[Matplotlib-users] Piecewise/derivative fit, WAS: Polyfit

[Jean-Baptiste C. <Jea...@de...>]

S=E6l !

Thanks for the tip, but I do not want to use the lagrangian: I want many sm=
all polynoms, not 1

What I want to do is very typical in Finite Element Method eventhough this =
is not the case here.
I just want to define many small polynoms between consecutives points.
Each one is stsifying the continuity of the value as well as the derivative
if I define my function as f(x)=3Dax*x+bx+c
At my points (X0,Y0) (X1,Y1) as well at teh derivative a X0 to be Z0 I get =
the follwoing
f(X0)=3DY0=3Da*X0*X0+b*X0+c
f(X1)=3DY1=3Da*X1*X1+b*X1+c
f'(X0)=3DZ0=3D 2aX0+b

After small manipulkation I can directly infere a,b,c

This is a very simple but useful routine that I was hoping people would hav=
e already written
Actually it is much smoother with a cubic polynomial, but it is a bit more =
complicated to implement

Thanks anyway

Jean-Baptiste



On Fri, 19 Mar 2004 23:49:28 +1000
"Gary Ruben" <ga...@em...> wrote:

> First, let me say, I don't know if there is code to do exactly what you w=
ant but here are my thoughts.
> It sounds to me like you're asking for Lagrange polynomial fitting routin=
es. Googling for "lagrange polynomial python" does return some code here: <=
http://www.stanford.edu/~sturdza/akimamod/akimamod.py>
> Another possibility is the spline fitting routines in Scipy (scipy.interp=
olate). These may be appropriate if what you're really after is just a way =
to fit smooth functions through points. I've used the splrep and splev func=
tions there successfully to fit spline functions through points. When I was=
 looking for curve fitting routines recently, I also came across some more =
generalized curve fitting modules for Python but I can't recall where :-( I=
 think they were SWIG wrappers for a C library.
> Also, look at this:
> <http://www.scipy.org/site_content/remap?rmurl=3Dhttp%3A//www.scipy.net/p=
ipermail/scipy-user/2003-August/001864.html>
> HTH,
> regards,
> Gary
>=20
> ----- Original Message -----
> From: Jean-Baptiste Cazier <Jea...@de...>
> Date: Fri, 19 Mar 2004 11:49:21 +0000
> To: "Gary Ruben" <ga...@em...>, jdh...@ni...
> Subject: Re: [Matplotlib-users] Polyfit
>=20
> >=20
> > Thanks to both of you. It worked just fine
> >=20
> > I will push my luck and ask if any of you knows of a module to fit a pi=
ecewise polynomial to a list of (X,Y) points.
> > something like=20
> > p=3Dpiece-wiseFit([1,2,5,7,8],[3,4,2,5,5],2)=20
> > would return [[A0,B0,C0],[A1,B1,C1}[A2,B2,C2},[A3,B3,C3]}, coefficients=
 for the 4 polynoms=20
> > A0+B0.X+C0.X.X
> > A1+B1.X+C1.X.X
> > A2+B2.X+C2.X.X
> > A3+B2.X+C3.X.X
> >=20
> > This is a classic and I expect the code to be written somewhere, eventh=
ough I could not find it even when I "Feel lucky" with Google.
> <snip>
> --=20
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>=20


--=20
-----------------------------
Jea...@de...

Department of Statistics
deCODE genetics     Sturlugata,8
570 2993          101 Reykjav=EDk