pylops

name	pylops
description	Linear operators for large-scale inverse problems with matrix-free representations. Use when Claude needs to: (1) Define linear operators for forward/adjoint operations, (2) Solve inverse problems (deconvolution, imaging, tomography), (3) Apply signal processing transforms (FFT, convolution, derivatives), (4) Compose operators for complex workflows, (5) Perform regularized inversion with smoothness or sparsity constraints, (6) Process seismic or image data at scale.
version	1.0.0
author	Geoscience Skills
license	MIT
tags	["Linear Operators","Inverse Problems","Deconvolution","Signal Processing"]
dependencies	["pylops>=2.0.0","numpy","scipy"]
complements	["devito","simpeg","segyio"]
workflow_role	modelling

PyLops - Linear Operators Library

Quick Reference

import numpy as np
import pylops

# Create operator and apply forward/adjoint
A = pylops.FirstDerivative(n=100, dtype='float64')
y = A @ x        # Forward: y = A @ x
x_adj = A.H @ y  # Adjoint: x = A.H @ y
x_est = A / y    # Solve inverse problem

Key Classes

Class	Purpose
LinearOperator	Base class for all operators
VStack/HStack	Vertical/horizontal operator stacking
BlockDiag	Block diagonal operator composition

Essential Operations

Basic Operators

# Diagonal operator
D = pylops.Diagonal(np.array([1., 2., 3.]))
y = D @ x; x_adj = D.H @ y

# Derivatives
D1 = pylops.FirstDerivative(n, dtype='float64')
D2 = pylops.SecondDerivative(n, dtype='float64')
G = pylops.Gradient(dims=(64, 64), dtype='float64')

Convolution

wavelet = np.sin(np.linspace(0, 2*np.pi, 21)) * np.hanning(21)
C = pylops.signalprocessing.Convolve1D(n, h=wavelet, offset=10)
y = C @ x      # Convolve
x_adj = C.H @ y  # Correlation (adjoint)

Compose and Stack Operators

# Chain: y = C @ B @ A @ x
composed = pylops.Smoothing1D(5, n) @ pylops.FirstDerivative(n) @ pylops.Identity(n)


V = pylops.VStack([A, B])     
H = pylops.HStack([A, B])     
BD = pylops.BlockDiag([A, B])