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 * 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
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 *      http://www.apache.org/licenses/LICENSE-2.0
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package org.apache.commons.math3.fitting;

import java.util.Collection;

import org.apache.commons.math3.analysis.MultivariateVectorFunction;
import org.apache.commons.math3.analysis.MultivariateMatrixFunction;
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;

Base class that contains common code for fitting parametric univariate
real functions y = f(pi;x), where x is the independent variable and the pi are the
parameters.


A fitter will find the optimal values of the parameters by
fitting the curve so it remains very close to a set of N observed points (xk, yk), 0 <= k < N. 

An algorithm usually performs the fit by finding the parameter
values that minimizes the objective function

 ∑yk - f(xk)2,
 which is actually a least-squares problem. This class contains boilerplate code for calling the fit(Collection<WeightedObservedPoint>) 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/**
 * 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>
 *  &sum;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.
Params:
points – Observations.
Returns:
the fitted parameters./**
     * 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.
 The default implementation uses a 
Levenberg-Marquardt optimizer. 
Returns:
the optimizer to use for fitting the curve to the given points./**
     * Creates an optimizer set up to fit the appropriate curve.
     * <p>
     * The default implementation uses a {@link LevenbergMarquardtOptimizer
     * Levenberg-Marquardt} optimizer.
     * </p>
     * @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.
Params:
points – Sample points.
Returns:
the least squares problem to use for fitting the curve to the given points./**
     * 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.
/**
     * Vector function for computing function theoretical values.
     */
    protected static class TheoreticalValuesFunction {
        
Function to fit. /** Function to fit. */
        private final ParametricUnivariateFunction f;
        
Observations. /** Observations. */
        private final double[] points;

        
Params:
f – function to fit.
observations – Observations./**
         * @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();
            }
        }

        
Returns:
the model function values./**
         * @return the model function values.
         */
        public MultivariateVectorFunction getModelFunction() {
            return new MultivariateVectorFunction() {
                
{@inheritDoc} /** {@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;
                }
            };
        }

        
Returns:
the model function Jacobian./**
         * @return the model function Jacobian.
         */
        public MultivariateMatrixFunction getModelFunctionJacobian() {
            return new MultivariateMatrixFunction() {
                
{@inheritDoc} /** {@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;
                }
            };
        }
    }
}