[Term Entry] PyTorch Tensor Operations: .frac() #7502 (#7674)

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* [Term Entry] PyTorch Tensor Operations: .frac()

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Author: mamtawardhani

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

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+---
+Title: 'frac()'
+Description: 'Returns the fractional part of each element in a PyTorch tensor.'
+Subjects:
+  - 'Computer Science'
+  - 'Data Science'
+Tags:
+  - 'Methods'
+  - 'Tensor'
+CatalogContent:
+  - 'learn-pytorch'
+  - 'intro-to-py-torch-and-neural-networks'
+  - 'learn-python-3'
+---
+
+In PyTorch, the **`torch.frac()`** function returns the **fractional part** of each element in a tensor. It removes the integer component and keeps only the decimal part. The fractional part preserves the sign of the original number, so negative values will have negative fractional parts.
+
+Mathematically, for each element `x` in the tensor:
+
+$$
+\text{out}_i = \text{input}_i - \lfloor | \text{input}_i | \rfloor \cdot \text{sgn}(\text{input}_i)
+$$
+
+## Syntax
+
+```pseudo
+torch.frac(input, *, out=None) → Tensor
+```
+
+**Parameters:**
+
+- `input`: The input tensor.
+- `out` (optional): Output tensor to store the result.
+
+**Return value:**
+
+A tensor of the same shape as the input, containing only the fractional parts of the elements.
+
+## Example 1: Fractional Part of a 1D Tensor
+
+This example shows how to extract fractional parts from a 1D tensor with positive and negative values:
+
+```py
+import torch
+
+x = torch.tensor([1.5, -2.7, 3.0, -4.9])
+result = torch.frac(x)
+print(result)
+```
+
+This example results in the following output:
+
+```shell
+tensor([ 0.5000, -0.7000,  0.0000, -0.9000])
+```
+
+## Example 2: Fractional Part of a 2D Tensor
+
+This example demonstrates computing fractional parts for elements in a 2D tensor (matrix):
+
+```py
+import torch
+
+x = torch.tensor([[2.3, -3.8],
+                  [4.0, -5.1]])
+print(torch.frac(x))
+```
+
+This example results in the following output:
+
+```shell
+tensor([[ 0.3000, -0.8000],
+        [ 0.0000, -0.1000]])
+```
+
+## Example 3: Using `out` Parameter
+
+This example shows how to use the `out` parameter to store results directly in a preallocated tensor:
+
+```py
+import torch
+
+x = torch.tensor([6.25, -7.75, 0.0])
+out_tensor = torch.empty_like(x)
+torch.frac(x, out=out_tensor)
+print(out_tensor)
+```
+
+This example results in the following output:
+
+```shell
+tensor([ 0.2500, -0.7500,  0.0000])
+```
+
+## Frequently Asked Questions
+
+### 1. What does `.frac()` do in PyTorch?
+
+The `torch.frac()` function extracts the fractional (decimal) part of each element in a tensor while removing the integer part.
+
+### 2. Does `.frac()` always return positive values?
+
+No. The fractional part preserves the sign of the original number. For example:
+
+```py
+import torch
+print(torch.frac(torch.tensor([-2.7])))  # tensor(-0.7000)
+```
+
+### 3. When would you use `.frac()`?
+
+- To isolate decimal values in data preprocessing.
+- For scientific computing when the fractional part of values is relevant.
+- In testing and numerical analysis to study non-integer behavior of data.