SingleBandCholeskyDecomposition Class

Members See Also

Represents the Cholesky decomposition of a positive-definite symmetric SingleBandMatrix.

Namespace: Extreme.Mathematics.LinearAlgebra
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 SingleBandCholeskyDecomposition : SingleDecomposition

Visual Basic (Declaration)
Public NotInheritable Class SingleBandCholeskyDecomposition _ Inherits SingleDecomposition

Visual C++
public ref class SingleBandCholeskyDecomposition sealed : public SingleDecomposition

F#
[<SealedAttribute>] type SingleBandCholeskyDecomposition = class inherit SingleDecomposition end

Remarks

The Cholesky decomposition of a real symmetric positive definite matrix A rewrites the matrix in the form A= LL^T, where L is a lower-triangular matrix.

SingleBandCholeskyDecomposition 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.

CholeskyDecomposition inherits from SingleLinearTransformation. This means you can use it to solve systems of linear equations where the matrix of the system is symmetric and positive definite. You can solve for a single right-hand side, or for multiple right-hand sides using the Solve(SingleDenseVector, Boolean) method. You can also calculate the determinant the inverse, and an estimate for the condition number.

To solve a general (non-symmetric or non-positive definite)system of equations, use the LUDecomposition class instead.

Inheritance Hierarchy

System..::..Object
  Extreme.Mathematics.LinearAlgebra..::..SingleLinearTransformation
    Extreme.Mathematics.LinearAlgebra..::..SingleDecomposition
      Extreme.Mathematics.LinearAlgebra..::..SingleBandCholeskyDecomposition