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