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

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

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+---
+Title: '.logaddexp()'
+Description: 'Computes the element-wise logarithm of the sum of exponentials of two input tensors.'
+Subjects:
+  - 'Code Foundations'
+  - 'Computer Science'
+  - 'Data Science'
+Tags:
+  - 'Elements'
+  - 'Methods'
+  - 'PyTorch'
+  - 'Tensors'
+CatalogContent:
+  - 'learn-python-3'
+  - 'paths/data-science'
+---
+
+The **`.logaddexp()`** function in PyTorch computes the point-wise value of:
+
+$$\log(\exp(x) + \exp(y))$$
+
+for two input tensors `x` and `y`. This operation is particularly useful for combining log-space values (such as log-probabilities) in a numerically stable way.
+
+## Syntax
+
+```pseudo
+torch.logaddexp(input, other, *, out=None) → Tensor
+```
+
+**Parameters:**
+
+- `input` (Tensor): The first input tensor.
+- `other` (Tensor): The second input tensor, broadcastable to the shape of `input`.
+- `out` (Tensor, optional): A tensor to store the output; must have the same shape as the broadcasted result if provided.
+
+**Return value:**
+
+Returns a new tensor of the same shape as the broadcasted `input` and `other`, where each element is:
+
+$$\log\left(\exp(\text{input}[i]) + \exp(\text{other}[i])\right)$$
+
+## Example 1: Combining log-probabilities
+
+In this example, two tensors representing log-probabilities are combined using `.logaddexp()`:
+
+```py
+import torch
+
+x = torch.tensor([ -0.5,  -1.2,  -3.0 ])
+y = torch.tensor([ -0.2,  -0.8,  -4.5 ])
+
+result = torch.logaddexp(x, y)
+print(result)
+```
+
+The ouput of this code is:
+
+```shell
+tensor([ 0.3544, -0.2870, -2.7986])
+```
+
+## Example 2: Broadcasting two tensors of different shapes
+
+In this example, a tensor and a scalar are combined with broadcasting using `.logaddexp()`:
+
+```py
+import torch
+
+x = torch.tensor([[ 1.0, 2.0 ,3.0],
+                  [ 4.0, 5.0 ,6.0]])
+y = torch.tensor( 2.0 )
+
+result = torch.logaddexp(x, y)
+print(result)
+```
+
+The output of this code is:
+
+```shell
+tensor([[2.3133, 2.6931, 3.3133],
+        [4.1269, 5.0486, 6.0181]])
+```