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Meta.Numerics.Matrices.CholeskyDecomposition Class Reference

Represents the Cholesky Decomposition of a symmetric, positive definite matrix. More...

+ Collaboration diagram for Meta.Numerics.Matrices.CholeskyDecomposition:

Public Member Functions

SquareMatrix SquareRootMatrix ()
 Returns the Cholesky square root matrix. More...
 
ColumnVector Solve (IList< double > rhs)
 Computes the solution vector that, when multiplied by the original matrix, produces the given left-hand side vector. More...
 
SymmetricMatrix Inverse ()
 Computes the inverse of the original matrix. More...
 
double Determinant ()
 Computes the determinant of the original matrix. More...
 

Properties

int Dimension [get]
 Gets the dimension of the system. More...
 

Detailed Description

Represents the Cholesky Decomposition of a symmetric, positive definite matrix.

A Cholesky decomposition represents a matrix as the product of a lower-left triangular matrix and its transpose. For example:

The Choleksy decomposition of a symmetric, positive definite matrix can be obtained using the SymmetricMatrix.CholeskyDecomposition method of the SymmetricMatrix class.

Here is an example that uses a Cholesky decomposition to solve a linear algebra problem.

// Solve Ax = b via Cholesky decomposition
CholeskyDecomposition CD = A.CholsekyDecomposition();
ColumnVector b = new ColumnVector(1.0, 2.0, 3.0);
ColumnVector x CD.Solve(b);
See also
SymmetricMatrix.CholeskyDecomposition

Member Function Documentation

SquareMatrix Meta.Numerics.Matrices.CholeskyDecomposition.SquareRootMatrix ( )
inline

Returns the Cholesky square root matrix.

Returns
A lower-left triangular matrix A, such that A AT = M.

Referenced by Test.MultivariateSampleTest.CreateMultivariateNormalSample().

ColumnVector Meta.Numerics.Matrices.CholeskyDecomposition.Solve ( IList< double >  rhs)
inline

Computes the solution vector that, when multiplied by the original matrix, produces the given left-hand side vector.

Parameters
rhsThe right-hand-side vector.
Returns
The left-hand-side (solution) vector.

Referenced by Meta.Numerics.Statistics.MultivariateSample.LinearRegression_Internal().

double Meta.Numerics.Matrices.CholeskyDecomposition.Determinant ( )
inline

Computes the determinant of the original matrix.

Returns
det M

Referenced by Test.SymmetricMatrixTest.CatalanHankelMatrixDeterminant(), and Test.MultiIntegrateTest.GaussianIntegrals().

Property Documentation

int Meta.Numerics.Matrices.CholeskyDecomposition.Dimension
get

Gets the dimension of the system.

Referenced by Test.SymmetricMatrixTest.SymmetricMatrixDecomposition().


The documentation for this class was generated from the following file: