Improvements to linear iterative solvers
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Key: MATH-735
URL: https://issues.apache.org/jira/browse/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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