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      1 /*
      2  * Licensed to the Apache Software Foundation (ASF) under one or more
      3  * contributor license agreements.  See the NOTICE file distributed with
      4  * this work for additional information regarding copyright ownership.
      5  * The ASF licenses this file to You under the Apache License, Version 2.0
      6  * (the "License"); you may not use this file except in compliance with
      7  * the License.  You may obtain a copy of the License at
      8  *
      9  *      http://www.apache.org/licenses/LICENSE-2.0
     10  *
     11  * Unless required by applicable law or agreed to in writing, software
     12  * distributed under the License is distributed on an "AS IS" BASIS,
     13  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     14  * See the License for the specific language governing permissions and
     15  * limitations under the License.
     16  */
     17 
     18 package org.apache.commons.math.optimization.fitting;
     19 
     20 import org.apache.commons.math.FunctionEvaluationException;
     21 import org.apache.commons.math.exception.util.LocalizedFormats;
     22 import org.apache.commons.math.optimization.DifferentiableMultivariateVectorialOptimizer;
     23 import org.apache.commons.math.optimization.OptimizationException;
     24 import org.apache.commons.math.util.FastMath;
     25 
     26 /** This class implements a curve fitting specialized for sinusoids.
     27  * <p>Harmonic fitting is a very simple case of curve fitting. The
     28  * estimated coefficients are the amplitude a, the pulsation &omega; and
     29  * the phase &phi;: <code>f (t) = a cos (&omega; t + &phi;)</code>. They are
     30  * searched by a least square estimator initialized with a rough guess
     31  * based on integrals.</p>
     32  * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 fvr. 2011) $
     33  * @since 2.0
     34  */
     35 public class HarmonicFitter {
     36 
     37     /** Fitter for the coefficients. */
     38     private final CurveFitter fitter;
     39 
     40     /** Values for amplitude, pulsation &omega; and phase &phi;. */
     41     private double[] parameters;
     42 
     43     /** Simple constructor.
     44      * @param optimizer optimizer to use for the fitting
     45      */
     46     public HarmonicFitter(final DifferentiableMultivariateVectorialOptimizer optimizer) {
     47         this.fitter = new CurveFitter(optimizer);
     48         parameters  = null;
     49     }
     50 
     51     /** Simple constructor.
     52      * <p>This constructor can be used when a first guess of the
     53      * coefficients is already known.</p>
     54      * @param optimizer optimizer to use for the fitting
     55      * @param initialGuess guessed values for amplitude (index 0),
     56      * pulsation &omega; (index 1) and phase &phi; (index 2)
     57      */
     58     public HarmonicFitter(final DifferentiableMultivariateVectorialOptimizer optimizer,
     59                           final double[] initialGuess) {
     60         this.fitter     = new CurveFitter(optimizer);
     61         this.parameters = initialGuess.clone();
     62     }
     63 
     64     /** Add an observed weighted (x,y) point to the sample.
     65      * @param weight weight of the observed point in the fit
     66      * @param x abscissa of the point
     67      * @param y observed value of the point at x, after fitting we should
     68      * have P(x) as close as possible to this value
     69      */
     70     public void addObservedPoint(double weight, double x, double y) {
     71         fitter.addObservedPoint(weight, x, y);
     72     }
     73 
     74     /** Fit an harmonic function to the observed points.
     75      * @return harmonic function best fitting the observed points
     76      * @throws OptimizationException if the sample is too short or if
     77      * the first guess cannot be computed
     78      */
     79     public HarmonicFunction fit() throws OptimizationException {
     80 
     81         // shall we compute the first guess of the parameters ourselves ?
     82         if (parameters == null) {
     83             final WeightedObservedPoint[] observations = fitter.getObservations();
     84             if (observations.length < 4) {
     85                 throw new OptimizationException(LocalizedFormats.INSUFFICIENT_OBSERVED_POINTS_IN_SAMPLE,
     86                                                 observations.length, 4);
     87             }
     88 
     89             HarmonicCoefficientsGuesser guesser = new HarmonicCoefficientsGuesser(observations);
     90             guesser.guess();
     91             parameters = new double[] {
     92                 guesser.getGuessedAmplitude(),
     93                 guesser.getGuessedPulsation(),
     94                 guesser.getGuessedPhase()
     95             };
     96 
     97         }
     98 
     99         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 }
    134