NumPy Mathematical Functions – Mastering Python

Arithmetic Operations

NumPy provides element-wise arithmetic operations directly on arrays. This means that operations are applied to each element individually, resulting in a new array of the same shape.

import numpy as np

a = np.array([1, 2, 3])
b = np.array([4, 5, 6])

c = a + b  # Output: array([5, 7, 9])

d = a - b  # Output: array([-3, -3, -3])

e = a * b  # Output: array([ 4, 10, 18])

f = a / b  # Output: array([0.25, 0.4 , 0.5 ])

g = a ** 2 # Output: array([1, 4, 9])

Trigonometric Functions

NumPy offers a suite of trigonometric functions, including sine, cosine, tangent, and their inverses (arcsin, arccos, arctan). These functions work seamlessly with arrays.

import numpy as np

x = np.array([0, np.pi/2, np.pi])

sin_x = np.sin(x) # Output: array([0.        , 1.        , 0.        ])

cos_x = np.cos(x) # Output: array([ 1.00000000e+00,  6.12323400e-17, -1.00000000e+00])

tan_x = np.tan(x) # Output: array([ 0.        ,  1.63312394e+16,  0.        ])

Note the slight numerical imprecision in the cosine example; this is typical of floating-point arithmetic.

Exponential and Logarithmic Functions

NumPy provides functions for exponential and logarithmic calculations, crucial for many scientific and engineering applications.

import numpy as np

a = np.array([1, 2, 3])

exp_a = np.exp(a)  # Output: array([ 2.71828183,  7.3890561 , 20.08553692])

log_a = np.log(a)  # Output: array([0.        , 0.69314718, 1.09861229])

log10_a = np.log10(a) # Output: array([0.        , 0.30103   , 0.47712125])

Rounding Functions

NumPy offers various functions for rounding numbers to the nearest integer or to a specified number of decimal places.

import numpy as np

a = np.array([1.2, 2.5, 3.8])

rounded_a = np.round(a)  # Output: array([1., 2., 4.])

floor_a = np.floor(a)  # Output: array([1., 2., 3.])

ceil_a = np.ceil(a)  # Output: array([2., 3., 4.])

Other Useful Functions

NumPy includes many more mathematical functions, including those for:

Statistical calculations: np.mean(), np.std(), np.median(), np.sum(), np.max(), np.min() etc.
Linear algebra: np.dot(), np.linalg.inv() (matrix inverse), etc.
Special functions: Bessel functions, Gamma function, etc. (found in scipy.special)

These functions offer a powerful and efficient way to perform complex mathematical operations on arrays, making NumPy an indispensable tool for numerical computation in Python. Refer to the official NumPy documentation for a complete list of available functions and their detailed descriptions.