Computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A.
Namespace: Extreme.Mathematics.LinearAlgebra.ImplementationAssembly: Extreme.Numerics.Net40 (in Extreme.Numerics.Net40.dll) Version: 6.0.16073.0 (6.0.17114.0)
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).
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
Numerical Libraries
Supported in: 6.0
Reference