org.gersteinlab.regulation.numeric
Class NewtonMethod

java.lang.Object
  org.gersteinlab.regulation.numeric.DescentMethod
      org.gersteinlab.regulation.numeric.NewtonMethod

public class NewtonMethod
extends DescentMethod

        A class for minimizing a doubly differentiable multivariate real
        function using the Newton's method.
        

Version:

1.0 (August 29, 2008)

        Change History:
        1.0     - Initial version
        

Author:

Kevin Yuk-Lap Yip

Field Summary

static double

EPSILON

Fields inherited from class org.gersteinlab.regulation.numeric.DescentMethod

ALPHA, BETA

Constructor Summary

NewtonMethod(DoublyDifferentiableMultivariateFunction funcIn)
Construct an instance for a function.

Method Summary

protected double	lambda2(double[] x) Get the error estimate, lambda^2, at a point.
protected double	lambda2(double[] dx, double[][] hfx) Get the error estimate, lambda^2, at a point, with precomputed Newton's direction and Hessian.
double[]	minimize(double[] x0) Perform the minimization using default parameters.
double[]	minimize(double[] x0, double alpha, double beta, double epsilon) Perform the minimization.
protected double[]	nd(double[] x) Get the standard Newton's direction at a point.
protected double[]	nd(double[] gfx, double[][] hfx) Get the standard Newton's direction at a point, with precomputed gradient and Hessian.

Methods inherited from class org.gersteinlab.regulation.numeric.DescentMethod

armijo, armijo

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

EPSILON

public static final double EPSILON

See Also:

Constant Field Values

Constructor Detail

NewtonMethod

public NewtonMethod(DoublyDifferentiableMultivariateFunction funcIn)

Construct an instance for a function.

Parameters:

funcIn - The function

Method Detail

minimize

public double[] minimize(double[] x0)

Perform the minimization using default parameters.

Specified by:

minimize in class DescentMethod

Parameters:

x0 - The initial estimate of x

Returns:

The final estimate of x

minimize

public double[] minimize(double[] x0,
                         double alpha,
                         double beta,
                         double epsilon)

Perform the minimization.

Parameters:

x0 - The initial estimate of x

alpha - The stopping parameter of backtracking line search

beta - The reduction factor of t of backtracking line search

epsilon - The stopping parameter

Returns:

The final estimate of x

nd

protected double[] nd(double[] x)

Get the standard Newton's direction at a point.

Parameters:

x - The point

Returns:

The Newton's direction at the point

nd

protected double[] nd(double[] gfx,
                      double[][] hfx)

Get the standard Newton's direction at a point, with precomputed gradient and Hessian.

Parameters:

gfx - The gradient at the point

hfx - The Hessian at the point

Returns:

The Newton's direction at the point

lambda2

protected double lambda2(double[] x)

Get the error estimate, lambda^2, at a point.

Parameters:

x - The point

Returns:

lambda^2 at the point

lambda2

protected double lambda2(double[] dx,
                         double[][] hfx)

Get the error estimate, lambda^2, at a point, with precomputed Newton's direction and Hessian.

Parameters:

dx - The Newton's direction at the point

hfx - The Hessian at the point

Returns:

lambda^2 at the point