DecompositionOperations<TReal, TComplex>.HermitianEigenvalueDecompose Method

public void HermitianEigenvalueDecompose(
	char jobz,
	MatrixTriangle uplo,
	int n,
	Array2D<TComplex> a,
	Array1D<TReal> w,
	out int info
)

Public Sub HermitianEigenvalueDecompose ( 
	jobz As Char,
	uplo As MatrixTriangle,
	n As Integer,
	a As Array2D(Of TComplex),
	w As Array1D(Of TReal),
	<OutAttribute> ByRef info As Integer
)

public:
void HermitianEigenvalueDecompose(
	wchar_t jobz, 
	MatrixTriangle uplo, 
	int n, 
	Array2D<TComplex> a, 
	Array1D<TReal> w, 
	[OutAttribute] int% info
)

member HermitianEigenvalueDecompose : 
        jobz : char * 
        uplo : MatrixTriangle * 
        n : int * 
        a : Array2D<'TComplex> * 
        w : Array1D<'TReal> * 
        info : int byref -> unit 

Parameters

jobz  Char

            = 'N':  Compute eigenvalues only;
            = 'V':  Compute eigenvalues and eigenvectors.
            

uplo  MatrixTriangle

            = 'U':  Upper triangle of A is stored;
            = 'L':  Lower triangle of A is stored.
            

n  Int32

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

a  Array2D<TComplex>

            A is TComplex array, dimension (LDA, N)
            On entry, the Hermitian matrix A.  If UPLO = 'U', the
            leading N-by-N upper triangular part of A contains the
            upper triangular part of the matrix A.  If UPLO = 'L',
            the leading N-by-N lower triangular part of A contains
            the lower triangular part of the matrix A.
            On exit, if JOBZ = 'V', then if INFO = 0, A contains the
            orthonormal eigenvectors of the matrix A.
            If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
            or the upper triangle (if UPLO='U') of A, including the
            diagonal, is destroyed.
            

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

w  Array1D<TReal>

            W is TReal array, dimension (N)
            If INFO = 0, the eigenvalues in ascending order.
            

info  Int32

            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
            > 0:  if INFO = i and JOBZ = 'N', then the algorithm failed
                  to converge; i off-diagonal elements of an intermediate
                  tridiagonal form did not converge to zero;
                  if INFO = i and JOBZ = 'V', then the algorithm failed
                  to compute an eigenvalue while working on the sub-matrix
                  lying in rows and columns INFO/(N+1) through
                  mod(INFO,N+1).
            

            If eigenvectors are desired, it uses a
            divide and conquer algorithm.
            The divide and conquer algorithm makes very mild assumptions about
            floating point arithmetic. It will work on machines with a guard
            digit in add/subtract, or on those binary machines without guard
            digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
            Cray-2. It could conceivably fail on hexadecimal or decimal machines
            without guard digits, but we know of none.
            

Further Details:

Modified description of INFO. Sven, 16 Feb 05.

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

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

Date: November 2011

public void HermitianEigenvalueDecompose(
	char jobz,
	MatrixTriangle uplo,
	int n,
	Span2D<TComplex> a,
	Span<TReal> w,
	out int info
)

Public Sub HermitianEigenvalueDecompose ( 
	jobz As Char,
	uplo As MatrixTriangle,
	n As Integer,
	a As Span2D(Of TComplex),
	w As Span(Of TReal),
	<OutAttribute> ByRef info As Integer
)

public:
void HermitianEigenvalueDecompose(
	wchar_t jobz, 
	MatrixTriangle uplo, 
	int n, 
	Span2D<TComplex> a, 
	Span<TReal> w, 
	[OutAttribute] int% info
)

member HermitianEigenvalueDecompose : 
        jobz : char * 
        uplo : MatrixTriangle * 
        n : int * 
        a : Span2D<'TComplex> * 
        w : Span<'TReal> * 
        info : int byref -> unit 

Parameters

jobz  Char

            = 'N':  Compute eigenvalues only;
            = 'V':  Compute eigenvalues and eigenvectors.
            

uplo  MatrixTriangle

            = 'U':  Upper triangle of A is stored;
            = 'L':  Lower triangle of A is stored.
            

n  Int32

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

a  Span2D<TComplex>

            A is TComplex array, dimension (LDA, N)
            On entry, the Hermitian matrix A.  If UPLO = 'U', the
            leading N-by-N upper triangular part of A contains the
            upper triangular part of the matrix A.  If UPLO = 'L',
            the leading N-by-N lower triangular part of A contains
            the lower triangular part of the matrix A.
            On exit, if JOBZ = 'V', then if INFO = 0, A contains the
            orthonormal eigenvectors of the matrix A.
            If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
            or the upper triangle (if UPLO='U') of A, including the
            diagonal, is destroyed.
            

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

w  Span<TReal>

            W is TReal array, dimension (N)
            If INFO = 0, the eigenvalues in ascending order.
            

info  Int32

            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
            > 0:  if INFO = i and JOBZ = 'N', then the algorithm failed
                  to converge; i off-diagonal elements of an intermediate
                  tridiagonal form did not converge to zero;
                  if INFO = i and JOBZ = 'V', then the algorithm failed
                  to compute an eigenvalue while working on the sub-matrix
                  lying in rows and columns INFO/(N+1) through
                  mod(INFO,N+1).
            

            If eigenvectors are desired, it uses a
            divide and conquer algorithm.
            The divide and conquer algorithm makes very mild assumptions about
            floating point arithmetic. It will work on machines with a guard
            digit in add/subtract, or on those binary machines without guard
            digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
            Cray-2. It could conceivably fail on hexadecimal or decimal machines
            without guard digits, but we know of none.
            

Further Details:

Modified description of INFO. Sven, 16 Feb 05.

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

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

Date: November 2011

public abstract void HermitianEigenvalueDecompose(
	char jobz,
	MatrixTriangle uplo,
	int n,
	Span<TComplex> a,
	int lda,
	Span<TReal> w,
	out int info
)

Public MustOverride Sub HermitianEigenvalueDecompose ( 
	jobz As Char,
	uplo As MatrixTriangle,
	n As Integer,
	a As Span(Of TComplex),
	lda As Integer,
	w As Span(Of TReal),
	<OutAttribute> ByRef info As Integer
)

public:
virtual void HermitianEigenvalueDecompose(
	wchar_t jobz, 
	MatrixTriangle uplo, 
	int n, 
	Span<TComplex> a, 
	int lda, 
	Span<TReal> w, 
	[OutAttribute] int% info
) abstract

abstract HermitianEigenvalueDecompose : 
        jobz : char * 
        uplo : MatrixTriangle * 
        n : int * 
        a : Span<'TComplex> * 
        lda : int * 
        w : Span<'TReal> * 
        info : int byref -> unit 

Parameters

jobz  Char

            = 'N':  Compute eigenvalues only;
            = 'V':  Compute eigenvalues and eigenvectors.
            

uplo  MatrixTriangle

            = 'U':  Upper triangle of A is stored;
            = 'L':  Lower triangle of A is stored.
            

n  Int32

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

a  Span<TComplex>

            A is TComplex array, dimension (LDA, N)
            On entry, the Hermitian matrix A.  If UPLO = 'U', the
            leading N-by-N upper triangular part of A contains the
            upper triangular part of the matrix A.  If UPLO = 'L',
            the leading N-by-N lower triangular part of A contains
            the lower triangular part of the matrix A.
            On exit, if JOBZ = 'V', then if INFO = 0, A contains the
            orthonormal eigenvectors of the matrix A.
            If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
            or the upper triangle (if UPLO='U') of A, including the
            diagonal, is destroyed.
            

lda  Int32

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

w  Span<TReal>

            W is TReal array, dimension (N)
            If INFO = 0, the eigenvalues in ascending order.
            

info  Int32

            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
            > 0:  if INFO = i and JOBZ = 'N', then the algorithm failed
                  to converge; i off-diagonal elements of an intermediate
                  tridiagonal form did not converge to zero;
                  if INFO = i and JOBZ = 'V', then the algorithm failed
                  to compute an eigenvalue while working on the sub-matrix
                  lying in rows and columns INFO/(N+1) through
                  mod(INFO,N+1).
            

            If eigenvectors are desired, it uses a
            divide and conquer algorithm.
            The divide and conquer algorithm makes very mild assumptions about
            floating point arithmetic. It will work on machines with a guard
            digit in add/subtract, or on those binary machines without guard
            digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
            Cray-2. It could conceivably fail on hexadecimal or decimal machines
            without guard digits, but we know of none.
            

Further Details:

Modified description of INFO. Sven, 16 Feb 05.

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

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

Date: November 2011

Reference