Package: pylops
A Linear Operator Library for PythonPyLops is an open-source Python library focused on providing a backend-agnostic, idiomatic, matrix-free library of linear operators and related computations.
It is inspired by the iconic MATLABSpot – A Linear-Operator Toolboxproject.InstallationTo get the most out of PyLops straight out of the box, we recommendcondato install PyLops:condainstall-cconda-forgepylopsYou can also install withpip:pipinstallpylopsSee the docs (Installation) for more information about dependencies and performance.Why PyLops?Linear operators and inverse problems are at the core of many of the most used algorithms in signal processing, image processing, and remote sensing.
For small-scale problems, matrices can be explicitly computed and manipulated with Python numerical scientific libraries such asNumPyandSciPy.On the other hand, large-scale problems often feature matrices that are prohibitive in size—but whose operations can be described by simple functions.
PyLops exploits this to represent linear operators not as array of numbers, but byfunctions which describe matrix-vector products.Indeed, many iterative methods (e.g. cg, lsqr) were designed to not rely on the elements of the matrix, only on the result of matrix-vector products.
PyLops offers many linear operators (derivatives, convolutions, FFTs and manyh more) as well as solvers for a variety of problems (e.g., least-squares and sparse inversion).
With these two ingredients, PyLops can describe and solve a variety of linear inverse problems which appear in many different areas.Example: A finite-difference operatorA first-order, central finite-difference derivative operator denoted D can be described either as a matrix (array of numbers), or as weighed stencil summation:importnumpyasnp# Setupnx=7x=np.arange(nx)-(nx-1)/2# MatrixD_mat=0.5*(np.diag(np.ones(nx-1),k=1)-np.diag(np.ones(nx-1),k=-1))D_mat[0]=D_mat[-1]=0# remove edge effects# Function: Stencil summationdefcentral_diff(x):y=np.zeros_like(x)y[1:-1]=0.5*(x[2:]-x[:-2])returny# y = Dxy=D_mat@xy_fun=central_diff(x)print(np.allclose(y,y_fun))# TrueThe matrix formulation can easily be paired with a SciPy least-squares solver to approximately invert the matrix, but this requires us to have an explicit representation for D (in this case,D_mat):fromscipy.linalgimportlstsq# xinv = D^-1 yxinv=lstsq(D_mat,y)[0]Relying on the functional approach, PyLops wraps a function similar tocentral_diffinto theFirstDerivativeoperator, defining not only the forward mode (Dx) but also the transpose mode (Dᵀy).
In fact, it goes even further as the forward slash operator applies least-squares inversion!frompylopsimportFirstDerivativeD_op=FirstDerivative(nx,dtype='float64')# y = Dxy=D_op@x# xinv = D^-1 yxinv_op=D_op/yprint(np.allclose(xinv,xinv_op))# TrueNote how the code becomes even more compact and expressive than in the previous case letting the user focus on the formulation of equations of the forward problem to be solved by inversion.
PyLops offers many other linear operators, as well as the ability to implement your own in a way that seamlessly interfaces with the rest of the ecosystem.ContributingFeel like contributing to the project? Adding new operators or tutorial?Follow the instructions detailed in theCONTRIBUTINGfile before getting started.DocumentationThe official documentation of PyLops is availablehere.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 theContributorslist.HistoryPyLops was initially written byEquinor.
It is a flexible and scalable python library for large-scale optimization with linear
operators that can be tailored to our needs, and as contribution to the free software community.
Since June 2021, PyLops is aNUMFOCUSAffiliated Project.CitingWhen using PyLops in scientific publications, please cite the following paper:Ravasi, M., and I. Vasconcelos, 2020,PyLops—A linear-operator Python library for scalable algebra and optimization,
SoftwareX, 11, 100361. doi: 10.1016/j.softx.2019.100361(link)TutorialsA list of video tutorials to learn more about PyLops:Transform 2022: Youtube videolinks.Transform 2021: Youtube videolinks.Swung Rendezvous 2021: Youtube videolinks.PyDataGlobal 2020: Youtube videolinks.ContributorsMatteo Ravasi, mrava87Carlos da Costa, cakoDieter Werthmüller, prisaeTristan van Leeuwen, TristanvanLeeuwenLeonardo Uieda, leouiedaFilippo Broggini, filippo82Tyler Hughes, twhughesLyubov Skopintseva, lskopintsevaFrancesco Picetti, fpicettiAlan Richardson, ar4BurningKarl, BurningKarlNick Luiken, NickLuikenBurningKarl, BurningKarlMuhammad Izzatullah, izzatumJuan Daniel Romero, jdromeromAniket Singh Rawat, dikwickleyRohan Babbar, rohanbabbar04Wei Zhang, ZhangWeiGeoFedor Goncharov, fedor-goncharov