LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cgeevx.f
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00001 *> \brief <b> CGEEVX 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 CGEEVX + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeevx.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeevx.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeevx.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE CGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL,
00022 *                          LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE,
00023 *                          RCONDV, WORK, LWORK, RWORK, INFO )
00024 * 
00025 *       .. Scalar Arguments ..
00026 *       CHARACTER          BALANC, JOBVL, JOBVR, SENSE
00027 *       INTEGER            IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N
00028 *       REAL               ABNRM
00029 *       ..
00030 *       .. Array Arguments ..
00031 *       REAL               RCONDE( * ), RCONDV( * ), RWORK( * ),
00032 *      $                   SCALE( * )
00033 *       COMPLEX            A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ),
00034 *      $                   W( * ), WORK( * )
00035 *       ..
00036 *  
00037 *
00038 *> \par Purpose:
00039 *  =============
00040 *>
00041 *> \verbatim
00042 *>
00043 *> CGEEVX computes for an N-by-N complex nonsymmetric matrix A, the
00044 *> eigenvalues and, optionally, the left and/or right eigenvectors.
00045 *>
00046 *> Optionally also, it computes a balancing transformation to improve
00047 *> the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
00048 *> SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues
00049 *> (RCONDE), and reciprocal condition numbers for the right
00050 *> eigenvectors (RCONDV).
00051 *>
00052 *> The right eigenvector v(j) of A satisfies
00053 *>                  A * v(j) = lambda(j) * v(j)
00054 *> where lambda(j) is its eigenvalue.
00055 *> The left eigenvector u(j) of A satisfies
00056 *>               u(j)**H * A = lambda(j) * u(j)**H
00057 *> where u(j)**H denotes the conjugate transpose of u(j).
00058 *>
00059 *> The computed eigenvectors are normalized to have Euclidean norm
00060 *> equal to 1 and largest component real.
00061 *>
00062 *> Balancing a matrix means permuting the rows and columns to make it
00063 *> more nearly upper triangular, and applying a diagonal similarity
00064 *> transformation D * A * D**(-1), where D is a diagonal matrix, to
00065 *> make its rows and columns closer in norm and the condition numbers
00066 *> of its eigenvalues and eigenvectors smaller.  The computed
00067 *> reciprocal condition numbers correspond to the balanced matrix.
00068 *> Permuting rows and columns will not change the condition numbers
00069 *> (in exact arithmetic) but diagonal scaling will.  For further
00070 *> explanation of balancing, see section 4.10.2 of the LAPACK
00071 *> Users' Guide.
00072 *> \endverbatim
00073 *
00074 *  Arguments:
00075 *  ==========
00076 *
00077 *> \param[in] BALANC
00078 *> \verbatim
00079 *>          BALANC is CHARACTER*1
00080 *>          Indicates how the input matrix should be diagonally scaled
00081 *>          and/or permuted to improve the conditioning of its
00082 *>          eigenvalues.
00083 *>          = 'N': Do not diagonally scale or permute;
00084 *>          = 'P': Perform permutations to make the matrix more nearly
00085 *>                 upper triangular. Do not diagonally scale;
00086 *>          = 'S': Diagonally scale the matrix, ie. replace A by
00087 *>                 D*A*D**(-1), where D is a diagonal matrix chosen
00088 *>                 to make the rows and columns of A more equal in
00089 *>                 norm. Do not permute;
00090 *>          = 'B': Both diagonally scale and permute A.
00091 *>
00092 *>          Computed reciprocal condition numbers will be for the matrix
00093 *>          after balancing and/or permuting. Permuting does not change
00094 *>          condition numbers (in exact arithmetic), but balancing does.
00095 *> \endverbatim
00096 *>
00097 *> \param[in] JOBVL
00098 *> \verbatim
00099 *>          JOBVL is CHARACTER*1
00100 *>          = 'N': left eigenvectors of A are not computed;
00101 *>          = 'V': left eigenvectors of A are computed.
00102 *>          If SENSE = 'E' or 'B', JOBVL must = 'V'.
00103 *> \endverbatim
00104 *>
00105 *> \param[in] JOBVR
00106 *> \verbatim
00107 *>          JOBVR is CHARACTER*1
00108 *>          = 'N': right eigenvectors of A are not computed;
00109 *>          = 'V': right eigenvectors of A are computed.
00110 *>          If SENSE = 'E' or 'B', JOBVR must = 'V'.
00111 *> \endverbatim
00112 *>
00113 *> \param[in] SENSE
00114 *> \verbatim
00115 *>          SENSE is CHARACTER*1
00116 *>          Determines which reciprocal condition numbers are computed.
00117 *>          = 'N': None are computed;
00118 *>          = 'E': Computed for eigenvalues only;
00119 *>          = 'V': Computed for right eigenvectors only;
00120 *>          = 'B': Computed for eigenvalues and right eigenvectors.
00121 *>
00122 *>          If SENSE = 'E' or 'B', both left and right eigenvectors
00123 *>          must also be computed (JOBVL = 'V' and JOBVR = 'V').
00124 *> \endverbatim
00125 *>
00126 *> \param[in] N
00127 *> \verbatim
00128 *>          N is INTEGER
00129 *>          The order of the matrix A. N >= 0.
00130 *> \endverbatim
00131 *>
00132 *> \param[in,out] A
00133 *> \verbatim
00134 *>          A is COMPLEX array, dimension (LDA,N)
00135 *>          On entry, the N-by-N matrix A.
00136 *>          On exit, A has been overwritten.  If JOBVL = 'V' or
00137 *>          JOBVR = 'V', A contains the Schur form of the balanced 
00138 *>          version of the matrix A.
00139 *> \endverbatim
00140 *>
00141 *> \param[in] LDA
00142 *> \verbatim
00143 *>          LDA is INTEGER
00144 *>          The leading dimension of the array A.  LDA >= max(1,N).
00145 *> \endverbatim
00146 *>
00147 *> \param[out] W
00148 *> \verbatim
00149 *>          W is COMPLEX array, dimension (N)
00150 *>          W contains the computed eigenvalues.
00151 *> \endverbatim
00152 *>
00153 *> \param[out] VL
00154 *> \verbatim
00155 *>          VL is COMPLEX array, dimension (LDVL,N)
00156 *>          If JOBVL = 'V', the left eigenvectors u(j) are stored one
00157 *>          after another in the columns of VL, in the same order
00158 *>          as their eigenvalues.
00159 *>          If JOBVL = 'N', VL is not referenced.
00160 *>          u(j) = VL(:,j), the j-th column of VL.
00161 *> \endverbatim
00162 *>
00163 *> \param[in] LDVL
00164 *> \verbatim
00165 *>          LDVL is INTEGER
00166 *>          The leading dimension of the array VL.  LDVL >= 1; if
00167 *>          JOBVL = 'V', LDVL >= N.
00168 *> \endverbatim
00169 *>
00170 *> \param[out] VR
00171 *> \verbatim
00172 *>          VR is COMPLEX array, dimension (LDVR,N)
00173 *>          If JOBVR = 'V', the right eigenvectors v(j) are stored one
00174 *>          after another in the columns of VR, in the same order
00175 *>          as their eigenvalues.
00176 *>          If JOBVR = 'N', VR is not referenced.
00177 *>          v(j) = VR(:,j), the j-th column of VR.
00178 *> \endverbatim
00179 *>
00180 *> \param[in] LDVR
00181 *> \verbatim
00182 *>          LDVR is INTEGER
00183 *>          The leading dimension of the array VR.  LDVR >= 1; if
00184 *>          JOBVR = 'V', LDVR >= N.
00185 *> \endverbatim
00186 *>
00187 *> \param[out] ILO
00188 *> \verbatim
00189 *>          ILO is INTEGER
00190 *> \endverbatim
00191 *>
00192 *> \param[out] IHI
00193 *> \verbatim
00194 *>          IHI is INTEGER
00195 *>          ILO and IHI are integer values determined when A was
00196 *>          balanced.  The balanced A(i,j) = 0 if I > J and
00197 *>          J = 1,...,ILO-1 or I = IHI+1,...,N.
00198 *> \endverbatim
00199 *>
00200 *> \param[out] SCALE
00201 *> \verbatim
00202 *>          SCALE is REAL array, dimension (N)
00203 *>          Details of the permutations and scaling factors applied
00204 *>          when balancing A.  If P(j) is the index of the row and column
00205 *>          interchanged with row and column j, and D(j) is the scaling
00206 *>          factor applied to row and column j, then
00207 *>          SCALE(J) = P(J),    for J = 1,...,ILO-1
00208 *>                   = D(J),    for J = ILO,...,IHI
00209 *>                   = P(J)     for J = IHI+1,...,N.
00210 *>          The order in which the interchanges are made is N to IHI+1,
00211 *>          then 1 to ILO-1.
00212 *> \endverbatim
00213 *>
00214 *> \param[out] ABNRM
00215 *> \verbatim
00216 *>          ABNRM is REAL
00217 *>          The one-norm of the balanced matrix (the maximum
00218 *>          of the sum of absolute values of elements of any column).
00219 *> \endverbatim
00220 *>
00221 *> \param[out] RCONDE
00222 *> \verbatim
00223 *>          RCONDE is REAL array, dimension (N)
00224 *>          RCONDE(j) is the reciprocal condition number of the j-th
00225 *>          eigenvalue.
00226 *> \endverbatim
00227 *>
00228 *> \param[out] RCONDV
00229 *> \verbatim
00230 *>          RCONDV is REAL array, dimension (N)
00231 *>          RCONDV(j) is the reciprocal condition number of the j-th
00232 *>          right eigenvector.
00233 *> \endverbatim
00234 *>
00235 *> \param[out] WORK
00236 *> \verbatim
00237 *>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
00238 *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00239 *> \endverbatim
00240 *>
00241 *> \param[in] LWORK
00242 *> \verbatim
00243 *>          LWORK is INTEGER
00244 *>          The dimension of the array WORK.  If SENSE = 'N' or 'E',
00245 *>          LWORK >= max(1,2*N), and if SENSE = 'V' or 'B',
00246 *>          LWORK >= N*N+2*N.
00247 *>          For good performance, LWORK must generally be larger.
00248 *>
00249 *>          If LWORK = -1, then a workspace query is assumed; the routine
00250 *>          only calculates the optimal size of the WORK array, returns
00251 *>          this value as the first entry of the WORK array, and no error
00252 *>          message related to LWORK is issued by XERBLA.
00253 *> \endverbatim
00254 *>
00255 *> \param[out] RWORK
00256 *> \verbatim
00257 *>          RWORK is REAL array, dimension (2*N)
00258 *> \endverbatim
00259 *>
00260 *> \param[out] INFO
00261 *> \verbatim
00262 *>          INFO is INTEGER
00263 *>          = 0:  successful exit
00264 *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
00265 *>          > 0:  if INFO = i, the QR algorithm failed to compute all the
00266 *>                eigenvalues, and no eigenvectors or condition numbers
00267 *>                have been computed; elements 1:ILO-1 and i+1:N of W
00268 *>                contain eigenvalues which have converged.
00269 *> \endverbatim
00270 *
00271 *  Authors:
00272 *  ========
00273 *
00274 *> \author Univ. of Tennessee 
00275 *> \author Univ. of California Berkeley 
00276 *> \author Univ. of Colorado Denver 
00277 *> \author NAG Ltd. 
00278 *
00279 *> \date November 2011
00280 *
00281 *> \ingroup complexGEeigen
00282 *
00283 *  =====================================================================
00284       SUBROUTINE CGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL,
00285      $                   LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE,
00286      $                   RCONDV, WORK, LWORK, RWORK, INFO )
00287 *
00288 *  -- LAPACK driver routine (version 3.4.0) --
00289 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00290 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00291 *     November 2011
00292 *
00293 *     .. Scalar Arguments ..
00294       CHARACTER          BALANC, JOBVL, JOBVR, SENSE
00295       INTEGER            IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N
00296       REAL               ABNRM
00297 *     ..
00298 *     .. Array Arguments ..
00299       REAL               RCONDE( * ), RCONDV( * ), RWORK( * ),
00300      $                   SCALE( * )
00301       COMPLEX            A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ),
00302      $                   W( * ), WORK( * )
00303 *     ..
00304 *
00305 *  =====================================================================
00306 *
00307 *     .. Parameters ..
00308       REAL               ZERO, ONE
00309       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
00310 *     ..
00311 *     .. Local Scalars ..
00312       LOGICAL            LQUERY, SCALEA, WANTVL, WANTVR, WNTSNB, WNTSNE,
00313      $                   WNTSNN, WNTSNV
00314       CHARACTER          JOB, SIDE
00315       INTEGER            HSWORK, I, ICOND, IERR, ITAU, IWRK, K, MAXWRK,
00316      $                   MINWRK, NOUT
00317       REAL               ANRM, BIGNUM, CSCALE, EPS, SCL, SMLNUM
00318       COMPLEX            TMP
00319 *     ..
00320 *     .. Local Arrays ..
00321       LOGICAL            SELECT( 1 )
00322       REAL               DUM( 1 )
00323 *     ..
00324 *     .. External Subroutines ..
00325       EXTERNAL           CGEBAK, CGEBAL, CGEHRD, CHSEQR, CLACPY, CLASCL,
00326      $                   CSCAL, CSSCAL, CTREVC, CTRSNA, CUNGHR, SLABAD,
00327      $                   SLASCL, XERBLA
00328 *     ..
00329 *     .. External Functions ..
00330       LOGICAL            LSAME
00331       INTEGER            ILAENV, ISAMAX
00332       REAL               CLANGE, SCNRM2, SLAMCH
00333       EXTERNAL           LSAME, ILAENV, ISAMAX, CLANGE, SCNRM2, SLAMCH
00334 *     ..
00335 *     .. Intrinsic Functions ..
00336       INTRINSIC          AIMAG, CMPLX, CONJG, MAX, REAL, SQRT
00337 *     ..
00338 *     .. Executable Statements ..
00339 *
00340 *     Test the input arguments
00341 *
00342       INFO = 0
00343       LQUERY = ( LWORK.EQ.-1 )
00344       WANTVL = LSAME( JOBVL, 'V' )
00345       WANTVR = LSAME( JOBVR, 'V' )
00346       WNTSNN = LSAME( SENSE, 'N' )
00347       WNTSNE = LSAME( SENSE, 'E' )
00348       WNTSNV = LSAME( SENSE, 'V' )
00349       WNTSNB = LSAME( SENSE, 'B' )
00350       IF( .NOT.( LSAME( BALANC, 'N' ) .OR. LSAME( BALANC, 'S' ) .OR.
00351      $    LSAME( BALANC, 'P' ) .OR. LSAME( BALANC, 'B' ) ) ) THEN
00352          INFO = -1
00353       ELSE IF( ( .NOT.WANTVL ) .AND. ( .NOT.LSAME( JOBVL, 'N' ) ) ) THEN
00354          INFO = -2
00355       ELSE IF( ( .NOT.WANTVR ) .AND. ( .NOT.LSAME( JOBVR, 'N' ) ) ) THEN
00356          INFO = -3
00357       ELSE IF( .NOT.( WNTSNN .OR. WNTSNE .OR. WNTSNB .OR. WNTSNV ) .OR.
00358      $         ( ( WNTSNE .OR. WNTSNB ) .AND. .NOT.( WANTVL .AND.
00359      $         WANTVR ) ) ) THEN
00360          INFO = -4
00361       ELSE IF( N.LT.0 ) THEN
00362          INFO = -5
00363       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00364          INFO = -7
00365       ELSE IF( LDVL.LT.1 .OR. ( WANTVL .AND. LDVL.LT.N ) ) THEN
00366          INFO = -10
00367       ELSE IF( LDVR.LT.1 .OR. ( WANTVR .AND. LDVR.LT.N ) ) THEN
00368          INFO = -12
00369       END IF
00370 *
00371 *     Compute workspace
00372 *      (Note: Comments in the code beginning "Workspace:" describe the
00373 *       minimal amount of workspace needed at that point in the code,
00374 *       as well as the preferred amount for good performance.
00375 *       CWorkspace refers to complex workspace, and RWorkspace to real
00376 *       workspace. NB refers to the optimal block size for the
00377 *       immediately following subroutine, as returned by ILAENV.
00378 *       HSWORK refers to the workspace preferred by CHSEQR, as
00379 *       calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
00380 *       the worst case.)
00381 *
00382       IF( INFO.EQ.0 ) THEN
00383          IF( N.EQ.0 ) THEN
00384             MINWRK = 1
00385             MAXWRK = 1
00386          ELSE
00387             MAXWRK = N + N*ILAENV( 1, 'CGEHRD', ' ', N, 1, N, 0 )
00388 *
00389             IF( WANTVL ) THEN
00390                CALL CHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VL, LDVL,
00391      $                WORK, -1, INFO )
00392             ELSE IF( WANTVR ) THEN
00393                CALL CHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VR, LDVR,
00394      $                WORK, -1, INFO )
00395             ELSE
00396                IF( WNTSNN ) THEN
00397                   CALL CHSEQR( 'E', 'N', N, 1, N, A, LDA, W, VR, LDVR,
00398      $                WORK, -1, INFO )
00399                ELSE
00400                   CALL CHSEQR( 'S', 'N', N, 1, N, A, LDA, W, VR, LDVR,
00401      $                WORK, -1, INFO )
00402                END IF
00403             END IF
00404             HSWORK = WORK( 1 )
00405 *
00406             IF( ( .NOT.WANTVL ) .AND. ( .NOT.WANTVR ) ) THEN
00407                MINWRK = 2*N
00408                IF( .NOT.( WNTSNN .OR. WNTSNE ) )
00409      $            MINWRK = MAX( MINWRK, N*N + 2*N )
00410                MAXWRK = MAX( MAXWRK, HSWORK )
00411                IF( .NOT.( WNTSNN .OR. WNTSNE ) )
00412      $            MAXWRK = MAX( MAXWRK, N*N + 2*N )
00413             ELSE
00414                MINWRK = 2*N
00415                IF( .NOT.( WNTSNN .OR. WNTSNE ) )
00416      $            MINWRK = MAX( MINWRK, N*N + 2*N )
00417                MAXWRK = MAX( MAXWRK, HSWORK )
00418                MAXWRK = MAX( MAXWRK, N + ( N - 1 )*ILAENV( 1, 'CUNGHR',
00419      $                       ' ', N, 1, N, -1 ) )
00420                IF( .NOT.( WNTSNN .OR. WNTSNE ) )
00421      $            MAXWRK = MAX( MAXWRK, N*N + 2*N )
00422                MAXWRK = MAX( MAXWRK, 2*N )
00423             END IF
00424             MAXWRK = MAX( MAXWRK, MINWRK )
00425          END IF
00426          WORK( 1 ) = MAXWRK
00427 *
00428          IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
00429             INFO = -20
00430          END IF
00431       END IF
00432 *
00433       IF( INFO.NE.0 ) THEN
00434          CALL XERBLA( 'CGEEVX', -INFO )
00435          RETURN
00436       ELSE IF( LQUERY ) THEN
00437          RETURN
00438       END IF
00439 *
00440 *     Quick return if possible
00441 *
00442       IF( N.EQ.0 )
00443      $   RETURN
00444 *
00445 *     Get machine constants
00446 *
00447       EPS = SLAMCH( 'P' )
00448       SMLNUM = SLAMCH( 'S' )
00449       BIGNUM = ONE / SMLNUM
00450       CALL SLABAD( SMLNUM, BIGNUM )
00451       SMLNUM = SQRT( SMLNUM ) / EPS
00452       BIGNUM = ONE / SMLNUM
00453 *
00454 *     Scale A if max element outside range [SMLNUM,BIGNUM]
00455 *
00456       ICOND = 0
00457       ANRM = CLANGE( 'M', N, N, A, LDA, DUM )
00458       SCALEA = .FALSE.
00459       IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
00460          SCALEA = .TRUE.
00461          CSCALE = SMLNUM
00462       ELSE IF( ANRM.GT.BIGNUM ) THEN
00463          SCALEA = .TRUE.
00464          CSCALE = BIGNUM
00465       END IF
00466       IF( SCALEA )
00467      $   CALL CLASCL( 'G', 0, 0, ANRM, CSCALE, N, N, A, LDA, IERR )
00468 *
00469 *     Balance the matrix and compute ABNRM
00470 *
00471       CALL CGEBAL( BALANC, N, A, LDA, ILO, IHI, SCALE, IERR )
00472       ABNRM = CLANGE( '1', N, N, A, LDA, DUM )
00473       IF( SCALEA ) THEN
00474          DUM( 1 ) = ABNRM
00475          CALL SLASCL( 'G', 0, 0, CSCALE, ANRM, 1, 1, DUM, 1, IERR )
00476          ABNRM = DUM( 1 )
00477       END IF
00478 *
00479 *     Reduce to upper Hessenberg form
00480 *     (CWorkspace: need 2*N, prefer N+N*NB)
00481 *     (RWorkspace: none)
00482 *
00483       ITAU = 1
00484       IWRK = ITAU + N
00485       CALL CGEHRD( N, ILO, IHI, A, LDA, WORK( ITAU ), WORK( IWRK ),
00486      $             LWORK-IWRK+1, IERR )
00487 *
00488       IF( WANTVL ) THEN
00489 *
00490 *        Want left eigenvectors
00491 *        Copy Householder vectors to VL
00492 *
00493          SIDE = 'L'
00494          CALL CLACPY( 'L', N, N, A, LDA, VL, LDVL )
00495 *
00496 *        Generate unitary matrix in VL
00497 *        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
00498 *        (RWorkspace: none)
00499 *
00500          CALL CUNGHR( N, ILO, IHI, VL, LDVL, WORK( ITAU ), WORK( IWRK ),
00501      $                LWORK-IWRK+1, IERR )
00502 *
00503 *        Perform QR iteration, accumulating Schur vectors in VL
00504 *        (CWorkspace: need 1, prefer HSWORK (see comments) )
00505 *        (RWorkspace: none)
00506 *
00507          IWRK = ITAU
00508          CALL CHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, W, VL, LDVL,
00509      $                WORK( IWRK ), LWORK-IWRK+1, INFO )
00510 *
00511          IF( WANTVR ) THEN
00512 *
00513 *           Want left and right eigenvectors
00514 *           Copy Schur vectors to VR
00515 *
00516             SIDE = 'B'
00517             CALL CLACPY( 'F', N, N, VL, LDVL, VR, LDVR )
00518          END IF
00519 *
00520       ELSE IF( WANTVR ) THEN
00521 *
00522 *        Want right eigenvectors
00523 *        Copy Householder vectors to VR
00524 *
00525          SIDE = 'R'
00526          CALL CLACPY( 'L', N, N, A, LDA, VR, LDVR )
00527 *
00528 *        Generate unitary matrix in VR
00529 *        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
00530 *        (RWorkspace: none)
00531 *
00532          CALL CUNGHR( N, ILO, IHI, VR, LDVR, WORK( ITAU ), WORK( IWRK ),
00533      $                LWORK-IWRK+1, IERR )
00534 *
00535 *        Perform QR iteration, accumulating Schur vectors in VR
00536 *        (CWorkspace: need 1, prefer HSWORK (see comments) )
00537 *        (RWorkspace: none)
00538 *
00539          IWRK = ITAU
00540          CALL CHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, W, VR, LDVR,
00541      $                WORK( IWRK ), LWORK-IWRK+1, INFO )
00542 *
00543       ELSE
00544 *
00545 *        Compute eigenvalues only
00546 *        If condition numbers desired, compute Schur form
00547 *
00548          IF( WNTSNN ) THEN
00549             JOB = 'E'
00550          ELSE
00551             JOB = 'S'
00552          END IF
00553 *
00554 *        (CWorkspace: need 1, prefer HSWORK (see comments) )
00555 *        (RWorkspace: none)
00556 *
00557          IWRK = ITAU
00558          CALL CHSEQR( JOB, 'N', N, ILO, IHI, A, LDA, W, VR, LDVR,
00559      $                WORK( IWRK ), LWORK-IWRK+1, INFO )
00560       END IF
00561 *
00562 *     If INFO > 0 from CHSEQR, then quit
00563 *
00564       IF( INFO.GT.0 )
00565      $   GO TO 50
00566 *
00567       IF( WANTVL .OR. WANTVR ) THEN
00568 *
00569 *        Compute left and/or right eigenvectors
00570 *        (CWorkspace: need 2*N)
00571 *        (RWorkspace: need N)
00572 *
00573          CALL CTREVC( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR,
00574      $                N, NOUT, WORK( IWRK ), RWORK, IERR )
00575       END IF
00576 *
00577 *     Compute condition numbers if desired
00578 *     (CWorkspace: need N*N+2*N unless SENSE = 'E')
00579 *     (RWorkspace: need 2*N unless SENSE = 'E')
00580 *
00581       IF( .NOT.WNTSNN ) THEN
00582          CALL CTRSNA( SENSE, 'A', SELECT, N, A, LDA, VL, LDVL, VR, LDVR,
00583      $                RCONDE, RCONDV, N, NOUT, WORK( IWRK ), N, RWORK,
00584      $                ICOND )
00585       END IF
00586 *
00587       IF( WANTVL ) THEN
00588 *
00589 *        Undo balancing of left eigenvectors
00590 *
00591          CALL CGEBAK( BALANC, 'L', N, ILO, IHI, SCALE, N, VL, LDVL,
00592      $                IERR )
00593 *
00594 *        Normalize left eigenvectors and make largest component real
00595 *
00596          DO 20 I = 1, N
00597             SCL = ONE / SCNRM2( N, VL( 1, I ), 1 )
00598             CALL CSSCAL( N, SCL, VL( 1, I ), 1 )
00599             DO 10 K = 1, N
00600                RWORK( K ) = REAL( VL( K, I ) )**2 +
00601      $                      AIMAG( VL( K, I ) )**2
00602    10       CONTINUE
00603             K = ISAMAX( N, RWORK, 1 )
00604             TMP = CONJG( VL( K, I ) ) / SQRT( RWORK( K ) )
00605             CALL CSCAL( N, TMP, VL( 1, I ), 1 )
00606             VL( K, I ) = CMPLX( REAL( VL( K, I ) ), ZERO )
00607    20    CONTINUE
00608       END IF
00609 *
00610       IF( WANTVR ) THEN
00611 *
00612 *        Undo balancing of right eigenvectors
00613 *
00614          CALL CGEBAK( BALANC, 'R', N, ILO, IHI, SCALE, N, VR, LDVR,
00615      $                IERR )
00616 *
00617 *        Normalize right eigenvectors and make largest component real
00618 *
00619          DO 40 I = 1, N
00620             SCL = ONE / SCNRM2( N, VR( 1, I ), 1 )
00621             CALL CSSCAL( N, SCL, VR( 1, I ), 1 )
00622             DO 30 K = 1, N
00623                RWORK( K ) = REAL( VR( K, I ) )**2 +
00624      $                      AIMAG( VR( K, I ) )**2
00625    30       CONTINUE
00626             K = ISAMAX( N, RWORK, 1 )
00627             TMP = CONJG( VR( K, I ) ) / SQRT( RWORK( K ) )
00628             CALL CSCAL( N, TMP, VR( 1, I ), 1 )
00629             VR( K, I ) = CMPLX( REAL( VR( K, I ) ), ZERO )
00630    40    CONTINUE
00631       END IF
00632 *
00633 *     Undo scaling if necessary
00634 *
00635    50 CONTINUE
00636       IF( SCALEA ) THEN
00637          CALL CLASCL( 'G', 0, 0, CSCALE, ANRM, N-INFO, 1, W( INFO+1 ),
00638      $                MAX( N-INFO, 1 ), IERR )
00639          IF( INFO.EQ.0 ) THEN
00640             IF( ( WNTSNV .OR. WNTSNB ) .AND. ICOND.EQ.0 )
00641      $         CALL SLASCL( 'G', 0, 0, CSCALE, ANRM, N, 1, RCONDV, N,
00642      $                      IERR )
00643          ELSE
00644             CALL CLASCL( 'G', 0, 0, CSCALE, ANRM, ILO-1, 1, W, N, IERR )
00645          END IF
00646       END IF
00647 *
00648       WORK( 1 ) = MAXWRK
00649       RETURN
00650 *
00651 *     End of CGEEVX
00652 *
00653       END
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