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

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

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+---
+Title: '.abs()'
+Description: 'Computes the absolute value of each element in a PyTorch tensor, returning the magnitude for complex numbers.'
+Subjects:
+  - 'Computer Science'
+  - 'Data Science'
+Tags:
+  - 'Deep Learning'
+  - 'Methods'
+  - 'Programming'
+  - 'PyTorch'
+CatalogContent:
+  - 'intro-to-py-torch-and-neural-networks'
+  - 'paths/data-science'
+---
+
+The **`.abs()`** method in PyTorch computes the absolute value of each [tensor](https://www.codecademy.com/resources/docs/pytorch/tensors) element. For real numbers, it returns the non-negative value. For complex numbers, it calculates the magnitude using √(real² + imag²). This method is useful in data preprocessing, signal processing, and mathematical transformations.
+
+## Syntax
+
+```pseudo
+torch.abs(input)
+```
+
+- `input` (Tensor): The input tensor (can be real or complex).
+
+The `.abs()` method returns a tensor where each element is the absolute value of the matching element in the input tensor.
+
+## Example
+
+This example shows how to use the `.abs()` method to compute absolute values for both real and complex tensors:
+
+```py
+import torch
+
+# Define a tensor with real and complex numbers
+tensor = torch.tensor([[-3.0, 2.5], [1 - 2j, 3 + 4j]])
+
+# Compute absolute values
+abs_tensor = tensor.abs()
+
+print("Original Tensor:")
+print(tensor)
+
+print("\nAbsolute Values:")
+print(abs_tensor)
+```
+
+This example results in the following output:
+
+```shell
+Original Tensor:
+tensor([[-3.0000+0.j,  2.5000+0.j],
+        [1.0000-2.j, 3.0000+4.j]])
+
+Absolute Values:
+tensor([[3.0000, 2.5000],
+        [2.2361, 5.0000]])
+```
+
+In this example:
+
+- **Real numbers**: -3.0 becomes 3.0, 2.5 remains 2.5.
+- **Complex numbers**: 1 - 2j → √(1² + (-2)²) ≈ 2.2361; 3 + 4j → √(3² + 4²) = 5.0