Original to Sparse Matrix and Sparse to Original Matrix
In computer science and mathematics, a sparse matrix is a particular data structure that is used to store and operate matrices with a large number of zero or empty entries in an efficient manner. Sparse matrices minimize memory consumption by storing only the non-zero elements along with their row and column indices, in contrast to dense matrices, where the majority of the components are non-zero.
Sparse matrices are very useful in many applications (numerical simulations, machine learning, image processing, network analysis) where memory efficiency is critical.
They provide a number of benefits:
Diminished Memory Footprint: When compared to dense matrices, sparse matrices can significantly reduce memory usage by storing just non-zero elements and their locations. This is particularly crucial when working with sizable datasets.
Faster Operations: It is possible to optimize a number of sparse matrix operations, such as addition and multiplication, to work directly with the non-zero members. For some jobs, this can result in significant speed gains over dense matrices.
Enhanced Computational Efficiency: Sparse matrices’ lower memory requirements might result in faster and more effective numerical algorithms for solving linear systems of equations or conducting matrix factorization.
In summary, sparse matrices are a vital tool for optimizing memory usage and improving computational efficiency when dealing with matrices with a large number of zero values, making them a fundamental concept in various computational fields.
For the benefit of the students sparse to original matrix conversion code is also added in this tutorial. I hope that will help you all to understand the sparse to original and original to sparse conversion easily and affectively.
For Such more codes click here and for video tutorial click here.
/* Original Matrix to Sparse Matrix*/
#include<stdio.h>
#include<stdlib.h>
void orgtosprs(int org[][20], int sparse[][3], int, int);
void sparsetooriginal(int sp[][3],int org[][20]);
int main() {
int org[20][20], sparse[20][3];
int row, col, i, j;
printf("\n\nEnter the Row and Column of the original matrix : ");
scanf("%d %d", & row, & col);
printf("\n\nEnter the values for original matrix : ");
for (i = 0; i < row; i++)
for (j = 0; j < col; j++)
scanf("%d", & org[i][j]);
orgtosprs(org, sparse, row, col);
printf("\nAfter converting in Sparse Matrix : \n");
for (i = 0; i < sparse[0][2] + 1; i++) {
for (j = 0; j < 3; j++)
printf("%d\t", sparse[i][j]);
printf("\n");
}
printf("\nAfter converting back to Original from Sparse : \n");
sparsetooriginal(sparse,org);
for(i=0; i<sparse[0][0]; i++)
{
for(j=0; j<sparse[0][1]; j++)
printf("%d\t",org[i][j]);
printf("\n");
}
}
void orgtosprs(int org[][20], int sparse[][3], int m, int n) {
int t = 1, i, j;
sparse[0][0] = m;
sparse[0][1] = n;
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
if (org[i][j] != 0) {
sparse[t][0] = i;
sparse[t][1] = j;
sparse[t][2] = org[i][j];
t++;
}
}
}
sparse[0][2] = t - 1;
}
void sparsetooriginal(int sp[][3],int org[][20])
{
int i,j,t;
for(i=0; i<sp[0][0]; i++)
for(j=0; j<sp[0][1]; j++)
org[i][j]=0;
for(i=1; i<=sp[0][2]; i++)
{
org[sp[i][0]][sp[i][1]]=sp[i][2];
}
}
