Annotation of rpl/lapack/lapack/zgegs.f, revision 1.16
1.8 bertrand 1: *> \brief <b> ZGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices</b>
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.14 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.14 bertrand 9: *> Download ZGEGS + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgegs.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgegs.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgegs.f">
1.8 bertrand 15: *> [TXT]</a>
1.14 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA,
22: * VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK,
23: * INFO )
1.14 bertrand 24: *
1.8 bertrand 25: * .. Scalar Arguments ..
26: * CHARACTER JOBVSL, JOBVSR
27: * INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N
28: * ..
29: * .. Array Arguments ..
30: * DOUBLE PRECISION RWORK( * )
31: * COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ),
32: * $ BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
33: * $ WORK( * )
34: * ..
1.14 bertrand 35: *
1.8 bertrand 36: *
37: *> \par Purpose:
38: * =============
39: *>
40: *> \verbatim
41: *>
42: *> This routine is deprecated and has been replaced by routine ZGGES.
43: *>
44: *> ZGEGS computes the eigenvalues, Schur form, and, optionally, the
45: *> left and or/right Schur vectors of a complex matrix pair (A,B).
46: *> Given two square matrices A and B, the generalized Schur
47: *> factorization has the form
1.14 bertrand 48: *>
1.8 bertrand 49: *> A = Q*S*Z**H, B = Q*T*Z**H
1.14 bertrand 50: *>
1.8 bertrand 51: *> where Q and Z are unitary matrices and S and T are upper triangular.
52: *> The columns of Q are the left Schur vectors
53: *> and the columns of Z are the right Schur vectors.
1.14 bertrand 54: *>
1.8 bertrand 55: *> If only the eigenvalues of (A,B) are needed, the driver routine
56: *> ZGEGV should be used instead. See ZGEGV for a description of the
57: *> eigenvalues of the generalized nonsymmetric eigenvalue problem
58: *> (GNEP).
59: *> \endverbatim
60: *
61: * Arguments:
62: * ==========
63: *
64: *> \param[in] JOBVSL
65: *> \verbatim
66: *> JOBVSL is CHARACTER*1
67: *> = 'N': do not compute the left Schur vectors;
68: *> = 'V': compute the left Schur vectors (returned in VSL).
69: *> \endverbatim
70: *>
71: *> \param[in] JOBVSR
72: *> \verbatim
73: *> JOBVSR is CHARACTER*1
74: *> = 'N': do not compute the right Schur vectors;
75: *> = 'V': compute the right Schur vectors (returned in VSR).
76: *> \endverbatim
77: *>
78: *> \param[in] N
79: *> \verbatim
80: *> N is INTEGER
81: *> The order of the matrices A, B, VSL, and VSR. N >= 0.
82: *> \endverbatim
83: *>
84: *> \param[in,out] A
85: *> \verbatim
86: *> A is COMPLEX*16 array, dimension (LDA, N)
87: *> On entry, the matrix A.
88: *> On exit, the upper triangular matrix S from the generalized
89: *> Schur factorization.
90: *> \endverbatim
91: *>
92: *> \param[in] LDA
93: *> \verbatim
94: *> LDA is INTEGER
95: *> The leading dimension of A. LDA >= max(1,N).
96: *> \endverbatim
97: *>
98: *> \param[in,out] B
99: *> \verbatim
100: *> B is COMPLEX*16 array, dimension (LDB, N)
101: *> On entry, the matrix B.
102: *> On exit, the upper triangular matrix T from the generalized
103: *> Schur factorization.
104: *> \endverbatim
105: *>
106: *> \param[in] LDB
107: *> \verbatim
108: *> LDB is INTEGER
109: *> The leading dimension of B. LDB >= max(1,N).
110: *> \endverbatim
111: *>
112: *> \param[out] ALPHA
113: *> \verbatim
114: *> ALPHA is COMPLEX*16 array, dimension (N)
115: *> The complex scalars alpha that define the eigenvalues of
116: *> GNEP. ALPHA(j) = S(j,j), the diagonal element of the Schur
117: *> form of A.
118: *> \endverbatim
119: *>
120: *> \param[out] BETA
121: *> \verbatim
122: *> BETA is COMPLEX*16 array, dimension (N)
123: *> The non-negative real scalars beta that define the
124: *> eigenvalues of GNEP. BETA(j) = T(j,j), the diagonal element
125: *> of the triangular factor T.
126: *>
127: *> Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
128: *> represent the j-th eigenvalue of the matrix pair (A,B), in
129: *> one of the forms lambda = alpha/beta or mu = beta/alpha.
130: *> Since either lambda or mu may overflow, they should not,
131: *> in general, be computed.
132: *> \endverbatim
133: *>
134: *> \param[out] VSL
135: *> \verbatim
136: *> VSL is COMPLEX*16 array, dimension (LDVSL,N)
137: *> If JOBVSL = 'V', the matrix of left Schur vectors Q.
138: *> Not referenced if JOBVSL = 'N'.
139: *> \endverbatim
140: *>
141: *> \param[in] LDVSL
142: *> \verbatim
143: *> LDVSL is INTEGER
144: *> The leading dimension of the matrix VSL. LDVSL >= 1, and
145: *> if JOBVSL = 'V', LDVSL >= N.
146: *> \endverbatim
147: *>
148: *> \param[out] VSR
149: *> \verbatim
150: *> VSR is COMPLEX*16 array, dimension (LDVSR,N)
151: *> If JOBVSR = 'V', the matrix of right Schur vectors Z.
152: *> Not referenced if JOBVSR = 'N'.
153: *> \endverbatim
154: *>
155: *> \param[in] LDVSR
156: *> \verbatim
157: *> LDVSR is INTEGER
158: *> The leading dimension of the matrix VSR. LDVSR >= 1, and
159: *> if JOBVSR = 'V', LDVSR >= N.
160: *> \endverbatim
161: *>
162: *> \param[out] WORK
163: *> \verbatim
164: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
165: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
166: *> \endverbatim
167: *>
168: *> \param[in] LWORK
169: *> \verbatim
170: *> LWORK is INTEGER
171: *> The dimension of the array WORK. LWORK >= max(1,2*N).
172: *> For good performance, LWORK must generally be larger.
173: *> To compute the optimal value of LWORK, call ILAENV to get
174: *> blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.) Then compute:
175: *> NB -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR;
176: *> the optimal LWORK is N*(NB+1).
177: *>
178: *> If LWORK = -1, then a workspace query is assumed; the routine
179: *> only calculates the optimal size of the WORK array, returns
180: *> this value as the first entry of the WORK array, and no error
181: *> message related to LWORK is issued by XERBLA.
182: *> \endverbatim
183: *>
184: *> \param[out] RWORK
185: *> \verbatim
186: *> RWORK is DOUBLE PRECISION array, dimension (3*N)
187: *> \endverbatim
188: *>
189: *> \param[out] INFO
190: *> \verbatim
191: *> INFO is INTEGER
192: *> = 0: successful exit
193: *> < 0: if INFO = -i, the i-th argument had an illegal value.
194: *> =1,...,N:
195: *> The QZ iteration failed. (A,B) are not in Schur
196: *> form, but ALPHA(j) and BETA(j) should be correct for
197: *> j=INFO+1,...,N.
198: *> > N: errors that usually indicate LAPACK problems:
199: *> =N+1: error return from ZGGBAL
200: *> =N+2: error return from ZGEQRF
201: *> =N+3: error return from ZUNMQR
202: *> =N+4: error return from ZUNGQR
203: *> =N+5: error return from ZGGHRD
204: *> =N+6: error return from ZHGEQZ (other than failed
205: *> iteration)
206: *> =N+7: error return from ZGGBAK (computing VSL)
207: *> =N+8: error return from ZGGBAK (computing VSR)
208: *> =N+9: error return from ZLASCL (various places)
209: *> \endverbatim
210: *
211: * Authors:
212: * ========
213: *
1.14 bertrand 214: *> \author Univ. of Tennessee
215: *> \author Univ. of California Berkeley
216: *> \author Univ. of Colorado Denver
217: *> \author NAG Ltd.
1.8 bertrand 218: *
1.14 bertrand 219: *> \date December 2016
1.8 bertrand 220: *
221: *> \ingroup complex16GEeigen
222: *
223: * =====================================================================
1.1 bertrand 224: SUBROUTINE ZGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA,
225: $ VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK,
226: $ INFO )
227: *
1.14 bertrand 228: * -- LAPACK driver routine (version 3.7.0) --
1.1 bertrand 229: * -- LAPACK is a software package provided by Univ. of Tennessee, --
230: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.14 bertrand 231: * December 2016
1.1 bertrand 232: *
233: * .. Scalar Arguments ..
234: CHARACTER JOBVSL, JOBVSR
235: INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N
236: * ..
237: * .. Array Arguments ..
238: DOUBLE PRECISION RWORK( * )
239: COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ),
240: $ BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
241: $ WORK( * )
242: * ..
243: *
244: * =====================================================================
245: *
246: * .. Parameters ..
247: DOUBLE PRECISION ZERO, ONE
248: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
249: COMPLEX*16 CZERO, CONE
250: PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ),
251: $ CONE = ( 1.0D0, 0.0D0 ) )
252: * ..
253: * .. Local Scalars ..
254: LOGICAL ILASCL, ILBSCL, ILVSL, ILVSR, LQUERY
255: INTEGER ICOLS, IHI, IINFO, IJOBVL, IJOBVR, ILEFT, ILO,
256: $ IRIGHT, IROWS, IRWORK, ITAU, IWORK, LOPT,
257: $ LWKMIN, LWKOPT, NB, NB1, NB2, NB3
258: DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS,
259: $ SAFMIN, SMLNUM
260: * ..
261: * .. External Subroutines ..
262: EXTERNAL XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHRD, ZHGEQZ,
263: $ ZLACPY, ZLASCL, ZLASET, ZUNGQR, ZUNMQR
264: * ..
265: * .. External Functions ..
266: LOGICAL LSAME
267: INTEGER ILAENV
268: DOUBLE PRECISION DLAMCH, ZLANGE
269: EXTERNAL LSAME, ILAENV, DLAMCH, ZLANGE
270: * ..
271: * .. Intrinsic Functions ..
272: INTRINSIC INT, MAX
273: * ..
274: * .. Executable Statements ..
275: *
276: * Decode the input arguments
277: *
278: IF( LSAME( JOBVSL, 'N' ) ) THEN
279: IJOBVL = 1
280: ILVSL = .FALSE.
281: ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN
282: IJOBVL = 2
283: ILVSL = .TRUE.
284: ELSE
285: IJOBVL = -1
286: ILVSL = .FALSE.
287: END IF
288: *
289: IF( LSAME( JOBVSR, 'N' ) ) THEN
290: IJOBVR = 1
291: ILVSR = .FALSE.
292: ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN
293: IJOBVR = 2
294: ILVSR = .TRUE.
295: ELSE
296: IJOBVR = -1
297: ILVSR = .FALSE.
298: END IF
299: *
300: * Test the input arguments
301: *
302: LWKMIN = MAX( 2*N, 1 )
303: LWKOPT = LWKMIN
304: WORK( 1 ) = LWKOPT
305: LQUERY = ( LWORK.EQ.-1 )
306: INFO = 0
307: IF( IJOBVL.LE.0 ) THEN
308: INFO = -1
309: ELSE IF( IJOBVR.LE.0 ) THEN
310: INFO = -2
311: ELSE IF( N.LT.0 ) THEN
312: INFO = -3
313: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
314: INFO = -5
315: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
316: INFO = -7
317: ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN
318: INFO = -11
319: ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
320: INFO = -13
321: ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
322: INFO = -15
323: END IF
324: *
325: IF( INFO.EQ.0 ) THEN
326: NB1 = ILAENV( 1, 'ZGEQRF', ' ', N, N, -1, -1 )
327: NB2 = ILAENV( 1, 'ZUNMQR', ' ', N, N, N, -1 )
328: NB3 = ILAENV( 1, 'ZUNGQR', ' ', N, N, N, -1 )
329: NB = MAX( NB1, NB2, NB3 )
330: LOPT = N*( NB+1 )
331: WORK( 1 ) = LOPT
332: END IF
333: *
334: IF( INFO.NE.0 ) THEN
335: CALL XERBLA( 'ZGEGS ', -INFO )
336: RETURN
337: ELSE IF( LQUERY ) THEN
338: RETURN
339: END IF
340: *
341: * Quick return if possible
342: *
343: IF( N.EQ.0 )
344: $ RETURN
345: *
346: * Get machine constants
347: *
348: EPS = DLAMCH( 'E' )*DLAMCH( 'B' )
349: SAFMIN = DLAMCH( 'S' )
350: SMLNUM = N*SAFMIN / EPS
351: BIGNUM = ONE / SMLNUM
352: *
353: * Scale A if max element outside range [SMLNUM,BIGNUM]
354: *
355: ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK )
356: ILASCL = .FALSE.
357: IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
358: ANRMTO = SMLNUM
359: ILASCL = .TRUE.
360: ELSE IF( ANRM.GT.BIGNUM ) THEN
361: ANRMTO = BIGNUM
362: ILASCL = .TRUE.
363: END IF
364: *
365: IF( ILASCL ) THEN
366: CALL ZLASCL( 'G', -1, -1, ANRM, ANRMTO, N, N, A, LDA, IINFO )
367: IF( IINFO.NE.0 ) THEN
368: INFO = N + 9
369: RETURN
370: END IF
371: END IF
372: *
373: * Scale B if max element outside range [SMLNUM,BIGNUM]
374: *
375: BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK )
376: ILBSCL = .FALSE.
377: IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
378: BNRMTO = SMLNUM
379: ILBSCL = .TRUE.
380: ELSE IF( BNRM.GT.BIGNUM ) THEN
381: BNRMTO = BIGNUM
382: ILBSCL = .TRUE.
383: END IF
384: *
385: IF( ILBSCL ) THEN
386: CALL ZLASCL( 'G', -1, -1, BNRM, BNRMTO, N, N, B, LDB, IINFO )
387: IF( IINFO.NE.0 ) THEN
388: INFO = N + 9
389: RETURN
390: END IF
391: END IF
392: *
393: * Permute the matrix to make it more nearly triangular
394: *
395: ILEFT = 1
396: IRIGHT = N + 1
397: IRWORK = IRIGHT + N
398: IWORK = 1
399: CALL ZGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ),
400: $ RWORK( IRIGHT ), RWORK( IRWORK ), IINFO )
401: IF( IINFO.NE.0 ) THEN
402: INFO = N + 1
403: GO TO 10
404: END IF
405: *
406: * Reduce B to triangular form, and initialize VSL and/or VSR
407: *
408: IROWS = IHI + 1 - ILO
409: ICOLS = N + 1 - ILO
410: ITAU = IWORK
411: IWORK = ITAU + IROWS
412: CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
413: $ WORK( IWORK ), LWORK+1-IWORK, IINFO )
414: IF( IINFO.GE.0 )
415: $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
416: IF( IINFO.NE.0 ) THEN
417: INFO = N + 2
418: GO TO 10
419: END IF
420: *
421: CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
422: $ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWORK ),
423: $ LWORK+1-IWORK, IINFO )
424: IF( IINFO.GE.0 )
425: $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
426: IF( IINFO.NE.0 ) THEN
427: INFO = N + 3
428: GO TO 10
429: END IF
430: *
431: IF( ILVSL ) THEN
432: CALL ZLASET( 'Full', N, N, CZERO, CONE, VSL, LDVSL )
433: CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
434: $ VSL( ILO+1, ILO ), LDVSL )
435: CALL ZUNGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL,
436: $ WORK( ITAU ), WORK( IWORK ), LWORK+1-IWORK,
437: $ IINFO )
438: IF( IINFO.GE.0 )
439: $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
440: IF( IINFO.NE.0 ) THEN
441: INFO = N + 4
442: GO TO 10
443: END IF
444: END IF
445: *
446: IF( ILVSR )
447: $ CALL ZLASET( 'Full', N, N, CZERO, CONE, VSR, LDVSR )
448: *
449: * Reduce to generalized Hessenberg form
450: *
451: CALL ZGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL,
452: $ LDVSL, VSR, LDVSR, IINFO )
453: IF( IINFO.NE.0 ) THEN
454: INFO = N + 5
455: GO TO 10
456: END IF
457: *
458: * Perform QZ algorithm, computing Schur vectors if desired
459: *
460: IWORK = ITAU
461: CALL ZHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB,
462: $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK( IWORK ),
463: $ LWORK+1-IWORK, RWORK( IRWORK ), IINFO )
464: IF( IINFO.GE.0 )
465: $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
466: IF( IINFO.NE.0 ) THEN
467: IF( IINFO.GT.0 .AND. IINFO.LE.N ) THEN
468: INFO = IINFO
469: ELSE IF( IINFO.GT.N .AND. IINFO.LE.2*N ) THEN
470: INFO = IINFO - N
471: ELSE
472: INFO = N + 6
473: END IF
474: GO TO 10
475: END IF
476: *
477: * Apply permutation to VSL and VSR
478: *
479: IF( ILVSL ) THEN
480: CALL ZGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ),
481: $ RWORK( IRIGHT ), N, VSL, LDVSL, IINFO )
482: IF( IINFO.NE.0 ) THEN
483: INFO = N + 7
484: GO TO 10
485: END IF
486: END IF
487: IF( ILVSR ) THEN
488: CALL ZGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ),
489: $ RWORK( IRIGHT ), N, VSR, LDVSR, IINFO )
490: IF( IINFO.NE.0 ) THEN
491: INFO = N + 8
492: GO TO 10
493: END IF
494: END IF
495: *
496: * Undo scaling
497: *
498: IF( ILASCL ) THEN
499: CALL ZLASCL( 'U', -1, -1, ANRMTO, ANRM, N, N, A, LDA, IINFO )
500: IF( IINFO.NE.0 ) THEN
501: INFO = N + 9
502: RETURN
503: END IF
504: CALL ZLASCL( 'G', -1, -1, ANRMTO, ANRM, N, 1, ALPHA, N, IINFO )
505: IF( IINFO.NE.0 ) THEN
506: INFO = N + 9
507: RETURN
508: END IF
509: END IF
510: *
511: IF( ILBSCL ) THEN
512: CALL ZLASCL( 'U', -1, -1, BNRMTO, BNRM, N, N, B, LDB, IINFO )
513: IF( IINFO.NE.0 ) THEN
514: INFO = N + 9
515: RETURN
516: END IF
517: CALL ZLASCL( 'G', -1, -1, BNRMTO, BNRM, N, 1, BETA, N, IINFO )
518: IF( IINFO.NE.0 ) THEN
519: INFO = N + 9
520: RETURN
521: END IF
522: END IF
523: *
524: 10 CONTINUE
525: WORK( 1 ) = LWKOPT
526: *
527: RETURN
528: *
529: * End of ZGEGS
530: *
531: END
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