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RiemannSums.java

/*************************************************************************
*                                                                        *
*  This source code file, and compiled classes derived from it, can      *
*  be used and distributed without restriction, including for commercial *
*  use.  (Attribution is not required but is appreciated.)               * 
*                                                                        *
*   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/            *
*                                                                        *
*************************************************************************/


// The SimpleGraph applet is a configurable applet that displays the graph of
// a single function of one variable and computes a Riemann sum for that
// function.

import java.awt.*;
import java.awt.event.*;
import java.applet.Applet;
import java.util.StringTokenizer;
import edu.hws.jcm.draw.*;
import edu.hws.jcm.data.*;
import edu.hws.jcm.functions.*;
import edu.hws.jcm.awt.*;


public class RiemannSums extends GenericGraphApplet {

   // Declare some private variables that are created in one method in
   // this class and used in a second method.

   private Variable intervals;       // Gives the number of intervals.
   private VariableInput intCtInput; // For letting the user enter the number of intervals.
   private Choice methodChoice;      // Gives the method to be used:  Left Endpoint, ..., Trapezoid.

   private Function func;   // The function that is graphed.
   private Graph1D graph;   // The graph of the function.
   
   private RiemannSumRects sums;

   public void itemStateChanged(ItemEvent evt) {
         // React when user changes the summation method.
       if (evt.getSource() == methodChoice) {
          sums.setMethod(methodChoice.getSelectedIndex());
          mainController.compute();
       }
       else
          super.itemStateChanged(evt);
   }
   
   protected void setUpParameterDefaults() { // Override to give a different default function
      parameterDefaults = new java.util.Hashtable();
      String func = " 3 / (1 + " + getParameter("Variable","x") + "^2)";
      parameterDefaults.put("Function",func);
      parameterDefaults.put("ComputeButtonName","Compute!");
   }

   protected void setUpCanvas() {  // Override this to add more stuff to the canvas.
   
      // When setUpCanvas is called, the functionInput already exists, if one is
      // to be used, since it is created in setUpBopttomPanel(), which is called
      // before setUpCanvas.  If functionInput exists, add a graph of the function
      // from functionInput to the canvas.  If not, create a graph of the function
      // specified by the parameter named "Function".
      
      if (functionInput != null)
         func = functionInput.getFunction(xVar);
      else {
         String def = getParameter("Function", " abs(" + xVar.getName() + ") ^ " + xVar.getName());
         Function f = new SimpleFunction( parser.parse(def), xVar );
         func = new WrapperFunction(f);
      }
      graph = new Graph1D(func);
      Color color = getColorParam("GraphColor");
      if (color != null)
         graph.setColor(color);
         
      // Get the data for the RiemannSumRects object.  Create it (along with other
      // associated objects) and add it to the canvas.
         
      double[] intCtD = getNumericParam("IntervalCount");
      if (intCtD == null || intCtD.length < 1)
         intCtD = new double[] { 5 };
      else if (Double.isNaN(intCtD[0]) || intCtD[0] < 1 || intCtD[0] > 5000)
         intCtD[0] = 5;
      int intCt = (int)(intCtD[0]+0.5);
      
      if ("yes".equalsIgnoreCase( getParameter("UseIntervalInput", "yes") )){
         intCtInput = new VariableInput(null, "" + intCt);
         intCtInput.setInputStyle(VariableInput.INTEGER);
         intCtInput.setMin(1);
         intCtInput.setMax(5000);
         intervals = intCtInput.getVariable();
      }
      else
         intervals = new Variable(null,intCt);
      
      int method = RiemannSumRects.LEFTENDPOINT;

      String methodStr = getParameter("Method");
      if (methodStr != null && methodStr.trim().length() > 0) {
         switch (methodStr.trim().charAt(0)) {
            case 'L': case 'l': method = RiemannSumRects.LEFTENDPOINT; break;
            case 'R': case 'r': method = RiemannSumRects.RIGHTENDPOINT; break;
            case 'M': case 'm': method = RiemannSumRects.MIDPOINT; break;
            case 'C': case 'c': method = RiemannSumRects.CIRCUMSCRIBED; break;
            case 'I': case 'i': method = RiemannSumRects.INSCRIBED; break;
            case 'T': case 't': method = RiemannSumRects.TRAPEZOID; break;
         }
      }
      
      if ("yes".equalsIgnoreCase( getParameter("UseMethodInput", "yes") )) {
         methodChoice = new Choice();
         methodChoice.add("Left Endpoint");
         methodChoice.add("Right Endpoint");
         methodChoice.add("Midpoint");
         methodChoice.add("~Circumscribed");
         methodChoice.add("~Inscribed");
         methodChoice.add("Trapezoid");
         methodChoice.select(method);
         methodChoice.addItemListener(this);
      }
      
      sums = new RiemannSumRects(func,intervals);
      sums.setMethod(method);
      canvas.add(sums);
      
      Color c = getColorParam("RectColor");
      if (c != null)
         sums.setColor(c);
      c = getColorParam("OutlineColor");
      if (c != null)
         sums.setOutlineColor(c);
         
      super.setUpCanvas();  // Do the common setup: Add the axes, for example.
      canvas.getCoordinateRect().setGap(10);  // Extra space around edges.
      canvas.add(graph);  // Add the graph to the canvas.
      
      // Add a DrawString to the canvas to show the value of the sum.

      DrawString ds = new DrawString("sum = #", DrawString.TOP_LEFT,
                           new Value[] { sums.getValueObject(RiemannSumRects.CURRENT_METHOD) } );
      ds.setBackgroundColor(getColorParam("TextBackground",Color.white));
      ds.setColor(getColorParam("TextColor",Color.black));
      ds.setFrameWidth(1);
      canvas.add(ds);
      
      mainController.add(ds);
      mainController.add(sums);
      if (intCtInput != null)
         intCtInput.setOnUserAction(mainController);
      canvas.getCoordinateRect().setOnChange(mainController);

   } // end setUpCanvas()
   
   

   protected void setUpMainPanel() {
         // Override this method to add the methodChoice menu and interval count inputs, if any,
         // to the panel.  (They were created in the setUpCanvas method.)
   
      super.setUpMainPanel(); // Do the common setup
      
      if (methodChoice == null && intCtInput == null)
         return;
         
         JCMPanel panel = new JCMPanel();
         panel.setLayout(new FlowLayout());
         panel.setBackground(getColorParam("PanelBackground",Color.lightGray));
         if (intCtInput != null) {
            panel.add(new Label("Intervals:"));
            panel.add(intCtInput);
         }
         if (methodChoice != null) {
            panel.add(new Label("Method:"));
            panel.add(methodChoice);
         }      
         if (inputPanel == null)
            mainPanel.add(panel, BorderLayout.SOUTH);
         else {
            inputPanel.setBackground(getColorParam("PanelBackground",Color.lightGray));
            inputPanel.add(panel, BorderLayout.SOUTH);
         }
      
   } // end setUpMainPanel()
   


   protected void doLoadExample(String example) {
         // This method is called when the user loads an example from the 
         // example menu (if there is one).  It overrides an empty method
         // in GenericGraphApplet.
         //   For this applet, the example string should contain
         // an expression that defines the function to be graphed.
         // This can optionally  be followed by a semicoloon and a list of four or five
         // numbers.  The first four numbers give the x- and y- limes to be used for the
         // example.  The fifth number, if present, gives the interval count.
         // After the numbers, there can be another semicolon
         // and the name of the summation method to be used.

      int pos = example.indexOf(";");

      double[] limits = { -5,5,-5,5 };  // x- and y-limits to use
      
      if (pos > 0) { // get limits, method from example text
         String limitsText = example.substring(pos+1);
         example = example.substring(0,pos);
         pos = limitsText.indexOf(";");
         if (pos > 0) {  // data includes a method name.
            String methodStr = limitsText.substring(pos+1).trim();
            limitsText = limitsText.substring(0,pos);
            if (methodStr.length() > 0) {
                int method;
                switch (methodStr.charAt(0)) {
                   case 'L': case 'l': method = RiemannSumRects.LEFTENDPOINT; break;
                   case 'R': case 'r': method = RiemannSumRects.RIGHTENDPOINT; break;
                   case 'M': case 'm': method = RiemannSumRects.MIDPOINT; break;
                   case 'C': case 'c': method = RiemannSumRects.CIRCUMSCRIBED; break;
                   case 'I': case 'i': method = RiemannSumRects.INSCRIBED; break;
                   case 'T': case 't': method = RiemannSumRects.TRAPEZOID; break;
                   default: method = -1;
               }
               if (method >= 0) {
                  sums.setMethod(method);
                  if (methodChoice != null)  
                     methodChoice.select(method);
               }
            }
         }
         StringTokenizer toks = new StringTokenizer(limitsText, " ,");
         if (toks.countTokens() >= 4) {
            for (int i = 0; i < 4; i++) {
               try {
                   Double d = new Double(toks.nextToken());
                   limits[i] = d.doubleValue();
               }
               catch (NumberFormatException e) {
               }
            }
            if (toks.countTokens() > 0) {
                  // get number of intervals
               try {
                   Double d = new Double(toks.nextToken());
                   double intCtD = d.doubleValue();
                   if (intCtD < 1)
                      intCtD = 1;
                   else if (intCtD > 5000)
                      intCtD = 5000;
                   intervals.setVal((int)(intCtD + 0.5));
               }
               catch (NumberFormatException e) {
               }
            }
         }
      }
      
      // Set up the example data and recompute everything.

      if (functionInput != null) {
            // If there is a function input box, put the example text in it.
         functionInput.setText(example);
      }
      else { 
           // If there is no user input, set the function in the graph directly.
           // Also, in this case, func is a "WrapperFunction".  Set the
           // definition of that WrapperFunction to be the same as f
         try {
            Function f = new SimpleFunction( parser.parse(example), xVar );
            ((WrapperFunction)func).setFunction(f);
         }
         catch (ParseError e) {  
             // There should't be parse error's in the Web-page
             // author's examples!  If there are, the function
             // just won't change.
         }
      }
      CoordinateRect coords = canvas.getCoordinateRect(0);
      coords.setLimits(limits);
      coords.setRestoreBuffer();
      mainController.compute();
      
   } // end doLoadExample()
   


} // end class RiemannSums

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