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 org.apache.commons.math.FunctionEvaluationException;
021 import org.apache.commons.math.exception.util.LocalizedFormats;
022 import org.apache.commons.math.optimization.DifferentiableMultivariateVectorialOptimizer;
023 import org.apache.commons.math.optimization.OptimizationException;
024 import org.apache.commons.math.util.FastMath;
025
026 /** This class implements a curve fitting specialized for sinusoids.
027 * <p>Harmonic fitting is a very simple case of curve fitting. The
028 * estimated coefficients are the amplitude a, the pulsation ω and
029 * the phase φ: <code>f (t) = a cos (ω t + φ)</code>. They are
030 * searched by a least square estimator initialized with a rough guess
031 * based on integrals.</p>
032 * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 f??vr. 2011) $
033 * @since 2.0
034 */
035 public class HarmonicFitter {
036
037 /** Fitter for the coefficients. */
038 private final CurveFitter fitter;
039
040 /** Values for amplitude, pulsation ω and phase φ. */
041 private double[] parameters;
042
043 /** Simple constructor.
044 * @param optimizer optimizer to use for the fitting
045 */
046 public HarmonicFitter(final DifferentiableMultivariateVectorialOptimizer optimizer) {
047 this.fitter = new CurveFitter(optimizer);
048 parameters = null;
049 }
050
051 /** Simple constructor.
052 * <p>This constructor can be used when a first guess of the
053 * coefficients is already known.</p>
054 * @param optimizer optimizer to use for the fitting
055 * @param initialGuess guessed values for amplitude (index 0),
056 * pulsation ω (index 1) and phase φ (index 2)
057 */
058 public HarmonicFitter(final DifferentiableMultivariateVectorialOptimizer optimizer,
059 final double[] initialGuess) {
060 this.fitter = new CurveFitter(optimizer);
061 this.parameters = initialGuess.clone();
062 }
063
064 /** Add an observed weighted (x,y) point to the sample.
065 * @param weight weight of the observed point in the fit
066 * @param x abscissa of the point
067 * @param y observed value of the point at x, after fitting we should
068 * have P(x) as close as possible to this value
069 */
070 public void addObservedPoint(double weight, double x, double y) {
071 fitter.addObservedPoint(weight, x, y);
072 }
073
074 /** Fit an harmonic function to the observed points.
075 * @return harmonic function best fitting the observed points
076 * @throws OptimizationException if the sample is too short or if
077 * the first guess cannot be computed
078 */
079 public HarmonicFunction fit() throws OptimizationException {
080
081 // shall we compute the first guess of the parameters ourselves ?
082 if (parameters == null) {
083 final WeightedObservedPoint[] observations = fitter.getObservations();
084 if (observations.length < 4) {
085 throw new OptimizationException(LocalizedFormats.INSUFFICIENT_OBSERVED_POINTS_IN_SAMPLE,
086 observations.length, 4);
087 }
088
089 HarmonicCoefficientsGuesser guesser = new HarmonicCoefficientsGuesser(observations);
090 guesser.guess();
091 parameters = new double[] {
092 guesser.getGuessedAmplitude(),
093 guesser.getGuessedPulsation(),
094 guesser.getGuessedPhase()
095 };
096
097 }
098
099 try {
100 double[] fitted = fitter.fit(new ParametricHarmonicFunction(), parameters);
101 return new HarmonicFunction(fitted[0], fitted[1], fitted[2]);
102 } catch (FunctionEvaluationException fee) {
103 // should never happen
104 throw new RuntimeException(fee);
105 }
106
107 }
108
109 /** Parametric harmonic function. */
110 private static class ParametricHarmonicFunction implements ParametricRealFunction {
111
112 /** {@inheritDoc} */
113 public double value(double x, double[] parameters) {
114 final double a = parameters[0];
115 final double omega = parameters[1];
116 final double phi = parameters[2];
117 return a * FastMath.cos(omega * x + phi);
118 }
119
120 /** {@inheritDoc} */
121 public double[] gradient(double x, double[] parameters) {
122 final double a = parameters[0];
123 final double omega = parameters[1];
124 final double phi = parameters[2];
125 final double alpha = omega * x + phi;
126 final double cosAlpha = FastMath.cos(alpha);
127 final double sinAlpha = FastMath.sin(alpha);
128 return new double[] { cosAlpha, -a * x * sinAlpha, -a * sinAlpha };
129 }
130
131 }
132
133 }