[pymvpa] detrend(): why Legendre polynomials?

[Emanuele Olivetti]

Howdy,

I'm still playing with polynomial detrend() and I'm wondering why
Legendr polynomials are used internally (see
mvpa/datasets/miscfx_sp.py) instead of standard polynomial fit, like
numpy.polyfit(). I'm fairly ignorant about numerical problems of
polynomial interpolation but could this be related to the "warning" in
the numpy.polyfit() docstring (which I partly understand)?
----
    DISCLAIMER: Power series fits are full of pitfalls for the unwary 
once the
    degree of the fit becomes large or the interval of sample points is 
badly
    centered. The basic problem is that the powers x**n are generally a poor
    basis for the functions on the sample interval with the result that the
    Vandermonde matrix is ill conditioned and computation of the polynomial
    values is sensitive to coefficient error. The quality of the 
resulting fit
    should be checked against the data whenever the condition number is 
large,
    as the quality of polynomial fits *can not* be taken for granted. If all
    you want to do is draw a smooth curve through the y values and 
polyfit is
    not doing the job, try centering the sample range or look into
    scipy.interpolate, which includes some nice spline fitting functions 
that
    may be of use.
----

Thanks in advance for any explanation,


Emanuele