Java tutorial
/* * Licensed to the Apache Software Foundation (ASF) under one or more * contributor license agreements. See the NOTICE file distributed with * this work for additional information regarding copyright ownership. * The ASF licenses this file to You 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.apache.commons.math.optimization.fitting; import java.util.ArrayList; import java.util.List; import org.apache.commons.math.analysis.DifferentiableMultivariateVectorialFunction; import org.apache.commons.math.analysis.MultivariateMatrixFunction; import org.apache.commons.math.FunctionEvaluationException; import org.apache.commons.math.optimization.DifferentiableMultivariateVectorialOptimizer; import org.apache.commons.math.optimization.OptimizationException; import org.apache.commons.math.optimization.VectorialPointValuePair; /** Fitter for parametric univariate real functions y = f(x). * <p>When a univariate real function y = f(x) does depend on some * unknown parameters p<sub>0</sub>, p<sub>1</sub> ... p<sub>n-1</sub>, * this class can be used to find these parameters. It does this * by <em>fitting</em> the curve so it remains very close to a set of * observed points (x<sub>0</sub>, y<sub>0</sub>), (x<sub>1</sub>, * y<sub>1</sub>) ... (x<sub>k-1</sub>, y<sub>k-1</sub>). This fitting * is done by finding the parameters values that minimizes the objective * function ∑(y<sub>i</sub>-f(x<sub>i</sub>))<sup>2</sup>. This is * really a least squares problem.</p> * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 fvr. 2011) $ * @since 2.0 */ public class CurveFitter { /** Optimizer to use for the fitting. */ private final DifferentiableMultivariateVectorialOptimizer optimizer; /** Observed points. */ private final List<WeightedObservedPoint> observations; /** Simple constructor. * @param optimizer optimizer to use for the fitting */ public CurveFitter(final DifferentiableMultivariateVectorialOptimizer optimizer) { this.optimizer = optimizer; observations = new ArrayList<WeightedObservedPoint>(); } /** Add an observed (x,y) point to the sample with unit weight. * <p>Calling this method is equivalent to call * <code>addObservedPoint(1.0, x, y)</code>.</p> * @param x abscissa of the point * @param y observed value of the point at x, after fitting we should * have f(x) as close as possible to this value * @see #addObservedPoint(double, double, double) * @see #addObservedPoint(WeightedObservedPoint) * @see #getObservations() */ public void addObservedPoint(double x, double y) { addObservedPoint(1.0, x, y); } /** Add an observed weighted (x,y) point to the sample. * @param weight weight of the observed point in the fit * @param x abscissa of the point * @param y observed value of the point at x, after fitting we should * have f(x) as close as possible to this value * @see #addObservedPoint(double, double) * @see #addObservedPoint(WeightedObservedPoint) * @see #getObservations() */ public void addObservedPoint(double weight, double x, double y) { observations.add(new WeightedObservedPoint(weight, x, y)); } /** Add an observed weighted (x,y) point to the sample. * @param observed observed point to add * @see #addObservedPoint(double, double) * @see #addObservedPoint(double, double, double) * @see #getObservations() */ public void addObservedPoint(WeightedObservedPoint observed) { observations.add(observed); } /** Get the observed points. * @return observed points * @see #addObservedPoint(double, double) * @see #addObservedPoint(double, double, double) * @see #addObservedPoint(WeightedObservedPoint) */ public WeightedObservedPoint[] getObservations() { return observations.toArray(new WeightedObservedPoint[observations.size()]); } /** * Remove all observations. */ public void clearObservations() { observations.clear(); } /** Fit a curve. * <p>This method compute the coefficients of the curve that best * fit the sample of observed points previously given through calls * to the {@link #addObservedPoint(WeightedObservedPoint) * addObservedPoint} method.</p> * @param f parametric function to fit * @param initialGuess first guess of the function parameters * @return fitted parameters * @exception FunctionEvaluationException if the objective function throws one during the search * @exception OptimizationException if the algorithm failed to converge * @exception IllegalArgumentException if the start point dimension is wrong */ public double[] fit(final ParametricRealFunction f, final double[] initialGuess) throws FunctionEvaluationException, OptimizationException, IllegalArgumentException { // prepare least squares problem double[] target = new double[observations.size()]; double[] weights = new double[observations.size()]; int i = 0; for (WeightedObservedPoint point : observations) { target[i] = point.getY(); weights[i] = point.getWeight(); ++i; } // perform the fit VectorialPointValuePair optimum = optimizer.optimize(new TheoreticalValuesFunction(f), target, weights, initialGuess); // extract the coefficients return optimum.getPointRef(); } /** Vectorial function computing function theoretical values. */ private class TheoreticalValuesFunction implements DifferentiableMultivariateVectorialFunction { /** Function to fit. */ private final ParametricRealFunction f; /** Simple constructor. * @param f function to fit. */ public TheoreticalValuesFunction(final ParametricRealFunction f) { this.f = f; } /** {@inheritDoc} */ public MultivariateMatrixFunction jacobian() { return new MultivariateMatrixFunction() { public double[][] value(double[] point) throws FunctionEvaluationException, IllegalArgumentException { final double[][] jacobian = new double[observations.size()][]; int i = 0; for (WeightedObservedPoint observed : observations) { jacobian[i++] = f.gradient(observed.getX(), point); } return jacobian; } }; } /** {@inheritDoc} */ public double[] value(double[] point) throws FunctionEvaluationException, IllegalArgumentException { // compute the residuals final double[] values = new double[observations.size()]; int i = 0; for (WeightedObservedPoint observed : observations) { values[i++] = f.value(observed.getX(), point); } return values; } } }