[Term Entry] PyTorch Tensor Operations: .addcmul() (#6330)

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

* fixed lint and format

* added backlink

* Update content/pytorch/concepts/tensor-operations/terms/addcmul/addcmul.md



* Update content/pytorch/concepts/tensor-operations/terms/addcmul/addcmul.md



* Update addcmul.md

---------

Author: mamtawardhani

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

@@ -0,0 +1,163 @@
+---
+Title: '.addcmul()'
+Description: 'Performs element-wise multiplication of two tensors and adds a scaled result to a third tensor.'
+Subjects:
+  - 'Computer Science'
+  - 'Machine Learning'
+Tags:
+  - 'Deep Learning'
+  - 'PyTorch'
+  - 'Tensors'
+CatalogContent:
+  - 'learn-python-3'
+  - 'paths/machine-learning'
+---
+
+**`.addcmul()`** is a PyTorch [tensor](https://www.codecademy.com/resources/docs/pytorch/tensors) operation that performs element-wise multiplication of two tensors and then adds a third tensor to the result, optionally scaled by a value. This operation combines multiplication and addition in a single efficient function call.
+
+The function is particularly useful in tensor operations where there is a need to perform element-wise multiplication and addition in sequence. It provides a concise way to perform these operations without creating intermediate tensors, which can help optimize memory usage in PyTorch applications.
+
+## Syntax
+
+```pseudo
+torch.addcmul(input, tensor1, tensor2, value=1, out=None)
+```
+
+**Parameters:**
+
+- `input` (Tensor): The tensor to be added to the result
+- `tensor1` (Tensor): The first tensor to be multiplied element-wise
+- `tensor2` (Tensor): The second tensor to be multiplied element-wise
+- `value` (Number, optional): Multiplier for the product of `tensor1` and `tensor2`. Default value is `1`
+- `out` (Tensor, optional): The output tensor to store the result
+
+**Return value:**
+
+Returns a new tensor containing the result of the operation, or modifies the `out` tensor if provided.
+
+## Example 1: Basic usage of `.addcmul()` with PyTorch tensors
+
+This example demonstrates the basic functionality of `.addcmul()` by applying it to random tensors to show how the element-wise multiplication and addition works:
+
+```py
+import torch
+
+# Create input tensor and two tensors to be multiplied
+input_tensor = torch.tensor([1.0, 2.0, 3.0])
+tensor1 = torch.tensor([2.0, 3.0, 4.0])
+tensor2 = torch.tensor([3.0, 2.0, 1.0])
+
+# Apply addcmul operation
+# Formula: result = input + value * (tensor1 * tensor2)
+result = torch.addcmul(input_tensor, tensor1, tensor2)
+
+# Display the tensors and result
+print("Input tensor:", input_tensor)
+print("Tensor 1:", tensor1)
+print("Tensor 2:", tensor2)
+print("Result of addcmul (default value=1):", result)
+
+# Try with a different value parameter
+scaled_result = torch.addcmul(input_tensor, tensor1, tensor2, value=0.5)
+print("Result of addcmul with value=0.5:", scaled_result)
+```
+
+This example results in the following output:
+
+```shell
+Input tensor: tensor([1., 2., 3.])
+Tensor 1: tensor([2., 3., 4.])
+Tensor 2: tensor([3., 2., 1.])
+Result of addcmul (default value=1): tensor([7., 8., 7.])
+Result of addcmul with value=0.5: tensor([4., 5., 5.])
+```
+
+## Example 2: Using `.addcmul()` with different scale values
+
+This example demonstrates how `.addcmul()` behaves with different scale values:
+
+```py
+import torch
+
+# Create three simple tensors
+input_tensor = torch.tensor([1.0, 2.0, 3.0])
+tensor1 = torch.tensor([2.0, 3.0, 4.0])
+tensor2 = torch.tensor([3.0, 2.0, 1.0])
+
+# Apply addcmul with different scale values
+result1 = torch.addcmul(input_tensor, tensor1, tensor2, value=1.0)
+result2 = torch.addcmul(input_tensor, tensor1, tensor2, value=0.5)
+result3 = torch.addcmul(input_tensor, tensor1, tensor2, value=2.0)
+
+# Print results
+print("Input tensor:", input_tensor)
+print("Tensor 1:", tensor1)
+print("Tensor 2:", tensor2)
+print("\naddcmul with value=1.0:", result1)
+print("addcmul with value=0.5:", result2)
+print("addcmul with value=2.0:", result3)
+
+# Show the calculations step by step
+print("\nCalculation steps for first element with value=1.0:")
+print(f"input[0] + value * (tensor1[0] * tensor2[0]) = {input_tensor[0]} + 1.0 * ({tensor1[0]} * {tensor2[0]}) = {result1[0]}")
+```
+
+This example results in the following output:
+
+```shell
+Input tensor: tensor([1., 2., 3.])
+Tensor 1: tensor([2., 3., 4.])
+Tensor 2: tensor([3., 2., 1.])
+
+addcmul with value=1.0: tensor([7., 8., 7.])
+addcmul with value=0.5: tensor([4., 5., 5.])
+addcmul with value=2.0: tensor([13., 14., 11.])
+
+Calculation steps for first element with value=1.0:
+input[0] + value * (tensor1[0] * tensor2[0]) = 1.0 + 1.0 * (2.0 * 3.0) = 7.0
+```
+
+## Example 3: Combining `.addcmul()` with in-place operations
+
+This example shows how to use `.addcmul_()` (the in-place version) to modify tensors directly:
+
+```py
+import torch
+
+# Create tensors
+x = torch.tensor([1.0, 2.0, 3.0])
+y = torch.tensor([0.1, 0.2, 0.3])
+z = torch.tensor([1.5, 2.5, 3.5])
+
+print("Original x:", x)
+print("y:", y)
+print("z:", z)
+
+# Use addcmul with a new tensor to store results
+result = torch.addcmul(x, y, z, value=2.0)
+print("\nResult of torch.addcmul(x, y, z, value=2.0):", result)
+print("Original x is unchanged:", x)
+
+# Use the in-place version addcmul_
+x.addcmul_(y, z, value=2.0)
+print("\nAfter x.addcmul_(y, z, value=2.0), x is now:", x)
+
+# Verify that x now has the same values as result
+print("x now equals the previous result:", torch.equal(x, result))
+```
+
+This example results in the following output:
+
+```shell
+Original x: tensor([1., 2., 3.])
+y: tensor([0.1, 0.2, 0.3])
+z: tensor([1.5, 2.5, 3.5])
+
+Result of torch.addcmul(x, y, z, value=2.0): tensor([1.3000, 3.0000, 5.1000])
+Original x is unchanged: tensor([1., 2., 3.])
+
+After x.addcmul_(y, z, value=2.0), x is now: tensor([1.3000, 3.0000, 5.1000])
+x now equals the previous result: True
+```
+
+To learn more about how to create, train, and test neural networks, check out this [Intro to PyTorch and Neural Networks](https://www.codecademy.com/enrolled/courses/intro-to-py-torch-and-neural-networks) course on Codecademy.