1: *> \brief <b> DGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices</b>
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DGGEV + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dggev.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dggev.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dggev.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI,
22: * BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER JOBVL, JOBVR
26: * INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, N
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
30: * $ B( LDB, * ), BETA( * ), VL( LDVL, * ),
31: * $ VR( LDVR, * ), WORK( * )
32: * ..
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> DGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B)
41: *> the generalized eigenvalues, and optionally, the left and/or right
42: *> generalized eigenvectors.
43: *>
44: *> A generalized eigenvalue for a pair of matrices (A,B) is a scalar
45: *> lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
46: *> singular. It is usually represented as the pair (alpha,beta), as
47: *> there is a reasonable interpretation for beta=0, and even for both
48: *> being zero.
49: *>
50: *> The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
51: *> of (A,B) satisfies
52: *>
53: *> A * v(j) = lambda(j) * B * v(j).
54: *>
55: *> The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
56: *> of (A,B) satisfies
57: *>
58: *> u(j)**H * A = lambda(j) * u(j)**H * B .
59: *>
60: *> where u(j)**H is the conjugate-transpose of u(j).
61: *>
62: *> \endverbatim
63: *
64: * Arguments:
65: * ==========
66: *
67: *> \param[in] JOBVL
68: *> \verbatim
69: *> JOBVL is CHARACTER*1
70: *> = 'N': do not compute the left generalized eigenvectors;
71: *> = 'V': compute the left generalized eigenvectors.
72: *> \endverbatim
73: *>
74: *> \param[in] JOBVR
75: *> \verbatim
76: *> JOBVR is CHARACTER*1
77: *> = 'N': do not compute the right generalized eigenvectors;
78: *> = 'V': compute the right generalized eigenvectors.
79: *> \endverbatim
80: *>
81: *> \param[in] N
82: *> \verbatim
83: *> N is INTEGER
84: *> The order of the matrices A, B, VL, and VR. N >= 0.
85: *> \endverbatim
86: *>
87: *> \param[in,out] A
88: *> \verbatim
89: *> A is DOUBLE PRECISION array, dimension (LDA, N)
90: *> On entry, the matrix A in the pair (A,B).
91: *> On exit, A has been overwritten.
92: *> \endverbatim
93: *>
94: *> \param[in] LDA
95: *> \verbatim
96: *> LDA is INTEGER
97: *> The leading dimension of A. LDA >= max(1,N).
98: *> \endverbatim
99: *>
100: *> \param[in,out] B
101: *> \verbatim
102: *> B is DOUBLE PRECISION array, dimension (LDB, N)
103: *> On entry, the matrix B in the pair (A,B).
104: *> On exit, B has been overwritten.
105: *> \endverbatim
106: *>
107: *> \param[in] LDB
108: *> \verbatim
109: *> LDB is INTEGER
110: *> The leading dimension of B. LDB >= max(1,N).
111: *> \endverbatim
112: *>
113: *> \param[out] ALPHAR
114: *> \verbatim
115: *> ALPHAR is DOUBLE PRECISION array, dimension (N)
116: *> \endverbatim
117: *>
118: *> \param[out] ALPHAI
119: *> \verbatim
120: *> ALPHAI is DOUBLE PRECISION array, dimension (N)
121: *> \endverbatim
122: *>
123: *> \param[out] BETA
124: *> \verbatim
125: *> BETA is DOUBLE PRECISION array, dimension (N)
126: *> On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
127: *> be the generalized eigenvalues. If ALPHAI(j) is zero, then
128: *> the j-th eigenvalue is real; if positive, then the j-th and
129: *> (j+1)-st eigenvalues are a complex conjugate pair, with
130: *> ALPHAI(j+1) negative.
131: *>
132: *> Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
133: *> may easily over- or underflow, and BETA(j) may even be zero.
134: *> Thus, the user should avoid naively computing the ratio
135: *> alpha/beta. However, ALPHAR and ALPHAI will be always less
136: *> than and usually comparable with norm(A) in magnitude, and
137: *> BETA always less than and usually comparable with norm(B).
138: *> \endverbatim
139: *>
140: *> \param[out] VL
141: *> \verbatim
142: *> VL is DOUBLE PRECISION array, dimension (LDVL,N)
143: *> If JOBVL = 'V', the left eigenvectors u(j) are stored one
144: *> after another in the columns of VL, in the same order as
145: *> their eigenvalues. If the j-th eigenvalue is real, then
146: *> u(j) = VL(:,j), the j-th column of VL. If the j-th and
147: *> (j+1)-th eigenvalues form a complex conjugate pair, then
148: *> u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1).
149: *> Each eigenvector is scaled so the largest component has
150: *> abs(real part)+abs(imag. part)=1.
151: *> Not referenced if JOBVL = 'N'.
152: *> \endverbatim
153: *>
154: *> \param[in] LDVL
155: *> \verbatim
156: *> LDVL is INTEGER
157: *> The leading dimension of the matrix VL. LDVL >= 1, and
158: *> if JOBVL = 'V', LDVL >= N.
159: *> \endverbatim
160: *>
161: *> \param[out] VR
162: *> \verbatim
163: *> VR is DOUBLE PRECISION array, dimension (LDVR,N)
164: *> If JOBVR = 'V', the right eigenvectors v(j) are stored one
165: *> after another in the columns of VR, in the same order as
166: *> their eigenvalues. If the j-th eigenvalue is real, then
167: *> v(j) = VR(:,j), the j-th column of VR. If the j-th and
168: *> (j+1)-th eigenvalues form a complex conjugate pair, then
169: *> v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1).
170: *> Each eigenvector is scaled so the largest component has
171: *> abs(real part)+abs(imag. part)=1.
172: *> Not referenced if JOBVR = 'N'.
173: *> \endverbatim
174: *>
175: *> \param[in] LDVR
176: *> \verbatim
177: *> LDVR is INTEGER
178: *> The leading dimension of the matrix VR. LDVR >= 1, and
179: *> if JOBVR = 'V', LDVR >= N.
180: *> \endverbatim
181: *>
182: *> \param[out] WORK
183: *> \verbatim
184: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
185: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
186: *> \endverbatim
187: *>
188: *> \param[in] LWORK
189: *> \verbatim
190: *> LWORK is INTEGER
191: *> The dimension of the array WORK. LWORK >= max(1,8*N).
192: *> For good performance, LWORK must generally be larger.
193: *>
194: *> If LWORK = -1, then a workspace query is assumed; the routine
195: *> only calculates the optimal size of the WORK array, returns
196: *> this value as the first entry of the WORK array, and no error
197: *> message related to LWORK is issued by XERBLA.
198: *> \endverbatim
199: *>
200: *> \param[out] INFO
201: *> \verbatim
202: *> INFO is INTEGER
203: *> = 0: successful exit
204: *> < 0: if INFO = -i, the i-th argument had an illegal value.
205: *> = 1,...,N:
206: *> The QZ iteration failed. No eigenvectors have been
207: *> calculated, but ALPHAR(j), ALPHAI(j), and BETA(j)
208: *> should be correct for j=INFO+1,...,N.
209: *> > N: =N+1: other than QZ iteration failed in DHGEQZ.
210: *> =N+2: error return from DTGEVC.
211: *> \endverbatim
212: *
213: * Authors:
214: * ========
215: *
216: *> \author Univ. of Tennessee
217: *> \author Univ. of California Berkeley
218: *> \author Univ. of Colorado Denver
219: *> \author NAG Ltd.
220: *
221: *> \date November 2011
222: *
223: *> \ingroup doubleGEeigen
224: *
225: * =====================================================================
226: SUBROUTINE DGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI,
227: $ BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )
228: *
229: * -- LAPACK driver routine (version 3.4.0) --
230: * -- LAPACK is a software package provided by Univ. of Tennessee, --
231: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
232: * November 2011
233: *
234: * .. Scalar Arguments ..
235: CHARACTER JOBVL, JOBVR
236: INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, N
237: * ..
238: * .. Array Arguments ..
239: DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
240: $ B( LDB, * ), BETA( * ), VL( LDVL, * ),
241: $ VR( LDVR, * ), WORK( * )
242: * ..
243: *
244: * =====================================================================
245: *
246: * .. Parameters ..
247: DOUBLE PRECISION ZERO, ONE
248: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
249: * ..
250: * .. Local Scalars ..
251: LOGICAL ILASCL, ILBSCL, ILV, ILVL, ILVR, LQUERY
252: CHARACTER CHTEMP
253: INTEGER ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT, ILO,
254: $ IN, IRIGHT, IROWS, ITAU, IWRK, JC, JR, MAXWRK,
255: $ MINWRK
256: DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS,
257: $ SMLNUM, TEMP
258: * ..
259: * .. Local Arrays ..
260: LOGICAL LDUMMA( 1 )
261: * ..
262: * .. External Subroutines ..
263: EXTERNAL DGEQRF, DGGBAK, DGGBAL, DGGHRD, DHGEQZ, DLABAD,
264: $ DLACPY,DLASCL, DLASET, DORGQR, DORMQR, DTGEVC,
265: $ XERBLA
266: * ..
267: * .. External Functions ..
268: LOGICAL LSAME
269: INTEGER ILAENV
270: DOUBLE PRECISION DLAMCH, DLANGE
271: EXTERNAL LSAME, ILAENV, DLAMCH, DLANGE
272: * ..
273: * .. Intrinsic Functions ..
274: INTRINSIC ABS, MAX, SQRT
275: * ..
276: * .. Executable Statements ..
277: *
278: * Decode the input arguments
279: *
280: IF( LSAME( JOBVL, 'N' ) ) THEN
281: IJOBVL = 1
282: ILVL = .FALSE.
283: ELSE IF( LSAME( JOBVL, 'V' ) ) THEN
284: IJOBVL = 2
285: ILVL = .TRUE.
286: ELSE
287: IJOBVL = -1
288: ILVL = .FALSE.
289: END IF
290: *
291: IF( LSAME( JOBVR, 'N' ) ) THEN
292: IJOBVR = 1
293: ILVR = .FALSE.
294: ELSE IF( LSAME( JOBVR, 'V' ) ) THEN
295: IJOBVR = 2
296: ILVR = .TRUE.
297: ELSE
298: IJOBVR = -1
299: ILVR = .FALSE.
300: END IF
301: ILV = ILVL .OR. ILVR
302: *
303: * Test the input arguments
304: *
305: INFO = 0
306: LQUERY = ( LWORK.EQ.-1 )
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( LDVL.LT.1 .OR. ( ILVL .AND. LDVL.LT.N ) ) THEN
318: INFO = -12
319: ELSE IF( LDVR.LT.1 .OR. ( ILVR .AND. LDVR.LT.N ) ) THEN
320: INFO = -14
321: END IF
322: *
323: * Compute workspace
324: * (Note: Comments in the code beginning "Workspace:" describe the
325: * minimal amount of workspace needed at that point in the code,
326: * as well as the preferred amount for good performance.
327: * NB refers to the optimal block size for the immediately
328: * following subroutine, as returned by ILAENV. The workspace is
329: * computed assuming ILO = 1 and IHI = N, the worst case.)
330: *
331: IF( INFO.EQ.0 ) THEN
332: MINWRK = MAX( 1, 8*N )
333: MAXWRK = MAX( 1, N*( 7 +
334: $ ILAENV( 1, 'DGEQRF', ' ', N, 1, N, 0 ) ) )
335: MAXWRK = MAX( MAXWRK, N*( 7 +
336: $ ILAENV( 1, 'DORMQR', ' ', N, 1, N, 0 ) ) )
337: IF( ILVL ) THEN
338: MAXWRK = MAX( MAXWRK, N*( 7 +
339: $ ILAENV( 1, 'DORGQR', ' ', N, 1, N, -1 ) ) )
340: END IF
341: WORK( 1 ) = MAXWRK
342: *
343: IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY )
344: $ INFO = -16
345: END IF
346: *
347: IF( INFO.NE.0 ) THEN
348: CALL XERBLA( 'DGGEV ', -INFO )
349: RETURN
350: ELSE IF( LQUERY ) THEN
351: RETURN
352: END IF
353: *
354: * Quick return if possible
355: *
356: IF( N.EQ.0 )
357: $ RETURN
358: *
359: * Get machine constants
360: *
361: EPS = DLAMCH( 'P' )
362: SMLNUM = DLAMCH( 'S' )
363: BIGNUM = ONE / SMLNUM
364: CALL DLABAD( SMLNUM, BIGNUM )
365: SMLNUM = SQRT( SMLNUM ) / EPS
366: BIGNUM = ONE / SMLNUM
367: *
368: * Scale A if max element outside range [SMLNUM,BIGNUM]
369: *
370: ANRM = DLANGE( 'M', N, N, A, LDA, WORK )
371: ILASCL = .FALSE.
372: IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
373: ANRMTO = SMLNUM
374: ILASCL = .TRUE.
375: ELSE IF( ANRM.GT.BIGNUM ) THEN
376: ANRMTO = BIGNUM
377: ILASCL = .TRUE.
378: END IF
379: IF( ILASCL )
380: $ CALL DLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
381: *
382: * Scale B if max element outside range [SMLNUM,BIGNUM]
383: *
384: BNRM = DLANGE( 'M', N, N, B, LDB, WORK )
385: ILBSCL = .FALSE.
386: IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
387: BNRMTO = SMLNUM
388: ILBSCL = .TRUE.
389: ELSE IF( BNRM.GT.BIGNUM ) THEN
390: BNRMTO = BIGNUM
391: ILBSCL = .TRUE.
392: END IF
393: IF( ILBSCL )
394: $ CALL DLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR )
395: *
396: * Permute the matrices A, B to isolate eigenvalues if possible
397: * (Workspace: need 6*N)
398: *
399: ILEFT = 1
400: IRIGHT = N + 1
401: IWRK = IRIGHT + N
402: CALL DGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, WORK( ILEFT ),
403: $ WORK( IRIGHT ), WORK( IWRK ), IERR )
404: *
405: * Reduce B to triangular form (QR decomposition of B)
406: * (Workspace: need N, prefer N*NB)
407: *
408: IROWS = IHI + 1 - ILO
409: IF( ILV ) THEN
410: ICOLS = N + 1 - ILO
411: ELSE
412: ICOLS = IROWS
413: END IF
414: ITAU = IWRK
415: IWRK = ITAU + IROWS
416: CALL DGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
417: $ WORK( IWRK ), LWORK+1-IWRK, IERR )
418: *
419: * Apply the orthogonal transformation to matrix A
420: * (Workspace: need N, prefer N*NB)
421: *
422: CALL DORMQR( 'L', 'T', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
423: $ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ),
424: $ LWORK+1-IWRK, IERR )
425: *
426: * Initialize VL
427: * (Workspace: need N, prefer N*NB)
428: *
429: IF( ILVL ) THEN
430: CALL DLASET( 'Full', N, N, ZERO, ONE, VL, LDVL )
431: IF( IROWS.GT.1 ) THEN
432: CALL DLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
433: $ VL( ILO+1, ILO ), LDVL )
434: END IF
435: CALL DORGQR( IROWS, IROWS, IROWS, VL( ILO, ILO ), LDVL,
436: $ WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR )
437: END IF
438: *
439: * Initialize VR
440: *
441: IF( ILVR )
442: $ CALL DLASET( 'Full', N, N, ZERO, ONE, VR, LDVR )
443: *
444: * Reduce to generalized Hessenberg form
445: * (Workspace: none needed)
446: *
447: IF( ILV ) THEN
448: *
449: * Eigenvectors requested -- work on whole matrix.
450: *
451: CALL DGGHRD( JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB, VL,
452: $ LDVL, VR, LDVR, IERR )
453: ELSE
454: CALL DGGHRD( 'N', 'N', IROWS, 1, IROWS, A( ILO, ILO ), LDA,
455: $ B( ILO, ILO ), LDB, VL, LDVL, VR, LDVR, IERR )
456: END IF
457: *
458: * Perform QZ algorithm (Compute eigenvalues, and optionally, the
459: * Schur forms and Schur vectors)
460: * (Workspace: need N)
461: *
462: IWRK = ITAU
463: IF( ILV ) THEN
464: CHTEMP = 'S'
465: ELSE
466: CHTEMP = 'E'
467: END IF
468: CALL DHGEQZ( CHTEMP, JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB,
469: $ ALPHAR, ALPHAI, BETA, VL, LDVL, VR, LDVR,
470: $ WORK( IWRK ), LWORK+1-IWRK, IERR )
471: IF( IERR.NE.0 ) THEN
472: IF( IERR.GT.0 .AND. IERR.LE.N ) THEN
473: INFO = IERR
474: ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN
475: INFO = IERR - N
476: ELSE
477: INFO = N + 1
478: END IF
479: GO TO 110
480: END IF
481: *
482: * Compute Eigenvectors
483: * (Workspace: need 6*N)
484: *
485: IF( ILV ) THEN
486: IF( ILVL ) THEN
487: IF( ILVR ) THEN
488: CHTEMP = 'B'
489: ELSE
490: CHTEMP = 'L'
491: END IF
492: ELSE
493: CHTEMP = 'R'
494: END IF
495: CALL DTGEVC( CHTEMP, 'B', LDUMMA, N, A, LDA, B, LDB, VL, LDVL,
496: $ VR, LDVR, N, IN, WORK( IWRK ), IERR )
497: IF( IERR.NE.0 ) THEN
498: INFO = N + 2
499: GO TO 110
500: END IF
501: *
502: * Undo balancing on VL and VR and normalization
503: * (Workspace: none needed)
504: *
505: IF( ILVL ) THEN
506: CALL DGGBAK( 'P', 'L', N, ILO, IHI, WORK( ILEFT ),
507: $ WORK( IRIGHT ), N, VL, LDVL, IERR )
508: DO 50 JC = 1, N
509: IF( ALPHAI( JC ).LT.ZERO )
510: $ GO TO 50
511: TEMP = ZERO
512: IF( ALPHAI( JC ).EQ.ZERO ) THEN
513: DO 10 JR = 1, N
514: TEMP = MAX( TEMP, ABS( VL( JR, JC ) ) )
515: 10 CONTINUE
516: ELSE
517: DO 20 JR = 1, N
518: TEMP = MAX( TEMP, ABS( VL( JR, JC ) )+
519: $ ABS( VL( JR, JC+1 ) ) )
520: 20 CONTINUE
521: END IF
522: IF( TEMP.LT.SMLNUM )
523: $ GO TO 50
524: TEMP = ONE / TEMP
525: IF( ALPHAI( JC ).EQ.ZERO ) THEN
526: DO 30 JR = 1, N
527: VL( JR, JC ) = VL( JR, JC )*TEMP
528: 30 CONTINUE
529: ELSE
530: DO 40 JR = 1, N
531: VL( JR, JC ) = VL( JR, JC )*TEMP
532: VL( JR, JC+1 ) = VL( JR, JC+1 )*TEMP
533: 40 CONTINUE
534: END IF
535: 50 CONTINUE
536: END IF
537: IF( ILVR ) THEN
538: CALL DGGBAK( 'P', 'R', N, ILO, IHI, WORK( ILEFT ),
539: $ WORK( IRIGHT ), N, VR, LDVR, IERR )
540: DO 100 JC = 1, N
541: IF( ALPHAI( JC ).LT.ZERO )
542: $ GO TO 100
543: TEMP = ZERO
544: IF( ALPHAI( JC ).EQ.ZERO ) THEN
545: DO 60 JR = 1, N
546: TEMP = MAX( TEMP, ABS( VR( JR, JC ) ) )
547: 60 CONTINUE
548: ELSE
549: DO 70 JR = 1, N
550: TEMP = MAX( TEMP, ABS( VR( JR, JC ) )+
551: $ ABS( VR( JR, JC+1 ) ) )
552: 70 CONTINUE
553: END IF
554: IF( TEMP.LT.SMLNUM )
555: $ GO TO 100
556: TEMP = ONE / TEMP
557: IF( ALPHAI( JC ).EQ.ZERO ) THEN
558: DO 80 JR = 1, N
559: VR( JR, JC ) = VR( JR, JC )*TEMP
560: 80 CONTINUE
561: ELSE
562: DO 90 JR = 1, N
563: VR( JR, JC ) = VR( JR, JC )*TEMP
564: VR( JR, JC+1 ) = VR( JR, JC+1 )*TEMP
565: 90 CONTINUE
566: END IF
567: 100 CONTINUE
568: END IF
569: *
570: * End of eigenvector calculation
571: *
572: END IF
573: *
574: * Undo scaling if necessary
575: *
576: IF( ILASCL ) THEN
577: CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAR, N, IERR )
578: CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAI, N, IERR )
579: END IF
580: *
581: IF( ILBSCL ) THEN
582: CALL DLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
583: END IF
584: *
585: 110 CONTINUE
586: *
587: WORK( 1 ) = MAXWRK
588: *
589: RETURN
590: *
591: * End of DGGEV
592: *
593: END
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