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Torch Named Linops

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Welcome to the documentation for torch-named-linops, a linear operator abstraction designed for matrix-free, large-scale numerical computing, optimization, and machine learning.

Quickstart

Installation

$ pip install torch-named-linops
# or with uv
$ uv add torch-named-linops

Create and Apply a Linear Operator

# Import torch and the core linear operator classes
import torch
from torchlinops import Dense, Dim  # Dense: matrix multiplication, Dim: named dimensions

# Define matrix dimensions
M, N = 3, 7  # M: output size, N: input size

# Create a random weight matrix for our linear operation
weight = torch.randn(M, N)

# Create a Dense linear operator with named dimensions
# Dense performs matrix-vector multiplication using the weight matrix
# weightshape=Dim("MN") names the weight matrix dimensions (M rows, N columns),
# ishape=Dim("N") sets the expected input shape,
# oshape=Dim("M") sets the expected output shape.
A = Dense(weight, weightshape=Dim("MN"), ishape=Dim("N"), oshape=Dim("M"))

# Create input data and apply the operator
x = torch.randn(N)  # Random input vector of size N
y = A(x)  # Apply the linear operator (equivalent to A @ x)
print(f"Input shape: {x.shape}, Output shape: {y.shape}")

Expected output: 

Input shape: torch.Size([7]), Output shape: torch.Size([3])

Features

  • Named dimensions -- A dedicated abstraction (Dim, NamedDimension, NamedShape) for naming linear operator dimensions, eliminating shape ambiguity.
  • Automatic adjoints and normals -- .H and .N properties to create adjoint (\(A^H\)) and normal (\(A^H A\)) operators with correct dimension handling.
  • Operator composition -- Compose operators with @ (chaining) and + (addition). Chain, Add, Concat, and Stack handle dimension matching automatically.
  • Core operator library -- Dense, Diagonal, FFT, NUFFT, Interpolate, ArrayToBlocks, Sampling, and more, all with named dimensions.
  • Multi-GPU splitting -- Split a single operator across multiple GPUs with split_linop and create_batched_linop.
  • Complex number support -- Full support for complex tensors. Adjoint takes the conjugate transpose.
  • Autograd integration -- Full support for autograd-based automatic differentiation through all operators.
  • Iterative solvers -- Built-in conjugate_gradients, power_method, and polynomial_preconditioner that work directly with named linops.

Other Interesting Packages

If you like this package, you may find these other packages interesting as well. Check them out! - SigPy - MIRTorch - SCICO - matmri - einops - torch_linops - PyLops - linear_operator