# 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 $$[N \times M]$$.

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 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