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<!doctype html>
<html lang="en">
<head>
<meta charset="UTF-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>PyLops | Linear Operators for Inverse Problems</title>
<meta
name="description"
content="PyLops is an open-source, backend-agnostic, matrix-free Python library of linear operators and inverse problem solvers."
/>
<link rel="stylesheet" href="./styles.css" />
</head>
<body>
<div class="bg-accent" aria-hidden="true"></div>
<header class="site-header section reveal">
<p class="eyebrow">PyLops</p>
<h1>Matrix-free linear operators for large-scale inverse problems.</h1>
<p class="lead">
An open-source, backend-agnostic, collection of stackable linear
operators and solvers for practical scientific workflows.
</p>
<a
class="cta cta-primary"
href="https://github.com/pylops/"
target="_blank"
rel="noreferrer"
aria-label="View PyLops on GitHub"
>
GitHub Org.
</a>
</header>
<main>
<section class="section reveal" id="features">
<h2>Key features</h2>
<div class="feature-grid">
<article class="feature-card">
<span class="feature-logo" aria-hidden="true">
<svg viewBox="0 0 24 24" fill="none">
<rect x="3.5" y="4.5" width="17" height="15" rx="2"></rect>
<path d="M8 9h8M8 13h8M8 17h5"></path>
</svg>
</span>
<h3>Matrix-free operators</h3>
<p>
Represent operators by forward and adjoint matrix-vector products
instead of explicit matrices.
</p>
</article>
<article class="feature-card">
<span class="feature-logo" aria-hidden="true">
<svg viewBox="0 0 24 24" fill="none">
<path d="M4 19h16"></path>
<path d="M6 16l4-4 3 3 5-6"></path>
<circle cx="10" cy="12" r="1"></circle>
</svg>
</span>
<h3>Large-scale ready</h3>
<p>
Designed for problems where explicit matrices are prohibitive in
memory and compute footprint.
</p>
</article>
<article class="feature-card">
<span class="feature-logo" aria-hidden="true">
<svg viewBox="0 0 24 24" fill="none">
<path d="M5 9h5V4"></path>
<path d="M19 15h-5v5"></path>
<path d="M19 9a7 7 0 0 0-12.2-4.8"></path>
<path d="M5 15a7 7 0 0 0 12.2 4.8"></path>
</svg>
</span>
<h3>State-of-the-art solvers</h3>
<p>
Includes iterative methods for least-squares and
proximal optimization.
</p>
</article>
<article class="feature-card">
<span class="feature-logo" aria-hidden="true">
<svg viewBox="0 0 24 24" fill="none">
<circle cx="12" cy="12" r="3"></circle>
<path d="M12 4v2M12 18v2M4 12h2M18 12h2M6.4 6.4l1.4 1.4M16.2 16.2l1.4 1.4M17.6 6.4l-1.4 1.4M7.8 16.2l-1.4 1.4"></path>
</svg>
</span>
<h3>Extensible base operators</h3>
<p>
Provides <code>LinearOperator</code> and
<code>ProxOperator</code> base classes inspired
by SciPy and easy to extend.
</p>
</article>
<article class="feature-card">
<span class="feature-logo" aria-hidden="true">
<svg viewBox="0 0 24 24" fill="none">
<path d="M7 7h10v4H7z"></path>
<path d="M10 11v3M14 11v3"></path>
<path d="M9 14h6"></path>
<path d="M12 14v5"></path>
</svg>
</span>
<h3>Backend-agnostic design</h3>
<p>
Uses an idiomatic approach to provide support
for multiple computational backends (NumPy / CuPy / JAX).
</p>
</article>
<article class="feature-card">
<span class="feature-logo" aria-hidden="true">
<svg viewBox="0 0 24 24" fill="none">
<circle cx="12" cy="12" r="8"></circle>
<path d="M4 12h16M12 4a12 12 0 0 1 0 16M12 4a12 12 0 0 0 0 16"></path>
</svg>
</span>
<h3>Open-source driven</h3>
<p>
Community-driven and affiliated with NumFOCUS, with strong focus
on transparent development.
</p>
</article>
</div>
</section>
<section class="section reveal" id="domains">
<h2>Domains</h2>
<p class="links-subtitle">
Maturity snapshot across key application areas.
</p>
<div class="domain-list" role="list" aria-label="Domain maturity">
<div class="domain-item" role="listitem">
<span class="domain-name">Signal processing</span>
<span class="domain-meta">
<span class="star-rating" aria-label="4 out of 5 stars">
<span class="star filled">★</span><span class="star filled">★</span
><span class="star filled">★</span
><span class="star filled">★</span
><span class="star empty">★</span>
</span>
<a
class="domain-example"
href="https://pylops.readthedocs.io/en/stable/tutorials/solvers.html#sphx-glr-tutorials-solvers-py"
target="_blank"
rel="noreferrer"
aria-label="Open signal processing example"
>Example</a
>
</span>
</div>
<div class="domain-item" role="listitem">
<span class="domain-name">Image processing</span>
<span class="domain-meta">
<span class="star-rating" aria-label="3 out of 5 stars">
<span class="star filled">★</span><span class="star filled">★</span
><span class="star filled">★</span><span class="star empty">★</span
><span class="star empty">★</span>
</span>
<a
class="domain-example"
href="https://pylops.readthedocs.io/en/stable/gallery/plot_slopeest.html#sphx-glr-gallery-plot-slopeest-py"
target="_blank"
rel="noreferrer"
aria-label="Open image processing example"
>Example</a
>
</span>
</div>
<div class="domain-item" role="listitem">
<span class="domain-name">Medical imaging</span>
<span class="domain-meta">
<span class="star-rating" aria-label="1 out of 5 stars">
<span class="star filled">★</span><span class="star empty">★</span
><span class="star empty">★</span><span class="star empty">★</span
><span class="star empty">★</span>
</span>
<a
class="domain-example"
href="https://pylops.readthedocs.io/en/stable/tutorials/ctscan.html#sphx-glr-tutorials-ctscan-py"
target="_blank"
rel="noreferrer"
aria-label="Open medical imaging example"
>Example</a
>
</span>
</div>
<div class="domain-item" role="listitem">
<span class="domain-name">Geophysics</span>
<span class="domain-meta">
<span class="star-rating" aria-label="5 out of 5 stars">
<span class="star filled">★</span><span class="star filled">★</span
><span class="star filled">★</span
><span class="star filled">★</span
><span class="star filled">★</span>
</span>
<a
class="domain-example"
href="https://pylops.readthedocs.io/en/stable/tutorials/deblending.html"
target="_blank"
rel="noreferrer"
aria-label="Open geophysics example"
>Example</a
>
</span>
</div>
</div>
<p class="domains-cta">
Want to grow PyLops' competency in one of these domains, or add
support for your own domain? Start a discussion
<a
href="https://github.com/orgs/PyLops/discussions"
target="_blank"
rel="noreferrer"
aria-label="Open PyLops discussions"
>here</a
>.
</p>
</section>
<section class="section reveal" id="links">
<h2>Explore our projects</h2>
<p class="links-subtitle">Official links and project stats.</p>
<p class="commit-bars-hint">
Bars compare commits on the default branch since each project’s latest
GitHub release (relative scale across the three projects below).
</p>
<div class="project-links">
<div class="project-row">
<p class="project-name">pylops</p>
<div class="links-grid">
<a
class="cta cta-link"
href="https://github.com/pylops/"
target="_blank"
rel="noreferrer"
aria-label="Open PyLops GitHub page"
>
<span>GitHub</span>
<span class="cta-badges">
<img
alt="PyLops GitHub stars"
src="https://img.shields.io/github/stars/PyLops/pylops?style=flat&label=Stars"
/>
<img
alt="PyLops GitHub forks"
src="https://img.shields.io/github/forks/PyLops/pylops?style=flat&label=Forks"
/>
</span>
</a>
<div
class="cta cta-link cta-docs"
aria-label="Open PyLops Documentation pages"
>
<span>Documentation</span>
<span class="cta-doc-links">
<a
href="https://pylops.readthedocs.io/en/stable/"
target="_blank"
rel="noreferrer"
aria-label="Open PyLops stable documentation"
>Stable</a
>
<a
href="https://pylops.readthedocs.io/en/latest/"
target="_blank"
rel="noreferrer"
aria-label="Open PyLops latest documentation"
>Latest</a
>
</span>
</div>
<a
class="cta cta-link"
href="https://pypi.org/project/pylops/"
target="_blank"
rel="noreferrer"
aria-label="Open PyLops PyPI page"
>
<span>PyPI</span>
<span class="cta-badges">
<img
alt="PyLops PyPI downloads"
src="https://img.shields.io/pypi/dm/pylops?style=flat&label=Downloads"
/>
</span>
</a>
<a
class="cta cta-link"
href="https://anaconda.org/channels/conda-forge/packages/pylops/files?version=1.4.0"
target="_blank"
rel="noreferrer"
aria-label="Open PyLops conda-forge page"
>
<span>conda-forge</span>
<span class="cta-badges">
<img
alt="PyLops conda-forge downloads"
src="https://img.shields.io/conda/dn/conda-forge/pylops?style=flat&label=Downloads"
/>
</span>
</a>
</div>
<div class="project-stats" data-repo="PyLops/pylops">
<div class="commit-activity" aria-live="polite" aria-busy="true">
<div class="commit-activity-head">
<span class="commit-activity-label"
>Commits since last release</span
>
<span class="commit-activity-count" data-role="count"
>…</span
>
</div>
<div
class="commit-bar-track"
role="progressbar"
aria-valuemin="0"
aria-valuemax="100"
aria-valuenow="0"
aria-label="Commits since last release"
>
<div class="commit-bar-fill" data-role="fill"></div>
</div>
<p class="commit-activity-meta" data-role="meta"></p>
</div>
<div
class="contributor-card"
aria-live="polite"
aria-busy="true"
>
<span class="contributor-label">Contributors</span>
<span class="contributor-count" data-role="contributor-count"
>…</span
>
<div
class="contributor-avatars"
data-role="contributor-avatars"
></div>
<p class="contributor-meta" data-role="contributor-meta"></p>
</div>
</div>
</div>
<div class="project-row">
<p class="project-name">pyproximal</p>
<div class="links-grid">
<a
class="cta cta-link"
href="http://github.com/pyLops/pyproximal"
target="_blank"
rel="noreferrer"
aria-label="Open pyproximal GitHub page"
>
<span>GitHub</span>
<span class="cta-badges">
<img
alt="pyproximal GitHub stars"
src="https://img.shields.io/github/stars/PyLops/pyproximal?style=flat&label=Stars"
/>
<img
alt="pyproximal GitHub forks"
src="https://img.shields.io/github/forks/PyLops/pyproximal?style=flat&label=Forks"
/>
</span>
</a>
<div
class="cta cta-link cta-docs"
aria-label="Open pyproximal Documentation pages"
>
<span>Documentation</span>
<span class="cta-doc-links">
<a
href="http://pyproximal.readthedocs.io/en/stable/"
target="_blank"
rel="noreferrer"
aria-label="Open pyproximal documentation"
>Stable</a
>
<a
href="http://pyproximal.readthedocs.io/en/latest/"
target="_blank"
rel="noreferrer"
aria-label="Open pyproximal latest documentation"
>Latest</a
>
</span>
</div>
<a
class="cta cta-link"
href="https://pypi.org/project/pyproximal/"
target="_blank"
rel="noreferrer"
aria-label="Open pyproximal PyPI page"
>
<span>PyPI</span>
<span class="cta-badges">
<img
alt="pyproximal PyPI downloads"
src="https://img.shields.io/pypi/dm/pyproximal?style=flat&label=Downloads"
/>
</span>
</a>
<a
class="cta cta-link"
href="https://anaconda.org/channels/conda-forge/packages/pyproximal/overview"
target="_blank"
rel="noreferrer"
aria-label="Open pyproximal conda-forge page"
>
<span>conda-forge</span>
<span class="cta-badges">
<img
alt="pyproximal conda-forge downloads"
src="https://img.shields.io/conda/dn/conda-forge/pyproximal?style=flat&label=Downloads"
/>
</span>
</a>
</div>
<div class="project-stats" data-repo="PyLops/pyproximal">
<div class="commit-activity" aria-live="polite" aria-busy="true">
<div class="commit-activity-head">
<span class="commit-activity-label"
>Commits since last release</span
>
<span class="commit-activity-count" data-role="count"
>…</span
>
</div>
<div
class="commit-bar-track"
role="progressbar"
aria-valuemin="0"
aria-valuemax="100"
aria-valuenow="0"
aria-label="Commits since last release"
>
<div class="commit-bar-fill" data-role="fill"></div>
</div>
<p class="commit-activity-meta" data-role="meta"></p>
</div>
<div
class="contributor-card"
aria-live="polite"
aria-busy="true"
>
<span class="contributor-label">Contributors</span>
<span class="contributor-count" data-role="contributor-count"
>…</span
>
<div
class="contributor-avatars"
data-role="contributor-avatars"
></div>
<p class="contributor-meta" data-role="contributor-meta"></p>
</div>
</div>
</div>
<div class="project-row">
<p class="project-name">pylops-mpi</p>
<div class="links-grid">
<a
class="cta cta-link"
href="http://github.com/pyLops/pylops-mpi"
target="_blank"
rel="noreferrer"
aria-label="Open pylops-mpi GitHub page"
>
<span>GitHub</span>
<span class="cta-badges">
<img
alt="pylops-mpi GitHub stars"
src="https://img.shields.io/github/stars/PyLops/pylops-mpi?style=flat&label=Stars"
/>
<img
alt="pylops-mpi GitHub forks"
src="https://img.shields.io/github/forks/PyLops/pylops-mpi?style=flat&label=Forks"
/>
</span>
</a>
<div
class="cta cta-link cta-docs"
aria-label="Open pylops-mpi Documentation pages"
>
<span>Documentation</span>
<span class="cta-doc-links">
<a
href="https://pylops.github.io/pylops-mpi/"
target="_blank"
rel="noreferrer"
aria-label="Open pylops-mpi latest documentation"
>Latest</a
>
</span>
</div>
<a
class="cta cta-link"
href="https://pypi.org/project/pylops-mpi/"
target="_blank"
rel="noreferrer"
aria-label="Open pylops-mpi PyPI page"
>
<span>PyPI</span>
<span class="cta-badges">
<img
alt="pylops-mpi PyPI downloads"
src="https://img.shields.io/pypi/dm/pylops-mpi?style=flat&label=Downloads"
/>
</span>
</a>
</div>
<div class="project-stats" data-repo="PyLops/pylops-mpi">
<div class="commit-activity" aria-live="polite" aria-busy="true">
<div class="commit-activity-head">
<span class="commit-activity-label"
>Commits since last release</span
>
<span class="commit-activity-count" data-role="count"
>…</span
>
</div>
<div
class="commit-bar-track"
role="progressbar"
aria-valuemin="0"
aria-valuemax="100"
aria-valuenow="0"
aria-label="Commits since last release"
>
<div class="commit-bar-fill" data-role="fill"></div>
</div>
<p class="commit-activity-meta" data-role="meta"></p>
</div>
<div
class="contributor-card"
aria-live="polite"
aria-busy="true"
>
<span class="contributor-label">Contributors</span>
<span class="contributor-count" data-role="contributor-count"
>…</span
>
<div
class="contributor-avatars"
data-role="contributor-avatars"
></div>
<p class="contributor-meta" data-role="contributor-meta"></p>
</div>
</div>
</div>
</div>
</section>
</main>
<footer class="site-footer section reveal">
<p>
© Copyright 2025, PyLops Development Team. Created with the help of
<a href="https://cursor.com" target="_blank" rel="noreferrer"
>Cursor</a
>.
</p>
</footer>
<script src="./script.js"></script>
</body>
</html>