zgeev(3S)

NAME
     ZGEEV - compute for an N-by-N complex nonsymmetric matrix A, the
     eigenvalues and, optionally, the left and/or right eigenvectors

SYNOPSIS
     SUBROUTINE ZGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, WORK,
                       LWORK, RWORK, INFO )

         CHARACTER     JOBVL, JOBVR

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

         DOUBLE        PRECISION RWORK( * )

         COMPLEX*16    A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), W( * ),
                       WORK( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the
     eigenvalues 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 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) COMPLEX*16 array, dimension (LDA,N)
             On entry, the N-by-N matrix A.  On exit, A has been overwritten.

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

     W       (output) COMPLEX*16 array, dimension (N)
             W contains the computed eigenvalues.

     VL      (output) COMPLEX*16 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
             eigenvalues.  If JOBVL = 'N', VL is not referenced.  u(j) =
             VL(:,j), the j-th column of VL.

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

     VR      (output) COMPLEX*16 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.  v(j) =
             VR(:,j), the j-th column of VR.

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

     WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)
             On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

     LWORK   (input) INTEGER
             The dimension of the array WORK.  LWORK >= max(1,2*N).  For good
             performance, 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.

     RWORK   (workspace) DOUBLE PRECISION array, dimension (2*N)

     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 and
             i+1:N of W contain eigenvalues which have converged.
SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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