How to Create a Sparse Matrix in Python

If most of the elements of the matrix have 0 value, then it is called a sparse matrix. The two major benefits of using sparse matrix instead of a simple matrix are:

• Storage: There are lesser non-zero elements than zeros and thus lesser memory can be used to store only those elements.
• Computing time: Computing time can be saved by logically designing a data structure traversing only non-zero elements.

Sparse matrices are generally utilized in applied machine learning such as in data containing data-encodings that map categories to count and also in entire subfields of machine learning such as natural language processing (NLP).

Example:

0 0 3 0 4            
0 0 5 7 0
0 0 0 0 0
0 2 6 0 0

Representing a sparse matrix by a 2D array leads to wastage of lots of memory as zeroes in the matrix are of no use in most of the cases. So, instead of storing zeroes with non-zero elements, we only store non-zero elements. This means storing non-zero elements with triples- (Row, Column, value).

Create a Sparse Matrix in Python

Python’s SciPy gives tools for creating sparse matrices using multiple data structures, as well as tools for converting a dense matrix to a sparse matrix. The function csr_matrix() is used to create a sparse matrix of compressed sparse row format whereas csc_matrix() is used to create a sparse matrix of compressed sparse column format.

# Using csr_matrix()

Syntax:

scipy.sparse.csr_matrix(shape=None, dtype=None)

 

Parameters:

shape: Get shape of a matrix

dtype: Data type of the matrix

Example 1:

# Python program to create
# sparse matrix using csr_matrix()

# Import required package
import numpy as np
from scipy.sparse import csr_matrix

# Creating a 3 * 4 sparse matrix
sparseMatrix = csr_matrix((3, 4), 
                          dtype = np.int8).toarray()

# Print the sparse matrix
print(sparseMatrix)

Output:

[[0 0 0 0]
 [0 0 0 0]
 [0 0 0 0]]

Example 2:

# Python program to create
# sparse matrix using csr_matrix()

# Import required package
import numpy as np
from scipy.sparse import csr_matrix

row = np.array([0, 0, 1, 1, 2, 1])
col = np.array([0, 1, 2, 0, 2, 2])

# taking data
data = np.array([1, 4, 5, 8, 9, 6])

# creating sparse matrix
sparseMatrix = csr_matrix((data, (row, col)), 
                          shape = (3, 3)).toarray()

# print the sparse matrix
print(sparseMatrix)

Output:

[[ 1  4  0]
 [ 8  0 11]
 [ 0  0  9]]

# Using csc_matrix()

Syntax:

scipy.sparse.csc_matrix(shape=None, dtype=None)

 

Parameters:

shape: Get shape of a matrix

dtype: Data type of the matrix

Example 1:

# Python program to create
# sparse matrix using csc_matrix()

# Import required package
import numpy as np
from scipy.sparse import csc_matrix

# Creating a 3 * 4 sparse matrix
sparseMatrix = csc_matrix((3, 4), 
                          dtype = np.int8).toarray()

# Print the sparse matrix
print(sparseMatrix)

Output:

[[0 0 0 0]
 [0 0 0 0]
 [0 0 0 0]]

Example 2:

# Python program to create
# sparse matrix using csc_matrix()

# Import required package
import numpy as np
from scipy.sparse import csc_matrix

row = np.array([0, 0, 1, 1, 2, 1])
col = np.array([0, 1, 2, 0, 2, 2])

# taking data
data = np.array([1, 4, 5, 8, 9, 6])

# creating sparse matrix
sparseMatrix = csc_matrix((data, (row, col)),
                          shape = (3, 3)).toarray()

# print the sparse matrix
print(sparseMatrix)

Output:

[[ 1  4  0]
 [ 8  0 11]
 [ 0  0  9]]