS,
423 *> IMODE Values to be passed to the matrix generators.
424 *> ANORM Norm of A; passed to matrix generators.
425 *>
426 *> OVFL, UNFL Overflow and underflow thresholds.
427 *> ULP, ULPINV Finest relative precision and its inverse.
428 *> RTULP, RTULPI Square roots of the previous 4 values.
429 *> The following four arrays decode JTYPE:
430 *> KTYPE(j) The general type (1-10) for type "j".
431 *> KMODE(j) The MODE value to be passed to the matrix
432 *> generator for type "j".
433 *> KMAGN(j) The order of magnitude ( O(1),
434 *> O(overflow^(1/2) ), O(underflow^(1/2) )
435 *> KCONDS(j) Selectw whether CONDS is to be 1 or
436 *> 1/sqrt(ulp). (0 means irrelevant.)
437 *> \endverbatim
438 *
439 * Authors:
440 * ========
441 *
442 *> \author Univ. of Tennessee
443 *> \author Univ. of California Berkeley
444 *> \author Univ. of Colorado Denver
445 *> \author NAG Ltd.
446 *
447 *> \date June 2016
448 *
449 *> \ingroup single_eig
450 *
451 * =====================================================================
452  SUBROUTINE sdrvsx( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
453  \$ niunit, nounit, a, lda, h, ht, wr, wi, wrt,
454  \$ wit, wrtmp, witmp, vs, ldvs, vs1, result, work,
455  \$ lwork, iwork, bwork, info )
456 *
457 * -- LAPACK test routine (version 3.6.1) --
458 * -- LAPACK is a software package provided by Univ. of Tennessee, --
459 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
460 * June 2016
461 *
462 * .. Scalar Arguments ..
463  INTEGER INFO, LDA, LDVS, LWORK, NIUNIT, NOUNIT, NSIZES,
464  \$ ntypes
465  REAL THRESH
466 * ..
467 * .. Array Arguments ..
468  LOGICAL BWORK( * ), DOTYPE( * )
469  INTEGER ISEED( 4 ), IWORK( * ), NN( * )
470  REAL A( lda, * ), H( lda, * ), HT( lda, * ),
471  \$ result( 17 ), vs( ldvs, * ), vs1( ldvs, * ),
472  \$ wi( * ), wit( * ), witmp( * ), work( * ),
473  \$ wr( * ), wrt( * ), wrtmp( * )
474 * ..
475 *
476 * =====================================================================
477 *
478 * .. Parameters ..
479  REAL ZERO, ONE
480  parameter ( zero = 0.0e0, one = 1.0e0 )
481  INTEGER MAXTYP
482  parameter ( maxtyp = 21 )
483 * ..
484 * .. Local Scalars ..
486  CHARACTER*3 PATH
487  INTEGER I, IINFO, IMODE, ITYPE, IWK, J, JCOL, JSIZE,
488  \$ jtype, mtypes, n, nerrs, nfail, nmax,
489  \$ nnwork, nslct, ntest, ntestf, ntestt
490  REAL ANORM, COND, CONDS, OVFL, RCDEIN, RCDVIN,
491  \$ rtulp, rtulpi, ulp, ulpinv, unfl
492 * ..
493 * .. Local Arrays ..
495  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), ISLCT( 20 ),
496  \$ kconds( maxtyp ), kmagn( maxtyp ),
497  \$ kmode( maxtyp ), ktype( maxtyp )
498 * ..
499 * .. Arrays in Common ..
500  LOGICAL SELVAL( 20 )
501  REAL SELWI( 20 ), SELWR( 20 )
502 * ..
503 * .. Scalars in Common ..
504  INTEGER SELDIM, SELOPT
505 * ..
506 * .. Common blocks ..
507  COMMON / sslct / selopt, seldim, selval, selwr, selwi
508 * ..
509 * .. External Functions ..
510  REAL SLAMCH
511  EXTERNAL slamch
512 * ..
513 * .. External Subroutines ..
514  EXTERNAL sget24, slabad, slasum, slatme, slatmr, slatms,
515  \$ slaset, xerbla
516 * ..
517 * .. Intrinsic Functions ..
518  INTRINSIC abs, max, min, sqrt
519 * ..
520 * .. Data statements ..
521  DATA ktype / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
522  DATA kmagn / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
523  \$ 3, 1, 2, 3 /
524  DATA kmode / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
525  \$ 1, 5, 5, 5, 4, 3, 1 /
526  DATA kconds / 3*0, 5*0, 4*1, 6*2, 3*0 /
527 * ..
528 * .. Executable Statements ..
529 *
530  path( 1: 1 ) = 'Single precision'
531  path( 2: 3 ) = 'SX'
532 *
533 * Check for errors
534 *
535  ntestt = 0
536  ntestf = 0
537  info = 0
538 *
539 * Important constants
540 *
542 *
543 * 12 is the largest dimension in the input file of precomputed
544 * problems
545 *
546  nmax = 12
547  DO 10 j = 1, nsizes
548  nmax = max( nmax, nn( j ) )
549  IF( nn( j ).LT.0 )
551  10 CONTINUE
552 *
553 * Check for errors
554 *
555  IF( nsizes.LT.0 ) THEN
556  info = -1
557  ELSE IF( badnn ) THEN
558  info = -2
559  ELSE IF( ntypes.LT.0 ) THEN
560  info = -3
561  ELSE IF( thresh.LT.zero ) THEN
562  info = -6
563  ELSE IF( niunit.LE.0 ) THEN
564  info = -7
565  ELSE IF( nounit.LE.0 ) THEN
566  info = -8
567  ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
568  info = -10
569  ELSE IF( ldvs.LT.1 .OR. ldvs.LT.nmax ) THEN
570  info = -20
571  ELSE IF( max( 3*nmax, 2*nmax**2 ).GT.lwork ) THEN
572  info = -24
573  END IF
574 *
575  IF( info.NE.0 ) THEN
576  CALL xerbla( 'SDRVSX', -info )
577  RETURN
578  END IF
579 *
580 * If nothing to do check on NIUNIT
581 *
582  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
583  \$ GO TO 150
584 *
585 * More Important constants
586 *
587  unfl = slamch( 'Safe minimum' )
588  ovfl = one / unfl
589  CALL slabad( unfl, ovfl )
590  ulp = slamch( 'Precision' )
591  ulpinv = one / ulp
592  rtulp = sqrt( ulp )
593  rtulpi = one / rtulp
594 *
595 * Loop over sizes, types
596 *
597  nerrs = 0
598 *
599  DO 140 jsize = 1, nsizes
600  n = nn( jsize )
601  IF( nsizes.NE.1 ) THEN
602  mtypes = min( maxtyp, ntypes )
603  ELSE
604  mtypes = min( maxtyp+1, ntypes )
605  END IF
606 *
607  DO 130 jtype = 1, mtypes
608  IF( .NOT.dotype( jtype ) )
609  \$ GO TO 130
610 *
611 * Save ISEED in case of an error.
612 *
613  DO 20 j = 1, 4
614  ioldsd( j ) = iseed( j )
615  20 CONTINUE
616 *
617 * Compute "A"
618 *
619 * Control parameters:
620 *
621 * KMAGN KCONDS KMODE KTYPE
622 * =1 O(1) 1 clustered 1 zero
623 * =2 large large clustered 2 identity
624 * =3 small exponential Jordan
625 * =4 arithmetic diagonal, (w/ eigenvalues)
626 * =5 random log symmetric, w/ eigenvalues
627 * =6 random general, w/ eigenvalues
628 * =7 random diagonal
629 * =8 random symmetric
630 * =9 random general
631 * =10 random triangular
632 *
633  IF( mtypes.GT.maxtyp )
634  \$ GO TO 90
635 *
636  itype = ktype( jtype )
637  imode = kmode( jtype )
638 *
639 * Compute norm
640 *
641  GO TO ( 30, 40, 50 )kmagn( jtype )
642 *
643  30 CONTINUE
644  anorm = one
645  GO TO 60
646 *
647  40 CONTINUE
648  anorm = ovfl*ulp
649  GO TO 60
650 *
651  50 CONTINUE
652  anorm = unfl*ulpinv
653  GO TO 60
654 *
655  60 CONTINUE
656 *
657  CALL slaset( 'Full', lda, n, zero, zero, a, lda )
658  iinfo = 0
659  cond = ulpinv
660 *
661 * Special Matrices -- Identity & Jordan block
662 *
663 * Zero
664 *
665  IF( itype.EQ.1 ) THEN
666  iinfo = 0
667 *
668  ELSE IF( itype.EQ.2 ) THEN
669 *
670 * Identity
671 *
672  DO 70 jcol = 1, n
673  a( jcol, jcol ) = anorm
674  70 CONTINUE
675 *
676  ELSE IF( itype.EQ.3 ) THEN
677 *
678 * Jordan Block
679 *
680  DO 80 jcol = 1, n
681  a( jcol, jcol ) = anorm
682  IF( jcol.GT.1 )
683  \$ a( jcol, jcol-1 ) = one
684  80 CONTINUE
685 *
686  ELSE IF( itype.EQ.4 ) THEN
687 *
688 * Diagonal Matrix, [Eigen]values Specified
689 *
690  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
691  \$ anorm, 0, 0, 'N', a, lda, work( n+1 ),
692  \$ iinfo )
693 *
694  ELSE IF( itype.EQ.5 ) THEN
695 *
696 * Symmetric, eigenvalues specified
697 *
698  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
699  \$ anorm, n, n, 'N', a, lda, work( n+1 ),
700  \$ iinfo )
701 *
702  ELSE IF( itype.EQ.6 ) THEN
703 *
704 * General, eigenvalues specified
705 *
706  IF( kconds( jtype ).EQ.1 ) THEN
707  conds = one
708  ELSE IF( kconds( jtype ).EQ.2 ) THEN
709  conds = rtulpi
710  ELSE
711  conds = zero
712  END IF
713 *
714  adumma( 1 ) = ' '
715  CALL slatme( n, 'S', iseed, work, imode, cond, one,
716  \$ adumma, 'T', 'T', 'T', work( n+1 ), 4,
717  \$ conds, n, n, anorm, a, lda, work( 2*n+1 ),
718  \$ iinfo )
719 *
720  ELSE IF( itype.EQ.7 ) THEN
721 *
722 * Diagonal, random eigenvalues
723 *
724  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
725  \$ 'T', 'N', work( n+1 ), 1, one,
726  \$ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
727  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
728 *
729  ELSE IF( itype.EQ.8 ) THEN
730 *
731 * Symmetric, random eigenvalues
732 *
733  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
734  \$ 'T', 'N', work( n+1 ), 1, one,
735  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
736  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
737 *
738  ELSE IF( itype.EQ.9 ) THEN
739 *
740 * General, random eigenvalues
741 *
742  CALL slatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
743  \$ 'T', 'N', work( n+1 ), 1, one,
744  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
745  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
746  IF( n.GE.4 ) THEN
747  CALL slaset( 'Full', 2, n, zero, zero, a, lda )
748  CALL slaset( 'Full', n-3, 1, zero, zero, a( 3, 1 ),
749  \$ lda )
750  CALL slaset( 'Full', n-3, 2, zero, zero, a( 3, n-1 ),
751  \$ lda )
752  CALL slaset( 'Full', 1, n, zero, zero, a( n, 1 ),
753  \$ lda )
754  END IF
755 *
756  ELSE IF( itype.EQ.10 ) THEN
757 *
758 * Triangular, random eigenvalues
759 *
760  CALL slatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
761  \$ 'T', 'N', work( n+1 ), 1, one,
762  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, 0,
763  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
764 *
765  ELSE
766 *
767  iinfo = 1
768  END IF
769 *
770  IF( iinfo.NE.0 ) THEN
771  WRITE( nounit, fmt = 9991 )'Generator', iinfo, n, jtype,
772  \$ ioldsd
773  info = abs( iinfo )
774  RETURN
775  END IF
776 *
777  90 CONTINUE
778 *
779 * Test for minimal and generous workspace
780 *
781  DO 120 iwk = 1, 2
782  IF( iwk.EQ.1 ) THEN
783  nnwork = 3*n
784  ELSE
785  nnwork = max( 3*n, 2*n*n )
786  END IF
787  nnwork = max( nnwork, 1 )
788 *
789  CALL sget24( .false., jtype, thresh, ioldsd, nounit, n,
790  \$ a, lda, h, ht, wr, wi, wrt, wit, wrtmp,
791  \$ witmp, vs, ldvs, vs1, rcdein, rcdvin, nslct,
792  \$ islct, result, work, nnwork, iwork, bwork,
793  \$ info )
794 *
795 * Check for RESULT(j) > THRESH
796 *
797  ntest = 0
798  nfail = 0
799  DO 100 j = 1, 15
800  IF( result( j ).GE.zero )
801  \$ ntest = ntest + 1
802  IF( result( j ).GE.thresh )
803  \$ nfail = nfail + 1
804  100 CONTINUE
805 *
806  IF( nfail.GT.0 )
807  \$ ntestf = ntestf + 1
808  IF( ntestf.EQ.1 ) THEN
809  WRITE( nounit, fmt = 9999 )path
810  WRITE( nounit, fmt = 9998 )
811  WRITE( nounit, fmt = 9997 )
812  WRITE( nounit, fmt = 9996 )
813  WRITE( nounit, fmt = 9995 )thresh
814  WRITE( nounit, fmt = 9994 )
815  ntestf = 2
816  END IF
817 *
818  DO 110 j = 1, 15
819  IF( result( j ).GE.thresh ) THEN
820  WRITE( nounit, fmt = 9993 )n, iwk, ioldsd, jtype,
821  \$ j, result( j )
822  END IF
823  110 CONTINUE
824 *
825  nerrs = nerrs + nfail
826  ntestt = ntestt + ntest
827 *
828  120 CONTINUE
829  130 CONTINUE
830  140 CONTINUE
831 *
832  150 CONTINUE
833 *
834 * Read in data from file to check accuracy of condition estimation
835 * Read input data until N=0
836 *
837  jtype = 0
838  160 CONTINUE
839  READ( niunit, fmt = *, end = 200 )n, nslct
840  IF( n.EQ.0 )
841  \$ GO TO 200
842  jtype = jtype + 1
843  iseed( 1 ) = jtype
844  IF( nslct.GT.0 )
845  \$ READ( niunit, fmt = * )( islct( i ), i = 1, nslct )
846  DO 170 i = 1, n
847  READ( niunit, fmt = * )( a( i, j ), j = 1, n )
848  170 CONTINUE
849  READ( niunit, fmt = * )rcdein, rcdvin
850 *
851  CALL sget24( .true., 22, thresh, iseed, nounit, n, a, lda, h, ht,
852  \$ wr, wi, wrt, wit, wrtmp, witmp, vs, ldvs, vs1,
853  \$ rcdein, rcdvin, nslct, islct, result, work, lwork,
854  \$ iwork, bwork, info )
855 *
856 * Check for RESULT(j) > THRESH
857 *
858  ntest = 0
859  nfail = 0
860  DO 180 j = 1, 17
861  IF( result( j ).GE.zero )
862  \$ ntest = ntest + 1
863  IF( result( j ).GE.thresh )
864  \$ nfail = nfail + 1
865  180 CONTINUE
866 *
867  IF( nfail.GT.0 )
868  \$ ntestf = ntestf + 1
869  IF( ntestf.EQ.1 ) THEN
870  WRITE( nounit, fmt = 9999 )path
871  WRITE( nounit, fmt = 9998 )
872  WRITE( nounit, fmt = 9997 )
873  WRITE( nounit, fmt = 9996 )
874  WRITE( nounit, fmt = 9995 )thresh
875  WRITE( nounit, fmt = 9994 )
876  ntestf = 2
877  END IF
878  DO 190 j = 1, 17
879  IF( result( j ).GE.thresh ) THEN
880  WRITE( nounit, fmt = 9992 )n, jtype, j, result( j )
881  END IF
882  190 CONTINUE
883 *
884  nerrs = nerrs + nfail
885  ntestt = ntestt + ntest
886  GO TO 160
887  200 CONTINUE
888 *
889 * Summary
890 *
891  CALL slasum( path, nounit, nerrs, ntestt )
892 *
893  9999 FORMAT( / 1x, a3, ' -- Real Schur Form Decomposition Expert ',
894  \$ 'Driver', / ' Matrix types (see SDRVSX for details):' )
895 *
896  9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
897  \$ ' ', ' 5=Diagonal: geometr. spaced entries.',
898  \$ / ' 2=Identity matrix. ', ' 6=Diagona',
899  \$ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
900  \$ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
901  \$ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
902  \$ 'mall, evenly spaced.' )
903  9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
904  \$ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
905  \$ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
906  \$ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
907  \$ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
908  \$ 'lex ', / ' 12=Well-cond., random complex ', ' ',
909  \$ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
910  \$ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
911  \$ ' complx ' )
912  9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
913  \$ 'with small random entries.', / ' 20=Matrix with large ran',
914  \$ 'dom entries. ', / )
915  9995 FORMAT( ' Tests performed with test threshold =', f8.2,
916  \$ / ' ( A denotes A on input and T denotes A on output)',
917  \$ / / ' 1 = 0 if T in Schur form (no sort), ',
918  \$ ' 1/ulp otherwise', /
919  \$ ' 2 = | A - VS T transpose(VS) | / ( n |A| ulp ) (no sort)',
920  \$ / ' 3 = | I - VS transpose(VS) | / ( n ulp ) (no sort) ', /
921  \$ ' 4 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (no sort),',
922  \$ ' 1/ulp otherwise', /
923  \$ ' 5 = 0 if T same no matter if VS computed (no sort),',
924  \$ ' 1/ulp otherwise', /
925  \$ ' 6 = 0 if WR, WI same no matter if VS computed (no sort)',
926  \$ ', 1/ulp otherwise' )
927  9994 FORMAT( ' 7 = 0 if T in Schur form (sort), ', ' 1/ulp otherwise',
928  \$ / ' 8 = | A - VS T transpose(VS) | / ( n |A| ulp ) (sort)',
929  \$ / ' 9 = | I - VS transpose(VS) | / ( n ulp ) (sort) ',
930  \$ / ' 10 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (sort),',
931  \$ ' 1/ulp otherwise', /
932  \$ ' 11 = 0 if T same no matter what else computed (sort),',
933  \$ ' 1/ulp otherwise', /
934  \$ ' 12 = 0 if WR, WI same no matter what else computed ',
935  \$ '(sort), 1/ulp otherwise', /
936  \$ ' 13 = 0 if sorting successful, 1/ulp otherwise',
937  \$ / ' 14 = 0 if RCONDE same no matter what else computed,',
938  \$ ' 1/ulp otherwise', /
939  \$ ' 15 = 0 if RCONDv same no matter what else computed,',
940  \$ ' 1/ulp otherwise', /
941  \$ ' 16 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),',
942  \$ / ' 17 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),' )
943  9993 FORMAT( ' N=', i5, ', IWK=', i2, ', seed=', 4( i4, ',' ),
944  \$ ' type ', i2, ', test(', i2, ')=', g10.3 )
945  9992 FORMAT( ' N=', i5, ', input example =', i3, ', test(', i2, ')=',
946  \$ g10.3 )
947  9991 FORMAT( ' SDRVSX: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
948  \$ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
949 *
950  RETURN
951 *
952 * End of SDRVSX
953 *
954  END
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 xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:323
subroutine sdrvsx(NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, NIUNIT, NOUNIT, A, LDA, H, HT, WR, WI, WRT, WIT, WRTMP, WITMP, VS, LDVS, VS1, RESULT, WORK, LWORK, IWORK, BWORK, INFO)
SDRVSX
Definition: sdrvsx.f:456
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
subroutine sget24(COMP, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA, H, HT, WR, WI, WRT, WIT, WRTMP, WITMP, VS, LDVS, VS1, RCDEIN, RCDVIN, NSLCT, ISLCT, RESULT, WORK, LWORK, IWORK, BWORK, INFO)
SGET24
Definition: sget24.f:345
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:42
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