Demystifying torch.sparse_csc_tensor: A Guide to Efficient Sparse Matrix Operations in PyTorch

What it is

• Sparse tensors represent matrices where most elements are zero. CSC is one way to store these matrices efficiently, focusing on the non-zero elements.
• torch.sparse_csc_tensor is a function in PyTorch that creates a sparse tensor in the Compressed Sparse Column (CSC) format.

How it works

• It takes four arguments:
  • ccol_indices (array-like): A (batch_size + 1)-dimensional array of size (*batch_size, ncols + 1). This array encodes the column indices of the non-zero elements in a compressed manner.
  • row_indices (array-like): An array of the same size as values, containing the row indices of the corresponding non-zero elements.
  • values (array-like): An array containing the actual values of the non-zero elements.
  • size (list, tuple, or torch.Size): The overall size of the sparse tensor.

Advantages of CSC format

• Sparse matrix multiplication operations are generally faster in CSC format compared to the Coordinate format (COO) that PyTorch uses by default. This is because CSC provides better cache locality for column-wise operations.

Important points

• PyTorch offers a separate library called torch_sparse that provides more advanced sparse tensor functionality, including efficient CSC operations. However, this library needs to be installed separately.
• torch.sparse_csc_tensor was introduced in PyTorch version 1.11.0. If you're using an older version, you might need to upgrade or consider using torch.sparse.SparseTensor with the csc layout (available since PyTorch 1.6).

Example

import torch

# Create a sparse CSC tensor
ccol_indices = torch.tensor([[0, 1, 2], [0, 2]])
row_indices = torch.tensor([0, 1, 0])
values = torch.tensor([3, 5, 2])
size = torch.Size([2, 3])

sparse_tensor = torch.sparse_csc_tensor(ccol_indices, row_indices, values, size)

print(sparse_tensor)

This code will create a sparse CSC tensor with the following structure:

[[3. 0. 2.]
 [5. 0. 0.]]

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Sparse Matrix Multiplication (CSC vs. COO)

This code compares the performance of sparse matrix multiplication using torch.sparse_csc_tensor and the default COO format in PyTorch:

import torch
import time

# Define sparse matrix dimensions and sparsity
n = 1000
m = 500
k = 200
density = 0.1  # Adjust for desired sparsity

# Create random sparse matrices (CSC and COO)
coo_indices = torch.sparse.random_sparse_coo(n, m, int(n * m * density))
csc_indices = coo_indices.to_csc()  # Convert COO to CSC
coo_values = coo_indices.values()
csc_values = csc_indices.values()

# Create dense matrices
A_dense = torch.randn(n, k)
B_dense = torch.randn(k, m)

# Measure execution times for multiplication
start_coo = time.time()
coo_result = coo_indices @ A_dense @ B_dense
end_coo = time.time()

start_csc = time.time()
csc_result = torch.sparse.mm(csc_indices, A_dense, B_dense)
end_csc = time.time()

print("COO multiplication time:", end_coo - start_coo)
print("CSC multiplication time:", end_csc - start_csc)

This code will show that CSC multiplication can be faster for sparse matrices with appropriate sparsity levels.

Converting between Sparse Formats

This code demonstrates converting a sparse tensor from one format (e.g., COO) to CSC:

import torch

# Create a sparse COO tensor
coo_indices = torch.sparse.random_sparse_coo(5, 5, 10)
coo_values = coo_indices.values()
size = coo_indices.size()

# Convert COO to CSC
csc_indices = coo_indices.to_csc()
csc_values = csc_indices.values()

# Create the sparse CSC tensor
sparse_csc_tensor = torch.sparse_csc_tensor(csc_indices, csc_values, size)

print("Original COO tensor:\n", coo_indices)
print("Converted CSC tensor:\n", sparse_csc_tensor)

Using torch_sparse library (if installed)

This code (assuming torch_sparse is installed) demonstrates using CSC operations:

import torch
from torch_sparse import SparseTensor

# Create sparse COO tensor
coo_indices = torch.sparse.random_sparse_coo(5, 5, 10)
coo_values = coo_indices.values()
size = coo_indices.size()

# Convert COO to CSC
sparse_tensor = SparseTensor(coo_indices, coo_values, size).csc()

# Sparse matrix multiplication with CSC operations
A_dense = torch.randn(size[0], size[1])
B_dense = torch.randn(size[1], size[2])
result = sparse_tensor.matmul(A_dense, B_dense)

print("Sparse matrix multiplication result:\n", result)

Remember that torch_sparse is a separate library and may require installation.

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torch.sparse.SparseTensor with csc layout

• May be a good choice if you already have a COO sparse tensor and want to convert it to CSC for specific operations.
• Available since PyTorch 1.6.
• This is the built-in PyTorch alternative to torch.sparse_csc_tensor. It offers the same functionality for creating and manipulating sparse tensors in the CSC format.

Using torch.sparse.mm

• Consider this if you don't need the explicit CSC representation and just want to perform the multiplication.
• This function performs sparse matrix multiplication directly on COO format sparse tensors. It can be efficient for many cases, especially if the sparsity pattern is well-suited for COO.

torch_sparse library (if installed)

• Consider this if you need advanced CSC operations beyond basic functionalities.
• The downside is that it requires separate installation.
• Offers a more comprehensive set of operations specifically designed for sparse tensors in various formats.
• This third-party library provides optimized sparse tensor operations, including a wider range of CSC functionality.

• Ease of use
  torch.sparse_csc_tensor and torch.sparse.SparseTensor with csc layout are directly integrated with PyTorch, while torch_sparse requires separate installation.
• Advanced CSC functionality
  If you require more specialized CSC operations not readily available in PyTorch, then torch_sparse becomes a good option.
• Operations
  If you primarily need sparse matrix multiplication, torch.sparse.mm with a COO tensor might suffice.
• PyTorch version
  If you're using an older version (pre-1.11.0), you don't have torch.sparse_csc_tensor and might need to rely on torch.sparse.SparseTensor with csc layout or torch.sparse.mm.