/*
 * 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.math.optimization.fitting;

import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math.optimization.DifferentiableMultivariateVectorialOptimizer;
import org.apache.commons.math.optimization.OptimizationException;

/**
 * This class implements a curve fitting specialized for polynomials.
 * <p>
 * Polynomial fitting is a very simple case of curve fitting. The estimated
 * coefficients are the polynomial coefficients. They are searched by a least
 * square estimator.
 * </p>
 * 
 * @version $Revision$ $Date$
 * @since 2.0
 */

public class PolynomialFitter {

	/** Fitter for the coefficients. */
	private final CurveFitter fitter;

	/** Polynomial degree. */
	private final int degree;

	/**
	 * Simple constructor.
	 * <p>
	 * The polynomial fitter built this way are complete polynomials, ie. a
	 * n-degree polynomial has n+1 coefficients.
	 * </p>
	 * 
	 * @param degree
	 *            maximal degree of the polynomial
	 * @param optimizer
	 *            optimizer to use for the fitting
	 */
	public PolynomialFitter(int degree, final DifferentiableMultivariateVectorialOptimizer optimizer) {
		this.fitter = new CurveFitter(optimizer);
		this.degree = degree;
	}

	/**
	 * Add an observed weighted (x,y) point to the sample.
	 * 
	 * @param weight
	 *            weight of the observed point in the fit
	 * @param x
	 *            abscissa of the point
	 * @param y
	 *            observed value of the point at x, after fitting we should have
	 *            P(x) as close as possible to this value
	 */
	public void addObservedPoint(double weight, double x, double y) {
		fitter.addObservedPoint(weight, x, y);
	}

	/**
	 * Get the polynomial fitting the weighted (x, y) points.
	 * 
	 * @return polynomial function best fitting the observed points
	 * @exception OptimizationException
	 *                if the algorithm failed to converge
	 */
	public PolynomialFunction fit() throws OptimizationException {
		try {
			return new PolynomialFunction(fitter.fit(new ParametricPolynomial(), new double[degree + 1]));
		} catch (FunctionEvaluationException fee) {
			// this should never happen
			throw MathRuntimeException.createInternalError(fee);
		}
	}

	/** Dedicated parametric polynomial class. */
	private static class ParametricPolynomial implements ParametricRealFunction {

		/** {@inheritDoc} */
		public double[] gradient(double x, double[] parameters) throws FunctionEvaluationException {
			final double[] gradient = new double[parameters.length];
			double xn = 1.0;
			for (int i = 0; i < parameters.length; ++i) {
				gradient[i] = xn;
				xn *= x;
			}
			return gradient;
		}

		/** {@inheritDoc} */
		public double value(final double x, final double[] parameters) {
			double y = 0;
			for (int i = parameters.length - 1; i >= 0; --i) {
				y = y * x + parameters[i];
			}
			return y;
		}

	}

}
