Representing sparse matrix in memory using array, Data Structure & Algorithms

Q. What do you understand by the term sparse matrix? How sparse matrix is stored in the memory of a computer? Write down the function to find out the transpose of a sparse matrix using this particular representation.                                                                                                             


Sparse Matrix is described below

A m x n matrix A would be a sparse if most of its elements are zero. A matrix that is not sparse is known as dense matrix.

Representing Sparse Matrix in Memory Using Array is described below

In an array representation an array of triplets of type < row, col, element> is used to store non-zero elements, where 1st field of the triplet is used to trace row position second to record column and the 3rd to record the non zero elements of  sparse matrix.

In addition, we are required to record the size of the matrix ( i.e. number of rows and the number of columns) and non zero elements of array of triplets are used for this purpose where the 1st filed saves the number of rows and the 2nd field saves the number of columns and the third field saves the number of non zero elements. The remaining elements of the array saves matrix on row major order. The array representation will be

[2 * (n+1) * size of (int) + n*size of(T)] bytes of memory where n is the number of non-zero elements and T is the data type of the element.

Ex: consider a 5*6 sparse matrix which is written below

1713_sparse matrix2.png 

Array Representation of Sparse Matrix is given below

1754_sparse matrix3.png

Here n = 5 but the size of array is 6 as first row saves the order of array along with a number non-zero elements.

Memory declaration will be as followsas shown below

# define Max 50 struct triplet

{   int row;

int col;

float element;


struct triplet sparse_mat [MAX];

sparse matrix represented as above

[n is the number of non zero elements in array]

for I= 1,2,...n+1 temp = a[I].row a[I].row= a[I].col a[I].col = temp endfor.

Posted Date: 7/13/2012 2:56:02 AM | Location : United States

Related Discussions:- Representing sparse matrix in memory using array, Assignment Help, Ask Question on Representing sparse matrix in memory using array, Get Answer, Expert's Help, Representing sparse matrix in memory using array Discussions

Write discussion on Representing sparse matrix in memory using array
Your posts are moderated
Related Questions
You are supposed to do the following: Write a parallel implementation of the raytracer using pthreads. Measure and compare the execution times for (i) the sequential ver

Q. Draw  the structures of complete  undirected  graphs  on  one,  two,  three,  four  and  five vertices also prove that the number of edges in an n vertex complete graph is n(n-1

The complexity of searching an element from a set of n elements using Binary search algorithm is   O(log n)

Determine the Components of Illumination The light reaching the eye when looking at a surface has clearly come from a source (or sources) of illumination and bounced off the su

Djikstra's algorithm (named after it is discovered by Dutch computer scientist E.W. Dijkstra) resolves the problem of finding the shortest path through a point in a graph (the sour

Comparison of Gouraud and Phong Shading Phong shading requires more calculations, but produces better results for specular reflection than Gouraud shading in the form of more r

Polynomials like  5x 4    +  2x 3    +  7x 2     +  10x  -  8  can  be  represented by using arrays. Arithmetic operations such as addition & multiplication of polynomials are com

Two linked lists are having information of the same type in ascending order. Write down a module to merge them to a single linked list that is sorted merge(struct node *p, stru

how to draw a 5 inch square on the screen using * symbol

how to write prims algorithms? with example