Python – scipy.linalg.expm

The expm() function of scipy.linalg package is used to compute the matrix exponential using Padé approximation. A Padé approximant is the "best" approximation of a function by a rational function of given order. Under this technique, the approximant's power series agrees with the power series of the function it is approximating.

Syntax

scipy.linalg.expm(x)

where x is the input matrix to be exponentiated.

Example 1

Let us consider the following example −

# Import the required libraries
from scipy import linalg
import numpy as np

# Define the input array
e = np.array([[100 , 5] , [78 , 36]])
print("Input Array :\n", e)

# Calculate the exponential
m = linalg.expm(e)

# Display the exponential of matrix
print("Exponential of e: \n", m)

Output

The above program will generate the following output −

Input Array :
 [[100 5]
 [ 78 36]]
Exponential of e:
 [[6.74928440e+45 4.84840154e+44]
 [7.56350640e+45 5.43330432e+44]]

Example 2

Let us take another example −

# Import the required libraries
from scipy import linalg
import numpy as np

# Define the input array
k = np.zeros((3, 3))
print("Input Array :\n", k)

# Calculate the exponential
n = linalg.expm(k)

# Display the exponential of matrix
print("Exponential of k: \n", n)

Output

It will generate the following output −

Input Array :
 [[0. 0. 0.]
 [0. 0. 0.]
 [0. 0. 0.]]
Exponential of k:
 [[1. 0. 0.]
 [0. 1. 0.]
 [0. 0. 1.]]