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

Class GoldfeldQuandtTrotter

java.lang.Object

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

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

All Implemented Interfaces:

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

public class GoldfeldQuandtTrotter
extends DenseMatrix

Goldfeld, Quandt and Trotter propose the following way to coerce a non-positive definite Hessian matrix to become symmetric, positive definite. For a non-positive definite Hessian matrix H, we compute \[ \widehat{H} = \frac{H + \beta I}{1 + \beta} \]

Constructor Summary

Constructors

Constructor and Description
GoldfeldQuandtTrotter(Matrix H, double beta) Constructs a symmetric, positive definite matrix using the Goldfeld-Quandt-Trotter algorithm.

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

GoldfeldQuandtTrotter

public GoldfeldQuandtTrotter(Matrix H,
                             double beta)

Constructs a symmetric, positive definite matrix using the Goldfeld-Quandt-Trotter algorithm.

Parameters:

H - a non-positive definite matrix

beta - a positive number. The bigger beta is, the closer H^ is to I. If beta == Double.POSITIVE_INFINITY, then H^ = I.