Creating sparse matrices in SciPy

Introduction

Sparse matrices save memory by storing only non-zero values. This helps when working with big data that has many zeros.

When you have a large dataset with mostly zero values.

When you want to speed up calculations by ignoring zeros.

When storing data like text documents or graphs where many entries are empty.

When you want to save memory in machine learning tasks with sparse features.

Syntax

SciPy

from scipy.sparse import csr_matrix, csc_matrix, coo_matrix

# Create sparse matrix from dense array
sparse_matrix = csr_matrix(dense_array)

# Create sparse matrix from data, row indices, and column indices
sparse_matrix = coo_matrix((data, (row_indices, col_indices)), shape=(rows, cols))

Common sparse formats are CSR, CSC, and COO.

COO format is good for building matrices; CSR and CSC are efficient for calculations.

Examples

Create a CSR sparse matrix from a small dense array.

SciPy

from scipy.sparse import csr_matrix
import numpy as np

dense = np.array([[0, 0, 1], [1, 0, 0], [0, 0, 0]])
sparse = csr_matrix(dense)
print(sparse)

Create a COO sparse matrix from data and their positions.

SciPy

from scipy.sparse import coo_matrix

data = [4, 5, 7]
rows = [0, 1, 2]
cols = [1, 2, 0]
sparse = coo_matrix((data, (rows, cols)), shape=(3, 3))
print(sparse)

Sample Program

This program shows two ways to create sparse matrices: from a dense array and from data with positions.

SciPy

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

# Create a dense numpy array
dense_array = np.array([
    [0, 0, 3],
    [4, 0, 0],
    [0, 0, 0],
    [0, 5, 0]
])

# Convert dense array to CSR sparse matrix
csr = csr_matrix(dense_array)
print('CSR matrix:')
print(csr)

# Create COO sparse matrix directly from data
data = [3, 4, 5]
row_indices = [0, 1, 3]
col_indices = [2, 0, 1]
coo = coo_matrix((data, (row_indices, col_indices)), shape=(4, 3))
print('\nCOO matrix:')
print(coo)

Important Notes

Use CSR or CSC format for fast arithmetic and matrix-vector operations.

COO format is easy to create but slower for calculations.

Always specify the shape when creating sparse matrices from data and indices.

Summary

Sparse matrices store only non-zero values to save memory.

Use scipy.sparse to create sparse matrices in different formats.

Choose the format based on your task: COO for building, CSR/CSC for calculations.