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

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

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+---
+Title: '.div()'
+Description: 'Performs element-wise division of tensors or divides a tensor by a scalar.'
+Subjects:
+  - 'Computer Science'
+  - 'Machine Learning'
+Tags:
+  - 'Neural Networks'
+  - 'PyTorch'
+  - 'Tensor'
+CatalogContent:
+  - 'learn-python-3'
+  - 'paths/machine-learning'
+---
+
+The **`.div()`** function performs element-wise division between tensors or divides a tensor by a scalar value. It is a fundamental tensor operation in [PyTorch](https://www.codecademy.com/resources/docs/pytorch) that is widely used in various machine learning and deep learning applications, including data preprocessing, normalization, and optimization algorithms.
+
+Element-wise operations are crucial in tensor computations as they allow for efficient parallel processing of data. The `.div()` function provides a simple and optimized way to perform division operations on tensors, which is often required in neural network implementations and mathematical transformations.
+
+## Syntax
+
+```pseudo
+torch.div(input, other, *, rounding_mode=None, out=None)
+```
+
+**Parameters:**
+
+- `input`: The input tensor (dividend).
+- `other`: The tensor or scalar to divide by (divisor).
+- `rounding_mode` (Optional): Controls the rounding behavior. Can be `None`, `trunc`, or `floor`.
+- `out` (Optional): The output tensor to store the result.
+
+**Return value:**
+
+Returns a new tensor with the result of the division operation unless `out` is specified.
+
+## Example 1: Basic Usage of `.div()` with tensors
+
+Let's start with a basic example to understand how `.div()` works with PyTorch tensors:
+
+```py
+import torch
+
+# Create input tensors
+tensor1 = torch.tensor([4.0, 9.0, 16.0, 25.0])
+tensor2 = torch.tensor([2.0, 3.0, 4.0, 5.0])
+
+# Perform element-wise division
+result = torch.div(tensor1, tensor2)
+
+# Print results
+print("Tensor1 (dividend):", tensor1)
+print("Tensor2 (divisor):", tensor2)
+print("Division result:", result)
+```
+
+This example results in the following output:
+
+```shell
+Tensor1 (dividend): tensor([ 4.,  9., 16., 25.])
+Tensor2 (divisor): tensor([2., 3., 4., 5.])
+Division result: tensor([2., 3., 4., 5.])
+```
+
+The `.div()` operation computes the element-wise division of `tensor1` by `tensor2`. Each element in the resulting tensor is the quotient of the corresponding elements in the input tensors.
+
+## Example 2: Division with Rounding Modes
+
+The `.div()` function supports different rounding modes, which can be useful in specific scenarios:
+
+```py
+import torch
+
+# Create input tensors
+tensor1 = torch.tensor([5, 7, 10, 15])
+tensor2 = torch.tensor([2, 2, 3, 4])
+
+# Division with different rounding modes
+result_default = torch.div(tensor1, tensor2)
+result_floor = torch.div(tensor1, tensor2, rounding_mode='floor')
+result_trunc = torch.div(tensor1, tensor2, rounding_mode='trunc')
+
+# Print results
+print("Default division:", result_default)
+print("Floor division:", result_floor)
+print("Trunc division:", result_trunc)
+```
+
+This example results in the following output:
+
+```shell
+Default division: tensor([2.5000, 3.5000, 3.3333, 3.7500])
+Floor division: tensor([2, 3, 3, 3])
+Trunc division: tensor([2, 3, 3, 3])
+```
+
+The rounding modes control how the division results are handled:
+
+- Default mode performs true division (floating-point result)
+- `floor` mode rounds down to the nearest integer
+- `trunc` mode truncates the decimal part (rounds toward zero)
+
+## Example 3: Data Normalization with `.div()`
+
+The `.div()` function is commonly used in data preprocessing and normalization. Here's an example of normalizing a dataset:
+
+```py
+import torch
+
+# Create a sample dataset (3 samples with 4 features each)
+dataset = torch.tensor([
+    [10.0, 20.0, 30.0, 40.0],
+    [15.0, 25.0, 35.0, 45.0],
+    [20.0, 30.0, 40.0, 50.0]
+])
+
+# Calculate the range (max - min) for each feature
+feature_min = dataset.min(dim=0).values
+feature_max = dataset.max(dim=0).values
+feature_range = feature_max - feature_min
+
+# Normalize the dataset to [0, 1] range using div
+normalized_data = torch.div(dataset - feature_min, feature_range)
+
+print("Original dataset:")
+print(dataset)
+print("\nNormalized dataset:")
+print(normalized_data)
+```
+
+This example results in the following output:
+
+```shell
+Original dataset:
+tensor([[10., 20., 30., 40.],
+        [15., 25., 35., 45.],
+        [20., 30., 40., 50.]])
+
+Normalized dataset:
+tensor([[0.0000, 0.0000, 0.0000, 0.0000],
+        [0.5000, 0.5000, 0.5000, 0.5000],
+        [1.0000, 1.0000, 1.0000, 1.0000]])
+```
+
+This example demonstrates how `.div()` can be used to normalize data to a specific range, which is a common preprocessing step in machine learning workflows.