// ******************************************************************************
   //
   // 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
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  // ******************************************************************************
  package ffx.numerics.switching;
  
  import static java.lang.String.format;
  import static org.apache.commons.math3.util.FastMath.cos;
  import static org.apache.commons.math3.util.FastMath.pow;
  import static org.apache.commons.math3.util.FastMath.sin;
  
  import java.util.function.DoubleUnaryOperator;
  
  /**
   * A SquaredTrigSwitch implements a 0-1 switch of form f(x) = sin^2(ax) or of form f(x) = cos^2(ax).
   * Cosine implementation is achieved by phase-shifting a sine wave.
   *
   * @author Jacob M. Litman
   * @author Michael J. Schnieders
   */
  public class SquaredTrigSwitch implements UnivariateSwitchingFunction {
  
    private static final double PI_OVER_TWO = Math.PI * 0.5;
    private final double multiplier;
    private final double halfPeriod;
    private final DoubleUnaryOperator xTransform;
    private final boolean cosine;
  
    /**
     * Default constructor, creating a switch sin^2(pi*x/2), or cos^2 if flag set. The sine form will
     * switch 0-1, and the cosine form switch 1-0.
     *
     * @param cosine Use a cos^2(pi*x/2) transform instead of sin^2(pi*x/2).
     */
    public SquaredTrigSwitch(boolean cosine) {
      this(PI_OVER_TWO, cosine);
    }
  
    /**
     * Constructor permitting a custom frequency "a" in the form sin^2(a*x) or cos^2(a*x). The sine
     * form will switch 0-1, and the cosine form switch 1-0.
     *
     * @param coefficient Value of a
     * @param cosine Use a cos^2(ax) transform instead of sin^2(ax).
     */
    public SquaredTrigSwitch(double coefficient, boolean cosine) {
      multiplier = coefficient;
      halfPeriod = PI_OVER_TWO / multiplier;
      xTransform = cosine ? this::cosineTransform : this::sineTransform;
      this.cosine = cosine;
    }
  
    /** {@inheritDoc} */
    @Override
    public boolean constantOutsideBounds() {
      return false;
    }
  
    /** {@inheritDoc} */
    @Override
    public double firstDerivative(double x) throws IllegalArgumentException {
      x = xTransform.applyAsDouble(x);
      return 2.0 * sin(x) * cos(x) * multiplier;
    }
  
    /** {@inheritDoc} */
   @Override
   public int getHighestOrderZeroDerivative() {
     return 1;
   }
 
   /** {@inheritDoc} */
   @Override
   public double getOneBound() {
     return cosine ? 0 : halfPeriod;
   }
 
   /**
    * Get the repeating period of this switch.
    *
    * @return Period
    */
   public double getPeriod() {
     return 2.0 * halfPeriod;
   }
 
   /** {@inheritDoc} */
   @Override
   public double getZeroBound() {
     return cosine ? halfPeriod : 0;
   }
 
   /**
    * Return true if a cos^2(ax) transform, false if a sin^2(ax) transform.
    *
    * @return a boolean.
    */
   public boolean isCosine() {
     return cosine;
   }
 
   /** {@inheritDoc} */
   @Override
   public double nthDerivative(double x, int order) throws IllegalArgumentException {
     if (order < 1) {
       throw new IllegalArgumentException("Order must be >= 1");
     }
     x = xTransform.applyAsDouble(x);
     double sinVal = sin(x);
     double cosVal = cos(x);
     double multPow = pow(multiplier, order);
 
     return switch (order % 4) {
       case 0 -> pow(2.0, order - 1) * multPow * ((sinVal * sinVal) - (cosVal * cosVal));
       case 1 -> pow(2.0, order) * multPow * sinVal * cosVal;
       case 2 -> pow(2.0, order - 1) * multPow * ((cosVal * cosVal) - (sinVal * sinVal));
       case 3 -> -1.0 * pow(2.0, order) * multPow * sinVal * cosVal;
       default -> throw new ArithmeticException("A positive number modulo 4 was not 0-3");
     };
   }
 
   /** {@inheritDoc} */
   @Override
   public double secondDerivative(double x) throws IllegalArgumentException {
     double val = 2.0 * multiplier * multiplier;
     x = xTransform.applyAsDouble(x);
     double cosTerm = cos(x);
     double sinTerm = sin(x);
 
     return val * ((cosTerm * cosTerm) - (sinTerm * sinTerm));
   }
 
   /** {@inheritDoc} */
   @Override
   public boolean symmetricToUnity() {
     return true;
   }
 
   /** {@inheritDoc} */
   @Override
   public String toString() {
     if (cosine) {
       return format("Cosine-squared switching function of form f(x) = cos^2(%8.4g * x)", multiplier);
     } else {
       return format("Sine-squared switching function of form f(x) = sin^2(%8.4g * x)", multiplier);
     }
   }
 
   /** {@inheritDoc} */
   @Override
   public boolean validOutsideBounds() {
     return true;
   }
 
   /** {@inheritDoc} */
   @Override
   public double valueAt(double x) throws IllegalArgumentException {
     x = xTransform.applyAsDouble(x);
     x = sin(x);
     x *= x;
     return x;
   }
 
   /**
    * Operate on a*x.
    *
    * @param x Input
    * @return Position along sine wave.
    */
   private double sineTransform(double x) {
     return x * multiplier;
   }
 
   /**
    * Operate on (pi/2) + a*x, period-shifting a sine wave into the desired cosine wave.
    *
    * @param x Input
    * @return Position along cosine wave.
    */
   private double cosineTransform(double x) {
     return PI_OVER_TWO + (x * multiplier);
   }
 }