code: ///////////////////////////////////////////////////////////////////////////////
  // For information as to what this class does, see the Javadoc, below.       //
  // Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006,       //
  // 2007, 2008, 2009, 2010, 2014, 2015 by Peter Spirtes, Richard Scheines, Joseph   //
  // Ramsey, and Clark Glymour.                                                //
  //                                                                           //
  // This program is free software; you can redistribute it and/or modify      //
  // it under the terms of the GNU General Public License as published by      //
  // the Free Software Foundation; either version 2 of the License, or         //
  // (at your option) any later version.                                       //
  //                                                                           //
  // This program 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 program; if not, write to the Free Software               //
  // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA //
  ///////////////////////////////////////////////////////////////////////////////
  
  package edu.cmu.tetrad.util;
  
  
  /**
   * Provides a static method for finding the cutoff value for a symmetric
   * probability distribution function about the origin.
   *
   * @author Joseph Ramsey
   */
  public class CutoffFinder {
  
      /**
       * Assumes f is a positive symmetric function between x1 and x2 about 0.
       * Integrates from 0 in the direction of x2 in intervals of deltaX until an
       * area of .5 * (1 - alpha) has been accumulated. Returns the x value at
       * the iteration where this amount of area has been accumulated.</p> </p>
       * <p>This is helpful for finding cutoff levels for normal curves,
       * distributions of correlation coefficients, Student's t, etc. It returns
       * significance level cutoffs.
       *
       * @param f           a function
       * @param xUpperBound an upper bound for the integration.
       * @param alpha       the significance level.
       * @param deltaX      the amount the integration jumps forward each time.
       * @return the cutoff value for these conditions.
       */
      public static double getCutoff(Function f, double xUpperBound, double alpha,
                                     double deltaX) {
  
          double area = 0.0;
          double x1 = 0.0, x2 = 0.0;
          double upperAreaLimit = .5 * (1 - alpha);
  
          while ((area < upperAreaLimit) && (x1 < xUpperBound)) {
              x1 = x2;
              x2 += deltaX;
  
              double yAve = .5 * (f.valueAt(x1) + f.valueAt(x2));
              area += yAve * deltaX;
          }
  
          return x1;
      }
  }
  
  
  
  
  
  