PyLops API

The Application Programming Interface (API) of PyLops can be loosely seen as composed of a stack of three main layers:

• Linear operators: building blocks for the setting up of inverse problems

• Solvers: interfaces to a variety of solvers, providing an easy way to augment an inverse problem with additional regularization and/or preconditioning term

• Applications: high-level interfaces allowing users to easily setup and solve specific problems (while hiding the non-needed details - i.e., creation and setup of linear operators and solvers).

Linear operators

Templates

LinearOperator([Op, dtype, shape, dims, ...])	Common interface for performing matrix-vector products.
FunctionOperator(f, *args, **kwargs)	Function Operator.
MemoizeOperator(Op[, max_neval])	Memoize Operator.
PyTensorOperator(LOp)	PyTensor Op which applies a PyLops Linear Operator, including gradient support.
TorchOperator(Op[, batch, flatten, device, ...])	Wrap a PyLops operator into a Torch function.
JaxOperator(Op)	Enable JAX backend for PyLops operator.

Basic operators

MatrixMult(A[, otherdims, forceflat, dtype, ...])	Matrix multiplication.
Identity(N[, M, inplace, forceflat, dtype, name])	Identity operator.
Zero(N[, M, forceflat, dtype, name])	Zero operator.
Diagonal(diag[, dims, axis, dtype, name])	Diagonal operator.
Transpose(dims, axes[, dtype, name])	Transpose operator.
Flip(dims[, axis, dtype, name])	Flip along an axis.
Roll(dims[, axis, shift, dtype, name])	Roll along an axis.
Pad(dims, pad[, dtype, name])	Pad operator.
Sum(dims[, axis, forceflat, dtype, name])	Sum operator.
Symmetrize(dims[, axis, dtype, name])	Symmetrize along an axis.
Restriction(dims, iava[, axis, inplace, ...])	Restriction (or sampling) operator.
Regression(taxis, order[, dtype, name])	Polynomial regression.
LinearRegression(taxis[, dtype, name])	Linear regression.
CausalIntegration(dims[, axis, sampling, ...])	Causal integration.
Spread(dims, dimsd[, table, dtable, fh, ...])	Spread operator.
VStack(ops[, nproc, forceflat, inoutengine, ...])	Vertical stacking.
HStack(ops[, nproc, forceflat, inoutengine, ...])	Horizontal stacking.
Block(ops[, nproc, forceflat, dtype])	Block operator.
BlockDiag(ops[, nproc, forceflat, ...])	Block-diagonal operator.
Kronecker(Op1, Op2[, dtype, name])	Kronecker operator.
Real(dims[, dtype, name])	Real operator.
Imag(dims[, dtype, name])	Imag operator.
Conj(dims[, dtype, name])	Complex conjugate operator.
ToCupy(dims[, dtype, name])	Convert to CuPy.

Smoothing and derivatives

Smoothing1D(nsmooth, dims[, axis, dtype, name])	1D Smoothing.
Smoothing2D(nsmooth, dims[, axes, dtype, name])	2D Smoothing.
FirstDerivative(dims[, axis, sampling, ...])	First derivative.
SecondDerivative(dims[, axis, sampling, ...])	Second derivative.
Laplacian(dims[, axes, weights, sampling, ...])	Laplacian.
Gradient(dims[, sampling, edge, kind, ...])	Gradient.
FirstDirectionalDerivative(dims, v[, ...])	First Directional derivative.
SecondDirectionalDerivative(dims, v[, ...])	Second Directional derivative.

Signal processing

Convolve1D(dims, h[, offset, axis, method, ...])	1D convolution operator.
Convolve2D(dims, h[, offset, axes, method, ...])	2D convolution operator.
ConvolveND(dims, h[, offset, axes, method, ...])	ND convolution operator.
NonStationaryConvolve1D(dims, hs, ih[, ...])	1D non-stationary convolution operator.
NonStationaryConvolve2D(dims, hs, ihx, ihz)	2D non-stationary convolution operator.
NonStationaryConvolve3D(dims, hs, ihx, ihy, ihz)	3D non-stationary convolution operator.
NonStationaryFilters1D(inp, hsize, ih[, ...])	1D non-stationary filter estimation operator.
NonStationaryFilters2D(inp, hshape, ihx, ihz)	2D non-stationary filter estimation operator.
Interp(dims, iava[, axis, kind, dtype, name])	Interpolation operator.
Bilinear(iava, dims[, forceflat, dtype, name])	Bilinear interpolation operator.
FFT(dims[, axis, nfft, sampling, norm, ...])	One dimensional Fast-Fourier Transform.
FFT2D(dims[, axes, nffts, sampling, norm, ...])	Two dimensional Fast-Fourier Transform.
FFTND(dims[, axes, nffts, sampling, norm, ...])	N-dimensional Fast-Fourier Transform.
Shift(dims, shift[, axis, nfft, sampling, ...])	Shift operator
DWT(dims[, axis, wavelet, level, dtype, name])	One dimensional Wavelet operator.
DWT2D(dims[, axes, wavelet, level, dtype, name])	Two dimensional Wavelet operator.
DWTND(dims[, axes, wavelet, level, dtype, name])	N-dimensional Wavelet operator.
DCT(dims[, type, axes, dtype, workers, name])	Discrete Cosine Transform.
DTCWT(dims[, biort, qshift, level, ...])	Dual-Tree Complex Wavelet Transform
Seislet(slopes[, sampling, level, kind, ...])	Two dimensional Seislet operator.
Radon2D(taxis, haxis, pxaxis[, kind, ...])	Two dimensional Radon transform.
Radon3D(taxis, hyaxis, hxaxis, pyaxis, pxaxis)	Three dimensional Radon transform.
FourierRadon2D(taxis, haxis, pxaxis, nfft[, ...])	2D Fourier Radon transform
FourierRadon3D(taxis, hyaxis, hxaxis, ...[, ...])	3D Fourier Radon transform
ChirpRadon2D(taxis, haxis, pmax[, dtype, name])	2D Chirp Radon transform
ChirpRadon3D(taxis, hyaxis, hxaxis, pmax[, ...])	3D Chirp Radon transform
Sliding1D(Op, dim, dimd, nwin, nover[, ...])	1D Sliding transform operator.
Sliding2D(Op, dims, dimsd, nwin, nover[, ...])	2D Sliding transform operator.
Sliding3D(Op, dims, dimsd, nwin, nover, nop)	3D Sliding transform operator.w
Patch2D(Op, dims, dimsd, nwin, nover, nop[, ...])	2D Patch transform operator.
Patch3D(Op, dims, dimsd, nwin, nover, nop[, ...])	3D Patch transform operator.
Fredholm1(G[, nz, saveGt, usematmul, dtype, ...])	Fredholm integral of first kind.

Wave-Equation processing

PressureToVelocity(nt, nr, dt, dr, rho, vel)	Pressure to Vertical velocity conversion.
UpDownComposition2D(nt, nr, dt, dr, rho, vel)	2D Up-down wavefield composition.
UpDownComposition3D(nt, nr, dt, dr, rho, vel)	3D Up-down wavefield composition.
BlendingContinuous(nt, nr, ns, dt, times[, ...])	Continuous blending operator
BlendingGroup(nt, nr, ns, dt, times, ...[, ...])	Group blending operator
BlendingHalf(nt, nr, ns, dt, times, ...[, ...])	Half blending operator
MDC(G, nt, nv[, dt, dr, twosided, ...])	Multi-dimensional convolution.
PhaseShift(vel, dz, nt, freq, kx[, ky, ...])	Phase shift operator
Kirchhoff(z, x, t, srcs, recs, vel, wav, ...)	Kirchhoff demigration operator.
AcousticWave2D(shape, origin, spacing, vp, ...)	Devito Acoustic propagator.

Geophysical subsurface characterization

avo.AVOLinearModelling(theta[, vsvp, nt0, ...])	AVO Linearized modelling.
poststack.PoststackLinearModelling(wav, nt0)	Post-stack linearized seismic modelling operator.
prestack.PrestackLinearModelling(wav, theta)	Pre-stack linearized seismic modelling operator.
prestack.PrestackWaveletModelling(m, theta, nwav)	Pre-stack linearized seismic modelling operator for wavelet.

Solvers

Template

Solver(Op[, callbacks])

This is a template class which a user must subclass when implementing a new solver.

Basic

CG(Op[, callbacks])	Conjugate gradient
CGLS(Op[, callbacks])	Conjugate gradient least squares
LSQR(Op)	Solve an overdetermined system of equations given an operator Op and data y using LSQR iterations.

cg(Op, y[, x0, niter, tol, show, itershow, ...])	Conjugate gradient
cgls(Op, y[, x0, niter, damp, tol, show, ...])	Conjugate gradient least squares
lsqr(Op, y[, x0, damp, atol, btol, conlim, ...])	LSQR

Least-squares

NormalEquationsInversion(Op[, callbacks])	Inversion of normal equations.
RegularizedInversion(Op[, callbacks])	Regularized inversion.
PreconditionedInversion(Op[, callbacks])	Preconditioned inversion.

normal_equations_inversion(Op, y, Regs[, ...])	Inversion of normal equations.
regularized_inversion(Op, y, Regs[, x0, ...])	Regularized inversion.
preconditioned_inversion(Op, y, P[, x0, ...])	Preconditioned inversion.

Sparsity

IRLS(Op[, callbacks])	Iteratively reweighted least squares.
OMP(Op[, callbacks])	Orthogonal Matching Pursuit (OMP).
ISTA(Op[, callbacks])	Iterative Shrinkage-Thresholding Algorithm (ISTA).
FISTA(Op[, callbacks])	Fast Iterative Shrinkage-Thresholding Algorithm (FISTA).
SPGL1(Op[, callbacks])	Spectral Projected-Gradient for L1 norm.
SplitBregman(Op[, callbacks])	Split Bregman for mixed L2-L1 norms.

irls(Op, y[, x0, nouter, threshR, epsR, ...])	Iteratively reweighted least squares.
omp(Op, y[, niter_outer, niter_inner, ...])	Orthogonal Matching Pursuit (OMP).
ista(Op, y[, x0, niter, SOp, eps, alpha, ...])	Iterative Shrinkage-Thresholding Algorithm (ISTA).
fista(Op, y[, x0, niter, SOp, eps, alpha, ...])	Fast Iterative Shrinkage-Thresholding Algorithm (FISTA).
spgl1(Op, y[, x0, SOp, tau, sigma, show])	Spectral Projected-Gradient for L1 norm.
splitbregman(Op, y, RegsL1[, x0, ...])	Split Bregman for mixed L2-L1 norms.

Callbacks

Callbacks()	This is a template class which a user must subclass when implementing callbacks for a solver.
MetricsCallback(xtrue[, Op, which])	Metrics callback

Applications

Wave-Equation processing

SeismicInterpolation(data, nrec, iava[, ...])	Seismic interpolation (or regularization).
Deghosting(p, nt, nr, dt, dr, vel, zrec[, ...])	Wavefield deghosting.
WavefieldDecomposition(p, vz, nt, nr, dt, ...)	Up-down wavefield decomposition.
MDD(G, d[, dt, dr, nfmax, wav, twosided, ...])	Multi-dimensional deconvolution.
Marchenko(R[, dt, nt, dr, nfmax, wav, toff, ...])	Marchenko redatuming
LSM(z, x, t, srcs, recs, vel, wav, wavcenter)	Least-squares Migration (LSM).

Geophysical subsurface characterization

poststack.PoststackInversion(data, wav[, ...])	Post-stack linearized seismic inversion.
prestack.PrestackInversion(data, theta, wav)	Pre-stack linearized seismic inversion.