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

Class PositiveDefiniteMatrixByPositiveDiagonal

java.lang.Object

com.numericalmethod.suanshu.algebra.linear.matrix.doubles.matrixtype.dense.DenseMatrix

com.numericalmethod.suanshu.algebra.linear.matrix.doubles.operation.positivedefinite.PositiveDefiniteMatrixByPositiveDiagonal

All Implemented Interfaces:

Matrix, MatrixAccess, MatrixRing, MatrixTable, Densifiable, AbelianGroup<Matrix>, Monoid<Matrix>, Ring<Matrix>, Table, DeepCopyable

Direct Known Subclasses:

PositiveSemiDefiniteMatrixNonNegativeDiagonal

public class PositiveDefiniteMatrixByPositiveDiagonal
extends DenseMatrix

This class "converts" a matrix into a symmetric, positive definite matrix, if it is not already so, by forcing the diagonal entries in the eigen decomposition to a small non-negative number, e.g., 0.

See Also:

• "Jin Wang, Chunlei Liu. "Generating Multivariate Mixture of Normal Distributions using a Modified Cholesky Decomposition," Simulation Conference, 2006. WSC 06. Proceedings of the Winter. p. 342 - 347. 3-6 Dec. 2006."
• "Higham, Nicholas J., "Computing a Nearest Symmetric Positive Semidefinite Matrix," Linear Algebra and its Applications, 1988, 103:103-118"

Constructor Summary

Constructors

Constructor and Description
PositiveDefiniteMatrixByPositiveDiagonal(Matrix A, double epsilon, double small) Constructs a positive definite matrix by forcing the diagonal entries in the eigen decomposition to a small non-negative number, e.g., 0.

Method Summary

Methods inherited from class com.numericalmethod.suanshu.algebra.linear.matrix.doubles.matrixtype.dense.DenseMatrix

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

Methods inherited from class java.lang.Object

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

Constructor Detail

PositiveDefiniteMatrixByPositiveDiagonal

public PositiveDefiniteMatrixByPositiveDiagonal(Matrix A,
                                                double epsilon,
                                                double small)

Constructs a positive definite matrix by forcing the diagonal entries in the eigen decomposition to a small non-negative number, e.g., 0.

Parameters:

A - a matrix

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0; used in the eigen decomposition (don't make it 0)

small - the minimum value of the new diagonal entries