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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief <b> DGGEV 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 DGGEV + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dggev.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dggev.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dggev.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, 00022 * BETA, VL, LDVL, VR, LDVR, WORK, LWORK, 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 A( LDA, * ), ALPHAI( * ), ALPHAR( * ), 00030 * $ B( LDB, * ), BETA( * ), VL( LDVL, * ), 00031 * $ VR( LDVR, * ), WORK( * ) 00032 * .. 00033 * 00034 * 00035 *> \par Purpose: 00036 * ============= 00037 *> 00038 *> \verbatim 00039 *> 00040 *> DGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B) 00041 *> the generalized eigenvalues, and optionally, the left and/or right 00042 *> generalized eigenvectors. 00043 *> 00044 *> A generalized eigenvalue for a pair of matrices (A,B) is a scalar 00045 *> lambda or a ratio alpha/beta = lambda, such that A - lambda*B is 00046 *> singular. It is usually represented as the pair (alpha,beta), as 00047 *> there is a reasonable interpretation for beta=0, and even for both 00048 *> being zero. 00049 *> 00050 *> The right eigenvector v(j) corresponding to the eigenvalue lambda(j) 00051 *> of (A,B) satisfies 00052 *> 00053 *> A * v(j) = lambda(j) * B * v(j). 00054 *> 00055 *> The left eigenvector u(j) corresponding to the eigenvalue lambda(j) 00056 *> of (A,B) satisfies 00057 *> 00058 *> u(j)**H * A = lambda(j) * u(j)**H * B . 00059 *> 00060 *> where u(j)**H is the conjugate-transpose of u(j). 00061 *> 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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] ALPHAR 00114 *> \verbatim 00115 *> ALPHAR is DOUBLE PRECISION array, dimension (N) 00116 *> \endverbatim 00117 *> 00118 *> \param[out] ALPHAI 00119 *> \verbatim 00120 *> ALPHAI is DOUBLE PRECISION array, dimension (N) 00121 *> \endverbatim 00122 *> 00123 *> \param[out] BETA 00124 *> \verbatim 00125 *> BETA is DOUBLE PRECISION array, dimension (N) 00126 *> On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will 00127 *> be the generalized eigenvalues. If ALPHAI(j) is zero, then 00128 *> the j-th eigenvalue is real; if positive, then the j-th and 00129 *> (j+1)-st eigenvalues are a complex conjugate pair, with 00130 *> ALPHAI(j+1) negative. 00131 *> 00132 *> Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) 00133 *> may easily over- or underflow, and BETA(j) may even be zero. 00134 *> Thus, the user should avoid naively computing the ratio 00135 *> alpha/beta. However, ALPHAR and ALPHAI will be always less 00136 *> than and usually comparable with norm(A) in magnitude, and 00137 *> BETA always less than and usually comparable with norm(B). 00138 *> \endverbatim 00139 *> 00140 *> \param[out] VL 00141 *> \verbatim 00142 *> VL is DOUBLE PRECISION array, dimension (LDVL,N) 00143 *> If JOBVL = 'V', the left eigenvectors u(j) are stored one 00144 *> after another in the columns of VL, in the same order as 00145 *> their eigenvalues. If the j-th eigenvalue is real, then 00146 *> u(j) = VL(:,j), the j-th column of VL. If the j-th and 00147 *> (j+1)-th eigenvalues form a complex conjugate pair, then 00148 *> u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1). 00149 *> Each eigenvector is scaled so the largest component has 00150 *> abs(real part)+abs(imag. part)=1. 00151 *> Not referenced if JOBVL = 'N'. 00152 *> \endverbatim 00153 *> 00154 *> \param[in] LDVL 00155 *> \verbatim 00156 *> LDVL is INTEGER 00157 *> The leading dimension of the matrix VL. LDVL >= 1, and 00158 *> if JOBVL = 'V', LDVL >= N. 00159 *> \endverbatim 00160 *> 00161 *> \param[out] VR 00162 *> \verbatim 00163 *> VR is DOUBLE PRECISION array, dimension (LDVR,N) 00164 *> If JOBVR = 'V', the right eigenvectors v(j) are stored one 00165 *> after another in the columns of VR, in the same order as 00166 *> their eigenvalues. If the j-th eigenvalue is real, then 00167 *> v(j) = VR(:,j), the j-th column of VR. If the j-th and 00168 *> (j+1)-th eigenvalues form a complex conjugate pair, then 00169 *> v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1). 00170 *> Each eigenvector is scaled so the largest component has 00171 *> abs(real part)+abs(imag. part)=1. 00172 *> Not referenced if JOBVR = 'N'. 00173 *> \endverbatim 00174 *> 00175 *> \param[in] LDVR 00176 *> \verbatim 00177 *> LDVR is INTEGER 00178 *> The leading dimension of the matrix VR. LDVR >= 1, and 00179 *> if JOBVR = 'V', LDVR >= N. 00180 *> \endverbatim 00181 *> 00182 *> \param[out] WORK 00183 *> \verbatim 00184 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00185 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00186 *> \endverbatim 00187 *> 00188 *> \param[in] LWORK 00189 *> \verbatim 00190 *> LWORK is INTEGER 00191 *> The dimension of the array WORK. LWORK >= max(1,8*N). 00192 *> For good performance, LWORK must generally be larger. 00193 *> 00194 *> If LWORK = -1, then a workspace query is assumed; the routine 00195 *> only calculates the optimal size of the WORK array, returns 00196 *> this value as the first entry of the WORK array, and no error 00197 *> message related to LWORK is issued by XERBLA. 00198 *> \endverbatim 00199 *> 00200 *> \param[out] INFO 00201 *> \verbatim 00202 *> INFO is INTEGER 00203 *> = 0: successful exit 00204 *> < 0: if INFO = -i, the i-th argument had an illegal value. 00205 *> = 1,...,N: 00206 *> The QZ iteration failed. No eigenvectors have been 00207 *> calculated, but ALPHAR(j), ALPHAI(j), and BETA(j) 00208 *> should be correct for j=INFO+1,...,N. 00209 *> > N: =N+1: other than QZ iteration failed in DHGEQZ. 00210 *> =N+2: error return from DTGEVC. 00211 *> \endverbatim 00212 * 00213 * Authors: 00214 * ======== 00215 * 00216 *> \author Univ. of Tennessee 00217 *> \author Univ. of California Berkeley 00218 *> \author Univ. of Colorado Denver 00219 *> \author NAG Ltd. 00220 * 00221 *> \date April 2012 00222 * 00223 *> \ingroup doubleGEeigen 00224 * 00225 * ===================================================================== 00226 SUBROUTINE DGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, 00227 $ BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO ) 00228 * 00229 * -- LAPACK driver routine (version 3.4.1) -- 00230 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00231 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00232 * April 2012 00233 * 00234 * .. Scalar Arguments .. 00235 CHARACTER JOBVL, JOBVR 00236 INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, N 00237 * .. 00238 * .. Array Arguments .. 00239 DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), 00240 $ B( LDB, * ), BETA( * ), VL( LDVL, * ), 00241 $ VR( LDVR, * ), WORK( * ) 00242 * .. 00243 * 00244 * ===================================================================== 00245 * 00246 * .. Parameters .. 00247 DOUBLE PRECISION ZERO, ONE 00248 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00249 * .. 00250 * .. Local Scalars .. 00251 LOGICAL ILASCL, ILBSCL, ILV, ILVL, ILVR, LQUERY 00252 CHARACTER CHTEMP 00253 INTEGER ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT, ILO, 00254 $ IN, IRIGHT, IROWS, ITAU, IWRK, JC, JR, MAXWRK, 00255 $ MINWRK 00256 DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, 00257 $ SMLNUM, TEMP 00258 * .. 00259 * .. Local Arrays .. 00260 LOGICAL LDUMMA( 1 ) 00261 * .. 00262 * .. External Subroutines .. 00263 EXTERNAL DGEQRF, DGGBAK, DGGBAL, DGGHRD, DHGEQZ, DLABAD, 00264 $ DLACPY,DLASCL, DLASET, DORGQR, DORMQR, DTGEVC, 00265 $ XERBLA 00266 * .. 00267 * .. External Functions .. 00268 LOGICAL LSAME 00269 INTEGER ILAENV 00270 DOUBLE PRECISION DLAMCH, DLANGE 00271 EXTERNAL LSAME, ILAENV, DLAMCH, DLANGE 00272 * .. 00273 * .. Intrinsic Functions .. 00274 INTRINSIC ABS, MAX, SQRT 00275 * .. 00276 * .. Executable Statements .. 00277 * 00278 * Decode the input arguments 00279 * 00280 IF( LSAME( JOBVL, 'N' ) ) THEN 00281 IJOBVL = 1 00282 ILVL = .FALSE. 00283 ELSE IF( LSAME( JOBVL, 'V' ) ) THEN 00284 IJOBVL = 2 00285 ILVL = .TRUE. 00286 ELSE 00287 IJOBVL = -1 00288 ILVL = .FALSE. 00289 END IF 00290 * 00291 IF( LSAME( JOBVR, 'N' ) ) THEN 00292 IJOBVR = 1 00293 ILVR = .FALSE. 00294 ELSE IF( LSAME( JOBVR, 'V' ) ) THEN 00295 IJOBVR = 2 00296 ILVR = .TRUE. 00297 ELSE 00298 IJOBVR = -1 00299 ILVR = .FALSE. 00300 END IF 00301 ILV = ILVL .OR. ILVR 00302 * 00303 * Test the input arguments 00304 * 00305 INFO = 0 00306 LQUERY = ( LWORK.EQ.-1 ) 00307 IF( IJOBVL.LE.0 ) THEN 00308 INFO = -1 00309 ELSE IF( IJOBVR.LE.0 ) THEN 00310 INFO = -2 00311 ELSE IF( N.LT.0 ) THEN 00312 INFO = -3 00313 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00314 INFO = -5 00315 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00316 INFO = -7 00317 ELSE IF( LDVL.LT.1 .OR. ( ILVL .AND. LDVL.LT.N ) ) THEN 00318 INFO = -12 00319 ELSE IF( LDVR.LT.1 .OR. ( ILVR .AND. LDVR.LT.N ) ) THEN 00320 INFO = -14 00321 END IF 00322 * 00323 * Compute workspace 00324 * (Note: Comments in the code beginning "Workspace:" describe the 00325 * minimal amount of workspace needed at that point in the code, 00326 * as well as the preferred amount for good performance. 00327 * NB refers to the optimal block size for the immediately 00328 * following subroutine, as returned by ILAENV. The workspace is 00329 * computed assuming ILO = 1 and IHI = N, the worst case.) 00330 * 00331 IF( INFO.EQ.0 ) THEN 00332 MINWRK = MAX( 1, 8*N ) 00333 MAXWRK = MAX( 1, N*( 7 + 00334 $ ILAENV( 1, 'DGEQRF', ' ', N, 1, N, 0 ) ) ) 00335 MAXWRK = MAX( MAXWRK, N*( 7 + 00336 $ ILAENV( 1, 'DORMQR', ' ', N, 1, N, 0 ) ) ) 00337 IF( ILVL ) THEN 00338 MAXWRK = MAX( MAXWRK, N*( 7 + 00339 $ ILAENV( 1, 'DORGQR', ' ', N, 1, N, -1 ) ) ) 00340 END IF 00341 WORK( 1 ) = MAXWRK 00342 * 00343 IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) 00344 $ INFO = -16 00345 END IF 00346 * 00347 IF( INFO.NE.0 ) THEN 00348 CALL XERBLA( 'DGGEV ', -INFO ) 00349 RETURN 00350 ELSE IF( LQUERY ) THEN 00351 RETURN 00352 END IF 00353 * 00354 * Quick return if possible 00355 * 00356 IF( N.EQ.0 ) 00357 $ RETURN 00358 * 00359 * Get machine constants 00360 * 00361 EPS = DLAMCH( 'P' ) 00362 SMLNUM = DLAMCH( 'S' ) 00363 BIGNUM = ONE / SMLNUM 00364 CALL DLABAD( SMLNUM, BIGNUM ) 00365 SMLNUM = SQRT( SMLNUM ) / EPS 00366 BIGNUM = ONE / SMLNUM 00367 * 00368 * Scale A if max element outside range [SMLNUM,BIGNUM] 00369 * 00370 ANRM = DLANGE( 'M', N, N, A, LDA, WORK ) 00371 ILASCL = .FALSE. 00372 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN 00373 ANRMTO = SMLNUM 00374 ILASCL = .TRUE. 00375 ELSE IF( ANRM.GT.BIGNUM ) THEN 00376 ANRMTO = BIGNUM 00377 ILASCL = .TRUE. 00378 END IF 00379 IF( ILASCL ) 00380 $ CALL DLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR ) 00381 * 00382 * Scale B if max element outside range [SMLNUM,BIGNUM] 00383 * 00384 BNRM = DLANGE( 'M', N, N, B, LDB, WORK ) 00385 ILBSCL = .FALSE. 00386 IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN 00387 BNRMTO = SMLNUM 00388 ILBSCL = .TRUE. 00389 ELSE IF( BNRM.GT.BIGNUM ) THEN 00390 BNRMTO = BIGNUM 00391 ILBSCL = .TRUE. 00392 END IF 00393 IF( ILBSCL ) 00394 $ CALL DLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR ) 00395 * 00396 * Permute the matrices A, B to isolate eigenvalues if possible 00397 * (Workspace: need 6*N) 00398 * 00399 ILEFT = 1 00400 IRIGHT = N + 1 00401 IWRK = IRIGHT + N 00402 CALL DGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, WORK( ILEFT ), 00403 $ WORK( IRIGHT ), WORK( IWRK ), IERR ) 00404 * 00405 * Reduce B to triangular form (QR decomposition of B) 00406 * (Workspace: need N, prefer N*NB) 00407 * 00408 IROWS = IHI + 1 - ILO 00409 IF( ILV ) THEN 00410 ICOLS = N + 1 - ILO 00411 ELSE 00412 ICOLS = IROWS 00413 END IF 00414 ITAU = IWRK 00415 IWRK = ITAU + IROWS 00416 CALL DGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ), 00417 $ WORK( IWRK ), LWORK+1-IWRK, IERR ) 00418 * 00419 * Apply the orthogonal transformation to matrix A 00420 * (Workspace: need N, prefer N*NB) 00421 * 00422 CALL DORMQR( 'L', 'T', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB, 00423 $ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ), 00424 $ LWORK+1-IWRK, IERR ) 00425 * 00426 * Initialize VL 00427 * (Workspace: need N, prefer N*NB) 00428 * 00429 IF( ILVL ) THEN 00430 CALL DLASET( 'Full', N, N, ZERO, ONE, VL, LDVL ) 00431 IF( IROWS.GT.1 ) THEN 00432 CALL DLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB, 00433 $ VL( ILO+1, ILO ), LDVL ) 00434 END IF 00435 CALL DORGQR( IROWS, IROWS, IROWS, VL( ILO, ILO ), LDVL, 00436 $ WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR ) 00437 END IF 00438 * 00439 * Initialize VR 00440 * 00441 IF( ILVR ) 00442 $ CALL DLASET( 'Full', N, N, ZERO, ONE, VR, LDVR ) 00443 * 00444 * Reduce to generalized Hessenberg form 00445 * (Workspace: none needed) 00446 * 00447 IF( ILV ) THEN 00448 * 00449 * Eigenvectors requested -- work on whole matrix. 00450 * 00451 CALL DGGHRD( JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB, VL, 00452 $ LDVL, VR, LDVR, IERR ) 00453 ELSE 00454 CALL DGGHRD( '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 forms and Schur vectors) 00460 * (Workspace: need N) 00461 * 00462 IWRK = ITAU 00463 IF( ILV ) THEN 00464 CHTEMP = 'S' 00465 ELSE 00466 CHTEMP = 'E' 00467 END IF 00468 CALL DHGEQZ( CHTEMP, JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB, 00469 $ ALPHAR, ALPHAI, BETA, VL, LDVL, VR, LDVR, 00470 $ WORK( IWRK ), LWORK+1-IWRK, IERR ) 00471 IF( IERR.NE.0 ) THEN 00472 IF( IERR.GT.0 .AND. IERR.LE.N ) THEN 00473 INFO = IERR 00474 ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN 00475 INFO = IERR - N 00476 ELSE 00477 INFO = N + 1 00478 END IF 00479 GO TO 110 00480 END IF 00481 * 00482 * Compute Eigenvectors 00483 * (Workspace: need 6*N) 00484 * 00485 IF( ILV ) THEN 00486 IF( ILVL ) THEN 00487 IF( ILVR ) THEN 00488 CHTEMP = 'B' 00489 ELSE 00490 CHTEMP = 'L' 00491 END IF 00492 ELSE 00493 CHTEMP = 'R' 00494 END IF 00495 CALL DTGEVC( CHTEMP, 'B', LDUMMA, N, A, LDA, B, LDB, VL, LDVL, 00496 $ VR, LDVR, N, IN, WORK( IWRK ), IERR ) 00497 IF( IERR.NE.0 ) THEN 00498 INFO = N + 2 00499 GO TO 110 00500 END IF 00501 * 00502 * Undo balancing on VL and VR and normalization 00503 * (Workspace: none needed) 00504 * 00505 IF( ILVL ) THEN 00506 CALL DGGBAK( 'P', 'L', N, ILO, IHI, WORK( ILEFT ), 00507 $ WORK( IRIGHT ), N, VL, LDVL, IERR ) 00508 DO 50 JC = 1, N 00509 IF( ALPHAI( JC ).LT.ZERO ) 00510 $ GO TO 50 00511 TEMP = ZERO 00512 IF( ALPHAI( JC ).EQ.ZERO ) THEN 00513 DO 10 JR = 1, N 00514 TEMP = MAX( TEMP, ABS( VL( JR, JC ) ) ) 00515 10 CONTINUE 00516 ELSE 00517 DO 20 JR = 1, N 00518 TEMP = MAX( TEMP, ABS( VL( JR, JC ) )+ 00519 $ ABS( VL( JR, JC+1 ) ) ) 00520 20 CONTINUE 00521 END IF 00522 IF( TEMP.LT.SMLNUM ) 00523 $ GO TO 50 00524 TEMP = ONE / TEMP 00525 IF( ALPHAI( JC ).EQ.ZERO ) THEN 00526 DO 30 JR = 1, N 00527 VL( JR, JC ) = VL( JR, JC )*TEMP 00528 30 CONTINUE 00529 ELSE 00530 DO 40 JR = 1, N 00531 VL( JR, JC ) = VL( JR, JC )*TEMP 00532 VL( JR, JC+1 ) = VL( JR, JC+1 )*TEMP 00533 40 CONTINUE 00534 END IF 00535 50 CONTINUE 00536 END IF 00537 IF( ILVR ) THEN 00538 CALL DGGBAK( 'P', 'R', N, ILO, IHI, WORK( ILEFT ), 00539 $ WORK( IRIGHT ), N, VR, LDVR, IERR ) 00540 DO 100 JC = 1, N 00541 IF( ALPHAI( JC ).LT.ZERO ) 00542 $ GO TO 100 00543 TEMP = ZERO 00544 IF( ALPHAI( JC ).EQ.ZERO ) THEN 00545 DO 60 JR = 1, N 00546 TEMP = MAX( TEMP, ABS( VR( JR, JC ) ) ) 00547 60 CONTINUE 00548 ELSE 00549 DO 70 JR = 1, N 00550 TEMP = MAX( TEMP, ABS( VR( JR, JC ) )+ 00551 $ ABS( VR( JR, JC+1 ) ) ) 00552 70 CONTINUE 00553 END IF 00554 IF( TEMP.LT.SMLNUM ) 00555 $ GO TO 100 00556 TEMP = ONE / TEMP 00557 IF( ALPHAI( JC ).EQ.ZERO ) THEN 00558 DO 80 JR = 1, N 00559 VR( JR, JC ) = VR( JR, JC )*TEMP 00560 80 CONTINUE 00561 ELSE 00562 DO 90 JR = 1, N 00563 VR( JR, JC ) = VR( JR, JC )*TEMP 00564 VR( JR, JC+1 ) = VR( JR, JC+1 )*TEMP 00565 90 CONTINUE 00566 END IF 00567 100 CONTINUE 00568 END IF 00569 * 00570 * End of eigenvector calculation 00571 * 00572 END IF 00573 * 00574 * Undo scaling if necessary 00575 * 00576 110 CONTINUE 00577 * 00578 IF( ILASCL ) THEN 00579 CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAR, N, IERR ) 00580 CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAI, N, IERR ) 00581 END IF 00582 * 00583 IF( ILBSCL ) THEN 00584 CALL DLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR ) 00585 END IF 00586 * 00587 WORK( 1 ) = MAXWRK 00588 RETURN 00589 * 00590 * End of DGGEV 00591 * 00592 END