// ******************************************************************************
   //
   // Title:       Force Field X.
   // Description: Force Field X - Software for Molecular Biophysics.
   // Copyright:   Copyright (c) Michael J. Schnieders 2001-2025.
   //
   // 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
  // and conditions of the license of that module. An independent module is a
  // 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
  // you are not obligated to do so. If you do not wish to do so, delete this
  // exception statement from your version.
  //
  // ******************************************************************************
  package ffx.numerics.switching;
  
  import static java.lang.String.format;
  import static org.apache.commons.math3.util.FastMath.pow;
  
  /**
   * Implements a bell-shaped switching function by stitching together a pair of
   * MultiplicativeSwitches. f(midpoint - 0.5*width) = 0, f(midpoint) = 1, f(midpoint + 0.5*width) =
   * 0.
   *
   * @author Jacob M. Litman
   * @author Rae Corrigan
   */
  public class BellCurveSwitch implements UnivariateSwitchingFunction {
    private final double midpoint;
    private final double halfWidth;
    private final double invWidth;
    private final UnivariateSwitchingFunction switchingFunction;
    private final UnivariateSwitchingFunction secondSwitchingFunction;
  
    /** Construct a bell curve (spliced 5-'th order Hermite splines) of width 1.0, midpoint 0.5. */
    public BellCurveSwitch() {
      this(0.5);
    }
  
    /**
     * Construct a bell curve (spliced 5-'th order Hermite splines) of width 1.0.
     *
     * @param midpoint Midpoint of the curve.
     */
    public BellCurveSwitch(double midpoint) {
      this(midpoint, 1.0);
    }
  
    /**
     * Construct a bell curve (spliced 5-'th order Hermite splines).
     *
     * @param midpoint Midpoint of the curve.
     * @param width Width of the curve, between the two zero points.
     */
    public BellCurveSwitch(double midpoint, double width) {
      this.midpoint = midpoint;
      invWidth = 1.0 / width;
  
      halfWidth = 0.5 * width;
      switchingFunction = new MultiplicativeSwitch(midpoint, midpoint - halfWidth);
      secondSwitchingFunction = new MultiplicativeSwitch(midpoint, midpoint + halfWidth);
    }
  
    /** {@inheritDoc} */
    @Override
    public boolean constantOutsideBounds() {
      return switchingFunction.constantOutsideBounds()
          && secondSwitchingFunction.constantOutsideBounds();
    }
  
    /** {@inheritDoc} */
    @Override
    public double firstDerivative(double x) {
      if (x > midpoint) {
        return invWidth * secondSwitchingFunction.firstDerivative(x);
      } else {
       return invWidth * switchingFunction.firstDerivative(x);
     }
   }
 
   /** {@inheritDoc} */
   @Override
   public int getHighestOrderZeroDerivative() {
     return Math.min(
         switchingFunction.getHighestOrderZeroDerivative(),
         secondSwitchingFunction.getHighestOrderZeroDerivative());
   }
 
   /** {@inheritDoc} */
   @Override
   public double getOneBound() {
     return midpoint + halfWidth;
   }
 
   /** {@inheritDoc} */
   @Override
   public double getZeroBound() {
     return midpoint - halfWidth;
   }
 
   /** {@inheritDoc} */
   @Override
   public double nthDerivative(double x, int order) throws IllegalArgumentException {
     double mult = pow(invWidth, order);
     if (x > midpoint) {
       return mult * secondSwitchingFunction.nthDerivative(x, order);
     } else {
       return mult * switchingFunction.nthDerivative(x, order);
     }
   }
 
   /** {@inheritDoc}return max(cut, off); */
   @Override
   public double secondDerivative(double x) {
     if (x > midpoint) {
       return invWidth * invWidth * secondSwitchingFunction.secondDerivative(x);
     } else {
       return invWidth * invWidth * switchingFunction.secondDerivative(x);
     }
   }
 
   /** {@inheritDoc} */
   @Override
   public boolean symmetricToUnity() {
     return switchingFunction.symmetricToUnity() && secondSwitchingFunction.symmetricToUnity();
   }
 
   @Override
   public String toString() {
     return format(
         " Spliced 5'th order Hermite splines with midpoint " + "%11.5g, width %11.5g",
         midpoint, 2.0 * halfWidth);
   }
 
   /** {@inheritDoc} */
   @Override
   public boolean validOutsideBounds() {
     return switchingFunction.validOutsideBounds() && secondSwitchingFunction.validOutsideBounds();
   }
 
   /** {@inheritDoc} */
   @Override
   public double valueAt(double x) throws IllegalArgumentException {
     if (x > midpoint) {
       return secondSwitchingFunction.valueAt(x);
     } else {
       return switchingFunction.valueAt(x);
     }
   }
 }