And here is the location of the problem in numpy/linalg/linalg.py :
def lstsq(a, b, rcond=1.e-10):
The 1e-10 is a bit conservative. On the other hand, I will note that the condition number of the dot(V^T ,V) matrix is somewhere around 1e22, which means in general terms that you need around 22 digits of accuracy. Inverting it only works sorta by accident in the current case. Generally, using Vandermonde matrices and polynomial fits it a bad idea when the dynamic range of the interval gets large and the degree gets up around 4-5 as it leads to ill conditioned sets of equations. When you really need the best start with chebychev polynomials or, bestest, compute a set of polynomials orthogonal over the sample points. Anyway, I think rcond should be something like 1e-12 or 1e-13 by default and be available as a keyword in the polyfit function. If no one complains I will make this change, although it is just a bandaid and things will fall apart again as soon as you call polyfit(x,y,4).
Hey that's great. I'm glad you tracked it down.
Pardon my ignorance of polyfit algorithm details.
Is there a way of choosing rcond based on N that would give sensible defaults for a variety of N?
Greg
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