content: /*
  * Copyright (c) 1997 - 2016
  * Actelion Pharmaceuticals Ltd.
  * Gewerbestrasse 16
  * CH-4123 Allschwil, Switzerland
  *
  * All rights reserved.
  *
  * Redistribution and use in source and binary forms, with or without
  * modification, are permitted provided that the following conditions are met:
  *
  * 1. Redistributions of source code must retain the above copyright notice, this
  *    list of conditions and the following disclaimer.
  * 2. Redistributions in binary form must reproduce the above copyright notice,
  *    this list of conditions and the following disclaimer in the documentation
  *    and/or other materials provided with the distribution.
  * 3. Neither the name of the the copyright holder nor the
  *    names of its contributors may be used to endorse or promote products
  *    derived from this software without specific prior written permission.
  *
  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
  * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
  * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
  * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
  * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
  * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
  * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  *
  */
  package com.actelion.research.util;
  
  import java.util.*;
  
  /**
   * Represents a polynomial spline function.
   */
  public final class FastSpline {
     
  	public final static class Polynome  {
  		private final double[] coeffs; //x0 x1 x2 x3
  		
  		public Polynome(double[] coeffs) {
  			this.coeffs = coeffs;			
  		}
  		
  		public Polynome derivative() {
  			return new Polynome(new double[] {coeffs[1], 2*coeffs[2], 3*coeffs[3], 0});
  		}
  
  		public double value(double x) {
  			return coeffs[0]+x*(coeffs[1]+x*(coeffs[2]+x*coeffs[3]));			
  		}
  		public double[] getCoefficients() {
  			return coeffs;
  		}
  	}
  
  
      /** Spline segment interval delimiters (knots).   Size is n+1 for n segments. */
      private final double[] knots;
  
      /**
       * The polynomial functions that make up the spline.  The first element
       * determines the value of the spline over the first subinterval, the
       * second over the second, etc.   Spline function values are determined by
       * evaluating these functions at <code>(x - knot[i])</code> where i is the
       * knot segment to which x belongs.
       */
      private final Polynome[] polynomials;
      
      /** 
       * Number of spline segments = number of polynomials
       *  = number of partition points - 1 
       */
      private final int n;
  
      /**
       * Construct a polynomial spline function with the given segment delimiters
       * and interpolating polynomials.
       */
      public FastSpline(double[] knots, Polynome[] polynomials) {
          this.n = knots.length -1;
          this.knots = new double[n + 1];
          this.polynomials = new Polynome[n];
          
          System.arraycopy(knots, 0, this.knots, 0, n + 1);
          System.arraycopy(polynomials, 0, this.polynomials, 0, n);
      }
  
      /**
       * Compute the value for the function.
       */
      public double value(double v) throws ArrayIndexOutOfBoundsException {
          int i = Arrays.binarySearch(knots, v);
          if (i < 0) i = -i - 2;
          if (i < 0) i = 0;
  		if ( i >= polynomials.length)
  			i--;
          return polynomials[i].value(v - knots[i]);
      }
          
      /**
       * Returns the derivative of the polynomial spline function as a PolynomialSplineFunction
       */
      public FastSpline derivative() {
      	Polynome[] derivativePolynomials = new Polynome[n];
          for (int i = 0; i < n; i++) derivativePolynomials[i] = polynomials[i].derivative();
          return new FastSpline(knots, derivativePolynomials);
      }
  }
  