com.asher_stern.crf.function.TwiceDerivableFunction Maven / Gradle / Ivy

Go to download

Show more of this group Show more artifacts with this name
Show all versions of CRF Show documentation

Implementation of linear-chain Conditional Random Fields (CRF) in pure Java

There is a newer version: 1.2.0

package com.asher_stern.crf.function;

/**
 * A multivariate differentiable function for which we know how to calculate the second derivative for every pair of variables.
 * See {@link Function} and {@link DerivableFunction} about the function and the gradient (which is the first derivative).
 * 

 * The second derivatives are represented as a matrix, named "Hessian". The cell (i,j) in the Hessian is the partial derivative
 * of f by the ith variable, derived again by the jth variable.
 * For example, let f(x_1,x_2) = (x_1)^2 + x_1*x_2.

 * Its gradient is the vector [2*x_1 + x_2 , x_1].

 * Its Hessian is
 *  * 2 1
 * 1 0
 * 
 * which means:

 * The partial derivative by x_1 is 2*x_1 + x_2, and its derivation by x_1 again is 2.

 * The partial derivative by x_1 is 2*x_1 + x_2, and its derivation by x_2 is 1.

 * The partial derivative by x_2 is x_1, and its derivation by x_1 is 1.

 * The partial derivative by x_2 is x_1, and its derivation by x_2 is 0.

 * 
 * 
 * @author Asher Stern
 * Date: Nov 6, 2014
 *
 */
public abstract class TwiceDerivableFunction extends DerivableFunction
{
	/**
	 * Returns the Hessian matrix for the given function in the given point (point is "x" -- the function input).
	 * @param point "point" is "x" -- the input for the function.
	 * @return the Hessian matrix -- the matrix of partial second derivations.
	 */
	public abstract double[][] hessian(double[] point);
}