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


LinearOperator([Op, explicit, clinear]) Common interface for performing matrix-vector products.
FunctionOperator(f, *args, **kwargs) Function Operator.
MemoizeOperator(Op[, max_neval]) Memoize Operator.

Basic operators

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

Smoothing and derivatives

Smoothing1D(nsmooth, dims[, dir, dtype]) 1D Smoothing.
Smoothing2D(nsmooth, dims[, nodir, dtype]) 2D Smoothing.
FirstDerivative(N[, dims, dir, sampling, …]) First derivative.
SecondDerivative(N[, dims, dir, sampling, …]) Second derivative.
Laplacian(dims[, dirs, weights, sampling, …]) Laplacian.
Gradient(dims[, sampling, edge, dtype, kind]) Gradient.
FirstDirectionalDerivative(dims, v[, …]) First Directional derivative.
SecondDirectionalDerivative(dims, v[, …]) Second Directional derivative.

Signal processing

Convolve1D(N, h[, offset, dims, dir, dtype, …]) 1D convolution operator.
Convolve2D(N, h, dims[, offset, nodir, …]) 2D convolution operator.
ConvolveND(N, h, dims[, offset, dirs, …]) ND convolution operator.
Interp(M, iava[, dims, dir, kind, dtype]) Interpolation operator.
Bilinear(iava, dims[, dtype]) Bilinear interpolation operator.
FFT(dims[, dir, nfft, sampling, real, …]) One dimensional Fast-Fourier Transform.
FFT2D(dims[, dirs, nffts, sampling, dtype]) Two dimensional Fast-Fourier Transform.
FFTND(dims[, dirs, nffts, sampling, dtype]) N-dimensional Fast-Fourier Transform.
DWT(dims[, dir, wavelet, level, dtype]) One dimensional Wavelet operator.
DWT2D(dims[, dirs, wavelet, level, dtype]) Two dimensional Wavelet operator.
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.
ChirpRadon2D(taxis, haxis, pmax[, dtype]) 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.
Patch2D(Op, dims, dimsd, nwin, nover, nop[, …]) 2D 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.
MDC(G, nt, nv[, dt, dr, twosided, fast, …]) Multi-dimensional convolution.
PhaseShift(vel, dz, nt, freq, kx[, ky, dtype]) Phase shift operator
Demigration(z, x, t, srcs, recs, vel, wav, …) Kirchoff Demigration operator.

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.


Basic, y, x0[, niter, damp, tol, …]) Conjugate gradient
solver.cgls(Op, y, x0[, niter, damp, tol, …]) Conjugate gradient least squares
solver.lsqr(Op, y, x0[, damp, atol, btol, …]) LSQR


leastsquares.NormalEquationsInversion(Op, …) Inversion of normal equations.
leastsquares.RegularizedInversion(Op, Regs, data) Regularized inversion.
leastsquares.PreconditionedInversion(Op, P, data) Preconditioned inversion.


sparsity.IRLS(Op, data, nouter[, threshR, …]) Iteratively reweighted least squares.
sparsity.OMP(Op, data[, niter_outer, …]) Orthogonal Matching Pursuit (OMP).
sparsity.ISTA(Op, data, niter[, eps, alpha, …]) Iterative Shrinkage-Thresholding Algorithm (ISTA).
sparsity.FISTA(Op, data, niter[, eps, …]) Fast Iterative Shrinkage-Thresholding Algorithm (FISTA).
sparsity.SPGL1(Op, data[, SOp, tau, sigma, x0]) Spectral Projected-Gradient for L1 norm.
sparsity.SplitBregman(Op, RegsL1, data[, …]) Split Bregman for mixed L2-L1 norms.


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[, R1, dt, nt, dr, nfmax, wav, …]) 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.