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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
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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 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(p_i;x), where {@code x} is
 * the independent variable and the p_i 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
 * {@code N} observed points (x_k, y_k),
 * {@code 0 <= k < N}.
 * 

 * An algorithm usually performs the fit by finding the parameter
 * values that minimizes the objective function
 * 
 *  ∑y_k - f(x_k)²,
 * 
 * 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 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 {@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 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 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;
                }
            };
        }
    }
}