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TableFunction.java

/*************************************************************************
*                                                                        *
*   1) This source code file, in unmodified form, and compiled classes   *
*      derived from it can be used and distributed without restriction,  *
*      including for commercial use.  (Attribution is not required       *
*      but is appreciated.)                                              *
*                                                                        *
*    2) Modified versions of this file can be made and distributed       *
*       provided:  the modified versions are put into a Java package     *
*       different from the original package, edu.hws;  modified          *
*       versions are distributed under the same terms as the original;   *
*       and the modifications are documented in comments.  (Modification *
*       here does not include simply making subclasses that belong to    *
*       a package other than edu.hws, which can be done without any      *
*       restriction.)                                                    *
*                                                                        *
*   David J. Eck                                                         *
*   Department of Mathematics and Computer Science                       *
*   Hobart and William Smith Colleges                                    *
*   Geneva, New York 14456,   USA                                        *
*   Email: eck@hws.edu          WWW: http://math.hws.edu/eck/            *
*                                                                        *
*************************************************************************/


package edu.hws.jcm.functions;
import edu.hws.jcm.data.*;

/**
 * A TableFunction is a function that is specified by a table of (x,y)-points.
 * Values are interpolated between the specified x-values.  This can be done
 * in several differnt ways; the method that is used is controlled by the
 * "Style" property.  Since a TableFunction extends FunctionParserExtension,
 * a TableFunction can be added to a Parser (provided it has a name), and
 * it can then be used in expressions parsed by that parser.  Note that this 
 * class is meant to be used for functions that are defined by a fairly
 * small number of points, since each function evaluation involves a linear
 * search through the list of x-values of the defining points.
 */
00040 public class TableFunction extends FunctionParserExtension {

   /** 
    * If the style of the function is set to SMOOTH,
    * then cubic interpolation is used to find the value
    * of the functions for x-values between the points that define the function.
    */
00047    public static final int SMOOTH = 0;
   
   /** 
    * If the style of the function is set to PIECEWISE_LINEAR,
    * then linear interpolation is used to find the value
    * of the functions for x-values between the points that define the function.
    */
00054    public static final int PIECEWISE_LINEAR = 1;

   /** 
    * If the style of the function is set to STEP, then the function is 
    * piecewise constant, and the value of the function at x is taken
    * from the nearest point in the list of points that define the function.
    */
00061    public static final int STEP = 2;

   /** 
    * If the style of the function is set to STEP_LEFT, then the function is 
    * piecewise constant, and the value of the function at x is taken
    * from the nearest point to the left in the list of points that define the function.
    */

00069    public static final int STEP_LEFT = 3;

   /** 
    * If the style of the function is set to STEP_RIGHT, then the function is 
    * piecewise constant, and the value of the function at x is taken
    * from the nearest point to the right in the list of points that define the function.
    */
00076    public static final int STEP_RIGHT = 4;


   private int style;  // Type of function, given by one of the above constants.
   private double[] xCoords = new double[10];    // x-coordinates, in increasing order
   private double[] yCoords = new double[10];    // the corresponding y-coordinates
   private CubicSegment[] segments;              // interpolation data for SMOOTH style
   private int pointCt;         // number of points (possibly less than xCoords.length)
   
   /** 
    * Create a TableFunction with SMOOTH style and no points.
    */
00088    public TableFunction() {
      this(SMOOTH);
   }
   
   /** 
    * Create a TableFunction with specified style and no points.
    *
    * @param style The style for the function: SMOOTH, PIECEWISE_LINEAR, STEP,
    *     STEP_LEFT, or STEP_RIGHT. 
    */
00098    public TableFunction(int sytle) {
      this.style = style;
      if (style == SMOOTH)
         segments = new CubicSegment[9];
   }
   
   /** 
    * Copy data from another TableFunction, except that the name of the funcion is 
    * not duplicated.  The new TableFunction is nameless.
    */
   
00109    public void copyDataFrom(TableFunction source) {
      xCoords = (double[])source.xCoords.clone();
      yCoords = (double[])source.yCoords.clone();
      style = -1;  // Force setStyle to compute data for SMOOTH style.
      setStyle(source.style);
   }
   
   /**
    * Set the style of this TableFunction, to specify how values are interpolated
    * between points on the curve.
    *
    * @param style One of the style constants SMOOTH, PIECEWISE_LINEAR, STEP,
    *     STEP_LEFT, STEP_RIGHT.  Other values are ignored.
    */
00123    public void setStyle(int style) {
      if (style == this.style || style < 0 || style > 4)
         return;
      this.style = style;
      if (style == SMOOTH) {
         segments = new CubicSegment[xCoords.length - 1];
         for (int i = 0; i < pointCt-1; i++)
            segments[i] = new CubicSegment(xCoords[i],xCoords[i+1],yCoords[i],yCoords[i+1],0,0);
         for (int i = 0; i < pointCt-1; i++)
            interpolateDerivatives(i);
      }
      else {
         segments = null;
      }
   }
   
   /**
    * Get the style of this TableFunction, which specifies how values are
    * interpolated between points on the curve.
    *
    * @return The style of this TableFunction.  This is one of the constants
    *    SMOOTH, PIECEWISE_LINEAR, STEP, STEP_LEFT, or STEP_RIGHT.
    */
00146    public int getStyle() {
      return style;
   }
   
   /**
    * Add points to the table.  The x-coordinates of the points are taken from
    * the xCoords array.  The y-coordinate for the i-th point is yCoords[i], if
    * an i-th position exists in this array.  Otherwise, the y-coordinate is
    * is zero.  (Note that if xCoords[i] duplicates an x-value already in
    * the table, then no new point is added but the corresponging y-value is changed.)
    *
    * @param xCoords A list of x-coordinates to be added to the table.  If this is
    *    null, then nothing is done.
    * @param yCoords The value of yCoords[i], if it exists, is the y-coordinate
    *    corresponding to xCoords[i].  Otherwise, the y-coordinate is undefined.
    *    This can be null, in which case all y-coordinates are zero.
    */
00163    public void addPoints(double[] xCoords, double[] yCoords) {
      if (xCoords == null)
         return;
      int ct = xCoords.length;
      if (yCoords == null)
         ct = 0;
      else if (yCoords.length < ct)
         ct = yCoords.length;
      for (int i = 0; i < ct; i++)
         addPoint(xCoords[i], yCoords[i]);
      for (int i = ct; i < xCoords.length; i++)
         addPoint(xCoords[i],0);
   }
   
   /**
    * Add points to the table.  The number of points added is intervals + 1.
    * The x-coordinates are evenly spaced between xmin and xmax.  The y-coordinates
    * are zero.
    *
    * @param intervals The number of intervals.  The number of points added is intervals + 1.
    *   The value should be at least 1.  If not, nothing is done.
    * @param xmin The minimim x-coordinate for added points.
    * @param xmax The maximum x-coodinate for added points.  Should be greater than
    *   xmin, for efficiency, but no error occurs if it is not.
    */
00188    public void addIntervals(int intervals, double xmin, double xmax) {
       if (intervals < 1)
          return;
       double dx = (xmax - xmin) / intervals;
       for (int i = 0; i < intervals; i++)
          addPoint(xmin + i*dx, 0);
       addPoint(xmax, 0);
   }
   
   /**
    * Add a point with the specified x and y coordinates.  If a point with the
    * given x coordinate already exists in the table, then no new point is added,
    * but the associated y-value is changed.
    * (If x is Double.NaN, then no change is made and the return value is -1.)
    *
    * @param x The x-coordinate of the point to be added or modified.
    * @param y The y-coordinate of the point.
    * @return the position of the point in the list of points, where the first point is at position zero.
    */
00207    public int addPoint(double x, double y) {
      if (Double.isNaN(x))
         return -1;
      int pos = 0;
      while (pos < pointCt && xCoords[pos] < x)
         pos++;
      if (pos < pointCt && xCoords[pos] == x) {
         yCoords[pos] = y;
      }
      else {
         if (pointCt == xCoords.length) {
            double[] temp = new double[2*xCoords.length];
            System.arraycopy(xCoords,0,temp,0,xCoords.length);
            xCoords = temp;
            temp = new double[2*yCoords.length];
            System.arraycopy(yCoords,0,temp,0,yCoords.length);
            yCoords = temp;
            if (style == SMOOTH) {
               CubicSegment[] temps = new CubicSegment[xCoords.length - 1];
               System.arraycopy(segments,0,temps,0,pointCt - 1);
               segments = temps;
            }
         }
         for (int i = pointCt; i > pos; i--) {
            xCoords[i] = xCoords[i-1];
            yCoords[i] = yCoords[i-1];
         }
         xCoords[pos] = x;
         yCoords[pos] = y;
         if (style == SMOOTH && pointCt > 0) {
            if (pos == pointCt)
               segments[pointCt - 1] = new CubicSegment();
            else {
               for (int i = pointCt-1; i > pos; i--)
                  segments[i] = segments[i-1];
               segments[pos] = new CubicSegment();
            }
         }
         pointCt++;
      }
      if (style == SMOOTH && pointCt > 0) {  // make sure segment data is OK for segments that depend on (x,y)
         if (pos > 0)
            segments[pos-1].setData(xCoords[pos-1],xCoords[pos],yCoords[pos-1],yCoords[pos],0,0);
         if (pos < pointCt-1)
            segments[pos].setData(xCoords[pos],xCoords[pos+1],yCoords[pos],yCoords[pos+1],0,0);
         for (int i = pos - 2; i <= pos + 1; i++)
            interpolateDerivatives(i);
      }
      return pos;
   }
   
   private void interpolateDerivatives(int pos) {
         // Compute correct derivatives for segments[pos] from data in coordinate arrays.
      if (pos < 0 || pos > pointCt - 2)
         return;
      // pointCt must be >= 2
      if (pointCt == 2) // pos must be 0
         segments[0].setDerivativesFromNeighbors(Double.NaN,0,Double.NaN,0);
      else if (pos == 0)
         segments[0].setDerivativesFromNeighbors(Double.NaN,0,xCoords[2],yCoords[2]);
      else if (pos == pointCt - 2)
         segments[pointCt-2].setDerivativesFromNeighbors(xCoords[pointCt-3],yCoords[pointCt-3],Double.NaN,0);
      else
         segments[pos].setDerivativesFromNeighbors(xCoords[pos-1],yCoords[pos-1],xCoords[pos+2],yCoords[pos+2]);
   }
   
   /**
    * Gets the number of points in the table.
    */
00276    public int getPointCount() {
      return pointCt;
   }
   
   /**
    * Get the x-coordinate in the i-th point, where the first point
    * is number zero.  Throws an IllegalArgumentException if i is
    * less than zero or greater than or equal to the number of points.
    */
00285    public double getX(int i) {
      if (i >= 0 && i < pointCt)
         return xCoords[i];
      else
         throw new IllegalArgumentException("Point index out of range: " + i);
   }
   
   /**
    * Get the y-coordinate in the i-th point, where the first point
    * is number zero.  Throws an IllegalArgumentException if i is
    * less than zero or greater than or equal to the number of points.
    */
00297    public double getY(int i) {
      if (i >= 0 && i < pointCt)
         return yCoords[i];
      else
         throw new IllegalArgumentException("Point index out of range: " + i);
   }
   
   /**
    * Set the y-coordinate in the i-th point to y, where the first point
    * is number zero.  Throws an IllegalArgumentException if i is
    * less than zero or greater than or equal to the number of points.
    */
00309    public void setY(int i, double y) {
      if (i >= 0 && i < pointCt)
         yCoords[i] = y;
      else
         throw new IllegalArgumentException("Point index out of range: " + i);
      if (style == SMOOTH) {
         if (i > 0)
             segments[i-1].setData(xCoords[i-1],xCoords[i],yCoords[i-1],yCoords[i],0,0);
         if (i < pointCt - 1)
             segments[i].setData(xCoords[i],xCoords[i+1],yCoords[i],yCoords[i+1],0,0);
         for (int j = i-2; j <= i+1; j++)
            interpolateDerivatives(j);
      }
   }
   
   /**
    * If there is a point in the list with x-coordinate x, then this function returns
    * the index of that point in the list (where the index of the first point is zero).
    * If there is no such point, then -1 is returned.
    */   
00329    public int findPoint(double x) {
       int i = 0;
       while (i < pointCt) {
          if (x == xCoords[i])
             return i;
          else if (x > xCoords[i])
             i++;
          else
             break;
       }
       return -1;
   }
   
   /**
    * Removes the i-th point from the list of points.  Throws an IllegalArgumentException if i is
    * less than zero or greater than or equal to the number of points. 
    */
00346    public void removePointAt(int i) {
      if (i < 0 || i >= pointCt)
         throw new IllegalArgumentException("Point index out of range: " + i);
      pointCt--;
      for (int j = i; j < pointCt; j++) {
         xCoords[j] = xCoords[j+1];
         yCoords[j] = yCoords[j+1];
      }
      if (style == SMOOTH) {
         style = -1;  // force recompute of data
         setStyle(SMOOTH);
      }
   }
   
   /**
    *  Remove all points.  The resulting function is undefined everywhere.
    */
00363    public void removeAllPoints() {
      pointCt = 0;
      xCoords = new double[10];
      yCoords = new double[10];
   }
   
   /**
    * Get the value of the function at x, using interpolation if x lies between
    * two x-coordinates in the list of points that define the function.  If x is
    * outside the range of x-coords in the table, the value of the function is Double.NaN.
    */
00374    public double getVal(double x) {
      return computeValue(x,null,0);
   }
   
   private double computeValue(double x, Cases cases, int derivativeLevel) {
           // Find the value of the function or one of its derivatives at x.
           // If cases is not null, then a value is added to cases to help
           // with continuity computations.
       if (Double.isNaN(x))
          return Double.NaN;
       if (pointCt == 0 || x < xCoords[0] || x > xCoords[pointCt-1])
          return Double.NaN;
       if (pointCt == 1) {
          if (derivativeLevel > 0)
             return Double.NaN;
          else {
             if (cases == null)
                cases.addCase(0);
             return yCoords[0];
          }
       }
       int casenum;
       double ans;
       int seg = 0;
       switch (style) {
          case STEP: {
             while (seg < pointCt - 1 && x > (xCoords[seg] + xCoords[seg+1])/2)
                seg++;
             casenum = seg;
             if (derivativeLevel == 0)
                ans = yCoords[seg];
             else if (x < (xCoords[seg] + xCoords[seg+1])/2 || seg == pointCt - 1 || yCoords[seg] == yCoords[seg + 1])
                ans = 0;
             else 
                ans = Double.NaN;
             break;
          }
          case STEP_RIGHT: {
             while (seg < pointCt-1 && x > xCoords[seg])
                seg++;
             casenum = seg;
             if (derivativeLevel == 0)
                ans = yCoords[seg];
             else if (x < xCoords[seg] || seg >= pointCt - 1 || yCoords[seg] == yCoords[seg+1])
                ans = 0;
             else
                ans = Double.NaN;
             break;
          }
          case STEP_LEFT: {
             while (seg < pointCt-1 && x >= xCoords[seg+1])
                seg++;
             casenum = seg;
             if (derivativeLevel == 0)
                ans = yCoords[seg];
             else if (x > xCoords[seg] || seg == 0 || yCoords[seg] == yCoords[seg-1])
                ans = 0;
             else
                ans = Double.NaN;
             break;
          }
          case PIECEWISE_LINEAR: {
             while (seg < pointCt-1 && x > xCoords[seg])
                seg++;
             casenum = seg;
             if (x == xCoords[seg]) {
                if (derivativeLevel == 0)
                   ans = yCoords[seg];
                else if (seg == 0) {
                   if (derivativeLevel == 1)
                      ans = (yCoords[1] - yCoords[0]) / (xCoords[1] - xCoords[0]);
                   else
                      ans = 0;
                }
                else if (seg == pointCt-1) {
                   if (derivativeLevel == 1)
                      ans = (yCoords[pointCt-1] - yCoords[pointCt-2]) / (xCoords[pointCt-1] - xCoords[pointCt-2]);
                   else
                      ans = 0;
                }
                else {  
                   double leftslope  = (yCoords[seg] - yCoords[seg-1]) / (xCoords[seg] - xCoords[seg-1]);
                   double rightslope = (yCoords[seg] - yCoords[seg+1]) / (xCoords[seg] - xCoords[seg+1]);
                   if (Math.abs(leftslope - rightslope) < 1e-12) {
                      if (derivativeLevel == 1)
                         ans = leftslope;
                      else
                         ans = 0;
                   }
                   else
                      ans = Double.NaN;
                }
             }
             else {  // x < xCoords[seg] && x > xCoords[seg-1]
                if (derivativeLevel == 0) {
                   ans = yCoords[seg-1] + ((yCoords[seg] - yCoords[seg-1]) / (xCoords[seg] - xCoords[seg-1]))*(x - xCoords[seg-1]);
                }
                else if (derivativeLevel == 1) {
                   ans = (yCoords[seg] - yCoords[seg-1]) / (xCoords[seg] - xCoords[seg-1]);
                }
                else
                   ans = 0;
             }
             break;
          }
          default: { // SMOOTH
             while (seg < pointCt-2 && x > xCoords[seg+1])
                seg++;
             casenum = seg;
             if (x == xCoords[seg+1] && seg < pointCt-2 && seg > 0) {
                if (derivativeLevel == 0)
                   ans = yCoords[seg+1];
                else if (derivativeLevel == 1)
                   ans = segments[seg].derivativeValue(x,1);
                else {
                   double leftslope  = segments[seg-1].derivativeValue(x,2);
                   double rightslope = segments[seg].derivativeValue(x,2);
                   if (Math.abs(leftslope - rightslope) < 1e-12)
                      ans = segments[seg].derivativeValue(x,derivativeLevel);
                   else
                      ans = Double.NaN;
                }
             }
             else {  // x < xCoords[seg] && x > xCoords[seg-1]
                ans = segments[seg].derivativeValue(x,derivativeLevel);
             }
          }
       }
       if (cases != null)
          cases.addCase(casenum);
       return ans;
   }
   
   //---------------- Methods from the Function class -----------------
   
   /**
    * Get the value of the function at the specified parameter value.
    *
    * @params param should be an array of length 1 holding the argument of the function.
    *          However if the length is greater than one, the extra arguments are simply ignored.
    * @cases if cases is non-null, a case value is stored here, for help in continuity computations.
    */
00516    public double getValueWithCases(double[] params, Cases cases) {
      return computeValue(params[0],cases,0);
   }
   
   /**
    * Get the value of the function at the specified parameter value.
    * 
    * @partam param should be an array of length 1 holding the argument of the function.
    *          However if the length is greater than one, the extra arguments are simply ignored.
    */
00526    public double getVal(double[] params) {
      return computeValue(params[0], null, 0);
   }
   
   /**
    * Compute the derivative of this function.  The value of the parameter, wrt, must be 1 or an
    * IllegalArguemntException will be thrown.
    */
00534    public Function derivative(int wrt) {
      if (wrt != 1)
         throw new IllegalArgumentException("Attempt to take the derivative of a function of one argument with respect to argument number " + wrt);
      return new Deriv(this);
   }
   
   /**
    * Returns null.
    * It really should be the constant function zero, but I don't expect this ever to be
    * called.  Since dependsOn(wrt) returns false, it will never be called within the JCM system.
    */
00545    public Function derivative(Variable wrt) {
      return null;
   }
   
   /**
    * Returns false.
    */
00552    public boolean dependsOn(Variable wrt) {
      return false;
   }
   
   /**
    * Returns the arity of the function, which is 1.
    */
00559    public int getArity() {
      return 1;
   }
   
   /**
    * Override method apply() from interface FunctionParserExtension, to handle cases properly.
    * Not meant to be called directly.
    */
00567    public void apply(StackOfDouble stack, Cases cases) {
      double x = stack.pop();
      stack.push(computeValue(x,cases,0));
   }
   
   //---------------- For creating derivatives ------------------------
   
   private static class Deriv extends FunctionParserExtension {
          // An object of this class represents a derivative function
          // of a TableFunction.

      TableFunction derivativeOf;  // The function from which this function is derived.

      int derivativeLevel;  // The order of the derivative.
      
      Deriv(Deriv f) {
         derivativeLevel = f.derivativeLevel + 1;
         derivativeOf = f.derivativeOf;
      }
      
      Deriv(TableFunction f) {
         derivativeLevel = 1;
         derivativeOf = f;
      }
      
      public String getName() { // Name comes from the name of the function.
         String name = derivativeOf.getName();
         for (int i = 0; i < derivativeLevel; i++)
            name += "'";
         return name;
      }
      
      public void setName(String name) {
      }
   
      public double getValueWithCases(double[] params, Cases cases) {
         return derivativeOf.computeValue(params[0],cases,derivativeLevel);
      }
      
      public double getVal(double[] params) {
         return derivativeOf.computeValue(params[0],null,derivativeLevel);
      }
      
      public Function derivative(int wrt) {
         if (wrt != 1)
            throw new IllegalArgumentException("Attempt to take the derivative of a function of one argument with respect to argument number " + wrt);
         return new Deriv(this);
      }
      
      public Function derivative(Variable wrt) {
         return null;
      }
      
      public boolean dependsOn(Variable wrt) {
         return false;
      }
      
      public int getArity() {
         return 1;
      }

      public void apply(StackOfDouble stack, Cases cases) {
         double x = stack.pop();
         stack.push(derivativeOf.computeValue(x,cases,derivativeLevel));
      }
      
   } // end class Deriv
   
}

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