How to create a sparse matrix in Python?

In this article, we will show you what a sparse matrix is ​​and how to create a sparse matrix in python.

What is a sparse matrix?

A sparse matrix is ​​a matrix in which most elements are 0. That is, the matrix contains data for only a few locations. Most of the memory consumed by a sparse matrix consists of zeros.

For example -

M = [
   [1, 0, 0, 0],
   [0, 0, 3, 0],
   [0, 0, 0, 0],
   [0, 0, 0, 2]
]

Using a two-dimensional array to represent a sparse matrix wastes a lot of memory because the zeros in the matrix are useless in most cases. So instead of storing zero along with non-zero elements, we store only non-zero elements. This involves using triples to store non-zero elements (row, column, value).

Natural language processing (NLP) and data encoding both make heavy use of sparse matrices. If most matrix elements are 0, the storage cost of storing all matrix elements will be high.

This is because we only have a few data points and most of the storage space is taken up by redundant zeros.

Advantages of sparse matrices

The following are the two main advantages of using a sparse matrix instead of a simple matrix -

• Storage - Because there are fewer non-zero elements than zero, less memory can be used to store these elements individually.

• Computation time - Computation time can be saved by logically creating a data structure that traverses only non-zero elements.

How to create a sparse matrix in Python?

ScPy in Python provides tools for creating sparse matrices using various data structures and converting dense matrices to sparse matrices.

In Python, we can create a sparse matrix using the following function -

• csr_matrix() function - Creates a sparse matrix in compressed sparse row format,

• csc_matrix() function - Creates a sparse matrix in compressed sparse column format. ,,

Method 1. Use the csr_matrix() function to create a sparse matrix

It creates a sparse matrix in compressed sparse row format.

grammar

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

parameter

• shape - it is the shape of the matrix

• dtype - It is the data type of the matrix

Algorithm (steps)

The following are the algorithms/steps that need to be followed to perform the required task -

• Use the import keyword to import the numpy module with an alias (np).

• Use the import keyword to import the csr_matrix function from the scipy module.

• Use the csr_matrix() function to create a 3 * 3 sparse matrix of int data type (row format) and use toarray to convert to array() function.

• Print the generated sparse matrix.

Example

The following program uses the csr_matrix() function to return a sparse matrix (3x3) -

# importing numpy module with an alias name
import numpy as np

# importing csr_matrix function from scipy module
from scipy.sparse import csr_matrix

# Using csr_matrix function to create a 3 * 3 sparse matrix of int datatype
# and converting into array
sparse_matrix = csr_matrix((3, 3), dtype = np.int8).toarray()

# printing the resultant sparse matrix
print("The resultant sparse matrix:\n", sparse_matrix)

Output

When executed, the above program will generate the following output -

The resultant sparse matrix:
 [[0 0 0]
 [0 0 0]
 [0 0 0]]

Method 2. Create a sparse matrix using the csr_matrix() function given a Numpy array

Algorithm (steps)

The following are the algorithms/steps that need to be followed to perform the required task -

• Use the import keyword to import the numpy module with an alias (np).

• Use the import keyword to import the csr_matrix function from the scipy module.

• Use the numpy.array() function to create an array (returns an ndarray. ndarray is an array object that meets the given requirements)

Example

# importing numpy module with alias name
import numpy as np

# importing csr_matrix function from scipy module
from scipy.sparse import csr_matrix

# Giving rows and columns values
rows = np.array([0, 1, 0, 2, 1, 1])
columns = np.array([1, 0, 0, 2, 1, 2])

# Giving array data
arrayData = np.array([1, 3, 2, 5, 7, 6])

# Using csr_matrix function to create a 3x3 sparse matrix
sparse_matrix = csr_matrix((arrayData, (rows, columns)),
   shape = (3, 3)).toarray()

# print the resultant sparse matrix
print("The resultant sparse matrix:\n", sparse_matrix)

Output

When executed, the above program will generate the following output -

The resultant sparse matrix:
 [[2 1 0]
 [3 7 6]
 [0 0 5]]

Method 3. Use the csc_matrix() function to create a sparse matrix

It creates a sparse matrix in compressed sparse column format.

grammar

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

parameter

• shape - it is the shape of the matrix

• dtype - It is the data type of the matrix

algorithm

The following are the algorithms/steps that need to be followed to perform the required task -

• Use the import keyword to import the numpy module with an alias (np).

• Use the import keyword to import the csc_matrix function from the scipy module.

• Use the csc_matrix() function to create a 3 * 3 sparse matrix of int data type ( column format) and use toarray to convert to array() function.

• Print the generated sparse matrix.

Example

The following program uses the csc_matrix() function to return a sparse matrix (3x3) in column format -

# importing numpy module with an alias name
import numpy as np

# importing csc_matrix function from scipy module
from scipy.sparse import csc_matrix

# Using csc_matrix function to create a 3 * 3 sparse matrix of int datatype
# and converting into array
sparse_matrix = csc_matrix((3, 3), dtype = np.int8).toarray()

# printing the resultant sparse matrix
print("The resultant sparse matrix:\n", sparse_matrix)

Output

When executed, the above program will generate the following output -

The resultant sparse matrix:
 [[0 0 0]
 [0 0 0]
 [0 0 0]]

Method 4. Create a sparse matrix using the csc_matrix() function given a Numpy array

Example

The following program uses the csc_matrix() function to return a sparse matrix (3x3) in integer column format -

import numpy as np
# importing csc_matrix function from scipy module
from scipy.sparse import csc_matrix

# Giving rows and columns values
rows = np.array([0, 1, 0, 2, 1, 1])
columns = np.array([1, 0, 0, 2, 1, 2])

# Giving array data
arrayData = np.array([1, 3, 2, 5, 7, 6])

# Using csc_matrix function to create a 3x3 sparse matrix in column format
sparse_matrix = csc_matrix((arrayData, (rows, columns)),
   shape = (3, 3)).toarray()

# print the resultant sparse matrix
print("The resultant sparse matrix:\n", sparse_matrix)

Output

When executed, the above program will generate the following output -

The resultant sparse matrix:
 [[2 1 0]
 [3 7 6]
 [0 0 5]]

in conclusion

In this tutorial, we learned four different ways to generate sparse matrices in Python. We also learned how to generate a sparse matrix from a numpy array.

The above is the detailed content of How to create a sparse matrix in Python?. For more information, please follow other related articles on the PHP Chinese website!