SciPy Sparse Matrix Multiplication (original) (raw)

Last Updated : 5 Jul, 2025

In scientific computing, large matrices often contain mostly zero values. Storing and multiplying these as dense arrays wastes both memory and processing time. SciPy’s **scipy.sparse module efficiently handles sparse matrices(2D arrays with mostly zero values) designed specifically for fast storage and computation.

Two commonly used classes in this module are:

• **csr_matrix: compressed Sparse Row matrix
• **csc_matrix: compressed Sparse Column matrix

To multiply two sparse matrices, ****.multiply()** method is used both in csr_matrix and in csc_matrix. This method supports multiplication between matrices of same format (e.g., CSR × CSR) or even different formats (e.g., CSR × CSC).

Let's understand it better through Example.

Example 1: Multiply Two csc_matrix Matrices

In this example two sparse matrices are created using **csc_matrix() class. These matrices are then multiplied element-wise using **multiply() method which performs efficient operations on only the non-zero elements.

Python `

import numpy as np from scipy.sparse import csc_matrix

Create first csc matrix A

row_A = np.array([0, 0, 1, 2]) col_A = np.array([0, 1, 0, 1]) data_A = np.array([4, 3, 8, 9]) csc_A = csc_matrix((data_A, (row_A, col_A)), shape=(3, 3))

print("First CSC matrix:\n", csc_A.toarray())

Create second csc matrix B

row_B = np.array([0, 1, 1, 2]) col_B = np.array([0, 0, 1, 0]) data_B = np.array([7, 2, 5, 1]) csc_B = csc_matrix((data_B, (row_B, col_B)), shape=(3, 3))

print("Second CSC matrix:\n", csc_B.toarray())

Element-wise multiplication

result = csc_A.multiply(csc_B) print("Element-wise Product (CSC x CSC):\n", result.toarray())

`

**Output

Output of Multiplication of Two CSC matrices

Example 2: Multiply Two csr_matrix Matrices

Here, two sparse matrices are created using **csr_matrix() class. These matrices are then multiplied element-wise using the **multiply() method focusing only on non-zero elements.

Python `

import numpy as np from scipy.sparse import csr_matrix

Create first csr matrix A

row_A = np.array([0, 0, 1, 2]) col_A = np.array([0, 1, 0, 1]) data_A = np.array([4, 3, 8, 9]) csr_A = csr_matrix((data_A, (row_A, col_A)), shape=(3, 3))

print("First CSR matrix:\n", csr_A.toarray())

Create second csr matrix B

row_B = np.array([0, 1, 1, 2]) col_B = np.array([0, 0, 1, 0]) data_B = np.array([7, 2, 5, 1]) csr_B = csr_matrix((data_B, (row_B, col_B)), shape=(3, 3))

print("Second CSR matrix:\n", csr_B.toarray())

Element-wise multiplication

result = csr_A.multiply(csr_B) print("Element-wise Product (CSR x CSR):\n", result.toarray())

`

**Output

Output of Multiplication of Two CSR matrices

Example 3: Multiply csc_matrix and csr_matrix

In this example two sparse matrices are created, one in **CSC format and other in **CSR format. Then element-wise multiplication is performed using **multiply() method to demonstrate compatibility between different sparse matrix.

Python `

import numpy as np from scipy.sparse import csc_matrix, csr_matrix

Create CSC matrix

row_A = np.array([0, 0, 1, 2]) col_A = np.array([0, 1, 0, 1]) data_A = np.array([4, 3, 8, 9]) csc_A = csc_matrix((data_A, (row_A, col_A)), shape=(3, 3))

print("CSC matrix:\n", csc_A.toarray())

Create CSR matrix

row_B = np.array([0, 1, 1, 2]) col_B = np.array([0, 0, 1, 0]) data_B = np.array([7, 2, 5, 1]) csr_B = csr_matrix((data_B, (row_B, col_B)), shape=(3, 3))

print("CSR matrix:\n", csr_B.toarray())

Multiply CSC with CSR

result1 = csc_A.multiply(csr_B) print("Element-wise Product (CSC x CSR):\n", result1.toarray())

Multiply CSR with CSC

result2 = csr_B.multiply(csc_A) print("Element-wise Product (CSR x CSC):\n", result2.toarray())

`