Unlocking Row Information in PyTorch Sparse Tensors: Exploring Alternatives to torch.sparse.Tensor.row_indices

Understanding Sparse Tensors

PyTorch offers two main sparse tensor formats: Coordinate List (COO) and Compressed Sparse Row (CSR).
Sparse tensors represent matrices where most elements are zero. They store only the non-zero elements and their corresponding indices, making them memory-efficient for large datasets with many zeros.

torch.sparse.Tensor.row_indices

It returns a LongTensor containing the indices of the first element in each row of the sparse matrix.
This attribute is specifically applicable to CSR format sparse tensors.

Key Points

Availability
Only for CSR format sparse tensors. COO format tensors don't have a direct equivalent for row_indices.
Data Type
LongTensor (torch.long)
Functionality
- row_indices provides a way to efficiently access the starting positions of each row's non-zero elements in the compressed format.
- This is useful for operations that require iterating over rows or performing row-wise computations.

Example

import torch

# Create a sparse CSR tensor
indices = torch.tensor([[0, 1, 2], [0, 0, 1]])
values = torch.tensor([3, 1, 2])
size = (2, 3)
sparse_tensor = torch.sparse_csr_tensor(indices, values, size)

# Access row indices
row_indices = sparse_tensor.crow_indices()
print(row_indices)  # Output: tensor([0, 1])

In essence

It's a valuable tool for sparse matrix operations that involve row-wise processing.
row_indices helps navigate the compressed structure of CSR tensors by providing starting points for each row's non-zero elements.

For more comprehensive sparse tensor manipulation, explore PyTorch's sparse functionality, including methods like sparse.mm for matrix multiplication and other sparse-specific operations.
If you're working with COO format sparse tensors, you might need to construct row information using torch.gather or similar operations to achieve row-wise access.

Accessing Elements by Row

This code shows how to use row_indices to iterate over rows and access their corresponding elements:

import torch

# Create a sparse CSR tensor
indices = torch.tensor([[0, 1, 2], [0, 0, 1]])
values = torch.tensor([3, 1, 2])
size = (2, 3)
sparse_tensor = torch.sparse_csr_tensor(indices, values, size)

# Get row indices
row_indices = sparse_tensor.crow_indices()

# Iterate over rows and access elements
for i, row_start in enumerate(row_indices):
  # Slice to get the non-zero elements in the current row
  row_elements = sparse_tensor.values[row_start: (row_indices[i + 1] if i < len(row_indices) - 1 else None)]
  print(f"Row {i}: {row_elements}")

This code iterates through row_indices and uses the starting index (inclusive) for each row to slice the values tensor. This way, it extracts the non-zero elements belonging to that specific row.

Row-wise Operations (Using torch.gather for COO)

This example demonstrates how to achieve row-wise operations even with a COO format sparse tensor:

import torch

# Create a sparse COO tensor
indices = torch.tensor([[0, 1, 2], [0, 0, 1]])
values = torch.tensor([3, 1, 2])
size = (2, 3)
sparse_tensor = torch.sparse_coo_tensor(indices, values, size)

# Simulate row-wise operation (e.g., adding a constant to each row)
def row_wise_add(sparse_tensor, constant):
  row_indices = sparse_tensor.indices[0]  # Get row indices from COO
  unique_rows, row_counts = torch.unique(row_indices, return_counts=True)
  updated_values = torch.zeros(sparse_tensor.shape[0])  # Create a dense tensor for updates
  for i, row in enumerate(unique_rows):
    start = row_counts[:i].sum()  # Calculate starting index for the row
    end = start + row_counts[i]
    updated_values[row] = sparse_tensor.values[start:end] + constant  # Add constant to row elements
  return torch.sparse_coo_tensor(sparse_tensor.indices, updated_values, size)

# Apply row-wise addition
updated_tensor = row_wise_add(sparse_tensor, 5)
print(updated_tensor)

This code constructs a workaround for COO tensors. It extracts row indices, calculates starting positions for each row using torch.unique and torch.cumsum, and then iterates over rows to perform the desired operation (adding a constant in this case) on the corresponding elements in the values tensor. Finally, it creates a new sparse COO tensor with the updated values.

COO Format Sparse Tensors

Since COO format doesn't have a direct equivalent to row_indices, you can achieve row-wise access by manually constructing row information:
- Use torch.gather to collect non-zero elements belonging to a specific row based on the corresponding row index in the indices tensor.
- Iterate through the unique row indices to process each row individually.

import torch

# Create a sparse COO tensor
indices = torch.tensor([[0, 1, 2], [0, 0, 1]])
values = torch.tensor([3, 1, 2])
size = (2, 3)
sparse_tensor = torch.sparse_coo_tensor(indices, values, size)

# Access elements by row using gather
def access_row_elements(sparse_tensor, row_index):
  row_mask = indices[0] == row_index  # Filter for elements in the desired row
  row_elements = sparse_tensor.values[row_mask]
  return row_elements

# Example usage
row_to_access = 1
row_elements = access_row_elements(sparse_tensor, row_to_access)
print(f"Elements in row {row_to_access}: {row_elements}")

Row-wise Operations

For each row, calculate the starting and ending indices within the values tensor using torch.unique and torch.cumsum. Then, perform the operation on the corresponding elements.
If you only need to perform row-wise operations (e.g., adding a constant to each row), you can iterate through the unique row indices in the indices tensor for COO format.

import torch

# (Code from previous example...)

# Row-wise addition
def row_wise_add(sparse_tensor, constant):
  row_indices = sparse_tensor.indices[0]  # Get row indices from COO
  unique_rows, row_counts = torch.unique(row_indices, return_counts=True)
  updated_values = torch.zeros(sparse_tensor.shape[0])  # Create a dense tensor for updates
  for i, row in enumerate(unique_rows):
    start = row_counts[:i].sum()  # Calculate starting index for the row
    end = start + row_counts[i]
    updated_values[row] = sparse_tensor.values[start:end] + constant  # Add constant to row elements
  return torch.sparse_coo_tensor(sparse_tensor.indices, updated_values, size)

# Apply row-wise addition
updated_tensor = row_wise_add(sparse_tensor, 5)
print(updated_tensor)

Always choose the method that aligns with your sparse tensor format and the specific operation you want to perform.
For COO format, use techniques like torch.gather and row-wise iteration to achieve similar results.
For CSR format, torch.sparse.Tensor.row_indices is the most efficient way to access row information.