Class CholeskyDecompositionFunctions

Namespace

NanoQL.Numerics

Assembly

NanoQL.dll

The Cholesky decomposition of a symmetric matrix, and the solve it gives.

public static class CholeskyDecompositionFunctions

Inheritance

object

CholeskyDecompositionFunctions

Inherited Members

object.GetType()

object.MemberwiseClone()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Methods

CholeskyDecomposition(Matrix, bool)

The lower-triangular L of the Cholesky decomposition S = L·Lᵀ of a symmetric positive definite matrix; with flexible, of a positive semi-definite one too, a non-positive pivot read as 0.

public static Matrix CholeskyDecomposition(Matrix m, bool flexible = false)

Parameters

m Matrix

The matrix, symmetric.

flexible bool

Whether a positive semi-definite matrix is accepted.

Returns

Matrix

A new lower-triangular matrix.

Exceptions

ArgumentException

m isn't square, or isn't positive definite and flexible is false.

CholeskySolveFor(Matrix, Vector)

The solution x of L·Lᵀ·x = b, for the lower-triangular L of a Cholesky decomposition: forward, then backward substitution.

public static Vector CholeskySolveFor(Matrix L, Vector b)

Parameters

L Matrix

The lower-triangular matrix.

b Vector

The right-hand side, of L's size.

Returns

Vector

A new vector.

Exceptions

ArgumentException

L isn't square of b's size.