1 SUBROUTINE SDRVES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
2 $ NOUNIT, A, LDA, H, HT, WR, WI, WRT, WIT, VS,
3 $ LDVS, RESULT, WORK, NWORK, IWORK, BWORK, INFO )
4 *
5 * -- LAPACK test routine (version 3.1) --
6 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
7 * November 2006
8 *
9 * .. Scalar Arguments ..
10 INTEGER INFO, LDA, LDVS, NOUNIT, NSIZES, NTYPES, NWORK
11 REAL THRESH
12 * ..
13 * .. Array Arguments ..
14 LOGICAL BWORK( * ), DOTYPE( * )
15 INTEGER ISEED( 4 ), IWORK( * ), NN( * )
16 REAL A( LDA, * ), H( LDA, * ), HT( LDA, * ),
17 $ RESULT( 13 ), VS( LDVS, * ), WI( * ), WIT( * ),
18 $ WORK( * ), WR( * ), WRT( * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 * SDRVES checks the nonsymmetric eigenvalue (Schur form) problem
25 * driver SGEES.
26 *
27 * When SDRVES is called, a number of matrix "sizes" ("n's") and a
28 * number of matrix "types" are specified. For each size ("n")
29 * and each type of matrix, one matrix will be generated and used
30 * to test the nonsymmetric eigenroutines. For each matrix, 13
31 * tests will be performed:
32 *
33 * (1) 0 if T is in Schur form, 1/ulp otherwise
34 * (no sorting of eigenvalues)
35 *
36 * (2) | A - VS T VS' | / ( n |A| ulp )
37 *
38 * Here VS is the matrix of Schur eigenvectors, and T is in Schur
39 * form (no sorting of eigenvalues).
40 *
41 * (3) | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).
42 *
43 * (4) 0 if WR+sqrt(-1)*WI are eigenvalues of T
44 * 1/ulp otherwise
45 * (no sorting of eigenvalues)
46 *
47 * (5) 0 if T(with VS) = T(without VS),
48 * 1/ulp otherwise
49 * (no sorting of eigenvalues)
50 *
51 * (6) 0 if eigenvalues(with VS) = eigenvalues(without VS),
52 * 1/ulp otherwise
53 * (no sorting of eigenvalues)
54 *
55 * (7) 0 if T is in Schur form, 1/ulp otherwise
56 * (with sorting of eigenvalues)
57 *
58 * (8) | A - VS T VS' | / ( n |A| ulp )
59 *
60 * Here VS is the matrix of Schur eigenvectors, and T is in Schur
61 * form (with sorting of eigenvalues).
62 *
63 * (9) | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).
64 *
65 * (10) 0 if WR+sqrt(-1)*WI are eigenvalues of T
66 * 1/ulp otherwise
67 * (with sorting of eigenvalues)
68 *
69 * (11) 0 if T(with VS) = T(without VS),
70 * 1/ulp otherwise
71 * (with sorting of eigenvalues)
72 *
73 * (12) 0 if eigenvalues(with VS) = eigenvalues(without VS),
74 * 1/ulp otherwise
75 * (with sorting of eigenvalues)
76 *
77 * (13) if sorting worked and SDIM is the number of
78 * eigenvalues which were SELECTed
79 *
80 * The "sizes" are specified by an array NN(1:NSIZES); the value of
81 * each element NN(j) specifies one size.
82 * The "types" are specified by a logical array DOTYPE( 1:NTYPES );
83 * if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
84 * Currently, the list of possible types is:
85 *
86 * (1) The zero matrix.
87 * (2) The identity matrix.
88 * (3) A (transposed) Jordan block, with 1's on the diagonal.
89 *
90 * (4) A diagonal matrix with evenly spaced entries
91 * 1, ..., ULP and random signs.
92 * (ULP = (first number larger than 1) - 1 )
93 * (5) A diagonal matrix with geometrically spaced entries
94 * 1, ..., ULP and random signs.
95 * (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
96 * and random signs.
97 *
98 * (7) Same as (4), but multiplied by a constant near
99 * the overflow threshold
100 * (8) Same as (4), but multiplied by a constant near
101 * the underflow threshold
102 *
103 * (9) A matrix of the form U' T U, where U is orthogonal and
104 * T has evenly spaced entries 1, ..., ULP with random signs
105 * on the diagonal and random O(1) entries in the upper
106 * triangle.
107 *
108 * (10) A matrix of the form U' T U, where U is orthogonal and
109 * T has geometrically spaced entries 1, ..., ULP with random
110 * signs on the diagonal and random O(1) entries in the upper
111 * triangle.
112 *
113 * (11) A matrix of the form U' T U, where U is orthogonal and
114 * T has "clustered" entries 1, ULP,..., ULP with random
115 * signs on the diagonal and random O(1) entries in the upper
116 * triangle.
117 *
118 * (12) A matrix of the form U' T U, where U is orthogonal and
119 * T has real or complex conjugate paired eigenvalues randomly
120 * chosen from ( ULP, 1 ) and random O(1) entries in the upper
121 * triangle.
122 *
123 * (13) A matrix of the form X' T X, where X has condition
124 * SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
125 * with random signs on the diagonal and random O(1) entries
126 * in the upper triangle.
127 *
128 * (14) A matrix of the form X' T X, where X has condition
129 * SQRT( ULP ) and T has geometrically spaced entries
130 * 1, ..., ULP with random signs on the diagonal and random
131 * O(1) entries in the upper triangle.
132 *
133 * (15) A matrix of the form X' T X, where X has condition
134 * SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
135 * with random signs on the diagonal and random O(1) entries
136 * in the upper triangle.
137 *
138 * (16) A matrix of the form X' T X, where X has condition
139 * SQRT( ULP ) and T has real or complex conjugate paired
140 * eigenvalues randomly chosen from ( ULP, 1 ) and random
141 * O(1) entries in the upper triangle.
142 *
143 * (17) Same as (16), but multiplied by a constant
144 * near the overflow threshold
145 * (18) Same as (16), but multiplied by a constant
146 * near the underflow threshold
147 *
148 * (19) Nonsymmetric matrix with random entries chosen from (-1,1).
149 * If N is at least 4, all entries in first two rows and last
150 * row, and first column and last two columns are zero.
151 * (20) Same as (19), but multiplied by a constant
152 * near the overflow threshold
153 * (21) Same as (19), but multiplied by a constant
154 * near the underflow threshold
155 *
156 * Arguments
157 * =========
158 *
159 * NSIZES (input) INTEGER
160 * The number of sizes of matrices to use. If it is zero,
161 * SDRVES does nothing. It must be at least zero.
162 *
163 * NN (input) INTEGER array, dimension (NSIZES)
164 * An array containing the sizes to be used for the matrices.
165 * Zero values will be skipped. The values must be at least
166 * zero.
167 *
168 * NTYPES (input) INTEGER
169 * The number of elements in DOTYPE. If it is zero, SDRVES
170 * does nothing. It must be at least zero. If it is MAXTYP+1
171 * and NSIZES is 1, then an additional type, MAXTYP+1 is
172 * defined, which is to use whatever matrix is in A. This
173 * is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
174 * DOTYPE(MAXTYP+1) is .TRUE. .
175 *
176 * DOTYPE (input) LOGICAL array, dimension (NTYPES)
177 * If DOTYPE(j) is .TRUE., then for each size in NN a
178 * matrix of that size and of type j will be generated.
179 * If NTYPES is smaller than the maximum number of types
180 * defined (PARAMETER MAXTYP), then types NTYPES+1 through
181 * MAXTYP will not be generated. If NTYPES is larger
182 * than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
183 * will be ignored.
184 *
185 * ISEED (input/output) INTEGER array, dimension (4)
186 * On entry ISEED specifies the seed of the random number
187 * generator. The array elements should be between 0 and 4095;
188 * if not they will be reduced mod 4096. Also, ISEED(4) must
189 * be odd. The random number generator uses a linear
190 * congruential sequence limited to small integers, and so
191 * should produce machine independent random numbers. The
192 * values of ISEED are changed on exit, and can be used in the
193 * next call to SDRVES to continue the same random number
194 * sequence.
195 *
196 * THRESH (input) REAL
197 * A test will count as "failed" if the "error", computed as
198 * described above, exceeds THRESH. Note that the error
199 * is scaled to be O(1), so THRESH should be a reasonably
200 * small multiple of 1, e.g., 10 or 100. In particular,
201 * it should not depend on the precision (single vs. double)
202 * or the size of the matrix. It must be at least zero.
203 *
204 * NOUNIT (input) INTEGER
205 * The FORTRAN unit number for printing out error messages
206 * (e.g., if a routine returns INFO not equal to 0.)
207 *
208 * A (workspace) REAL array, dimension (LDA, max(NN))
209 * Used to hold the matrix whose eigenvalues are to be
210 * computed. On exit, A contains the last matrix actually used.
211 *
212 * LDA (input) INTEGER
213 * The leading dimension of A, and H. LDA must be at
214 * least 1 and at least max(NN).
215 *
216 * H (workspace) REAL array, dimension (LDA, max(NN))
217 * Another copy of the test matrix A, modified by SGEES.
218 *
219 * HT (workspace) REAL array, dimension (LDA, max(NN))
220 * Yet another copy of the test matrix A, modified by SGEES.
221 *
222 * WR (workspace) REAL array, dimension (max(NN))
223 * WI (workspace) REAL array, dimension (max(NN))
224 * The real and imaginary parts of the eigenvalues of A.
225 * On exit, WR + WI*i are the eigenvalues of the matrix in A.
226 *
227 * WRT (workspace) REAL array, dimension (max(NN))
228 * WIT (workspace) REAL array, dimension (max(NN))
229 * Like WR, WI, these arrays contain the eigenvalues of A,
230 * but those computed when SGEES only computes a partial
231 * eigendecomposition, i.e. not Schur vectors
232 *
233 * VS (workspace) REAL array, dimension (LDVS, max(NN))
234 * VS holds the computed Schur vectors.
235 *
236 * LDVS (input) INTEGER
237 * Leading dimension of VS. Must be at least max(1,max(NN)).
238 *
239 * RESULT (output) REAL array, dimension (13)
240 * The values computed by the 13 tests described above.
241 * The values are currently limited to 1/ulp, to avoid overflow.
242 *
243 * WORK (workspace) REAL array, dimension (NWORK)
244 *
245 * NWORK (input) INTEGER
246 * The number of entries in WORK. This must be at least
247 * 5*NN(j)+2*NN(j)**2 for all j.
248 *
249 * IWORK (workspace) INTEGER array, dimension (max(NN))
250 *
251 * INFO (output) INTEGER
252 * If 0, then everything ran OK.
253 * -1: NSIZES < 0
254 * -2: Some NN(j) < 0
255 * -3: NTYPES < 0
256 * -6: THRESH < 0
257 * -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
258 * -17: LDVS < 1 or LDVS < NMAX, where NMAX is max( NN(j) ).
259 * -20: NWORK too small.
260 * If SLATMR, SLATMS, SLATME or SGEES returns an error code,
261 * the absolute value of it is returned.
262 *
263 *-----------------------------------------------------------------------
264 *
265 * Some Local Variables and Parameters:
266 * ---- ----- --------- --- ----------
267 *
268 * ZERO, ONE Real 0 and 1.
269 * MAXTYP The number of types defined.
270 * NMAX Largest value in NN.
271 * NERRS The number of tests which have exceeded THRESH
272 * COND, CONDS,
273 * IMODE Values to be passed to the matrix generators.
274 * ANORM Norm of A; passed to matrix generators.
275 *
276 * OVFL, UNFL Overflow and underflow thresholds.
277 * ULP, ULPINV Finest relative precision and its inverse.
278 * RTULP, RTULPI Square roots of the previous 4 values.
279 *
280 * The following four arrays decode JTYPE:
281 * KTYPE(j) The general type (1-10) for type "j".
282 * KMODE(j) The MODE value to be passed to the matrix
283 * generator for type "j".
284 * KMAGN(j) The order of magnitude ( O(1),
285 * O(overflow^(1/2) ), O(underflow^(1/2) )
286 * KCONDS(j) Selectw whether CONDS is to be 1 or
287 * 1/sqrt(ulp). (0 means irrelevant.)
288 *
289 * =====================================================================
290 *
291 * .. Parameters ..
292 REAL ZERO, ONE
293 PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
294 INTEGER MAXTYP
295 PARAMETER ( MAXTYP = 21 )
296 * ..
297 * .. Local Scalars ..
298 LOGICAL BADNN
299 CHARACTER SORT
300 CHARACTER*3 PATH
301 INTEGER I, IINFO, IMODE, ISORT, ITYPE, IWK, J, JCOL,
302 $ JSIZE, JTYPE, KNTEIG, LWORK, MTYPES, N,
303 $ NERRS, NFAIL, NMAX, NNWORK, NTEST, NTESTF,
304 $ NTESTT, RSUB, SDIM
305 REAL ANORM, COND, CONDS, OVFL, RTULP, RTULPI, TMP,
306 $ ULP, ULPINV, UNFL
307 * ..
308 * .. Local Arrays ..
309 CHARACTER ADUMMA( 1 )
310 INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
311 $ KMAGN( MAXTYP ), KMODE( MAXTYP ),
312 $ KTYPE( MAXTYP )
313 REAL RES( 2 )
314 * ..
315 * .. Arrays in Common ..
316 LOGICAL SELVAL( 20 )
317 REAL SELWI( 20 ), SELWR( 20 )
318 * ..
319 * .. Scalars in Common ..
320 INTEGER SELDIM, SELOPT
321 * ..
322 * .. Common blocks ..
323 COMMON / SSLCT / SELOPT, SELDIM, SELVAL, SELWR, SELWI
324 * ..
325 * .. External Functions ..
326 LOGICAL SSLECT
327 REAL SLAMCH
328 EXTERNAL SSLECT, SLAMCH
329 * ..
330 * .. External Subroutines ..
331 EXTERNAL SGEES, SHST01, SLABAD, SLACPY, SLASUM, SLATME,
332 $ SLATMR, SLATMS, SLASET, XERBLA
333 * ..
334 * .. Intrinsic Functions ..
335 INTRINSIC ABS, MAX, SIGN, SQRT
336 * ..
337 * .. Data statements ..
338 DATA KTYPE / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
339 DATA KMAGN / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
340 $ 3, 1, 2, 3 /
341 DATA KMODE / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
342 $ 1, 5, 5, 5, 4, 3, 1 /
343 DATA KCONDS / 3*0, 5*0, 4*1, 6*2, 3*0 /
344 * ..
345 * .. Executable Statements ..
346 *
347 PATH( 1: 1 ) = 'Single precision'
348 PATH( 2: 3 ) = 'ES'
349 *
350 * Check for errors
351 *
352 NTESTT = 0
353 NTESTF = 0
354 INFO = 0
355 SELOPT = 0
356 *
357 * Important constants
358 *
359 BADNN = .FALSE.
360 NMAX = 0
361 DO 10 J = 1, NSIZES
362 NMAX = MAX( NMAX, NN( J ) )
363 IF( NN( J ).LT.0 )
364 $ BADNN = .TRUE.
365 10 CONTINUE
366 *
367 * Check for errors
368 *
369 IF( NSIZES.LT.0 ) THEN
370 INFO = -1
371 ELSE IF( BADNN ) THEN
372 INFO = -2
373 ELSE IF( NTYPES.LT.0 ) THEN
374 INFO = -3
375 ELSE IF( THRESH.LT.ZERO ) THEN
376 INFO = -6
377 ELSE IF( NOUNIT.LE.0 ) THEN
378 INFO = -7
379 ELSE IF( LDA.LT.1 .OR. LDA.LT.NMAX ) THEN
380 INFO = -9
381 ELSE IF( LDVS.LT.1 .OR. LDVS.LT.NMAX ) THEN
382 INFO = -17
383 ELSE IF( 5*NMAX+2*NMAX**2.GT.NWORK ) THEN
384 INFO = -20
385 END IF
386 *
387 IF( INFO.NE.0 ) THEN
388 CALL XERBLA( 'SDRVES', -INFO )
389 RETURN
390 END IF
391 *
392 * Quick return if nothing to do
393 *
394 IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
395 $ RETURN
396 *
397 * More Important constants
398 *
399 UNFL = SLAMCH( 'Safe minimum' )
400 OVFL = ONE / UNFL
401 CALL SLABAD( UNFL, OVFL )
402 ULP = SLAMCH( 'Precision' )
403 ULPINV = ONE / ULP
404 RTULP = SQRT( ULP )
405 RTULPI = ONE / RTULP
406 *
407 * Loop over sizes, types
408 *
409 NERRS = 0
410 *
411 DO 270 JSIZE = 1, NSIZES
412 N = NN( JSIZE )
413 MTYPES = MAXTYP
414 IF( NSIZES.EQ.1 .AND. NTYPES.EQ.MAXTYP+1 )
415 $ MTYPES = MTYPES + 1
416 *
417 DO 260 JTYPE = 1, MTYPES
418 IF( .NOT.DOTYPE( JTYPE ) )
419 $ GO TO 260
420 *
421 * Save ISEED in case of an error.
422 *
423 DO 20 J = 1, 4
424 IOLDSD( J ) = ISEED( J )
425 20 CONTINUE
426 *
427 * Compute "A"
428 *
429 * Control parameters:
430 *
431 * KMAGN KCONDS KMODE KTYPE
432 * =1 O(1) 1 clustered 1 zero
433 * =2 large large clustered 2 identity
434 * =3 small exponential Jordan
435 * =4 arithmetic diagonal, (w/ eigenvalues)
436 * =5 random log symmetric, w/ eigenvalues
437 * =6 random general, w/ eigenvalues
438 * =7 random diagonal
439 * =8 random symmetric
440 * =9 random general
441 * =10 random triangular
442 *
443 IF( MTYPES.GT.MAXTYP )
444 $ GO TO 90
445 *
446 ITYPE = KTYPE( JTYPE )
447 IMODE = KMODE( JTYPE )
448 *
449 * Compute norm
450 *
451 GO TO ( 30, 40, 50 )KMAGN( JTYPE )
452 *
453 30 CONTINUE
454 ANORM = ONE
455 GO TO 60
456 *
457 40 CONTINUE
458 ANORM = OVFL*ULP
459 GO TO 60
460 *
461 50 CONTINUE
462 ANORM = UNFL*ULPINV
463 GO TO 60
464 *
465 60 CONTINUE
466 *
467 CALL SLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
468 IINFO = 0
469 COND = ULPINV
470 *
471 * Special Matrices -- Identity & Jordan block
472 *
473 * Zero
474 *
475 IF( ITYPE.EQ.1 ) THEN
476 IINFO = 0
477 *
478 ELSE IF( ITYPE.EQ.2 ) THEN
479 *
480 * Identity
481 *
482 DO 70 JCOL = 1, N
483 A( JCOL, JCOL ) = ANORM
484 70 CONTINUE
485 *
486 ELSE IF( ITYPE.EQ.3 ) THEN
487 *
488 * Jordan Block
489 *
490 DO 80 JCOL = 1, N
491 A( JCOL, JCOL ) = ANORM
492 IF( JCOL.GT.1 )
493 $ A( JCOL, JCOL-1 ) = ONE
494 80 CONTINUE
495 *
496 ELSE IF( ITYPE.EQ.4 ) THEN
497 *
498 * Diagonal Matrix, [Eigen]values Specified
499 *
500 CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
501 $ ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ),
502 $ IINFO )
503 *
504 ELSE IF( ITYPE.EQ.5 ) THEN
505 *
506 * Symmetric, eigenvalues specified
507 *
508 CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
509 $ ANORM, N, N, 'N', A, LDA, WORK( N+1 ),
510 $ IINFO )
511 *
512 ELSE IF( ITYPE.EQ.6 ) THEN
513 *
514 * General, eigenvalues specified
515 *
516 IF( KCONDS( JTYPE ).EQ.1 ) THEN
517 CONDS = ONE
518 ELSE IF( KCONDS( JTYPE ).EQ.2 ) THEN
519 CONDS = RTULPI
520 ELSE
521 CONDS = ZERO
522 END IF
523 *
524 ADUMMA( 1 ) = ' '
525 CALL SLATME( N, 'S', ISEED, WORK, IMODE, COND, ONE,
526 $ ADUMMA, 'T', 'T', 'T', WORK( N+1 ), 4,
527 $ CONDS, N, N, ANORM, A, LDA, WORK( 2*N+1 ),
528 $ IINFO )
529 *
530 ELSE IF( ITYPE.EQ.7 ) THEN
531 *
532 * Diagonal, random eigenvalues
533 *
534 CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
535 $ 'T', 'N', WORK( N+1 ), 1, ONE,
536 $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
537 $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
538 *
539 ELSE IF( ITYPE.EQ.8 ) THEN
540 *
541 * Symmetric, random eigenvalues
542 *
543 CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
544 $ 'T', 'N', WORK( N+1 ), 1, ONE,
545 $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
546 $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
547 *
548 ELSE IF( ITYPE.EQ.9 ) THEN
549 *
550 * General, random eigenvalues
551 *
552 CALL SLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
553 $ 'T', 'N', WORK( N+1 ), 1, ONE,
554 $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
555 $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
556 IF( N.GE.4 ) THEN
557 CALL SLASET( 'Full', 2, N, ZERO, ZERO, A, LDA )
558 CALL SLASET( 'Full', N-3, 1, ZERO, ZERO, A( 3, 1 ),
559 $ LDA )
560 CALL SLASET( 'Full', N-3, 2, ZERO, ZERO, A( 3, N-1 ),
561 $ LDA )
562 CALL SLASET( 'Full', 1, N, ZERO, ZERO, A( N, 1 ),
563 $ LDA )
564 END IF
565 *
566 ELSE IF( ITYPE.EQ.10 ) THEN
567 *
568 * Triangular, random eigenvalues
569 *
570 CALL SLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
571 $ 'T', 'N', WORK( N+1 ), 1, ONE,
572 $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, 0,
573 $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
574 *
575 ELSE
576 *
577 IINFO = 1
578 END IF
579 *
580 IF( IINFO.NE.0 ) THEN
581 WRITE( NOUNIT, FMT = 9992 )'Generator', IINFO, N, JTYPE,
582 $ IOLDSD
583 INFO = ABS( IINFO )
584 RETURN
585 END IF
586 *
587 90 CONTINUE
588 *
589 * Test for minimal and generous workspace
590 *
591 DO 250 IWK = 1, 2
592 IF( IWK.EQ.1 ) THEN
593 NNWORK = 3*N
594 ELSE
595 NNWORK = 5*N + 2*N**2
596 END IF
597 NNWORK = MAX( NNWORK, 1 )
598 *
599 * Initialize RESULT
600 *
601 DO 100 J = 1, 13
602 RESULT( J ) = -ONE
603 100 CONTINUE
604 *
605 * Test with and without sorting of eigenvalues
606 *
607 DO 210 ISORT = 0, 1
608 IF( ISORT.EQ.0 ) THEN
609 SORT = 'N'
610 RSUB = 0
611 ELSE
612 SORT = 'S'
613 RSUB = 6
614 END IF
615 *
616 * Compute Schur form and Schur vectors, and test them
617 *
618 CALL SLACPY( 'F', N, N, A, LDA, H, LDA )
619 CALL SGEES( 'V', SORT, SSLECT, N, H, LDA, SDIM, WR,
620 $ WI, VS, LDVS, WORK, NNWORK, BWORK, IINFO )
621 IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
622 RESULT( 1+RSUB ) = ULPINV
623 WRITE( NOUNIT, FMT = 9992 )'SGEES1', IINFO, N,
624 $ JTYPE, IOLDSD
625 INFO = ABS( IINFO )
626 GO TO 220
627 END IF
628 *
629 * Do Test (1) or Test (7)
630 *
631 RESULT( 1+RSUB ) = ZERO
632 DO 120 J = 1, N - 2
633 DO 110 I = J + 2, N
634 IF( H( I, J ).NE.ZERO )
635 $ RESULT( 1+RSUB ) = ULPINV
636 110 CONTINUE
637 120 CONTINUE
638 DO 130 I = 1, N - 2
639 IF( H( I+1, I ).NE.ZERO .AND. H( I+2, I+1 ).NE.
640 $ ZERO )RESULT( 1+RSUB ) = ULPINV
641 130 CONTINUE
642 DO 140 I = 1, N - 1
643 IF( H( I+1, I ).NE.ZERO ) THEN
644 IF( H( I, I ).NE.H( I+1, I+1 ) .OR.
645 $ H( I, I+1 ).EQ.ZERO .OR.
646 $ SIGN( ONE, H( I+1, I ) ).EQ.
647 $ SIGN( ONE, H( I, I+1 ) ) )RESULT( 1+RSUB )
648 $ = ULPINV
649 END IF
650 140 CONTINUE
651 *
652 * Do Tests (2) and (3) or Tests (8) and (9)
653 *
654 LWORK = MAX( 1, 2*N*N )
655 CALL SHST01( N, 1, N, A, LDA, H, LDA, VS, LDVS, WORK,
656 $ LWORK, RES )
657 RESULT( 2+RSUB ) = RES( 1 )
658 RESULT( 3+RSUB ) = RES( 2 )
659 *
660 * Do Test (4) or Test (10)
661 *
662 RESULT( 4+RSUB ) = ZERO
663 DO 150 I = 1, N
664 IF( H( I, I ).NE.WR( I ) )
665 $ RESULT( 4+RSUB ) = ULPINV
666 150 CONTINUE
667 IF( N.GT.1 ) THEN
668 IF( H( 2, 1 ).EQ.ZERO .AND. WI( 1 ).NE.ZERO )
669 $ RESULT( 4+RSUB ) = ULPINV
670 IF( H( N, N-1 ).EQ.ZERO .AND. WI( N ).NE.ZERO )
671 $ RESULT( 4+RSUB ) = ULPINV
672 END IF
673 DO 160 I = 1, N - 1
674 IF( H( I+1, I ).NE.ZERO ) THEN
675 TMP = SQRT( ABS( H( I+1, I ) ) )*
676 $ SQRT( ABS( H( I, I+1 ) ) )
677 RESULT( 4+RSUB ) = MAX( RESULT( 4+RSUB ),
678 $ ABS( WI( I )-TMP ) /
679 $ MAX( ULP*TMP, UNFL ) )
680 RESULT( 4+RSUB ) = MAX( RESULT( 4+RSUB ),
681 $ ABS( WI( I+1 )+TMP ) /
682 $ MAX( ULP*TMP, UNFL ) )
683 ELSE IF( I.GT.1 ) THEN
684 IF( H( I+1, I ).EQ.ZERO .AND. H( I, I-1 ).EQ.
685 $ ZERO .AND. WI( I ).NE.ZERO )RESULT( 4+RSUB )
686 $ = ULPINV
687 END IF
688 160 CONTINUE
689 *
690 * Do Test (5) or Test (11)
691 *
692 CALL SLACPY( 'F', N, N, A, LDA, HT, LDA )
693 CALL SGEES( 'N', SORT, SSLECT, N, HT, LDA, SDIM, WRT,
694 $ WIT, VS, LDVS, WORK, NNWORK, BWORK,
695 $ IINFO )
696 IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
697 RESULT( 5+RSUB ) = ULPINV
698 WRITE( NOUNIT, FMT = 9992 )'SGEES2', IINFO, N,
699 $ JTYPE, IOLDSD
700 INFO = ABS( IINFO )
701 GO TO 220
702 END IF
703 *
704 RESULT( 5+RSUB ) = ZERO
705 DO 180 J = 1, N
706 DO 170 I = 1, N
707 IF( H( I, J ).NE.HT( I, J ) )
708 $ RESULT( 5+RSUB ) = ULPINV
709 170 CONTINUE
710 180 CONTINUE
711 *
712 * Do Test (6) or Test (12)
713 *
714 RESULT( 6+RSUB ) = ZERO
715 DO 190 I = 1, N
716 IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) )
717 $ RESULT( 6+RSUB ) = ULPINV
718 190 CONTINUE
719 *
720 * Do Test (13)
721 *
722 IF( ISORT.EQ.1 ) THEN
723 RESULT( 13 ) = ZERO
724 KNTEIG = 0
725 DO 200 I = 1, N
726 IF( SSLECT( WR( I ), WI( I ) ) .OR.
727 $ SSLECT( WR( I ), -WI( I ) ) )
728 $ KNTEIG = KNTEIG + 1
729 IF( I.LT.N ) THEN
730 IF( ( SSLECT( WR( I+1 ),
731 $ WI( I+1 ) ) .OR. SSLECT( WR( I+1 ),
732 $ -WI( I+1 ) ) ) .AND.
733 $ ( .NOT.( SSLECT( WR( I ),
734 $ WI( I ) ) .OR. SSLECT( WR( I ),
735 $ -WI( I ) ) ) ) .AND. IINFO.NE.N+2 )
736 $ RESULT( 13 ) = ULPINV
737 END IF
738 200 CONTINUE
739 IF( SDIM.NE.KNTEIG ) THEN
740 RESULT( 13 ) = ULPINV
741 END IF
742 END IF
743 *
744 210 CONTINUE
745 *
746 * End of Loop -- Check for RESULT(j) > THRESH
747 *
748 220 CONTINUE
749 *
750 NTEST = 0
751 NFAIL = 0
752 DO 230 J = 1, 13
753 IF( RESULT( J ).GE.ZERO )
754 $ NTEST = NTEST + 1
755 IF( RESULT( J ).GE.THRESH )
756 $ NFAIL = NFAIL + 1
757 230 CONTINUE
758 *
759 IF( NFAIL.GT.0 )
760 $ NTESTF = NTESTF + 1
761 IF( NTESTF.EQ.1 ) THEN
762 WRITE( NOUNIT, FMT = 9999 )PATH
763 WRITE( NOUNIT, FMT = 9998 )
764 WRITE( NOUNIT, FMT = 9997 )
765 WRITE( NOUNIT, FMT = 9996 )
766 WRITE( NOUNIT, FMT = 9995 )THRESH
767 WRITE( NOUNIT, FMT = 9994 )
768 NTESTF = 2
769 END IF
770 *
771 DO 240 J = 1, 13
772 IF( RESULT( J ).GE.THRESH ) THEN
773 WRITE( NOUNIT, FMT = 9993 )N, IWK, IOLDSD, JTYPE,
774 $ J, RESULT( J )
775 END IF
776 240 CONTINUE
777 *
778 NERRS = NERRS + NFAIL
779 NTESTT = NTESTT + NTEST
780 *
781 250 CONTINUE
782 260 CONTINUE
783 270 CONTINUE
784 *
785 * Summary
786 *
787 CALL SLASUM( PATH, NOUNIT, NERRS, NTESTT )
788 *
789 9999 FORMAT( / 1X, A3, ' -- Real Schur Form Decomposition Driver',
790 $ / ' Matrix types (see SDRVES for details): ' )
791 *
792 9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
793 $ ' ', ' 5=Diagonal: geometr. spaced entries.',
794 $ / ' 2=Identity matrix. ', ' 6=Diagona',
795 $ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
796 $ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
797 $ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
798 $ 'mall, evenly spaced.' )
799 9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
800 $ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
801 $ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
802 $ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
803 $ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
804 $ 'lex ', / ' 12=Well-cond., random complex ', 6X, ' ',
805 $ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
806 $ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
807 $ ' complx ' )
808 9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
809 $ 'with small random entries.', / ' 20=Matrix with large ran',
810 $ 'dom entries. ', / )
811 9995 FORMAT( ' Tests performed with test threshold =', F8.2,
812 $ / ' ( A denotes A on input and T denotes A on output)',
813 $ / / ' 1 = 0 if T in Schur form (no sort), ',
814 $ ' 1/ulp otherwise', /
815 $ ' 2 = | A - VS T transpose(VS) | / ( n |A| ulp ) (no sort)',
816 $ / ' 3 = | I - VS transpose(VS) | / ( n ulp ) (no sort) ', /
817 $ ' 4 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (no sort),',
818 $ ' 1/ulp otherwise', /
819 $ ' 5 = 0 if T same no matter if VS computed (no sort),',
820 $ ' 1/ulp otherwise', /
821 $ ' 6 = 0 if WR, WI same no matter if VS computed (no sort)',
822 $ ', 1/ulp otherwise' )
823 9994 FORMAT( ' 7 = 0 if T in Schur form (sort), ', ' 1/ulp otherwise',
824 $ / ' 8 = | A - VS T transpose(VS) | / ( n |A| ulp ) (sort)',
825 $ / ' 9 = | I - VS transpose(VS) | / ( n ulp ) (sort) ',
826 $ / ' 10 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (sort),',
827 $ ' 1/ulp otherwise', /
828 $ ' 11 = 0 if T same no matter if VS computed (sort),',
829 $ ' 1/ulp otherwise', /
830 $ ' 12 = 0 if WR, WI same no matter if VS computed (sort),',
831 $ ' 1/ulp otherwise', /
832 $ ' 13 = 0 if sorting succesful, 1/ulp otherwise', / )
833 9993 FORMAT( ' N=', I5, ', IWK=', I2, ', seed=', 4( I4, ',' ),
834 $ ' type ', I2, ', test(', I2, ')=', G10.3 )
835 9992 FORMAT( ' SDRVES: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
836 $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
837 *
838 RETURN
839 *
840 * End of SDRVES
841 *
842 END
2 $ NOUNIT, A, LDA, H, HT, WR, WI, WRT, WIT, VS,
3 $ LDVS, RESULT, WORK, NWORK, IWORK, BWORK, INFO )
4 *
5 * -- LAPACK test routine (version 3.1) --
6 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
7 * November 2006
8 *
9 * .. Scalar Arguments ..
10 INTEGER INFO, LDA, LDVS, NOUNIT, NSIZES, NTYPES, NWORK
11 REAL THRESH
12 * ..
13 * .. Array Arguments ..
14 LOGICAL BWORK( * ), DOTYPE( * )
15 INTEGER ISEED( 4 ), IWORK( * ), NN( * )
16 REAL A( LDA, * ), H( LDA, * ), HT( LDA, * ),
17 $ RESULT( 13 ), VS( LDVS, * ), WI( * ), WIT( * ),
18 $ WORK( * ), WR( * ), WRT( * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 * SDRVES checks the nonsymmetric eigenvalue (Schur form) problem
25 * driver SGEES.
26 *
27 * When SDRVES is called, a number of matrix "sizes" ("n's") and a
28 * number of matrix "types" are specified. For each size ("n")
29 * and each type of matrix, one matrix will be generated and used
30 * to test the nonsymmetric eigenroutines. For each matrix, 13
31 * tests will be performed:
32 *
33 * (1) 0 if T is in Schur form, 1/ulp otherwise
34 * (no sorting of eigenvalues)
35 *
36 * (2) | A - VS T VS' | / ( n |A| ulp )
37 *
38 * Here VS is the matrix of Schur eigenvectors, and T is in Schur
39 * form (no sorting of eigenvalues).
40 *
41 * (3) | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).
42 *
43 * (4) 0 if WR+sqrt(-1)*WI are eigenvalues of T
44 * 1/ulp otherwise
45 * (no sorting of eigenvalues)
46 *
47 * (5) 0 if T(with VS) = T(without VS),
48 * 1/ulp otherwise
49 * (no sorting of eigenvalues)
50 *
51 * (6) 0 if eigenvalues(with VS) = eigenvalues(without VS),
52 * 1/ulp otherwise
53 * (no sorting of eigenvalues)
54 *
55 * (7) 0 if T is in Schur form, 1/ulp otherwise
56 * (with sorting of eigenvalues)
57 *
58 * (8) | A - VS T VS' | / ( n |A| ulp )
59 *
60 * Here VS is the matrix of Schur eigenvectors, and T is in Schur
61 * form (with sorting of eigenvalues).
62 *
63 * (9) | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).
64 *
65 * (10) 0 if WR+sqrt(-1)*WI are eigenvalues of T
66 * 1/ulp otherwise
67 * (with sorting of eigenvalues)
68 *
69 * (11) 0 if T(with VS) = T(without VS),
70 * 1/ulp otherwise
71 * (with sorting of eigenvalues)
72 *
73 * (12) 0 if eigenvalues(with VS) = eigenvalues(without VS),
74 * 1/ulp otherwise
75 * (with sorting of eigenvalues)
76 *
77 * (13) if sorting worked and SDIM is the number of
78 * eigenvalues which were SELECTed
79 *
80 * The "sizes" are specified by an array NN(1:NSIZES); the value of
81 * each element NN(j) specifies one size.
82 * The "types" are specified by a logical array DOTYPE( 1:NTYPES );
83 * if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
84 * Currently, the list of possible types is:
85 *
86 * (1) The zero matrix.
87 * (2) The identity matrix.
88 * (3) A (transposed) Jordan block, with 1's on the diagonal.
89 *
90 * (4) A diagonal matrix with evenly spaced entries
91 * 1, ..., ULP and random signs.
92 * (ULP = (first number larger than 1) - 1 )
93 * (5) A diagonal matrix with geometrically spaced entries
94 * 1, ..., ULP and random signs.
95 * (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
96 * and random signs.
97 *
98 * (7) Same as (4), but multiplied by a constant near
99 * the overflow threshold
100 * (8) Same as (4), but multiplied by a constant near
101 * the underflow threshold
102 *
103 * (9) A matrix of the form U' T U, where U is orthogonal and
104 * T has evenly spaced entries 1, ..., ULP with random signs
105 * on the diagonal and random O(1) entries in the upper
106 * triangle.
107 *
108 * (10) A matrix of the form U' T U, where U is orthogonal and
109 * T has geometrically spaced entries 1, ..., ULP with random
110 * signs on the diagonal and random O(1) entries in the upper
111 * triangle.
112 *
113 * (11) A matrix of the form U' T U, where U is orthogonal and
114 * T has "clustered" entries 1, ULP,..., ULP with random
115 * signs on the diagonal and random O(1) entries in the upper
116 * triangle.
117 *
118 * (12) A matrix of the form U' T U, where U is orthogonal and
119 * T has real or complex conjugate paired eigenvalues randomly
120 * chosen from ( ULP, 1 ) and random O(1) entries in the upper
121 * triangle.
122 *
123 * (13) A matrix of the form X' T X, where X has condition
124 * SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
125 * with random signs on the diagonal and random O(1) entries
126 * in the upper triangle.
127 *
128 * (14) A matrix of the form X' T X, where X has condition
129 * SQRT( ULP ) and T has geometrically spaced entries
130 * 1, ..., ULP with random signs on the diagonal and random
131 * O(1) entries in the upper triangle.
132 *
133 * (15) A matrix of the form X' T X, where X has condition
134 * SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
135 * with random signs on the diagonal and random O(1) entries
136 * in the upper triangle.
137 *
138 * (16) A matrix of the form X' T X, where X has condition
139 * SQRT( ULP ) and T has real or complex conjugate paired
140 * eigenvalues randomly chosen from ( ULP, 1 ) and random
141 * O(1) entries in the upper triangle.
142 *
143 * (17) Same as (16), but multiplied by a constant
144 * near the overflow threshold
145 * (18) Same as (16), but multiplied by a constant
146 * near the underflow threshold
147 *
148 * (19) Nonsymmetric matrix with random entries chosen from (-1,1).
149 * If N is at least 4, all entries in first two rows and last
150 * row, and first column and last two columns are zero.
151 * (20) Same as (19), but multiplied by a constant
152 * near the overflow threshold
153 * (21) Same as (19), but multiplied by a constant
154 * near the underflow threshold
155 *
156 * Arguments
157 * =========
158 *
159 * NSIZES (input) INTEGER
160 * The number of sizes of matrices to use. If it is zero,
161 * SDRVES does nothing. It must be at least zero.
162 *
163 * NN (input) INTEGER array, dimension (NSIZES)
164 * An array containing the sizes to be used for the matrices.
165 * Zero values will be skipped. The values must be at least
166 * zero.
167 *
168 * NTYPES (input) INTEGER
169 * The number of elements in DOTYPE. If it is zero, SDRVES
170 * does nothing. It must be at least zero. If it is MAXTYP+1
171 * and NSIZES is 1, then an additional type, MAXTYP+1 is
172 * defined, which is to use whatever matrix is in A. This
173 * is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
174 * DOTYPE(MAXTYP+1) is .TRUE. .
175 *
176 * DOTYPE (input) LOGICAL array, dimension (NTYPES)
177 * If DOTYPE(j) is .TRUE., then for each size in NN a
178 * matrix of that size and of type j will be generated.
179 * If NTYPES is smaller than the maximum number of types
180 * defined (PARAMETER MAXTYP), then types NTYPES+1 through
181 * MAXTYP will not be generated. If NTYPES is larger
182 * than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
183 * will be ignored.
184 *
185 * ISEED (input/output) INTEGER array, dimension (4)
186 * On entry ISEED specifies the seed of the random number
187 * generator. The array elements should be between 0 and 4095;
188 * if not they will be reduced mod 4096. Also, ISEED(4) must
189 * be odd. The random number generator uses a linear
190 * congruential sequence limited to small integers, and so
191 * should produce machine independent random numbers. The
192 * values of ISEED are changed on exit, and can be used in the
193 * next call to SDRVES to continue the same random number
194 * sequence.
195 *
196 * THRESH (input) REAL
197 * A test will count as "failed" if the "error", computed as
198 * described above, exceeds THRESH. Note that the error
199 * is scaled to be O(1), so THRESH should be a reasonably
200 * small multiple of 1, e.g., 10 or 100. In particular,
201 * it should not depend on the precision (single vs. double)
202 * or the size of the matrix. It must be at least zero.
203 *
204 * NOUNIT (input) INTEGER
205 * The FORTRAN unit number for printing out error messages
206 * (e.g., if a routine returns INFO not equal to 0.)
207 *
208 * A (workspace) REAL array, dimension (LDA, max(NN))
209 * Used to hold the matrix whose eigenvalues are to be
210 * computed. On exit, A contains the last matrix actually used.
211 *
212 * LDA (input) INTEGER
213 * The leading dimension of A, and H. LDA must be at
214 * least 1 and at least max(NN).
215 *
216 * H (workspace) REAL array, dimension (LDA, max(NN))
217 * Another copy of the test matrix A, modified by SGEES.
218 *
219 * HT (workspace) REAL array, dimension (LDA, max(NN))
220 * Yet another copy of the test matrix A, modified by SGEES.
221 *
222 * WR (workspace) REAL array, dimension (max(NN))
223 * WI (workspace) REAL array, dimension (max(NN))
224 * The real and imaginary parts of the eigenvalues of A.
225 * On exit, WR + WI*i are the eigenvalues of the matrix in A.
226 *
227 * WRT (workspace) REAL array, dimension (max(NN))
228 * WIT (workspace) REAL array, dimension (max(NN))
229 * Like WR, WI, these arrays contain the eigenvalues of A,
230 * but those computed when SGEES only computes a partial
231 * eigendecomposition, i.e. not Schur vectors
232 *
233 * VS (workspace) REAL array, dimension (LDVS, max(NN))
234 * VS holds the computed Schur vectors.
235 *
236 * LDVS (input) INTEGER
237 * Leading dimension of VS. Must be at least max(1,max(NN)).
238 *
239 * RESULT (output) REAL array, dimension (13)
240 * The values computed by the 13 tests described above.
241 * The values are currently limited to 1/ulp, to avoid overflow.
242 *
243 * WORK (workspace) REAL array, dimension (NWORK)
244 *
245 * NWORK (input) INTEGER
246 * The number of entries in WORK. This must be at least
247 * 5*NN(j)+2*NN(j)**2 for all j.
248 *
249 * IWORK (workspace) INTEGER array, dimension (max(NN))
250 *
251 * INFO (output) INTEGER
252 * If 0, then everything ran OK.
253 * -1: NSIZES < 0
254 * -2: Some NN(j) < 0
255 * -3: NTYPES < 0
256 * -6: THRESH < 0
257 * -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
258 * -17: LDVS < 1 or LDVS < NMAX, where NMAX is max( NN(j) ).
259 * -20: NWORK too small.
260 * If SLATMR, SLATMS, SLATME or SGEES returns an error code,
261 * the absolute value of it is returned.
262 *
263 *-----------------------------------------------------------------------
264 *
265 * Some Local Variables and Parameters:
266 * ---- ----- --------- --- ----------
267 *
268 * ZERO, ONE Real 0 and 1.
269 * MAXTYP The number of types defined.
270 * NMAX Largest value in NN.
271 * NERRS The number of tests which have exceeded THRESH
272 * COND, CONDS,
273 * IMODE Values to be passed to the matrix generators.
274 * ANORM Norm of A; passed to matrix generators.
275 *
276 * OVFL, UNFL Overflow and underflow thresholds.
277 * ULP, ULPINV Finest relative precision and its inverse.
278 * RTULP, RTULPI Square roots of the previous 4 values.
279 *
280 * The following four arrays decode JTYPE:
281 * KTYPE(j) The general type (1-10) for type "j".
282 * KMODE(j) The MODE value to be passed to the matrix
283 * generator for type "j".
284 * KMAGN(j) The order of magnitude ( O(1),
285 * O(overflow^(1/2) ), O(underflow^(1/2) )
286 * KCONDS(j) Selectw whether CONDS is to be 1 or
287 * 1/sqrt(ulp). (0 means irrelevant.)
288 *
289 * =====================================================================
290 *
291 * .. Parameters ..
292 REAL ZERO, ONE
293 PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
294 INTEGER MAXTYP
295 PARAMETER ( MAXTYP = 21 )
296 * ..
297 * .. Local Scalars ..
298 LOGICAL BADNN
299 CHARACTER SORT
300 CHARACTER*3 PATH
301 INTEGER I, IINFO, IMODE, ISORT, ITYPE, IWK, J, JCOL,
302 $ JSIZE, JTYPE, KNTEIG, LWORK, MTYPES, N,
303 $ NERRS, NFAIL, NMAX, NNWORK, NTEST, NTESTF,
304 $ NTESTT, RSUB, SDIM
305 REAL ANORM, COND, CONDS, OVFL, RTULP, RTULPI, TMP,
306 $ ULP, ULPINV, UNFL
307 * ..
308 * .. Local Arrays ..
309 CHARACTER ADUMMA( 1 )
310 INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
311 $ KMAGN( MAXTYP ), KMODE( MAXTYP ),
312 $ KTYPE( MAXTYP )
313 REAL RES( 2 )
314 * ..
315 * .. Arrays in Common ..
316 LOGICAL SELVAL( 20 )
317 REAL SELWI( 20 ), SELWR( 20 )
318 * ..
319 * .. Scalars in Common ..
320 INTEGER SELDIM, SELOPT
321 * ..
322 * .. Common blocks ..
323 COMMON / SSLCT / SELOPT, SELDIM, SELVAL, SELWR, SELWI
324 * ..
325 * .. External Functions ..
326 LOGICAL SSLECT
327 REAL SLAMCH
328 EXTERNAL SSLECT, SLAMCH
329 * ..
330 * .. External Subroutines ..
331 EXTERNAL SGEES, SHST01, SLABAD, SLACPY, SLASUM, SLATME,
332 $ SLATMR, SLATMS, SLASET, XERBLA
333 * ..
334 * .. Intrinsic Functions ..
335 INTRINSIC ABS, MAX, SIGN, SQRT
336 * ..
337 * .. Data statements ..
338 DATA KTYPE / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
339 DATA KMAGN / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
340 $ 3, 1, 2, 3 /
341 DATA KMODE / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
342 $ 1, 5, 5, 5, 4, 3, 1 /
343 DATA KCONDS / 3*0, 5*0, 4*1, 6*2, 3*0 /
344 * ..
345 * .. Executable Statements ..
346 *
347 PATH( 1: 1 ) = 'Single precision'
348 PATH( 2: 3 ) = 'ES'
349 *
350 * Check for errors
351 *
352 NTESTT = 0
353 NTESTF = 0
354 INFO = 0
355 SELOPT = 0
356 *
357 * Important constants
358 *
359 BADNN = .FALSE.
360 NMAX = 0
361 DO 10 J = 1, NSIZES
362 NMAX = MAX( NMAX, NN( J ) )
363 IF( NN( J ).LT.0 )
364 $ BADNN = .TRUE.
365 10 CONTINUE
366 *
367 * Check for errors
368 *
369 IF( NSIZES.LT.0 ) THEN
370 INFO = -1
371 ELSE IF( BADNN ) THEN
372 INFO = -2
373 ELSE IF( NTYPES.LT.0 ) THEN
374 INFO = -3
375 ELSE IF( THRESH.LT.ZERO ) THEN
376 INFO = -6
377 ELSE IF( NOUNIT.LE.0 ) THEN
378 INFO = -7
379 ELSE IF( LDA.LT.1 .OR. LDA.LT.NMAX ) THEN
380 INFO = -9
381 ELSE IF( LDVS.LT.1 .OR. LDVS.LT.NMAX ) THEN
382 INFO = -17
383 ELSE IF( 5*NMAX+2*NMAX**2.GT.NWORK ) THEN
384 INFO = -20
385 END IF
386 *
387 IF( INFO.NE.0 ) THEN
388 CALL XERBLA( 'SDRVES', -INFO )
389 RETURN
390 END IF
391 *
392 * Quick return if nothing to do
393 *
394 IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
395 $ RETURN
396 *
397 * More Important constants
398 *
399 UNFL = SLAMCH( 'Safe minimum' )
400 OVFL = ONE / UNFL
401 CALL SLABAD( UNFL, OVFL )
402 ULP = SLAMCH( 'Precision' )
403 ULPINV = ONE / ULP
404 RTULP = SQRT( ULP )
405 RTULPI = ONE / RTULP
406 *
407 * Loop over sizes, types
408 *
409 NERRS = 0
410 *
411 DO 270 JSIZE = 1, NSIZES
412 N = NN( JSIZE )
413 MTYPES = MAXTYP
414 IF( NSIZES.EQ.1 .AND. NTYPES.EQ.MAXTYP+1 )
415 $ MTYPES = MTYPES + 1
416 *
417 DO 260 JTYPE = 1, MTYPES
418 IF( .NOT.DOTYPE( JTYPE ) )
419 $ GO TO 260
420 *
421 * Save ISEED in case of an error.
422 *
423 DO 20 J = 1, 4
424 IOLDSD( J ) = ISEED( J )
425 20 CONTINUE
426 *
427 * Compute "A"
428 *
429 * Control parameters:
430 *
431 * KMAGN KCONDS KMODE KTYPE
432 * =1 O(1) 1 clustered 1 zero
433 * =2 large large clustered 2 identity
434 * =3 small exponential Jordan
435 * =4 arithmetic diagonal, (w/ eigenvalues)
436 * =5 random log symmetric, w/ eigenvalues
437 * =6 random general, w/ eigenvalues
438 * =7 random diagonal
439 * =8 random symmetric
440 * =9 random general
441 * =10 random triangular
442 *
443 IF( MTYPES.GT.MAXTYP )
444 $ GO TO 90
445 *
446 ITYPE = KTYPE( JTYPE )
447 IMODE = KMODE( JTYPE )
448 *
449 * Compute norm
450 *
451 GO TO ( 30, 40, 50 )KMAGN( JTYPE )
452 *
453 30 CONTINUE
454 ANORM = ONE
455 GO TO 60
456 *
457 40 CONTINUE
458 ANORM = OVFL*ULP
459 GO TO 60
460 *
461 50 CONTINUE
462 ANORM = UNFL*ULPINV
463 GO TO 60
464 *
465 60 CONTINUE
466 *
467 CALL SLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
468 IINFO = 0
469 COND = ULPINV
470 *
471 * Special Matrices -- Identity & Jordan block
472 *
473 * Zero
474 *
475 IF( ITYPE.EQ.1 ) THEN
476 IINFO = 0
477 *
478 ELSE IF( ITYPE.EQ.2 ) THEN
479 *
480 * Identity
481 *
482 DO 70 JCOL = 1, N
483 A( JCOL, JCOL ) = ANORM
484 70 CONTINUE
485 *
486 ELSE IF( ITYPE.EQ.3 ) THEN
487 *
488 * Jordan Block
489 *
490 DO 80 JCOL = 1, N
491 A( JCOL, JCOL ) = ANORM
492 IF( JCOL.GT.1 )
493 $ A( JCOL, JCOL-1 ) = ONE
494 80 CONTINUE
495 *
496 ELSE IF( ITYPE.EQ.4 ) THEN
497 *
498 * Diagonal Matrix, [Eigen]values Specified
499 *
500 CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
501 $ ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ),
502 $ IINFO )
503 *
504 ELSE IF( ITYPE.EQ.5 ) THEN
505 *
506 * Symmetric, eigenvalues specified
507 *
508 CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
509 $ ANORM, N, N, 'N', A, LDA, WORK( N+1 ),
510 $ IINFO )
511 *
512 ELSE IF( ITYPE.EQ.6 ) THEN
513 *
514 * General, eigenvalues specified
515 *
516 IF( KCONDS( JTYPE ).EQ.1 ) THEN
517 CONDS = ONE
518 ELSE IF( KCONDS( JTYPE ).EQ.2 ) THEN
519 CONDS = RTULPI
520 ELSE
521 CONDS = ZERO
522 END IF
523 *
524 ADUMMA( 1 ) = ' '
525 CALL SLATME( N, 'S', ISEED, WORK, IMODE, COND, ONE,
526 $ ADUMMA, 'T', 'T', 'T', WORK( N+1 ), 4,
527 $ CONDS, N, N, ANORM, A, LDA, WORK( 2*N+1 ),
528 $ IINFO )
529 *
530 ELSE IF( ITYPE.EQ.7 ) THEN
531 *
532 * Diagonal, random eigenvalues
533 *
534 CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
535 $ 'T', 'N', WORK( N+1 ), 1, ONE,
536 $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
537 $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
538 *
539 ELSE IF( ITYPE.EQ.8 ) THEN
540 *
541 * Symmetric, random eigenvalues
542 *
543 CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
544 $ 'T', 'N', WORK( N+1 ), 1, ONE,
545 $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
546 $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
547 *
548 ELSE IF( ITYPE.EQ.9 ) THEN
549 *
550 * General, random eigenvalues
551 *
552 CALL SLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
553 $ 'T', 'N', WORK( N+1 ), 1, ONE,
554 $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
555 $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
556 IF( N.GE.4 ) THEN
557 CALL SLASET( 'Full', 2, N, ZERO, ZERO, A, LDA )
558 CALL SLASET( 'Full', N-3, 1, ZERO, ZERO, A( 3, 1 ),
559 $ LDA )
560 CALL SLASET( 'Full', N-3, 2, ZERO, ZERO, A( 3, N-1 ),
561 $ LDA )
562 CALL SLASET( 'Full', 1, N, ZERO, ZERO, A( N, 1 ),
563 $ LDA )
564 END IF
565 *
566 ELSE IF( ITYPE.EQ.10 ) THEN
567 *
568 * Triangular, random eigenvalues
569 *
570 CALL SLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
571 $ 'T', 'N', WORK( N+1 ), 1, ONE,
572 $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, 0,
573 $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
574 *
575 ELSE
576 *
577 IINFO = 1
578 END IF
579 *
580 IF( IINFO.NE.0 ) THEN
581 WRITE( NOUNIT, FMT = 9992 )'Generator', IINFO, N, JTYPE,
582 $ IOLDSD
583 INFO = ABS( IINFO )
584 RETURN
585 END IF
586 *
587 90 CONTINUE
588 *
589 * Test for minimal and generous workspace
590 *
591 DO 250 IWK = 1, 2
592 IF( IWK.EQ.1 ) THEN
593 NNWORK = 3*N
594 ELSE
595 NNWORK = 5*N + 2*N**2
596 END IF
597 NNWORK = MAX( NNWORK, 1 )
598 *
599 * Initialize RESULT
600 *
601 DO 100 J = 1, 13
602 RESULT( J ) = -ONE
603 100 CONTINUE
604 *
605 * Test with and without sorting of eigenvalues
606 *
607 DO 210 ISORT = 0, 1
608 IF( ISORT.EQ.0 ) THEN
609 SORT = 'N'
610 RSUB = 0
611 ELSE
612 SORT = 'S'
613 RSUB = 6
614 END IF
615 *
616 * Compute Schur form and Schur vectors, and test them
617 *
618 CALL SLACPY( 'F', N, N, A, LDA, H, LDA )
619 CALL SGEES( 'V', SORT, SSLECT, N, H, LDA, SDIM, WR,
620 $ WI, VS, LDVS, WORK, NNWORK, BWORK, IINFO )
621 IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
622 RESULT( 1+RSUB ) = ULPINV
623 WRITE( NOUNIT, FMT = 9992 )'SGEES1', IINFO, N,
624 $ JTYPE, IOLDSD
625 INFO = ABS( IINFO )
626 GO TO 220
627 END IF
628 *
629 * Do Test (1) or Test (7)
630 *
631 RESULT( 1+RSUB ) = ZERO
632 DO 120 J = 1, N - 2
633 DO 110 I = J + 2, N
634 IF( H( I, J ).NE.ZERO )
635 $ RESULT( 1+RSUB ) = ULPINV
636 110 CONTINUE
637 120 CONTINUE
638 DO 130 I = 1, N - 2
639 IF( H( I+1, I ).NE.ZERO .AND. H( I+2, I+1 ).NE.
640 $ ZERO )RESULT( 1+RSUB ) = ULPINV
641 130 CONTINUE
642 DO 140 I = 1, N - 1
643 IF( H( I+1, I ).NE.ZERO ) THEN
644 IF( H( I, I ).NE.H( I+1, I+1 ) .OR.
645 $ H( I, I+1 ).EQ.ZERO .OR.
646 $ SIGN( ONE, H( I+1, I ) ).EQ.
647 $ SIGN( ONE, H( I, I+1 ) ) )RESULT( 1+RSUB )
648 $ = ULPINV
649 END IF
650 140 CONTINUE
651 *
652 * Do Tests (2) and (3) or Tests (8) and (9)
653 *
654 LWORK = MAX( 1, 2*N*N )
655 CALL SHST01( N, 1, N, A, LDA, H, LDA, VS, LDVS, WORK,
656 $ LWORK, RES )
657 RESULT( 2+RSUB ) = RES( 1 )
658 RESULT( 3+RSUB ) = RES( 2 )
659 *
660 * Do Test (4) or Test (10)
661 *
662 RESULT( 4+RSUB ) = ZERO
663 DO 150 I = 1, N
664 IF( H( I, I ).NE.WR( I ) )
665 $ RESULT( 4+RSUB ) = ULPINV
666 150 CONTINUE
667 IF( N.GT.1 ) THEN
668 IF( H( 2, 1 ).EQ.ZERO .AND. WI( 1 ).NE.ZERO )
669 $ RESULT( 4+RSUB ) = ULPINV
670 IF( H( N, N-1 ).EQ.ZERO .AND. WI( N ).NE.ZERO )
671 $ RESULT( 4+RSUB ) = ULPINV
672 END IF
673 DO 160 I = 1, N - 1
674 IF( H( I+1, I ).NE.ZERO ) THEN
675 TMP = SQRT( ABS( H( I+1, I ) ) )*
676 $ SQRT( ABS( H( I, I+1 ) ) )
677 RESULT( 4+RSUB ) = MAX( RESULT( 4+RSUB ),
678 $ ABS( WI( I )-TMP ) /
679 $ MAX( ULP*TMP, UNFL ) )
680 RESULT( 4+RSUB ) = MAX( RESULT( 4+RSUB ),
681 $ ABS( WI( I+1 )+TMP ) /
682 $ MAX( ULP*TMP, UNFL ) )
683 ELSE IF( I.GT.1 ) THEN
684 IF( H( I+1, I ).EQ.ZERO .AND. H( I, I-1 ).EQ.
685 $ ZERO .AND. WI( I ).NE.ZERO )RESULT( 4+RSUB )
686 $ = ULPINV
687 END IF
688 160 CONTINUE
689 *
690 * Do Test (5) or Test (11)
691 *
692 CALL SLACPY( 'F', N, N, A, LDA, HT, LDA )
693 CALL SGEES( 'N', SORT, SSLECT, N, HT, LDA, SDIM, WRT,
694 $ WIT, VS, LDVS, WORK, NNWORK, BWORK,
695 $ IINFO )
696 IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
697 RESULT( 5+RSUB ) = ULPINV
698 WRITE( NOUNIT, FMT = 9992 )'SGEES2', IINFO, N,
699 $ JTYPE, IOLDSD
700 INFO = ABS( IINFO )
701 GO TO 220
702 END IF
703 *
704 RESULT( 5+RSUB ) = ZERO
705 DO 180 J = 1, N
706 DO 170 I = 1, N
707 IF( H( I, J ).NE.HT( I, J ) )
708 $ RESULT( 5+RSUB ) = ULPINV
709 170 CONTINUE
710 180 CONTINUE
711 *
712 * Do Test (6) or Test (12)
713 *
714 RESULT( 6+RSUB ) = ZERO
715 DO 190 I = 1, N
716 IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) )
717 $ RESULT( 6+RSUB ) = ULPINV
718 190 CONTINUE
719 *
720 * Do Test (13)
721 *
722 IF( ISORT.EQ.1 ) THEN
723 RESULT( 13 ) = ZERO
724 KNTEIG = 0
725 DO 200 I = 1, N
726 IF( SSLECT( WR( I ), WI( I ) ) .OR.
727 $ SSLECT( WR( I ), -WI( I ) ) )
728 $ KNTEIG = KNTEIG + 1
729 IF( I.LT.N ) THEN
730 IF( ( SSLECT( WR( I+1 ),
731 $ WI( I+1 ) ) .OR. SSLECT( WR( I+1 ),
732 $ -WI( I+1 ) ) ) .AND.
733 $ ( .NOT.( SSLECT( WR( I ),
734 $ WI( I ) ) .OR. SSLECT( WR( I ),
735 $ -WI( I ) ) ) ) .AND. IINFO.NE.N+2 )
736 $ RESULT( 13 ) = ULPINV
737 END IF
738 200 CONTINUE
739 IF( SDIM.NE.KNTEIG ) THEN
740 RESULT( 13 ) = ULPINV
741 END IF
742 END IF
743 *
744 210 CONTINUE
745 *
746 * End of Loop -- Check for RESULT(j) > THRESH
747 *
748 220 CONTINUE
749 *
750 NTEST = 0
751 NFAIL = 0
752 DO 230 J = 1, 13
753 IF( RESULT( J ).GE.ZERO )
754 $ NTEST = NTEST + 1
755 IF( RESULT( J ).GE.THRESH )
756 $ NFAIL = NFAIL + 1
757 230 CONTINUE
758 *
759 IF( NFAIL.GT.0 )
760 $ NTESTF = NTESTF + 1
761 IF( NTESTF.EQ.1 ) THEN
762 WRITE( NOUNIT, FMT = 9999 )PATH
763 WRITE( NOUNIT, FMT = 9998 )
764 WRITE( NOUNIT, FMT = 9997 )
765 WRITE( NOUNIT, FMT = 9996 )
766 WRITE( NOUNIT, FMT = 9995 )THRESH
767 WRITE( NOUNIT, FMT = 9994 )
768 NTESTF = 2
769 END IF
770 *
771 DO 240 J = 1, 13
772 IF( RESULT( J ).GE.THRESH ) THEN
773 WRITE( NOUNIT, FMT = 9993 )N, IWK, IOLDSD, JTYPE,
774 $ J, RESULT( J )
775 END IF
776 240 CONTINUE
777 *
778 NERRS = NERRS + NFAIL
779 NTESTT = NTESTT + NTEST
780 *
781 250 CONTINUE
782 260 CONTINUE
783 270 CONTINUE
784 *
785 * Summary
786 *
787 CALL SLASUM( PATH, NOUNIT, NERRS, NTESTT )
788 *
789 9999 FORMAT( / 1X, A3, ' -- Real Schur Form Decomposition Driver',
790 $ / ' Matrix types (see SDRVES for details): ' )
791 *
792 9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
793 $ ' ', ' 5=Diagonal: geometr. spaced entries.',
794 $ / ' 2=Identity matrix. ', ' 6=Diagona',
795 $ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
796 $ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
797 $ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
798 $ 'mall, evenly spaced.' )
799 9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
800 $ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
801 $ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
802 $ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
803 $ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
804 $ 'lex ', / ' 12=Well-cond., random complex ', 6X, ' ',
805 $ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
806 $ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
807 $ ' complx ' )
808 9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
809 $ 'with small random entries.', / ' 20=Matrix with large ran',
810 $ 'dom entries. ', / )
811 9995 FORMAT( ' Tests performed with test threshold =', F8.2,
812 $ / ' ( A denotes A on input and T denotes A on output)',
813 $ / / ' 1 = 0 if T in Schur form (no sort), ',
814 $ ' 1/ulp otherwise', /
815 $ ' 2 = | A - VS T transpose(VS) | / ( n |A| ulp ) (no sort)',
816 $ / ' 3 = | I - VS transpose(VS) | / ( n ulp ) (no sort) ', /
817 $ ' 4 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (no sort),',
818 $ ' 1/ulp otherwise', /
819 $ ' 5 = 0 if T same no matter if VS computed (no sort),',
820 $ ' 1/ulp otherwise', /
821 $ ' 6 = 0 if WR, WI same no matter if VS computed (no sort)',
822 $ ', 1/ulp otherwise' )
823 9994 FORMAT( ' 7 = 0 if T in Schur form (sort), ', ' 1/ulp otherwise',
824 $ / ' 8 = | A - VS T transpose(VS) | / ( n |A| ulp ) (sort)',
825 $ / ' 9 = | I - VS transpose(VS) | / ( n ulp ) (sort) ',
826 $ / ' 10 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (sort),',
827 $ ' 1/ulp otherwise', /
828 $ ' 11 = 0 if T same no matter if VS computed (sort),',
829 $ ' 1/ulp otherwise', /
830 $ ' 12 = 0 if WR, WI same no matter if VS computed (sort),',
831 $ ' 1/ulp otherwise', /
832 $ ' 13 = 0 if sorting succesful, 1/ulp otherwise', / )
833 9993 FORMAT( ' N=', I5, ', IWK=', I2, ', seed=', 4( I4, ',' ),
834 $ ' type ', I2, ', test(', I2, ')=', G10.3 )
835 9992 FORMAT( ' SDRVES: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
836 $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
837 *
838 RETURN
839 *
840 * End of SDRVES
841 *
842 END