SystemObject Extreme.Mathematics.LinearAlgebra.ComplexSingleComplexLinearTransformation Extreme.Mathematics.LinearAlgebra.ComplexSingleComplexDecomposition Extreme.Mathematics.LinearAlgebra.ComplexSingleComplexCholeskyDecomposition
Namespace: Extreme.Mathematics.LinearAlgebra.ComplexAssembly: Extreme.Numerics.Version4x.Net40 (in Extreme.Numerics.Version4x.Net40.dll) Version: 4.2.11333.0 (5.0.12317.0)
public sealed class SingleComplexCholeskyDecomposition : SingleComplexDecomposition
Public NotInheritable Class SingleComplexCholeskyDecomposition
Inherits SingleComplexDecomposition
public ref class SingleComplexCholeskyDecomposition sealed : public SingleComplexDecomposition
[<SealedAttribute>]
type SingleComplexCholeskyDecomposition =
class
inherit SingleComplexDecomposition
end
The SingleComplexCholeskyDecomposition type exposes the following members.
Top
Top
Top
The Cholesky decomposition of a real hermitian positive
definite matrix
A rewrites the
matrix in the form
A=
LLH, where
L is a
lower-triangular
matrix or in the form
A=
UHU, where
U is a
upper-triangular
matrix.. Which form depends on whether the elements of the Hermitian
matrix are stored in the lower or upper triangular part.
ComplexCholeskyDecomposition can operate in two modes.
In overwrite mode, the original matrix is overwritten
with the result of the decomposition. In preserve mode, the original matrix
is preserved, and a new matrix is created to hold the
decomposition. You can set the mode through the
Overwrite property.
ComplexCholeskyDecomposition inherits from
SingleLinearTransformation. This means you can
use it to solve systems of linear equations where the
matrix of the system is hermitian and positive definite.
You can solve for a single right-hand side, or for multiple
right-hand sides using the Solve(SingleComplexDenseVector, Boolean) method.
You can also calculate the determinant
the inverse, and an estimate for the
condition number.
To solve a general (non-hermitian or non-positive
definite)system of equations, use the ComplexLUDecomposition class instead.
Numerical Libraries
Supported in: 5.x, 4.x
Reference