.atan2()

The .atan2() function in PyTorch computes the element-wise arctangent of the quotient of two tensors. It is particularly useful in applications involving polar coordinates and can be visualized to understand its behavior across a range of input values. This function is commonly used to convert Cartesian coordinates to polar form by computing the angle (θ), making it especially useful in vector and trigonometric computations.

Syntax

torch.atan2(input, other, *, out=None)

Parameters:

• input: The first input tensor (numerator) containing values for which to calculate the arctangent.
• other: The second input tensor (denominator) containing values for which to calculate the arctangent.
• out (Optional): The output tensor to store the result. If provided, its shape must match with the shape that the inputs broadcast to.

Return value:

Returns a tensor of the same shape as input and other containing the arctangent of each element, with values in the range [-π, π] radians.

Example 1: Basic Usage of .atan2()

This example demonstrates how to apply the .atan2() function to two tensors and understand its output:

import torch

# Create two tensors with different values
x = torch.FloatTensor([1.0, -0.5, 3.4, 0.2, 0.0, -2])
y = torch.FloatTensor([0.0, 1.0, -1.0, 0.5, -0.5, 2.0])

print("Input tensors:")
print(x)
print(y)

# Apply the .atan2() function
result = torch.atan2(x, y)
print("\nArctangent of the input tensors:")
print(result)

to clipboard
Copy to clipboard

This example results in the following output:

Input tensors:
tensor([ 1.0000, -0.5000,  3.4000,  0.2000,  0.0000, -2.0000])
tensor([ 0.0000,  1.0000, -1.0000,  0.5000, -0.5000,  2.0000])

Arctangent of the input tensors:
tensor([-1.5708, -0.4636,  1.1659,  0.3805, -0.0000, -0.7854])

to clipboard
Copy to clipboard

In the output, it can be seen that the arctangent of (1.0, 0.0) is approximately -1.5708 radians (or -90 degrees), while the arctangent of (0.0, 1.0) is 0.0 radians (0 degrees).

Example 2: Visualizing the .atan2() Function

This example visualizes the .atan2() function to better understand its behavior across a range of input values:

import torch
import numpy as np
import matplotlib.pyplot as plt

# Generate values for x-axis (input values)
x = np.linspace(-10, 10, 100)
y = np.linspace(-10, 10, 100)

# Convert NumPy arrays to PyTorch tensors
x_tensor = torch.FloatTensor(x)
y_tensor = torch.FloatTensor(y)

# Calculate arctangent values
z_tensor = torch.atan2(x_tensor.unsqueeze(1), y_tensor.unsqueeze(0))
z = z_tensor.numpy()

# Create the plot
plt.figure(figsize=(8, 6))
plt.contourf(x, y, z, levels=100, cmap='viridis')
plt.colorbar(label='Arctangent')
plt.title('Arctangent Function Visualization')
plt.xlabel('X-axis')
plt.ylabel('Y-axis')
plt.grid(True)
plt.show()

to clipboard
Copy to clipboard

This example results in the following output: