[Numpy-discussion] polynomial with negative exponents

[Gregor Thalhammer]

Am 12.12.2011 um 15:04 schrieb LASAGNA DAVIDE:

> Hi,
> 
> I have written a class for polynomials with negative 
> exponents like:
> 
> p(x) = a0 + a1*x**-1 + ... + an*x**-n
> 
> The code is this one:
> 
> class NegativeExpPolynomial( object ):
>      def __init__ ( self, coeffs ):
>          self.coeffs = np.array( coeffs )
> 
>      def __call__( self, x ):
>          return sum( (c*x**(-i) for i, c in enumerate( 
> self.coeffs ) ) )
> 
> where coeffs = [a0, a1, ..., an].
> 
> I find that the way i evaluate the polynomial is kind of 
> *slow*, especially for polynomial with order larger than 
> ~200 and for arrays x large enough.

I fear that such high orders create a lot of troubles since evaluating them is very sensitive to numerical errors.

> Do you have suggestions on how to speed up this code?
> 

Your polynomials with negative exponents are equivalent to a polynomial with positive exponents, but evaluated at 1/x. Therefore you can make use of the efficient polynomial functions of numpy. Try

np.polyval(self.coeffs, x)


Gregor