Write an algorithm and program for multiplication of three Sparse matr

Question

Write an algorithm and program for multiplication of three Sparse matrices

21 Jan 2021

Answer :

Word Count : 1210

Multiplication of three sparse matrices is a more complex operation than multiplying two sparse matrices. To multiply three sparse matrices (A, B, and C), you need to perform two multiplications: A * B and then (A * B) * C. Here's an algorithm and a Python program to multiply three sparse matrices.

Before we start, let's define what a sparse matrix is. A sparse matrix is a matrix in which most of the elements are zero. To represent a sparse matrix efficiently, we often use the Compressed Sparse Row (CSR) format. In CSR format, we store the non-zero elements along with their row indices and column pointers.

Here's the algorithm to multiply three sparse matrices A, B, and C:

1. Convert matrices A, B, and C into CSR format if they are not already in CSR format.

2. Initialize an empty result matrix D in CSR format, where D has the same number of rows as A and the same number of columns as C.

3. For each row i in A:
a. For each non-zero element A[i][j] in row i:
i. For each row k in B:
ii. For each non-zero element B[k][l] in row k:
1. Compute the product: temp = A[i][j] * B[k][l].
2. Add temp to the corresponding entry in the result matrix D[i][l].

4. After completing the above steps, you will have a temporary result matrix (A * B) in CSR format.

5. Initialize another empty result matrix E in CSR format, where E has the same number of rows as (A * B) and the same number of columns as C.

6. For each row i in (A * B):
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