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 * 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
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 * distributed under the License is distributed on an "AS IS" BASIS,
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 * See the License for the specific language governing permissions and
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package org.apache.commons.math3.fitting;

import java.util.Collection;

import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math3.exception.MathInternalError;
import org.apache.commons.math3.fitting.leastsquares.LeastSquaresBuilder;
import org.apache.commons.math3.fitting.leastsquares.LeastSquaresProblem;
import org.apache.commons.math3.linear.DiagonalMatrix;

Fits points to a polynomial function. 
 The size of the initial guess array defines the degree of the polynomial to be fitted. They must be sorted in increasing order of the polynomial's degree. The optimal values of the coefficients will be returned in the same order. 
Since:
3.3/**
 * Fits points to a {@link
 * org.apache.commons.math3.analysis.polynomials.PolynomialFunction.Parametric polynomial}
 * function.
 * <br/>
 * The size of the {@link #withStartPoint(double[]) initial guess} array defines the
 * degree of the polynomial to be fitted.
 * They must be sorted in increasing order of the polynomial's degree.
 * The optimal values of the coefficients will be returned in the same order.
 *
 * @since 3.3
 */
public class PolynomialCurveFitter extends AbstractCurveFitter {
    
Parametric function to be fitted. /** Parametric function to be fitted. */
    private static final PolynomialFunction.Parametric FUNCTION = new PolynomialFunction.Parametric();
    
Initial guess. /** Initial guess. */
    private final double[] initialGuess;
    
Maximum number of iterations of the optimization algorithm. /** Maximum number of iterations of the optimization algorithm. */
    private final int maxIter;

    
Contructor used by the factory methods.
Params:
initialGuess – Initial guess.
maxIter – Maximum number of iterations of the optimization algorithm.
Throws:
MathInternalError – if initialGuess is null./**
     * Contructor used by the factory methods.
     *
     * @param initialGuess Initial guess.
     * @param maxIter Maximum number of iterations of the optimization algorithm.
     * @throws MathInternalError if {@code initialGuess} is {@code null}.
     */
    private PolynomialCurveFitter(double[] initialGuess,
                                  int maxIter) {
        this.initialGuess = initialGuess;
        this.maxIter = maxIter;
    }

    
Creates a default curve fitter. Zero will be used as initial guess for the coefficients, and the maximum number of iterations of the optimization algorithm is set to Integer.MAX_VALUE. 
Params:
degree – Degree of the polynomial to be fitted.
See Also:
withStartPoint(double[])
withMaxIterations(int)
Returns:
a curve fitter./**
     * Creates a default curve fitter.
     * Zero will be used as initial guess for the coefficients, and the maximum
     * number of iterations of the optimization algorithm is set to
     * {@link Integer#MAX_VALUE}.
     *
     * @param degree Degree of the polynomial to be fitted.
     * @return a curve fitter.
     *
     * @see #withStartPoint(double[])
     * @see #withMaxIterations(int)
     */
    public static PolynomialCurveFitter create(int degree) {
        return new PolynomialCurveFitter(new double[degree + 1], Integer.MAX_VALUE);
    }

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

    
Configure the maximum number of iterations.
Params:
newMaxIter – maximum number of iterations
Returns:
a new instance./**
     * Configure the maximum number of iterations.
     * @param newMaxIter maximum number of iterations
     * @return a new instance.
     */
    public PolynomialCurveFitter withMaxIterations(int newMaxIter) {
        return new PolynomialCurveFitter(initialGuess,
                                         newMaxIter);
    }

    
{@inheritDoc} /** {@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);

        if (initialGuess == null) {
            throw new MathInternalError();
        }

        // Return a new least squares problem set up to fit a polynomial curve to the
        // observed points.
        return new LeastSquaresBuilder().
                maxEvaluations(Integer.MAX_VALUE).
                maxIterations(maxIter).
                start(initialGuess).
                target(target).
                weight(new DiagonalMatrix(weights)).
                model(model.getModelFunction(), model.getModelFunctionJacobian()).
                build();

    }

}