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Java example source code file (HarmonicCurveFitter.java)
The HarmonicCurveFitter.java Java example source code/* * Licensed to the Apache Software Foundation (ASF) under one or more * contributor license agreements. See the NOTICE file distributed with * this work for additional information regarding copyright ownership. * The ASF licenses this file to You under the Apache License, Version 2.0 * (the "License"); you may not use this file except in compliance with * the License. You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package org.apache.commons.math3.fitting; import java.util.ArrayList; import java.util.Collection; import java.util.List; import org.apache.commons.math3.analysis.function.HarmonicOscillator; import org.apache.commons.math3.exception.MathIllegalStateException; import org.apache.commons.math3.exception.NumberIsTooSmallException; import org.apache.commons.math3.exception.ZeroException; import org.apache.commons.math3.exception.util.LocalizedFormats; import org.apache.commons.math3.fitting.leastsquares.LeastSquaresBuilder; import org.apache.commons.math3.fitting.leastsquares.LeastSquaresProblem; import org.apache.commons.math3.linear.DiagonalMatrix; import org.apache.commons.math3.util.FastMath; /** * Fits points to a {@link * org.apache.commons.math3.analysis.function.HarmonicOscillator.Parametric harmonic oscillator} * function. * <br/> * The {@link #withStartPoint(double[]) initial guess values} must be passed * in the following order: * <ul> * <li>Amplitude * <li>Angular frequency * <li>phase * </ul> * The optimal values will be returned in the same order. * * @since 3.3 */ public class HarmonicCurveFitter extends AbstractCurveFitter { /** Parametric function to be fitted. */ private static final HarmonicOscillator.Parametric FUNCTION = new HarmonicOscillator.Parametric(); /** Initial guess. */ private final double[] initialGuess; /** Maximum number of iterations of the optimization algorithm. */ private final int maxIter; /** * Contructor used by the factory methods. * * @param initialGuess Initial guess. If set to {@code null}, the initial guess * will be estimated using the {@link ParameterGuesser}. * @param maxIter Maximum number of iterations of the optimization algorithm. */ private HarmonicCurveFitter(double[] initialGuess, int maxIter) { this.initialGuess = initialGuess; this.maxIter = maxIter; } /** * Creates a default curve fitter. * The initial guess for the parameters will be {@link ParameterGuesser} * computed automatically, and the maximum number of iterations of the * optimization algorithm is set to {@link Integer#MAX_VALUE}. * * @return a curve fitter. * * @see #withStartPoint(double[]) * @see #withMaxIterations(int) */ public static HarmonicCurveFitter create() { return new HarmonicCurveFitter(null, Integer.MAX_VALUE); } /** * Configure the start point (initial guess). * @param newStart new start point (initial guess) * @return a new instance. */ public HarmonicCurveFitter withStartPoint(double[] newStart) { return new HarmonicCurveFitter(newStart.clone(), maxIter); } /** * Configure the maximum number of iterations. * @param newMaxIter maximum number of iterations * @return a new instance. */ public HarmonicCurveFitter withMaxIterations(int newMaxIter) { return new HarmonicCurveFitter(initialGuess, newMaxIter); } /** {@inheritDoc} */ @Override protected LeastSquaresProblem getProblem(Collection<WeightedObservedPoint> observations) { // Prepare least-squares problem. final int len = observations.size(); final double[] target = new double[len]; final double[] weights = new double[len]; int i = 0; for (WeightedObservedPoint obs : observations) { target[i] = obs.getY(); weights[i] = obs.getWeight(); ++i; } final AbstractCurveFitter.TheoreticalValuesFunction model = new AbstractCurveFitter.TheoreticalValuesFunction(FUNCTION, observations); final double[] startPoint = initialGuess != null ? initialGuess : // Compute estimation. new ParameterGuesser(observations).guess(); // Return a new optimizer set up to fit a Gaussian curve to the // observed points. return new LeastSquaresBuilder(). maxEvaluations(Integer.MAX_VALUE). maxIterations(maxIter). start(startPoint). target(target). weight(new DiagonalMatrix(weights)). model(model.getModelFunction(), model.getModelFunctionJacobian()). build(); } /** * This class guesses harmonic coefficients from a sample. * <p>The algorithm used to guess the coefficients is as follows: * * <p>We know \( f(t) \) at some sampling points \( t_i \) and want * to find \( a \), \( \omega \) and \( \phi \) such that * \( f(t) = a \cos (\omega t + \phi) \). * </p> * * <p>From the analytical expression, we can compute two primitives : * \[ * If2(t) = \int f^2 dt = a^2 (t + S(t)) / 2 * \] * \[ * If'2(t) = \int f'^2 dt = a^2 \omega^2 (t - S(t)) / 2 * \] * where \(S(t) = \frac{\sin(2 (\omega t + \phi))}{2\omega}\) * </p> * * <p>We can remove \(S\) between these expressions : * \[ * If'2(t) = a^2 \omega^2 t - \omega^2 If2(t) * \] * </p> * * <p>The preceding expression shows that \(If'2 (t)\) is a linear * combination of both \(t\) and \(If2(t)\): * \[ * If'2(t) = A t + B If2(t) * \] * </p> * * <p>From the primitive, we can deduce the same form for definite * integrals between \(t_1\) and \(t_i\) for each \(t_i\) : * \[ * If2(t_i) - If2(t_1) = A (t_i - t_1) + B (If2 (t_i) - If2(t_1)) * \] * </p> * * <p>We can find the coefficients \(A\) and \(B\) that best fit the sample * to this linear expression by computing the definite integrals for * each sample points. * </p> * * <p>For a bilinear expression \(z(x_i, y_i) = A x_i + B y_i\), the * coefficients \(A\) and \(B\) that minimize a least-squares criterion * \(\sum (z_i - z(x_i, y_i))^2\) are given by these expressions:</p> * \[ * A = \frac{\sum y_i y_i \sum x_i z_i - \sum x_i y_i \sum y_i z_i} * {\sum x_i x_i \sum y_i y_i - \sum x_i y_i \sum x_i y_i} * \] * \[ * B = \frac{\sum x_i x_i \sum y_i z_i - \sum x_i y_i \sum x_i z_i} * {\sum x_i x_i \sum y_i y_i - \sum x_i y_i \sum x_i y_i} * * \] * * <p>In fact, we can assume that both \(a\) and \(\omega\) are positive and * compute them directly, knowing that \(A = a^2 \omega^2\) and that * \(B = -\omega^2\). The complete algorithm is therefore:</p> * * For each \(t_i\) from \(t_1\) to \(t_{n-1}\), compute: * \[ f(t_i) \] * \[ f'(t_i) = \frac{f (t_{i+1}) - f(t_{i-1})}{t_{i+1} - t_{i-1}} \] * \[ x_i = t_i - t_1 \] * \[ y_i = \int_{t_1}^{t_i} f^2(t) dt \] * \[ z_i = \int_{t_1}^{t_i} f'^2(t) dt \] * and update the sums: * \[ \sum x_i x_i, \sum y_i y_i, \sum x_i y_i, \sum x_i z_i, \sum y_i z_i \] * * Then: * \[ * a = \sqrt{\frac{\sum y_i y_i \sum x_i z_i - \sum x_i y_i \sum y_i z_i } * {\sum x_i y_i \sum x_i z_i - \sum x_i x_i \sum y_i z_i }} * \] * \[ * \omega = \sqrt{\frac{\sum x_i y_i \sum x_i z_i - \sum x_i x_i \sum y_i z_i} * {\sum x_i x_i \sum y_i y_i - \sum x_i y_i \sum x_i y_i}} * \] * * <p>Once we know \(\omega\) we can compute: * \[ * fc = \omega f(t) \cos(\omega t) - f'(t) \sin(\omega t) * \] * \[ * fs = \omega f(t) \sin(\omega t) + f'(t) \cos(\omega t) * \] * </p> * * <p>It appears that \(fc = a \omega \cos(\phi)\) and * \(fs = -a \omega \sin(\phi)\), so we can use these * expressions to compute \(\phi\). The best estimate over the sample is * given by averaging these expressions. * </p> * * <p>Since integrals and means are involved in the preceding * estimations, these operations run in \(O(n)\) time, where \(n\) is the * number of measurements.</p> */ public static class ParameterGuesser { /** Amplitude. */ private final double a; /** Angular frequency. */ private final double omega; /** Phase. */ private final double phi; /** * Simple constructor. * * @param observations Sampled observations. * @throws NumberIsTooSmallException if the sample is too short. * @throws ZeroException if the abscissa range is zero. * @throws MathIllegalStateException when the guessing procedure cannot * produce sensible results. */ public ParameterGuesser(Collection<WeightedObservedPoint> observations) { if (observations.size() < 4) { throw new NumberIsTooSmallException(LocalizedFormats.INSUFFICIENT_OBSERVED_POINTS_IN_SAMPLE, observations.size(), 4, true); } final WeightedObservedPoint[] sorted = sortObservations(observations).toArray(new WeightedObservedPoint[0]); final double aOmega[] = guessAOmega(sorted); a = aOmega[0]; omega = aOmega[1]; phi = guessPhi(sorted); } /** * Gets an estimation of the parameters. * * @return the guessed parameters, in the following order: * <ul> * <li>Amplitude * <li>Angular frequency * <li>Phase * </ul> */ public double[] guess() { return new double[] { a, omega, phi }; } /** * Sort the observations with respect to the abscissa. * * @param unsorted Input observations. * @return the input observations, sorted. */ private List<WeightedObservedPoint> sortObservations(Collection Other Java examples (source code examples)Here is a short list of links related to this Java HarmonicCurveFitter.java source code file: |
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