pylops.optimization.basic.cgls#
- pylops.optimization.basic.cgls(Op, y, x0=None, niter=10, damp=0.0, tol=0.0001, show=False, itershow=(10, 10, 10), callback=None)[source]#
Conjugate gradient least squares
Solve an overdetermined system of equations given an operator
Op
and datay
using conjugate gradient iterations.- Parameters
- Op
pylops.LinearOperator
Operator to invert of size \([N \times M]\)
- y
np.ndarray
Data of size \([N \times 1]\)
- x0
np.ndarray
, optional Initial guess
- niter
int
, optional Number of iterations
- damp
float
, optional Damping coefficient
- tol
float
, optional Tolerance on residual norm
- show
bool
, optional Display iterations log
- itershow
tuple
, optional Display set log for the first N1 steps, last N2 steps, and every N3 steps in between where N1, N2, N3 are the three element of the list.
- callback
callable
, optional Function with signature (
callback(x)
) to call after each iteration wherex
is the current model vector
- Op
- Returns
- x
np.ndarray
Estimated model of size \([M \times 1]\)
- 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- iit
int
Iteration number upon termination
- r1norm
float
\(||\mathbf{r}||_2\), 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 \(\epsilon=0\)- cost
numpy.ndarray
, optional History of r1norm through iterations
- x
Notes