Re: [Matplotlib-users] polyfit implementation

[Jean-Michel P. <jea...@ar...>]

jea...@ar... wrote:
> I'm having some troubles while fitting data with high order polynomials
> (typically order 6). I looked at the polyfit function in
> 'matplotlib/mlab.py' and I must say I don't understand why the
> least-square problem isn't solved using the matrix multiplication
> instead of the * multiplication. Unless I misunderstood something,
> shouldn't the following line:

Obviously I misunderstood something since quick trials gave me:

 >>> array([[0,1],[1,0]]) * array([[2],[3]])
array([[0, 2],
        [3, 0]])

 >>> matrixmultiply(array([[0,1],[1,0]]), array([[2],[3]]))
array([[3],
        [2]])

as the polyfit function works well...

Anyway it seems that my polyfit troubles come from computation precision 
issues. Indeed my polynomial may be of too high order than data actually 
need so that some coefficients are very low (eg. 1e-20). I made some 
experiments that show the results depend on the use of Numeric/numarray:

* Numeric
I must use polyfit(x,y,N) with Float64 for x because it crashes with 
Float32, but results are very inaccurate

* numarray
I can use either Float64 or Float32, but only Float32 give good results 
(may someone have an explanation...)

Compared to Matlab, polynomial fitting with Python is not as good in 
this case. For people who are interested in testing my data I provided 
an attached text file of x and y, the polynomial order is 6.



JM. Philippe