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.MathRuntimeException;
022 import org.apache.commons.math.optimization.DifferentiableMultivariateVectorialOptimizer;
023 import org.apache.commons.math.optimization.OptimizationException;
024
025 /** This class implements a curve fitting specialized for sinusoids.
026 * <p>Harmonic fitting is a very simple case of curve fitting. The
027 * estimated coefficients are the amplitude a, the pulsation ω and
028 * the phase φ: <code>f (t) = a cos (ω t + φ)</code>. They are
029 * searched by a least square estimator initialized with a rough guess
030 * based on integrals.</p>
031 * @version $Revision: 786479 $ $Date: 2009-06-19 08:36:16 -0400 (Fri, 19 Jun 2009) $
032 * @since 2.0
033 */
034 public class HarmonicFitter {
035
036 /** Fitter for the coefficients. */
037 private final CurveFitter fitter;
038
039 /** Values for amplitude, pulsation ω and phase φ. */
040 private double[] parameters;
041
042 /** Simple constructor.
043 * @param optimizer optimizer to use for the fitting
044 */
045 public HarmonicFitter(final DifferentiableMultivariateVectorialOptimizer optimizer) {
046 this.fitter = new CurveFitter(optimizer);
047 parameters = null;
048 }
049
050 /** Simple constructor.
051 * <p>This constructor can be used when a first guess of the
052 * coefficients is already known.</p>
053 * @param optimizer optimizer to use for the fitting
054 * @param initialGuess guessed values for amplitude (index 0),
055 * pulsation ω (index 1) and phase φ (index 2)
056 */
057 public HarmonicFitter(final DifferentiableMultivariateVectorialOptimizer optimizer,
058 final double[] initialGuess) {
059 this.fitter = new CurveFitter(optimizer);
060 this.parameters = initialGuess.clone();
061 }
062
063 /** Add an observed weighted (x,y) point to the sample.
064 * @param weight weight of the observed point in the fit
065 * @param x abscissa of the point
066 * @param y observed value of the point at x, after fitting we should
067 * have P(x) as close as possible to this value
068 */
069 public void addObservedPoint(double weight, double x, double y) {
070 fitter.addObservedPoint(weight, x, y);
071 }
072
073 /** Fit an harmonic function to the observed points.
074 * @return harmonic function best fitting the observed points
075 * @throws OptimizationException if the sample is too short or if
076 * the first guess cannot be computed
077 */
078 public HarmonicFunction fit() throws OptimizationException {
079 try {
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("sample contains {0} observed points, at least {1} are required",
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 double[] fitted = fitter.fit(new ParametricHarmonicFunction(), parameters);
100 return new HarmonicFunction(fitted[0], fitted[1], fitted[2]);
101
102 } catch (FunctionEvaluationException fee) {
103 // this should never happen
104 throw MathRuntimeException.createInternalError(fee);
105 }
106 }
107
108 /** Parametric harmonic function. */
109 private static class ParametricHarmonicFunction implements ParametricRealFunction {
110
111 /** {@inheritDoc} */
112 public double value(double x, double[] parameters) {
113 final double a = parameters[0];
114 final double omega = parameters[1];
115 final double phi = parameters[2];
116 return a * Math.cos(omega * x + phi);
117 }
118
119 /** {@inheritDoc} */
120 public double[] gradient(double x, double[] parameters) {
121 final double a = parameters[0];
122 final double omega = parameters[1];
123 final double phi = parameters[2];
124 final double alpha = omega * x + phi;
125 final double cosAlpha = Math.cos(alpha);
126 final double sinAlpha = Math.sin(alpha);
127 return new double[] { cosAlpha, -a * x * sinAlpha, -a * sinAlpha };
128 }
129
130 }
131
132 }