Programming Assignment 1 (100 points)

    • You want to implement a data structure that allows to tabulate data coming from many different models such as communication or social networks. The entries in a table may express a relation between two groups of people, e.g. the number 1 could denote friends and 0 otherwise. This type of data structure could be also used to represent a location of an object in a two-dimensional space using its coordinates, e.g. a pair (i, j) to refer to a particular element of the table. These tables are called two-dimensional arrays or matrices. The Background section of this assignment provides some basic information about matrices and their operations.

    • The purpose of this individual programming assignment is to learn about an elementary design, implementa-tion, and testing of a simple C++ class called My_matrix. The class implementation allows you to understand and overview the basic C++ concepts like pointers, memory allocation, deallocation, dynamic arrays, con-structors, copy or move constructors and assignments, destructors, operator overloading, reading from and writing to a file.

    • In the first phase of the assignment, implement in C++ a class My_matrix that can hold data of integer type (int). The two parameters representing a matrix dimensions are usually not known in advance so it is necessary to allocate the arrays dynamically. The description of dynamic matrix type for data manipulation is provided in the course textbook, see the section “Dynamic Allocation of Matrices,” pp. 112-113. The first part of the assignment is due by January 28 with pre-grading done in the labs.

    • In the second phase, which is due by February 4th, you will need to write a generic version of the class My_matrix that can handle different types of data.

    • The private members of the class My_matrix should contain at least these elements (do not use the STL class vector):

– n is the number of rows in the matrix (n >= 0)

– m is the number of columns in the matrix (m >= 0)

– ptr is a pointer to the dynamic array of rows of type int** (a pointer to a pointer of int)

– ptr[i] is a pointer to the ith row of type int*.

– Matrix elements will be accessed by indices i and j using ptr[i][j].

See the file My_matrix.h.

    • The public interface of the class My_matrix should contain at least the operations listed below.

– number_of_rows() returns the number of rows.

– number_of_columns() returns the number of columns.

– elem(i,j) returns or sets a matrix element at row i and column j with an array bound checking. An out_of_range exception is thrown if i and/or j is not in range of the matrix dimensions.
– operator()(i) returns an access to the ith row of the matrix, without performing array bound checking.

– operator()(i,j) returns the (i,j) element of the matrix, without performing array bound checking.

– default constructor with 0 rows and 0 column, and ptr is nullptr.

– a constructor with two positive arguments n and m creates a matrix with n rows and m columns.

– copy constructor makes a copy of an object of type My_matrix.

– destructor deallocates allocated memory of an My_matrix object.

– copy assignment assigns an object of type My_matrix to another object of the same type.

– move copy operator and move assignment operator used to optimize object copying code (optional).

See the file My_matrix.h.

    • Non-member overloaded operators:



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– operator>> (input operator) reads input, row by row, to a My_matrix object. The first line should have only two numbers: the number of rows and columns. The remaining lines contain matrix rows. If the input format is not correct your program should throw the user-defined exception incorrect_input(). Read about exceptions in “Programming Principles and Practices using C++”, pp. 1138-1139. Also, read the Section 2.4 (pp. 93-) in the textbook.

– operator<< (output operator) prints the content of an My_matrix object, row by row, and each row is displayed in a separate line.

– overloading the addition (+) and product (∗) operators for matrices. Both the operators work on My_matrix objects. That is, C=A+B is equivalent to C[i][j]=A[i][j]+B[i][j], and C=A*B is equivalent C[i][j]=Pnk=1 A[i][k]*B[k][j], see the Background section of this assignment for more details. Notice that the number of rows must be the same as the number of columns for both the matrix arguments for the addition operator. If this condition is not satisfied an exception should be thrown. Also, the number of columns of the first argument must be the same as the number of rows of the second argument for the product operator. If this condition is not satisfied an exception should be thrown.

Implementation and Testing

    1. Download the supplementary tar file with a sample code from the class webpage.

    2. Your files should be arranged as follows

        (a) Declaration of My_matrix class in My_matrix.h

        (b) Definition (implementation) of My_matrix class in My_matrix.cpp

        (c) Reading from a file, writing to a file and testing My_matrix operations in main.cpp

        (d) Makefile is called by make

    3. (50 points) Implement, compile, run and test Phase 1 of the assignment. Compile your program using the following Linux machine command line: g++ -std=c++11 *.cpp

or

make all

And then run your program by executing

./main

    4. (20 pt) Implement,compile, run and test Phase 2 of the assignment: A generic version of My_matrix

        (a) The templated class My_matrix uses data type as a parameter. Recall the templated vector material, slides 16-22 and follow the instructions below

            i. Templates should be declared and defined in the TemplatedMy_matrix.h file. Move the content of My_matrix.cpp and My_matrix.h to TemplatedMy_matrix.h
            ii. Replace int type by generic type T. Later, in the main function, T could be specified as any numeric type: double, float, long, or possibly a user-defined type.
            iii. To create a templated class with generic type T, you must replace declaration and/or return type int by T.
            iv. Use the generic type T anywhere throughout the class TemplatedMy_matrix.

            v. Add the keyword template <typename T> before a class declaration.

            vi. If a member function is defined outside the class declaration, change the function signature by replacing My_matrix:: with TemplatedMy_matrix<T>::
        (b) Compile and run the generic version similarly as in Part 1 of the assignment.

        (c) Test all the operations for the generic version using at least three different types of objects.

    5. (30 points) Prepare a report (PDF and LyX) and cover page (PDF and LyX) in the electronic version.

        (a) (1 point) Program description and purpose of the assignment

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    (b) (1 point) Description of data structures

    (c) (1 point) Instructions to compile and run your program including input and output specifications (if any).
    (d) (4 point) Logical exceptions (and possible bug descriptions)

    (e) (2 point) C++ object oriented or generic programming features, including C++11 features.

    (f) (16 points) Evidences of testing of the part 1 and 2 operations.

Bonus (20 points) Implement Part 1 and Part 2 of the assignment using the STL class vector instead of two-dimensional array (ptr) and provide the overloaded operations for My_matrix type of objects.

Submission to eCampus no latter than February 4 and follow the steps.

    1. Create a folder for the assignment report files, in LyX and PDF formats.

    2. Create a folder for each phase (1 and 2) of the class My_matrix.

    3. Create a directory named FirstName_SecondName_PA1_18A and move the three directories created in the step 1 and 2 into this one.

    4. Compress the directory FirstName_SecondName_PA1_18A using the tar program, see the instructions link. Name the tar file FirstName_SecondName_PA1_18A.tar

    5. Submit the FirstName_SecondName_PA1_18A.tar file obtained in step 4 to eCampus.


Background

•
An example of a 3
×
2 matrix with 3 rows and 2 columns:

1
1






1
3






0
2

• An example of a n × m matrix, n rows and m columns, n and m are positive integers:

a21
a22
. . .
a2m


a11
a12
. . .
a1m
A =

...  ...  ...  ...







...  ...  ...  ...

an1   an2   . . .  anm

    • The ith row of A is the 1 × m matrix [ai1, ai2, . . . , aim].

a1j

    • The jth column of A is the n × 1 matrix   . . .  .
anj

    • The (i, j)th element or entry of A is the element aij . Further on, we will use the notation A = [aij ] to denote that the matrix consists of these elements.

Matrix Arithmetic: Addition

Let A = [aij ] and B = [bij ] be m × n matrices. The sum of A and B, denoted by A + B, is the m × n matrix that has aij + bij as its (i, j)th element. In other words, A + B = [aij + bij ]. Example:

0
2
+
0
3
=
0
5
.
1
1

2
5

3
6

1
33
44
7





4
Note that matrices of different sizes cannot be added.

Matrix Arithmetic: Product

Let A be an n × k matrix and B be a k × m matrix. The product of A and B, denoted by AB, or sometimes A ∗ B, is the n × m matrix that has its (i, j)th element equal to the sum of the products of the corresponding elements from the ith row of A and the jth column of B. In other words, if AB = [cij ] then cij = ai1b1j + ai2b2j + . . . + aikbkj .

Fact: The product of two matrices is undefined when the number of columns in the first matrix is not the same as the number of rows in the second matrix. Example:

1
0
4

2
4


14
4

2  1
1




=
8
9




1
1






3
1
0

3
0


7
13


0  2
2





8
2

























where c21 = 2 · 2 + 1 · 1 + 1 · 3 = 8.

c Teresa Leyk















































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