[Numpy-discussion] Polynomial evaluation inconsistencies (original) (raw)

Charles R Harris charlesr.harris at gmail.com
Fri Jun 29 23:10:16 EDT 2018

On Fri, Jun 29, 2018 at 8:21 PM, Maxwell Aifer <maifer at haverford.edu> wrote:

Hi, I noticed some frustrating inconsistencies in the various ways to evaluate polynomials using numpy. Numpy has three ways of evaluating polynomials (that I know of) and each of them has a different syntax:

- numpy.polynomial.polynomial.Polynomial <https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.polynomial.polynomial.Polynomial.html#numpy.polynomial.polynomial.Polynomial>: You define a polynomial by a list of coefficients *in order of increasing degree*, and then use the class’s call() function. - np.polyval <https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.polyval.html>: Evaluates a polynomial at a point. First argument is the polynomial, or list of coefficients in order of decreasing degree, and the second argument is the point to evaluate at. - np.polynomial.polynomial.polyval <https://docs.scipy.org/doc/numpy-1.12.0/reference/generated/numpy.polynomial.polynomial.polyval.html>: Also evaluates a polynomial at a point, but has more support for vectorization. First argument is the point to evaluate at, and second argument the list of coefficients *in order of increasing degree*. Not only the order of arguments is changed between different methods, but the order of the coefficients is reversed as well, leading to puzzling bugs (in my experience). What could be the reason for this madness? As polyval is a shameless ripoff of Matlab’s function of the same name <https://www.mathworks.com/help/matlab/ref/polyval.html> anyway, why not just use matlab’s syntax (polyval([c0, c1, c2...], x)) across the board? ​ The polynomial package, with its various basis, deals with series, and especially with the truncated series approximations that are used in numerical work. Series are universally written in increasing order of the degree. The Polynomial class is efficient in a single variable, while the numpy.polynomial.polynomial.polyval function is intended as a building block and can also deal with multivariate polynomials or multidimensional arrays of polynomials, or a mix. See the simple implementation of polyval3d for an example. If you are just dealing with a single variable, use Polynomial, which will also track scaling and offsets for numerical stability and is generally much superior to the simple polyval function from a numerical point of view.

As to the ordering of the degrees, learning that the degree matches the index is pretty easy and is a more natural fit for the implementation code, especially as the number of variables increases. I note that Matlab has ones based indexing, so that was really not an option for them.

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