On Thu, Nov 21, 2024 at 03:09:37PM +0000, Ed . wrote:
> Hi Luis,
>
> Thank you for both the code and the explanation! I was aware of the
> limitations of diffover for this (including its name - just "diff" caused
> clashes with Text::Diff in a downstream module). I'm proposing to rename
> "diffover" to "numdiff" (for numerical differentiation) in the next version
> of PDL, any objections?
However, it just takes the differences between consecutive values. I
would call it firstdiff, as there are also second, third,
etc. diffs. These are analogous, but not equal, to the corresponding
(first, second, etc.) derivatives one find in calculus, and may be
used to build approximate derivatives, as in the examples.
> I considered using diff2 in my quickly-written prototype, but chose
> diffover so as not to shrink the dim by 1.
There are other PDL methods that allow the user to specify what to do
with the boundaries. Maybe the same should be done here. In my
solution the boundary could be kept if the function is periodic, but
otherwise, it should be thrown away. Another alternative is to add
values beyond the boundary: repeating the boundary value would
correspond to a 0 value for the derivative at the boundary. One could
also add f_{n+1}=2f_{n}-f_{n-1}, which would correspond to a null
curvature at the boundary. Or the easiest, which is to trim down the
derivative at the boundary by droping the last element for forward
differences, the first for backward differences and both for centered
differences.
> I am also keen to capture the 3 functions you've made, probably with
> "partial" going into Ufunc, and gaining an options param that has
> "difference" of either "forward", "backward", or "centred", or
> "shrink" using diff2. "div" and "curl" would then "just" be examples
> in the docs. Does anyone see any difficulties with this? Boyd, I don't
> feel this would clash with an Advent posting in any important way, but
> I'm very pleased to hear your thoughts if you disagree :-)
Would be useful.
Notice that I assumed the function was defined on a regular grid. If
not, more elaborate schemes would be needed to estimate the centered
derivative.
Another alternative for finding derivative, which may be useful in
some cases, is to make a Fourier transform of the data, multiply it by
i()*(wavevector) and then transform back.
Best regards,
Luis
>
> Best regards,
> Ed
>
--
o
W. Luis Mochán, | tel:(52)(777)329-1734 /<(*)
Instituto de Ciencias Físicas, UNAM | fax:(52)(777)317-5388 `>/ /\
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