SciPy · Module

scipy.sparse

scipy.sparse provides sparse-array formats that store data efficiently when most positions are empty. Its formats support different construction, arithmetic, slicing, linear-algebra, and graph-computation workloads.

How it works

The module represents mostly empty numeric arrays by storing only nonzero entries in a selected sparse format. Choose a format according to the access or computation pattern, and convert between formats when another operation is better served by a different representation.

Syntax

import scipy.sparse

Key points

scipy.sparse and its submodules provide the sparse-array data structures and operations.
Sparse arrays target data with relatively few populated positions.
Sparse representations can improve memory usage and computational efficiency for appropriate linear-algebra workloads.
Graph algorithms are one documented application area, through scipy.sparse.csgraph.
COO is useful when building a sparse array or changing entries during construction.
CSR is a strong choice for arithmetic, matrix-vector products, and row-oriented slicing.
CSC is a strong choice for arithmetic, matrix-vector products, and column-oriented slicing.

Common mistakes

Sparse arrays are efficient for suitable computations but may be inconvenient for slicing, reshaping, and assignment.

Example: Create and multiply a CSR sparse array

from scipy.sparse import csr_array

A = csr_array(([1, 2, 3], ([0, 1, 2], [0, 2, 1])), shape=(3, 3))
print(A @ A)

Builds a CSR sparse array from nonzero values and coordinates, then performs sparse matrix multiplication.

When to use it

Memory-efficient numeric arrays

Large matrices with relatively few nonzero entries

Fast sparse linear algebra

Matrix-vector products and row-oriented slicing

Graph computation

Graphs represented by sparse adjacency structures

Sparse construction with COO

Incrementally assembling sparse data

Interview questions

QWhat problem does scipy.sparse solve?

scipy.sparse provides tools for arrays in which only a small number of locations contain data. Avoiding storage for the many empty locations can reduce memory use and enable faster linear-algebra or graph computations.

Follow-up: Which related SciPy areas use sparse arrays? scipy.sparse.linalg supports linear algebra, while scipy.sparse.csgraph supports graph-based computations.

QHow do CSR and CSC differ?

CSR is suited to fast arithmetic, vector products, and row slicing. CSC has similar strengths for column slicing, so the choice should follow the dominant access pattern.

Follow-up: What format is a reasonable construction starting point? COO is simple to construct and can be converted quickly to CSR, CSC, or BSR.

QHow should a sparse format be selected?

The module offers several formats with different trade-offs: BSR for contiguous blocks, COO for construction and in-place modification, CSR for row-oriented operations, CSC for column-oriented operations, and DIA when values lie mainly on diagonals.

Follow-up: Why not use one universal format? Sparse operations and storage layouts are optimized for different data patterns and access patterns.

scipy.sparse.bsr_array
scipy.sparse.coo_array
scipy.sparse.csr_array
scipy.sparse.csc_array
scipy.sparse.dia_array
scipy.sparse.linalg
scipy.sparse.csgraph

Source: Sparse Arrays (scipy.sparse). Checked 2026-10-15.