A package for fast evaluation of multivariate polynomials.
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September 2017


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FixedPolynomials.jl is a library for really fast evaluation of multivariate polynomials. Here are the latest benchmark results.

Since FixedPolynomials polynomials are optimised for fast evaluation they are not suited for construction of polynomials. It is recommended to construct a polynomial with an implementation of MultivariatePolynomials.jl, e.g. DynamicPolynomials.jl, and to convert it then into a FixedPolynomials.Polynomial for further computations.

Getting started

Here is an example on how to create a Polynomial with Float64 coefficients:

using FixedPolynomials
import DynamicPolynomials: @polyvar

@polyvar x y z

f = Polynomial{Float64}(x^2+y^3*z-2x*y)

To evaluate f you simply have to pass in a Vector{Float64}

x = rand(3)
f(x) # alternatively evaluate(f, x)

But this is not the fastest way possible. In order to achieve the best performance we need to precompute some things and also preallocate intermediate storage. For this we have GradientConfig and JacobianConfig. For single polynomial the API is as follows

cfg = GradientConfig(f) # this can be reused!
f(x) == evaluate(f, x, cfg)
# We can also compute the gradient of f at x
map(g -> g(x), ∇f) == gradient(f, x, cfg)

We also have support for systems of polynomials:

cfg = JacobianConfig([f, f]) # this can be reused!
[f(x), f(x)] == evaluate([f, f] x, cfg)
# We can also compute the jacobian of [f, f] at x
jacobian(f, x, cfg)