The numpy.exp() method calculates the exponential of each element of an input array, returning (e^x), where (e) is the base of the natural logarithm (~2.71828) and (x) is the input value.

import numpy as np

# 1D Numpy array
arr = np.array([0, 1, 2])

print(np.exp(arr))

# Output: [1.     2.71828183   7.3890561 ]

The above output shows that it works element-wise, meaning if the input array contains three elements, the output array will have three elements as well, with each element being e^ corresponding to the input array’s element.

Syntax

numpy.exp(x,
         out=None, 
         where=True, 
         casting='same_kind', 
         order='K', 
         dtype=None, 
         subok=True)

Parameters

Exponential of a scalar value

If the input value is not an array but a scalar, the output value shall be a scalar too!

import numpy as np

# Scalar value
scalar = 10

print(np.exp(scalar))

# Output: 22026.465794806718

Exponential of a 2D array

Even if the input array is a multidimensional array like 2D or 3D, it works the same and returns the output of the same shape as the input.

import numpy as np

# 2D Numpy array
array_2d = np.array([[0, 1], [3, 4]])

# Calculate the exponential of each element in the 2D array
print(np.exp(array_2d))

# Output:
# [[ 1.          2.71828183]
#  [20.08553692 54.59815003]]

Boolean Input

The boolean values are either True or False.

If you pass True, that means 1 and e^1 = 2.719 (rounded)

If you pass False, that means 0, and e^0 = 1.

import numpy as np

# Array with boolean values
boolean_array = np.array([True, False])

print(np.exp(boolean_array))

# Output: [2.719     1.]

Using “where” Mask and “out” array

With the help of the “where” mask, we can apply a condition to select which value’s exponential we want to calculate.

Uncomputed elements are either set to zero or retain their original values, depending on implementation.

But what do I mean by implementation? Well, that’s a tricky part, and that’s where the “out” argument comes into the picture.

For uncomputed elements, the result is not always predictable. However, for predictable results in where=False positions, explicitly set an out array with 0 values.

import numpy as np

arr_1d = np.array([2, 4, 6])

output_array = np.full_like(arr_1d, fill_value=0, dtype=float)

condition = np.array([True, False, False])

print(np.exp(arr_1d, where=condition, out=output_array))

# Output: [7.3890561 0.        0.       ]

In this code, we set a mask True, False, and False. It means we only need to calculate the exponential of the first element.

Now, we are also pre-defining an array called output_array, whose values we are explicitly setting to 0. It will have three 0s since the input array has three elements. In the future, we will store the values in it.

Based on the mask, we calculate the first element’s exponential value and store it in the output_array. The rest of the array’s values are already set to 0, resulting in the final output.

Negative elements

Even if the array contains negative values, (e^x) produces values between 0 and 1, which is helpful in decay models.

import numpy as np

neg_arr = np.array([-1, -2])

print(np.exp(neg_arr))

# Output: [0.36787944 0.13533528]

Plotting

To plot a chart of exponential values, we can use the matplotlib library. 

To install it if you have not, use this command: pip install matplotlib

Here, we will plot the e^x for values between -3 and 3. We will label axes and show a grid using numpy.exp() method to calculate the values.

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(-3, 3, 100)  # from -3 to 3
y = np.exp(x)

# Create the plot
plt.figure(figsize=(6, 4))
plt.plot(x, y, label=r"$e^x$", color='blue')
plt.title("NumPy exp() Function")
plt.xlabel("x")
plt.ylabel("exp(x)")
plt.grid(True, linestyle='--', alpha=0.6)
plt.legend()
plt.show()

The above figure shows the classic exponential curve.

That’s all!

Krunal Lathiya

With a career spanning over eight years in the field of Computer Science, Krunal’s expertise is rooted in a solid foundation of hands-on experience, complemented by a continuous pursuit of knowledge.