pylops_gpu.optimization.cg.cgls¶
-
pylops_gpu.optimization.cg.
cgls
(A, y, x=None, niter=10, damp=0.0, tol=1e-10)[source]¶ Conjugate gradient least squares
Solve an overdetermined system of equations given an operator
A
and datay
using conjugate gradient iterations.Parameters: - A :
pylops_gpu.LinearOperator
Operator to invert of size \([N \times M]\)
- y :
torch.Tensor
Data of size \([N \times 1]\)
- x0 :
torch.Tensor
, optional Initial guess
- niter :
int
, optional Number of iterations
- damp :
float
, optional Damping coefficient
- tol :
int
, optional Residual norm tolerance
Returns: - x :
torch.Tensor
Estimated model
- iiter :
torch.Tensor
Max number of iterations model
Notes
Minimize the following functional using conjugate gradient iterations:
\[J = || \mathbf{y} - \mathbf{Ax} ||^2 + \epsilon || \mathbf{x} ||^2\]where \(\epsilon\) is the damping coefficient.
- A :