1: *> \brief <b> ZGEEVX 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 ZGEEVX + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeevx.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgeevx.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeevx.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL,
22: * LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE,
23: * RCONDV, WORK, LWORK, RWORK, INFO )
24: *
25: * .. Scalar Arguments ..
26: * CHARACTER BALANC, JOBVL, JOBVR, SENSE
27: * INTEGER IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N
28: * DOUBLE PRECISION ABNRM
29: * ..
30: * .. Array Arguments ..
31: * DOUBLE PRECISION RCONDE( * ), RCONDV( * ), RWORK( * ),
32: * $ SCALE( * )
33: * COMPLEX*16 A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ),
34: * $ W( * ), WORK( * )
35: * ..
36: *
37: *
38: *> \par Purpose:
39: * =============
40: *>
41: *> \verbatim
42: *>
43: *> ZGEEVX computes for an N-by-N complex nonsymmetric matrix A, the
44: *> eigenvalues and, optionally, the left and/or right eigenvectors.
45: *>
46: *> Optionally also, it computes a balancing transformation to improve
47: *> the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
48: *> SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues
49: *> (RCONDE), and reciprocal condition numbers for the right
50: *> eigenvectors (RCONDV).
51: *>
52: *> The right eigenvector v(j) of A satisfies
53: *> A * v(j) = lambda(j) * v(j)
54: *> where lambda(j) is its eigenvalue.
55: *> The left eigenvector u(j) of A satisfies
56: *> u(j)**H * A = lambda(j) * u(j)**H
57: *> where u(j)**H denotes the conjugate transpose of u(j).
58: *>
59: *> The computed eigenvectors are normalized to have Euclidean norm
60: *> equal to 1 and largest component real.
61: *>
62: *> Balancing a matrix means permuting the rows and columns to make it
63: *> more nearly upper triangular, and applying a diagonal similarity
64: *> transformation D * A * D**(-1), where D is a diagonal matrix, to
65: *> make its rows and columns closer in norm and the condition numbers
66: *> of its eigenvalues and eigenvectors smaller. The computed
67: *> reciprocal condition numbers correspond to the balanced matrix.
68: *> Permuting rows and columns will not change the condition numbers
69: *> (in exact arithmetic) but diagonal scaling will. For further
70: *> explanation of balancing, see section 4.10.2 of the LAPACK
71: *> Users' Guide.
72: *> \endverbatim
73: *
74: * Arguments:
75: * ==========
76: *
77: *> \param[in] BALANC
78: *> \verbatim
79: *> BALANC is CHARACTER*1
80: *> Indicates how the input matrix should be diagonally scaled
81: *> and/or permuted to improve the conditioning of its
82: *> eigenvalues.
83: *> = 'N': Do not diagonally scale or permute;
84: *> = 'P': Perform permutations to make the matrix more nearly
85: *> upper triangular. Do not diagonally scale;
86: *> = 'S': Diagonally scale the matrix, ie. replace A by
87: *> D*A*D**(-1), where D is a diagonal matrix chosen
88: *> to make the rows and columns of A more equal in
89: *> norm. Do not permute;
90: *> = 'B': Both diagonally scale and permute A.
91: *>
92: *> Computed reciprocal condition numbers will be for the matrix
93: *> after balancing and/or permuting. Permuting does not change
94: *> condition numbers (in exact arithmetic), but balancing does.
95: *> \endverbatim
96: *>
97: *> \param[in] JOBVL
98: *> \verbatim
99: *> JOBVL is CHARACTER*1
100: *> = 'N': left eigenvectors of A are not computed;
101: *> = 'V': left eigenvectors of A are computed.
102: *> If SENSE = 'E' or 'B', JOBVL must = 'V'.
103: *> \endverbatim
104: *>
105: *> \param[in] JOBVR
106: *> \verbatim
107: *> JOBVR is CHARACTER*1
108: *> = 'N': right eigenvectors of A are not computed;
109: *> = 'V': right eigenvectors of A are computed.
110: *> If SENSE = 'E' or 'B', JOBVR must = 'V'.
111: *> \endverbatim
112: *>
113: *> \param[in] SENSE
114: *> \verbatim
115: *> SENSE is CHARACTER*1
116: *> Determines which reciprocal condition numbers are computed.
117: *> = 'N': None are computed;
118: *> = 'E': Computed for eigenvalues only;
119: *> = 'V': Computed for right eigenvectors only;
120: *> = 'B': Computed for eigenvalues and right eigenvectors.
121: *>
122: *> If SENSE = 'E' or 'B', both left and right eigenvectors
123: *> must also be computed (JOBVL = 'V' and JOBVR = 'V').
124: *> \endverbatim
125: *>
126: *> \param[in] N
127: *> \verbatim
128: *> N is INTEGER
129: *> The order of the matrix A. N >= 0.
130: *> \endverbatim
131: *>
132: *> \param[in,out] A
133: *> \verbatim
134: *> A is COMPLEX*16 array, dimension (LDA,N)
135: *> On entry, the N-by-N matrix A.
136: *> On exit, A has been overwritten. If JOBVL = 'V' or
137: *> JOBVR = 'V', A contains the Schur form of the balanced
138: *> version of the matrix A.
139: *> \endverbatim
140: *>
141: *> \param[in] LDA
142: *> \verbatim
143: *> LDA is INTEGER
144: *> The leading dimension of the array A. LDA >= max(1,N).
145: *> \endverbatim
146: *>
147: *> \param[out] W
148: *> \verbatim
149: *> W is COMPLEX*16 array, dimension (N)
150: *> W contains the computed eigenvalues.
151: *> \endverbatim
152: *>
153: *> \param[out] VL
154: *> \verbatim
155: *> VL is COMPLEX*16 array, dimension (LDVL,N)
156: *> If JOBVL = 'V', the left eigenvectors u(j) are stored one
157: *> after another in the columns of VL, in the same order
158: *> as their eigenvalues.
159: *> If JOBVL = 'N', VL is not referenced.
160: *> u(j) = VL(:,j), the j-th column of VL.
161: *> \endverbatim
162: *>
163: *> \param[in] LDVL
164: *> \verbatim
165: *> LDVL is INTEGER
166: *> The leading dimension of the array VL. LDVL >= 1; if
167: *> JOBVL = 'V', LDVL >= N.
168: *> \endverbatim
169: *>
170: *> \param[out] VR
171: *> \verbatim
172: *> VR is COMPLEX*16 array, dimension (LDVR,N)
173: *> If JOBVR = 'V', the right eigenvectors v(j) are stored one
174: *> after another in the columns of VR, in the same order
175: *> as their eigenvalues.
176: *> If JOBVR = 'N', VR is not referenced.
177: *> v(j) = VR(:,j), the j-th column of VR.
178: *> \endverbatim
179: *>
180: *> \param[in] LDVR
181: *> \verbatim
182: *> LDVR is INTEGER
183: *> The leading dimension of the array VR. LDVR >= 1; if
184: *> JOBVR = 'V', LDVR >= N.
185: *> \endverbatim
186: *>
187: *> \param[out] ILO
188: *> \verbatim
189: *> ILO is INTEGER
190: *> \endverbatim
191: *>
192: *> \param[out] IHI
193: *> \verbatim
194: *> IHI is INTEGER
195: *> ILO and IHI are integer values determined when A was
196: *> balanced. The balanced A(i,j) = 0 if I > J and
197: *> J = 1,...,ILO-1 or I = IHI+1,...,N.
198: *> \endverbatim
199: *>
200: *> \param[out] SCALE
201: *> \verbatim
202: *> SCALE is DOUBLE PRECISION array, dimension (N)
203: *> Details of the permutations and scaling factors applied
204: *> when balancing A. If P(j) is the index of the row and column
205: *> interchanged with row and column j, and D(j) is the scaling
206: *> factor applied to row and column j, then
207: *> SCALE(J) = P(J), for J = 1,...,ILO-1
208: *> = D(J), for J = ILO,...,IHI
209: *> = P(J) for J = IHI+1,...,N.
210: *> The order in which the interchanges are made is N to IHI+1,
211: *> then 1 to ILO-1.
212: *> \endverbatim
213: *>
214: *> \param[out] ABNRM
215: *> \verbatim
216: *> ABNRM is DOUBLE PRECISION
217: *> The one-norm of the balanced matrix (the maximum
218: *> of the sum of absolute values of elements of any column).
219: *> \endverbatim
220: *>
221: *> \param[out] RCONDE
222: *> \verbatim
223: *> RCONDE is DOUBLE PRECISION array, dimension (N)
224: *> RCONDE(j) is the reciprocal condition number of the j-th
225: *> eigenvalue.
226: *> \endverbatim
227: *>
228: *> \param[out] RCONDV
229: *> \verbatim
230: *> RCONDV is DOUBLE PRECISION array, dimension (N)
231: *> RCONDV(j) is the reciprocal condition number of the j-th
232: *> right eigenvector.
233: *> \endverbatim
234: *>
235: *> \param[out] WORK
236: *> \verbatim
237: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
238: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
239: *> \endverbatim
240: *>
241: *> \param[in] LWORK
242: *> \verbatim
243: *> LWORK is INTEGER
244: *> The dimension of the array WORK. If SENSE = 'N' or 'E',
245: *> LWORK >= max(1,2*N), and if SENSE = 'V' or 'B',
246: *> LWORK >= N*N+2*N.
247: *> For good performance, LWORK must generally be larger.
248: *>
249: *> If LWORK = -1, then a workspace query is assumed; the routine
250: *> only calculates the optimal size of the WORK array, returns
251: *> this value as the first entry of the WORK array, and no error
252: *> message related to LWORK is issued by XERBLA.
253: *> \endverbatim
254: *>
255: *> \param[out] RWORK
256: *> \verbatim
257: *> RWORK is DOUBLE PRECISION array, dimension (2*N)
258: *> \endverbatim
259: *>
260: *> \param[out] INFO
261: *> \verbatim
262: *> INFO is INTEGER
263: *> = 0: successful exit
264: *> < 0: if INFO = -i, the i-th argument had an illegal value.
265: *> > 0: if INFO = i, the QR algorithm failed to compute all the
266: *> eigenvalues, and no eigenvectors or condition numbers
267: *> have been computed; elements 1:ILO-1 and i+1:N of W
268: *> contain eigenvalues which have converged.
269: *> \endverbatim
270: *
271: * Authors:
272: * ========
273: *
274: *> \author Univ. of Tennessee
275: *> \author Univ. of California Berkeley
276: *> \author Univ. of Colorado Denver
277: *> \author NAG Ltd.
278: *
279: *
280: * @precisions fortran z -> c
281: *
282: *> \ingroup complex16GEeigen
283: *
284: * =====================================================================
285: SUBROUTINE ZGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL,
286: $ LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE,
287: $ RCONDV, WORK, LWORK, RWORK, INFO )
288: implicit none
289: *
290: * -- LAPACK driver routine --
291: * -- LAPACK is a software package provided by Univ. of Tennessee, --
292: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
293: *
294: * .. Scalar Arguments ..
295: CHARACTER BALANC, JOBVL, JOBVR, SENSE
296: INTEGER IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N
297: DOUBLE PRECISION ABNRM
298: * ..
299: * .. Array Arguments ..
300: DOUBLE PRECISION RCONDE( * ), RCONDV( * ), RWORK( * ),
301: $ SCALE( * )
302: COMPLEX*16 A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ),
303: $ W( * ), WORK( * )
304: * ..
305: *
306: * =====================================================================
307: *
308: * .. Parameters ..
309: DOUBLE PRECISION ZERO, ONE
310: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
311: * ..
312: * .. Local Scalars ..
313: LOGICAL LQUERY, SCALEA, WANTVL, WANTVR, WNTSNB, WNTSNE,
314: $ WNTSNN, WNTSNV
315: CHARACTER JOB, SIDE
316: INTEGER HSWORK, I, ICOND, IERR, ITAU, IWRK, K,
317: $ LWORK_TREVC, MAXWRK, MINWRK, NOUT
318: DOUBLE PRECISION ANRM, BIGNUM, CSCALE, EPS, SCL, SMLNUM
319: COMPLEX*16 TMP
320: * ..
321: * .. Local Arrays ..
322: LOGICAL SELECT( 1 )
323: DOUBLE PRECISION DUM( 1 )
324: * ..
325: * .. External Subroutines ..
326: EXTERNAL DLABAD, DLASCL, XERBLA, ZDSCAL, ZGEBAK, ZGEBAL,
327: $ ZGEHRD, ZHSEQR, ZLACPY, ZLASCL, ZSCAL, ZTREVC3,
328: $ ZTRSNA, ZUNGHR
329: * ..
330: * .. External Functions ..
331: LOGICAL LSAME
332: INTEGER IDAMAX, ILAENV
333: DOUBLE PRECISION DLAMCH, DZNRM2, ZLANGE
334: EXTERNAL LSAME, IDAMAX, ILAENV, DLAMCH, DZNRM2, ZLANGE
335: * ..
336: * .. Intrinsic Functions ..
337: INTRINSIC DBLE, DCMPLX, CONJG, AIMAG, MAX, SQRT
338: * ..
339: * .. Executable Statements ..
340: *
341: * Test the input arguments
342: *
343: INFO = 0
344: LQUERY = ( LWORK.EQ.-1 )
345: WANTVL = LSAME( JOBVL, 'V' )
346: WANTVR = LSAME( JOBVR, 'V' )
347: WNTSNN = LSAME( SENSE, 'N' )
348: WNTSNE = LSAME( SENSE, 'E' )
349: WNTSNV = LSAME( SENSE, 'V' )
350: WNTSNB = LSAME( SENSE, 'B' )
351: IF( .NOT.( LSAME( BALANC, 'N' ) .OR. LSAME( BALANC, 'S' ) .OR.
352: $ LSAME( BALANC, 'P' ) .OR. LSAME( BALANC, 'B' ) ) ) THEN
353: INFO = -1
354: ELSE IF( ( .NOT.WANTVL ) .AND. ( .NOT.LSAME( JOBVL, 'N' ) ) ) THEN
355: INFO = -2
356: ELSE IF( ( .NOT.WANTVR ) .AND. ( .NOT.LSAME( JOBVR, 'N' ) ) ) THEN
357: INFO = -3
358: ELSE IF( .NOT.( WNTSNN .OR. WNTSNE .OR. WNTSNB .OR. WNTSNV ) .OR.
359: $ ( ( WNTSNE .OR. WNTSNB ) .AND. .NOT.( WANTVL .AND.
360: $ WANTVR ) ) ) THEN
361: INFO = -4
362: ELSE IF( N.LT.0 ) THEN
363: INFO = -5
364: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
365: INFO = -7
366: ELSE IF( LDVL.LT.1 .OR. ( WANTVL .AND. LDVL.LT.N ) ) THEN
367: INFO = -10
368: ELSE IF( LDVR.LT.1 .OR. ( WANTVR .AND. LDVR.LT.N ) ) THEN
369: INFO = -12
370: END IF
371: *
372: * Compute workspace
373: * (Note: Comments in the code beginning "Workspace:" describe the
374: * minimal amount of workspace needed at that point in the code,
375: * as well as the preferred amount for good performance.
376: * CWorkspace refers to complex workspace, and RWorkspace to real
377: * workspace. NB refers to the optimal block size for the
378: * immediately following subroutine, as returned by ILAENV.
379: * HSWORK refers to the workspace preferred by ZHSEQR, as
380: * calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
381: * the worst case.)
382: *
383: IF( INFO.EQ.0 ) THEN
384: IF( N.EQ.0 ) THEN
385: MINWRK = 1
386: MAXWRK = 1
387: ELSE
388: MAXWRK = N + N*ILAENV( 1, 'ZGEHRD', ' ', N, 1, N, 0 )
389: *
390: IF( WANTVL ) THEN
391: CALL ZTREVC3( 'L', 'B', SELECT, N, A, LDA,
392: $ VL, LDVL, VR, LDVR,
393: $ N, NOUT, WORK, -1, RWORK, -1, IERR )
394: LWORK_TREVC = INT( WORK(1) )
395: MAXWRK = MAX( MAXWRK, LWORK_TREVC )
396: CALL ZHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VL, LDVL,
397: $ WORK, -1, INFO )
398: ELSE IF( WANTVR ) THEN
399: CALL ZTREVC3( 'R', 'B', SELECT, N, A, LDA,
400: $ VL, LDVL, VR, LDVR,
401: $ N, NOUT, WORK, -1, RWORK, -1, IERR )
402: LWORK_TREVC = INT( WORK(1) )
403: MAXWRK = MAX( MAXWRK, LWORK_TREVC )
404: CALL ZHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VR, LDVR,
405: $ WORK, -1, INFO )
406: ELSE
407: IF( WNTSNN ) THEN
408: CALL ZHSEQR( 'E', 'N', N, 1, N, A, LDA, W, VR, LDVR,
409: $ WORK, -1, INFO )
410: ELSE
411: CALL ZHSEQR( 'S', 'N', N, 1, N, A, LDA, W, VR, LDVR,
412: $ WORK, -1, INFO )
413: END IF
414: END IF
415: HSWORK = INT( WORK(1) )
416: *
417: IF( ( .NOT.WANTVL ) .AND. ( .NOT.WANTVR ) ) THEN
418: MINWRK = 2*N
419: IF( .NOT.( WNTSNN .OR. WNTSNE ) )
420: $ MINWRK = MAX( MINWRK, N*N + 2*N )
421: MAXWRK = MAX( MAXWRK, HSWORK )
422: IF( .NOT.( WNTSNN .OR. WNTSNE ) )
423: $ MAXWRK = MAX( MAXWRK, N*N + 2*N )
424: ELSE
425: MINWRK = 2*N
426: IF( .NOT.( WNTSNN .OR. WNTSNE ) )
427: $ MINWRK = MAX( MINWRK, N*N + 2*N )
428: MAXWRK = MAX( MAXWRK, HSWORK )
429: MAXWRK = MAX( MAXWRK, N + ( N - 1 )*ILAENV( 1, 'ZUNGHR',
430: $ ' ', N, 1, N, -1 ) )
431: IF( .NOT.( WNTSNN .OR. WNTSNE ) )
432: $ MAXWRK = MAX( MAXWRK, N*N + 2*N )
433: MAXWRK = MAX( MAXWRK, 2*N )
434: END IF
435: MAXWRK = MAX( MAXWRK, MINWRK )
436: END IF
437: WORK( 1 ) = MAXWRK
438: *
439: IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
440: INFO = -20
441: END IF
442: END IF
443: *
444: IF( INFO.NE.0 ) THEN
445: CALL XERBLA( 'ZGEEVX', -INFO )
446: RETURN
447: ELSE IF( LQUERY ) THEN
448: RETURN
449: END IF
450: *
451: * Quick return if possible
452: *
453: IF( N.EQ.0 )
454: $ RETURN
455: *
456: * Get machine constants
457: *
458: EPS = DLAMCH( 'P' )
459: SMLNUM = DLAMCH( 'S' )
460: BIGNUM = ONE / SMLNUM
461: CALL DLABAD( SMLNUM, BIGNUM )
462: SMLNUM = SQRT( SMLNUM ) / EPS
463: BIGNUM = ONE / SMLNUM
464: *
465: * Scale A if max element outside range [SMLNUM,BIGNUM]
466: *
467: ICOND = 0
468: ANRM = ZLANGE( 'M', N, N, A, LDA, DUM )
469: SCALEA = .FALSE.
470: IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
471: SCALEA = .TRUE.
472: CSCALE = SMLNUM
473: ELSE IF( ANRM.GT.BIGNUM ) THEN
474: SCALEA = .TRUE.
475: CSCALE = BIGNUM
476: END IF
477: IF( SCALEA )
478: $ CALL ZLASCL( 'G', 0, 0, ANRM, CSCALE, N, N, A, LDA, IERR )
479: *
480: * Balance the matrix and compute ABNRM
481: *
482: CALL ZGEBAL( BALANC, N, A, LDA, ILO, IHI, SCALE, IERR )
483: ABNRM = ZLANGE( '1', N, N, A, LDA, DUM )
484: IF( SCALEA ) THEN
485: DUM( 1 ) = ABNRM
486: CALL DLASCL( 'G', 0, 0, CSCALE, ANRM, 1, 1, DUM, 1, IERR )
487: ABNRM = DUM( 1 )
488: END IF
489: *
490: * Reduce to upper Hessenberg form
491: * (CWorkspace: need 2*N, prefer N+N*NB)
492: * (RWorkspace: none)
493: *
494: ITAU = 1
495: IWRK = ITAU + N
496: CALL ZGEHRD( N, ILO, IHI, A, LDA, WORK( ITAU ), WORK( IWRK ),
497: $ LWORK-IWRK+1, IERR )
498: *
499: IF( WANTVL ) THEN
500: *
501: * Want left eigenvectors
502: * Copy Householder vectors to VL
503: *
504: SIDE = 'L'
505: CALL ZLACPY( 'L', N, N, A, LDA, VL, LDVL )
506: *
507: * Generate unitary matrix in VL
508: * (CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
509: * (RWorkspace: none)
510: *
511: CALL ZUNGHR( N, ILO, IHI, VL, LDVL, WORK( ITAU ), WORK( IWRK ),
512: $ LWORK-IWRK+1, IERR )
513: *
514: * Perform QR iteration, accumulating Schur vectors in VL
515: * (CWorkspace: need 1, prefer HSWORK (see comments) )
516: * (RWorkspace: none)
517: *
518: IWRK = ITAU
519: CALL ZHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, W, VL, LDVL,
520: $ WORK( IWRK ), LWORK-IWRK+1, INFO )
521: *
522: IF( WANTVR ) THEN
523: *
524: * Want left and right eigenvectors
525: * Copy Schur vectors to VR
526: *
527: SIDE = 'B'
528: CALL ZLACPY( 'F', N, N, VL, LDVL, VR, LDVR )
529: END IF
530: *
531: ELSE IF( WANTVR ) THEN
532: *
533: * Want right eigenvectors
534: * Copy Householder vectors to VR
535: *
536: SIDE = 'R'
537: CALL ZLACPY( 'L', N, N, A, LDA, VR, LDVR )
538: *
539: * Generate unitary matrix in VR
540: * (CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
541: * (RWorkspace: none)
542: *
543: CALL ZUNGHR( N, ILO, IHI, VR, LDVR, WORK( ITAU ), WORK( IWRK ),
544: $ LWORK-IWRK+1, IERR )
545: *
546: * Perform QR iteration, accumulating Schur vectors in VR
547: * (CWorkspace: need 1, prefer HSWORK (see comments) )
548: * (RWorkspace: none)
549: *
550: IWRK = ITAU
551: CALL ZHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, W, VR, LDVR,
552: $ WORK( IWRK ), LWORK-IWRK+1, INFO )
553: *
554: ELSE
555: *
556: * Compute eigenvalues only
557: * If condition numbers desired, compute Schur form
558: *
559: IF( WNTSNN ) THEN
560: JOB = 'E'
561: ELSE
562: JOB = 'S'
563: END IF
564: *
565: * (CWorkspace: need 1, prefer HSWORK (see comments) )
566: * (RWorkspace: none)
567: *
568: IWRK = ITAU
569: CALL ZHSEQR( JOB, 'N', N, ILO, IHI, A, LDA, W, VR, LDVR,
570: $ WORK( IWRK ), LWORK-IWRK+1, INFO )
571: END IF
572: *
573: * If INFO .NE. 0 from ZHSEQR, then quit
574: *
575: IF( INFO.NE.0 )
576: $ GO TO 50
577: *
578: IF( WANTVL .OR. WANTVR ) THEN
579: *
580: * Compute left and/or right eigenvectors
581: * (CWorkspace: need 2*N, prefer N + 2*N*NB)
582: * (RWorkspace: need N)
583: *
584: CALL ZTREVC3( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR,
585: $ N, NOUT, WORK( IWRK ), LWORK-IWRK+1,
586: $ RWORK, N, IERR )
587: END IF
588: *
589: * Compute condition numbers if desired
590: * (CWorkspace: need N*N+2*N unless SENSE = 'E')
591: * (RWorkspace: need 2*N unless SENSE = 'E')
592: *
593: IF( .NOT.WNTSNN ) THEN
594: CALL ZTRSNA( SENSE, 'A', SELECT, N, A, LDA, VL, LDVL, VR, LDVR,
595: $ RCONDE, RCONDV, N, NOUT, WORK( IWRK ), N, RWORK,
596: $ ICOND )
597: END IF
598: *
599: IF( WANTVL ) THEN
600: *
601: * Undo balancing of left eigenvectors
602: *
603: CALL ZGEBAK( BALANC, 'L', N, ILO, IHI, SCALE, N, VL, LDVL,
604: $ IERR )
605: *
606: * Normalize left eigenvectors and make largest component real
607: *
608: DO 20 I = 1, N
609: SCL = ONE / DZNRM2( N, VL( 1, I ), 1 )
610: CALL ZDSCAL( N, SCL, VL( 1, I ), 1 )
611: DO 10 K = 1, N
612: RWORK( K ) = DBLE( VL( K, I ) )**2 +
613: $ AIMAG( VL( K, I ) )**2
614: 10 CONTINUE
615: K = IDAMAX( N, RWORK, 1 )
616: TMP = CONJG( VL( K, I ) ) / SQRT( RWORK( K ) )
617: CALL ZSCAL( N, TMP, VL( 1, I ), 1 )
618: VL( K, I ) = DCMPLX( DBLE( VL( K, I ) ), ZERO )
619: 20 CONTINUE
620: END IF
621: *
622: IF( WANTVR ) THEN
623: *
624: * Undo balancing of right eigenvectors
625: *
626: CALL ZGEBAK( BALANC, 'R', N, ILO, IHI, SCALE, N, VR, LDVR,
627: $ IERR )
628: *
629: * Normalize right eigenvectors and make largest component real
630: *
631: DO 40 I = 1, N
632: SCL = ONE / DZNRM2( N, VR( 1, I ), 1 )
633: CALL ZDSCAL( N, SCL, VR( 1, I ), 1 )
634: DO 30 K = 1, N
635: RWORK( K ) = DBLE( VR( K, I ) )**2 +
636: $ AIMAG( VR( K, I ) )**2
637: 30 CONTINUE
638: K = IDAMAX( N, RWORK, 1 )
639: TMP = CONJG( VR( K, I ) ) / SQRT( RWORK( K ) )
640: CALL ZSCAL( N, TMP, VR( 1, I ), 1 )
641: VR( K, I ) = DCMPLX( DBLE( VR( K, I ) ), ZERO )
642: 40 CONTINUE
643: END IF
644: *
645: * Undo scaling if necessary
646: *
647: 50 CONTINUE
648: IF( SCALEA ) THEN
649: CALL ZLASCL( 'G', 0, 0, CSCALE, ANRM, N-INFO, 1, W( INFO+1 ),
650: $ MAX( N-INFO, 1 ), IERR )
651: IF( INFO.EQ.0 ) THEN
652: IF( ( WNTSNV .OR. WNTSNB ) .AND. ICOND.EQ.0 )
653: $ CALL DLASCL( 'G', 0, 0, CSCALE, ANRM, N, 1, RCONDV, N,
654: $ IERR )
655: ELSE
656: CALL ZLASCL( 'G', 0, 0, CSCALE, ANRM, ILO-1, 1, W, N, IERR )
657: END IF
658: END IF
659: *
660: WORK( 1 ) = MAXWRK
661: RETURN
662: *
663: * End of ZGEEVX
664: *
665: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zgeevx.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack