// ******************************************************************************
   //
   // Title:       Force Field X.
   // Description: Force Field X - Software for Molecular Biophysics.
   // Copyright:   Copyright (c) Michael J. Schnieders 2001-2024.
   //
   // This file is part of Force Field X.
   //
   // Force Field X is free software; you can redistribute it and/or modify it
  // under the terms of the GNU General Public License version 3 as published by
  // the Free Software Foundation.
  //
  // Force Field X 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
  // Force Field X; if not, write to the Free Software Foundation, Inc., 59 Temple
  // Place, Suite 330, Boston, MA 02111-1307 USA
  //
  // Linking this library statically or dynamically with other modules is making a
  // combined work based on this library. Thus, the terms and conditions of the
  // GNU General Public License cover the whole combination.
  //
  // As a special exception, the copyright holders of this library give you
  // permission to link this library with independent modules to produce an
  // executable, regardless of the license terms of these independent modules, and
  // to copy and distribute the resulting executable under terms of your choice,
  // provided that you also meet, for each linked independent module, the terms
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  // module which is not derived from or based on this library. If you modify this
  // library, you may extend this exception to your version of the library, but
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  // exception statement from your version.
  //
  // ******************************************************************************
  package ffx.numerics.integrate;
  
  import static java.lang.String.format;
  import static java.lang.System.arraycopy;
  import static org.apache.commons.math3.util.FastMath.abs;
  import static org.apache.commons.math3.util.FastMath.max;
  import static org.apache.commons.math3.util.FastMath.ulp;
  
  /**
   * A FunctionDataCurve represents a set of points along a 1-dimensional, analytically integrable
   * function.
   *
   * @author Jacob M. Litman
   */
  public abstract class FunctionDataCurve implements DataSet {
  
    /** Lower bound. */
    protected double lb;
    /** Upper bound. */
    protected double ub;
    /** Function values. */
    protected double[] points;
    /** Input points. */
    protected double[] x;
    /** If ends should have 1/2 regular separation. */
    protected boolean halfWidthEnd;
  
    /**
     * Checks for equality to +/- 10 ulp.
     *
     * @param x1 a double.
     * @param x2 a double.
     * @return a boolean.
     */
    public static boolean approxEquals(double x1, double x2) {
      return (approxEquals(x1, x2, 10.0));
    }
  
    /**
     * Compare two doubles to machine precision.
     *
     * @param x1 The first point.
     * @param x2 The second point.
     * @param ulpMultiple A multiple to apply to the ULP of the larger of the two values.
     * @return True if the two values are within the specified ULPs of each other.
     */
    public static boolean approxEquals(double x1, double x2, double ulpMultiple) {
      double diff = abs(x1 - x2);
      // Ulp the larger of the two values.
      double ulp = ulp(max(abs(x1), abs(x2)));
      return (diff < (ulp * ulpMultiple));
    }
  
    /**
     * Evaluates the functions analytical integral over the entire range of points.
     *
     * @return Exact finite integral
     */
    public double analyticalIntegral() {
      return analyticalIntegral(lowerBound(), upperBound());
    }
  
   /**
    * Evaluates the function's analytical integral over a range.
    *
    * @param lb Lower integration bound
    * @param ub Upper integration bound
    * @return Exact finite integral of range
    */
   public double analyticalIntegral(double lb, double ub) {
     return integralAt(ub) - integralAt(lb);
   }
 
   /** {@inheritDoc} */
   @Override
   public double binWidth() {
     double divisor = halfWidthEnds() ? (double) (points.length - 2) : (double) (points.length - 1);
     return (ub - lb) / divisor;
   }
 
   /**
    * Evaluates the function at x.
    *
    * @param x x
    * @return f(x)
    */
   public abstract double fX(double x);
 
   /** {@inheritDoc} */
   @Override
   public double[] getAllFxPoints() {
     int nPoints = points.length;
     double[] retArray = new double[nPoints];
     arraycopy(points, 0, retArray, 0, nPoints);
     return retArray;
   }
 
   /** {@inheritDoc} */
   @Override
   public double getFxPoint(int index) {
     return points[index];
   }
 
   /** {@inheritDoc} */
   @Override
   public double[] getX() {
     double[] copyX = new double[x.length];
     arraycopy(x, 0, copyX, 0, x.length);
     return copyX;
   }
 
   /** {@inheritDoc} */
   @Override
   public boolean halfWidthEnds() {
     return halfWidthEnd;
   }
 
   /**
    * Analytical integral at a point.
    *
    * @param x Point
    * @return Exact finite integral of 0 to this point
    */
   public abstract double integralAt(double x);
 
   /** {@inheritDoc} */
   @Override
   public double lowerBound() {
     return lb;
   }
 
   /** {@inheritDoc} */
   @Override
   public int numPoints() {
     return points.length;
   }
 
   /** {@inheritDoc} */
   @Override
   public String toString() {
     StringBuilder sb =
         new StringBuilder(
             format(
                 "Function f(x) curve with %d points from lower bound %9.3g and upper bound %9.3g",
                 points.length, lb, ub));
     if (halfWidthEnd) {
       sb.append(" and half-width start/end bins");
     }
     sb.append(".");
     return sb.toString();
   }
 
   /** {@inheritDoc} */
   @Override
   public double upperBound() {
     return ub;
   }
 
   /**
    * Used to check that x array is composed of equally-spaced points from lb to ub.
    */
   protected final void assertXIntegrity() {
     assert ub > lb;
     int nX = numPoints();
     double sep = binWidth();
     if (halfWidthEnd) {
       assert x.length == nX;
       assert lb == x[0];
       assert ub == x[nX - 1];
 
       assert approxEquals(x[1], lb + 0.5 * sep);
       assert approxEquals(x[nX - 2], (ub - 0.5 * sep));
 
       for (int i = 2; i < (nX - 2); i++) {
         double target = lb + 0.5 * sep;
         target += ((i - 1) * sep);
         assert approxEquals(x[i], target);
       }
     } else {
       for (int i = 0; i < x.length; i++) {
         assert approxEquals(x[i], x[0] + i * sep);
       }
     }
   }
 }