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    • DecompositionOperations(T) Class
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  • HermitianEigenvalueDecompose Method
DecompositionOperationsTReal, TComplexHermitianEigenvalueDecompose Method Extreme Optimization Numerical Libraries for .NET Professional

Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.

Namespace: Extreme.Mathematics.LinearAlgebra.Implementation
Assembly: Extreme.Numerics.Net40 (in Extreme.Numerics.Net40.dll) Version: 6.0.16073.0 (6.0.17114.0)
Syntax

C#
VB
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public abstract void HermitianEigenvalueDecompose(
	char jobz,
	MatrixTriangle uplo,
	int n,
	Array2D<TComplex> a,
	Array1D<TReal> w,
	out int info
)
Public MustOverride 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:
virtual void HermitianEigenvalueDecompose(
	wchar_t jobz, 
	MatrixTriangle uplo, 
	int n, 
	Array2D<TComplex> a, 
	Array1D<TReal> w, 
	[OutAttribute] int% info
) abstract
abstract HermitianEigenvalueDecompose : 
        jobz : char * 
        uplo : MatrixTriangle * 
        n : int * 
        a : Array2D<'TComplex> * 
        w : Array1D<'TReal> * 
        info : int byref -> unit 

Parameters

jobz
Type: SystemChar
            = 'N':  Compute eigenvalues only;
            = 'V':  Compute eigenvalues and eigenvectors.
            
uplo
Type: Extreme.MathematicsMatrixTriangle
            = 'U':  Upper triangle of A is stored;
            = 'L':  Lower triangle of A is stored.
            
n
Type: SystemInt32
            The order of the matrix A.  N >= 0.
            
a
Type: Extreme.CollectionsArray2DTComplex
            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
Type: Extreme.CollectionsArray1DTReal
            W is TReal array, dimension (N)
            If INFO = 0, the eigenvalues in ascending order.
            
info
Type: SystemInt32
            = 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).
            
Remarks

            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

Version Information

Numerical Libraries

Supported in: 6.0
See Also

Reference

DecompositionOperationsTReal, TComplex Class
Extreme.Mathematics.LinearAlgebra.Implementation Namespace

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