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Re: pchip with 2 variables
Posted:
Jan 16, 2013 1:48 PM
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On Thursday, January 17, 2013 7:37:08 AM UTC+13, samar wrote:
> Dear Cédric,
>
>
>
> I want tu use Pchip function to interpolate my 2-dimensional data set.
>
> I'm actually using spline interpolation (with csapi function) but it doesn't work well.
>
> I think that Pchip will be better for my data set but I have no idea how to use it with 2 variables ( x1 and x2 are my variables they take their values over a given list and V=f(X1,X2) is the matrix that gives the value taken by f on each couple (x1,x2))
>
>
>
> The second question can we have the result of pchip in PPFORM?
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>
>
> Thank you very much for you help!
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>
>
> "Cédric Louyot" <cedric.louyot@NOSPAMonera.fr> wrote in message <eee8cbc.3@webx.raydaftYaTP>...
>
> > In fact, I'm not having any problem with the pchip function.
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> > Actually, it works real fine on the set of data I'm dealing with in
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> > 2D. However I also have to work on a set of 3D data (that looks
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> > really similar to the 2D set). Therefore, I try to understand the 2D
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> > algorithm in details in order to build a pchip3d (or even a pchipnd)
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> > function that could work on sets of data of the form:
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> > z(x,y) = f(x,y) (or even z(x1, x2, ..., xn))
>
> >
>
> > I've already tried the interp2 options ('linear','spline' and
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> > 'cubic') but they don't yield satisfactory results with my data.
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> > That's why I try to build a pchip3d function.
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> >
>
> > Is there any chance it has already been done before by someone else ?
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> > Do you know where I could find the Fritsch and Carlson paper ? I've
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> > already looked for it in vain.
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> >
>
> > Thanks,
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> >
>
> > Cédric
>
> >
>
> > John D'Errico wrote:
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> > >
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> > >
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> > > In article <eee8cbc.-1@webx.raydaftYaTP>,
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> > > "Cédric Louyot" <cedric.louyot@NOSPAMonera.fr> wrote:
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> > >
>
> > >> I'm looking for a precision regarding the algorithm that the
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> > > function
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> > >> pchip uses. In particular, according to the MATLAB function
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> > > reference
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> > >> :
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> > >> "The slopes at the xj are chosen in such a way that P(x)
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> > > preserves
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> > >> the shape of the data and respects monoticity."
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> > >>
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> > >> Could anybody explain to me what is hidden behing "in such a
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> > way"
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> > > ?
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> > >> How does pchip computes the slopes at the xj ?
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> > >>
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> > >> Thanks for your help,
>
> > >>
>
> > >> Cédric
>
> > >
>
> > > From the comments, we see that pchip is derived from
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> > > a nice paper by Fritsch and Carlson.
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> > >
>
> > > % F. N. Fritsch and R. E. Carlson, "Monotone Piecewise Cubic
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> > > % Interpolation", SIAM J. Numerical Analysis 17, 1980, 238-246.
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> > >
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> > > The idea is you choose a decent set of estimates of the
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> > > slopes at the knots. Then you test to see if they satisfy
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> > > some approximation to the monotonicity constraints put
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> > > forth in the F&C paper.
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> > >
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> > > These constraints form a boundary, one edge of which is
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> > > elliptic, around the set of cubic segments. If the choice
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> > > of slopes falls outside the set of monotone cubic segments,
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> > > then you adjust the derivatives so this does not happen.
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> > > Its a nice algorithm that runs quite quickly and does not
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> > > require the solution of a set of simultaneous linear
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> > > equations as a simple interpolating spline does.
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> > >
>
> > > The disadvantages to pchip are
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> > >
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> > > 1. It results in a C1 interpolant. (Discontinuous second
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> > > derivatives, whereas an interpolating cubic spline is C2.)
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> > > This is rarely a problem, although I have seen cases where
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> > > the second derivative discontinuities were a significant
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> > > flaw.
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> > >
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> > > 2. Since pchip is designed to produce locally monotone
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> > > interpolants, it sometimes produces less than desireable
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> > > results on spiky data. (By locally monotone, I mean it
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> > > does not introduce any extrema in the curve that is not
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> > > already in the data.)
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> > >
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> > > What happens when you have a spike in your data? Pchip
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> > > forces the derivative to zero at the maximum (or minimum)
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> > > of the spike. Again, this is by design.
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> > >
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> > > Are you having problems with pchip? Very often this
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> > > suggests that you may have data which is inappropriate
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> > > for pchip. For example, I would not use pchip to
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> > > interpolate an illuminant spectral power curve.
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> > > Especially not for one derived from a fluorescent light.
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> > >
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> > > HTH,
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> > > John D'Errico
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> > >
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> > >
>
> > > --
>
> > > There are no questions "?" about my real address.
>
> > >
>
> > > The best material model of a cat is another, or
>
> > > preferably the same, cat.
>
> > > A. Rosenblueth, Philosophy of Science, 1945
>
> > >
First of all, don't top post. It makes the thread hard to follow.
Put your reply UNDERNEATH.
Simply use interp1:
pp=interp1(x,y,'pchip');
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