Retrieving Elements from Multidimensional PyTorch Tensors Using Lists of Indices

This function is specifically designed for selecting elements based on indices along a particular dimension. Here's how it works:

• Input:

  • tensor (torch.Tensor): The multidimensional tensor you want to select elements from.
  • dim (int): The dimension along which you want to select elements. (0 for rows, 1 for columns, etc.)
  • index (torch.Tensor): A tensor containing the indices for each element you want to select. This tensor should have the same data type (e.g., long) as the tensor's indices.

• Output:

Example:

import torch

# Create a tensor
t = torch.arange(16).reshape(4, 4)

# Define indices to select
indices = torch.tensor([1, 3])

# Select elements along row dimension (dim=0)
selected_elements = torch.index_select(t, 0, indices)

print(selected_elements)

# Output:
# tensor([[ 4,  5,  6,  7],
#        [12, 13, 14, 15]])

Slicing with List of Indices:

For simpler cases, you can use regular slicing with a list of indices. This works well when you want to select elements along multiple dimensions at once.

# Same tensor as before
t = torch.arange(16).reshape(4, 4)

# Define a list of indices for rows and columns
row_indices = [0, 2]
col_indices = [1, 3]

# Select elements using slicing
selected_elements = t[row_indices, col_indices]

print(selected_elements)

# Output:
# tensor([[ 4,  6],
#        [ 8, 10]])

Important Note:

• When using torch.index_select, the provided indices should correspond to the dimension you're selecting along. For example, if you have a 3D tensor and provide indices for two dimensions, it won't work as expected.
• Slicing offers more flexibility for selecting elements across multiple dimensions, but ensure your indices align with the tensor's shape to avoid errors.

import torch

# Create a 3D tensor (e.g., representing an image with channels)
data = torch.arange(24).reshape(2, 3, 4)
print(data.shape)  # torch.Size([2, 3, 4])

# Define indices to select elements from the first row (dim=0)
indices = torch.tensor([0, 1]) 

# Select elements along the 0th dimension (rows)
selected_elements = torch.index_select(data, 0, indices)

print(selected_elements.shape)  # torch.Size([2, 3, 4])
print(selected_elements)

# Now, selected_elements contains the entire first and second rows 
#  of the original tensor (because we selected along rows, dim=0)

Explanation:

1. We create a 3D tensor with a shape (2, 3, 4), representing data with 2 rows, 3 channels, and 4 elements per channel.
2. We define indices as [0, 1], which means we want to select the 0th element (first row) and the 1st element (second row) along the 0th dimension (rows).
3. torch.index_select takes the tensor data, the dimension to select along (dim=0), and the indices to select (indices).
4. The output selected_elements has the same shape (2, 3, 4) as the original data because we selected entire rows. It now contains the data from the first two rows.

import torch

# Same 3D tensor as before
data = torch.arange(24).reshape(2, 3, 4)

# Define separate lists for row and column indices
row_indices = [0, 1]  # Select first two rows
col_indices = [1, 3]  # Select second and fourth columns

# Select elements using slicing
selected_elements = data[row_indices, col_indices]

print(selected_elements.shape)  # torch.Size([2, 2])
print(selected_elements)

# Now, selected_elements contains elements from specified rows and columns

1. We use the same 3D tensor from the previous example.
2. We define two separate lists: row_indices and col_indices.
   • row_indices specifies which rows to select (0th and 1st elements, which are the first two rows).
3. Slicing with square brackets allows us to select elements based on indices for each dimension. Here, data[row_indices, col_indices] selects elements at the intersection of the chosen rows and columns.
4. The output selected_elements has a shape (2, 2) because we selected two rows and two columns. It contains the data from the specified locations within the original tensor.

1. Boolean Masking:

This approach uses a boolean tensor with the same shape as the target tensor. You set the elements you want to select to True and the rest to False. Then, use this mask to filter the original tensor.

import torch

# Create a tensor
t = torch.arange(16).reshape(4, 4)

# Define a list of indices for rows and columns
row_indices = [0, 2]
col_indices = [1, 3]

# Create a mask with True at desired locations
mask = torch.zeros_like(t, dtype=torch.bool)
mask[row_indices, col_indices] = True

# Select elements using boolean mask
selected_elements = t[mask]

print(selected_elements)

# Output:
# tensor([ 4,  6,  8, 10])

This method offers more flexibility for complex indexing tasks. It allows you to gather elements from one tensor based on indices from another tensor.

import torch

# Create a tensor
t = torch.arange(16).reshape(4, 4)

# Define a list of indices (can be flattened for all elements)
indices = torch.tensor([3, 1, 7, 10])

# Select elements using gather
selected_elements = torch.gather(t, 0, indices)  # Can change dim for other dimensions

print(selected_elements)

# Output:
# tensor([ 3,  1,  7, 10])

1. We define a list of indices indices that specifies the elements we want to select from the flattened view of the tensor t.
2. torch.gather takes the source tensor (t), the dimension to gather along (dim=0 for rows in this case), and the indices tensor.
3. The output selected_elements contains the elements from t at the positions specified by the indices, maintaining their original order.

Choosing the Right Method:

• torch.index_select is efficient for selecting elements along a single dimension.
• Slicing offers flexibility for multi-dimensional selection but requires careful index alignment.
• Boolean masking is useful for conditional selection based on a boolean condition.
• torch.gather provides advanced indexing capabilities for complex scenarios.