Annotation of rpl/lapack/lapack/zgegv.f, revision 1.8
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: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZGEGV + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgegv.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgegv.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgegv.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZGEGV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA,
! 22: * VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, 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 RWORK( * )
! 30: * COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ),
! 31: * $ BETA( * ), VL( LDVL, * ), VR( LDVR, * ),
! 32: * $ WORK( * )
! 33: * ..
! 34: *
! 35: *
! 36: *> \par Purpose:
! 37: * =============
! 38: *>
! 39: *> \verbatim
! 40: *>
! 41: *> This routine is deprecated and has been replaced by routine ZGGEV.
! 42: *>
! 43: *> ZGEGV computes the eigenvalues and, optionally, the left and/or right
! 44: *> eigenvectors of a complex matrix pair (A,B).
! 45: *> Given two square matrices A and B,
! 46: *> the generalized nonsymmetric eigenvalue problem (GNEP) is to find the
! 47: *> eigenvalues lambda and corresponding (non-zero) eigenvectors x such
! 48: *> that
! 49: *> A*x = lambda*B*x.
! 50: *>
! 51: *> An alternate form is to find the eigenvalues mu and corresponding
! 52: *> eigenvectors y such that
! 53: *> mu*A*y = B*y.
! 54: *>
! 55: *> These two forms are equivalent with mu = 1/lambda and x = y if
! 56: *> neither lambda nor mu is zero. In order to deal with the case that
! 57: *> lambda or mu is zero or small, two values alpha and beta are returned
! 58: *> for each eigenvalue, such that lambda = alpha/beta and
! 59: *> mu = beta/alpha.
! 60: *>
! 61: *> The vectors x and y in the above equations are right eigenvectors of
! 62: *> the matrix pair (A,B). Vectors u and v satisfying
! 63: *> u**H*A = lambda*u**H*B or mu*v**H*A = v**H*B
! 64: *> are left eigenvectors of (A,B).
! 65: *>
! 66: *> Note: this routine performs "full balancing" on A and B
! 67: *> \endverbatim
! 68: *
! 69: * Arguments:
! 70: * ==========
! 71: *
! 72: *> \param[in] JOBVL
! 73: *> \verbatim
! 74: *> JOBVL is CHARACTER*1
! 75: *> = 'N': do not compute the left generalized eigenvectors;
! 76: *> = 'V': compute the left generalized eigenvectors (returned
! 77: *> in VL).
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] JOBVR
! 81: *> \verbatim
! 82: *> JOBVR is CHARACTER*1
! 83: *> = 'N': do not compute the right generalized eigenvectors;
! 84: *> = 'V': compute the right generalized eigenvectors (returned
! 85: *> in VR).
! 86: *> \endverbatim
! 87: *>
! 88: *> \param[in] N
! 89: *> \verbatim
! 90: *> N is INTEGER
! 91: *> The order of the matrices A, B, VL, and VR. N >= 0.
! 92: *> \endverbatim
! 93: *>
! 94: *> \param[in,out] A
! 95: *> \verbatim
! 96: *> A is COMPLEX*16 array, dimension (LDA, N)
! 97: *> On entry, the matrix A.
! 98: *> If JOBVL = 'V' or JOBVR = 'V', then on exit A
! 99: *> contains the Schur form of A from the generalized Schur
! 100: *> factorization of the pair (A,B) after balancing. If no
! 101: *> eigenvectors were computed, then only the diagonal elements
! 102: *> of the Schur form will be correct. See ZGGHRD and ZHGEQZ
! 103: *> for details.
! 104: *> \endverbatim
! 105: *>
! 106: *> \param[in] LDA
! 107: *> \verbatim
! 108: *> LDA is INTEGER
! 109: *> The leading dimension of A. LDA >= max(1,N).
! 110: *> \endverbatim
! 111: *>
! 112: *> \param[in,out] B
! 113: *> \verbatim
! 114: *> B is COMPLEX*16 array, dimension (LDB, N)
! 115: *> On entry, the matrix B.
! 116: *> If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the
! 117: *> upper triangular matrix obtained from B in the generalized
! 118: *> Schur factorization of the pair (A,B) after balancing.
! 119: *> If no eigenvectors were computed, then only the diagonal
! 120: *> elements of B will be correct. See ZGGHRD and ZHGEQZ for
! 121: *> details.
! 122: *> \endverbatim
! 123: *>
! 124: *> \param[in] LDB
! 125: *> \verbatim
! 126: *> LDB is INTEGER
! 127: *> The leading dimension of B. LDB >= max(1,N).
! 128: *> \endverbatim
! 129: *>
! 130: *> \param[out] ALPHA
! 131: *> \verbatim
! 132: *> ALPHA is COMPLEX*16 array, dimension (N)
! 133: *> The complex scalars alpha that define the eigenvalues of
! 134: *> GNEP.
! 135: *> \endverbatim
! 136: *>
! 137: *> \param[out] BETA
! 138: *> \verbatim
! 139: *> BETA is COMPLEX*16 array, dimension (N)
! 140: *> The complex scalars beta that define the eigenvalues of GNEP.
! 141: *>
! 142: *> Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
! 143: *> represent the j-th eigenvalue of the matrix pair (A,B), in
! 144: *> one of the forms lambda = alpha/beta or mu = beta/alpha.
! 145: *> Since either lambda or mu may overflow, they should not,
! 146: *> in general, be computed.
! 147: *> \endverbatim
! 148: *>
! 149: *> \param[out] VL
! 150: *> \verbatim
! 151: *> VL is COMPLEX*16 array, dimension (LDVL,N)
! 152: *> If JOBVL = 'V', the left eigenvectors u(j) are stored
! 153: *> in the columns of VL, in the same order as their eigenvalues.
! 154: *> Each eigenvector is scaled so that its largest component has
! 155: *> abs(real part) + abs(imag. part) = 1, except for eigenvectors
! 156: *> corresponding to an eigenvalue with alpha = beta = 0, which
! 157: *> are set to zero.
! 158: *> Not referenced if JOBVL = 'N'.
! 159: *> \endverbatim
! 160: *>
! 161: *> \param[in] LDVL
! 162: *> \verbatim
! 163: *> LDVL is INTEGER
! 164: *> The leading dimension of the matrix VL. LDVL >= 1, and
! 165: *> if JOBVL = 'V', LDVL >= N.
! 166: *> \endverbatim
! 167: *>
! 168: *> \param[out] VR
! 169: *> \verbatim
! 170: *> VR is COMPLEX*16 array, dimension (LDVR,N)
! 171: *> If JOBVR = 'V', the right eigenvectors x(j) are stored
! 172: *> in the columns of VR, in the same order as their eigenvalues.
! 173: *> Each eigenvector is scaled so that its largest component has
! 174: *> abs(real part) + abs(imag. part) = 1, except for eigenvectors
! 175: *> corresponding to an eigenvalue with alpha = beta = 0, which
! 176: *> are set to zero.
! 177: *> Not referenced if JOBVR = 'N'.
! 178: *> \endverbatim
! 179: *>
! 180: *> \param[in] LDVR
! 181: *> \verbatim
! 182: *> LDVR is INTEGER
! 183: *> The leading dimension of the matrix VR. LDVR >= 1, and
! 184: *> if JOBVR = 'V', LDVR >= N.
! 185: *> \endverbatim
! 186: *>
! 187: *> \param[out] WORK
! 188: *> \verbatim
! 189: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
! 190: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 191: *> \endverbatim
! 192: *>
! 193: *> \param[in] LWORK
! 194: *> \verbatim
! 195: *> LWORK is INTEGER
! 196: *> The dimension of the array WORK. LWORK >= max(1,2*N).
! 197: *> For good performance, LWORK must generally be larger.
! 198: *> To compute the optimal value of LWORK, call ILAENV to get
! 199: *> blocksizes (for ZGEQRF, ZUNMQR, and ZUNGQR.) Then compute:
! 200: *> NB -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and ZUNGQR;
! 201: *> The optimal LWORK is MAX( 2*N, N*(NB+1) ).
! 202: *>
! 203: *> If LWORK = -1, then a workspace query is assumed; the routine
! 204: *> only calculates the optimal size of the WORK array, returns
! 205: *> this value as the first entry of the WORK array, and no error
! 206: *> message related to LWORK is issued by XERBLA.
! 207: *> \endverbatim
! 208: *>
! 209: *> \param[out] RWORK
! 210: *> \verbatim
! 211: *> RWORK is DOUBLE PRECISION array, dimension (8*N)
! 212: *> \endverbatim
! 213: *>
! 214: *> \param[out] INFO
! 215: *> \verbatim
! 216: *> INFO is INTEGER
! 217: *> = 0: successful exit
! 218: *> < 0: if INFO = -i, the i-th argument had an illegal value.
! 219: *> =1,...,N:
! 220: *> The QZ iteration failed. No eigenvectors have been
! 221: *> calculated, but ALPHA(j) and BETA(j) should be
! 222: *> correct for j=INFO+1,...,N.
! 223: *> > N: errors that usually indicate LAPACK problems:
! 224: *> =N+1: error return from ZGGBAL
! 225: *> =N+2: error return from ZGEQRF
! 226: *> =N+3: error return from ZUNMQR
! 227: *> =N+4: error return from ZUNGQR
! 228: *> =N+5: error return from ZGGHRD
! 229: *> =N+6: error return from ZHGEQZ (other than failed
! 230: *> iteration)
! 231: *> =N+7: error return from ZTGEVC
! 232: *> =N+8: error return from ZGGBAK (computing VL)
! 233: *> =N+9: error return from ZGGBAK (computing VR)
! 234: *> =N+10: error return from ZLASCL (various calls)
! 235: *> \endverbatim
! 236: *
! 237: * Authors:
! 238: * ========
! 239: *
! 240: *> \author Univ. of Tennessee
! 241: *> \author Univ. of California Berkeley
! 242: *> \author Univ. of Colorado Denver
! 243: *> \author NAG Ltd.
! 244: *
! 245: *> \date November 2011
! 246: *
! 247: *> \ingroup complex16GEeigen
! 248: *
! 249: *> \par Further Details:
! 250: * =====================
! 251: *>
! 252: *> \verbatim
! 253: *>
! 254: *> Balancing
! 255: *> ---------
! 256: *>
! 257: *> This driver calls ZGGBAL to both permute and scale rows and columns
! 258: *> of A and B. The permutations PL and PR are chosen so that PL*A*PR
! 259: *> and PL*B*R will be upper triangular except for the diagonal blocks
! 260: *> A(i:j,i:j) and B(i:j,i:j), with i and j as close together as
! 261: *> possible. The diagonal scaling matrices DL and DR are chosen so
! 262: *> that the pair DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to
! 263: *> one (except for the elements that start out zero.)
! 264: *>
! 265: *> After the eigenvalues and eigenvectors of the balanced matrices
! 266: *> have been computed, ZGGBAK transforms the eigenvectors back to what
! 267: *> they would have been (in perfect arithmetic) if they had not been
! 268: *> balanced.
! 269: *>
! 270: *> Contents of A and B on Exit
! 271: *> -------- -- - --- - -- ----
! 272: *>
! 273: *> If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or
! 274: *> both), then on exit the arrays A and B will contain the complex Schur
! 275: *> form[*] of the "balanced" versions of A and B. If no eigenvectors
! 276: *> are computed, then only the diagonal blocks will be correct.
! 277: *>
! 278: *> [*] In other words, upper triangular form.
! 279: *> \endverbatim
! 280: *>
! 281: * =====================================================================
1.1 bertrand 282: SUBROUTINE ZGEGV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA,
283: $ VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO )
284: *
1.8 ! bertrand 285: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 286: * -- LAPACK is a software package provided by Univ. of Tennessee, --
287: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 288: * November 2011
1.1 bertrand 289: *
290: * .. Scalar Arguments ..
291: CHARACTER JOBVL, JOBVR
292: INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, N
293: * ..
294: * .. Array Arguments ..
295: DOUBLE PRECISION RWORK( * )
296: COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ),
297: $ BETA( * ), VL( LDVL, * ), VR( LDVR, * ),
298: $ WORK( * )
299: * ..
300: *
301: * =====================================================================
302: *
303: * .. Parameters ..
304: DOUBLE PRECISION ZERO, ONE
305: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
306: COMPLEX*16 CZERO, CONE
307: PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ),
308: $ CONE = ( 1.0D0, 0.0D0 ) )
309: * ..
310: * .. Local Scalars ..
311: LOGICAL ILIMIT, ILV, ILVL, ILVR, LQUERY
312: CHARACTER CHTEMP
313: INTEGER ICOLS, IHI, IINFO, IJOBVL, IJOBVR, ILEFT, ILO,
314: $ IN, IRIGHT, IROWS, IRWORK, ITAU, IWORK, JC, JR,
315: $ LOPT, LWKMIN, LWKOPT, NB, NB1, NB2, NB3
316: DOUBLE PRECISION ABSAI, ABSAR, ABSB, ANRM, ANRM1, ANRM2, BNRM,
317: $ BNRM1, BNRM2, EPS, SAFMAX, SAFMIN, SALFAI,
318: $ SALFAR, SBETA, SCALE, TEMP
319: COMPLEX*16 X
320: * ..
321: * .. Local Arrays ..
322: LOGICAL LDUMMA( 1 )
323: * ..
324: * .. External Subroutines ..
325: EXTERNAL XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHRD, ZHGEQZ,
326: $ ZLACPY, ZLASCL, ZLASET, ZTGEVC, ZUNGQR, ZUNMQR
327: * ..
328: * .. External Functions ..
329: LOGICAL LSAME
330: INTEGER ILAENV
331: DOUBLE PRECISION DLAMCH, ZLANGE
332: EXTERNAL LSAME, ILAENV, DLAMCH, ZLANGE
333: * ..
334: * .. Intrinsic Functions ..
335: INTRINSIC ABS, DBLE, DCMPLX, DIMAG, INT, MAX
336: * ..
337: * .. Statement Functions ..
338: DOUBLE PRECISION ABS1
339: * ..
340: * .. Statement Function definitions ..
341: ABS1( X ) = ABS( DBLE( X ) ) + ABS( DIMAG( X ) )
342: * ..
343: * .. Executable Statements ..
344: *
345: * Decode the input arguments
346: *
347: IF( LSAME( JOBVL, 'N' ) ) THEN
348: IJOBVL = 1
349: ILVL = .FALSE.
350: ELSE IF( LSAME( JOBVL, 'V' ) ) THEN
351: IJOBVL = 2
352: ILVL = .TRUE.
353: ELSE
354: IJOBVL = -1
355: ILVL = .FALSE.
356: END IF
357: *
358: IF( LSAME( JOBVR, 'N' ) ) THEN
359: IJOBVR = 1
360: ILVR = .FALSE.
361: ELSE IF( LSAME( JOBVR, 'V' ) ) THEN
362: IJOBVR = 2
363: ILVR = .TRUE.
364: ELSE
365: IJOBVR = -1
366: ILVR = .FALSE.
367: END IF
368: ILV = ILVL .OR. ILVR
369: *
370: * Test the input arguments
371: *
372: LWKMIN = MAX( 2*N, 1 )
373: LWKOPT = LWKMIN
374: WORK( 1 ) = LWKOPT
375: LQUERY = ( LWORK.EQ.-1 )
376: INFO = 0
377: IF( IJOBVL.LE.0 ) THEN
378: INFO = -1
379: ELSE IF( IJOBVR.LE.0 ) THEN
380: INFO = -2
381: ELSE IF( N.LT.0 ) THEN
382: INFO = -3
383: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
384: INFO = -5
385: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
386: INFO = -7
387: ELSE IF( LDVL.LT.1 .OR. ( ILVL .AND. LDVL.LT.N ) ) THEN
388: INFO = -11
389: ELSE IF( LDVR.LT.1 .OR. ( ILVR .AND. LDVR.LT.N ) ) THEN
390: INFO = -13
391: ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
392: INFO = -15
393: END IF
394: *
395: IF( INFO.EQ.0 ) THEN
396: NB1 = ILAENV( 1, 'ZGEQRF', ' ', N, N, -1, -1 )
397: NB2 = ILAENV( 1, 'ZUNMQR', ' ', N, N, N, -1 )
398: NB3 = ILAENV( 1, 'ZUNGQR', ' ', N, N, N, -1 )
399: NB = MAX( NB1, NB2, NB3 )
400: LOPT = MAX( 2*N, N*( NB+1 ) )
401: WORK( 1 ) = LOPT
402: END IF
403: *
404: IF( INFO.NE.0 ) THEN
405: CALL XERBLA( 'ZGEGV ', -INFO )
406: RETURN
407: ELSE IF( LQUERY ) THEN
408: RETURN
409: END IF
410: *
411: * Quick return if possible
412: *
413: IF( N.EQ.0 )
414: $ RETURN
415: *
416: * Get machine constants
417: *
418: EPS = DLAMCH( 'E' )*DLAMCH( 'B' )
419: SAFMIN = DLAMCH( 'S' )
420: SAFMIN = SAFMIN + SAFMIN
421: SAFMAX = ONE / SAFMIN
422: *
423: * Scale A
424: *
425: ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK )
426: ANRM1 = ANRM
427: ANRM2 = ONE
428: IF( ANRM.LT.ONE ) THEN
429: IF( SAFMAX*ANRM.LT.ONE ) THEN
430: ANRM1 = SAFMIN
431: ANRM2 = SAFMAX*ANRM
432: END IF
433: END IF
434: *
435: IF( ANRM.GT.ZERO ) THEN
436: CALL ZLASCL( 'G', -1, -1, ANRM, ONE, N, N, A, LDA, IINFO )
437: IF( IINFO.NE.0 ) THEN
438: INFO = N + 10
439: RETURN
440: END IF
441: END IF
442: *
443: * Scale B
444: *
445: BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK )
446: BNRM1 = BNRM
447: BNRM2 = ONE
448: IF( BNRM.LT.ONE ) THEN
449: IF( SAFMAX*BNRM.LT.ONE ) THEN
450: BNRM1 = SAFMIN
451: BNRM2 = SAFMAX*BNRM
452: END IF
453: END IF
454: *
455: IF( BNRM.GT.ZERO ) THEN
456: CALL ZLASCL( 'G', -1, -1, BNRM, ONE, N, N, B, LDB, IINFO )
457: IF( IINFO.NE.0 ) THEN
458: INFO = N + 10
459: RETURN
460: END IF
461: END IF
462: *
463: * Permute the matrix to make it more nearly triangular
464: * Also "balance" the matrix.
465: *
466: ILEFT = 1
467: IRIGHT = N + 1
468: IRWORK = IRIGHT + N
469: CALL ZGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ),
470: $ RWORK( IRIGHT ), RWORK( IRWORK ), IINFO )
471: IF( IINFO.NE.0 ) THEN
472: INFO = N + 1
473: GO TO 80
474: END IF
475: *
476: * Reduce B to triangular form, and initialize VL and/or VR
477: *
478: IROWS = IHI + 1 - ILO
479: IF( ILV ) THEN
480: ICOLS = N + 1 - ILO
481: ELSE
482: ICOLS = IROWS
483: END IF
484: ITAU = 1
485: IWORK = ITAU + IROWS
486: CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
487: $ WORK( IWORK ), LWORK+1-IWORK, IINFO )
488: IF( IINFO.GE.0 )
489: $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
490: IF( IINFO.NE.0 ) THEN
491: INFO = N + 2
492: GO TO 80
493: END IF
494: *
495: CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
496: $ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWORK ),
497: $ LWORK+1-IWORK, IINFO )
498: IF( IINFO.GE.0 )
499: $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
500: IF( IINFO.NE.0 ) THEN
501: INFO = N + 3
502: GO TO 80
503: END IF
504: *
505: IF( ILVL ) THEN
506: CALL ZLASET( 'Full', N, N, CZERO, CONE, VL, LDVL )
507: CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
508: $ VL( ILO+1, ILO ), LDVL )
509: CALL ZUNGQR( IROWS, IROWS, IROWS, VL( ILO, ILO ), LDVL,
510: $ WORK( ITAU ), WORK( IWORK ), LWORK+1-IWORK,
511: $ IINFO )
512: IF( IINFO.GE.0 )
513: $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
514: IF( IINFO.NE.0 ) THEN
515: INFO = N + 4
516: GO TO 80
517: END IF
518: END IF
519: *
520: IF( ILVR )
521: $ CALL ZLASET( 'Full', N, N, CZERO, CONE, VR, LDVR )
522: *
523: * Reduce to generalized Hessenberg form
524: *
525: IF( ILV ) THEN
526: *
527: * Eigenvectors requested -- work on whole matrix.
528: *
529: CALL ZGGHRD( JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB, VL,
530: $ LDVL, VR, LDVR, IINFO )
531: ELSE
532: CALL ZGGHRD( 'N', 'N', IROWS, 1, IROWS, A( ILO, ILO ), LDA,
533: $ B( ILO, ILO ), LDB, VL, LDVL, VR, LDVR, IINFO )
534: END IF
535: IF( IINFO.NE.0 ) THEN
536: INFO = N + 5
537: GO TO 80
538: END IF
539: *
540: * Perform QZ algorithm
541: *
542: IWORK = ITAU
543: IF( ILV ) THEN
544: CHTEMP = 'S'
545: ELSE
546: CHTEMP = 'E'
547: END IF
548: CALL ZHGEQZ( CHTEMP, JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB,
549: $ ALPHA, BETA, VL, LDVL, VR, LDVR, WORK( IWORK ),
550: $ LWORK+1-IWORK, RWORK( IRWORK ), IINFO )
551: IF( IINFO.GE.0 )
552: $ LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
553: IF( IINFO.NE.0 ) THEN
554: IF( IINFO.GT.0 .AND. IINFO.LE.N ) THEN
555: INFO = IINFO
556: ELSE IF( IINFO.GT.N .AND. IINFO.LE.2*N ) THEN
557: INFO = IINFO - N
558: ELSE
559: INFO = N + 6
560: END IF
561: GO TO 80
562: END IF
563: *
564: IF( ILV ) THEN
565: *
566: * Compute Eigenvectors
567: *
568: IF( ILVL ) THEN
569: IF( ILVR ) THEN
570: CHTEMP = 'B'
571: ELSE
572: CHTEMP = 'L'
573: END IF
574: ELSE
575: CHTEMP = 'R'
576: END IF
577: *
578: CALL ZTGEVC( CHTEMP, 'B', LDUMMA, N, A, LDA, B, LDB, VL, LDVL,
579: $ VR, LDVR, N, IN, WORK( IWORK ), RWORK( IRWORK ),
580: $ IINFO )
581: IF( IINFO.NE.0 ) THEN
582: INFO = N + 7
583: GO TO 80
584: END IF
585: *
586: * Undo balancing on VL and VR, rescale
587: *
588: IF( ILVL ) THEN
589: CALL ZGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ),
590: $ RWORK( IRIGHT ), N, VL, LDVL, IINFO )
591: IF( IINFO.NE.0 ) THEN
592: INFO = N + 8
593: GO TO 80
594: END IF
595: DO 30 JC = 1, N
596: TEMP = ZERO
597: DO 10 JR = 1, N
598: TEMP = MAX( TEMP, ABS1( VL( JR, JC ) ) )
599: 10 CONTINUE
600: IF( TEMP.LT.SAFMIN )
601: $ GO TO 30
602: TEMP = ONE / TEMP
603: DO 20 JR = 1, N
604: VL( JR, JC ) = VL( JR, JC )*TEMP
605: 20 CONTINUE
606: 30 CONTINUE
607: END IF
608: IF( ILVR ) THEN
609: CALL ZGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ),
610: $ RWORK( IRIGHT ), N, VR, LDVR, IINFO )
611: IF( IINFO.NE.0 ) THEN
612: INFO = N + 9
613: GO TO 80
614: END IF
615: DO 60 JC = 1, N
616: TEMP = ZERO
617: DO 40 JR = 1, N
618: TEMP = MAX( TEMP, ABS1( VR( JR, JC ) ) )
619: 40 CONTINUE
620: IF( TEMP.LT.SAFMIN )
621: $ GO TO 60
622: TEMP = ONE / TEMP
623: DO 50 JR = 1, N
624: VR( JR, JC ) = VR( JR, JC )*TEMP
625: 50 CONTINUE
626: 60 CONTINUE
627: END IF
628: *
629: * End of eigenvector calculation
630: *
631: END IF
632: *
633: * Undo scaling in alpha, beta
634: *
635: * Note: this does not give the alpha and beta for the unscaled
636: * problem.
637: *
638: * Un-scaling is limited to avoid underflow in alpha and beta
639: * if they are significant.
640: *
641: DO 70 JC = 1, N
642: ABSAR = ABS( DBLE( ALPHA( JC ) ) )
643: ABSAI = ABS( DIMAG( ALPHA( JC ) ) )
644: ABSB = ABS( DBLE( BETA( JC ) ) )
645: SALFAR = ANRM*DBLE( ALPHA( JC ) )
646: SALFAI = ANRM*DIMAG( ALPHA( JC ) )
647: SBETA = BNRM*DBLE( BETA( JC ) )
648: ILIMIT = .FALSE.
649: SCALE = ONE
650: *
651: * Check for significant underflow in imaginary part of ALPHA
652: *
653: IF( ABS( SALFAI ).LT.SAFMIN .AND. ABSAI.GE.
654: $ MAX( SAFMIN, EPS*ABSAR, EPS*ABSB ) ) THEN
655: ILIMIT = .TRUE.
656: SCALE = ( SAFMIN / ANRM1 ) / MAX( SAFMIN, ANRM2*ABSAI )
657: END IF
658: *
659: * Check for significant underflow in real part of ALPHA
660: *
661: IF( ABS( SALFAR ).LT.SAFMIN .AND. ABSAR.GE.
662: $ MAX( SAFMIN, EPS*ABSAI, EPS*ABSB ) ) THEN
663: ILIMIT = .TRUE.
664: SCALE = MAX( SCALE, ( SAFMIN / ANRM1 ) /
665: $ MAX( SAFMIN, ANRM2*ABSAR ) )
666: END IF
667: *
668: * Check for significant underflow in BETA
669: *
670: IF( ABS( SBETA ).LT.SAFMIN .AND. ABSB.GE.
671: $ MAX( SAFMIN, EPS*ABSAR, EPS*ABSAI ) ) THEN
672: ILIMIT = .TRUE.
673: SCALE = MAX( SCALE, ( SAFMIN / BNRM1 ) /
674: $ MAX( SAFMIN, BNRM2*ABSB ) )
675: END IF
676: *
677: * Check for possible overflow when limiting scaling
678: *
679: IF( ILIMIT ) THEN
680: TEMP = ( SCALE*SAFMIN )*MAX( ABS( SALFAR ), ABS( SALFAI ),
681: $ ABS( SBETA ) )
682: IF( TEMP.GT.ONE )
683: $ SCALE = SCALE / TEMP
684: IF( SCALE.LT.ONE )
685: $ ILIMIT = .FALSE.
686: END IF
687: *
688: * Recompute un-scaled ALPHA, BETA if necessary.
689: *
690: IF( ILIMIT ) THEN
691: SALFAR = ( SCALE*DBLE( ALPHA( JC ) ) )*ANRM
692: SALFAI = ( SCALE*DIMAG( ALPHA( JC ) ) )*ANRM
693: SBETA = ( SCALE*BETA( JC ) )*BNRM
694: END IF
695: ALPHA( JC ) = DCMPLX( SALFAR, SALFAI )
696: BETA( JC ) = SBETA
697: 70 CONTINUE
698: *
699: 80 CONTINUE
700: WORK( 1 ) = LWKOPT
701: *
702: RETURN
703: *
704: * End of ZGEGV
705: *
706: END
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