NumPy: Find point by point distances of a random vector with shape (10,2) representing coordinates
Write a NumPy program to find point by point distances of a random vector with shape (10,2) representing coordinates.
Sample Solution :
Python Code :
# Importing the NumPy library as np
import numpy as np
# Generating a 10x2 array 'a' with random values between 0 and 1 using np.random.random()
a = np.random.random((10, 2))
# Extracting x and y coordinates from the array 'a' using np.atleast_2d() method
# at least 2-dimensional arrays from the columns of 'a'
x, y = np.atleast_2d(a[:, 0], a[:, 1])
# Calculating the Euclidean distance between points in the 'a' array using the formula:
# d = sqrt((x - x_transpose)^2 + (y - y_transpose)^2)
# where x and y are the coordinate matrices created, and T is the transpose of those matrices
d = np.sqrt((x - x.T) ** 2 + (y - y.T) ** 2)
# Displaying the resultant matrix containing the distances between points
print(d)
Sample Output:
[[ 0. 0.42309206 0.59799949 0.44076341 0.64568848 0.53547789 0.39263926 0.38982854 0.39228612 0.44529689] [ 0.42309206 0. 1.0208224 0.38421553 0.92200913 0.73182405 0.73513877 0.80796679 0.64687549 0.73308548] [ 0.59799949 1.0208224 0. 0.94341451 0.66895368 0.71852306 0.48605697 0.22453123 0.64173589 0.55440442] [ 0.44076341 0.38421553 0.94341451 0. 0.60846866 0.9467662 0.51350109 0.78044594 0.36885259 0.88113793] [ 0.64568848 0.92200913 0.66895368 0.60846866 0. 1.12199998 0.27042981 0.66189707 0.27709162 0.98097303] [ 0.53547789 0.73182405 0.71852306 0.9467662 1.12199998 0. 0.85159212 0.53429835 0.90830578 0.1651062 ] [ 0.39263926 0.73513877 0.48605697 0.51350109 0.27042981 0.85159212 0. 0.41507505 0.16091134 0.71215345] [ 0.38982854 0.80796679 0.22453123 0.78044594 0.66189707 0.53429835 0.41507505 0. 0.54198973 0.370672 ] [ 0.39228612 0.64687549 0.64173589 0.36885259 0.27709162 0.90830578 0.16091134 0.54198973 0. 0.78707458] [ 0.44529689 0.73308548 0.55440442 0.88113793 0.98097303 0.1651062 0.71215345 0.370672 0.78707458 0. ]]
Explanation:
In the above code –
a = np.random.random((10,2)): This line creates a 10x2 array a with random floating-point values between 0 and 1 using the np.random.random() function.
x, y = np.atleast_2d(a[:,0], a[:,1]): This line separates the two columns of a into two 1D arrays and converts them into 2D arrays with shape (10,1) using the np.atleast_2d() function. x contains the first column of a and y contains the second column of a.
d = np.sqrt( (x-x.T)**2 + (y-y.T)**2): This line computes the Euclidean distance between all pairs of points (rows) in a using the following steps:
- x-x.T and y-y.T compute the difference between all pairs of x and y coordinates, respectively. Since x and y have shape (10,1), subtracting their transposes (with shape (1,10)) results in broadcasting, producing two 10x10 arrays where each element represents the difference in x or y coordinates between a pair of points.
- (x-x.T)**2 and (y-y.T)**2 square each element of the resulting arrays from the previous step.
- (x-x.T)**2 + (y-y.T)**2 adds the squared differences element-wise, resulting in a 10x10 array where each element represents the squared Euclidean distance between a pair of points.
- np.sqrt() computes the square root of each element in the resulting array, resulting in a 10x10 array d where each element represents the Euclidean distance between a pair of points in a.
Python-Numpy Code Editor: