DecompositionOperations<TReal, TComplex>.EigenvalueDecompose Method

public void EigenvalueDecompose(
	char jobvl,
	char jobvr,
	int n,
	Array2D<TComplex> a,
	Array1D<TComplex> w,
	Array2D<TComplex> vl,
	Array2D<TComplex> vr,
	out int info
)

Public Sub EigenvalueDecompose ( 
	jobvl As Char,
	jobvr As Char,
	n As Integer,
	a As Array2D(Of TComplex),
	w As Array1D(Of TComplex),
	vl As Array2D(Of TComplex),
	vr As Array2D(Of TComplex),
	<OutAttribute> ByRef info As Integer
)

public:
void EigenvalueDecompose(
	wchar_t jobvl, 
	wchar_t jobvr, 
	int n, 
	Array2D<TComplex> a, 
	Array1D<TComplex> w, 
	Array2D<TComplex> vl, 
	Array2D<TComplex> vr, 
	[OutAttribute] int% info
)

member EigenvalueDecompose : 
        jobvl : char * 
        jobvr : char * 
        n : int * 
        a : Array2D<'TComplex> * 
        w : Array1D<'TComplex> * 
        vl : Array2D<'TComplex> * 
        vr : Array2D<'TComplex> * 
        info : int byref -> unit 

Parameters

jobvl  Char

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

jobvr  Char

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

n  Int32

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

a  Array2D<TComplex>

            A is TComplex 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).
            

w  Array1D<TComplex>

            W is TComplex array, dimension (N)
            W contains the computed eigenvalues.
            

vl  Array2D<TComplex>

            VL is TComplex 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.
            

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

vr  Array2D<TComplex>

            VR is TComplex 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.
            

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

info  Int32

            = 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.
            

            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.
            

Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Date: November 2011

public void EigenvalueDecompose(
	char jobvl,
	char jobvr,
	int n,
	Span2D<TComplex> a,
	Span<TComplex> w,
	Span2D<TComplex> vl,
	Span2D<TComplex> vr,
	out int info
)

Public Sub EigenvalueDecompose ( 
	jobvl As Char,
	jobvr As Char,
	n As Integer,
	a As Span2D(Of TComplex),
	w As Span(Of TComplex),
	vl As Span2D(Of TComplex),
	vr As Span2D(Of TComplex),
	<OutAttribute> ByRef info As Integer
)

public:
void EigenvalueDecompose(
	wchar_t jobvl, 
	wchar_t jobvr, 
	int n, 
	Span2D<TComplex> a, 
	Span<TComplex> w, 
	Span2D<TComplex> vl, 
	Span2D<TComplex> vr, 
	[OutAttribute] int% info
)

member EigenvalueDecompose : 
        jobvl : char * 
        jobvr : char * 
        n : int * 
        a : Span2D<'TComplex> * 
        w : Span<'TComplex> * 
        vl : Span2D<'TComplex> * 
        vr : Span2D<'TComplex> * 
        info : int byref -> unit 

Parameters

jobvl  Char

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

jobvr  Char

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

n  Int32

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

a  Span2D<TComplex>

            A is TComplex 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).
            

w  Span<TComplex>

            W is TComplex array, dimension (N)
            W contains the computed eigenvalues.
            

vl  Span2D<TComplex>

            VL is TComplex 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.
            

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

vr  Span2D<TComplex>

            VR is TComplex 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.
            

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

info  Int32

            = 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.
            

            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.
            

Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Date: November 2011

public 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 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:
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
)

member 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  Char

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

jobvr  Char

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

n  Int32

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

a  Array2D<TReal>

            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  Array1D<TReal>

            WR is TReal array, dimension (N)
            

wi  Array1D<TReal>

            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  Array2D<TReal>

            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  Array2D<TReal>

            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  Int32

            = 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.

public void EigenvalueDecompose(
	char jobvl,
	char jobvr,
	int n,
	Span2D<TReal> a,
	Span<TReal> wr,
	Span<TReal> wi,
	Span2D<TReal> vl,
	Span2D<TReal> vr,
	out int info
)

Public Sub EigenvalueDecompose ( 
	jobvl As Char,
	jobvr As Char,
	n As Integer,
	a As Span2D(Of TReal),
	wr As Span(Of TReal),
	wi As Span(Of TReal),
	vl As Span2D(Of TReal),
	vr As Span2D(Of TReal),
	<OutAttribute> ByRef info As Integer
)

public:
void EigenvalueDecompose(
	wchar_t jobvl, 
	wchar_t jobvr, 
	int n, 
	Span2D<TReal> a, 
	Span<TReal> wr, 
	Span<TReal> wi, 
	Span2D<TReal> vl, 
	Span2D<TReal> vr, 
	[OutAttribute] int% info
)

member EigenvalueDecompose : 
        jobvl : char * 
        jobvr : char * 
        n : int * 
        a : Span2D<'TReal> * 
        wr : Span<'TReal> * 
        wi : Span<'TReal> * 
        vl : Span2D<'TReal> * 
        vr : Span2D<'TReal> * 
        info : int byref -> unit 

Parameters

jobvl  Char

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

jobvr  Char

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

n  Int32

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

a  Span2D<TReal>

            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  Span<TReal>

            WR is TReal array, dimension (N)
            

wi  Span<TReal>

            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  Span2D<TReal>

            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  Span2D<TReal>

            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  Int32

            = 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.

public abstract void EigenvalueDecompose(
	char jobvl,
	char jobvr,
	int n,
	Span<TComplex> a,
	int lda,
	Span<TComplex> w,
	Span<TComplex> vl,
	int ldvl,
	Span<TComplex> vr,
	int ldvr,
	out int info
)

Public MustOverride Sub EigenvalueDecompose ( 
	jobvl As Char,
	jobvr As Char,
	n As Integer,
	a As Span(Of TComplex),
	lda As Integer,
	w As Span(Of TComplex),
	vl As Span(Of TComplex),
	ldvl As Integer,
	vr As Span(Of TComplex),
	ldvr As Integer,
	<OutAttribute> ByRef info As Integer
)

public:
virtual void EigenvalueDecompose(
	wchar_t jobvl, 
	wchar_t jobvr, 
	int n, 
	Span<TComplex> a, 
	int lda, 
	Span<TComplex> w, 
	Span<TComplex> vl, 
	int ldvl, 
	Span<TComplex> vr, 
	int ldvr, 
	[OutAttribute] int% info
) abstract

abstract EigenvalueDecompose : 
        jobvl : char * 
        jobvr : char * 
        n : int * 
        a : Span<'TComplex> * 
        lda : int * 
        w : Span<'TComplex> * 
        vl : Span<'TComplex> * 
        ldvl : int * 
        vr : Span<'TComplex> * 
        ldvr : int * 
        info : int byref -> unit 

Parameters

jobvl  Char

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

jobvr  Char

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

n  Int32

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

a  Span<TComplex>

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

lda  Int32

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

w  Span<TComplex>

            W is TComplex array, dimension (N)
            W contains the computed eigenvalues.
            

vl  Span<TComplex>

            VL is TComplex 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  Int32

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

vr  Span<TComplex>

            VR is TComplex 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  Int32

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

info  Int32

            = 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.
            

            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.
            

Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Date: November 2011

public abstract void EigenvalueDecompose(
	char jobvl,
	char jobvr,
	int n,
	Span<TReal> a,
	int lda,
	Span<TReal> wr,
	Span<TReal> wi,
	Span<TReal> vl,
	int ldvl,
	Span<TReal> vr,
	int ldvr,
	out int info
)

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

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

abstract EigenvalueDecompose : 
        jobvl : char * 
        jobvr : char * 
        n : int * 
        a : Span<'TReal> * 
        lda : int * 
        wr : Span<'TReal> * 
        wi : Span<'TReal> * 
        vl : Span<'TReal> * 
        ldvl : int * 
        vr : Span<'TReal> * 
        ldvr : int * 
        info : int byref -> unit 

Parameters

jobvl  Char

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

jobvr  Char

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

n  Int32

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

a  Span<TReal>

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

lda  Int32

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

wr  Span<TReal>

            WR is TReal array, dimension (N)
            

wi  Span<TReal>

            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  Span<TReal>

            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).
            

ldvl  Int32

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

vr  Span<TReal>

            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).
            

ldvr  Int32

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

info  Int32

            = 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.

Reference