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DDogleg Numerics is a high performance Java library for non-linear optimization, robust model fitting, polynomial root finding, sorting, and more.

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/*
 * Copyright (c) 2012-2018, Peter Abeles. All Rights Reserved.
 *
 * This file is part of DDogleg (http://ddogleg.org).
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *   http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.ddogleg.optimization.derivative;

import org.ddogleg.optimization.functions.FunctionNtoM;
import org.ddogleg.optimization.functions.FunctionNtoMxN;
import org.ejml.UtilEjml;
import org.ejml.data.DMatrixRMaj;

/**
 * Finite difference numerical jacobian calculation using the forward+backwards equation.
 * Difference equation, f'(x) = (f(x+h)-f(x-h))/(2*h).  Scaling is taken in account by h based
 * upon the magnitude of the elements in variable x.
 *
 * 
 * NOTE: If multiple input parameters are modified by the function when a single one is changed numerical
 * derivatives aren't reliable.
 * 
 *
 * @author Peter Abeles
 */
public class NumericalJacobianFB implements FunctionNtoMxN
{
	// number of input variables
	private final int N;
	// number of functions
	private final int M;

	// function being differentiated
	private FunctionNtoM function;

	// scaling of the difference parameter
	private double differenceScale;

	private double output0[];
	private double output1[];

	public NumericalJacobianFB(FunctionNtoM function, double differenceScale) {
		this.function = function;
		this.differenceScale = differenceScale;
		this.N = function.getNumOfInputsN();
		this.M = function.getNumOfOutputsM();
		output0 = new double[M];
		output1 = new double[M];
	}

	public NumericalJacobianFB(FunctionNtoM function) {
		this(function,Math.sqrt(UtilEjml.EPS));
	}

	@Override
	public int getNumOfInputsN() {
		return N;
	}

	@Override
	public int getNumOfOutputsM() {
		return M;
	}

	@Override
	public void process(double[] input, DMatrixRMaj jacobian) {
		DMatrixRMaj J = jacobian;
		
		for( int i = 0; i < N; i++ ) {
			double x = input[i];
			double h = x != 0 ? differenceScale*Math.abs(x) : differenceScale;

			// backwards sample
			double temp0 = x-h;
			input[i] = temp0;
			double h0 = x-temp0;
			function.process(input,output0);

			// forwards sample
			double temp1 = x+h;
			double h1 = temp1-x;
			input[i] = temp1;
			function.process(input,output1);
			for( int j = 0; j < M; j++ ) {
				J.unsafe_set(j,i,(output1[j] - output0[j])/(h0+h1));
			}
			input[i] = x;
		}
	}

	@Override
	public DMatrixRMaj declareMatrixMxN() {
		return new DMatrixRMaj(M,N);
	}
}