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 018package org.apache.commons.math3.optimization.fitting; 019 020import java.util.ArrayList; 021import java.util.List; 022 023import org.apache.commons.math3.analysis.DifferentiableMultivariateVectorFunction; 024import org.apache.commons.math3.analysis.MultivariateMatrixFunction; 025import org.apache.commons.math3.analysis.ParametricUnivariateFunction; 026import org.apache.commons.math3.analysis.differentiation.DerivativeStructure; 027import org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction; 028import org.apache.commons.math3.optimization.DifferentiableMultivariateVectorOptimizer; 029import org.apache.commons.math3.optimization.MultivariateDifferentiableVectorOptimizer; 030import org.apache.commons.math3.optimization.PointVectorValuePair; 031 032/** Fitter for parametric univariate real functions y = f(x). 033 * <br/> 034 * When a univariate real function y = f(x) does depend on some 035 * unknown parameters p<sub>0</sub>, p<sub>1</sub> ... p<sub>n-1</sub>, 036 * this class can be used to find these parameters. It does this 037 * by <em>fitting</em> the curve so it remains very close to a set of 038 * observed points (x<sub>0</sub>, y<sub>0</sub>), (x<sub>1</sub>, 039 * y<sub>1</sub>) ... (x<sub>k-1</sub>, y<sub>k-1</sub>). This fitting 040 * is done by finding the parameters values that minimizes the objective 041 * function ∑(y<sub>i</sub>-f(x<sub>i</sub>))<sup>2</sup>. This is 042 * really a least squares problem. 043 * 044 * @param <T> Function to use for the fit. 045 * 046 * @deprecated As of 3.1 (to be removed in 4.0). 047 * @since 2.0 048 */ 049@Deprecated 050public class CurveFitter<T extends ParametricUnivariateFunction> { 051 052 /** Optimizer to use for the fitting. 053 * @deprecated as of 3.1 replaced by {@link #optimizer} 054 */ 055 @Deprecated 056 private final DifferentiableMultivariateVectorOptimizer oldOptimizer; 057 058 /** Optimizer to use for the fitting. */ 059 private final MultivariateDifferentiableVectorOptimizer optimizer; 060 061 /** Observed points. */ 062 private final List<WeightedObservedPoint> observations; 063 064 /** Simple constructor. 065 * @param optimizer optimizer to use for the fitting 066 * @deprecated as of 3.1 replaced by {@link #CurveFitter(MultivariateDifferentiableVectorOptimizer)} 067 */ 068 @Deprecated 069 public CurveFitter(final DifferentiableMultivariateVectorOptimizer optimizer) { 070 this.oldOptimizer = optimizer; 071 this.optimizer = null; 072 observations = new ArrayList<WeightedObservedPoint>(); 073 } 074 075 /** Simple constructor. 076 * @param optimizer optimizer to use for the fitting 077 * @since 3.1 078 */ 079 public CurveFitter(final MultivariateDifferentiableVectorOptimizer optimizer) { 080 this.oldOptimizer = null; 081 this.optimizer = optimizer; 082 observations = new ArrayList<WeightedObservedPoint>(); 083 } 084 085 /** Add an observed (x,y) point to the sample with unit weight. 086 * <p>Calling this method is equivalent to call 087 * {@code addObservedPoint(1.0, x, y)}.</p> 088 * @param x abscissa of the point 089 * @param y observed value of the point at x, after fitting we should 090 * have f(x) as close as possible to this value 091 * @see #addObservedPoint(double, double, double) 092 * @see #addObservedPoint(WeightedObservedPoint) 093 * @see #getObservations() 094 */ 095 public void addObservedPoint(double x, double y) { 096 addObservedPoint(1.0, x, y); 097 } 098 099 /** Add an observed weighted (x,y) point to the sample. 100 * @param weight weight of the observed point in the fit 101 * @param x abscissa of the point 102 * @param y observed value of the point at x, after fitting we should 103 * have f(x) as close as possible to this value 104 * @see #addObservedPoint(double, double) 105 * @see #addObservedPoint(WeightedObservedPoint) 106 * @see #getObservations() 107 */ 108 public void addObservedPoint(double weight, double x, double y) { 109 observations.add(new WeightedObservedPoint(weight, x, y)); 110 } 111 112 /** Add an observed weighted (x,y) point to the sample. 113 * @param observed observed point to add 114 * @see #addObservedPoint(double, double) 115 * @see #addObservedPoint(double, double, double) 116 * @see #getObservations() 117 */ 118 public void addObservedPoint(WeightedObservedPoint observed) { 119 observations.add(observed); 120 } 121 122 /** Get the observed points. 123 * @return observed points 124 * @see #addObservedPoint(double, double) 125 * @see #addObservedPoint(double, double, double) 126 * @see #addObservedPoint(WeightedObservedPoint) 127 */ 128 public WeightedObservedPoint[] getObservations() { 129 return observations.toArray(new WeightedObservedPoint[observations.size()]); 130 } 131 132 /** 133 * Remove all observations. 134 */ 135 public void clearObservations() { 136 observations.clear(); 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 * @return the fitted parameters. 149 * @throws org.apache.commons.math3.exception.DimensionMismatchException 150 * if the start point dimension is wrong. 151 */ 152 public double[] fit(T f, final double[] initialGuess) { 153 return fit(Integer.MAX_VALUE, f, initialGuess); 154 } 155 156 /** 157 * Fit a curve. 158 * This method compute the coefficients of the curve that best 159 * fit the sample of observed points previously given through calls 160 * to the {@link #addObservedPoint(WeightedObservedPoint) 161 * addObservedPoint} method. 162 * 163 * @param f parametric function to fit. 164 * @param initialGuess first guess of the function parameters. 165 * @param maxEval Maximum number of function evaluations. 166 * @return the fitted parameters. 167 * @throws org.apache.commons.math3.exception.TooManyEvaluationsException 168 * if the number of allowed evaluations is exceeded. 169 * @throws org.apache.commons.math3.exception.DimensionMismatchException 170 * if the start point dimension is wrong. 171 * @since 3.0 172 */ 173 public double[] fit(int maxEval, T f, 174 final double[] initialGuess) { 175 // prepare least squares problem 176 double[] target = new double[observations.size()]; 177 double[] weights = new double[observations.size()]; 178 int i = 0; 179 for (WeightedObservedPoint point : observations) { 180 target[i] = point.getY(); 181 weights[i] = point.getWeight(); 182 ++i; 183 } 184 185 // perform the fit 186 final PointVectorValuePair optimum; 187 if (optimizer == null) { 188 // to be removed in 4.0 189 optimum = oldOptimizer.optimize(maxEval, new OldTheoreticalValuesFunction(f), 190 target, weights, initialGuess); 191 } else { 192 optimum = optimizer.optimize(maxEval, new TheoreticalValuesFunction(f), 193 target, weights, initialGuess); 194 } 195 196 // extract the coefficients 197 return optimum.getPointRef(); 198 } 199 200 /** Vectorial function computing function theoretical values. */ 201 @Deprecated 202 private class OldTheoreticalValuesFunction 203 implements DifferentiableMultivariateVectorFunction { 204 /** Function to fit. */ 205 private final ParametricUnivariateFunction f; 206 207 /** Simple constructor. 208 * @param f function to fit. 209 */ 210 OldTheoreticalValuesFunction(final ParametricUnivariateFunction f) { 211 this.f = f; 212 } 213 214 /** {@inheritDoc} */ 215 public MultivariateMatrixFunction jacobian() { 216 return new MultivariateMatrixFunction() { 217 /** {@inheritDoc} */ 218 public double[][] value(double[] point) { 219 final double[][] jacobian = new double[observations.size()][]; 220 221 int i = 0; 222 for (WeightedObservedPoint observed : observations) { 223 jacobian[i++] = f.gradient(observed.getX(), point); 224 } 225 226 return jacobian; 227 } 228 }; 229 } 230 231 /** {@inheritDoc} */ 232 public double[] value(double[] point) { 233 // compute the residuals 234 final double[] values = new double[observations.size()]; 235 int i = 0; 236 for (WeightedObservedPoint observed : observations) { 237 values[i++] = f.value(observed.getX(), point); 238 } 239 240 return values; 241 } 242 } 243 244 /** Vectorial function computing function theoretical values. */ 245 private class TheoreticalValuesFunction implements MultivariateDifferentiableVectorFunction { 246 247 /** Function to fit. */ 248 private final ParametricUnivariateFunction f; 249 250 /** Simple constructor. 251 * @param f function to fit. 252 */ 253 TheoreticalValuesFunction(final ParametricUnivariateFunction f) { 254 this.f = f; 255 } 256 257 /** {@inheritDoc} */ 258 public double[] value(double[] point) { 259 // compute the residuals 260 final double[] values = new double[observations.size()]; 261 int i = 0; 262 for (WeightedObservedPoint observed : observations) { 263 values[i++] = f.value(observed.getX(), point); 264 } 265 266 return values; 267 } 268 269 /** {@inheritDoc} */ 270 public DerivativeStructure[] value(DerivativeStructure[] point) { 271 272 // extract parameters 273 final double[] parameters = new double[point.length]; 274 for (int k = 0; k < point.length; ++k) { 275 parameters[k] = point[k].getValue(); 276 } 277 278 // compute the residuals 279 final DerivativeStructure[] values = new DerivativeStructure[observations.size()]; 280 int i = 0; 281 for (WeightedObservedPoint observed : observations) { 282 283 // build the DerivativeStructure by adding first the value as a constant 284 // and then adding derivatives 285 DerivativeStructure vi = new DerivativeStructure(point.length, 1, f.value(observed.getX(), parameters)); 286 for (int k = 0; k < point.length; ++k) { 287 vi = vi.add(new DerivativeStructure(point.length, 1, k, 0.0)); 288 } 289 290 values[i++] = vi; 291 292 } 293 294 return values; 295 } 296 297 } 298 299}