Detailed explanation of the use examples of cdist and sum functions in PyTorch

It is a function used in PyTorch to calculate the pairwise distance between two tensors. It is often used in point cloud processing, graph neural networks, similarity measurement and other scenarios.

Basic syntax

(x1, x2, p=2.0)

Parameter description:

Output

The output is a tensor with a shape:

• if = [M, D]and = [N, D], the output shape is[M, N]；
• Each(i, j)Position representationx1[i]andx2[j]The distance between.

Example

1. Simple 2D Euclidean distance

import torch
x1 = ([[0.0, 0.0], [1.0, 0.0]])  # 2 pointsx2 = ([[0.0, 1.0], [1.0, 1.0]])  # 2 pointsdist = (x1, x2, p=2)
print(dist)

The output is:

tensor([[1.0000, 1.4142],
        [1.4142, 1.0000]])

Right now:

• The distance between x1[0] and x2[0] is 1;
• The distance between x1[0] and x2[1] is sqrt(2), etc.

2. Bulk form (3D Tensor)

x1 = (2, 5, 3)  # batch=2, 5 3D points per groupx2 = (2, 4, 3)  # batch=2, 4 3D points per groupout = (x1, x2)  # The output shape is [2, 5, 4]

3. Use different norms

(x1, x2, p=1)   # Manhattan Distance(x1, x2, p=2)   # Euclidian distance (default)(x1, x2, p=inf) # Maximum Dimensional Difference

Things to note

• x1andx2The last dimension (feature dimension) of   must be the same.
• p=2The most efficient time, other norms may be slower.
• If both tensors are large, this operation can be very memory-consuming.

Examples of application scenarios

• Distance calculation between point clouds (such as ISS, FPFH, ICP)
• The distance graph construction of matching point pairs
• KNN query
• Graph construction (adjacent matrix, compatibility matrix)

It is a function used in PyTorch to sum tensor elements, and its function is similar to that in NumPy, but you can choose dimensions more flexibly to operate.

Basic usage

(input, dim=None, keepdim=False)

Parameter description:

• input: Tensors to be summed;
• dim(Optional): Specify the dimension in which sum is performed;
• keepdim(Optional): Boolean value, whether to retain the summed dimension (not retained by default).

Sample explanation

Example 1: Sum all elements

x = ([[1, 2], [3, 4]])
(x)
# Output：tensor(10)

Example 2: Specify dimension sum

x = ([[1, 2], [3, 4]])
(x, dim=0)  # Sum by column: 1+3, 2+4# Output: tensor([4, 6])(x, dim=1)  # Sum by line: 1+2, 3+4# Output：tensor([3, 7])

Example 3: Preserve the dimension

x = ([[1, 2], [3, 4]])
(x, dim=1, keepdim=True)
# Output：tensor([[3], [7]])

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