/*
 * This code is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public 
 * License as published by the Free Software Foundation; either 
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This code 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 Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public 
 * License along with this program; if not, write to the Free 
 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, 
 * MA  02111-1307, USA.
 */
package no.geosoft.cc.math.calculus;



import Jama.Matrix;



/**
 * Given n points (x0,y0)...(xn-1,yn-1), the following methid computes
 * the polynomial factors of the n-1't degree polynomial passing through
 * the n points.
 *
 * Example: Passing in three points (2,3) (1,4) and (3,7) will produce
 * the results [2.5, -8.5, 10] which means that the points is on the
 * curve y = 2.5x - 8.5x + 10.
 * 
 * @author <a href="mailto:info@geosoft.no">GeoSoft</a>
 */   
public class LagrangeInterpolation
{
  public static double[] findPolynomialFactors (double[] x, double[] y)
    throws RuntimeException
  {
    int n = x.length;

    double[][] data = new double[n][n];
    double[]   rhs  = new double[n];
    
    for (int i = 0; i < n; i++) {
      double v = 1;
      for (int j = 0; j < n; j++) {
        data[i][n-j-1] = v;
        v *= x[i];
      }

      rhs[i] = y[i];
    }

    // Solve m * s = b
    
    Matrix m = new Matrix (data);
    Matrix b = new Matrix (rhs, n);

    Matrix s = m.solve (b);

    return s.getRowPackedCopy();
  }


  public static void main (String args[])
  {
    double x[] = {2.0, 1.0, 3.0};
    double y[] = {3.0, 4.0, 7.0};

    double f[] = LagrangeInterpolation.findPolynomialFactors (x, y);

    for (int i = 0; i < 3; i++)
      System.out.println (f[i]);
  }
}