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日期:2020-11-22 04:55

McMaster University

Dept. Electrical and Comp. Engineering COE 2SH4 - Fall 2020

LAB 4 - Java Classes

Assessment: 7% of the total course mark.

1 General Instructions

? Your programs should be written in a good programming style, including instructive

comments and well-formatted, well-indented code. Use self-explanatory names for variables

as much as possible. (≈ 5% of the mark)

? You have to make sure you pass all the tests. Please note that passing the tests does

not grant you automatically the full mark, we run other hidden test cases that are not

shared with you to further assess your code. You are required to make sure your work is

correctly implemented to the best of your knowledge. One task that can help you with

that is to add further tests to stress the corner cases of each question.

? For each method, you are required to add at least one additional test to the matrexTestAll.java

test class.

2 Submission Deadline

The deadline for lab5 is Nov 20th. Please note that this is a programmed deadline in the

environment, so make sure you submit in time since you will not be able to submit after that

dictated deadline.

3 Environment Setup

3.1 Add Java JDK to System Path

Please follow the steps in the document named Installing Java JDK.

3.2 Download and Run Eclipse IDE for Java

Please go to https://www.eclipse.org/downloads/packages/ and download ”Eclipse IDE

for Java Developers” the version that corresponds to your operating system.

3.3 Importing the starter code of the lab

You should follow exactly the same process you have been following in past labs to import

the starter code from the following invitation link and to create the project:

https://classroom.github.com/a/N16Z3W64

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McMaster University

Dept. Electrical and Comp. Engineering COE 2SH4 - Fall 2020

Importing JUNIT into your project. We will be using the JUNIT to create and run

test cases. JUNIT comes already shipped with Eclipse for Java. So, you do not need to install

anything. However, you should perform the following step to include the JUNIT library into

the project to be able to run the test cases:

Open one of the project files by double clicking it, then: select

File->New->JUnit Test Case

This will create another class for testing. You need to delete this file since we already

have our own test cases in the UpperTriangularMatrix.java class. However, this step also

will include the JUNIT (probably JUnit 5) to the project, which is what we need.

You can read about the Java JUnit here: https://courses.cs.washington.edu/courses/

cse143/11wi/eclipse-tutorial/junit.shtml

4 Lab Questions

Write two Java classes:

? Matrix, which represents matrices with integer elements, and

? UpperTriangularMatrix to represent upper triangular matrices with integer elements

stored efficiently.

The accompanying files Matrix.java and UpperTriangularMatrix in the provided starter

code contains an incomplete declaration of the method’s of both classes. You need to complete

the declarations of incomplete methods or constructors according to the specifications given

below.

Finally, a class named UpperTriangularMatrix.java includes all the test cases. You

should, as usual, write at least one additional test case for every method.

4.1 Matrix Class

? Class Matrix has only the following instance fields, which have to be private:

- an integer to store the number of rows

- an integer to store the number of columns.

- a two dimensional array of integers to store the matrix elements.

? Class Matrix contains at least the following constructors:

- public Matrix(int row, int col) - constructs a row-by-col matrix with all

elements equal to 0; if row ≤ 0, the number of rows of the matrix is set to 3;

likewise, if col ≤ 0 the number of columns of the matrix is set to 3.

- public Matrix(int[][] table) - constructs a matrix out of the two dimensional

array table, with the same number of rows, columns, and the same element in

each position as array table.

? Class Matrix contains at least the following methods:

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McMaster University

Dept. Electrical and Comp. Engineering COE 2SH4 - Fall 2020

1) public int getElement(int i, int j) throws IndexOutOfBoundsException -

returns the element on row i and column j of this matrix; it throws an exception

if any of indexes i and j is not in the required range (rows and columns indexing

starts with 0); the detail message of the exception should read: ”Invalid indexes”.

2) public boolean setElement(int x, int i, int j) - if i and j are valid indexes

of this matrix, then the element on row i and column j of this matrix

is assigned the value x and true is returned; otherwise false is returned and no

change in the matrix is performed.

3) public Matrix copy() - returns a deep copy of this Matrix. Note: A deep

copy does not share any piece of memory with the original. Thus, any change

performed on the copy will not affect the original.

4) public void addTo(Matrix m) throws ArithmeticException - adds Matrix m

to this Matrix (note: this Matrix WILL BE CHANGED) ; it throws an exception

if the matrix addition is not defined (i.e, if the matrices do not have the same

dimensions); the detail message of the exception should read: ”Invalid operation”.

5) public Matrix subMatrix(int i, int j) throws ArithmeticException - returns

a new Matrix object, which represents a submatrix of this Matrix, formed

out of rows 0 through i and columns 0 through j. The method should first check

if values i and j are within the required range, and throw an exception if any of

them is not. The exception detail message should read: ”Submatrix not defined”.

Note: The new object should be constructed in such a way that changes in the

new matrix do not affect this Matrix.

6) public boolean isUpperTr() - returns true if this Matrix is upper triangular,

and false otherwise. A matrix is said to be upper triangular if all elements below

the main diagonal are 0. Note that the main diagonal contains the elements situated

at positions where the row index equals the column index. In the following

examples the main diagonal contains elements 1,9,3.

Example of a 3-by-3 upper triangular matrix:

1 4 1

0 9 0

0 0 3

Example of a 3-by-4 upper triangular matrix:

1 5 1 4

0 9 6 6

0 0 3 8

Example of a 4-by-3 upper triangular matrix:

1 4 2

0 9 6

0 0 3

0 0 0

7) public static Matrix sum(Matrix[] matArray) throws ArithmeticExceptionreturns

a new matrix representing the sum of all matrices in matArray. The method

throws an exception if the matrices do not have the same dimensions. This method

MUST USE method addTo() to perform the addition of two matrices.

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McMaster University

Dept. Electrical and Comp. Engineering COE 2SH4 - Fall 2020

8) public String toString() - returns a string representing the matrix, with each

row on a separate line, and the elements in a row being separated by 1 blank space.

For instance like this:

1 2 3

4 5 6

7 8 9

4.2 UpperTriangularMatrix Class

? An n-by-n matrix a is said to be upper triangular if all elements below the main diagonal

are 0. Such a matrix can be represented efficiently by using only a one dimensional array

of size n(n+1)/2, which stores the matrix elements row by row, skipping the zeros below

the diagonal, i.e., in the following order: a(0,0), a(0,1), a(0,2), · · · , a(0,n-1),

a(1,1), a(1,2), · · · , a(1,n-1), a(2,2), a(2,3), · · · , a(2,n-1) · · · a(n-1,n-1).

The Java class UpperTriangularMatrix has to model square upper triangular matrices

of integers, stored in efficient format as described above. Class UpperTriangularMatrix

should have two private instance variables: an integer to represent the matrix size (i.e.

the number of rows n), and a one dimensional array to store the matrix elements in

efficient format.

? Class UpperTriangularMatrix contains at least the following constructors:

- public UpperTriangularMatrix(int n) - if n ≤ 0, changes n to 1; initializes the

UpperTriangularMatrix object to represent the all-zero n-by-n matrix.

- public UpperTriangularMatrix(Matrix upTriM) throws IllegalArgumentException

- initializes the UpperTriangularMatrix object to represent the upper triangular

matrix upTriM. Note that upTriM is an object of the class Matrix that you have to

write for this assignment. The method throws an exception if upTriM is not upper

triangular. The exception detail message should read: Not an upper triangular

matrix To check if the upper triangular condition is satisfied you MUST USE the

method isUpperTr() of class Matrix.

? Class UpperTriangularMatrix contains at least the following instance methods:

- public int getDim() - returns the number of rows of this matrix.

- public int getElement(int i, int j) throws IndexOutOfBoundsException -

returns the matrix element on row i and column j if i and j are valid indices of

this matrix (indexing starts at 0); otherwise an IndexOutOfBoundsException is

thrown, with message ”Invalid index”.

- public void setElement(int x, int i, int j) throws IndexOutOfBoundsException,

IllegalArgumentException - if i and j are valid indexes of the matrix, then the

element on row i and column j of the matrix is assigned the value x; however, if

indexes i and j correspond to a position in the lower part of the matrix and x is not

0 then an IllegalArgumentException has to be thrown with message ”Incorrect

argument”; finally, if indexes i and j do not represent a valid position in the matrix

then an IndexOutOfBoundsException is thrown, with message ”Invalid index”.

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McMaster University

Dept. Electrical and Comp. Engineering COE 2SH4 - Fall 2020

- public Matrix fullMatrix() - returns a Matrix object corresponding to this

UpperTriangularMatrix. Note that the Matrix object will store the full matrix

including all the zeros from the lower part.

- public String toString() - returns a string representing this UpperTriangularMatrix

object. The representation should show all elements of the full matrix with each

row on a separate line.

- public int getDet() - returns the determinant of the matrix, which equals the

product of the elements on the main diagonal.

- public double[] effSolve(double[] b) throws IllegalArgumentException -

This method solves the matrix equation Ax=b, where A is this UpperTriangularMatrix,

if the determinant of A is non-zero. Otherwise it throws an exception, with message

”The determinant of the matrix is 0”. The method returns array x. The method

has to be efficient, which means that it has to use an efficient way to solve the

equation and implement it without wasting time or memory resources, in other

words, without allocating arrays (except for x) or invoking other methods. Partial

marks will be awarded for correct, but less efficient solutions. Note that the

method should also check if the dimension of b is appropriate and if not throw

an exception, with the message: ”The dimension of the matrix is not defined for

operation”.

INSTRUCTIONS: You may implement public methods in class Matrix to return the number of rows and

the number of columns.

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