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

* Added term entry for Pytorch's .copysign function

* Corrected formatting errors in copysign.md  before making a PR

* Update copysign.md

* Update copysign.md

* Update copysign.md

---------

Author: JGVSAI16

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

@@ -0,0 +1,93 @@
+---
+Title: '.copysign()'
+Description: 'Returns a tensor with the magnitude of the first input and the sign of the second input, element-wise.'
+Subjects:
+  - 'AI'
+  - 'Data Science'
+Tags:
+  - 'Functions'
+  - 'PyTorch'
+  - 'Tensor'
+CatalogContent:
+  - 'learn-pytorch'
+  - 'paths/data-science'
+---
+
+PyTorch's **`.copysign()`** function creates a new tensor by combining the magnitude of the first input with the sign of the second input, element-wise.
+
+> **Note:** If the first input contains booleans, they are cast to floats (`True` becomes `1.0`, `False` becomes `0.0`). `-0.0` or `-0` in the second input is treated as a negative sign, while `0.0` or `0` is treated as positive, and these signs are preserved when copied.
+
+## Syntax
+
+```pseudo
+torch.copysign(input, other, *, out=None)
+```
+
+**Parameters:**
+
+- `input` (Tensor): The input tensor providing magnitudes.
+- `other` (Tensor): The tensor whose sign will be copied to input. Must be broadcastable to the shape of `input`.
+- `out` (Tensor, optional): The tensor to store the output. Must have the same shape as the broadcasted result.
+
+> **Note:** The tensors must be [broadcastable](https://www.codecademy.com/resources/docs/numpy/array-broadcasting) in order to perform the operation. Otherwise, this will result in a `RuntimeError`.
+
+**Return value:**
+
+A tensor where each element has the absolute value of the corresponding element in `input` and the sign of the corresponding element in `other`.
+
+## Example 1
+
+This example shows how to copy signs from the `signs` tensor to the `magnitudes` tensor using `.copysign()`:
+
+```py
+import torch
+
+# Initializing tensors
+magnitudes = torch.tensor([-5.0, True, -8.0])
+signs = torch.tensor([-0.0, 0.0, 3.0])
+
+# Using torch.copysign to copy the sign from 'signs' to 'magnitudes'
+result = torch.copysign(magnitudes, signs)
+print(result)
+```
+
+The output of this code is:
+
+```shell
+tensor([-5., 1., 8.])
+```
+
+## Example 2
+
+This example shows how to copy the sign from a one-dimensional `signs` tensor to a two-dimensional `magnitudes` tensor using broadcasting. Each row of `magnitudes` is aligned with the corresponding value in `signs`, and the sign is applied column-wise:
+
+```py
+import torch
+
+torch.manual_seed(0)
+
+# Create a 3x3 tensor of magnitudes
+magnitudes = torch.rand(3, 3)
+print("Magnitudes:\n", magnitudes)
+
+# 1D tensor whose signs will be broadcast across rows
+signs = torch.tensor([0.6323, 0.3489, -0.4017])
+
+# Apply copysign with broadcasting
+result = torch.copysign(magnitudes, signs)
+print("\nResult:\n", result)
+```
+
+The output of this code is:
+
+```shell
+Magnitudes:
+ tensor([[0.4963, 0.7682, 0.0885],
+        [0.1320, 0.3074, 0.6341],
+        [0.4901, 0.8964, 0.4556]])
+
+Result:
+ tensor([[ 0.4963,  0.7682, -0.0885],
+        [ 0.1320,  0.3074, -0.6341],
+        [ 0.4901,  0.8964, -0.4556]])
+```