conjugate_gradient_normal¶

odl.solvers.iterative.iterative.conjugate_gradient_normal(op, x, rhs, niter=1, callback=None)[source]¶

Optimized implementation of CG for the normal equation.

This method solves the inverse problem (of the first kind)

A(x) == rhs

with a linear Operator A by looking at the normal equation

A.adjoint(A(x)) == A.adjoint(rhs)

It uses a minimum amount of memory copies by applying re-usable temporaries and in-place evaluation.

The method is described (for linear systems) in a Wikipedia article.

Parameters

opOperator: Operator in the inverse problem. If not linear, it must have an implementation of Operator.derivative, which in turn must implement Operator.adjoint, i.e. the call op.derivative(x).adjoint must be valid.
xop.domain element: Element to which the result is written. Its initial value is used as starting point of the iteration, and its values are updated in each iteration step.
rhsop.range element: Right-hand side of the equation defining the inverse problem
niterint: Number of iterations.
callbackcallable, optional: Object executing code per iteration, e.g. plotting each iterate.