• In this exercise you will practice encapsulation in class design.
• You are given an API for a class Matrix that represents matrices of numeric values and the operations that can be performed on them.
• You will produce an implementation of Matrix that hides the internal matrix representation details.
• To start, download this zipped NetBeans project: CS_2511_Class_Design.zip
• Then, unzip it and open the CS_2511_Class_Design project in NetBeans

This section presents documentation of the application programming interface (API) for the Matrix class, as well as the source and test classes for this exercise.

To understand the use of the Matrix API, look at MatrixTest, a class that uses Matrix and is written for you.

Observe:

• How the Matrix constructor is used
• How the accessor get and mutator set are used
• How bad row and column indexes are handled using MatrixException
• How matrices are tested for equality using equals
• How matrices are added and multipled using add and multiply

A matrix is a two-dimensional structure of numerical values a_ij, where i is the (zero-origin) row index and j is the (zero-origin) column index.

If r is the number of rows and c is the number of columns in a matrix A, then it has the form:

To add two matrices, they must have the same dimensions, i.e. the same number of rows and columns.

The result of adding matrices A and B is a matrix C of the same dimensions, where c_ij = a_ij + b_ij.

For example:

To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. Matrix multiplication is not commutative.

The result of multiplying an m×n matrix A and an n×p matrix B is an m×p matrix C where c_ij is the dot product of the i^th row of A and the j^th column of B.

For example,

• The third row (index 2) of matrix A below contains the values  6   5   1 
• The first column (index 0) of matrix B contains the values  2   4   3 
• The dot product of  6   5   1  and  2   4   3  =
   6×2 + 5×4 +1×3  =
   12 + 20 + 3  =
   35 
• So the first column of the third row of C (c₂₀) = 35

Your tasks, in order:

• Create an internal Java representation of a matrix
• Implement the Matrix constructor
• Implement the set mutator and the get, getRows, and getColumns accessors
• Implement the equals method
• Implement the add and multiply methods

The set, get, add, and multiply methods must also throw MatrixException objects where appropriate.

First decide how to internally represent a matrix. Suggestion:

• Store the matrix elements in a two-dimensional Java array:

       private double[]][] elements;

• In the constructor, initialize the array as:

       elements = new double[r][c];

  where r and c are the number of rows and columns, respectively.
• Define set and get to access the element at row i and column j as elements[i][j].
• Define accessors getRows and getColumns to return the number of rows and columns, respectively.

Test the constructor, set, and get by running the testSetAndGet1 and testSetAndGet2 methods in the MatrixTest class. Note:

• You need not handle bad row and column indexes in these tests.
• testSetAndGet2 uses the toMatrix and toString convenience methods to populate and inspect a matrix. These methods are fully implemented for you in the Matrix class.

Now add index bounds testing to the get and set methods:

• Note that testBounds in MatrixTest catches MatrixException objects.
• The MatrixException class is fully implemented for you in the matrix source package.
• The testBounds method indicates the exact wording of the relevant error messages to be sent to the MatrixException constructor.
• MatrixException objects are thrown using:

       throw new MatrixException(error_string);

  where error_string is the relevant error message.

Test your index bounds testing by running the testBounds test.

Two matrices are equal if they have the same dimensions and all elements are equal by the == test.

To check for matrix equality your equals method must iterate through the matrices' rows and columns. Suggestion:

• Instead of directly accessing the 2-D elements array when iterating through a matrix, use the API methods getRows, getColumns, and get.
• Why? If the internal representation of a matrix is ever changed from the 2-D array representation, the equals method will not have to be rewritten.
• Use the toString method as a model for how to iterate through a matrix's rows and columns using just the API methods getRows, getColumns, and get.

Test your equality testing by running the testEquals test.

The add and multiply methods both require iterating through rows and columns, so they also benefit from abstraction by using just the API methods getRows, getColumns, and get.

Note that both testAdd and testMultiply catch MatrixException objects and indicate the exact wording of the relevant error messages when the number of rows and columns in the operand matrices do not meet the preconditions of the add or multiply methods.

Test your matrix addition and multiplication operations by running the testAdd and testMultiply methods.

When all test methods execute successfully your Test Results window should include:

To verify that your Matrix implementation throws MatrixException objects when appropriate, the catch clauses in the test methods print the error messages to System.out.

In addition to reporting that all 6 tests passed, your Test Results window should also include:

When finished, zip your project folder as your-login-LEX4.zip.

Email the zip file to your TA.

• Successful running of testSetAndGet1, testSetAndGet2, and testBounds: 3 points
• Successful running of testEquals: 2 points
• Successful running of testAdd: 2 points
• Successful running of testMultiply: 3 points