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

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

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+---
+Title: '.sinc()'
+Description: 'Computes the normalized sinc function of each element in a PyTorch tensor.'
+Subjects:
+  - 'Computer Science'
+  - 'Data Science'
+  - 'Machine Learning'
+Tags:
+  - 'Deep Learning'
+  - 'Integers'
+  - 'Math'
+  - 'Python'
+  - 'Tensor'
+CatalogContent:
+  - 'intro-to-py-torch-and-neural-networks'
+  - 'paths/computer-science'
+---
+
+The **`.sinc()`** function in PyTorch computes the normalized sinc function of each element in the input [tensor](https://www.codecademy.com/resources/docs/pytorch/tensors). The operation is applied element-wise and is defined as:
+
+$$
+\[
+\text{sinc}(x) =
+\begin{cases}
+\dfrac{\sin(\pi x)}{\pi x}, & x \neq 0 \\
+1, & x = 0
+\end{cases}
+\]
+$$
+
+This function is widely used in signal processing, interpolation, and numerical analysis.
+
+## Syntax
+
+```pseudo
+torch.sinc(input, *, out=None) → Tensor
+```
+
+**Parameters:**
+
+- `input`: A tensor containing the input values.
+- `out` (optional): A tensor to store the output. If provided, the result is written into this tensor.
+
+**Return value:**
+
+Returns a new tensor where each element is the normalized sinc of the corresponding value in the input tensor.
+
+## Example 1: Basic Usage of `.sinc()` with 1D Tensor
+
+This example shows how `.sinc()` behaves for zero and non-zero values:
+
+```py
+import torch
+
+x = torch.tensor([-2.0, -1.0, 0.0, 1.0, 2.0])
+
+result = torch.sinc(x)
+
+print("Input:", x)
+print("sinc(x):", result)
+```
+
+The output of this code is:
+
+```shell
+Input: tensor([-2., -1.,  0.,  1.,  2.])
+sinc(x): tensor([ 2.7828e-08, -2.7828e-08,  1.0000e+00, -2.7828e-08,  2.7828e-08])
+```
+
+## Example 2: Applying `.sinc()` to a 2D Tensor
+
+This example demonstrates element-wise application of `.sinc()` on a 2D tensor:
+
+```py
+import torch
+
+values = torch.tensor([[0.0, 0.25],
+                        [0.5, 0.75]])
+
+result = torch.sinc(values)
+
+print("Input tensor:")
+print(values)
+print("\nSinc of tensor:")
+print(result)
+```
+
+The output of this code is as follows:
+
+```shell
+Input tensor:
+tensor([[0.0000, 0.2500],
+        [0.5000, 0.7500]])
+
+Sinc of tensor:
+tensor([[1.0000, 0.9003],
+        [0.6366, 0.3001]])
+```
+
+The `.sinc()` function preserves the shape of the input tensor and computes values using the normalized definition based on `π`.