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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
1
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:
2
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.
3
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”.
4
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.
5
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
1
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:
2
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.
3
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”.
4
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.
5