On 30.09.2015 13:21, Pauli Virtanen wrote:
Juha Jeronen <juha.jeronen <at> jyu.fi> writes:
I recently developed a Cython-based, OpenMP-accelerated quartic (and
cubic, quadratic) polynomial solver to address a personal research need
for quickly solving a very large number of independent low-degree
polynomial equations for both real and complex coefficients.
My 2c in this context would be to also think how this best fits
in how collections of polynomials are represented in Numpy.
AFAICS, Numpy's polynomial module supports evaluation of polynomial
collections (cf. numpy.polynomial.polynomial.polyval),
but the corresponding root finding routine
(numpy.polynomial.polynomial.polyroots) only deals with one
polynomial at a time.
The present code in principle could be used to speed up the latter
routine after it is generalized to multiple polynomials. The general
case is probably doable just by coding up the companion matrix
approach using low-level routines (or maybe with the new vectorized
np.linalg routines).
Some relevant code elsewhere for similar purposes can be
found in scipy.inteprolate.PPoly/BPoly (and in the future BSpline).
https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.PPoly.html
However, since it's piecewise, there's purposefully support only
for real-valued roots.
Thanks.
It sounds like numpy.polynomial.polynomial.polyroots() is a good
candidate place for this, if as you suggest, it is first generalized to
handle multiple polynomials.
-J
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