numpoly 0.1.4

Polynomials as a numpy datatype

Numpoly is a generic library for creating, manipulating polynomial arrays.

Many numerical analysis, prominent in for example uncertainty quantification, uses polynomial approximations as proxy for real models to do analysis on. These models are often solutions to non-linear problems discretized with high mesh. As such, the corresponding polynomial approximation consist of high number of dimensions and large multi-dimensional polynomial coefficients.

The polynomial base class numpoly.ndpoly is a subclass of numpy.ndarray implemented to represent polynomials as array element. As such is fast and scales very well with the size of the coefficients. It is also compatible with most numpy functions, where that makes sense, making the interface fairly intuitive. Some of the interface is also inspired by the sympy interface.

Table of Contents:

• Installation

• Example usage

• Rational

• Development

• Questions & Troubleshooting

Installation

Installation should be straight forward:

pip install numpoly

And you should be ready to go.

Example usage

Constructing polynomial is typically done using one of the available constructors:

>>> numpoly.monomial(start=0, stop=4, names=("x", "y"))
polynomial([1, y, x, y**2, x*y, x**2, y**3, x*y**2, x**2*y, x**3])

It is also possible to construct your own from symbols:

>>> x, y = numpoly.symbols("x y")
>>> numpoly.polynomial([1, x**2-1, x*y, y**2-1])
polynomial([1, -1+x**2, x*y, -1+y**2])

Or in combination with other numpy objects:

>>> x**numpy.arange(4)-y**numpy.arange(3, -1, -1)
polynomial([1-y**3, x-y**2, x**2-y, -1+x**3])

The polynomials can be evaluated as needed:

>>> poly = 3*x+2*y+1
>>> poly(x=y, y=[1, 2, 3])
polynomial([3+3*y, 5+3*y, 7+3*y])

The polynomials also support many numpy operations:

>>> numpy.reshape(x**numpy.arange(4), (2, 2))
polynomial([[1, x],
            [x**2, x**3]])
>>> numpy.sum(numpoly.monomial(13)[::3])
polynomial(1+q**3+q**6+q**9+q**12)

There are also several polynomial specific operators:

>>> numpoly.diff([1, x, x**2], x)
polynomial([0, 1, 2*x])
>>> numpoly.gradient([x*y, x+y])
polynomial([[y, 1],
            [x, 1]])

Rational

The main reason for creating this is because I need it as a backend component for the chaospy library. It can be replaced by alternative software, but for its particular requirements, building something from scratch made the most sense.

• Why not numpy.polynomial?

  The numpy native polynomial class is likely better at what it does, but it is limited to only 3 dimensions. This makes it a non-starter as a backend for chaospy.

• Why not sympy?

  sympy is a great option that can do the same as numpoly and quite a bit more. However it is not using the vectorization utilized by numpy and relies on pure python for its operations. A process notably slower than what it could be in many instances.

Development

Development is done using Poetry manager. Inside the repository directory, install and create a virtual environment with:

poetry install

To run tests, run:

poentry run pytest numpoly test doc --doctest-modules

Questions & Troubleshooting

For any problems and questions you might have related to numpoly, please feel free to file an issue.