SingleComplexCholeskyDecomposition Class

Members See Also

Represents the Cholesky decomposition of a positive-definite SingleComplexHermitianMatrix.

Namespace: Extreme.Mathematics.LinearAlgebra.Complex
Assembly: Extreme.Numerics.SinglePrecision.Net40 (in Extreme.Numerics.SinglePrecision.Net40.dll) Version: 4.0.10170.0 (4.0.11003.0)

Syntax

C#
public sealed class SingleComplexCholeskyDecomposition : SingleComplexDecomposition

Visual Basic (Declaration)
Public NotInheritable Class SingleComplexCholeskyDecomposition _ Inherits SingleComplexDecomposition

Visual C++
public ref class SingleComplexCholeskyDecomposition sealed : public SingleComplexDecomposition

F#
[<SealedAttribute>] type SingleComplexCholeskyDecomposition = class inherit SingleComplexDecomposition end

Remarks

The Cholesky decomposition of a real hermitian positive definite matrix A rewrites the matrix in the form A= LL^H, where L is a lower-triangular matrix or in the form A= U^HU, 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.

Inheritance Hierarchy

System..::..Object
  Extreme.Mathematics.LinearAlgebra.Complex..::..SingleComplexLinearTransformation
    Extreme.Mathematics.LinearAlgebra.Complex..::..SingleComplexDecomposition
      Extreme.Mathematics.LinearAlgebra.Complex..::..SingleComplexCholeskyDecomposition