NumPy: Convert cartesian coordinates to polar coordinates
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].
Python-Numpy Code Editor: