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

SGEEV(l)					)					 SGEEV(l)

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

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

	   CHARACTER	 JOBVL, JOBVR

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

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

PURPOSE
       SGEEV 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) REAL 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) REAL array, dimension (N)
	       WI      (output) REAL array, dimension (N) WR and WI contain the real  and  imagi-
	       nary parts, respectively, of the computed eigenvalues.  Complex conjugate pairs of
	       eigenvalues appear consecutively with the eigenvalue having the positive imaginary
	       part first.

       VL      (output) REAL 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) REAL 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) REAL 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 				 SGEEV(l)


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