1 SUBROUTINE CDRGSX( NSIZE, NCMAX, THRESH, NIN, NOUT, A, LDA, B,
2 $ AI, BI, Z, Q, ALPHA, BETA, C, LDC, S, WORK,
3 $ LWORK, RWORK, IWORK, LIWORK, 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, LDC, LIWORK, LWORK, NCMAX, NIN,
11 $ NOUT, NSIZE
12 REAL THRESH
13 * ..
14 * .. Array Arguments ..
15 LOGICAL BWORK( * )
16 INTEGER IWORK( * )
17 REAL RWORK( * ), S( * )
18 COMPLEX A( LDA, * ), AI( LDA, * ), ALPHA( * ),
19 $ B( LDA, * ), BETA( * ), BI( LDA, * ),
20 $ C( LDC, * ), Q( LDA, * ), WORK( * ),
21 $ Z( LDA, * )
22 * ..
23 *
24 * Purpose
25 * =======
26 *
27 * CDRGSX checks the nonsymmetric generalized eigenvalue (Schur form)
28 * problem expert driver CGGESX.
29 *
30 * CGGES factors A and B as Q*S*Z' and Q*T*Z' , where ' means conjugate
31 * transpose, S and T are upper triangular (i.e., in generalized Schur
32 * form), and Q and Z are unitary. It also computes the generalized
33 * eigenvalues (alpha(j),beta(j)), j=1,...,n. Thus,
34 * w(j) = alpha(j)/beta(j) is a root of the characteristic equation
35 *
36 * det( A - w(j) B ) = 0
37 *
38 * Optionally it also reorders the eigenvalues so that a selected
39 * cluster of eigenvalues appears in the leading diagonal block of the
40 * Schur forms; computes a reciprocal condition number for the average
41 * of the selected eigenvalues; and computes a reciprocal condition
42 * number for the right and left deflating subspaces corresponding to
43 * the selected eigenvalues.
44 *
45 * When CDRGSX is called with NSIZE > 0, five (5) types of built-in
46 * matrix pairs are used to test the routine CGGESX.
47 *
48 * When CDRGSX is called with NSIZE = 0, it reads in test matrix data
49 * to test CGGESX.
50 * (need more details on what kind of read-in data are needed).
51 *
52 * For each matrix pair, the following tests will be performed and
53 * compared with the threshhold THRESH except for the tests (7) and (9):
54 *
55 * (1) | A - Q S Z' | / ( |A| n ulp )
56 *
57 * (2) | B - Q T Z' | / ( |B| n ulp )
58 *
59 * (3) | I - QQ' | / ( n ulp )
60 *
61 * (4) | I - ZZ' | / ( n ulp )
62 *
63 * (5) if A is in Schur form (i.e. triangular form)
64 *
65 * (6) maximum over j of D(j) where:
66 *
67 * |alpha(j) - S(j,j)| |beta(j) - T(j,j)|
68 * D(j) = ------------------------ + -----------------------
69 * max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|)
70 *
71 * (7) if sorting worked and SDIM is the number of eigenvalues
72 * which were selected.
73 *
74 * (8) the estimated value DIF does not differ from the true values of
75 * Difu and Difl more than a factor 10*THRESH. If the estimate DIF
76 * equals zero the corresponding true values of Difu and Difl
77 * should be less than EPS*norm(A, B). If the true value of Difu
78 * and Difl equal zero, the estimate DIF should be less than
79 * EPS*norm(A, B).
80 *
81 * (9) If INFO = N+3 is returned by CGGESX, the reordering "failed"
82 * and we check that DIF = PL = PR = 0 and that the true value of
83 * Difu and Difl is < EPS*norm(A, B). We count the events when
84 * INFO=N+3.
85 *
86 * For read-in test matrices, the same tests are run except that the
87 * exact value for DIF (and PL) is input data. Additionally, there is
88 * one more test run for read-in test matrices:
89 *
90 * (10) the estimated value PL does not differ from the true value of
91 * PLTRU more than a factor THRESH. If the estimate PL equals
92 * zero the corresponding true value of PLTRU should be less than
93 * EPS*norm(A, B). If the true value of PLTRU equal zero, the
94 * estimate PL should be less than EPS*norm(A, B).
95 *
96 * Note that for the built-in tests, a total of 10*NSIZE*(NSIZE-1)
97 * matrix pairs are generated and tested. NSIZE should be kept small.
98 *
99 * SVD (routine CGESVD) is used for computing the true value of DIF_u
100 * and DIF_l when testing the built-in test problems.
101 *
102 * Built-in Test Matrices
103 * ======================
104 *
105 * All built-in test matrices are the 2 by 2 block of triangular
106 * matrices
107 *
108 * A = [ A11 A12 ] and B = [ B11 B12 ]
109 * [ A22 ] [ B22 ]
110 *
111 * where for different type of A11 and A22 are given as the following.
112 * A12 and B12 are chosen so that the generalized Sylvester equation
113 *
114 * A11*R - L*A22 = -A12
115 * B11*R - L*B22 = -B12
116 *
117 * have prescribed solution R and L.
118 *
119 * Type 1: A11 = J_m(1,-1) and A_22 = J_k(1-a,1).
120 * B11 = I_m, B22 = I_k
121 * where J_k(a,b) is the k-by-k Jordan block with ``a'' on
122 * diagonal and ``b'' on superdiagonal.
123 *
124 * Type 2: A11 = (a_ij) = ( 2(.5-sin(i)) ) and
125 * B11 = (b_ij) = ( 2(.5-sin(ij)) ) for i=1,...,m, j=i,...,m
126 * A22 = (a_ij) = ( 2(.5-sin(i+j)) ) and
127 * B22 = (b_ij) = ( 2(.5-sin(ij)) ) for i=m+1,...,k, j=i,...,k
128 *
129 * Type 3: A11, A22 and B11, B22 are chosen as for Type 2, but each
130 * second diagonal block in A_11 and each third diagonal block
131 * in A_22 are made as 2 by 2 blocks.
132 *
133 * Type 4: A11 = ( 20(.5 - sin(ij)) ) and B22 = ( 2(.5 - sin(i+j)) )
134 * for i=1,...,m, j=1,...,m and
135 * A22 = ( 20(.5 - sin(i+j)) ) and B22 = ( 2(.5 - sin(ij)) )
136 * for i=m+1,...,k, j=m+1,...,k
137 *
138 * Type 5: (A,B) and have potentially close or common eigenvalues and
139 * very large departure from block diagonality A_11 is chosen
140 * as the m x m leading submatrix of A_1:
141 * | 1 b |
142 * | -b 1 |
143 * | 1+d b |
144 * | -b 1+d |
145 * A_1 = | d 1 |
146 * | -1 d |
147 * | -d 1 |
148 * | -1 -d |
149 * | 1 |
150 * and A_22 is chosen as the k x k leading submatrix of A_2:
151 * | -1 b |
152 * | -b -1 |
153 * | 1-d b |
154 * | -b 1-d |
155 * A_2 = | d 1+b |
156 * | -1-b d |
157 * | -d 1+b |
158 * | -1+b -d |
159 * | 1-d |
160 * and matrix B are chosen as identity matrices (see SLATM5).
161 *
162 *
163 * Arguments
164 * =========
165 *
166 * NSIZE (input) INTEGER
167 * The maximum size of the matrices to use. NSIZE >= 0.
168 * If NSIZE = 0, no built-in tests matrices are used, but
169 * read-in test matrices are used to test SGGESX.
170 *
171 * NCMAX (input) INTEGER
172 * Maximum allowable NMAX for generating Kroneker matrix
173 * in call to CLAKF2
174 *
175 * THRESH (input) REAL
176 * A test will count as "failed" if the "error", computed as
177 * described above, exceeds THRESH. Note that the error
178 * is scaled to be O(1), so THRESH should be a reasonably
179 * small multiple of 1, e.g., 10 or 100. In particular,
180 * it should not depend on the precision (single vs. double)
181 * or the size of the matrix. THRESH >= 0.
182 *
183 * NIN (input) INTEGER
184 * The FORTRAN unit number for reading in the data file of
185 * problems to solve.
186 *
187 * NOUT (input) INTEGER
188 * The FORTRAN unit number for printing out error messages
189 * (e.g., if a routine returns INFO not equal to 0.)
190 *
191 * A (workspace) COMPLEX array, dimension (LDA, NSIZE)
192 * Used to store the matrix whose eigenvalues are to be
193 * computed. On exit, A contains the last matrix actually used.
194 *
195 * LDA (input) INTEGER
196 * The leading dimension of A, B, AI, BI, Z and Q,
197 * LDA >= max( 1, NSIZE ). For the read-in test,
198 * LDA >= max( 1, N ), N is the size of the test matrices.
199 *
200 * B (workspace) COMPLEX array, dimension (LDA, NSIZE)
201 * Used to store the matrix whose eigenvalues are to be
202 * computed. On exit, B contains the last matrix actually used.
203 *
204 * AI (workspace) COMPLEX array, dimension (LDA, NSIZE)
205 * Copy of A, modified by CGGESX.
206 *
207 * BI (workspace) COMPLEX array, dimension (LDA, NSIZE)
208 * Copy of B, modified by CGGESX.
209 *
210 * Z (workspace) COMPLEX array, dimension (LDA, NSIZE)
211 * Z holds the left Schur vectors computed by CGGESX.
212 *
213 * Q (workspace) COMPLEX array, dimension (LDA, NSIZE)
214 * Q holds the right Schur vectors computed by CGGESX.
215 *
216 * ALPHA (workspace) COMPLEX array, dimension (NSIZE)
217 * BETA (workspace) COMPLEX array, dimension (NSIZE)
218 * On exit, ALPHA/BETA are the eigenvalues.
219 *
220 * C (workspace) COMPLEX array, dimension (LDC, LDC)
221 * Store the matrix generated by subroutine CLAKF2, this is the
222 * matrix formed by Kronecker products used for estimating
223 * DIF.
224 *
225 * LDC (input) INTEGER
226 * The leading dimension of C. LDC >= max(1, LDA*LDA/2 ).
227 *
228 * S (workspace) REAL array, dimension (LDC)
229 * Singular values of C
230 *
231 * WORK (workspace) COMPLEX array, dimension (LWORK)
232 *
233 * LWORK (input) INTEGER
234 * The dimension of the array WORK. LWORK >= 3*NSIZE*NSIZE/2
235 *
236 * RWORK (workspace) REAL array,
237 * dimension (5*NSIZE*NSIZE/2 - 4)
238 *
239 * IWORK (workspace) INTEGER array, dimension (LIWORK)
240 *
241 * LIWORK (input) INTEGER
242 * The dimension of the array IWORK. LIWORK >= NSIZE + 2.
243 *
244 * BWORK (workspace) LOGICAL array, dimension (NSIZE)
245 *
246 * INFO (output) INTEGER
247 * = 0: successful exit
248 * < 0: if INFO = -i, the i-th argument had an illegal value.
249 * > 0: A routine returned an error code.
250 *
251 * =====================================================================
252 *
253 * .. Parameters ..
254 REAL ZERO, ONE, TEN
255 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TEN = 1.0E+1 )
256 COMPLEX CZERO
257 PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ) )
258 * ..
259 * .. Local Scalars ..
260 LOGICAL ILABAD
261 CHARACTER SENSE
262 INTEGER BDSPAC, I, IFUNC, J, LINFO, MAXWRK, MINWRK, MM,
263 $ MN2, NERRS, NPTKNT, NTEST, NTESTT, PRTYPE, QBA,
264 $ QBB
265 REAL ABNRM, BIGNUM, DIFTRU, PLTRU, SMLNUM, TEMP1,
266 $ TEMP2, THRSH2, ULP, ULPINV, WEIGHT
267 COMPLEX X
268 * ..
269 * .. Local Arrays ..
270 REAL DIFEST( 2 ), PL( 2 ), RESULT( 10 )
271 * ..
272 * .. External Functions ..
273 LOGICAL CLCTSX
274 INTEGER ILAENV
275 REAL CLANGE, SLAMCH
276 EXTERNAL CLCTSX, ILAENV, CLANGE, SLAMCH
277 * ..
278 * .. External Subroutines ..
279 EXTERNAL ALASVM, CGESVD, CGET51, CGGESX, CLACPY, CLAKF2,
280 $ CLASET, CLATM5, SLABAD, XERBLA
281 * ..
282 * .. Scalars in Common ..
283 LOGICAL FS
284 INTEGER K, M, MPLUSN, N
285 * ..
286 * .. Common blocks ..
287 COMMON / MN / M, N, MPLUSN, K, FS
288 * ..
289 * .. Intrinsic Functions ..
290 INTRINSIC ABS, AIMAG, MAX, REAL, SQRT
291 * ..
292 * .. Statement Functions ..
293 REAL ABS1
294 * ..
295 * .. Statement Function definitions ..
296 ABS1( X ) = ABS( REAL( X ) ) + ABS( AIMAG( X ) )
297 * ..
298 * .. Executable Statements ..
299 *
300 * Check for errors
301 *
302 IF( NSIZE.LT.0 ) THEN
303 INFO = -1
304 ELSE IF( THRESH.LT.ZERO ) THEN
305 INFO = -2
306 ELSE IF( NIN.LE.0 ) THEN
307 INFO = -3
308 ELSE IF( NOUT.LE.0 ) THEN
309 INFO = -4
310 ELSE IF( LDA.LT.1 .OR. LDA.LT.NSIZE ) THEN
311 INFO = -6
312 ELSE IF( LDC.LT.1 .OR. LDC.LT.NSIZE*NSIZE / 2 ) THEN
313 INFO = -15
314 ELSE IF( LIWORK.LT.NSIZE+2 ) THEN
315 INFO = -21
316 END IF
317 *
318 * Compute workspace
319 * (Note: Comments in the code beginning "Workspace:" describe the
320 * minimal amount of workspace needed at that point in the code,
321 * as well as the preferred amount for good performance.
322 * NB refers to the optimal block size for the immediately
323 * following subroutine, as returned by ILAENV.)
324 *
325 MINWRK = 1
326 IF( INFO.EQ.0 .AND. LWORK.GE.1 ) THEN
327 MINWRK = 3*NSIZE*NSIZE / 2
328 *
329 * workspace for cggesx
330 *
331 MAXWRK = NSIZE*( 1+ILAENV( 1, 'CGEQRF', ' ', NSIZE, 1, NSIZE,
332 $ 0 ) )
333 MAXWRK = MAX( MAXWRK, NSIZE*( 1+ILAENV( 1, 'CUNGQR', ' ',
334 $ NSIZE, 1, NSIZE, -1 ) ) )
335 *
336 * workspace for cgesvd
337 *
338 BDSPAC = 3*NSIZE*NSIZE / 2
339 MAXWRK = MAX( MAXWRK, NSIZE*NSIZE*
340 $ ( 1+ILAENV( 1, 'CGEBRD', ' ', NSIZE*NSIZE / 2,
341 $ NSIZE*NSIZE / 2, -1, -1 ) ) )
342 MAXWRK = MAX( MAXWRK, BDSPAC )
343 *
344 MAXWRK = MAX( MAXWRK, MINWRK )
345 *
346 WORK( 1 ) = MAXWRK
347 END IF
348 *
349 IF( LWORK.LT.MINWRK )
350 $ INFO = -18
351 *
352 IF( INFO.NE.0 ) THEN
353 CALL XERBLA( 'CDRGSX', -INFO )
354 RETURN
355 END IF
356 *
357 * Important constants
358 *
359 ULP = SLAMCH( 'P' )
360 ULPINV = ONE / ULP
361 SMLNUM = SLAMCH( 'S' ) / ULP
362 BIGNUM = ONE / SMLNUM
363 CALL SLABAD( SMLNUM, BIGNUM )
364 THRSH2 = TEN*THRESH
365 NTESTT = 0
366 NERRS = 0
367 *
368 * Go to the tests for read-in matrix pairs
369 *
370 IFUNC = 0
371 IF( NSIZE.EQ.0 )
372 $ GO TO 70
373 *
374 * Test the built-in matrix pairs.
375 * Loop over different functions (IFUNC) of CGGESX, types (PRTYPE)
376 * of test matrices, different size (M+N)
377 *
378 PRTYPE = 0
379 QBA = 3
380 QBB = 4
381 WEIGHT = SQRT( ULP )
382 *
383 DO 60 IFUNC = 0, 3
384 DO 50 PRTYPE = 1, 5
385 DO 40 M = 1, NSIZE - 1
386 DO 30 N = 1, NSIZE - M
387 *
388 WEIGHT = ONE / WEIGHT
389 MPLUSN = M + N
390 *
391 * Generate test matrices
392 *
393 FS = .TRUE.
394 K = 0
395 *
396 CALL CLASET( 'Full', MPLUSN, MPLUSN, CZERO, CZERO, AI,
397 $ LDA )
398 CALL CLASET( 'Full', MPLUSN, MPLUSN, CZERO, CZERO, BI,
399 $ LDA )
400 *
401 CALL CLATM5( PRTYPE, M, N, AI, LDA, AI( M+1, M+1 ),
402 $ LDA, AI( 1, M+1 ), LDA, BI, LDA,
403 $ BI( M+1, M+1 ), LDA, BI( 1, M+1 ), LDA,
404 $ Q, LDA, Z, LDA, WEIGHT, QBA, QBB )
405 *
406 * Compute the Schur factorization and swapping the
407 * m-by-m (1,1)-blocks with n-by-n (2,2)-blocks.
408 * Swapping is accomplished via the function CLCTSX
409 * which is supplied below.
410 *
411 IF( IFUNC.EQ.0 ) THEN
412 SENSE = 'N'
413 ELSE IF( IFUNC.EQ.1 ) THEN
414 SENSE = 'E'
415 ELSE IF( IFUNC.EQ.2 ) THEN
416 SENSE = 'V'
417 ELSE IF( IFUNC.EQ.3 ) THEN
418 SENSE = 'B'
419 END IF
420 *
421 CALL CLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, A, LDA )
422 CALL CLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, B, LDA )
423 *
424 CALL CGGESX( 'V', 'V', 'S', CLCTSX, SENSE, MPLUSN, AI,
425 $ LDA, BI, LDA, MM, ALPHA, BETA, Q, LDA, Z,
426 $ LDA, PL, DIFEST, WORK, LWORK, RWORK,
427 $ IWORK, LIWORK, BWORK, LINFO )
428 *
429 IF( LINFO.NE.0 .AND. LINFO.NE.MPLUSN+2 ) THEN
430 RESULT( 1 ) = ULPINV
431 WRITE( NOUT, FMT = 9999 )'CGGESX', LINFO, MPLUSN,
432 $ PRTYPE
433 INFO = LINFO
434 GO TO 30
435 END IF
436 *
437 * Compute the norm(A, B)
438 *
439 CALL CLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, WORK,
440 $ MPLUSN )
441 CALL CLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA,
442 $ WORK( MPLUSN*MPLUSN+1 ), MPLUSN )
443 ABNRM = CLANGE( 'Fro', MPLUSN, 2*MPLUSN, WORK, MPLUSN,
444 $ RWORK )
445 *
446 * Do tests (1) to (4)
447 *
448 RESULT( 2 ) = ZERO
449 CALL CGET51( 1, MPLUSN, A, LDA, AI, LDA, Q, LDA, Z,
450 $ LDA, WORK, RWORK, RESULT( 1 ) )
451 CALL CGET51( 1, MPLUSN, B, LDA, BI, LDA, Q, LDA, Z,
452 $ LDA, WORK, RWORK, RESULT( 2 ) )
453 CALL CGET51( 3, MPLUSN, B, LDA, BI, LDA, Q, LDA, Q,
454 $ LDA, WORK, RWORK, RESULT( 3 ) )
455 CALL CGET51( 3, MPLUSN, B, LDA, BI, LDA, Z, LDA, Z,
456 $ LDA, WORK, RWORK, RESULT( 4 ) )
457 NTEST = 4
458 *
459 * Do tests (5) and (6): check Schur form of A and
460 * compare eigenvalues with diagonals.
461 *
462 TEMP1 = ZERO
463 RESULT( 5 ) = ZERO
464 RESULT( 6 ) = ZERO
465 *
466 DO 10 J = 1, MPLUSN
467 ILABAD = .FALSE.
468 TEMP2 = ( ABS1( ALPHA( J )-AI( J, J ) ) /
469 $ MAX( SMLNUM, ABS1( ALPHA( J ) ),
470 $ ABS1( AI( J, J ) ) )+
471 $ ABS1( BETA( J )-BI( J, J ) ) /
472 $ MAX( SMLNUM, ABS1( BETA( J ) ),
473 $ ABS1( BI( J, J ) ) ) ) / ULP
474 IF( J.LT.MPLUSN ) THEN
475 IF( AI( J+1, J ).NE.ZERO ) THEN
476 ILABAD = .TRUE.
477 RESULT( 5 ) = ULPINV
478 END IF
479 END IF
480 IF( J.GT.1 ) THEN
481 IF( AI( J, J-1 ).NE.ZERO ) THEN
482 ILABAD = .TRUE.
483 RESULT( 5 ) = ULPINV
484 END IF
485 END IF
486 TEMP1 = MAX( TEMP1, TEMP2 )
487 IF( ILABAD ) THEN
488 WRITE( NOUT, FMT = 9997 )J, MPLUSN, PRTYPE
489 END IF
490 10 CONTINUE
491 RESULT( 6 ) = TEMP1
492 NTEST = NTEST + 2
493 *
494 * Test (7) (if sorting worked)
495 *
496 RESULT( 7 ) = ZERO
497 IF( LINFO.EQ.MPLUSN+3 ) THEN
498 RESULT( 7 ) = ULPINV
499 ELSE IF( MM.NE.N ) THEN
500 RESULT( 7 ) = ULPINV
501 END IF
502 NTEST = NTEST + 1
503 *
504 * Test (8): compare the estimated value DIF and its
505 * value. first, compute the exact DIF.
506 *
507 RESULT( 8 ) = ZERO
508 MN2 = MM*( MPLUSN-MM )*2
509 IF( IFUNC.GE.2 .AND. MN2.LE.NCMAX*NCMAX ) THEN
510 *
511 * Note: for either following two cases, there are
512 * almost same number of test cases fail the test.
513 *
514 CALL CLAKF2( MM, MPLUSN-MM, AI, LDA,
515 $ AI( MM+1, MM+1 ), BI,
516 $ BI( MM+1, MM+1 ), C, LDC )
517 *
518 CALL CGESVD( 'N', 'N', MN2, MN2, C, LDC, S, WORK,
519 $ 1, WORK( 2 ), 1, WORK( 3 ), LWORK-2,
520 $ RWORK, INFO )
521 DIFTRU = S( MN2 )
522 *
523 IF( DIFEST( 2 ).EQ.ZERO ) THEN
524 IF( DIFTRU.GT.ABNRM*ULP )
525 $ RESULT( 8 ) = ULPINV
526 ELSE IF( DIFTRU.EQ.ZERO ) THEN
527 IF( DIFEST( 2 ).GT.ABNRM*ULP )
528 $ RESULT( 8 ) = ULPINV
529 ELSE IF( ( DIFTRU.GT.THRSH2*DIFEST( 2 ) ) .OR.
530 $ ( DIFTRU*THRSH2.LT.DIFEST( 2 ) ) ) THEN
531 RESULT( 8 ) = MAX( DIFTRU / DIFEST( 2 ),
532 $ DIFEST( 2 ) / DIFTRU )
533 END IF
534 NTEST = NTEST + 1
535 END IF
536 *
537 * Test (9)
538 *
539 RESULT( 9 ) = ZERO
540 IF( LINFO.EQ.( MPLUSN+2 ) ) THEN
541 IF( DIFTRU.GT.ABNRM*ULP )
542 $ RESULT( 9 ) = ULPINV
543 IF( ( IFUNC.GT.1 ) .AND. ( DIFEST( 2 ).NE.ZERO ) )
544 $ RESULT( 9 ) = ULPINV
545 IF( ( IFUNC.EQ.1 ) .AND. ( PL( 1 ).NE.ZERO ) )
546 $ RESULT( 9 ) = ULPINV
547 NTEST = NTEST + 1
548 END IF
549 *
550 NTESTT = NTESTT + NTEST
551 *
552 * Print out tests which fail.
553 *
554 DO 20 J = 1, 9
555 IF( RESULT( J ).GE.THRESH ) THEN
556 *
557 * If this is the first test to fail,
558 * print a header to the data file.
559 *
560 IF( NERRS.EQ.0 ) THEN
561 WRITE( NOUT, FMT = 9996 )'CGX'
562 *
563 * Matrix types
564 *
565 WRITE( NOUT, FMT = 9994 )
566 *
567 * Tests performed
568 *
569 WRITE( NOUT, FMT = 9993 )'unitary', '''',
570 $ 'transpose', ( '''', I = 1, 4 )
571 *
572 END IF
573 NERRS = NERRS + 1
574 IF( RESULT( J ).LT.10000.0 ) THEN
575 WRITE( NOUT, FMT = 9992 )MPLUSN, PRTYPE,
576 $ WEIGHT, M, J, RESULT( J )
577 ELSE
578 WRITE( NOUT, FMT = 9991 )MPLUSN, PRTYPE,
579 $ WEIGHT, M, J, RESULT( J )
580 END IF
581 END IF
582 20 CONTINUE
583 *
584 30 CONTINUE
585 40 CONTINUE
586 50 CONTINUE
587 60 CONTINUE
588 *
589 GO TO 150
590 *
591 70 CONTINUE
592 *
593 * Read in data from file to check accuracy of condition estimation
594 * Read input data until N=0
595 *
596 NPTKNT = 0
597 *
598 80 CONTINUE
599 READ( NIN, FMT = *, END = 140 )MPLUSN
600 IF( MPLUSN.EQ.0 )
601 $ GO TO 140
602 READ( NIN, FMT = *, END = 140 )N
603 DO 90 I = 1, MPLUSN
604 READ( NIN, FMT = * )( AI( I, J ), J = 1, MPLUSN )
605 90 CONTINUE
606 DO 100 I = 1, MPLUSN
607 READ( NIN, FMT = * )( BI( I, J ), J = 1, MPLUSN )
608 100 CONTINUE
609 READ( NIN, FMT = * )PLTRU, DIFTRU
610 *
611 NPTKNT = NPTKNT + 1
612 FS = .TRUE.
613 K = 0
614 M = MPLUSN - N
615 *
616 CALL CLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, A, LDA )
617 CALL CLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, B, LDA )
618 *
619 * Compute the Schur factorization while swaping the
620 * m-by-m (1,1)-blocks with n-by-n (2,2)-blocks.
621 *
622 CALL CGGESX( 'V', 'V', 'S', CLCTSX, 'B', MPLUSN, AI, LDA, BI, LDA,
623 $ MM, ALPHA, BETA, Q, LDA, Z, LDA, PL, DIFEST, WORK,
624 $ LWORK, RWORK, IWORK, LIWORK, BWORK, LINFO )
625 *
626 IF( LINFO.NE.0 .AND. LINFO.NE.MPLUSN+2 ) THEN
627 RESULT( 1 ) = ULPINV
628 WRITE( NOUT, FMT = 9998 )'CGGESX', LINFO, MPLUSN, NPTKNT
629 GO TO 130
630 END IF
631 *
632 * Compute the norm(A, B)
633 * (should this be norm of (A,B) or (AI,BI)?)
634 *
635 CALL CLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, WORK, MPLUSN )
636 CALL CLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA,
637 $ WORK( MPLUSN*MPLUSN+1 ), MPLUSN )
638 ABNRM = CLANGE( 'Fro', MPLUSN, 2*MPLUSN, WORK, MPLUSN, RWORK )
639 *
640 * Do tests (1) to (4)
641 *
642 CALL CGET51( 1, MPLUSN, A, LDA, AI, LDA, Q, LDA, Z, LDA, WORK,
643 $ RWORK, RESULT( 1 ) )
644 CALL CGET51( 1, MPLUSN, B, LDA, BI, LDA, Q, LDA, Z, LDA, WORK,
645 $ RWORK, RESULT( 2 ) )
646 CALL CGET51( 3, MPLUSN, B, LDA, BI, LDA, Q, LDA, Q, LDA, WORK,
647 $ RWORK, RESULT( 3 ) )
648 CALL CGET51( 3, MPLUSN, B, LDA, BI, LDA, Z, LDA, Z, LDA, WORK,
649 $ RWORK, RESULT( 4 ) )
650 *
651 * Do tests (5) and (6): check Schur form of A and compare
652 * eigenvalues with diagonals.
653 *
654 NTEST = 6
655 TEMP1 = ZERO
656 RESULT( 5 ) = ZERO
657 RESULT( 6 ) = ZERO
658 *
659 DO 110 J = 1, MPLUSN
660 ILABAD = .FALSE.
661 TEMP2 = ( ABS1( ALPHA( J )-AI( J, J ) ) /
662 $ MAX( SMLNUM, ABS1( ALPHA( J ) ), ABS1( AI( J, J ) ) )+
663 $ ABS1( BETA( J )-BI( J, J ) ) /
664 $ MAX( SMLNUM, ABS1( BETA( J ) ), ABS1( BI( J, J ) ) ) )
665 $ / ULP
666 IF( J.LT.MPLUSN ) THEN
667 IF( AI( J+1, J ).NE.ZERO ) THEN
668 ILABAD = .TRUE.
669 RESULT( 5 ) = ULPINV
670 END IF
671 END IF
672 IF( J.GT.1 ) THEN
673 IF( AI( J, J-1 ).NE.ZERO ) THEN
674 ILABAD = .TRUE.
675 RESULT( 5 ) = ULPINV
676 END IF
677 END IF
678 TEMP1 = MAX( TEMP1, TEMP2 )
679 IF( ILABAD ) THEN
680 WRITE( NOUT, FMT = 9997 )J, MPLUSN, NPTKNT
681 END IF
682 110 CONTINUE
683 RESULT( 6 ) = TEMP1
684 *
685 * Test (7) (if sorting worked) <--------- need to be checked.
686 *
687 NTEST = 7
688 RESULT( 7 ) = ZERO
689 IF( LINFO.EQ.MPLUSN+3 )
690 $ RESULT( 7 ) = ULPINV
691 *
692 * Test (8): compare the estimated value of DIF and its true value.
693 *
694 NTEST = 8
695 RESULT( 8 ) = ZERO
696 IF( DIFEST( 2 ).EQ.ZERO ) THEN
697 IF( DIFTRU.GT.ABNRM*ULP )
698 $ RESULT( 8 ) = ULPINV
699 ELSE IF( DIFTRU.EQ.ZERO ) THEN
700 IF( DIFEST( 2 ).GT.ABNRM*ULP )
701 $ RESULT( 8 ) = ULPINV
702 ELSE IF( ( DIFTRU.GT.THRSH2*DIFEST( 2 ) ) .OR.
703 $ ( DIFTRU*THRSH2.LT.DIFEST( 2 ) ) ) THEN
704 RESULT( 8 ) = MAX( DIFTRU / DIFEST( 2 ), DIFEST( 2 ) / DIFTRU )
705 END IF
706 *
707 * Test (9)
708 *
709 NTEST = 9
710 RESULT( 9 ) = ZERO
711 IF( LINFO.EQ.( MPLUSN+2 ) ) THEN
712 IF( DIFTRU.GT.ABNRM*ULP )
713 $ RESULT( 9 ) = ULPINV
714 IF( ( IFUNC.GT.1 ) .AND. ( DIFEST( 2 ).NE.ZERO ) )
715 $ RESULT( 9 ) = ULPINV
716 IF( ( IFUNC.EQ.1 ) .AND. ( PL( 1 ).NE.ZERO ) )
717 $ RESULT( 9 ) = ULPINV
718 END IF
719 *
720 * Test (10): compare the estimated value of PL and it true value.
721 *
722 NTEST = 10
723 RESULT( 10 ) = ZERO
724 IF( PL( 1 ).EQ.ZERO ) THEN
725 IF( PLTRU.GT.ABNRM*ULP )
726 $ RESULT( 10 ) = ULPINV
727 ELSE IF( PLTRU.EQ.ZERO ) THEN
728 IF( PL( 1 ).GT.ABNRM*ULP )
729 $ RESULT( 10 ) = ULPINV
730 ELSE IF( ( PLTRU.GT.THRESH*PL( 1 ) ) .OR.
731 $ ( PLTRU*THRESH.LT.PL( 1 ) ) ) THEN
732 RESULT( 10 ) = ULPINV
733 END IF
734 *
735 NTESTT = NTESTT + NTEST
736 *
737 * Print out tests which fail.
738 *
739 DO 120 J = 1, NTEST
740 IF( RESULT( J ).GE.THRESH ) THEN
741 *
742 * If this is the first test to fail,
743 * print a header to the data file.
744 *
745 IF( NERRS.EQ.0 ) THEN
746 WRITE( NOUT, FMT = 9996 )'CGX'
747 *
748 * Matrix types
749 *
750 WRITE( NOUT, FMT = 9995 )
751 *
752 * Tests performed
753 *
754 WRITE( NOUT, FMT = 9993 )'unitary', '''', 'transpose',
755 $ ( '''', I = 1, 4 )
756 *
757 END IF
758 NERRS = NERRS + 1
759 IF( RESULT( J ).LT.10000.0 ) THEN
760 WRITE( NOUT, FMT = 9990 )NPTKNT, MPLUSN, J, RESULT( J )
761 ELSE
762 WRITE( NOUT, FMT = 9989 )NPTKNT, MPLUSN, J, RESULT( J )
763 END IF
764 END IF
765 *
766 120 CONTINUE
767 *
768 130 CONTINUE
769 GO TO 80
770 140 CONTINUE
771 *
772 150 CONTINUE
773 *
774 * Summary
775 *
776 CALL ALASVM( 'CGX', NOUT, NERRS, NTESTT, 0 )
777 *
778 WORK( 1 ) = MAXWRK
779 *
780 RETURN
781 *
782 9999 FORMAT( ' CDRGSX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
783 $ I6, ', JTYPE=', I6, ')' )
784 *
785 9998 FORMAT( ' CDRGSX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
786 $ I6, ', Input Example #', I2, ')' )
787 *
788 9997 FORMAT( ' CDRGSX: S not in Schur form at eigenvalue ', I6, '.',
789 $ / 9X, 'N=', I6, ', JTYPE=', I6, ')' )
790 *
791 9996 FORMAT( / 1X, A3, ' -- Complex Expert Generalized Schur form',
792 $ ' problem driver' )
793 *
794 9995 FORMAT( 'Input Example' )
795 *
796 9994 FORMAT( ' Matrix types: ', /
797 $ ' 1: A is a block diagonal matrix of Jordan blocks ',
798 $ 'and B is the identity ', / ' matrix, ',
799 $ / ' 2: A and B are upper triangular matrices, ',
800 $ / ' 3: A and B are as type 2, but each second diagonal ',
801 $ 'block in A_11 and ', /
802 $ ' each third diaongal block in A_22 are 2x2 blocks,',
803 $ / ' 4: A and B are block diagonal matrices, ',
804 $ / ' 5: (A,B) has potentially close or common ',
805 $ 'eigenvalues.', / )
806 *
807 9993 FORMAT( / ' Tests performed: (S is Schur, T is triangular, ',
808 $ 'Q and Z are ', A, ',', / 19X,
809 $ ' a is alpha, b is beta, and ', A, ' means ', A, '.)',
810 $ / ' 1 = | A - Q S Z', A,
811 $ ' | / ( |A| n ulp ) 2 = | B - Q T Z', A,
812 $ ' | / ( |B| n ulp )', / ' 3 = | I - QQ', A,
813 $ ' | / ( n ulp ) 4 = | I - ZZ', A,
814 $ ' | / ( n ulp )', / ' 5 = 1/ULP if A is not in ',
815 $ 'Schur form S', / ' 6 = difference between (alpha,beta)',
816 $ ' and diagonals of (S,T)', /
817 $ ' 7 = 1/ULP if SDIM is not the correct number of ',
818 $ 'selected eigenvalues', /
819 $ ' 8 = 1/ULP if DIFEST/DIFTRU > 10*THRESH or ',
820 $ 'DIFTRU/DIFEST > 10*THRESH',
821 $ / ' 9 = 1/ULP if DIFEST <> 0 or DIFTRU > ULP*norm(A,B) ',
822 $ 'when reordering fails', /
823 $ ' 10 = 1/ULP if PLEST/PLTRU > THRESH or ',
824 $ 'PLTRU/PLEST > THRESH', /
825 $ ' ( Test 10 is only for input examples )', / )
826 9992 FORMAT( ' Matrix order=', I2, ', type=', I2, ', a=', E10.4,
827 $ ', order(A_11)=', I2, ', result ', I2, ' is ', 0P, F8.2 )
828 9991 FORMAT( ' Matrix order=', I2, ', type=', I2, ', a=', E10.4,
829 $ ', order(A_11)=', I2, ', result ', I2, ' is ', 0P, E10.4 )
830 9990 FORMAT( ' Input example #', I2, ', matrix order=', I4, ',',
831 $ ' result ', I2, ' is', 0P, F8.2 )
832 9989 FORMAT( ' Input example #', I2, ', matrix order=', I4, ',',
833 $ ' result ', I2, ' is', 1P, E10.3 )
834 *
835 * End of CDRGSX
836 *
837 END
2 $ AI, BI, Z, Q, ALPHA, BETA, C, LDC, S, WORK,
3 $ LWORK, RWORK, IWORK, LIWORK, 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, LDC, LIWORK, LWORK, NCMAX, NIN,
11 $ NOUT, NSIZE
12 REAL THRESH
13 * ..
14 * .. Array Arguments ..
15 LOGICAL BWORK( * )
16 INTEGER IWORK( * )
17 REAL RWORK( * ), S( * )
18 COMPLEX A( LDA, * ), AI( LDA, * ), ALPHA( * ),
19 $ B( LDA, * ), BETA( * ), BI( LDA, * ),
20 $ C( LDC, * ), Q( LDA, * ), WORK( * ),
21 $ Z( LDA, * )
22 * ..
23 *
24 * Purpose
25 * =======
26 *
27 * CDRGSX checks the nonsymmetric generalized eigenvalue (Schur form)
28 * problem expert driver CGGESX.
29 *
30 * CGGES factors A and B as Q*S*Z' and Q*T*Z' , where ' means conjugate
31 * transpose, S and T are upper triangular (i.e., in generalized Schur
32 * form), and Q and Z are unitary. It also computes the generalized
33 * eigenvalues (alpha(j),beta(j)), j=1,...,n. Thus,
34 * w(j) = alpha(j)/beta(j) is a root of the characteristic equation
35 *
36 * det( A - w(j) B ) = 0
37 *
38 * Optionally it also reorders the eigenvalues so that a selected
39 * cluster of eigenvalues appears in the leading diagonal block of the
40 * Schur forms; computes a reciprocal condition number for the average
41 * of the selected eigenvalues; and computes a reciprocal condition
42 * number for the right and left deflating subspaces corresponding to
43 * the selected eigenvalues.
44 *
45 * When CDRGSX is called with NSIZE > 0, five (5) types of built-in
46 * matrix pairs are used to test the routine CGGESX.
47 *
48 * When CDRGSX is called with NSIZE = 0, it reads in test matrix data
49 * to test CGGESX.
50 * (need more details on what kind of read-in data are needed).
51 *
52 * For each matrix pair, the following tests will be performed and
53 * compared with the threshhold THRESH except for the tests (7) and (9):
54 *
55 * (1) | A - Q S Z' | / ( |A| n ulp )
56 *
57 * (2) | B - Q T Z' | / ( |B| n ulp )
58 *
59 * (3) | I - QQ' | / ( n ulp )
60 *
61 * (4) | I - ZZ' | / ( n ulp )
62 *
63 * (5) if A is in Schur form (i.e. triangular form)
64 *
65 * (6) maximum over j of D(j) where:
66 *
67 * |alpha(j) - S(j,j)| |beta(j) - T(j,j)|
68 * D(j) = ------------------------ + -----------------------
69 * max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|)
70 *
71 * (7) if sorting worked and SDIM is the number of eigenvalues
72 * which were selected.
73 *
74 * (8) the estimated value DIF does not differ from the true values of
75 * Difu and Difl more than a factor 10*THRESH. If the estimate DIF
76 * equals zero the corresponding true values of Difu and Difl
77 * should be less than EPS*norm(A, B). If the true value of Difu
78 * and Difl equal zero, the estimate DIF should be less than
79 * EPS*norm(A, B).
80 *
81 * (9) If INFO = N+3 is returned by CGGESX, the reordering "failed"
82 * and we check that DIF = PL = PR = 0 and that the true value of
83 * Difu and Difl is < EPS*norm(A, B). We count the events when
84 * INFO=N+3.
85 *
86 * For read-in test matrices, the same tests are run except that the
87 * exact value for DIF (and PL) is input data. Additionally, there is
88 * one more test run for read-in test matrices:
89 *
90 * (10) the estimated value PL does not differ from the true value of
91 * PLTRU more than a factor THRESH. If the estimate PL equals
92 * zero the corresponding true value of PLTRU should be less than
93 * EPS*norm(A, B). If the true value of PLTRU equal zero, the
94 * estimate PL should be less than EPS*norm(A, B).
95 *
96 * Note that for the built-in tests, a total of 10*NSIZE*(NSIZE-1)
97 * matrix pairs are generated and tested. NSIZE should be kept small.
98 *
99 * SVD (routine CGESVD) is used for computing the true value of DIF_u
100 * and DIF_l when testing the built-in test problems.
101 *
102 * Built-in Test Matrices
103 * ======================
104 *
105 * All built-in test matrices are the 2 by 2 block of triangular
106 * matrices
107 *
108 * A = [ A11 A12 ] and B = [ B11 B12 ]
109 * [ A22 ] [ B22 ]
110 *
111 * where for different type of A11 and A22 are given as the following.
112 * A12 and B12 are chosen so that the generalized Sylvester equation
113 *
114 * A11*R - L*A22 = -A12
115 * B11*R - L*B22 = -B12
116 *
117 * have prescribed solution R and L.
118 *
119 * Type 1: A11 = J_m(1,-1) and A_22 = J_k(1-a,1).
120 * B11 = I_m, B22 = I_k
121 * where J_k(a,b) is the k-by-k Jordan block with ``a'' on
122 * diagonal and ``b'' on superdiagonal.
123 *
124 * Type 2: A11 = (a_ij) = ( 2(.5-sin(i)) ) and
125 * B11 = (b_ij) = ( 2(.5-sin(ij)) ) for i=1,...,m, j=i,...,m
126 * A22 = (a_ij) = ( 2(.5-sin(i+j)) ) and
127 * B22 = (b_ij) = ( 2(.5-sin(ij)) ) for i=m+1,...,k, j=i,...,k
128 *
129 * Type 3: A11, A22 and B11, B22 are chosen as for Type 2, but each
130 * second diagonal block in A_11 and each third diagonal block
131 * in A_22 are made as 2 by 2 blocks.
132 *
133 * Type 4: A11 = ( 20(.5 - sin(ij)) ) and B22 = ( 2(.5 - sin(i+j)) )
134 * for i=1,...,m, j=1,...,m and
135 * A22 = ( 20(.5 - sin(i+j)) ) and B22 = ( 2(.5 - sin(ij)) )
136 * for i=m+1,...,k, j=m+1,...,k
137 *
138 * Type 5: (A,B) and have potentially close or common eigenvalues and
139 * very large departure from block diagonality A_11 is chosen
140 * as the m x m leading submatrix of A_1:
141 * | 1 b |
142 * | -b 1 |
143 * | 1+d b |
144 * | -b 1+d |
145 * A_1 = | d 1 |
146 * | -1 d |
147 * | -d 1 |
148 * | -1 -d |
149 * | 1 |
150 * and A_22 is chosen as the k x k leading submatrix of A_2:
151 * | -1 b |
152 * | -b -1 |
153 * | 1-d b |
154 * | -b 1-d |
155 * A_2 = | d 1+b |
156 * | -1-b d |
157 * | -d 1+b |
158 * | -1+b -d |
159 * | 1-d |
160 * and matrix B are chosen as identity matrices (see SLATM5).
161 *
162 *
163 * Arguments
164 * =========
165 *
166 * NSIZE (input) INTEGER
167 * The maximum size of the matrices to use. NSIZE >= 0.
168 * If NSIZE = 0, no built-in tests matrices are used, but
169 * read-in test matrices are used to test SGGESX.
170 *
171 * NCMAX (input) INTEGER
172 * Maximum allowable NMAX for generating Kroneker matrix
173 * in call to CLAKF2
174 *
175 * THRESH (input) REAL
176 * A test will count as "failed" if the "error", computed as
177 * described above, exceeds THRESH. Note that the error
178 * is scaled to be O(1), so THRESH should be a reasonably
179 * small multiple of 1, e.g., 10 or 100. In particular,
180 * it should not depend on the precision (single vs. double)
181 * or the size of the matrix. THRESH >= 0.
182 *
183 * NIN (input) INTEGER
184 * The FORTRAN unit number for reading in the data file of
185 * problems to solve.
186 *
187 * NOUT (input) INTEGER
188 * The FORTRAN unit number for printing out error messages
189 * (e.g., if a routine returns INFO not equal to 0.)
190 *
191 * A (workspace) COMPLEX array, dimension (LDA, NSIZE)
192 * Used to store the matrix whose eigenvalues are to be
193 * computed. On exit, A contains the last matrix actually used.
194 *
195 * LDA (input) INTEGER
196 * The leading dimension of A, B, AI, BI, Z and Q,
197 * LDA >= max( 1, NSIZE ). For the read-in test,
198 * LDA >= max( 1, N ), N is the size of the test matrices.
199 *
200 * B (workspace) COMPLEX array, dimension (LDA, NSIZE)
201 * Used to store the matrix whose eigenvalues are to be
202 * computed. On exit, B contains the last matrix actually used.
203 *
204 * AI (workspace) COMPLEX array, dimension (LDA, NSIZE)
205 * Copy of A, modified by CGGESX.
206 *
207 * BI (workspace) COMPLEX array, dimension (LDA, NSIZE)
208 * Copy of B, modified by CGGESX.
209 *
210 * Z (workspace) COMPLEX array, dimension (LDA, NSIZE)
211 * Z holds the left Schur vectors computed by CGGESX.
212 *
213 * Q (workspace) COMPLEX array, dimension (LDA, NSIZE)
214 * Q holds the right Schur vectors computed by CGGESX.
215 *
216 * ALPHA (workspace) COMPLEX array, dimension (NSIZE)
217 * BETA (workspace) COMPLEX array, dimension (NSIZE)
218 * On exit, ALPHA/BETA are the eigenvalues.
219 *
220 * C (workspace) COMPLEX array, dimension (LDC, LDC)
221 * Store the matrix generated by subroutine CLAKF2, this is the
222 * matrix formed by Kronecker products used for estimating
223 * DIF.
224 *
225 * LDC (input) INTEGER
226 * The leading dimension of C. LDC >= max(1, LDA*LDA/2 ).
227 *
228 * S (workspace) REAL array, dimension (LDC)
229 * Singular values of C
230 *
231 * WORK (workspace) COMPLEX array, dimension (LWORK)
232 *
233 * LWORK (input) INTEGER
234 * The dimension of the array WORK. LWORK >= 3*NSIZE*NSIZE/2
235 *
236 * RWORK (workspace) REAL array,
237 * dimension (5*NSIZE*NSIZE/2 - 4)
238 *
239 * IWORK (workspace) INTEGER array, dimension (LIWORK)
240 *
241 * LIWORK (input) INTEGER
242 * The dimension of the array IWORK. LIWORK >= NSIZE + 2.
243 *
244 * BWORK (workspace) LOGICAL array, dimension (NSIZE)
245 *
246 * INFO (output) INTEGER
247 * = 0: successful exit
248 * < 0: if INFO = -i, the i-th argument had an illegal value.
249 * > 0: A routine returned an error code.
250 *
251 * =====================================================================
252 *
253 * .. Parameters ..
254 REAL ZERO, ONE, TEN
255 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TEN = 1.0E+1 )
256 COMPLEX CZERO
257 PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ) )
258 * ..
259 * .. Local Scalars ..
260 LOGICAL ILABAD
261 CHARACTER SENSE
262 INTEGER BDSPAC, I, IFUNC, J, LINFO, MAXWRK, MINWRK, MM,
263 $ MN2, NERRS, NPTKNT, NTEST, NTESTT, PRTYPE, QBA,
264 $ QBB
265 REAL ABNRM, BIGNUM, DIFTRU, PLTRU, SMLNUM, TEMP1,
266 $ TEMP2, THRSH2, ULP, ULPINV, WEIGHT
267 COMPLEX X
268 * ..
269 * .. Local Arrays ..
270 REAL DIFEST( 2 ), PL( 2 ), RESULT( 10 )
271 * ..
272 * .. External Functions ..
273 LOGICAL CLCTSX
274 INTEGER ILAENV
275 REAL CLANGE, SLAMCH
276 EXTERNAL CLCTSX, ILAENV, CLANGE, SLAMCH
277 * ..
278 * .. External Subroutines ..
279 EXTERNAL ALASVM, CGESVD, CGET51, CGGESX, CLACPY, CLAKF2,
280 $ CLASET, CLATM5, SLABAD, XERBLA
281 * ..
282 * .. Scalars in Common ..
283 LOGICAL FS
284 INTEGER K, M, MPLUSN, N
285 * ..
286 * .. Common blocks ..
287 COMMON / MN / M, N, MPLUSN, K, FS
288 * ..
289 * .. Intrinsic Functions ..
290 INTRINSIC ABS, AIMAG, MAX, REAL, SQRT
291 * ..
292 * .. Statement Functions ..
293 REAL ABS1
294 * ..
295 * .. Statement Function definitions ..
296 ABS1( X ) = ABS( REAL( X ) ) + ABS( AIMAG( X ) )
297 * ..
298 * .. Executable Statements ..
299 *
300 * Check for errors
301 *
302 IF( NSIZE.LT.0 ) THEN
303 INFO = -1
304 ELSE IF( THRESH.LT.ZERO ) THEN
305 INFO = -2
306 ELSE IF( NIN.LE.0 ) THEN
307 INFO = -3
308 ELSE IF( NOUT.LE.0 ) THEN
309 INFO = -4
310 ELSE IF( LDA.LT.1 .OR. LDA.LT.NSIZE ) THEN
311 INFO = -6
312 ELSE IF( LDC.LT.1 .OR. LDC.LT.NSIZE*NSIZE / 2 ) THEN
313 INFO = -15
314 ELSE IF( LIWORK.LT.NSIZE+2 ) THEN
315 INFO = -21
316 END IF
317 *
318 * Compute workspace
319 * (Note: Comments in the code beginning "Workspace:" describe the
320 * minimal amount of workspace needed at that point in the code,
321 * as well as the preferred amount for good performance.
322 * NB refers to the optimal block size for the immediately
323 * following subroutine, as returned by ILAENV.)
324 *
325 MINWRK = 1
326 IF( INFO.EQ.0 .AND. LWORK.GE.1 ) THEN
327 MINWRK = 3*NSIZE*NSIZE / 2
328 *
329 * workspace for cggesx
330 *
331 MAXWRK = NSIZE*( 1+ILAENV( 1, 'CGEQRF', ' ', NSIZE, 1, NSIZE,
332 $ 0 ) )
333 MAXWRK = MAX( MAXWRK, NSIZE*( 1+ILAENV( 1, 'CUNGQR', ' ',
334 $ NSIZE, 1, NSIZE, -1 ) ) )
335 *
336 * workspace for cgesvd
337 *
338 BDSPAC = 3*NSIZE*NSIZE / 2
339 MAXWRK = MAX( MAXWRK, NSIZE*NSIZE*
340 $ ( 1+ILAENV( 1, 'CGEBRD', ' ', NSIZE*NSIZE / 2,
341 $ NSIZE*NSIZE / 2, -1, -1 ) ) )
342 MAXWRK = MAX( MAXWRK, BDSPAC )
343 *
344 MAXWRK = MAX( MAXWRK, MINWRK )
345 *
346 WORK( 1 ) = MAXWRK
347 END IF
348 *
349 IF( LWORK.LT.MINWRK )
350 $ INFO = -18
351 *
352 IF( INFO.NE.0 ) THEN
353 CALL XERBLA( 'CDRGSX', -INFO )
354 RETURN
355 END IF
356 *
357 * Important constants
358 *
359 ULP = SLAMCH( 'P' )
360 ULPINV = ONE / ULP
361 SMLNUM = SLAMCH( 'S' ) / ULP
362 BIGNUM = ONE / SMLNUM
363 CALL SLABAD( SMLNUM, BIGNUM )
364 THRSH2 = TEN*THRESH
365 NTESTT = 0
366 NERRS = 0
367 *
368 * Go to the tests for read-in matrix pairs
369 *
370 IFUNC = 0
371 IF( NSIZE.EQ.0 )
372 $ GO TO 70
373 *
374 * Test the built-in matrix pairs.
375 * Loop over different functions (IFUNC) of CGGESX, types (PRTYPE)
376 * of test matrices, different size (M+N)
377 *
378 PRTYPE = 0
379 QBA = 3
380 QBB = 4
381 WEIGHT = SQRT( ULP )
382 *
383 DO 60 IFUNC = 0, 3
384 DO 50 PRTYPE = 1, 5
385 DO 40 M = 1, NSIZE - 1
386 DO 30 N = 1, NSIZE - M
387 *
388 WEIGHT = ONE / WEIGHT
389 MPLUSN = M + N
390 *
391 * Generate test matrices
392 *
393 FS = .TRUE.
394 K = 0
395 *
396 CALL CLASET( 'Full', MPLUSN, MPLUSN, CZERO, CZERO, AI,
397 $ LDA )
398 CALL CLASET( 'Full', MPLUSN, MPLUSN, CZERO, CZERO, BI,
399 $ LDA )
400 *
401 CALL CLATM5( PRTYPE, M, N, AI, LDA, AI( M+1, M+1 ),
402 $ LDA, AI( 1, M+1 ), LDA, BI, LDA,
403 $ BI( M+1, M+1 ), LDA, BI( 1, M+1 ), LDA,
404 $ Q, LDA, Z, LDA, WEIGHT, QBA, QBB )
405 *
406 * Compute the Schur factorization and swapping the
407 * m-by-m (1,1)-blocks with n-by-n (2,2)-blocks.
408 * Swapping is accomplished via the function CLCTSX
409 * which is supplied below.
410 *
411 IF( IFUNC.EQ.0 ) THEN
412 SENSE = 'N'
413 ELSE IF( IFUNC.EQ.1 ) THEN
414 SENSE = 'E'
415 ELSE IF( IFUNC.EQ.2 ) THEN
416 SENSE = 'V'
417 ELSE IF( IFUNC.EQ.3 ) THEN
418 SENSE = 'B'
419 END IF
420 *
421 CALL CLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, A, LDA )
422 CALL CLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, B, LDA )
423 *
424 CALL CGGESX( 'V', 'V', 'S', CLCTSX, SENSE, MPLUSN, AI,
425 $ LDA, BI, LDA, MM, ALPHA, BETA, Q, LDA, Z,
426 $ LDA, PL, DIFEST, WORK, LWORK, RWORK,
427 $ IWORK, LIWORK, BWORK, LINFO )
428 *
429 IF( LINFO.NE.0 .AND. LINFO.NE.MPLUSN+2 ) THEN
430 RESULT( 1 ) = ULPINV
431 WRITE( NOUT, FMT = 9999 )'CGGESX', LINFO, MPLUSN,
432 $ PRTYPE
433 INFO = LINFO
434 GO TO 30
435 END IF
436 *
437 * Compute the norm(A, B)
438 *
439 CALL CLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, WORK,
440 $ MPLUSN )
441 CALL CLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA,
442 $ WORK( MPLUSN*MPLUSN+1 ), MPLUSN )
443 ABNRM = CLANGE( 'Fro', MPLUSN, 2*MPLUSN, WORK, MPLUSN,
444 $ RWORK )
445 *
446 * Do tests (1) to (4)
447 *
448 RESULT( 2 ) = ZERO
449 CALL CGET51( 1, MPLUSN, A, LDA, AI, LDA, Q, LDA, Z,
450 $ LDA, WORK, RWORK, RESULT( 1 ) )
451 CALL CGET51( 1, MPLUSN, B, LDA, BI, LDA, Q, LDA, Z,
452 $ LDA, WORK, RWORK, RESULT( 2 ) )
453 CALL CGET51( 3, MPLUSN, B, LDA, BI, LDA, Q, LDA, Q,
454 $ LDA, WORK, RWORK, RESULT( 3 ) )
455 CALL CGET51( 3, MPLUSN, B, LDA, BI, LDA, Z, LDA, Z,
456 $ LDA, WORK, RWORK, RESULT( 4 ) )
457 NTEST = 4
458 *
459 * Do tests (5) and (6): check Schur form of A and
460 * compare eigenvalues with diagonals.
461 *
462 TEMP1 = ZERO
463 RESULT( 5 ) = ZERO
464 RESULT( 6 ) = ZERO
465 *
466 DO 10 J = 1, MPLUSN
467 ILABAD = .FALSE.
468 TEMP2 = ( ABS1( ALPHA( J )-AI( J, J ) ) /
469 $ MAX( SMLNUM, ABS1( ALPHA( J ) ),
470 $ ABS1( AI( J, J ) ) )+
471 $ ABS1( BETA( J )-BI( J, J ) ) /
472 $ MAX( SMLNUM, ABS1( BETA( J ) ),
473 $ ABS1( BI( J, J ) ) ) ) / ULP
474 IF( J.LT.MPLUSN ) THEN
475 IF( AI( J+1, J ).NE.ZERO ) THEN
476 ILABAD = .TRUE.
477 RESULT( 5 ) = ULPINV
478 END IF
479 END IF
480 IF( J.GT.1 ) THEN
481 IF( AI( J, J-1 ).NE.ZERO ) THEN
482 ILABAD = .TRUE.
483 RESULT( 5 ) = ULPINV
484 END IF
485 END IF
486 TEMP1 = MAX( TEMP1, TEMP2 )
487 IF( ILABAD ) THEN
488 WRITE( NOUT, FMT = 9997 )J, MPLUSN, PRTYPE
489 END IF
490 10 CONTINUE
491 RESULT( 6 ) = TEMP1
492 NTEST = NTEST + 2
493 *
494 * Test (7) (if sorting worked)
495 *
496 RESULT( 7 ) = ZERO
497 IF( LINFO.EQ.MPLUSN+3 ) THEN
498 RESULT( 7 ) = ULPINV
499 ELSE IF( MM.NE.N ) THEN
500 RESULT( 7 ) = ULPINV
501 END IF
502 NTEST = NTEST + 1
503 *
504 * Test (8): compare the estimated value DIF and its
505 * value. first, compute the exact DIF.
506 *
507 RESULT( 8 ) = ZERO
508 MN2 = MM*( MPLUSN-MM )*2
509 IF( IFUNC.GE.2 .AND. MN2.LE.NCMAX*NCMAX ) THEN
510 *
511 * Note: for either following two cases, there are
512 * almost same number of test cases fail the test.
513 *
514 CALL CLAKF2( MM, MPLUSN-MM, AI, LDA,
515 $ AI( MM+1, MM+1 ), BI,
516 $ BI( MM+1, MM+1 ), C, LDC )
517 *
518 CALL CGESVD( 'N', 'N', MN2, MN2, C, LDC, S, WORK,
519 $ 1, WORK( 2 ), 1, WORK( 3 ), LWORK-2,
520 $ RWORK, INFO )
521 DIFTRU = S( MN2 )
522 *
523 IF( DIFEST( 2 ).EQ.ZERO ) THEN
524 IF( DIFTRU.GT.ABNRM*ULP )
525 $ RESULT( 8 ) = ULPINV
526 ELSE IF( DIFTRU.EQ.ZERO ) THEN
527 IF( DIFEST( 2 ).GT.ABNRM*ULP )
528 $ RESULT( 8 ) = ULPINV
529 ELSE IF( ( DIFTRU.GT.THRSH2*DIFEST( 2 ) ) .OR.
530 $ ( DIFTRU*THRSH2.LT.DIFEST( 2 ) ) ) THEN
531 RESULT( 8 ) = MAX( DIFTRU / DIFEST( 2 ),
532 $ DIFEST( 2 ) / DIFTRU )
533 END IF
534 NTEST = NTEST + 1
535 END IF
536 *
537 * Test (9)
538 *
539 RESULT( 9 ) = ZERO
540 IF( LINFO.EQ.( MPLUSN+2 ) ) THEN
541 IF( DIFTRU.GT.ABNRM*ULP )
542 $ RESULT( 9 ) = ULPINV
543 IF( ( IFUNC.GT.1 ) .AND. ( DIFEST( 2 ).NE.ZERO ) )
544 $ RESULT( 9 ) = ULPINV
545 IF( ( IFUNC.EQ.1 ) .AND. ( PL( 1 ).NE.ZERO ) )
546 $ RESULT( 9 ) = ULPINV
547 NTEST = NTEST + 1
548 END IF
549 *
550 NTESTT = NTESTT + NTEST
551 *
552 * Print out tests which fail.
553 *
554 DO 20 J = 1, 9
555 IF( RESULT( J ).GE.THRESH ) THEN
556 *
557 * If this is the first test to fail,
558 * print a header to the data file.
559 *
560 IF( NERRS.EQ.0 ) THEN
561 WRITE( NOUT, FMT = 9996 )'CGX'
562 *
563 * Matrix types
564 *
565 WRITE( NOUT, FMT = 9994 )
566 *
567 * Tests performed
568 *
569 WRITE( NOUT, FMT = 9993 )'unitary', '''',
570 $ 'transpose', ( '''', I = 1, 4 )
571 *
572 END IF
573 NERRS = NERRS + 1
574 IF( RESULT( J ).LT.10000.0 ) THEN
575 WRITE( NOUT, FMT = 9992 )MPLUSN, PRTYPE,
576 $ WEIGHT, M, J, RESULT( J )
577 ELSE
578 WRITE( NOUT, FMT = 9991 )MPLUSN, PRTYPE,
579 $ WEIGHT, M, J, RESULT( J )
580 END IF
581 END IF
582 20 CONTINUE
583 *
584 30 CONTINUE
585 40 CONTINUE
586 50 CONTINUE
587 60 CONTINUE
588 *
589 GO TO 150
590 *
591 70 CONTINUE
592 *
593 * Read in data from file to check accuracy of condition estimation
594 * Read input data until N=0
595 *
596 NPTKNT = 0
597 *
598 80 CONTINUE
599 READ( NIN, FMT = *, END = 140 )MPLUSN
600 IF( MPLUSN.EQ.0 )
601 $ GO TO 140
602 READ( NIN, FMT = *, END = 140 )N
603 DO 90 I = 1, MPLUSN
604 READ( NIN, FMT = * )( AI( I, J ), J = 1, MPLUSN )
605 90 CONTINUE
606 DO 100 I = 1, MPLUSN
607 READ( NIN, FMT = * )( BI( I, J ), J = 1, MPLUSN )
608 100 CONTINUE
609 READ( NIN, FMT = * )PLTRU, DIFTRU
610 *
611 NPTKNT = NPTKNT + 1
612 FS = .TRUE.
613 K = 0
614 M = MPLUSN - N
615 *
616 CALL CLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, A, LDA )
617 CALL CLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, B, LDA )
618 *
619 * Compute the Schur factorization while swaping the
620 * m-by-m (1,1)-blocks with n-by-n (2,2)-blocks.
621 *
622 CALL CGGESX( 'V', 'V', 'S', CLCTSX, 'B', MPLUSN, AI, LDA, BI, LDA,
623 $ MM, ALPHA, BETA, Q, LDA, Z, LDA, PL, DIFEST, WORK,
624 $ LWORK, RWORK, IWORK, LIWORK, BWORK, LINFO )
625 *
626 IF( LINFO.NE.0 .AND. LINFO.NE.MPLUSN+2 ) THEN
627 RESULT( 1 ) = ULPINV
628 WRITE( NOUT, FMT = 9998 )'CGGESX', LINFO, MPLUSN, NPTKNT
629 GO TO 130
630 END IF
631 *
632 * Compute the norm(A, B)
633 * (should this be norm of (A,B) or (AI,BI)?)
634 *
635 CALL CLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, WORK, MPLUSN )
636 CALL CLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA,
637 $ WORK( MPLUSN*MPLUSN+1 ), MPLUSN )
638 ABNRM = CLANGE( 'Fro', MPLUSN, 2*MPLUSN, WORK, MPLUSN, RWORK )
639 *
640 * Do tests (1) to (4)
641 *
642 CALL CGET51( 1, MPLUSN, A, LDA, AI, LDA, Q, LDA, Z, LDA, WORK,
643 $ RWORK, RESULT( 1 ) )
644 CALL CGET51( 1, MPLUSN, B, LDA, BI, LDA, Q, LDA, Z, LDA, WORK,
645 $ RWORK, RESULT( 2 ) )
646 CALL CGET51( 3, MPLUSN, B, LDA, BI, LDA, Q, LDA, Q, LDA, WORK,
647 $ RWORK, RESULT( 3 ) )
648 CALL CGET51( 3, MPLUSN, B, LDA, BI, LDA, Z, LDA, Z, LDA, WORK,
649 $ RWORK, RESULT( 4 ) )
650 *
651 * Do tests (5) and (6): check Schur form of A and compare
652 * eigenvalues with diagonals.
653 *
654 NTEST = 6
655 TEMP1 = ZERO
656 RESULT( 5 ) = ZERO
657 RESULT( 6 ) = ZERO
658 *
659 DO 110 J = 1, MPLUSN
660 ILABAD = .FALSE.
661 TEMP2 = ( ABS1( ALPHA( J )-AI( J, J ) ) /
662 $ MAX( SMLNUM, ABS1( ALPHA( J ) ), ABS1( AI( J, J ) ) )+
663 $ ABS1( BETA( J )-BI( J, J ) ) /
664 $ MAX( SMLNUM, ABS1( BETA( J ) ), ABS1( BI( J, J ) ) ) )
665 $ / ULP
666 IF( J.LT.MPLUSN ) THEN
667 IF( AI( J+1, J ).NE.ZERO ) THEN
668 ILABAD = .TRUE.
669 RESULT( 5 ) = ULPINV
670 END IF
671 END IF
672 IF( J.GT.1 ) THEN
673 IF( AI( J, J-1 ).NE.ZERO ) THEN
674 ILABAD = .TRUE.
675 RESULT( 5 ) = ULPINV
676 END IF
677 END IF
678 TEMP1 = MAX( TEMP1, TEMP2 )
679 IF( ILABAD ) THEN
680 WRITE( NOUT, FMT = 9997 )J, MPLUSN, NPTKNT
681 END IF
682 110 CONTINUE
683 RESULT( 6 ) = TEMP1
684 *
685 * Test (7) (if sorting worked) <--------- need to be checked.
686 *
687 NTEST = 7
688 RESULT( 7 ) = ZERO
689 IF( LINFO.EQ.MPLUSN+3 )
690 $ RESULT( 7 ) = ULPINV
691 *
692 * Test (8): compare the estimated value of DIF and its true value.
693 *
694 NTEST = 8
695 RESULT( 8 ) = ZERO
696 IF( DIFEST( 2 ).EQ.ZERO ) THEN
697 IF( DIFTRU.GT.ABNRM*ULP )
698 $ RESULT( 8 ) = ULPINV
699 ELSE IF( DIFTRU.EQ.ZERO ) THEN
700 IF( DIFEST( 2 ).GT.ABNRM*ULP )
701 $ RESULT( 8 ) = ULPINV
702 ELSE IF( ( DIFTRU.GT.THRSH2*DIFEST( 2 ) ) .OR.
703 $ ( DIFTRU*THRSH2.LT.DIFEST( 2 ) ) ) THEN
704 RESULT( 8 ) = MAX( DIFTRU / DIFEST( 2 ), DIFEST( 2 ) / DIFTRU )
705 END IF
706 *
707 * Test (9)
708 *
709 NTEST = 9
710 RESULT( 9 ) = ZERO
711 IF( LINFO.EQ.( MPLUSN+2 ) ) THEN
712 IF( DIFTRU.GT.ABNRM*ULP )
713 $ RESULT( 9 ) = ULPINV
714 IF( ( IFUNC.GT.1 ) .AND. ( DIFEST( 2 ).NE.ZERO ) )
715 $ RESULT( 9 ) = ULPINV
716 IF( ( IFUNC.EQ.1 ) .AND. ( PL( 1 ).NE.ZERO ) )
717 $ RESULT( 9 ) = ULPINV
718 END IF
719 *
720 * Test (10): compare the estimated value of PL and it true value.
721 *
722 NTEST = 10
723 RESULT( 10 ) = ZERO
724 IF( PL( 1 ).EQ.ZERO ) THEN
725 IF( PLTRU.GT.ABNRM*ULP )
726 $ RESULT( 10 ) = ULPINV
727 ELSE IF( PLTRU.EQ.ZERO ) THEN
728 IF( PL( 1 ).GT.ABNRM*ULP )
729 $ RESULT( 10 ) = ULPINV
730 ELSE IF( ( PLTRU.GT.THRESH*PL( 1 ) ) .OR.
731 $ ( PLTRU*THRESH.LT.PL( 1 ) ) ) THEN
732 RESULT( 10 ) = ULPINV
733 END IF
734 *
735 NTESTT = NTESTT + NTEST
736 *
737 * Print out tests which fail.
738 *
739 DO 120 J = 1, NTEST
740 IF( RESULT( J ).GE.THRESH ) THEN
741 *
742 * If this is the first test to fail,
743 * print a header to the data file.
744 *
745 IF( NERRS.EQ.0 ) THEN
746 WRITE( NOUT, FMT = 9996 )'CGX'
747 *
748 * Matrix types
749 *
750 WRITE( NOUT, FMT = 9995 )
751 *
752 * Tests performed
753 *
754 WRITE( NOUT, FMT = 9993 )'unitary', '''', 'transpose',
755 $ ( '''', I = 1, 4 )
756 *
757 END IF
758 NERRS = NERRS + 1
759 IF( RESULT( J ).LT.10000.0 ) THEN
760 WRITE( NOUT, FMT = 9990 )NPTKNT, MPLUSN, J, RESULT( J )
761 ELSE
762 WRITE( NOUT, FMT = 9989 )NPTKNT, MPLUSN, J, RESULT( J )
763 END IF
764 END IF
765 *
766 120 CONTINUE
767 *
768 130 CONTINUE
769 GO TO 80
770 140 CONTINUE
771 *
772 150 CONTINUE
773 *
774 * Summary
775 *
776 CALL ALASVM( 'CGX', NOUT, NERRS, NTESTT, 0 )
777 *
778 WORK( 1 ) = MAXWRK
779 *
780 RETURN
781 *
782 9999 FORMAT( ' CDRGSX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
783 $ I6, ', JTYPE=', I6, ')' )
784 *
785 9998 FORMAT( ' CDRGSX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
786 $ I6, ', Input Example #', I2, ')' )
787 *
788 9997 FORMAT( ' CDRGSX: S not in Schur form at eigenvalue ', I6, '.',
789 $ / 9X, 'N=', I6, ', JTYPE=', I6, ')' )
790 *
791 9996 FORMAT( / 1X, A3, ' -- Complex Expert Generalized Schur form',
792 $ ' problem driver' )
793 *
794 9995 FORMAT( 'Input Example' )
795 *
796 9994 FORMAT( ' Matrix types: ', /
797 $ ' 1: A is a block diagonal matrix of Jordan blocks ',
798 $ 'and B is the identity ', / ' matrix, ',
799 $ / ' 2: A and B are upper triangular matrices, ',
800 $ / ' 3: A and B are as type 2, but each second diagonal ',
801 $ 'block in A_11 and ', /
802 $ ' each third diaongal block in A_22 are 2x2 blocks,',
803 $ / ' 4: A and B are block diagonal matrices, ',
804 $ / ' 5: (A,B) has potentially close or common ',
805 $ 'eigenvalues.', / )
806 *
807 9993 FORMAT( / ' Tests performed: (S is Schur, T is triangular, ',
808 $ 'Q and Z are ', A, ',', / 19X,
809 $ ' a is alpha, b is beta, and ', A, ' means ', A, '.)',
810 $ / ' 1 = | A - Q S Z', A,
811 $ ' | / ( |A| n ulp ) 2 = | B - Q T Z', A,
812 $ ' | / ( |B| n ulp )', / ' 3 = | I - QQ', A,
813 $ ' | / ( n ulp ) 4 = | I - ZZ', A,
814 $ ' | / ( n ulp )', / ' 5 = 1/ULP if A is not in ',
815 $ 'Schur form S', / ' 6 = difference between (alpha,beta)',
816 $ ' and diagonals of (S,T)', /
817 $ ' 7 = 1/ULP if SDIM is not the correct number of ',
818 $ 'selected eigenvalues', /
819 $ ' 8 = 1/ULP if DIFEST/DIFTRU > 10*THRESH or ',
820 $ 'DIFTRU/DIFEST > 10*THRESH',
821 $ / ' 9 = 1/ULP if DIFEST <> 0 or DIFTRU > ULP*norm(A,B) ',
822 $ 'when reordering fails', /
823 $ ' 10 = 1/ULP if PLEST/PLTRU > THRESH or ',
824 $ 'PLTRU/PLEST > THRESH', /
825 $ ' ( Test 10 is only for input examples )', / )
826 9992 FORMAT( ' Matrix order=', I2, ', type=', I2, ', a=', E10.4,
827 $ ', order(A_11)=', I2, ', result ', I2, ' is ', 0P, F8.2 )
828 9991 FORMAT( ' Matrix order=', I2, ', type=', I2, ', a=', E10.4,
829 $ ', order(A_11)=', I2, ', result ', I2, ' is ', 0P, E10.4 )
830 9990 FORMAT( ' Input example #', I2, ', matrix order=', I4, ',',
831 $ ' result ', I2, ' is', 0P, F8.2 )
832 9989 FORMAT( ' Input example #', I2, ', matrix order=', I4, ',',
833 $ ' result ', I2, ' is', 1P, E10.3 )
834 *
835 * End of CDRGSX
836 *
837 END