public abstract void EigenvalueDecompose(
	char jobvl,
	char jobvr,
	int n,
	Array2D<TReal> a,
	Array1D<TReal> wr,
	Array1D<TReal> wi,
	Array2D<TReal> vl,
	Array2D<TReal> vr,
	out int info
)

Public MustOverride Sub EigenvalueDecompose ( 
	jobvl As Char,
	jobvr As Char,
	n As Integer,
	a As Array2D(Of TReal),
	wr As Array1D(Of TReal),
	wi As Array1D(Of TReal),
	vl As Array2D(Of TReal),
	vr As Array2D(Of TReal),
	<OutAttribute> ByRef info As Integer
)

public:
virtual void EigenvalueDecompose(
	wchar_t jobvl, 
	wchar_t jobvr, 
	int n, 
	Array2D<TReal> a, 
	Array1D<TReal> wr, 
	Array1D<TReal> wi, 
	Array2D<TReal> vl, 
	Array2D<TReal> vr, 
	[OutAttribute] int% info
) abstract

abstract EigenvalueDecompose : 
        jobvl : char * 
        jobvr : char * 
        n : int * 
        a : Array2D<'TReal> * 
        wr : Array1D<'TReal> * 
        wi : Array1D<'TReal> * 
        vl : Array2D<'TReal> * 
        vr : Array2D<'TReal> * 
        info : int byref -> unit 

Parameters

jobvl

Type: SystemChar

            = 'N': left eigenvectors of A are not computed;
            = 'V': left eigenvectors of A are computed.
            

jobvr

Type: SystemChar

            = 'N': right eigenvectors of A are not computed;
            = 'V': right eigenvectors of A are computed.
            

n

Type: SystemInt32

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

a

Type: Extreme.CollectionsArray2DTReal

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

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

wr

Type: Extreme.CollectionsArray1DTReal

            WR is TReal array, dimension (N)
            

wi

Type: Extreme.CollectionsArray1DTReal

            WI is TReal 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

Type: Extreme.CollectionsArray2DTReal

            VL is TReal 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).
            

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

vr

Type: Extreme.CollectionsArray2DTReal

            VR is TReal 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).
            

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

info

Type: SystemInt32

            = 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.
            

            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.
            

This method corresponds to the LAPACK routine ?GEEV.

Numerical Libraries

Reference