    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    }