![]() |
LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
|
00001 *> \brief <b> ZGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices</b> 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZGGEV + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zggev.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zggev.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zggev.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, 00022 * VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER JOBVL, JOBVR 00026 * INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, N 00027 * .. 00028 * .. Array Arguments .. 00029 * DOUBLE PRECISION RWORK( * ) 00030 * COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ), 00031 * $ BETA( * ), VL( LDVL, * ), VR( LDVR, * ), 00032 * $ WORK( * ) 00033 * .. 00034 * 00035 * 00036 *> \par Purpose: 00037 * ============= 00038 *> 00039 *> \verbatim 00040 *> 00041 *> ZGGEV computes for a pair of N-by-N complex nonsymmetric matrices 00042 *> (A,B), the generalized eigenvalues, and optionally, the left and/or 00043 *> right generalized eigenvectors. 00044 *> 00045 *> A generalized eigenvalue for a pair of matrices (A,B) is a scalar 00046 *> lambda or a ratio alpha/beta = lambda, such that A - lambda*B is 00047 *> singular. It is usually represented as the pair (alpha,beta), as 00048 *> there is a reasonable interpretation for beta=0, and even for both 00049 *> being zero. 00050 *> 00051 *> The right generalized eigenvector v(j) corresponding to the 00052 *> generalized eigenvalue lambda(j) of (A,B) satisfies 00053 *> 00054 *> A * v(j) = lambda(j) * B * v(j). 00055 *> 00056 *> The left generalized eigenvector u(j) corresponding to the 00057 *> generalized eigenvalues lambda(j) of (A,B) satisfies 00058 *> 00059 *> u(j)**H * A = lambda(j) * u(j)**H * B 00060 *> 00061 *> where u(j)**H is the conjugate-transpose of u(j). 00062 *> \endverbatim 00063 * 00064 * Arguments: 00065 * ========== 00066 * 00067 *> \param[in] JOBVL 00068 *> \verbatim 00069 *> JOBVL is CHARACTER*1 00070 *> = 'N': do not compute the left generalized eigenvectors; 00071 *> = 'V': compute the left generalized eigenvectors. 00072 *> \endverbatim 00073 *> 00074 *> \param[in] JOBVR 00075 *> \verbatim 00076 *> JOBVR is CHARACTER*1 00077 *> = 'N': do not compute the right generalized eigenvectors; 00078 *> = 'V': compute the right generalized eigenvectors. 00079 *> \endverbatim 00080 *> 00081 *> \param[in] N 00082 *> \verbatim 00083 *> N is INTEGER 00084 *> The order of the matrices A, B, VL, and VR. N >= 0. 00085 *> \endverbatim 00086 *> 00087 *> \param[in,out] A 00088 *> \verbatim 00089 *> A is COMPLEX*16 array, dimension (LDA, N) 00090 *> On entry, the matrix A in the pair (A,B). 00091 *> On exit, A has been overwritten. 00092 *> \endverbatim 00093 *> 00094 *> \param[in] LDA 00095 *> \verbatim 00096 *> LDA is INTEGER 00097 *> The leading dimension of A. LDA >= max(1,N). 00098 *> \endverbatim 00099 *> 00100 *> \param[in,out] B 00101 *> \verbatim 00102 *> B is COMPLEX*16 array, dimension (LDB, N) 00103 *> On entry, the matrix B in the pair (A,B). 00104 *> On exit, B has been overwritten. 00105 *> \endverbatim 00106 *> 00107 *> \param[in] LDB 00108 *> \verbatim 00109 *> LDB is INTEGER 00110 *> The leading dimension of B. LDB >= max(1,N). 00111 *> \endverbatim 00112 *> 00113 *> \param[out] ALPHA 00114 *> \verbatim 00115 *> ALPHA is COMPLEX*16 array, dimension (N) 00116 *> \endverbatim 00117 *> 00118 *> \param[out] BETA 00119 *> \verbatim 00120 *> BETA is COMPLEX*16 array, dimension (N) 00121 *> On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the 00122 *> generalized eigenvalues. 00123 *> 00124 *> Note: the quotients ALPHA(j)/BETA(j) may easily over- or 00125 *> underflow, and BETA(j) may even be zero. Thus, the user 00126 *> should avoid naively computing the ratio alpha/beta. 00127 *> However, ALPHA will be always less than and usually 00128 *> comparable with norm(A) in magnitude, and BETA always less 00129 *> than and usually comparable with norm(B). 00130 *> \endverbatim 00131 *> 00132 *> \param[out] VL 00133 *> \verbatim 00134 *> VL is COMPLEX*16 array, dimension (LDVL,N) 00135 *> If JOBVL = 'V', the left generalized eigenvectors u(j) are 00136 *> stored one after another in the columns of VL, in the same 00137 *> order as their eigenvalues. 00138 *> Each eigenvector is scaled so the largest component has 00139 *> abs(real part) + abs(imag. part) = 1. 00140 *> Not referenced if JOBVL = 'N'. 00141 *> \endverbatim 00142 *> 00143 *> \param[in] LDVL 00144 *> \verbatim 00145 *> LDVL is INTEGER 00146 *> The leading dimension of the matrix VL. LDVL >= 1, and 00147 *> if JOBVL = 'V', LDVL >= N. 00148 *> \endverbatim 00149 *> 00150 *> \param[out] VR 00151 *> \verbatim 00152 *> VR is COMPLEX*16 array, dimension (LDVR,N) 00153 *> If JOBVR = 'V', the right generalized eigenvectors v(j) are 00154 *> stored one after another in the columns of VR, in the same 00155 *> order as their eigenvalues. 00156 *> Each eigenvector is scaled so the largest component has 00157 *> abs(real part) + abs(imag. part) = 1. 00158 *> Not referenced if JOBVR = 'N'. 00159 *> \endverbatim 00160 *> 00161 *> \param[in] LDVR 00162 *> \verbatim 00163 *> LDVR is INTEGER 00164 *> The leading dimension of the matrix VR. LDVR >= 1, and 00165 *> if JOBVR = 'V', LDVR >= N. 00166 *> \endverbatim 00167 *> 00168 *> \param[out] WORK 00169 *> \verbatim 00170 *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) 00171 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00172 *> \endverbatim 00173 *> 00174 *> \param[in] LWORK 00175 *> \verbatim 00176 *> LWORK is INTEGER 00177 *> The dimension of the array WORK. LWORK >= max(1,2*N). 00178 *> For good performance, LWORK must generally be larger. 00179 *> 00180 *> If LWORK = -1, then a workspace query is assumed; the routine 00181 *> only calculates the optimal size of the WORK array, returns 00182 *> this value as the first entry of the WORK array, and no error 00183 *> message related to LWORK is issued by XERBLA. 00184 *> \endverbatim 00185 *> 00186 *> \param[out] RWORK 00187 *> \verbatim 00188 *> RWORK is DOUBLE PRECISION array, dimension (8*N) 00189 *> \endverbatim 00190 *> 00191 *> \param[out] INFO 00192 *> \verbatim 00193 *> INFO is INTEGER 00194 *> = 0: successful exit 00195 *> < 0: if INFO = -i, the i-th argument had an illegal value. 00196 *> =1,...,N: 00197 *> The QZ iteration failed. No eigenvectors have been 00198 *> calculated, but ALPHA(j) and BETA(j) should be 00199 *> correct for j=INFO+1,...,N. 00200 *> > N: =N+1: other then QZ iteration failed in DHGEQZ, 00201 *> =N+2: error return from DTGEVC. 00202 *> \endverbatim 00203 * 00204 * Authors: 00205 * ======== 00206 * 00207 *> \author Univ. of Tennessee 00208 *> \author Univ. of California Berkeley 00209 *> \author Univ. of Colorado Denver 00210 *> \author NAG Ltd. 00211 * 00212 *> \date April 2012 00213 * 00214 *> \ingroup complex16GEeigen 00215 * 00216 * ===================================================================== 00217 SUBROUTINE ZGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, 00218 $ VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO ) 00219 * 00220 * -- LAPACK driver routine (version 3.4.1) -- 00221 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00222 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00223 * April 2012 00224 * 00225 * .. Scalar Arguments .. 00226 CHARACTER JOBVL, JOBVR 00227 INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, N 00228 * .. 00229 * .. Array Arguments .. 00230 DOUBLE PRECISION RWORK( * ) 00231 COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ), 00232 $ BETA( * ), VL( LDVL, * ), VR( LDVR, * ), 00233 $ WORK( * ) 00234 * .. 00235 * 00236 * ===================================================================== 00237 * 00238 * .. Parameters .. 00239 DOUBLE PRECISION ZERO, ONE 00240 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) 00241 COMPLEX*16 CZERO, CONE 00242 PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ), 00243 $ CONE = ( 1.0D0, 0.0D0 ) ) 00244 * .. 00245 * .. Local Scalars .. 00246 LOGICAL ILASCL, ILBSCL, ILV, ILVL, ILVR, LQUERY 00247 CHARACTER CHTEMP 00248 INTEGER ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT, ILO, 00249 $ IN, IRIGHT, IROWS, IRWRK, ITAU, IWRK, JC, JR, 00250 $ LWKMIN, LWKOPT 00251 DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, 00252 $ SMLNUM, TEMP 00253 COMPLEX*16 X 00254 * .. 00255 * .. Local Arrays .. 00256 LOGICAL LDUMMA( 1 ) 00257 * .. 00258 * .. External Subroutines .. 00259 EXTERNAL DLABAD, XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHRD, 00260 $ ZHGEQZ, ZLACPY, ZLASCL, ZLASET, ZTGEVC, ZUNGQR, 00261 $ ZUNMQR 00262 * .. 00263 * .. External Functions .. 00264 LOGICAL LSAME 00265 INTEGER ILAENV 00266 DOUBLE PRECISION DLAMCH, ZLANGE 00267 EXTERNAL LSAME, ILAENV, DLAMCH, ZLANGE 00268 * .. 00269 * .. Intrinsic Functions .. 00270 INTRINSIC ABS, DBLE, DIMAG, MAX, SQRT 00271 * .. 00272 * .. Statement Functions .. 00273 DOUBLE PRECISION ABS1 00274 * .. 00275 * .. Statement Function definitions .. 00276 ABS1( X ) = ABS( DBLE( X ) ) + ABS( DIMAG( X ) ) 00277 * .. 00278 * .. Executable Statements .. 00279 * 00280 * Decode the input arguments 00281 * 00282 IF( LSAME( JOBVL, 'N' ) ) THEN 00283 IJOBVL = 1 00284 ILVL = .FALSE. 00285 ELSE IF( LSAME( JOBVL, 'V' ) ) THEN 00286 IJOBVL = 2 00287 ILVL = .TRUE. 00288 ELSE 00289 IJOBVL = -1 00290 ILVL = .FALSE. 00291 END IF 00292 * 00293 IF( LSAME( JOBVR, 'N' ) ) THEN 00294 IJOBVR = 1 00295 ILVR = .FALSE. 00296 ELSE IF( LSAME( JOBVR, 'V' ) ) THEN 00297 IJOBVR = 2 00298 ILVR = .TRUE. 00299 ELSE 00300 IJOBVR = -1 00301 ILVR = .FALSE. 00302 END IF 00303 ILV = ILVL .OR. ILVR 00304 * 00305 * Test the input arguments 00306 * 00307 INFO = 0 00308 LQUERY = ( LWORK.EQ.-1 ) 00309 IF( IJOBVL.LE.0 ) THEN 00310 INFO = -1 00311 ELSE IF( IJOBVR.LE.0 ) THEN 00312 INFO = -2 00313 ELSE IF( N.LT.0 ) THEN 00314 INFO = -3 00315 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00316 INFO = -5 00317 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00318 INFO = -7 00319 ELSE IF( LDVL.LT.1 .OR. ( ILVL .AND. LDVL.LT.N ) ) THEN 00320 INFO = -11 00321 ELSE IF( LDVR.LT.1 .OR. ( ILVR .AND. LDVR.LT.N ) ) THEN 00322 INFO = -13 00323 END IF 00324 * 00325 * Compute workspace 00326 * (Note: Comments in the code beginning "Workspace:" describe the 00327 * minimal amount of workspace needed at that point in the code, 00328 * as well as the preferred amount for good performance. 00329 * NB refers to the optimal block size for the immediately 00330 * following subroutine, as returned by ILAENV. The workspace is 00331 * computed assuming ILO = 1 and IHI = N, the worst case.) 00332 * 00333 IF( INFO.EQ.0 ) THEN 00334 LWKMIN = MAX( 1, 2*N ) 00335 LWKOPT = MAX( 1, N + N*ILAENV( 1, 'ZGEQRF', ' ', N, 1, N, 0 ) ) 00336 LWKOPT = MAX( LWKOPT, N + 00337 $ N*ILAENV( 1, 'ZUNMQR', ' ', N, 1, N, 0 ) ) 00338 IF( ILVL ) THEN 00339 LWKOPT = MAX( LWKOPT, N + 00340 $ N*ILAENV( 1, 'ZUNGQR', ' ', N, 1, N, -1 ) ) 00341 END IF 00342 WORK( 1 ) = LWKOPT 00343 * 00344 IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) 00345 $ INFO = -15 00346 END IF 00347 * 00348 IF( INFO.NE.0 ) THEN 00349 CALL XERBLA( 'ZGGEV ', -INFO ) 00350 RETURN 00351 ELSE IF( LQUERY ) THEN 00352 RETURN 00353 END IF 00354 * 00355 * Quick return if possible 00356 * 00357 IF( N.EQ.0 ) 00358 $ RETURN 00359 * 00360 * Get machine constants 00361 * 00362 EPS = DLAMCH( 'E' )*DLAMCH( 'B' ) 00363 SMLNUM = DLAMCH( 'S' ) 00364 BIGNUM = ONE / SMLNUM 00365 CALL DLABAD( SMLNUM, BIGNUM ) 00366 SMLNUM = SQRT( SMLNUM ) / EPS 00367 BIGNUM = ONE / SMLNUM 00368 * 00369 * Scale A if max element outside range [SMLNUM,BIGNUM] 00370 * 00371 ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK ) 00372 ILASCL = .FALSE. 00373 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN 00374 ANRMTO = SMLNUM 00375 ILASCL = .TRUE. 00376 ELSE IF( ANRM.GT.BIGNUM ) THEN 00377 ANRMTO = BIGNUM 00378 ILASCL = .TRUE. 00379 END IF 00380 IF( ILASCL ) 00381 $ CALL ZLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR ) 00382 * 00383 * Scale B if max element outside range [SMLNUM,BIGNUM] 00384 * 00385 BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK ) 00386 ILBSCL = .FALSE. 00387 IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN 00388 BNRMTO = SMLNUM 00389 ILBSCL = .TRUE. 00390 ELSE IF( BNRM.GT.BIGNUM ) THEN 00391 BNRMTO = BIGNUM 00392 ILBSCL = .TRUE. 00393 END IF 00394 IF( ILBSCL ) 00395 $ CALL ZLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR ) 00396 * 00397 * Permute the matrices A, B to isolate eigenvalues if possible 00398 * (Real Workspace: need 6*N) 00399 * 00400 ILEFT = 1 00401 IRIGHT = N + 1 00402 IRWRK = IRIGHT + N 00403 CALL ZGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ), 00404 $ RWORK( IRIGHT ), RWORK( IRWRK ), IERR ) 00405 * 00406 * Reduce B to triangular form (QR decomposition of B) 00407 * (Complex Workspace: need N, prefer N*NB) 00408 * 00409 IROWS = IHI + 1 - ILO 00410 IF( ILV ) THEN 00411 ICOLS = N + 1 - ILO 00412 ELSE 00413 ICOLS = IROWS 00414 END IF 00415 ITAU = 1 00416 IWRK = ITAU + IROWS 00417 CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ), 00418 $ WORK( IWRK ), LWORK+1-IWRK, IERR ) 00419 * 00420 * Apply the orthogonal transformation to matrix A 00421 * (Complex Workspace: need N, prefer N*NB) 00422 * 00423 CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB, 00424 $ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ), 00425 $ LWORK+1-IWRK, IERR ) 00426 * 00427 * Initialize VL 00428 * (Complex Workspace: need N, prefer N*NB) 00429 * 00430 IF( ILVL ) THEN 00431 CALL ZLASET( 'Full', N, N, CZERO, CONE, VL, LDVL ) 00432 IF( IROWS.GT.1 ) THEN 00433 CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB, 00434 $ VL( ILO+1, ILO ), LDVL ) 00435 END IF 00436 CALL ZUNGQR( IROWS, IROWS, IROWS, VL( ILO, ILO ), LDVL, 00437 $ WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR ) 00438 END IF 00439 * 00440 * Initialize VR 00441 * 00442 IF( ILVR ) 00443 $ CALL ZLASET( 'Full', N, N, CZERO, CONE, VR, LDVR ) 00444 * 00445 * Reduce to generalized Hessenberg form 00446 * 00447 IF( ILV ) THEN 00448 * 00449 * Eigenvectors requested -- work on whole matrix. 00450 * 00451 CALL ZGGHRD( JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB, VL, 00452 $ LDVL, VR, LDVR, IERR ) 00453 ELSE 00454 CALL ZGGHRD( 'N', 'N', IROWS, 1, IROWS, A( ILO, ILO ), LDA, 00455 $ B( ILO, ILO ), LDB, VL, LDVL, VR, LDVR, IERR ) 00456 END IF 00457 * 00458 * Perform QZ algorithm (Compute eigenvalues, and optionally, the 00459 * Schur form and Schur vectors) 00460 * (Complex Workspace: need N) 00461 * (Real Workspace: need N) 00462 * 00463 IWRK = ITAU 00464 IF( ILV ) THEN 00465 CHTEMP = 'S' 00466 ELSE 00467 CHTEMP = 'E' 00468 END IF 00469 CALL ZHGEQZ( CHTEMP, JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB, 00470 $ ALPHA, BETA, VL, LDVL, VR, LDVR, WORK( IWRK ), 00471 $ LWORK+1-IWRK, RWORK( IRWRK ), IERR ) 00472 IF( IERR.NE.0 ) THEN 00473 IF( IERR.GT.0 .AND. IERR.LE.N ) THEN 00474 INFO = IERR 00475 ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN 00476 INFO = IERR - N 00477 ELSE 00478 INFO = N + 1 00479 END IF 00480 GO TO 70 00481 END IF 00482 * 00483 * Compute Eigenvectors 00484 * (Real Workspace: need 2*N) 00485 * (Complex Workspace: need 2*N) 00486 * 00487 IF( ILV ) THEN 00488 IF( ILVL ) THEN 00489 IF( ILVR ) THEN 00490 CHTEMP = 'B' 00491 ELSE 00492 CHTEMP = 'L' 00493 END IF 00494 ELSE 00495 CHTEMP = 'R' 00496 END IF 00497 * 00498 CALL ZTGEVC( CHTEMP, 'B', LDUMMA, N, A, LDA, B, LDB, VL, LDVL, 00499 $ VR, LDVR, N, IN, WORK( IWRK ), RWORK( IRWRK ), 00500 $ IERR ) 00501 IF( IERR.NE.0 ) THEN 00502 INFO = N + 2 00503 GO TO 70 00504 END IF 00505 * 00506 * Undo balancing on VL and VR and normalization 00507 * (Workspace: none needed) 00508 * 00509 IF( ILVL ) THEN 00510 CALL ZGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ), 00511 $ RWORK( IRIGHT ), N, VL, LDVL, IERR ) 00512 DO 30 JC = 1, N 00513 TEMP = ZERO 00514 DO 10 JR = 1, N 00515 TEMP = MAX( TEMP, ABS1( VL( JR, JC ) ) ) 00516 10 CONTINUE 00517 IF( TEMP.LT.SMLNUM ) 00518 $ GO TO 30 00519 TEMP = ONE / TEMP 00520 DO 20 JR = 1, N 00521 VL( JR, JC ) = VL( JR, JC )*TEMP 00522 20 CONTINUE 00523 30 CONTINUE 00524 END IF 00525 IF( ILVR ) THEN 00526 CALL ZGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ), 00527 $ RWORK( IRIGHT ), N, VR, LDVR, IERR ) 00528 DO 60 JC = 1, N 00529 TEMP = ZERO 00530 DO 40 JR = 1, N 00531 TEMP = MAX( TEMP, ABS1( VR( JR, JC ) ) ) 00532 40 CONTINUE 00533 IF( TEMP.LT.SMLNUM ) 00534 $ GO TO 60 00535 TEMP = ONE / TEMP 00536 DO 50 JR = 1, N 00537 VR( JR, JC ) = VR( JR, JC )*TEMP 00538 50 CONTINUE 00539 60 CONTINUE 00540 END IF 00541 END IF 00542 * 00543 * Undo scaling if necessary 00544 * 00545 70 CONTINUE 00546 * 00547 IF( ILASCL ) 00548 $ CALL ZLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR ) 00549 * 00550 IF( ILBSCL ) 00551 $ CALL ZLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR ) 00552 * 00553 WORK( 1 ) = LWKOPT 00554 RETURN 00555 * 00556 * End of ZGGEV 00557 * 00558 END