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With inspiration from other libraries
/*
* 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.Arrays;
import java.util.Comparator;
import org.apache.commons.math3.analysis.function.Gaussian;
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.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.optim.nonlinear.vector.MultivariateVectorOptimizer;
import org.apache.commons.math3.util.FastMath;
/**
* Fits points to a {@link
* org.apache.commons.math3.analysis.function.Gaussian.Parametric Gaussian} function.
*
* Usage example:
*
* GaussianFitter fitter = new GaussianFitter(
* new LevenbergMarquardtOptimizer());
* fitter.addObservedPoint(4.0254623, 531026.0);
* fitter.addObservedPoint(4.03128248, 984167.0);
* fitter.addObservedPoint(4.03839603, 1887233.0);
* fitter.addObservedPoint(4.04421621, 2687152.0);
* fitter.addObservedPoint(4.05132976, 3461228.0);
* fitter.addObservedPoint(4.05326982, 3580526.0);
* fitter.addObservedPoint(4.05779662, 3439750.0);
* fitter.addObservedPoint(4.0636168, 2877648.0);
* fitter.addObservedPoint(4.06943698, 2175960.0);
* fitter.addObservedPoint(4.07525716, 1447024.0);
* fitter.addObservedPoint(4.08237071, 717104.0);
* fitter.addObservedPoint(4.08366408, 620014.0);
* double[] parameters = fitter.fit();
*
*
* @since 2.2
* @deprecated As of 3.3. Please use {@link GaussianCurveFitter} and
* {@link WeightedObservedPoints} instead.
*/
@Deprecated
public class GaussianFitter extends CurveFitter {
/**
* Constructs an instance using the specified optimizer.
*
* @param optimizer Optimizer to use for the fitting.
*/
public GaussianFitter(MultivariateVectorOptimizer optimizer) {
super(optimizer);
}
/**
* Fits a Gaussian function to the observed points.
*
* @param initialGuess First guess values in the following order:
*
* - Norm
* - Mean
* - Sigma
*
* @return the parameters of the Gaussian function that best fits the
* observed points (in the same order as above).
* @since 3.0
*/
public double[] fit(double[] initialGuess) {
final Gaussian.Parametric f = 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;
}
};
return fit(f, initialGuess);
}
/**
* Fits a Gaussian function to the observed points.
*
* @return the parameters of the Gaussian function that best fits the
* observed points (in the same order as above).
*/
public double[] fit() {
final double[] guess = (new ParameterGuesser(getObservations())).guess();
return fit(guess);
}
/**
* 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(WeightedObservedPoint[] observations) {
if (observations == null) {
throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY);
}
if (observations.length < 3) {
throw new NumberIsTooSmallException(observations.length, 3, true);
}
final WeightedObservedPoint[] sorted = sortObservations(observations);
final double[] params = basicGuess(sorted);
norm = params[0];
mean = params[1];
sigma = params[2];
}
/**
* Gets an estimation of the parameters.
*
* @return the guessed parameters, in the following order:
*
* - Normalization factor
* - Mean
* - Standard deviation
*
*/
public double[] guess() {
return new double[] { norm, mean, sigma };
}
/**
* Sort the observations.
*
* @param unsorted Input observations.
* @return the input observations, sorted.
*/
private WeightedObservedPoint[] sortObservations(WeightedObservedPoint[] unsorted) {
final WeightedObservedPoint[] observations = unsorted.clone();
final Comparator 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;
}
};
Arrays.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);
}
}
}