SciPy Sparse Matrix

The sparse matrix allows the data structure to store large sparse matrices, and provide the functionality to perform complex matrix computations. In simple words, suppose you have a 2-D matrix with hundreds of elements, where only a few of them contain a non-zero value. When sorting this matrix using the sorting approach, we would waste a lot of space for zeros.

The sparse data structure allows us to store only non-zero values assuming the rest of them are zeros.

Sparse matrix types in SciPy

There are various ways to represent a sparse matrix; SciPy provides seven of them.

Block Sparse Row matrix (BSR)
Coordinate list matrix (COO)
Compressed Sparse Column matrix (CSC)
Compressed Sparse Row matrix (CSR)
Sparse matrix with Diagonal storage (DIA)
Dictionary Of Keys based sparse matrix (DOK)
Row-based linked list sparse matrix (LIL)

Consider the following example:

import numpy as np
from scipy.sparse import random
np.random.seed(10)
# Generate a random binary sparse matrix
matrix = random(5, 5, format='csr', density=0.25)
# Substitute all non zero values with index number
matrix.data[:] = np.arange(1, matrix.data.shape[0]+1)
# We can access and modify these arrays:
print(matrix.toarray())
print("The data is",matrix.data)
print("Cell which consits the non-zero values",matrix.indptr)

Output:

[[0. 1. 0. 0. 0.]
 [2. 0. 0. 0. 0.]
 [3. 0. 4. 0. 0.]
 [0. 0. 5. 0. 0.]
 [0. 0. 0. 6. 0.]]
The data is [1. 2. 3. 4. 5. 6.]
Cell which consits the non-zero values [0 1 2 4 5 6]

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