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dgeev examples
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Man Page Details
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NAME
       DGEEV  - for an N-by-N real nonsymmetric matrix A, the eigenvalues and,
       optionally, the left and/or right eigenvectors

SYNOPSIS
       SUBROUTINE DGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR,  LDVR,
                         WORK, LWORK, INFO )

           CHARACTER     JOBVL, JOBVR

           INTEGER       INFO, LDA, LDVL, LDVR, LWORK, N

           DOUBLE        PRECISION  A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ),
                         WI( * ), WORK( * ), WR( * )

PURPOSE
       DGEEV computes for an N-by-N real nonsymmetric matrix A, the  eigenval-
       ues and, optionally, the left and/or right eigenvectors.

       The right eigenvector v(j) of A satisfies
                        A * v(j) = lambda(j) * v(j)
       where lambda(j) is its eigenvalue.
       The left eigenvector u(j) of A satisfies
                     u(j)**H * A = lambda(j) * u(j)**H
       where u(j)**H denotes the conjugate transpose of u(j).

       The  computed  eigenvectors are normalized to have Euclidean norm equal
       to 1 and largest component real.


ARGUMENTS
       JOBVL   (input) CHARACTER*1
               = 'N': left eigenvectors of A are not computed;
               = 'V': left eigenvectors of A are computed.

       JOBVR   (input) CHARACTER*1
               = 'N': right eigenvectors of A are not computed;
               = 'V': right eigenvectors of A are computed.

       N       (input) INTEGER
               The order of the matrix A. N >= 0.

       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
               On entry, the N-by-N matrix A.  On exit, A has  been  overwrit-
               ten.

       LDA     (input) INTEGER
               The leading dimension of the array A.  LDA >= max(1,N).

       WR      (output) DOUBLE PRECISION array, dimension (N)
               WI       (output)  DOUBLE PRECISION array, dimension (N) WR and
               WI contain the real and imaginary parts, respectively,  of  the
               computed  eigenvalues.   Complex conjugate pairs of eigenvalues
               appear consecutively with the eigenvalue  having  the  positive
               imaginary part first.

       VL      (output) DOUBLE PRECISION array, dimension (LDVL,N)
               If JOBVL = 'V', the left eigenvectors u(j) are stored one after
               another in the columns of VL, in the same order as their eigen-
               values.   If  JOBVL  =  'N', VL is not referenced.  If the j-th
               eigenvalue is real, then u(j) = VL(:,j), the j-th column of VL.
               If  the  j-th and (j+1)-st eigenvalues form a complex conjugate
               pair, then u(j) = VL(:,j) + i*VL(:,j+1) and
               u(j+1) = VL(:,j) - i*VL(:,j+1).

       LDVL    (input) INTEGER
               The leading dimension of the array VL.  LDVL >= 1; if  JOBVL  =
               'V', LDVL >= N.

       VR      (output) DOUBLE PRECISION array, dimension (LDVR,N)
               If  JOBVR  =  'V',  the  right eigenvectors v(j) are stored one
               after another in the columns of VR, in the same order as  their
               eigenvalues.   If JOBVR = 'N', VR is not referenced.  If the j-
               th eigenvalue is real, then v(j) = VR(:,j), the j-th column  of
               VR.  If the j-th and (j+1)-st eigenvalues form a complex conju-
               gate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and
               v(j+1) = VR(:,j) - i*VR(:,j+1).

       LDVR    (input) INTEGER
               The leading dimension of the array VR.  LDVR >= 1; if  JOBVR  =
               'V', LDVR >= N.

       WORK       (workspace/output)   DOUBLE   PRECISION   array,   dimension
       (MAX(1,LWORK))
               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
               The  dimension  of the array WORK.  LWORK >= max(1,3*N), and if
               JOBVL = 'V' or JOBVR = 'V', LWORK >=  4*N.   For  good  perfor-
               mance, LWORK must generally be larger.

               If  LWORK  = -1, then a workspace query is assumed; the routine
               only calculates the optimal size of  the  WORK  array,  returns
               this  value  as the first entry of the WORK array, and no error
               message related to LWORK is issued by XERBLA.

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an illegal value.
               > 0:  if INFO = i, the QR algorithm failed to compute  all  the
               eigenvalues,  and  no eigenvectors have been computed; elements
               i+1:N of WR and WI contain eigenvalues which have converged.

