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Python - Matrix Operations with SciPy

By IncludeHelp Last updated : September 14, 2024

Python SciPy provides various methods for performing different matrix operations.

Let us understand some examples of matrix operations using SciPy:

Example 1: Matrix Inversion

To find the matrix inversion, we can use the inv() method of scipy.linalg package.

# Import numpy
import numpy as np

# Import inv function from scipy
from scipy.linalg import inv

# Creating an array
arr = np.array([[1, 2], [3, 4]])

# Display original array
print("Original array:\n", arr, "\n")

# Finding inverse of array
arr_inv = inv(arr)

# Display result
print("Inverse matrix:\n", arr_inv)

Output

Original array:
 [[1 2]
 [3 4]] 

Inverse matrix:
 [[-2.   1. ]
 [ 1.5 -0.5]]

Example 2: Solving Linear Systems

Use solve() method of scipy.linalg module to solve a system of linear equations. This method takes two input matrices and convert them into a system of linear equation.

# Import numpy
import numpy as np

# Import solve function from scipy
from scipy.linalg import solve

# Creating square matrix
arr1 = np.array([[3, 2, 0], [1, -1, 0], [0, 5, 1]])

# Creating right-hand side vector
arr2 = np.array([2, 4, -1])

# Display square matrix
print("Square matrix:\n", arr1, "\n")

# Display right-hand side vector
print("Right-hand side vector:\n", arr2, "\n")

# Solving linear equations (represented by arrays)
res = solve(arr1, arr2)

# Display result
print("Result:\n", res)

Output

Square matrix:
 [[ 3  2  0]
 [ 1 -1  0]
 [ 0  5  1]] 

Right-hand side vector:
 [ 2  4 -1] 

Result:
 [ 2. -2.  9.]

Example 3: Constructing Sparse Matrices

To create sparse matrix, we can use csr_matrix() method from scipy.sparse module. The sparse csr matrix can be created in the following ways:

• As a dense matrix
• With another sparse matrix
• As empty matrix
• With data, row_indices and column_indices
• With data, indices, Indptr and shape attributes

Let us see how we can create a sparse csr matrix using data, indices of rows, and indices of columns.

# Import numpy
import numpy as np

# Import csr_matrix function
from scipy.sparse import csr_matrix

# Defining the data, row, and column
data = np.array([1, 2, 3, 4])
row = np.array([0, 0, 1, 2])
col = np.array([0, 2, 2, 0])

# Defining the shape of the matrix
shape = (3, 3)

# Creating the CSR matrix
csr = csr_matrix((data, (row, col)), shape).toarray()

# Display created csr matrix
print("Created CSR matrix:\n", csr)

Output

Created CSR matrix:
 [[1 0 2]
 [0 0 3]
 [4 0 0]]

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