NumPy - Mathematical Functions

NumPy provides a rich library of mathematical functions that operate element-wise on arrays. These Universal Functions (ufuncs) include standard trigonometric operations, rounding functions, arithmetic operations, functions for complex numbers, and much more.

Trigonometric Functions

NumPy includes standard trigonometric functions like np.sin(), np.cos(), and np.tan(). These functions expect the input angle(s) to be in radians. You can convert degrees to radians by multiplying with np.pi / 180.

Example: Calculating Sine, Cosine, and Tangent

Applying trigonometric functions to an array of angles (in degrees).

import numpy as np

angles_deg = np.array([0, 30, 45, 60, 90])
angles_rad = angles_deg * np.pi / 180 # Convert degrees to radians

print('Angles in Degrees:', angles_deg)
print('Angles in Radians:', angles_rad)
print('\n')

print('Sine values:')
print(np.sin(angles_rad))
print('\n')

print('Cosine values:')
print(np.cos(angles_rad))
print('\n')

print('Tangent values:')
print(np.tan(angles_rad))

Output (values may have minor floating-point variations):

Angles in Degrees: [ 0 30 45 60 90]
Angles in Radians: [0.         0.52359878 0.78539816 1.04719755 1.57079633]


Sine values:
[0.         0.5        0.70710678 0.8660254  1.        ]


Cosine values:
[1.00000000e+00 8.66025404e-01 7.07106781e-01 5.00000000e-01
 6.12323400e-17]


Tangent values:
[0.00000000e+00 5.77350269e-01 1.00000000e+00 1.73205081e+00
 1.63312394e+16]

Inverse trigonometric functions (np.arcsin(), np.arccos(), np.arctan()) are also available. They return the angle in radians corresponding to the given trigonometric ratio. You can use np.degrees() to convert the result back to degrees for verification.

Example: Inverse Trigonometric Functions

Calculating inverse sine and converting back to degrees.

import numpy as np

angles_deg = np.array([0, 30, 45, 60, 90])
angles_rad = np.deg2rad(angles_deg) # Use np.deg2rad for convenience
sine_values = np.sin(angles_rad)

print('Original angles (degrees):', angles_deg)
print('Sine values:', sine_values)
print('\n')

print('Inverse sine (result in radians):')
inv_sine_rad = np.arcsin(sine_values)
print(inv_sine_rad)
print('\n')

print('Inverse sine converted back to degrees:')
inv_sine_deg = np.degrees(inv_sine_rad)
print(inv_sine_deg)
print('\n')

# Similar process applies to arccos and arctan
cosine_values = np.cos(angles_rad)
inv_cosine_deg = np.degrees(np.arccos(cosine_values))
print('Inverse cosine (degrees):', inv_cosine_deg)

Output (values may have minor floating-point variations):

Original angles (degrees): [ 0 30 45 60 90]
Sine values: [0.         0.5        0.70710678 0.8660254  1.        ]


Inverse sine (result in radians):
[0.         0.52359878 0.78539816 1.04719755 1.57079633]


Inverse sine converted back to degrees:
[ 0. 30. 45. 60. 90.]


Inverse cosine (degrees): [ 0. 30. 45. 60. 90.]

Functions for Rounding

numpy.around()

Rounds array elements to a specified number of decimal places. It uses a “round half to even” strategy for values exactly halfway between two representable numbers (e.g., 2.5 rounds to 2.0, 3.5 rounds to 4.0).

numpy.around(a, decimals=0)

Parameters:

Parameter	Description
a	Input array.
decimals	Number of decimal places to round to (default is 0). If negative, rounds to the left of the decimal point.

Example: Using np.around

Demonstrating rounding to different decimal places.

import numpy as np

a = np.array([1.0, 5.55, 123, 0.567, 25.532, -1.25])

print('Original array:')
print(a)
print('\n')

print('Rounded to 0 decimals (default):')
print(np.around(a))

print('\nRounded to 1 decimal place:')
print(np.around(a, decimals=1))

print('\nRounded to -1 decimal place (nearest 10):')
print(np.around(a, decimals=-1))

Output:

Original array:
[  1.     5.55  123.     0.567  25.532 -1.25 ]


Rounded to 0 decimals (default):
[  1.   6. 123.   1.  26.  -1.]


Rounded to 1 decimal place:
[  1.    5.6 123.    0.6  25.5  -1.2]


Rounded to -1 decimal place (nearest 10):
[  0.  10. 120.   0.  30.  -0.]

numpy.floor()

Returns the floor of each element, which is the largest integer less than or equal to the element.

Example: Using np.floor

Finding the largest integer not greater than each element.

import numpy as np

a = np.array([-1.7, 1.5, -0.2, 0.6, 10.0])

print('Original array:')
print(a)
print('\n')

print('After applying np.floor():')
print(np.floor(a))

Output:

Original array:
[-1.7  1.5 -0.2  0.6 10. ]


After applying np.floor():
[-2.  1. -1.  0. 10.]

numpy.ceil()

Returns the ceiling of each element, which is the smallest integer greater than or equal to the element.

Example: Using np.ceil

Finding the smallest integer not less than each element.

import numpy as np

a = np.array([-1.7, 1.5, -0.2, 0.6, 10.0])

print('Original array:')
print(a)
print('\n')

print('After applying np.ceil():')
print(np.ceil(a))

Output:

Original array:
[-1.7  1.5 -0.2  0.6 10. ]


After applying np.ceil():
[-1.  2. -0.  1. 10.]