pylops.optimization.cls_basic.LSQR#
- class pylops.optimization.cls_basic.LSQR(Op)[source]#
Solve an overdetermined system of equations given an operator
Op
and datay
using LSQR iterations.\[\DeclareMathOperator{\cond}{cond}\]- Parameters
- Op
pylops.LinearOperator
Operator to invert of size \([N \times M]\)
- Op
Notes
Minimize the following functional using LSQR iterations [1]:
\[J = || \mathbf{y} - \mathbf{Op}\,\mathbf{x} ||_2^2 + \epsilon^2 || \mathbf{x} ||_2^2\]where \(\epsilon\) is the damping coefficient.
- 1
Paige, C. C., and Saunders, M. A. “LSQR: An algorithm for sparse linear equations and sparse least squares”, ACM TOMS, vol. 8, pp. 43-71, 1982.
Methods
__init__
(Op)callback
(x, *args, **kwargs)Callback routine
finalize
([show])Finalize solver
run
(x[, niter, show, itershow])Run solver
setup
(y[, x0, damp, atol, btol, conlim, ...])Setup solver
solve
(y[, x0, damp, atol, btol, conlim, ...])Run entire solver
step
(x[, show])Run one step of solver