com.numericalmethod.suanshu.optimization.unconstrained.hessian
Class GoldfeldQuandtTrotter

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixMathImpl<T>
      com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixStorageImpl<DenseMatrix>
          com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.DenseMatrix
              com.numericalmethod.suanshu.optimization.unconstrained.hessian.GoldfeldQuandtTrotter

All Implemented Interfaces:

DeepCopyable, AbelianGroup<Matrix>, Monoid<Matrix>, Ring<Matrix>, Matrix, MatrixAccessor, MatrixRing, Densifiable, MatrixDimension

public class GoldfeldQuandtTrotter
extends DenseMatrix

Goldfeld, Quandt and Trotter propose the following way to coerce a non-positive definite Hessian matrix to become positive definite. For a non-positive definite Hessian matrix H, we compute

        H + βI
 H^ = -----------
         1 + β
 

Constructor Summary

GoldfeldQuandtTrotter(Matrix H, double beta)
Construct a positive definite matrix using the Goldfeld-Quandt-Trotter algorithm.

Method Summary

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

add, deepCopy, getColumn, getColumn, getMatrixData, getRow, getRow, getSample, minus, multiply, multiply, ONE, overwrite, scaled, t, toDense, ZERO

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixStorageImpl

equals, get, hashCode, set, setMatrixData

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixMathImpl

add, call, minus, multiply, nCols, nRows, opposite, setColumn, setColumn, setRow, setRow, toString

Methods inherited from class java.lang.Object

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

Constructor Detail

GoldfeldQuandtTrotter

public GoldfeldQuandtTrotter(Matrix H,
                             double beta)

Construct a positive definite matrix using the Goldfeld-Quandt-Trotter algorithm.

Parameters:

H - a non-positive definite matrix

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