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https://issues.apache.org/jira/browse/MATH-562?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13023431#comment-13023431
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Gilles commented on MATH-562:
-----------------------------
{quote}
Is the idea that the data are assumed to be coming from a periodic function
with known period?
{quote}
Yes.
{quote}
Is there any constraint on the number of periods that the sample data is
supposed to represent, or are we assuming that it represents just one period
with some points extending before and after?
{quote}
No, it is just assumed that the underlying time series is periodic with the
given period.
However, there might be a problem if more than one period is covered by the
sample data: If there are 2 samples exactly one period apart, they will be
mapped to the same point and the interpolator will throw an exception because
"xval" is not strictly increasing...
{quote}
[...] the application is to extend the domain of the interpolating function
outside of the domain determined by the data?
{quote}
Yes.
{quote}
Don't you maybe need two parameters for "extend" (number before beginning of
function period and number after) [...]
{quote}
Why? The "extend" points are there only to avoid that the interpolating
algorithm fails because it would lack the required number of points when trying
to interpolate at the ends of the interval: For example, the linear
interpolation needs one point before and one point after the interpolated point
but the latter won't exist when x > xval[xval.length - 1]. Hence, we replace
"xval" with an _extended_ "xvalP" such that
{code}
xvalP[xvalP.length - 1] = xval[0] + period
{code}
{quote}
Don't you [...] maybe even [need] two "offset" parameters (distance between
beginning of the period and the first "interior" domain value and between last
"interior" domain value and end of the period)?
{quote}
I'm not sure that we mean the same thing with that "offset". I only meant it as
the "zero-point" of the periodic signal.
I didn't get the "fitness" idea. Maybe that you target something more powerful
than what I had in mind.
> "UnivariateRealPeriodicInterpolator"
> ------------------------------------
>
> Key: MATH-562
> URL: https://issues.apache.org/jira/browse/MATH-562
> Project: Commons Math
> Issue Type: New Feature
> Reporter: Gilles
> Assignee: Gilles
> Priority: Minor
> Fix For: 3.0
>
>
> It would be an interpolator implementation that assumes that the data to be
> interpolated is periodic. Thus values that are outside of the range can be
> passed to the interpolation function:
> They will be wrapped into the initial range before being passed to the class
> that actually computes the interpolation.
> The constructor prototype would be:
> {code}
> /**
> * Builds an interpolator.
> *
> * @param interpolator Interpolator.
> * @param period Period.
> * @param offset Offset.
> * @param extend Number of points to be appended at the beginning and
> * end of the sample arrays in order to avoid interpolation failure at
> * the (periodic) boundaries of the orginal interval. The value is the
> * number of sample points which the original {@code interpolator} needs
> * on each side of the interpolation point.
> */
> public UnivariateRealPeriodicInterpolator(UnivariateRealInterpolator
> interpolator,
> double period,
> double offset,
> int extend) {
> // ...
> }
> {code}
> Would it be useful to have that in CM?
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