pylops.optimization.cls_leastsquares.PreconditionedInversion

class pylops.optimization.cls_leastsquares.PreconditionedInversion(Op, callbacks=None)[source]

Preconditioned inversion.

Solve a system of preconditioned equations given the operator Op and a preconditioner P.

Parameters:
Oppylops.LinearOperator

Operator to invert of size \([N \times M]\).

Attributes:
ncpmodule

Array module used by the solver (obtained via pylops.utils.backend.get_array_module) ). Available only after setup is called.

POppylops.LinearOperator

Product of operator and preconditioner (Op @ P)

See also

RegularizedInversion

Regularized inversion

NormalEquationsInversion

Normal equations inversion

Notes

Solve the following system of preconditioned equations given the operator \(\mathbf{Op}\), a preconditioner \(\mathbf{P}\), the data \(\mathbf{y}\)

\[\mathbf{y} = \mathbf{Op}\,\mathbf{P} \mathbf{p}\]

where \(\mathbf{p}\) is the solution in the preconditioned space and \(\mathbf{x} = \mathbf{P}\mathbf{p}\) is the solution in the original space.

Methods

__init__(Op[, callbacks])

callback(x, *args, **kwargs)

Callback routine

finalize(*args[, show])

Finalize solver

memory_usage([show, unit])

Compute memory usage of the solver

run(x[, engine, show])

Run solver

setup(y, P[, show])

Setup solver

solve(y, P[, x0, engine, show])

Run entire solver

step()

Run one step of solver