com.numericalmethod.suanshu.matrix.doubles.operation.positivedefinite

Class CholeskyWang2006

java.lang.Object

com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.triangle.LowerTriangularMatrix

com.numericalmethod.suanshu.matrix.doubles.operation.positivedefinite.CholeskyWang2006

All Implemented Interfaces:

Table, DeepCopyable, AbelianGroup<Matrix>, Monoid<Matrix>, Ring<Matrix>, Matrix, MatrixAccess, MatrixRing, MatrixTable, Densifiable, java.io.Serializable

public class CholeskyWang2006
extends LowerTriangularMatrix

Cholesky decomposition works only for a positive definite matrix. If a matrix is not positive definite, Wang (2006) suggests to first do an eigen decomposition. Second, force the non-negative diagonal elements in the diagonal matrix to to a small non-negative number, e.g., 0. Third, re-construct a positive definite matrix from the new diagonal elements. Finally, Cholesky decomposition can proceed as usual to the "modified" matrix.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
CholeskyWang2006(Matrix Sigma, double epsilon) Construct the Cholesky decomposition of a matrix.

Method Summary

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.triangle.LowerTriangularMatrix

add, deepCopy, equals, get, getColumn, getRow, hashCode, minus, multiply, multiply, nCols, nRows, ONE, opposite, scaled, set, t, toDense, toString, ZERO

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

CholeskyWang2006

public CholeskyWang2006(Matrix Sigma,
                        double epsilon)

Construct the Cholesky decomposition of a matrix.

Parameters:

Sigma - a matrix, e.g., a covariance matrix

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0