=============== multivar_horner

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multivar_horner is a python package implementing a multivariate Horner scheme ("Horner's method", "Horner's rule") <https://en.wikipedia.org/wiki/Horner%27s_method>__ for efficiently evaluating multivariate polynomials.

Quick Guide:

.. code-block:: console

pip install multivar_horner

For efficiency this package is compiling the instructions required for polynomial evaluation to C by default. If you don't have a C compiler (gcc or cc) installed you also need to install numba for using an alternative method:

.. code-block:: console

pip install multivar_horner[numba]

Simple example:

.. code-block:: python

import numpy as np
from multivar_horner import HornerMultivarPolynomial

# input parameters defining the polynomial
#   p(x) = 5.0 + 1.0 x_1^3 x_2^1 + 2.0 x_1^2 x_3^1 + 3.0 x_1^1 x_2^1 x_3^1
coefficients = np.array([[5.0], [1.0], [2.0], [3.0]], dtype=np.float64)
exponents = np.array([[0, 0, 0], [3, 1, 0], [2, 0, 1], [1, 1, 1]], dtype=np.uint32)

# [#ops=7] p(x) = x_1 (x_1 (x_1 (1.0 x_2) + 2.0 x_3) + 3.0 x_2 x_3) + 5.0
horner_polynomial = HornerMultivarPolynomial(coefficients, exponents)
x = np.array([-2.0, 3.0, 1.0], dtype=np.float64)
p_x = horner_polynomial(x)

Also see:

• Documentation <https://multivar-horner.readthedocs.io/en/latest/>__
• GitHub <https://github.com/jannikmi/multivar_horner>__
• PyPI <https://pypi.python.org/pypi/multivar_horner/>__
• paper (JOSS) <https://joss.theoj.org/papers/10.21105/joss.02392>__
• paper (arXiv) <https://arxiv.org/abs/2007.13152>__