1 SUBROUTINE ZGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA,
2 $ VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK,
3 $ INFO )
4 *
5 * -- LAPACK driver routine (version 3.2) --
6 * -- LAPACK is a software package provided by Univ. of Tennessee, --
7 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
8 * November 2006
9 *
10 * .. Scalar Arguments ..
11 CHARACTER JOBVSL, JOBVSR
12 INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N
13 * ..
14 * .. Array Arguments ..
15 DOUBLE PRECISION RWORK( * )
16 COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ),
17 $ BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
18 $ WORK( * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 * This routine is deprecated and has been replaced by routine ZGGES.
25 *
26 * ZGEGS computes the eigenvalues, Schur form, and, optionally, the
27 * left and or/right Schur vectors of a complex matrix pair (A,B).
28 * Given two square matrices A and B, the generalized Schur
29 * factorization has the form
30 *
31 * A = Q*S*Z**H, B = Q*T*Z**H
32 *
33 * where Q and Z are unitary matrices and S and T are upper triangular.
34 * The columns of Q are the left Schur vectors
35 * and the columns of Z are the right Schur vectors.
36 *
37 * If only the eigenvalues of (A,B) are needed, the driver routine
38 * ZGEGV should be used instead. See ZGEGV for a description of the
39 * eigenvalues of the generalized nonsymmetric eigenvalue problem
40 * (GNEP).
41 *
42 * Arguments
43 * =========
44 *
45 * JOBVSL (input) CHARACTER*1
46 * = 'N': do not compute the left Schur vectors;
47 * = 'V': compute the left Schur vectors (returned in VSL).
48 *
49 * JOBVSR (input) CHARACTER*1
50 * = 'N': do not compute the right Schur vectors;
51 * = 'V': compute the right Schur vectors (returned in VSR).
52 *
53 * N (input) INTEGER
54 * The order of the matrices A, B, VSL, and VSR. N >= 0.
55 *
56 * A (input/output) COMPLEX*16 array, dimension (LDA, N)
57 * On entry, the matrix A.
58 * On exit, the upper triangular matrix S from the generalized
59 * Schur factorization.
60 *
61 * LDA (input) INTEGER
62 * The leading dimension of A. LDA >= max(1,N).
63 *
64 * B (input/output) COMPLEX*16 array, dimension (LDB, N)
65 * On entry, the matrix B.
66 * On exit, the upper triangular matrix T from the generalized
67 * Schur factorization.
68 *
69 * LDB (input) INTEGER
70 * The leading dimension of B. LDB >= max(1,N).
71 *
72 * ALPHA (output) COMPLEX*16 array, dimension (N)
73 * The complex scalars alpha that define the eigenvalues of
74 * GNEP. ALPHA(j) = S(j,j), the diagonal element of the Schur
75 * form of A.
76 *
77 * BETA (output) COMPLEX*16 array, dimension (N)
78 * The non-negative real scalars beta that define the
79 * eigenvalues of GNEP. BETA(j) = T(j,j), the diagonal element
80 * of the triangular factor T.
81 *
82 * Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
83 * represent the j-th eigenvalue of the matrix pair (A,B), in
84 * one of the forms lambda = alpha/beta or mu = beta/alpha.
85 * Since either lambda or mu may overflow, they should not,
86 * in general, be computed.
87 *
88 *
89 * VSL (output) COMPLEX*16 array, dimension (LDVSL,N)
90 * If JOBVSL = 'V', the matrix of left Schur vectors Q.
91 * Not referenced if JOBVSL = 'N'.
92 *
93 * LDVSL (input) INTEGER
94 * The leading dimension of the matrix VSL. LDVSL >= 1, and
95 * if JOBVSL = 'V', LDVSL >= N.
96 *
97 * VSR (output) COMPLEX*16 array, dimension (LDVSR,N)
98 * If JOBVSR = 'V', the matrix of right Schur vectors Z.
99 * Not referenced if JOBVSR = 'N'.
100 *
101 * LDVSR (input) INTEGER
102 * The leading dimension of the matrix VSR. LDVSR >= 1, and
103 * if JOBVSR = 'V', LDVSR >= N.
104 *
105 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
106 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
107 *
108 * LWORK (input) INTEGER
109 * The dimension of the array WORK. LWORK >= max(1,2*N).
110 * For good performance, LWORK must generally be larger.
111 * To compute the optimal value of LWORK, call ILAENV to get
112 * blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.) Then compute:
113 * NB -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR;
114 * the optimal LWORK is N*(NB+1).
115 *
116 * If LWORK = -1, then a workspace query is assumed; the routine
117 * only calculates the optimal size of the WORK array, returns
118 * this value as the first entry of the WORK array, and no error
119 * message related to LWORK is issued by XERBLA.
120 *
121 * RWORK (workspace) DOUBLE PRECISION array, dimension (3*N)
122 *
123 * INFO (output) INTEGER
124 * = 0: successful exit
125 * < 0: if INFO = -i, the i-th argument had an illegal value.
126 * =1,...,N:
127 * The QZ iteration failed. (A,B) are not in Schur
128 * form, but ALPHA(j) and BETA(j) should be correct for
129 * j=INFO+1,...,N.
130 * > N: errors that usually indicate LAPACK problems:
131 * =N+1: error return from ZGGBAL
132 * =N+2: error return from ZGEQRF
133 * =N+3: error return from ZUNMQR
134 * =N+4: error return from ZUNGQR
135 * =N+5: error return from ZGGHRD
136 * =N+6: error return from ZHGEQZ (other than failed
137 * iteration)
138 * =N+7: error return from ZGGBAK (computing VSL)
139 * =N+8: error return from ZGGBAK (computing VSR)
140 * =N+9: error return from ZLASCL (various places)
141 *
142 * =====================================================================
143 *
144 * .. Parameters ..
145 DOUBLE PRECISION ZERO, ONE
146 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
147 COMPLEX*16 CZERO, CONE
148 PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ),
149 $ CONE = ( 1.0D0, 0.0D0 ) )
150 * ..
151 * .. Local Scalars ..
152 LOGICAL ILASCL, ILBSCL, ILVSL, ILVSR, LQUERY
153 INTEGER ICOLS, IHI, IINFO, IJOBVL, IJOBVR, ILEFT, ILO,
154 $ IRIGHT, IROWS, IRWORK, ITAU, IWORK, LOPT,
155 $ LWKMIN, LWKOPT, NB, NB1, NB2, NB3
156 DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS,
157 $ SAFMIN, SMLNUM
158 * ..
159 * .. External Subroutines ..
160 EXTERNAL XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHRD, ZHGEQZ,
161 $ ZLACPY, ZLASCL, ZLASET, ZUNGQR, ZUNMQR
162 * ..
163 * .. External Functions ..
164 LOGICAL LSAME
165 INTEGER ILAENV
166 DOUBLE PRECISION DLAMCH, ZLANGE
167 EXTERNAL LSAME, ILAENV, DLAMCH, ZLANGE
168 * ..
169 * .. Intrinsic Functions ..
170 INTRINSIC INT, MAX
171 * ..
172 * .. Executable Statements ..
173 *
174 * Decode the input arguments
175 *
176 IF( LSAME( JOBVSL, 'N' ) ) THEN
177 IJOBVL = 1
178 ILVSL = .FALSE.
179 ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN
180 IJOBVL = 2
181 ILVSL = .TRUE.
182 ELSE
183 IJOBVL = -1
184 ILVSL = .FALSE.
185 END IF
186 *
187 IF( LSAME( JOBVSR, 'N' ) ) THEN
188 IJOBVR = 1
189 ILVSR = .FALSE.
190 ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN
191 IJOBVR = 2
192 ILVSR = .TRUE.
193 ELSE
194 IJOBVR = -1
195 ILVSR = .FALSE.
196 END IF
197 *
198 * Test the input arguments
199 *
200 LWKMIN = MAX( 2*N, 1 )
201 LWKOPT = LWKMIN
202 WORK( 1 ) = LWKOPT
203 LQUERY = ( LWORK.EQ.-1 )
204 INFO = 0
205 IF( IJOBVL.LE.0 ) THEN
206 INFO = -1
207 ELSE IF( IJOBVR.LE.0 ) THEN
208 INFO = -2
209 ELSE IF( N.LT.0 ) THEN
210 INFO = -3
211 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
212 INFO = -5
213 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
214 INFO = -7
215 ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN
216 INFO = -11
217 ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
218 INFO = -13
219 ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
220 INFO = -15
221 END IF
222 *
223 IF( INFO.EQ.0 ) THEN
224 NB1 = ILAENV( 1, 'ZGEQRF', ' ', N, N, -1, -1 )
225 NB2 = ILAENV( 1, 'ZUNMQR', ' ', N, N, N, -1 )
226 NB3 = ILAENV( 1, 'ZUNGQR', ' ', N, N, N, -1 )
227 NB = MAX( NB1, NB2, NB3 )
228 LOPT = N*( NB+1 )
229 WORK( 1 ) = LOPT
230 END IF
231 *
232 IF( INFO.NE.0 ) THEN
233 CALL XERBLA( 'ZGEGS ', -INFO )
234 RETURN
235 ELSE IF( LQUERY ) THEN
236 RETURN
237 END IF
238 *
239 * Quick return if possible
240 *
241 IF( N.EQ.0 )
242 $ RETURN
243 *
244 * Get machine constants
245 *
246 EPS = DLAMCH( 'E' )*DLAMCH( 'B' )
247 SAFMIN = DLAMCH( 'S' )
248 SMLNUM = N*SAFMIN / EPS
249 BIGNUM = ONE / SMLNUM
250 *
251 * Scale A if max element outside range [SMLNUM,BIGNUM]
252 *
253 ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK )
254 ILASCL = .FALSE.
255 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
256 ANRMTO = SMLNUM
257 ILASCL = .TRUE.
258 ELSE IF( ANRM.GT.BIGNUM ) THEN
259 ANRMTO = BIGNUM
260 ILASCL = .TRUE.
261 END IF
262 *
263 IF( ILASCL ) THEN
264 CALL ZLASCL( 'G', -1, -1, ANRM, ANRMTO, N, N, A, LDA, IINFO )
265 IF( IINFO.NE.0 ) THEN
266 INFO = N + 9
267 RETURN
268 END IF
269 END IF
270 *
271 * Scale B if max element outside range [SMLNUM,BIGNUM]
272 *
273 BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK )
274 ILBSCL = .FALSE.
275 IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
276 BNRMTO = SMLNUM
277 ILBSCL = .TRUE.
278 ELSE IF( BNRM.GT.BIGNUM ) THEN
279 BNRMTO = BIGNUM
280 ILBSCL = .TRUE.
281 END IF
282 *
283 IF( ILBSCL ) THEN
284 CALL ZLASCL( 'G', -1, -1, BNRM, BNRMTO, N, N, B, LDB, IINFO )
285 IF( IINFO.NE.0 ) THEN
286 INFO = N + 9
287 RETURN
288 END IF
289 END IF
290 *
291 * Permute the matrix to make it more nearly triangular
292 *
293 ILEFT = 1
294 IRIGHT = N + 1
295 IRWORK = IRIGHT + N
296 IWORK = 1
297 CALL ZGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ),
298 $ RWORK( IRIGHT ), RWORK( IRWORK ), IINFO )
299 IF( IINFO.NE.0 ) THEN
300 INFO = N + 1
301 GO TO 10
302 END IF
303 *
304 * Reduce B to triangular form, and initialize VSL and/or VSR
305 *
306 IROWS = IHI + 1 - ILO
307 ICOLS = N + 1 - ILO
308 ITAU = IWORK
309 IWORK = ITAU + IROWS
310 CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
311 $ WORK( IWORK ), LWORK+1-IWORK, IINFO )
312 IF( IINFO.GE.0 )
313 $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
314 IF( IINFO.NE.0 ) THEN
315 INFO = N + 2
316 GO TO 10
317 END IF
318 *
319 CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
320 $ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWORK ),
321 $ LWORK+1-IWORK, IINFO )
322 IF( IINFO.GE.0 )
323 $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
324 IF( IINFO.NE.0 ) THEN
325 INFO = N + 3
326 GO TO 10
327 END IF
328 *
329 IF( ILVSL ) THEN
330 CALL ZLASET( 'Full', N, N, CZERO, CONE, VSL, LDVSL )
331 CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
332 $ VSL( ILO+1, ILO ), LDVSL )
333 CALL ZUNGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL,
334 $ WORK( ITAU ), WORK( IWORK ), LWORK+1-IWORK,
335 $ IINFO )
336 IF( IINFO.GE.0 )
337 $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
338 IF( IINFO.NE.0 ) THEN
339 INFO = N + 4
340 GO TO 10
341 END IF
342 END IF
343 *
344 IF( ILVSR )
345 $ CALL ZLASET( 'Full', N, N, CZERO, CONE, VSR, LDVSR )
346 *
347 * Reduce to generalized Hessenberg form
348 *
349 CALL ZGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL,
350 $ LDVSL, VSR, LDVSR, IINFO )
351 IF( IINFO.NE.0 ) THEN
352 INFO = N + 5
353 GO TO 10
354 END IF
355 *
356 * Perform QZ algorithm, computing Schur vectors if desired
357 *
358 IWORK = ITAU
359 CALL ZHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB,
360 $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK( IWORK ),
361 $ LWORK+1-IWORK, RWORK( IRWORK ), IINFO )
362 IF( IINFO.GE.0 )
363 $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
364 IF( IINFO.NE.0 ) THEN
365 IF( IINFO.GT.0 .AND. IINFO.LE.N ) THEN
366 INFO = IINFO
367 ELSE IF( IINFO.GT.N .AND. IINFO.LE.2*N ) THEN
368 INFO = IINFO - N
369 ELSE
370 INFO = N + 6
371 END IF
372 GO TO 10
373 END IF
374 *
375 * Apply permutation to VSL and VSR
376 *
377 IF( ILVSL ) THEN
378 CALL ZGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ),
379 $ RWORK( IRIGHT ), N, VSL, LDVSL, IINFO )
380 IF( IINFO.NE.0 ) THEN
381 INFO = N + 7
382 GO TO 10
383 END IF
384 END IF
385 IF( ILVSR ) THEN
386 CALL ZGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ),
387 $ RWORK( IRIGHT ), N, VSR, LDVSR, IINFO )
388 IF( IINFO.NE.0 ) THEN
389 INFO = N + 8
390 GO TO 10
391 END IF
392 END IF
393 *
394 * Undo scaling
395 *
396 IF( ILASCL ) THEN
397 CALL ZLASCL( 'U', -1, -1, ANRMTO, ANRM, N, N, A, LDA, IINFO )
398 IF( IINFO.NE.0 ) THEN
399 INFO = N + 9
400 RETURN
401 END IF
402 CALL ZLASCL( 'G', -1, -1, ANRMTO, ANRM, N, 1, ALPHA, N, IINFO )
403 IF( IINFO.NE.0 ) THEN
404 INFO = N + 9
405 RETURN
406 END IF
407 END IF
408 *
409 IF( ILBSCL ) THEN
410 CALL ZLASCL( 'U', -1, -1, BNRMTO, BNRM, N, N, B, LDB, IINFO )
411 IF( IINFO.NE.0 ) THEN
412 INFO = N + 9
413 RETURN
414 END IF
415 CALL ZLASCL( 'G', -1, -1, BNRMTO, BNRM, N, 1, BETA, N, IINFO )
416 IF( IINFO.NE.0 ) THEN
417 INFO = N + 9
418 RETURN
419 END IF
420 END IF
421 *
422 10 CONTINUE
423 WORK( 1 ) = LWKOPT
424 *
425 RETURN
426 *
427 * End of ZGEGS
428 *
429 END
2 $ VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK,
3 $ INFO )
4 *
5 * -- LAPACK driver routine (version 3.2) --
6 * -- LAPACK is a software package provided by Univ. of Tennessee, --
7 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
8 * November 2006
9 *
10 * .. Scalar Arguments ..
11 CHARACTER JOBVSL, JOBVSR
12 INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N
13 * ..
14 * .. Array Arguments ..
15 DOUBLE PRECISION RWORK( * )
16 COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ),
17 $ BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
18 $ WORK( * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 * This routine is deprecated and has been replaced by routine ZGGES.
25 *
26 * ZGEGS computes the eigenvalues, Schur form, and, optionally, the
27 * left and or/right Schur vectors of a complex matrix pair (A,B).
28 * Given two square matrices A and B, the generalized Schur
29 * factorization has the form
30 *
31 * A = Q*S*Z**H, B = Q*T*Z**H
32 *
33 * where Q and Z are unitary matrices and S and T are upper triangular.
34 * The columns of Q are the left Schur vectors
35 * and the columns of Z are the right Schur vectors.
36 *
37 * If only the eigenvalues of (A,B) are needed, the driver routine
38 * ZGEGV should be used instead. See ZGEGV for a description of the
39 * eigenvalues of the generalized nonsymmetric eigenvalue problem
40 * (GNEP).
41 *
42 * Arguments
43 * =========
44 *
45 * JOBVSL (input) CHARACTER*1
46 * = 'N': do not compute the left Schur vectors;
47 * = 'V': compute the left Schur vectors (returned in VSL).
48 *
49 * JOBVSR (input) CHARACTER*1
50 * = 'N': do not compute the right Schur vectors;
51 * = 'V': compute the right Schur vectors (returned in VSR).
52 *
53 * N (input) INTEGER
54 * The order of the matrices A, B, VSL, and VSR. N >= 0.
55 *
56 * A (input/output) COMPLEX*16 array, dimension (LDA, N)
57 * On entry, the matrix A.
58 * On exit, the upper triangular matrix S from the generalized
59 * Schur factorization.
60 *
61 * LDA (input) INTEGER
62 * The leading dimension of A. LDA >= max(1,N).
63 *
64 * B (input/output) COMPLEX*16 array, dimension (LDB, N)
65 * On entry, the matrix B.
66 * On exit, the upper triangular matrix T from the generalized
67 * Schur factorization.
68 *
69 * LDB (input) INTEGER
70 * The leading dimension of B. LDB >= max(1,N).
71 *
72 * ALPHA (output) COMPLEX*16 array, dimension (N)
73 * The complex scalars alpha that define the eigenvalues of
74 * GNEP. ALPHA(j) = S(j,j), the diagonal element of the Schur
75 * form of A.
76 *
77 * BETA (output) COMPLEX*16 array, dimension (N)
78 * The non-negative real scalars beta that define the
79 * eigenvalues of GNEP. BETA(j) = T(j,j), the diagonal element
80 * of the triangular factor T.
81 *
82 * Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
83 * represent the j-th eigenvalue of the matrix pair (A,B), in
84 * one of the forms lambda = alpha/beta or mu = beta/alpha.
85 * Since either lambda or mu may overflow, they should not,
86 * in general, be computed.
87 *
88 *
89 * VSL (output) COMPLEX*16 array, dimension (LDVSL,N)
90 * If JOBVSL = 'V', the matrix of left Schur vectors Q.
91 * Not referenced if JOBVSL = 'N'.
92 *
93 * LDVSL (input) INTEGER
94 * The leading dimension of the matrix VSL. LDVSL >= 1, and
95 * if JOBVSL = 'V', LDVSL >= N.
96 *
97 * VSR (output) COMPLEX*16 array, dimension (LDVSR,N)
98 * If JOBVSR = 'V', the matrix of right Schur vectors Z.
99 * Not referenced if JOBVSR = 'N'.
100 *
101 * LDVSR (input) INTEGER
102 * The leading dimension of the matrix VSR. LDVSR >= 1, and
103 * if JOBVSR = 'V', LDVSR >= N.
104 *
105 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
106 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
107 *
108 * LWORK (input) INTEGER
109 * The dimension of the array WORK. LWORK >= max(1,2*N).
110 * For good performance, LWORK must generally be larger.
111 * To compute the optimal value of LWORK, call ILAENV to get
112 * blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.) Then compute:
113 * NB -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR;
114 * the optimal LWORK is N*(NB+1).
115 *
116 * If LWORK = -1, then a workspace query is assumed; the routine
117 * only calculates the optimal size of the WORK array, returns
118 * this value as the first entry of the WORK array, and no error
119 * message related to LWORK is issued by XERBLA.
120 *
121 * RWORK (workspace) DOUBLE PRECISION array, dimension (3*N)
122 *
123 * INFO (output) INTEGER
124 * = 0: successful exit
125 * < 0: if INFO = -i, the i-th argument had an illegal value.
126 * =1,...,N:
127 * The QZ iteration failed. (A,B) are not in Schur
128 * form, but ALPHA(j) and BETA(j) should be correct for
129 * j=INFO+1,...,N.
130 * > N: errors that usually indicate LAPACK problems:
131 * =N+1: error return from ZGGBAL
132 * =N+2: error return from ZGEQRF
133 * =N+3: error return from ZUNMQR
134 * =N+4: error return from ZUNGQR
135 * =N+5: error return from ZGGHRD
136 * =N+6: error return from ZHGEQZ (other than failed
137 * iteration)
138 * =N+7: error return from ZGGBAK (computing VSL)
139 * =N+8: error return from ZGGBAK (computing VSR)
140 * =N+9: error return from ZLASCL (various places)
141 *
142 * =====================================================================
143 *
144 * .. Parameters ..
145 DOUBLE PRECISION ZERO, ONE
146 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
147 COMPLEX*16 CZERO, CONE
148 PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ),
149 $ CONE = ( 1.0D0, 0.0D0 ) )
150 * ..
151 * .. Local Scalars ..
152 LOGICAL ILASCL, ILBSCL, ILVSL, ILVSR, LQUERY
153 INTEGER ICOLS, IHI, IINFO, IJOBVL, IJOBVR, ILEFT, ILO,
154 $ IRIGHT, IROWS, IRWORK, ITAU, IWORK, LOPT,
155 $ LWKMIN, LWKOPT, NB, NB1, NB2, NB3
156 DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS,
157 $ SAFMIN, SMLNUM
158 * ..
159 * .. External Subroutines ..
160 EXTERNAL XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHRD, ZHGEQZ,
161 $ ZLACPY, ZLASCL, ZLASET, ZUNGQR, ZUNMQR
162 * ..
163 * .. External Functions ..
164 LOGICAL LSAME
165 INTEGER ILAENV
166 DOUBLE PRECISION DLAMCH, ZLANGE
167 EXTERNAL LSAME, ILAENV, DLAMCH, ZLANGE
168 * ..
169 * .. Intrinsic Functions ..
170 INTRINSIC INT, MAX
171 * ..
172 * .. Executable Statements ..
173 *
174 * Decode the input arguments
175 *
176 IF( LSAME( JOBVSL, 'N' ) ) THEN
177 IJOBVL = 1
178 ILVSL = .FALSE.
179 ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN
180 IJOBVL = 2
181 ILVSL = .TRUE.
182 ELSE
183 IJOBVL = -1
184 ILVSL = .FALSE.
185 END IF
186 *
187 IF( LSAME( JOBVSR, 'N' ) ) THEN
188 IJOBVR = 1
189 ILVSR = .FALSE.
190 ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN
191 IJOBVR = 2
192 ILVSR = .TRUE.
193 ELSE
194 IJOBVR = -1
195 ILVSR = .FALSE.
196 END IF
197 *
198 * Test the input arguments
199 *
200 LWKMIN = MAX( 2*N, 1 )
201 LWKOPT = LWKMIN
202 WORK( 1 ) = LWKOPT
203 LQUERY = ( LWORK.EQ.-1 )
204 INFO = 0
205 IF( IJOBVL.LE.0 ) THEN
206 INFO = -1
207 ELSE IF( IJOBVR.LE.0 ) THEN
208 INFO = -2
209 ELSE IF( N.LT.0 ) THEN
210 INFO = -3
211 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
212 INFO = -5
213 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
214 INFO = -7
215 ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN
216 INFO = -11
217 ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
218 INFO = -13
219 ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
220 INFO = -15
221 END IF
222 *
223 IF( INFO.EQ.0 ) THEN
224 NB1 = ILAENV( 1, 'ZGEQRF', ' ', N, N, -1, -1 )
225 NB2 = ILAENV( 1, 'ZUNMQR', ' ', N, N, N, -1 )
226 NB3 = ILAENV( 1, 'ZUNGQR', ' ', N, N, N, -1 )
227 NB = MAX( NB1, NB2, NB3 )
228 LOPT = N*( NB+1 )
229 WORK( 1 ) = LOPT
230 END IF
231 *
232 IF( INFO.NE.0 ) THEN
233 CALL XERBLA( 'ZGEGS ', -INFO )
234 RETURN
235 ELSE IF( LQUERY ) THEN
236 RETURN
237 END IF
238 *
239 * Quick return if possible
240 *
241 IF( N.EQ.0 )
242 $ RETURN
243 *
244 * Get machine constants
245 *
246 EPS = DLAMCH( 'E' )*DLAMCH( 'B' )
247 SAFMIN = DLAMCH( 'S' )
248 SMLNUM = N*SAFMIN / EPS
249 BIGNUM = ONE / SMLNUM
250 *
251 * Scale A if max element outside range [SMLNUM,BIGNUM]
252 *
253 ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK )
254 ILASCL = .FALSE.
255 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
256 ANRMTO = SMLNUM
257 ILASCL = .TRUE.
258 ELSE IF( ANRM.GT.BIGNUM ) THEN
259 ANRMTO = BIGNUM
260 ILASCL = .TRUE.
261 END IF
262 *
263 IF( ILASCL ) THEN
264 CALL ZLASCL( 'G', -1, -1, ANRM, ANRMTO, N, N, A, LDA, IINFO )
265 IF( IINFO.NE.0 ) THEN
266 INFO = N + 9
267 RETURN
268 END IF
269 END IF
270 *
271 * Scale B if max element outside range [SMLNUM,BIGNUM]
272 *
273 BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK )
274 ILBSCL = .FALSE.
275 IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
276 BNRMTO = SMLNUM
277 ILBSCL = .TRUE.
278 ELSE IF( BNRM.GT.BIGNUM ) THEN
279 BNRMTO = BIGNUM
280 ILBSCL = .TRUE.
281 END IF
282 *
283 IF( ILBSCL ) THEN
284 CALL ZLASCL( 'G', -1, -1, BNRM, BNRMTO, N, N, B, LDB, IINFO )
285 IF( IINFO.NE.0 ) THEN
286 INFO = N + 9
287 RETURN
288 END IF
289 END IF
290 *
291 * Permute the matrix to make it more nearly triangular
292 *
293 ILEFT = 1
294 IRIGHT = N + 1
295 IRWORK = IRIGHT + N
296 IWORK = 1
297 CALL ZGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ),
298 $ RWORK( IRIGHT ), RWORK( IRWORK ), IINFO )
299 IF( IINFO.NE.0 ) THEN
300 INFO = N + 1
301 GO TO 10
302 END IF
303 *
304 * Reduce B to triangular form, and initialize VSL and/or VSR
305 *
306 IROWS = IHI + 1 - ILO
307 ICOLS = N + 1 - ILO
308 ITAU = IWORK
309 IWORK = ITAU + IROWS
310 CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
311 $ WORK( IWORK ), LWORK+1-IWORK, IINFO )
312 IF( IINFO.GE.0 )
313 $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
314 IF( IINFO.NE.0 ) THEN
315 INFO = N + 2
316 GO TO 10
317 END IF
318 *
319 CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
320 $ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWORK ),
321 $ LWORK+1-IWORK, IINFO )
322 IF( IINFO.GE.0 )
323 $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
324 IF( IINFO.NE.0 ) THEN
325 INFO = N + 3
326 GO TO 10
327 END IF
328 *
329 IF( ILVSL ) THEN
330 CALL ZLASET( 'Full', N, N, CZERO, CONE, VSL, LDVSL )
331 CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
332 $ VSL( ILO+1, ILO ), LDVSL )
333 CALL ZUNGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL,
334 $ WORK( ITAU ), WORK( IWORK ), LWORK+1-IWORK,
335 $ IINFO )
336 IF( IINFO.GE.0 )
337 $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
338 IF( IINFO.NE.0 ) THEN
339 INFO = N + 4
340 GO TO 10
341 END IF
342 END IF
343 *
344 IF( ILVSR )
345 $ CALL ZLASET( 'Full', N, N, CZERO, CONE, VSR, LDVSR )
346 *
347 * Reduce to generalized Hessenberg form
348 *
349 CALL ZGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL,
350 $ LDVSL, VSR, LDVSR, IINFO )
351 IF( IINFO.NE.0 ) THEN
352 INFO = N + 5
353 GO TO 10
354 END IF
355 *
356 * Perform QZ algorithm, computing Schur vectors if desired
357 *
358 IWORK = ITAU
359 CALL ZHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB,
360 $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK( IWORK ),
361 $ LWORK+1-IWORK, RWORK( IRWORK ), IINFO )
362 IF( IINFO.GE.0 )
363 $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
364 IF( IINFO.NE.0 ) THEN
365 IF( IINFO.GT.0 .AND. IINFO.LE.N ) THEN
366 INFO = IINFO
367 ELSE IF( IINFO.GT.N .AND. IINFO.LE.2*N ) THEN
368 INFO = IINFO - N
369 ELSE
370 INFO = N + 6
371 END IF
372 GO TO 10
373 END IF
374 *
375 * Apply permutation to VSL and VSR
376 *
377 IF( ILVSL ) THEN
378 CALL ZGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ),
379 $ RWORK( IRIGHT ), N, VSL, LDVSL, IINFO )
380 IF( IINFO.NE.0 ) THEN
381 INFO = N + 7
382 GO TO 10
383 END IF
384 END IF
385 IF( ILVSR ) THEN
386 CALL ZGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ),
387 $ RWORK( IRIGHT ), N, VSR, LDVSR, IINFO )
388 IF( IINFO.NE.0 ) THEN
389 INFO = N + 8
390 GO TO 10
391 END IF
392 END IF
393 *
394 * Undo scaling
395 *
396 IF( ILASCL ) THEN
397 CALL ZLASCL( 'U', -1, -1, ANRMTO, ANRM, N, N, A, LDA, IINFO )
398 IF( IINFO.NE.0 ) THEN
399 INFO = N + 9
400 RETURN
401 END IF
402 CALL ZLASCL( 'G', -1, -1, ANRMTO, ANRM, N, 1, ALPHA, N, IINFO )
403 IF( IINFO.NE.0 ) THEN
404 INFO = N + 9
405 RETURN
406 END IF
407 END IF
408 *
409 IF( ILBSCL ) THEN
410 CALL ZLASCL( 'U', -1, -1, BNRMTO, BNRM, N, N, B, LDB, IINFO )
411 IF( IINFO.NE.0 ) THEN
412 INFO = N + 9
413 RETURN
414 END IF
415 CALL ZLASCL( 'G', -1, -1, BNRMTO, BNRM, N, 1, BETA, N, IINFO )
416 IF( IINFO.NE.0 ) THEN
417 INFO = N + 9
418 RETURN
419 END IF
420 END IF
421 *
422 10 CONTINUE
423 WORK( 1 ) = LWKOPT
424 *
425 RETURN
426 *
427 * End of ZGEGS
428 *
429 END