How do you multiply sparse matrices?

How do you multiply sparse matrices?

Steps

1. Create a result matrix C for storing the final result.
2. Transform B into sparse representation such as a list of (y, val) pair.
3. Iterate over A, jump over 0s and multiply the elements with the same k in A nd B, at the same time update C.
4. Return C as the final output.

What is SpGEMM?

Sparse matrix-matrix multiplication (SpGEMM) is a computational primitive that is widely used in areas ranging from traditional numerical applications to recent big data analysis and machine learning.

What are the properties of sparse matrix?

A sparse matrix is a matrix that is comprised of mostly zero values. Sparse matrices are distinct from matrices with mostly non-zero values, which are referred to as dense matrices. A matrix is sparse if many of its coefficients are zero.

How is sparse matrix more efficient than conventional matrix?

If most of the elements in the matrix are zero then the matrix is called a sparse matrix. It is wasteful to store the zero elements in the matrix since they do not affect the results of our computation. This is why we implement these matrices in more efficient representations than the standard 2D Array.

What are the advantages of sparse matrices over normal matrices?

Using sparse matrices to store data that contains a large number of zero-valued elements can both save a significant amount of memory and speed up the processing of that data. sparse is an attribute that you can assign to any two-dimensional MATLAB® matrix that is composed of double or logical elements.

How is sparse matrix represented in memory?

Representing a sparse matrix by a 2D array leads to wastage of lots of memory as zeroes in the matrix are of no use in most of the cases. So, instead of storing zeroes with non-zero elements, we only store non-zero elements. This means storing non-zero elements with triples- (Row, Column, value).

How a sparse matrix can be defined?

Sparse matrices are those matrices that have the majority of their elements equal to zero. In other words, the sparse matrix can be defined as the matrix that has a greater number of zero elements than the non-zero elements.