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
018 package org.apache.commons.math.optimization.fitting;
019
020 import java.util.ArrayList;
021 import java.util.List;
022
023 import org.apache.commons.math.FunctionEvaluationException;
024 import org.apache.commons.math.analysis.DifferentiableMultivariateVectorialFunction;
025 import org.apache.commons.math.analysis.MultivariateMatrixFunction;
026 import org.apache.commons.math.optimization.DifferentiableMultivariateVectorialOptimizer;
027 import org.apache.commons.math.optimization.OptimizationException;
028 import org.apache.commons.math.optimization.VectorialPointValuePair;
029
030 /** Fitter for parametric univariate real functions y = f(x).
031 * <p>When a univariate real function y = f(x) does depend on some
032 * unknown parameters p<sub>0</sub>, p<sub>1</sub> ... p<sub>n-1</sub>,
033 * this class can be used to find these parameters. It does this
034 * by <em>fitting</em> the curve so it remains very close to a set of
035 * observed points (x<sub>0</sub>, y<sub>0</sub>), (x<sub>1</sub>,
036 * y<sub>1</sub>) ... (x<sub>k-1</sub>, y<sub>k-1</sub>). This fitting
037 * is done by finding the parameters values that minimizes the objective
038 * function ∑(y<sub>i</sub>-f(x<sub>i</sub>))<sup>2</sup>. This is
039 * really a least squares problem.</p>
040 * @version $Revision: 790380 $ $Date: 2009-07-01 17:03:38 -0400 (Wed, 01 Jul 2009) $
041 * @since 2.0
042 */
043 public class CurveFitter {
044
045 /** Optimizer to use for the fitting. */
046 private final DifferentiableMultivariateVectorialOptimizer optimizer;
047
048 /** Observed points. */
049 private final List<WeightedObservedPoint> observations;
050
051 /** Simple constructor.
052 * @param optimizer optimizer to use for the fitting
053 */
054 public CurveFitter(final DifferentiableMultivariateVectorialOptimizer optimizer) {
055 this.optimizer = optimizer;
056 observations = new ArrayList<WeightedObservedPoint>();
057 }
058
059 /** Add an observed (x,y) point to the sample with unit weight.
060 * <p>Calling this method is equivalent to call
061 * <code>addObservedPoint(1.0, x, y)</code>.</p>
062 * @param x abscissa of the point
063 * @param y observed value of the point at x, after fitting we should
064 * have f(x) as close as possible to this value
065 * @see #addObservedPoint(double, double, double)
066 * @see #addObservedPoint(WeightedObservedPoint)
067 * @see #getObservations()
068 */
069 public void addObservedPoint(double x, double y) {
070 addObservedPoint(1.0, x, y);
071 }
072
073 /** Add an observed weighted (x,y) point to the sample.
074 * @param weight weight of the observed point in the fit
075 * @param x abscissa of the point
076 * @param y observed value of the point at x, after fitting we should
077 * have f(x) as close as possible to this value
078 * @see #addObservedPoint(double, double)
079 * @see #addObservedPoint(WeightedObservedPoint)
080 * @see #getObservations()
081 */
082 public void addObservedPoint(double weight, double x, double y) {
083 observations.add(new WeightedObservedPoint(weight, x, y));
084 }
085
086 /** Add an observed weighted (x,y) point to the sample.
087 * @param observed observed point to add
088 * @see #addObservedPoint(double, double)
089 * @see #addObservedPoint(double, double, double)
090 * @see #getObservations()
091 */
092 public void addObservedPoint(WeightedObservedPoint observed) {
093 observations.add(observed);
094 }
095
096 /** Get the observed points.
097 * @return observed points
098 * @see #addObservedPoint(double, double)
099 * @see #addObservedPoint(double, double, double)
100 * @see #addObservedPoint(WeightedObservedPoint)
101 */
102 public WeightedObservedPoint[] getObservations() {
103 return observations.toArray(new WeightedObservedPoint[observations.size()]);
104 }
105
106 /** Fit a curve.
107 * <p>This method compute the coefficients of the curve that best
108 * fit the sample of observed points previously given through calls
109 * to the {@link #addObservedPoint(WeightedObservedPoint)
110 * addObservedPoint} method.</p>
111 * @param f parametric function to fit
112 * @param initialGuess first guess of the function parameters
113 * @return fitted parameters
114 * @exception FunctionEvaluationException if the objective function throws one during
115 * the search
116 * @exception OptimizationException if the algorithm failed to converge
117 * @exception IllegalArgumentException if the start point dimension is wrong
118 */
119 public double[] fit(final ParametricRealFunction f,
120 final double[] initialGuess)
121 throws FunctionEvaluationException, OptimizationException, IllegalArgumentException {
122
123 // prepare least squares problem
124 double[] target = new double[observations.size()];
125 double[] weights = new double[observations.size()];
126 int i = 0;
127 for (WeightedObservedPoint point : observations) {
128 target[i] = point.getY();
129 weights[i] = point.getWeight();
130 ++i;
131 }
132
133 // perform the fit
134 VectorialPointValuePair optimum =
135 optimizer.optimize(new TheoreticalValuesFunction(f), target, weights, initialGuess);
136
137 // extract the coefficients
138 return optimum.getPointRef();
139
140 }
141
142 /** Vectorial function computing function theoretical values. */
143 private class TheoreticalValuesFunction
144 implements DifferentiableMultivariateVectorialFunction {
145
146 /** Function to fit. */
147 private final ParametricRealFunction f;
148
149 /** Simple constructor.
150 * @param f function to fit.
151 */
152 public TheoreticalValuesFunction(final ParametricRealFunction f) {
153 this.f = f;
154 }
155
156 /** {@inheritDoc} */
157 public MultivariateMatrixFunction jacobian() {
158 return new MultivariateMatrixFunction() {
159 public double[][] value(double[] point)
160 throws FunctionEvaluationException, IllegalArgumentException {
161
162 final double[][] jacobian = new double[observations.size()][];
163
164 int i = 0;
165 for (WeightedObservedPoint observed : observations) {
166 jacobian[i++] = f.gradient(observed.getX(), point);
167 }
168
169 return jacobian;
170
171 }
172 };
173 }
174
175 /** {@inheritDoc} */
176 public double[] value(double[] point)
177 throws FunctionEvaluationException, IllegalArgumentException {
178
179 // compute the residuals
180 final double[] values = new double[observations.size()];
181 int i = 0;
182 for (WeightedObservedPoint observed : observations) {
183 values[i++] = f.value(observed.getX(), point);
184 }
185
186 return values;
187
188 }
189
190 }
191
192 }