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/*
* 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 org.apache.commons.math3.analysis.MultivariateMatrixFunction;
import org.apache.commons.math3.analysis.MultivariateVectorFunction;
import org.apache.commons.math3.analysis.ParametricUnivariateFunction;
import org.apache.commons.math3.fitting.leastsquares.LeastSquaresOptimizer;
import org.apache.commons.math3.fitting.leastsquares.LeastSquaresProblem;
import org.apache.commons.math3.fitting.leastsquares.LevenbergMarquardtOptimizer;
import java.util.Collection;
/**
* Base class that contains common code for fitting parametric univariate real functions <code>
* y = f(p<sub>i</sub>;x)</code>, where {@code x} is the independent variable and the <code>
* p<sub>i</sub></code> are the <em>parameters</em>. <br>
* A fitter will find the optimal values of the parameters by <em>fitting</em> the curve so it
* remains very close to a set of {@code N} observed points <code>(x<sub>k</sub>, y<sub>k</sub>)
* </code>, {@code 0 <= k < N}. <br>
* An algorithm usually performs the fit by finding the parameter values that minimizes the
* objective function
*
* <pre><code>
* ∑y<sub>k</sub> - f(x<sub>k</sub>)<sup>2</sup>,
* </code></pre>
*
* which is actually a least-squares problem. This class contains boilerplate code for calling the
* {@link #fit(Collection)} method for obtaining the parameters. The problem setup, such as the
* choice of optimization algorithm for fitting a specific function is delegated to subclasses.
*
* @since 3.3
*/
public abstract class AbstractCurveFitter {
/**
* Fits a curve. This method computes the coefficients of the curve that best fit the sample of
* observed points.
*
* @param points Observations.
* @return the fitted parameters.
*/
public double[] fit(Collection<WeightedObservedPoint> points) {
// Perform the fit.
return getOptimizer().optimize(getProblem(points)).getPoint().toArray();
}
/**
* Creates an optimizer set up to fit the appropriate curve.
*
* <p>The default implementation uses a {@link LevenbergMarquardtOptimizer Levenberg-Marquardt}
* optimizer.
*
* @return the optimizer to use for fitting the curve to the given {@code points}.
*/
protected LeastSquaresOptimizer getOptimizer() {
return new LevenbergMarquardtOptimizer();
}
/**
* Creates a least squares problem corresponding to the appropriate curve.
*
* @param points Sample points.
* @return the least squares problem to use for fitting the curve to the given {@code points}.
*/
protected abstract LeastSquaresProblem getProblem(Collection<WeightedObservedPoint> points);
/** Vector function for computing function theoretical values. */
protected static class TheoreticalValuesFunction {
/** Function to fit. */
private final ParametricUnivariateFunction f;
/** Observations. */
private final double[] points;
/**
* @param f function to fit.
* @param observations Observations.
*/
public TheoreticalValuesFunction(
final ParametricUnivariateFunction f,
final Collection<WeightedObservedPoint> observations) {
this.f = f;
final int len = observations.size();
this.points = new double[len];
int i = 0;
for (WeightedObservedPoint obs : observations) {
this.points[i++] = obs.getX();
}
}
/**
* @return the model function values.
*/
public MultivariateVectorFunction getModelFunction() {
return new MultivariateVectorFunction() {
/** {@inheritDoc} */
public double[] value(double[] p) {
final int len = points.length;
final double[] values = new double[len];
for (int i = 0; i < len; i++) {
values[i] = f.value(points[i], p);
}
return values;
}
};
}
/**
* @return the model function Jacobian.
*/
public MultivariateMatrixFunction getModelFunctionJacobian() {
return new MultivariateMatrixFunction() {
/** {@inheritDoc} */
public double[][] value(double[] p) {
final int len = points.length;
final double[][] jacobian = new double[len][];
for (int i = 0; i < len; i++) {
jacobian[i] = f.gradient(points[i], p);
}
return jacobian;
}
};
}
}
}
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