sgeev.f(3)							      LAPACK								sgeev.f(3)

NAME

       sgeev.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sgeev (JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR, LDVR, WORK, LWORK, INFO)
	    SGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Function/Subroutine Documentation
   subroutine sgeev (characterJOBVL, characterJOBVR, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )WR, real, dimension( *
       )WI, real, dimension( ldvl, * )VL, integerLDVL, real, dimension( ldvr, * )VR, integerLDVR, real, dimension( * )WORK, integerLWORK,
       integerINFO)
	SGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

       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)**T * A = lambda(j) * u(j)**T
	    where u(j)**T denotes the transpose of u(j).

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

       Parameters:
	   JOBVL

		     JOBVL is CHARACTER*1
		     = 'N': left eigenvectors of A are not computed;
		     = 'V': left eigenvectors of A are computed.

	   JOBVR

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

	   N

		     N is INTEGER
		     The order of the matrix A. N >= 0.

	   A

		     A is REAL array, dimension (LDA,N)
		     On entry, the N-by-N matrix A.
		     On exit, A has been overwritten.

	   LDA

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

	   WR

		     WR is REAL array, dimension (N)

	   WI

		     WI is REAL 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

		     VL is 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

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

	   VR

		     VR is 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

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

	   WORK

		     WORK is REAL array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

	   LWORK

		     LWORK is 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

		     INFO is 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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 189 of file sgeev.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013							sgeev.f(3)