[Term Entry] PyTorch Tensor Operations: .hypot()

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

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+---
+Title: '.hypot()'
+Description: 'Calculates the hypotenuse of a right triangle given the lengths of its two legs.'
+Subjects:
+  - 'AI'
+  - 'Computer Science'
+  - 'Data Science'
+Tags: 
+  - 'AI'
+  - 'Functions'
+  - 'Pytorch'
+  - 'Trigonometry'
+CatalogContent: 
+  - 'intro-to-py-torch-and-neural-networks'
+  - 'paths/data-science'
+---
+
+The **`torch.hypot`** function in PyTorch calculates the hypotenuse of right triangles, given the lengths of the two legs.
+
+Element-wise, `torch.hypot()` computes:
+
+$$
+\text{out}_i = \sqrt{(\text{input}_i)^2 + (\text{other}_i)^2}
+$$
+
+## Syntax
+
+```pseudo
+torch.hypot(input, other, *, out=None)
+```
+
+**Parameters:**
+
+- `input`: The first input tensor.
+- `other`: The second input tensor. This must be broadcastable with `input`.
+- `out` (Optional): The output tensor to store the result.
+
+**Return value**
+
+Returns a tensor containing the element-wise Euclidean norm: $\sqrt{(\text{input}_i)^2 + (\text{other}_i)^2}$.
+
+## Example 1: Basic Element-Wise Hypotenuse
+
+In this example, `torch.hypot()` calculates the hypotenuse for corresponding elements of two 1D tensors:
+
+```py
+import torch
+
+# Create input tensors
+x = torch.tensor ([3.0, 5.0, 8.0])
+y = torch.tensor ([4.0, 12.0, 15.0])
+
+# Perform element-wise operation
+hypotenuse = torch.hypot(x, y)
+
+# Print the result
+print(hypotenuse)
+```
+
+This code would output the following:
+
+```shell
+tensor([5., 13., 17.])
+```
+
+## Example 2L 2D Distance Between Points
+
+In this example, `torch.hypot()` calculates the distance from the origin for 2D points stored as x, y coordinates:
+
+```py
+import torch
+
+# For the following array:
+points = torch.tensor([
+    [3.0], [4.0],
+    [5.0], [12.0],
+    [8.0], [15.0],
+])
+
+# Split into x and y columns:
+x = points[:, 0]
+y = points[:, 1]
+
+distances = torch.hypot(x, y)
+print(distances)
+```
+
+This will output:
+
+```shell
+tensor([ 5., 13., 17. ])
+```
+
+This example organizes the `6 x 1` tensor into `x, y` pairs, and calculates each one individually:
+
+- $\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt {25} = 5$
+- $\sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt {169} = 13$
+- $\sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt {289} = 17$