pylops.optimization.cls_basic.LSQR#

class pylops.optimization.cls_basic.LSQR(Op)[source]#

Solve an overdetermined system of equations given an operator Op and data y using LSQR iterations.

\[\DeclareMathOperator{\cond}{cond}\]
Parameters
Oppylops.LinearOperator

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

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
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