scipy implementation of Carathéodory-Fejér method for approximating with rational function

[jason-s]

See http://eprints.maths.ox.ac.uk/926/1/NA-10-03.pdf. MATLAB implementation in https://github.com/chebfun/chebfun/blob/34f92d12ca51003f5c0033bbeb4ff57ac9c84e78/%40chebfun/cf.m (BSD-licensed); I tried to port (I know MATLAB reasonably well) but I'm stuck in the mud trying to understand what it's doing in places, like the vscale method.

See also http://www.chebfun.org/examples/approx/CF30.html which contains an earlier, less complicated version.

[jason-s]

whee! I was able to get the CF30 function working, by comparing the Matlab code executed running in Octave (I don't have Matlab).

see https://gist.github.com/jason-s/81c57b337ebc39da9eaa30d239116a52 -- I hereby release this to scipy per the SciPy license, in case you find this useful.

sample output:

x=np.linspace(-1,1,128) 
p,q=cf0.rcf(np.sin,3,4,128,20)
print p
print q
plt.plot(x,np.sin(x)-p(x)/q(x))

yields

cheb([  1.24209651e-14   8.93118270e-01   1.26614923e-14  -2.53849881e-02])
cheb([  1.00000000e+00   2.83675893e-14   3.09682831e-02   1.63235467e-15   2.41732589e-04])

[person142]

I'm going to close this; I think it comes under the category of "things we would probably accept a PR for" (though it should still be proposed on the mailing list first), but we don't want to keep issues around for every such thing.