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An extension to PyLops for linear operators on GPUs.

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:vertical_traffic_light: :vertical_traffic_light: This library is under early development. Expect things to constantly change until version v1.0.0. :vertical_traffic_light: :vertical_traffic_light:


This library is an extension of PyLops to run operators on GPUs.

As much as numpy and scipy lie at the core of the parent project PyLops, PyLops-GPU heavily builds on top of PyTorch and takes advantage of the same optimized tensor computations used in PyTorch for deep learning using GPUs and CPUs.

Doing so, linear operators can be computed on GPUs.

Here is a simple example showing how a diagonal operator can be created, applied and inverted using PyLops:

import numpy as np
from pylops import Diagonal

n = int(1e6)
x = np.ones(n)
d = np.arange(n) + 1.

Dop = Diagonal(d)

# y = Dx
y = Dop*x

and similarly using PyLops-gpu:

import numpy as np
import torch
from pylops_gpu.utils.backend import device
from pylops_gpu import Diagonal

dev = device()

n = int(1e6)
x = torch.ones(n, dtype=torch.float64).to(dev)
d = (torch.arange(0, n, dtype=torch.float64) + 1.).to(dev)

Dop = Diagonal(d, device=dev)

# y = Dx
y = Dop*x

Running these two snippets of code in Google Colab with GPU enabled gives a 50+ speed up for the forward pass.

As a by-product of implementing PyLops linear operators in PyTorch, we can easily chain our operators with any nonlinear mathematical operation (e.g., log, sin, tan, pow, ...) as well as with operators from the torch.nn submodule and obtain Automatic Differentiation (AD) for the entire chain. Since the gradient of a linear operator is simply its adjoint, we have implemented a single class, pylops_gpu.TorchOperator, which can wrap any linear operator from PyLops and PyLops-gpu libraries and return a torch.autograd.Function object.

Project structure

This repository is organized as follows:

  • pylops_gpu: python library containing various GPU-powered linear operators and auxiliary routines
  • pytests: set of pytests
  • testdata: sample datasets used in pytests and documentation
  • docs: sphinx documentation
  • examples: set of python script examples for each linear operator to be embedded in documentation using sphinx-gallery
  • tutorials: set of python script tutorials to be embedded in documentation using sphinx-gallery

Getting started

You need Python 3.5 or greater.

From PyPi

Coming soon...

From Github

You can also directly install from the master node

pip install git+


Feel like contributing to the project? Adding new operators or tutorial?

Follow the instructions from PyLops official documentation.


The official documentation of PyLops-gpu is available here.

Visit this page to get started learning about different operators and their applications as well as how to create new operators yourself and make it to the Contributors list.

Moreover, if you have installed PyLops using the developer environment you can also build the documentation locally by typing the following command:

make doc

Once the documentation is created, you can make any change to the source code and rebuild the documentation by simply typing

make docupdate

Note that if a new example or tutorial is created (and if any change is made to a previously available example or tutorial) you are required to rebuild the entire documentation before your changes will be visible.


PyLops-GPU was initially written and it is currently maintained by Equinor. It is an extension of PyLops for large-scale optimization with GPU-driven linear operators on that can be tailored to our needs, and as contribution to the free software community.


  • Matteo Ravasi, mrava87

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