# [Numpy-discussion] polynomial with negative exponents

Gregor Thalhammer gregor.thalhammer at gmail.com
Mon Dec 12 12:17:35 EST 2011

```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
```