Create atan2 function in pytorch

content/pytorch/concepts/tensor-operations/terms/atan2/atan2.md

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+---
+Title: '.atan2()'
+Description: 'Computes the arctangent of the quotient of two tensors, element-wise.'
+Subjects:
+  - 'Data Science'
+  - 'Machine Learning'
+Tags:
+  - 'Deep Learning'
+  - 'Math'
+  - 'PyTorch'
+  - 'Tensors'
+CatalogContent:
+  - 'learn-python-3'
+  - 'paths/computer-science'
+---
+
+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
+
+```pseudo
+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:
+
+```py
+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)
+```
+
+This example results in the following output:
+
+```shell
+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])
+```
+
+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:
+
+```py
+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()
+```
+
+This example results in the following output:
+
+![A 2D plot, representing the output for the above .atan2() example, showing a smooth contour with labeled axes](https://raw.githubusercontent.com/Codecademy/docs/main/media/atan2_output1.png)