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From Sébastien Brisard (Created) (JIRA) <>
Subject [jira] [Created] (MATH-735) Improvements to linear iterative solvers
Date Sat, 28 Jan 2012 09:33:11 GMT
Improvements to linear iterative solvers

                 Key: MATH-735
             Project: Commons Math
          Issue Type: Improvement
    Affects Versions: 3.0
            Reporter: Sébastien Brisard
            Assignee: Sébastien Brisard

Before we release version 3.0, I would like to perform some changes to the general framework
for linear iterative solvers.
# Remove interface {{InvertibleRealLinearOperator}}: this was only proposed for handling preconditioners.
Let {{M}} be this preconditioner. In the course of the iterations, only matrix-vector products
of the form {{M^(-1) . y}} are needed, never direct products {{M . x}}. So it's just as simple
to provide {{M^(-1)}} as a standard {{RealLinearOperator}}, rather than {{M}} as an {{InvertibleRealLinearOperator}}.
This removes a little bit of clutter in the class hierarchy.
# {{o.a.c.m.util.IterationEvent}} should at the very least have a method to get the current
iteration number. Overwise, I find myself keeping track of the number of times {{o.a.c.m.util.IterationManager.fireIterationPerformedEvent(IterationEvent)}}
is called, which is both ugly and painfull.
# {{o.a.c.m.util.linear.IterativeLinearSolverEvent}} should have a method to access the norm
of the residual. I was reluctant to specify such a method in the interface at the start, because
I was not sure any iterative solver provides an updated estimate of this quantity at each
iteration. In fact, I've realized that most (if not all) solvers do, and it's quite nice to
be able to access this value while monitoring the progress of the inversion (through {{o.a.c.m.utils.IterationListener}}).
Otherwise, one has to compute {{b - A . x}} inside the listener, which *doubles* the cost
of each iteration!
# {{o.a.c.m.util.linear.IterativeLinearSolverEvent}} should have a method to access the residual
(the vector itself, not only its norm). I'm not sure *all* solvers can do that, so this should
be an optional feature, which might be useful. I see two different possible implementations
## specify {{RealVector o.a.c.m.util.linear.IterativeLinearSolverEvent.getResidual()}} as
an optional feature (potentially throwing {{UnsupportedOperationException}}), together with
a method {{boolean o.a.c.m.util.linear.IterativeLinearSolverEvent.providesResidual()}}. I
think some of us do not like {{UnsupportedOperationException}}, but this would be similar
to what was done in {{RealLinearOperator.operateTranspose(RealVector)}}.
## create a new interface {{RealVector o.a.c.m.util.linear.IterativeLinearSolverWithResidualEvent}}.

I would love to have some feedback on the last point.

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