LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sggev.f
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00001 *> \brief <b> SGGEV 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 SGGEV + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sggev.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sggev.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sggev.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE SGGEV( 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 *       REAL               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 *> SGGEV 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 REAL 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 REAL 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 REAL array, dimension (N)
00116 *> \endverbatim
00117 *>
00118 *> \param[out] ALPHAI
00119 *> \verbatim
00120 *>          ALPHAI is REAL array, dimension (N)
00121 *> \endverbatim
00122 *>
00123 *> \param[out] BETA
00124 *> \verbatim
00125 *>          BETA is REAL 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 REAL 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 REAL 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 REAL 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 SHGEQZ.
00210 *>                =N+2: error return from STGEVC.
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 realGEeigen
00224 *
00225 *  =====================================================================
00226       SUBROUTINE SGGEV( 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       REAL               A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
00240      $                   B( LDB, * ), BETA( * ), VL( LDVL, * ),
00241      $                   VR( LDVR, * ), WORK( * )
00242 *     ..
00243 *
00244 *  =====================================================================
00245 *
00246 *     .. Parameters ..
00247       REAL               ZERO, ONE
00248       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+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       REAL               ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS,
00257      $                   SMLNUM, TEMP
00258 *     ..
00259 *     .. Local Arrays ..
00260       LOGICAL            LDUMMA( 1 )
00261 *     ..
00262 *     .. External Subroutines ..
00263       EXTERNAL           SGEQRF, SGGBAK, SGGBAL, SGGHRD, SHGEQZ, SLABAD,
00264      $                   SLACPY, SLASCL, SLASET, SORGQR, SORMQR, STGEVC,
00265      $                   XERBLA
00266 *     ..
00267 *     .. External Functions ..
00268       LOGICAL            LSAME
00269       INTEGER            ILAENV
00270       REAL               SLAMCH, SLANGE
00271       EXTERNAL           LSAME, ILAENV, SLAMCH, SLANGE
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, 'SGEQRF', ' ', N, 1, N, 0 ) ) )
00335          MAXWRK = MAX( MAXWRK, N*( 7 +
00336      $                 ILAENV( 1, 'SORMQR', ' ', N, 1, N, 0 ) ) )
00337          IF( ILVL ) THEN
00338             MAXWRK = MAX( MAXWRK, N*( 7 +
00339      $                 ILAENV( 1, 'SORGQR', ' ', 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( 'SGGEV ', -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 = SLAMCH( 'P' )
00362       SMLNUM = SLAMCH( 'S' )
00363       BIGNUM = ONE / SMLNUM
00364       CALL SLABAD( 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 = SLANGE( '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 SLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
00381 *
00382 *     Scale B if max element outside range [SMLNUM,BIGNUM]
00383 *
00384       BNRM = SLANGE( '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 SLASCL( '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 SGGBAL( '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 SGEQRF( 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 SORMQR( '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 SLASET( 'Full', N, N, ZERO, ONE, VL, LDVL )
00431          IF( IROWS.GT.1 ) THEN
00432             CALL SLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
00433      $                   VL( ILO+1, ILO ), LDVL )
00434          END IF
00435          CALL SORGQR( 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 SLASET( '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 SGGHRD( JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB, VL,
00452      $                LDVL, VR, LDVR, IERR )
00453       ELSE
00454          CALL SGGHRD( '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 SHGEQZ( 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 STGEVC( 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 SGGBAK( '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 SGGBAK( '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 SLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAR, N, IERR )
00580          CALL SLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAI, N, IERR )
00581       END IF
00582 *
00583       IF( ILBSCL ) THEN
00584          CALL SLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
00585       END IF
00586 *
00587       WORK( 1 ) = MAXWRK
00588       RETURN
00589 *
00590 *     End of SGGEV
00591 *
00592       END
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