Generic Decomposition Operations<T>.Symmetric Eigenvalue Decompose Method
Definition
Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET.Generic (in Numerics.NET.Generic.dll) Version: 9.0.1
Assembly: Numerics.NET.Generic (in Numerics.NET.Generic.dll) Version: 9.0.1
Overload List
Symmetric | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. |
Symmetric | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. |
Symmetric | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. |
SymmetricEigenvalueDecompose(Char, MatrixTriangle, Int32, Span<T>, Int32, Span<T>, Int32)
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A.
public override void SymmetricEigenvalueDecompose(
char jobz,
MatrixTriangle storedTriangle,
int n,
Span<T> a,
int lda,
Span<T> w,
out int info
)
Parameters
- jobz Char
= 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors.
- storedTriangle 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<T>
A is TReal array, dimension (LDA, N) On entry, the symmetric 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<T>
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).
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. Because of large use of BLAS of level 3, DSYEVD needs N**2 more workspace than DSYEVX.
Contributors:
Jeff Rutter, Computer Science Division, University of California at Berkeley, USA \n Modified by Francoise Tisseur, University of Tennessee \n Modified description of INFO. Sven, 16 Feb 05. \n
This method corresponds to the LAPACK routine DSYEVD.