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 &omega; and
029     * the phase &phi;: <code>f (t) = a cos (&omega; t + &phi;)</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 &omega; and phase &phi;. */
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 &omega; (index 1) and phase &phi; (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    }