001 /* 002 * Licensed to the Apache Software Foundation (ASF) under one or more 003 * contributor license agreements. See the NOTICE file distributed with 004 * this work for additional information regarding copyright ownership. 005 * The ASF licenses this file to You under the Apache License, Version 2.0 006 * (the "License"); you may not use this file except in compliance with 007 * the License. You may obtain a copy of the License at 008 * 009 * http://www.apache.org/licenses/LICENSE-2.0 010 * 011 * Unless required by applicable law or agreed to in writing, software 012 * distributed under the License is distributed on an "AS IS" BASIS, 013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 014 * See the License for the specific language governing permissions and 015 * limitations under the License. 016 */ 017 package org.apache.commons.math3.fitting; 018 019 import java.util.ArrayList; 020 import java.util.List; 021 import org.apache.commons.math3.analysis.MultivariateVectorFunction; 022 import org.apache.commons.math3.analysis.MultivariateMatrixFunction; 023 import org.apache.commons.math3.analysis.ParametricUnivariateFunction; 024 import org.apache.commons.math3.optim.MaxEval; 025 import org.apache.commons.math3.optim.InitialGuess; 026 import org.apache.commons.math3.optim.PointVectorValuePair; 027 import org.apache.commons.math3.optim.nonlinear.vector.MultivariateVectorOptimizer; 028 import org.apache.commons.math3.optim.nonlinear.vector.ModelFunction; 029 import org.apache.commons.math3.optim.nonlinear.vector.ModelFunctionJacobian; 030 import org.apache.commons.math3.optim.nonlinear.vector.Target; 031 import org.apache.commons.math3.optim.nonlinear.vector.Weight; 032 033 /** 034 * Fitter for parametric univariate real functions y = f(x). 035 * <br/> 036 * When a univariate real function y = f(x) does depend on some 037 * unknown parameters p<sub>0</sub>, p<sub>1</sub> ... p<sub>n-1</sub>, 038 * this class can be used to find these parameters. It does this 039 * by <em>fitting</em> the curve so it remains very close to a set of 040 * observed points (x<sub>0</sub>, y<sub>0</sub>), (x<sub>1</sub>, 041 * y<sub>1</sub>) ... (x<sub>k-1</sub>, y<sub>k-1</sub>). This fitting 042 * is done by finding the parameters values that minimizes the objective 043 * function ∑(y<sub>i</sub>-f(x<sub>i</sub>))<sup>2</sup>. This is 044 * really a least squares problem. 045 * 046 * @param <T> Function to use for the fit. 047 * 048 * @version $Id: CurveFitter.java 1416643 2012-12-03 19:37:14Z tn $ 049 * @since 2.0 050 */ 051 public class CurveFitter<T extends ParametricUnivariateFunction> { 052 /** Optimizer to use for the fitting. */ 053 private final MultivariateVectorOptimizer optimizer; 054 /** Observed points. */ 055 private final List<WeightedObservedPoint> observations; 056 057 /** 058 * Simple constructor. 059 * 060 * @param optimizer Optimizer to use for the fitting. 061 * @since 3.1 062 */ 063 public CurveFitter(final MultivariateVectorOptimizer optimizer) { 064 this.optimizer = optimizer; 065 observations = new ArrayList<WeightedObservedPoint>(); 066 } 067 068 /** Add an observed (x,y) point to the sample with unit weight. 069 * <p>Calling this method is equivalent to call 070 * {@code addObservedPoint(1.0, x, y)}.</p> 071 * @param x abscissa of the point 072 * @param y observed value of the point at x, after fitting we should 073 * have f(x) as close as possible to this value 074 * @see #addObservedPoint(double, double, double) 075 * @see #addObservedPoint(WeightedObservedPoint) 076 * @see #getObservations() 077 */ 078 public void addObservedPoint(double x, double y) { 079 addObservedPoint(1.0, x, y); 080 } 081 082 /** Add an observed weighted (x,y) point to the sample. 083 * @param weight weight of the observed point in the fit 084 * @param x abscissa of the point 085 * @param y observed value of the point at x, after fitting we should 086 * have f(x) as close as possible to this value 087 * @see #addObservedPoint(double, double) 088 * @see #addObservedPoint(WeightedObservedPoint) 089 * @see #getObservations() 090 */ 091 public void addObservedPoint(double weight, double x, double y) { 092 observations.add(new WeightedObservedPoint(weight, x, y)); 093 } 094 095 /** Add an observed weighted (x,y) point to the sample. 096 * @param observed observed point to add 097 * @see #addObservedPoint(double, double) 098 * @see #addObservedPoint(double, double, double) 099 * @see #getObservations() 100 */ 101 public void addObservedPoint(WeightedObservedPoint observed) { 102 observations.add(observed); 103 } 104 105 /** Get the observed points. 106 * @return observed points 107 * @see #addObservedPoint(double, double) 108 * @see #addObservedPoint(double, double, double) 109 * @see #addObservedPoint(WeightedObservedPoint) 110 */ 111 public WeightedObservedPoint[] getObservations() { 112 return observations.toArray(new WeightedObservedPoint[observations.size()]); 113 } 114 115 /** 116 * Remove all observations. 117 */ 118 public void clearObservations() { 119 observations.clear(); 120 } 121 122 /** 123 * Fit a curve. 124 * This method compute the coefficients of the curve that best 125 * fit the sample of observed points previously given through calls 126 * to the {@link #addObservedPoint(WeightedObservedPoint) 127 * addObservedPoint} method. 128 * 129 * @param f parametric function to fit. 130 * @param initialGuess first guess of the function parameters. 131 * @return the fitted parameters. 132 * @throws org.apache.commons.math3.exception.DimensionMismatchException 133 * if the start point dimension is wrong. 134 */ 135 public double[] fit(T f, final double[] initialGuess) { 136 return fit(Integer.MAX_VALUE, f, initialGuess); 137 } 138 139 /** 140 * Fit a curve. 141 * This method compute the coefficients of the curve that best 142 * fit the sample of observed points previously given through calls 143 * to the {@link #addObservedPoint(WeightedObservedPoint) 144 * addObservedPoint} method. 145 * 146 * @param f parametric function to fit. 147 * @param initialGuess first guess of the function parameters. 148 * @param maxEval Maximum number of function evaluations. 149 * @return the fitted parameters. 150 * @throws org.apache.commons.math3.exception.TooManyEvaluationsException 151 * if the number of allowed evaluations is exceeded. 152 * @throws org.apache.commons.math3.exception.DimensionMismatchException 153 * if the start point dimension is wrong. 154 * @since 3.0 155 */ 156 public double[] fit(int maxEval, T f, 157 final double[] initialGuess) { 158 // Prepare least squares problem. 159 double[] target = new double[observations.size()]; 160 double[] weights = new double[observations.size()]; 161 int i = 0; 162 for (WeightedObservedPoint point : observations) { 163 target[i] = point.getY(); 164 weights[i] = point.getWeight(); 165 ++i; 166 } 167 168 // Input to the optimizer: the model and its Jacobian. 169 final TheoreticalValuesFunction model = new TheoreticalValuesFunction(f); 170 171 // Perform the fit. 172 final PointVectorValuePair optimum 173 = optimizer.optimize(new MaxEval(maxEval), 174 model.getModelFunction(), 175 model.getModelFunctionJacobian(), 176 new Target(target), 177 new Weight(weights), 178 new InitialGuess(initialGuess)); 179 // Extract the coefficients. 180 return optimum.getPointRef(); 181 } 182 183 /** Vectorial function computing function theoretical values. */ 184 private class TheoreticalValuesFunction { 185 /** Function to fit. */ 186 private final ParametricUnivariateFunction f; 187 188 /** 189 * @param f function to fit. 190 */ 191 public TheoreticalValuesFunction(final ParametricUnivariateFunction f) { 192 this.f = f; 193 } 194 195 /** 196 * @return the model function values. 197 */ 198 public ModelFunction getModelFunction() { 199 return new ModelFunction(new MultivariateVectorFunction() { 200 /** {@inheritDoc} */ 201 public double[] value(double[] point) { 202 // compute the residuals 203 final double[] values = new double[observations.size()]; 204 int i = 0; 205 for (WeightedObservedPoint observed : observations) { 206 values[i++] = f.value(observed.getX(), point); 207 } 208 209 return values; 210 } 211 }); 212 } 213 214 /** 215 * @return the model function Jacobian. 216 */ 217 public ModelFunctionJacobian getModelFunctionJacobian() { 218 return new ModelFunctionJacobian(new MultivariateMatrixFunction() { 219 public double[][] value(double[] point) { 220 final double[][] jacobian = new double[observations.size()][]; 221 int i = 0; 222 for (WeightedObservedPoint observed : observations) { 223 jacobian[i++] = f.gradient(observed.getX(), point); 224 } 225 return jacobian; 226 } 227 }); 228 } 229 } 230 }