pylops.optimization.leastsquares.preconditioned_inversion#
- pylops.optimization.leastsquares.preconditioned_inversion(Op, y, P, x0=None, engine='scipy', show=False, **kwargs_solver)[source]#
Preconditioned inversion.
Solve a system of preconditioned equations given the operator
Op
and a preconditionerP
.- Parameters
- Op
pylops.LinearOperator
Operator to invert of size \([N \times M]\)
- y
numpy.ndarray
Data of size \([N \times 1]\)
- P
pylops.LinearOperator
Preconditioner
- x0
numpy.ndarray
Initial guess of size \([M \times 1]\)
- engine
str
, optional Solver to use (
scipy
orpylops
)- show
bool
, optional Display normal equations solver log
- **kwargs_solver
Arbitrary keyword arguments for chosen solver (
scipy.sparse.linalg.lsqr
andpylops.optimization.solver.cgls
are used as default for numpy and cupy data, respectively)
- Op
- Returns
- xinv
numpy.ndarray
Inverted model.
- istop
int
Gives the reason for termination
1
means \(\mathbf{x}\) is an approximate solution to \(\mathbf{y} = \mathbf{Op}\,\mathbf{x}\)2
means \(\mathbf{x}\) approximately solves the least-squares problem- itn
int
Iteration number upon termination
- r1norm
float
\(||\mathbf{r}||_2^2\), where \(\mathbf{r} = \mathbf{y} - \mathbf{Op}\,\mathbf{x}\)
- r2norm
float
\(\sqrt{\mathbf{r}^T\mathbf{r} + \epsilon^2 \mathbf{x}^T\mathbf{x}}\). Equal to
r1norm
if \(\epsilon=0\)
- xinv
See also
RegularizedInversion
Regularized inversion
NormalEquationsInversion
Normal equations inversion
Notes
See
pylops.optimization.cls_leastsquares.PreconditionedInversion