/*
* Open Source Physics software is free software as described near the bottom of this code file.
*
* For additional information and documentation on Open Source Physics please see:
* <http://www.opensourcephysics.org/>
*/
package org.opensourcephysics.numerics.specialfunctions;
import java.util.ArrayList;
import org.opensourcephysics.numerics.Polynomial;
/**
* Calculates Hermite polynomials.
*
* @author W. Christian
* @version 1.0
*/
public class Hermite {
static final ArrayList<Polynomial> hermiteList;
static final Polynomial twoX = new Polynomial(new double[] {0, 2.0}); // 2x used in recursion
private Hermite() {} // all methods are static so prohibit instantiation
/**
* Gets the n-th Hermite polynomial. If it has already been calculated
* it just returns it from the list. If we have not calculated it uses
* the recursion relationship to construct the polynomial based on the prior
* polynomials.
*
* @param n degree of polynomial
*/
public static synchronized Polynomial getPolynomial(int n) {
if(n<0) {
throw new IllegalArgumentException(Messages.getString("Hermite.neg_degree")); //$NON-NLS-1$
}
if(n<hermiteList.size()) {
return hermiteList.get(n);
}
Polynomial p1 = getPolynomial(n-1).multiply(twoX);
Polynomial p2 = getPolynomial(n-2).multiply(2*(n-1));
Polynomial p = p1.subtract(p2);
hermiteList.add(p); // polynomial was not on the list so add it.
return p;
}
/**
* Evaluates the n-th Hermite polynomial at x.
*
* @return the value of the function
*/
public static double evaluate(int n, double x) {
return getPolynomial(n).evaluate(x);
}
static {
hermiteList = new ArrayList<Polynomial>();
Polynomial p = new Polynomial(new double[] {1.0});
hermiteList.add(p);
p = new Polynomial(new double[] {0, 2.0});
hermiteList.add(p);
}
}
/*
* Open Source Physics software 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 2 of the License,
* or(at your option) any later version.
* Code that uses any portion of the code in the org.opensourcephysics package
* or any subpackage (subdirectory) of this package must must also be be released
* under the GNU GPL license.
*
* This software 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.
*
* You should have received a copy of the GNU General Public License
* along with this; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston MA 02111-1307 USA
* or view the license online at http://www.gnu.org/copyleft/gpl.html
*
* Copyright (c) 2007 The Open Source Physics project
* http://www.opensourcephysics.org
*/