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SSJ is a Java library for stochastic simulation, developed under the direction of Pierre L'Ecuyer, in the Département d'Informatique et de Recherche Opérationnelle (DIRO), at the Université de Montréal. It provides facilities for generating uniform and nonuniform random variates, computing different measures related to probability distributions, performing goodness-of-fit tests, applying quasi-Monte Carlo methods, collecting (elementary) statistics, and programming discrete-event simulations with both events and processes.

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/*
 * Class:        LeastSquares
 * Description:  polynomial obtained by the least squares method on set of points
 * Environment:  Java
 * Software:     SSJ 
 * Copyright (C) 2001  Pierre L'Ecuyer and Université de Montréal
 * Organization: DIRO, Université de Montréal
 * @author       
 * @since

 * SSJ is free software: you can redistribute it and/or modify it under
 * the terms of the GNU General Public License (GPL) as published by the
 * Free Software Foundation, either version 3 of the License, or
 * any later version.

 * SSJ is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.

 * A copy of the GNU General Public License is available at
   GPL licence site.
 */

package umontreal.iro.lecuyer.functionfit;
   import umontreal.iro.lecuyer.functions.Polynomial;


import java.io.Serializable;
import cern.colt.matrix.DoubleMatrix2D;
import cern.colt.matrix.impl.DenseDoubleMatrix2D;
import cern.colt.matrix.linalg.Algebra;


/**
 * Represents a polynomial obtained by the least squares method on a set of points.
 * More specifically, let 
 * (x₀, y₀),…,(x_n, y_n) be a set of points and
 * p(x) the constructed polynomial of degree m. The constructed polynomial
 * minimizes the square error 
 * 
 * 
 * E² = ∑_i=0ⁿ[y_i - p(x_i)]².
 * 

 * 
 */
public class LeastSquares extends Polynomial implements Serializable {
   private static final long serialVersionUID = -4997132164503234983L;
   private static final Algebra alg = new Algebra ();
   private double[] x;
   private double[] y;



   /**
    * Constructs a new least squares polynomial with points (x[0],
    *  y[0]),..., (x[n], y[n]). The constructed polynomial has degree
    *  degree.
    * 
    * @param x the x coordinates of the points.
    * 
    *    @param y the y coordinates of the points.
    * 
    *    @param degree the degree of the polynomial.
    * 
    *    @exception NullPointerException if x or y are null.
    * 
    *    @exception IllegalArgumentException if the lengths of x and y are different,
    *                or if less than degree + 1 points are specified.
    * 
    */
   public LeastSquares (double[] x, double[] y, int degree) {
      super (getCoefficients (x, y, degree));
      this.x = x.clone ();
      this.y = y.clone ();
   }


   /**
    * Computes and returns the coefficients of the fitting polynomial of
    *   degree degree.
    *  The coordinates of the given points are  (x[i], y[i]).
    * 
    * @param x the x coordinates of the points.
    * 
    *    @param y the y coordinates of the points.
    * 
    *    @param degree the degree of the polynomial.
    * 
    *    @return the coefficients of the fitting polynomial.
    * 
    */
   public static double[] getCoefficients (double[] x, double[] y,
                                           int degree) {
      if (x.length != y.length)
         throw new IllegalArgumentException ("Length of x and y not equal");
      if (x.length < degree + 1)
         throw new IllegalArgumentException ("Not enough points");

      final double[] xSums = new double[2 * degree + 1];
      final double[] xySums = new double[degree + 1];
      xSums[0] = x.length;
      for (int i = 0; i < x.length; i++) {
         double xv = x[i];
         xySums[0] += y[i];
         for (int j = 1; j <= 2 * degree; j++) {
            xSums[j] += xv;
            if (j <= degree)
               xySums[j] += xv * y[i];
            xv *= x[i];
         }
      }
      final DoubleMatrix2D A = new DenseDoubleMatrix2D (degree + 1, degree + 1);
      final DoubleMatrix2D B = new DenseDoubleMatrix2D (degree + 1, 1);
      for (int i = 0; i <= degree; i++) {
         for (int j = 0; j <= degree; j++) {
            final int d = i + j;
            A.setQuick (i, j, xSums[d]);
         }
         B.setQuick (i, 0, xySums[i]);
      }
      final DoubleMatrix2D aVec = alg.solve (A, B);
      return aVec.viewColumn (0).toArray ();
   }


   /**
    * Returns the x coordinates of the fitted points.
    * 
    * @return the x coordinates of the fitted points.
    * 
    */
   public double[] getX() {
      return x;
   }


   /**
    * Returns the y coordinates of the fitted points.
    * 
    * @return the y coordinates of the fitted points.
    * 
    */
   public double[] getY() {
      return y;
   }


   /**
    * Calls {@link umontreal.iro.lecuyer.functionfit.PolInterp#toString(double[], double[]) toString}
    *  with the associated points.
    * 
    * @return a string containing the points.
    * 
    */
   public String toString() {
      return PolInterp.toString (x, y);
   }

   @Override



   public LeastSquares clone() {
      final LeastSquares ls = (LeastSquares) super.clone ();
      ls.x = x.clone ();
      ls.y = y.clone ();
      return ls;
   }
}