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Java example source code file (GaussianCurveFitter.java)

This example Java source code file (GaussianCurveFitter.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

arraylist, comparator, diagonalmatrix, gaussiancurvefitter, leastsquaresbuilder, leastsquaresproblem, list, nopmd, notstrictlypositiveexception, outofrangeexception, override, parameterguesser, util, weightedobservedpoint, zeroexception

The GaussianCurveFitter.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.Collections;
import java.util.Comparator;
import java.util.List;

import org.apache.commons.math3.analysis.function.Gaussian;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.OutOfRangeException;
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.Gaussian.Parametric Gaussian}
 * function.
 * <br/>
 * The {@link #withStartPoint(double[]) initial guess values} must be passed
 * in the following order:
 * <ul>
 *  <li>Normalization
 *  <li>Mean
 *  <li>Sigma
 * </ul>
 * The optimal values will be returned in the same order.
 *
 * <p>
 * Usage example:
 * <pre>
 *   WeightedObservedPoints obs = new WeightedObservedPoints();
 *   obs.add(4.0254623,  531026.0);
 *   obs.add(4.03128248, 984167.0);
 *   obs.add(4.03839603, 1887233.0);
 *   obs.add(4.04421621, 2687152.0);
 *   obs.add(4.05132976, 3461228.0);
 *   obs.add(4.05326982, 3580526.0);
 *   obs.add(4.05779662, 3439750.0);
 *   obs.add(4.0636168,  2877648.0);
 *   obs.add(4.06943698, 2175960.0);
 *   obs.add(4.07525716, 1447024.0);
 *   obs.add(4.08237071, 717104.0);
 *   obs.add(4.08366408, 620014.0);
 *   double[] parameters = GaussianCurveFitter.create().fit(obs.toList());
 * </pre>
 *
 * @since 3.3
 */
public class GaussianCurveFitter extends AbstractCurveFitter {
    /** Parametric function to be fitted. */
    private static final Gaussian.Parametric FUNCTION = new Gaussian.Parametric() {
            /** {@inheritDoc} */
            @Override
            public double value(double x, double ... p) {
                double v = Double.POSITIVE_INFINITY;
                try {
                    v = super.value(x, p);
                } catch (NotStrictlyPositiveException e) { // NOPMD
                    // Do nothing.
                }
                return v;
            }

            /** {@inheritDoc} */
            @Override
            public double[] gradient(double x, double ... p) {
                double[] v = { Double.POSITIVE_INFINITY,
                               Double.POSITIVE_INFINITY,
                               Double.POSITIVE_INFINITY };
                try {
                    v = super.gradient(x, p);
                } catch (NotStrictlyPositiveException e) { // NOPMD
                    // Do nothing.
                }
                return v;
            }
        };
    /** 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 GaussianCurveFitter(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 GaussianCurveFitter create() {
        return new GaussianCurveFitter(null, Integer.MAX_VALUE);
    }

    /**
     * Configure the start point (initial guess).
     * @param newStart new start point (initial guess)
     * @return a new instance.
     */
    public GaussianCurveFitter withStartPoint(double[] newStart) {
        return new GaussianCurveFitter(newStart.clone(),
                                       maxIter);
    }

    /**
     * Configure the maximum number of iterations.
     * @param newMaxIter maximum number of iterations
     * @return a new instance.
     */
    public GaussianCurveFitter withMaxIterations(int newMaxIter) {
        return new GaussianCurveFitter(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 least squares problem 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();

    }

    /**
     * Guesses the parameters {@code norm}, {@code mean}, and {@code sigma}
     * of a {@link org.apache.commons.math3.analysis.function.Gaussian.Parametric}
     * based on the specified observed points.
     */
    public static class ParameterGuesser {
        /** Normalization factor. */
        private final double norm;
        /** Mean. */
        private final double mean;
        /** Standard deviation. */
        private final double sigma;

        /**
         * Constructs instance with the specified observed points.
         *
         * @param observations Observed points from which to guess the
         * parameters of the Gaussian.
         * @throws NullArgumentException if {@code observations} is
         * {@code null}.
         * @throws NumberIsTooSmallException if there are less than 3
         * observations.
         */
        public ParameterGuesser(Collection<WeightedObservedPoint> observations) {
            if (observations == null) {
                throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY);
            }
            if (observations.size() < 3) {
                throw new NumberIsTooSmallException(observations.size(), 3, true);
            }

            final List<WeightedObservedPoint> sorted = sortObservations(observations);
            final double[] params = basicGuess(sorted.toArray(new WeightedObservedPoint[0]));

            norm = params[0];
            mean = params[1];
            sigma = params[2];
        }

        /**
         * Gets an estimation of the parameters.
         *
         * @return the guessed parameters, in the following order:
         * <ul>
         *  <li>Normalization factor
         *  <li>Mean
         *  <li>Standard deviation
         * </ul>
         */
        public double[] guess() {
            return new double[] { norm, mean, sigma };
        }

        /**
         * Sort the observations.
         *
         * @param unsorted Input observations.
         * @return the input observations, sorted.
         */
        private List<WeightedObservedPoint> sortObservations(Collection unsorted) {
            final List<WeightedObservedPoint> observations = new ArrayList(unsorted);

            final Comparator<WeightedObservedPoint> cmp = new Comparator() {
                /** {@inheritDoc} */
                public int compare(WeightedObservedPoint p1,
                                   WeightedObservedPoint p2) {
                    if (p1 == null && p2 == null) {
                        return 0;
                    }
                    if (p1 == null) {
                        return -1;
                    }
                    if (p2 == null) {
                        return 1;
                    }
                    final int cmpX = Double.compare(p1.getX(), p2.getX());
                    if (cmpX < 0) {
                        return -1;
                    }
                    if (cmpX > 0) {
                        return 1;
                    }
                    final int cmpY = Double.compare(p1.getY(), p2.getY());
                    if (cmpY < 0) {
                        return -1;
                    }
                    if (cmpY > 0) {
                        return 1;
                    }
                    final int cmpW = Double.compare(p1.getWeight(), p2.getWeight());
                    if (cmpW < 0) {
                        return -1;
                    }
                    if (cmpW > 0) {
                        return 1;
                    }
                    return 0;
                }
            };

            Collections.sort(observations, cmp);
            return observations;
        }

        /**
         * Guesses the parameters based on the specified observed points.
         *
         * @param points Observed points, sorted.
         * @return the guessed parameters (normalization factor, mean and
         * sigma).
         */
        private double[] basicGuess(WeightedObservedPoint[] points) {
            final int maxYIdx = findMaxY(points);
            final double n = points[maxYIdx].getY();
            final double m = points[maxYIdx].getX();

            double fwhmApprox;
            try {
                final double halfY = n + ((m - n) / 2);
                final double fwhmX1 = interpolateXAtY(points, maxYIdx, -1, halfY);
                final double fwhmX2 = interpolateXAtY(points, maxYIdx, 1, halfY);
                fwhmApprox = fwhmX2 - fwhmX1;
            } catch (OutOfRangeException e) {
                // TODO: Exceptions should not be used for flow control.
                fwhmApprox = points[points.length - 1].getX() - points[0].getX();
            }
            final double s = fwhmApprox / (2 * FastMath.sqrt(2 * FastMath.log(2)));

            return new double[] { n, m, s };
        }

        /**
         * Finds index of point in specified points with the largest Y.
         *
         * @param points Points to search.
         * @return the index in specified points array.
         */
        private int findMaxY(WeightedObservedPoint[] points) {
            int maxYIdx = 0;
            for (int i = 1; i < points.length; i++) {
                if (points[i].getY() > points[maxYIdx].getY()) {
                    maxYIdx = i;
                }
            }
            return maxYIdx;
        }

        /**
         * Interpolates using the specified points to determine X at the
         * specified Y.
         *
         * @param points Points to use for interpolation.
         * @param startIdx Index within points from which to start the search for
         * interpolation bounds points.
         * @param idxStep Index step for searching interpolation bounds points.
         * @param y Y value for which X should be determined.
         * @return the value of X for the specified Y.
         * @throws ZeroException if {@code idxStep} is 0.
         * @throws OutOfRangeException if specified {@code y} is not within the
         * range of the specified {@code points}.
         */
        private double interpolateXAtY(WeightedObservedPoint[] points,
                                       int startIdx,
                                       int idxStep,
                                       double y)
            throws OutOfRangeException {
            if (idxStep == 0) {
                throw new ZeroException();
            }
            final WeightedObservedPoint[] twoPoints
                = getInterpolationPointsForY(points, startIdx, idxStep, y);
            final WeightedObservedPoint p1 = twoPoints[0];
            final WeightedObservedPoint p2 = twoPoints[1];
            if (p1.getY() == y) {
                return p1.getX();
            }
            if (p2.getY() == y) {
                return p2.getX();
            }
            return p1.getX() + (((y - p1.getY()) * (p2.getX() - p1.getX())) /
                                (p2.getY() - p1.getY()));
        }

        /**
         * Gets the two bounding interpolation points from the specified points
         * suitable for determining X at the specified Y.
         *
         * @param points Points to use for interpolation.
         * @param startIdx Index within points from which to start search for
         * interpolation bounds points.
         * @param idxStep Index step for search for interpolation bounds points.
         * @param y Y value for which X should be determined.
         * @return the array containing two points suitable for determining X at
         * the specified Y.
         * @throws ZeroException if {@code idxStep} is 0.
         * @throws OutOfRangeException if specified {@code y} is not within the
         * range of the specified {@code points}.
         */
        private WeightedObservedPoint[] getInterpolationPointsForY(WeightedObservedPoint[] points,
                                                                   int startIdx,
                                                                   int idxStep,
                                                                   double y)
            throws OutOfRangeException {
            if (idxStep == 0) {
                throw new ZeroException();
            }
            for (int i = startIdx;
                 idxStep < 0 ? i + idxStep >= 0 : i + idxStep < points.length;
                 i += idxStep) {
                final WeightedObservedPoint p1 = points[i];
                final WeightedObservedPoint p2 = points[i + idxStep];
                if (isBetween(y, p1.getY(), p2.getY())) {
                    if (idxStep < 0) {
                        return new WeightedObservedPoint[] { p2, p1 };
                    } else {
                        return new WeightedObservedPoint[] { p1, p2 };
                    }
                }
            }

            // Boundaries are replaced by dummy values because the raised
            // exception is caught and the message never displayed.
            // TODO: Exceptions should not be used for flow control.
            throw new OutOfRangeException(y,
                                          Double.NEGATIVE_INFINITY,
                                          Double.POSITIVE_INFINITY);
        }

        /**
         * Determines whether a value is between two other values.
         *
         * @param value Value to test whether it is between {@code boundary1}
         * and {@code boundary2}.
         * @param boundary1 One end of the range.
         * @param boundary2 Other end of the range.
         * @return {@code true} if {@code value} is between {@code boundary1} and
         * {@code boundary2} (inclusive), {@code false} otherwise.
         */
        private boolean isBetween(double value,
                                  double boundary1,
                                  double boundary2) {
            return (value >= boundary1 && value <= boundary2) ||
                (value >= boundary2 && value <= boundary1);
        }
    }
}

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