Skip to main content

A Python module to compute multidimensional arrays of evaluated functions.

Project description

# PyFunctionBases
A Python module to compute multidimensional arrays of evaluated functions based on Numpy.

Specifically, the module evaluates basis functions on intervals by employing a recursive formula of type
<p align="center">
<img src="{n&plus;1}(x)&space;=&space;g(f_n(x),&space;\dots,&space;f_0(x),x)." title="f_{n+1}(x) = g(f_n(x), \dots, f_0(x),x)." />

This is generalized to the multi-dimensional case by using a tensor product
<p align="center">
<img src=",y)&space;\mapsto&space;f_i(x)f_j(y)" />

repeatedly on coordinate wise one-dimensional function bases. The code is vectorized over the evalution points

<img src=";\in&space;\mathbb{R}^{num\_dim},&space;m&space;\in&space;\{1,&space;\dots,&space;num\_samples\}" />

and returns a multi-dimensional array of shape `(num_samples, degree+1, ..., degree+1)`, where `degree`
is the cardinality of the one-dimensional bases omitting a constant function. Currently, the following functions are available:

| Name | Domain |
| [`standard_poly`]( | `[-Inf, Inf]`|
| [`legendre_poly`]( | `[-1, 1]`|
| [`legendre_rational`]( | `[0, Inf]`|
| [`chebyshev_poly`]( | `[-1, 1]`|

Please make sure that your data lies in these domains, checks will be run if desired.

### Contents
[1. Installation](#installation)
[2. Simple Usage](#simple-usage)

## Installation
Requirements: `pip3 install numpy`

pip3 install pyfunctionbases

## Simple Usage
Now a simple example using standard polynomials is given. By exchanging the name parameter, you can try different functions.

from pyfunctionbases import RecursiveExpansion
import numpy as np

# create some data to evaluate basis functions on<
num_samples = 1000
num_dim = 2
x = np.random.uniform(low=0.0, high=1.0, size=(num_samples, num_dim))

# create an expansion object where name can be any
# function name, that is in the table below
degree = 10
name = 'standard_poly'
expn = RecursiveExpansion(degree, recf=name)

# evaluate the function, result is of shape (num_samples, degree+1, degree+1)
f_ij = expn.execute(x, check=True)

# flatten the result if needed
f_k = f_ij.reshape(num_samples,(degree+1)**num_dim)

Project details

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

pyfunctionbases-0.0.post68.tar.gz (6.9 kB view hashes)

Uploaded Source

Built Distribution

pyfunctionbases-0.0.post68-py2-none-any.whl (7.5 kB view hashes)

Uploaded Python 2

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page