Homework Assignment 4

Due: November 17, 2006.
No extensions. I will hand out solutions next Friday and you should study them for midterm2.

This assignment will give you practice at:

Using branching and looping constructs to solve simple engineering problems.
Partitioning solution procedures in to smaller parts, which each will be implemented in their own method.
Working with arrays.

Write Java programs to solve Problems 16, 19 and 20 in the Java Exercises Handout (see the yellow book).

Hints

I suggest that you start with Problem 20 because it is the most straight forward. Random numbers that are uniformly distributed between zero and one can be generated with Math.random().
I will give you source code outlines to each problem asap, but no later than Monday.

Source Code Schematic for Problem 16

/*
 *  =====================================================================
 *  RainfallAnalysis.java: The java program conducts a simple statistical
 *                         analysis on monthly rainfall measurements.
 *
 *  Written By: Mark Austin                         
 *  Modified By: ...........                                November 2006
 *  =====================================================================
 */

import java.text.*;
import java.lang.Math;

public class RainfallAnalysis {

   // No of columns in print array task...

   public final static int NoColumns = 6;

   // =========================================================
   // main method : this is where the program execution begins.
   // =========================================================

   public static void main ( String [] args ) {

       // [a] Populate rainfall data array (measured over 30 days)

       double [] fRainfall = { 1.1 ... fill in missing details ..... };

       // [b] Print contents of fRainfall in six columns ...

       System.out.println("Array: fRainfall");
       System.out.println("----------------");

       ... fill in missing details ....

       System.out.println("----------------");

       // [b] Compute and print rainfall measurement statistics..

       System.out.println("");
       System.out.println("Statistics of Daily Rainfall");
       System.out.println("============================");

       System.out.printf("Max value = %5.2f\n", maxValue( fRainfall ));
       System.out.printf("Min value = %5.2f\n", minValue( fRainfall ));
       System.out.printf("Range of values = %5.2f\n", range( fRainfall ));
       System.out.printf("Mean value = %5.2f\n", mean( fRainfall ));
       System.out.printf("Standard deviation = %5.2f\n", std( fRainfall ));
       System.out.println("============================");
   }

   /* ================================================== */
   /* Methods to compute maximum/minimum daily rainfalls */
   /* ================================================== */

   public static double maxValue ( double dA [] ) {
      ... fill in missing details ....
   }

   public static double minValue ( double dA [] ) {
      ... fill in missing details ....
   }

   /* ========================================== */
   /* Method to compute range in daily rainfalls */
   /* ========================================== */

   public static double range ( double dA [] ) {
      ... fill in missing details ....
   }

   /* ====================================================== */
   /* Compute mean and standard deviation of daily rainfalls */
   /* ====================================================== */

   public static double mean ( double dA [] ) {
      ... fill in missing details ....
   }

   public static double std ( double dA [] ) {
      ... fill in missing details ....
   }
}

The output generated by my version of the program is:

prompt >> java RainfallAnalysis
Array: fRainfall
----------------
 1.10 0.80 1.10 1.20 0.50 0.20
 0.05 0.00 0.00 0.00 0.40 0.50
 0.60 0.80 1.00 1.20 3.00 2.40
 1.50 1.00 1.00 0.00 0.00 0.00
 0.00 0.00 0.00 2.00 2.00 2.40
----------------

Statistics of Daily Rainfall
============================
Max value =  3.00
Min value =  0.00
Range of values =  3.00
Mean value =  0.83
Standard deviation =  0.84
============================
prompt >>

Source Code Schematic for Problem 19

/*
 *  ===========================================================================
 *  CubeRoot.java: This program prompts the user for a number and then computes
 *                 and prints its cube root.
 *
 *  Draft: Mark Austin  
 *  Finished By: ........                                        November, 2006
 *  ===========================================================================
 */

import java.lang.Math;
import java.util.*;
import java.io.*;
import java.text.*;

public class CubeRoot {

    public static void main( String args[] ) {
        double dNumber;
        String sLine;

        // Print welcome message.

        .... fill in details .....

        // Prompt user for number...

        .... fill in details .....

        // Compute and print cube root...

        System.out.printf("CubeRoot( %8.2f ) = %8.2f\n",
                           dNumber, cubeRoot (dNumber));
    }

    /* 
     *  ==================================================================
     *  cubeRoot(): Compute cube root of a floating-point no.
     *
     *  Input  : double dNumber -- Number that cube root is to be computed.
     *  Output : double dX      -- Cube root of dNumber.
     *  ==================================================================
     */ 

    public static final double EPSILON = 0.00001;

    public static double cubeRoot ( double dNumber ) {
       boolean bConvergenceAchieved = false;
       double dX, dXnext;

       /* [a] : No iteration is required for trivial cases */

       .... fill in details .....

       /* [b] : Compute cube root */

       dX = dNumber/2.0;  // initial guess for cube root of dNumber ...
       while( bConvergenceAchieved == false ) {

          // Compute next estimate of cube root ...

          .... fill in details .....

          // Check for convergence of answer ...

          .... fill in details .....

          // Update estimate of cube root...

          .... fill in details .....
       }

       return dX;
    }

    /* 
     *  =============================================================
     *  Method getTextFromConsole() : Get line of input from keyboard
     * 
     *  Input  : None.
     *  Output : String sLine -- character string of keyboard input
     *  =============================================================
     */

    public static String getTextFromConsole() {
       String inLine = "";
  
       .... fill in details ....
}

Here is a sample output from my program:

Script started on Thu Nov 09 14:42:33 2006
prompt >>
prompt >> java CubeRoo
Compute Cube Root of Number            
---------------------------------------
Input Number: -81.00
 *** Cube root estimate = -27.01646091
 *** Cube root estimate = -18.04796585
 *** Cube root estimate = -12.11486821
 *** Cube root estimate =  -8.26054007
 *** Cube root estimate =  -5.90270925
 *** Cube root estimate =  -4.71006683
 *** Cube root estimate =  -4.35709793
 *** Cube root estimate =  -4.32695962
 *** Cube root estimate =  -4.32674872
 *** Cube root estimate =  -4.32674871
CubeRoot(   -81.00 ) =    -4.33
prompt >> exit
script done on Thu Nov 09 14:42:48 2006

I have put a print statement inside the loop so that you can see how the algorithm converges.

Source Code Schematic for Problem 20

/*
 *  ===========================================================================
 *  DartExperiment.java: This program simulates and experiment where darts are
 *                       thrown at a board. The proportion of darts falling
 *                       inside a circle relative to the total number of darts
 *                       thrown provides an approximate estimate of pi.
 *
 *  Draft: Mark Austin  
 *  Finished By: ........                                        November, 2006
 *  ===========================================================================
 */

import java.lang.Math;
import java.util.*;
import java.io.*;
import java.text.*;

public class DartExperiment {

    public static void main( String args[] ) {
        double dX, dY;
        int iNoPoints = 100000;
        int iNoInside =      0;

        // Print welcome message.

        System.out.println("Estimating pi with Dart Experiment     ");
        System.out.println("---------------------------------------");

        // Conduct numerical experiment ...

        for ( int i = 1; i <= iNoPoints; i = i + 1 ) {

           // Generate scaled coordinate point (dX, dY) ...

           .... details of code removed ....

           // Is point inside the circle? ....

           .... details of code removed ....
        }

        // Compute and print estimate of pi ...

        .... details of code removed ....
    }
}

Here is the output from my program when the experiment is conducted with 100,000 data points.

Estimating pi with Dart Experiment     
---------------------------------------
(X,Y) = (-0.010970, -0.430134)
(X,Y) = (0.817009, -0.484418)
(X,Y) = (0.542297, -0.721900)

... 99,995 lines of output removed ....

(X,Y) = (-0.030996, -0.524783)
(X,Y) = (0.279210, -0.171811)
Estimate of pi = 3.145920

Note. For each problem, hand in a copy of your program source code and a script of I/O for typical program usage. To create a script, type something like:

    prompt >> script output-file

Now all input/output on the screen will be echoed to the file "output-file". To terminate the script, type:

    prompt >> exit

Now print "output-file" and hand it in.