pylops.optimization.basic.cg

pylops.optimization.basic.cg(Op, y, x0=None, niter=10, tol=0.0001, show=False, itershow=[10, 10, 10], callback=None)[source]

Conjugate gradient

Solve a square system of equations given an operator Op and data y using conjugate gradient iterations.

Parameters:
Op : pylops.LinearOperator

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

y : np.ndarray

Data of size \([N \times 1]\)

x0 : np.ndarray, optional

Initial guess

niter : int, optional

Number of iterations

tol : float, optional

Tolerance on residual norm

show : bool, optional

Display iterations log

itershow : list, 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 where x is the current model vector

Returns:
x : np.ndarray

Estimated model of size \([N \times 1]\)

iit : int

Number of executed iterations

cost : numpy.ndarray, optional

History of the L2 norm of the residual

Notes

See pylops.optimization.cls_basic.CG