| Re: Non-monotonic Abscissa values for IDL function SPLINE_P [message #66702] |
Wed, 03 June 2009 11:31 |
Jeremy Bailin
Messages: 618
Registered: April 2008
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Senior Member |
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On Jun 3, 11:50 am, Xavier Ceamanos García <xavier.ceama...@gmail.com>
wrote:
> Thank you so much Jeremy for the answer!
>
> You are very right. I use splines to interpolate spectra. Then, the
> main goal is to re-sample these spectra. Each value of a spectrum
> corresponds to a given wavelength and in my case all points are
> separated by a constant wavelength distance. Hence, it is crucial to
> know which wavelengths corresponds to each point of the over-sampled
> spectra. A good re-sampling is not possible otherwise.
>
> Then, are you telling me that the number of points of the output
> vector depends on the input data? That would mean that it would be
> different for each spectrum interpolation...
>
> So far, I am using the "SPLINE" function which produces a monotonic
> output. In this case, it is easy to know the output wavelengths. It is
> slower though...
>
> I was just wandering if there is any way to get the same results I get
> with SPLINE but using SPLINE_P...
>
> Thanks again!
>
> Xavi
Xavi,
Yes, the number of points in the output vector depends on the input
data. For example:
IDL> x = findgen(20)
IDL> y = sin(0.5*x)
IDL> spline_p, x, y, xr, yr, interval=0.25
IDL> help, xr, yr
XR FLOAT = Array[96]
YR FLOAT = Array[96]
IDL> y = sin(0.5*x)+x
IDL> spline_p, x, y, xr, yr, interval=0.25
IDL> help, xr, yr
XR FLOAT = Array[120]
YR FLOAT = Array[120]
So it will indeed be different for each spectrum. But your code should
be general enough to deal with that using n_elements(xr).
You might want to directly use SPL_INIT and SPL_INTERP... I suspect
that may do what you want.
-Jeremy.
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| Re: Non-monotonic Abscissa values for IDL function SPLINE_P [message #66708 is a reply to message #66702] |
Wed, 03 June 2009 09:00  |
Jeremy Bailin
Messages: 618
Registered: April 2008
|
Senior Member |
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> nxr = n_elements(Xr)
> goodpoints = where(Xr ge max(total(identity(nxr),/cumul,2) * rebin
> (Xr,nxr,nxr), dimen=1))
Incidentally, if nxr is large, that code will run out of memory pretty
quickly and you're better off with an iterative solution like this:
goodpoints = lindgen(n_elements(Xr))
repeat begin
nowinc = where(Xr[goodpoints[1:*]] gt Xr[goodpoints], ninc,
ncomp=ndec)
if ninc gt 0 then goodpoints = [0,goodpoints[nowinc+1]]
endrep until ndec eq 0
-Jeremy.
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| Re: Non-monotonic Abscissa values for IDL function SPLINE_P [message #66709 is a reply to message #66708] |
Wed, 03 June 2009 08:50 |
Xavier Ceamanos Garci
Messages: 2
Registered: June 2009
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Junior Member |
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Thank you so much Jeremy for the answer!
You are very right. I use splines to interpolate spectra. Then, the
main goal is to re-sample these spectra. Each value of a spectrum
corresponds to a given wavelength and in my case all points are
separated by a constant wavelength distance. Hence, it is crucial to
know which wavelengths corresponds to each point of the over-sampled
spectra. A good re-sampling is not possible otherwise.
Then, are you telling me that the number of points of the output
vector depends on the input data? That would mean that it would be
different for each spectrum interpolation...
So far, I am using the "SPLINE" function which produces a monotonic
output. In this case, it is easy to know the output wavelengths. It is
slower though...
I was just wandering if there is any way to get the same results I get
with SPLINE but using SPLINE_P...
Thanks again!
Xavi
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| Re: Non-monotonic Abscissa values for IDL function SPLINE_P [message #66710 is a reply to message #66709] |
Wed, 03 June 2009 07:52 |
Jeremy Bailin
Messages: 618
Registered: April 2008
|
Senior Member |
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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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