CSC 3102 Programming Assignment 1: Sparse Matrix Transpose
Due: October 6, Tuesday (by 11:55 pm)
Points: 5
Penalty: You will lose one point per delayed day
Submit your work as instructed towards the end of this document.
Contact the teaching assistant Di Lin by e-mail to [email protected] for help.
Objective:
To empirically demonstrate the difference in the performance between the naive (brute-force)
and fast-transpose algorithms on sparse matrices.
Definition:
A matrix is a concise and useful way of uniquely representing and working with linear
transformations. In particular, for every linear transformation, there exists exactly one
corresponding matrix, and every matrix corresponds to a unique linear transformation.
Matrices have wide-ranging applications in such areas as image processing, information
retrieval, computer graphics, scientific visualization, dynamical systems, etc. In this
assignment, you are dealing with the sparse matrix of order n, which has only a small number
(t) of non-zero elements. In the class, we have learned how a sparse matrix is represented as
a set of order triplets and also learned about two algorithms for obtaining its transpose (see
the lecture notes). The time-efficiency of the brute-force transpose algorithm is O(nt)
whereas that of the fast-transpose algorithm is O(n + t).
Project Task:
You will implement a sparse matrix ADT containing various functions to do the following
tasks. You can use C/C++ or JAVA programming language.
Read each input matrix Mnxn.mat. The values of n and t are given in the first line of the
input matrix M.
Find the transpose of the matrix M using the naïve (brute-forces) algorithm.
Find the transpose of the matrix M using the fast-transpose algorithm.
Print the original matrix (M) and its transpose matrix (M') in the cases of small input sizes.
Compute the time taken to find the transpose (M') using each algorithm in all input cases
using one of the two ways (see the section 2.6 of the textbook for more information).
One way is to count the number of times the basic operation is executed by putting a counter
within the innermost loop. The other way is to measure the actual execution time by using the
clock function. However, since the algorithms run very fast for the input sizes given, you
need to write and insert some delay function within the innermost loop. The delay function
can be a simple loop doing nothing. Note that in the case of the fast-transpose algorithm, you
might need to insert the counter or delay function in more than one part of the algorithm.
Once you have all these functions ready, you will read a 5 by 5 matrix from a file called
M5x5.mat, find the transpose of this matrix using the brute-force and fast-transpose
