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RedHat 9 (Linux i386) - man page for dgeev (redhat section l)

DGEEV(l)					)					 DGEEV(l)

NAME
       DGEEV - compute 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 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 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 overwritten.

       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 eigenvalues.	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 conjugate 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 (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 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.

       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.

LAPACK version 3.0			   15 June 2000 				 DGEEV(l)


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