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.                                                                                                             

Ans.

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
an electrical student designed a circuit in which the impedence in one part of a series circuit is 2+j8 ohms and the impedent is another part of the circuit is 4-j60 ohm mm program

Step 1: Choose a vertex in the graph and make it the source vertex & mark it visited. Step 2: Determine a vertex which is adjacent to the source vertex and begun a new search if

Using Assertions When writing code, programmer must state pre- and subtle post conditions for public operations, state class invariants and insert unreachable code assertions a

Your objective is to write a generic doubly linked list class called CS228LinkedList that implements the List interface and uses a type variable T. All methods except for subList a

#question.explain different types of errors in data transmission.

Program: Creation of a Circular linked list ALGORITHM (Insertion of an element into a Circular Linked List) Step 1        Begin Step 2      if the list is empty or new


Q. What do you mean by the best case complexity of quick sort and outline why it is so. How would its worst case behaviour arise?

How to construct a data flow diagram for a college assignment and marking systemA

A binary search tree is constructed through the repeated insertion of new nodes in a binary tree structure. Insertion has to maintain the order of the tree. The value to the lef