Sparse matrix Algorithm
Sparse Matrix Algorithm is a mathematical technique used to efficiently store and perform operations on sparse matrices, which are matrices that have a significant number of zero elements. In most practical applications, these algorithms prove to be highly beneficial as they reduce the storage space and computational complexity associated with large matrices. Sparse matrix algorithms represent the non-zero elements along with their corresponding row and column indices, thus allowing for faster and more efficient operations, such as matrix addition, subtraction, and multiplication, as well as solving linear systems of equations.
There are several data structures and algorithms that have been developed to work with sparse matrices, such as Compressed Sparse Row (CSR), Compressed Sparse Column (CSC), and Coordinate List (COO) formats. These formats store the non-zero elements in a compact and organized manner, making it easier to perform operations on the sparse matrices without the need for excessive memory usage or computational power. In addition, specialized algorithms, such as the Conjugate Gradient Method and Preconditioned Conjugate Gradient Method, have been developed to solve linear systems involving sparse matrices effectively. These algorithms are widely used in various fields, including scientific computing, computer graphics, machine learning, and network analysis, where sparse matrices are often encountered.
/*A sparse matrix is a matrix which has number of zeroes greater than (m*n)/2,
where m and n are the dimensions of the matrix.*/
#include <iostream>
using namespace std;
int main()
{
int m, n;
int counterZeros = 0;
cout << "Enter dimensions of matrix (seperated with space): ";
cin >> m >> n;
int a[m][n];
cout << "Enter matrix elements:";
cout << "\n";
// reads the matrix from stdin
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
cout << "element? ";
cin >> a[i][j];
}
}
// counts the zero's
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
if (a[i][j] == 0)
counterZeros++; //Counting number of zeroes
}
}
// makes sure the matrix is a sparse matrix
if (counterZeros > ((m * n) / 2)) //Checking for sparse matrix
cout << "Sparse matrix";
else
cout << "Not a sparse matrix";
}
