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.

Basic operators

MatrixMult(A[, otherdims, dtype, name]) Matrix multiplication.
Identity(N[, M, dtype, inplace, name]) Identity operator.
Zero(N[, M, 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, dtype, name]) Sum operator.
Symmetrize(dims[, axis, dtype, name]) Symmetrize along an axis.
Restriction(dims, iava[, axis, dtype, …]) Restriction (or sampling) operator.
Regression(taxis, order[, dtype, name]) Polynomial regression.
LinearRegression(taxis[, dtype]) Linear regression.
CausalIntegration(dims[, axis, 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, name]) Kronecker operator.
Real(dims[, dtype, name]) Real operator.
Imag(dims[, dtype, name]) Imag operator.
Conj(dims[, dtype, name]) Complex conjugate operator.

Smoothing and derivatives

Smoothing1D(nsmooth, dims[, axis, dtype]) 1D Smoothing.
Smoothing2D(nsmooth, dims[, axes, dtype]) 2D Smoothing.
FirstDerivative(dims[, axis, sampling, …]) First derivative.
SecondDerivative(dims[, axis, sampling, …]) Second derivative.
Laplacian(dims[, axes, 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(dims, h[, offset, axis, dtype, …]) 1D convolution operator.
Convolve2D(dims, h[, offset, axes, dtype, …]) 2D convolution operator.
ConvolveND(dims, h[, offset, axes, method, …]) ND convolution operator.
Interp(dims, iava[, axis, kind, dtype, name]) Interpolation operator.
Bilinear(iava, dims[, 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.
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, 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.
MDC(G, nt, nv[, dt, dr, twosided, …]) Multi-dimensional convolution.
PhaseShift(vel, dz, nt, freq, kx[, ky, …]) Phase shift operator
Demigration(z, x, t, srcs, recs, vel, wav, …) Kirchhoff 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.

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.

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.