StepNormalizer extension with normalization mode and bounds settings

Key: MATH595
URL: https://issues.apache.org/jira/browse/MATH595
Project: Commons Math
Issue Type: Improvement
Reporter: Dennis Hendriks
Fix For: 3.0
Attachments: stepnormalizermodebounds.patch
While I was the StepNormalizer to get output at fixed interval points instead of the points
determined by the ODE integrator, I noticed the following:
1. It returns the first point (t0), and integer multiples of the step size add to it (t0+h,
t0+2h, ...). Let's call these the 'normalized points'. I wanted it to return values at multiples
of the step size, regardless of the start vaule. This would be a different semantics of 'normalized
points'.
2. It returns the first point (t0), and the last point only if it is a 'normalized point'.
I wanted it to never return the first point, and always return the last point, regardless
of the 'normalized points'. If one used a StepHandler directly, and not a StepNormalizer,
the first point would not be given to the handler, and the last point would. Thus, there is
a difference in first/last point handling for 'normal' StepHandlers and StepNormalizer with
FixedStepHandler.
Therefore I generalized the StepNormalizer:
1. It now has two modes (StepNormalizerMode enumeration). The first is INCREMENT, which has
the old semantics for 'normalized points'. The second is MULTIPLES, which has the newly proposed
semantics.
2. It is now possible to specify whether the first and last points should be given to the
underlying fixed step size step handler (StepNormalizerBounds enumeration).
The changes should be transparent to already existing code, as I used the old semantics for
existing constructors. The only change is in the calculation that determines whether the next
'normalized point' is in the current step interval. For forward integration, the end point
was considered to be in the interval, while for backward integration the end point was considered
NOT to be in the interval. I changed this so that the end point is in the interval regardless
of the direction. This is the only nonbackward compatible change. I personally consider the
old behavior to be wrong... This change is also required for the correct functioning of the
new bounds settings.
I also added a whole bunch of unit tests to test all different combinations of normalization
modes, bounds settings (first/last inclusion), integration direction, and whether the 'normalized
points' coincide/overlap the first/last points. This results in 2*4*2*2=32 unit tests.
I believe that the generalizations that I introduced make the StepNormalizer more powerful,
and make it useful in more scenarios.

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