NumPy: Convert cartesian coordinates to polar coordinates

Last update on August 30 2025 12:30:11 (UTC/GMT +8 hours)

14. Cartesian to Polar Conversion

Write a NumPy program to convert cartesian coordinates to polar coordinates of a random 10x2 matrix representing cartesian coordinates.

Sample Solution:

Python Code:

# Importing the NumPy library as np
import numpy as np

# Generating a random 10x2 array 'z' with random numbers between 0 and 1
z = np.random.random((10, 2))

# Extracting the first column as 'x' and the second column as 'y' from the array 'z'
x, y = z[:, 0], z[:, 1]

# Calculating the Euclidean distance (r) using the formula sqrt(x^2 + y^2)
r = np.sqrt(x**2 + y**2)

# Calculating the angles (t) using arctan2() function, which returns the arctangent of y/x in radians
t = np.arctan2(y, x)

# Displaying the calculated Euclidean distances (r)
print(r)

# Displaying the calculated angles (t) in radians
print(t)

Sample Output:

[ 0.46197382  0.07034582  0.89015703  1.06227375  1.29780158  0.32823362                                                                      
  0.99823096  0.74005334  0.38023205  0.62537423]                      
[ 1.05405564  1.09799508  0.75642993  0.97273388  0.86502465  0.88995172                                                                      
  0.3019899   1.05539822  0.91697477  1.22828465]

Explanation:

In the above exercise –

z = np.random.random((10, 2)): This line generates a 10x2 array of random float numbers between 0 and 1, representing the x and y coordinates of 10 points in 2D space.

x, y = z[:, 0], z[:, 1]: These lines separate the x and y coordinates of the points into two separate 1D arrays.

r = np.sqrt(x**2 + y**2): This line calculates the radius (distance from the origin) for each point using the Pythagorean theorem, i.e., r = sqrt(x^2 + y^2), where r is the radius, and x and y are the coordinates of the point.

t = np.arctan2(y, x): This line calculates the angle in radians for each point, measured counterclockwise from the positive x-axis, using the arctan2() function, which takes the y and x coordinates as arguments and returns the angle t in the range (-π, π].

For more Practice: Solve these Related Problems:

Write a function that converts a set of Cartesian coordinates from a 10x2 array into polar coordinates (r, theta).
Create a solution that computes both the magnitude and the angle for each point using np.hypot and np.arctan2.
Test the conversion on an array with negative and positive coordinates to ensure correct angle computation.
Implement a program that converts the polar coordinates back to Cartesian and verifies the reconstruction accuracy.

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Python-Numpy Code Editor:

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