On Jun 2, 12:40 pm, Xavier Ceamanos García <xavier.ceama...@gmail.com>
wrote:
> Hi folks!
>
> I have a question regarding the IDL SPLINE_P function. It works as
> follows...
>
> SPLINE_P, X, Y, Xr, Yr, [INTERVAL]
>
> Where 'X' is the original abscissa vector (let's say 0:1:249, in my
> example) and 'Y' the vector I'd like to interpolate (n_elements(Y)
> =250, of course).
>
> Then 'Xr' and 'Yr' are the outputs containing the abscissa values of
> the interpolated function and the interpolated vector, respectively.
>
> The keyword INTERVAL sets the desired interval between interpolants.
>
> The problem appears when checking the output Xr and Yr size. Normally,
> their size should be (250-1)*INTERVAL+1. However, that is not the
> case. For INTERVAL=100 I get an output size equal to 25147 instead of
> 24901. The reason is that the output abscissa is not monotonic and
> that does allow me to continue working with the Y output.
>
> Does anyone know how to make it monotonic?
>
> I would like to use this function instead of SPLINE since the latter
> is bloody slower than the the first!
>
> I thank you all in advance,
>
> Cheers,
>
> Xavi
Two things here...
First, I think that INTERVAL is in physical units, so the number of
elements you get out for a given value of INTERVAL depends on what Y
does (i.e. if you double the actual values of Y, the number of output
points should approximately double). The actual number can vary a bit
from a simple calculation because SPLINE_P seems to always put output
values at each input value, and then within each interval it puts a
fixed number of output points between the input points that are spaced
equidistantly.
Second, if Xr ends up being non-monotonic, it's because that's what
the spline does... you can't force it to be monotonic if that's not
the solution. Why do you need it to be monotonic? (for interpolation,
maybe?) If you want to excise any times when Xr goes backwards, you
could do something like this:
nxr = n_elements(Xr)
goodpoints = where(Xr ge max(total(identity(nxr),/cumul,2) * rebin
(Xr,nxr,nxr), dimen=1))
...and then just use Xr[goodpoints] and Yr[goodpoints]. But that may
not really be what you want - if X is monotonic but Xr isn't, that may
well be a sign that your spline is not really a good interpolating
function. For example, I was playing around with the following:
X = findgen(5)
Y = [0., 100., 100., 0., -100.]
SPLINE_P, X, Y, Xr, Yr, INTERVAL=10
PLOT, X, Y, XRANGE=[-20,20]
OPLOT, Xr, Yr, PSYM=-4, LINES=2
You can see that the spline is pretty disastrous in this case (and the
"excise all points that aren't greater than the cumulative maximum"
approach that I listed above won't give you anything remotely like the
data points).
-Jeremy.
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