riemann 0.9.0

A package for computing Riemann summations in n-dimensional space

riemann

Riemann is a pure-Python package for computing Riemann sums of functions in $n$-dimensional space.

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Basic Usage

Riemann provides an intuitive syntax for calculating the Riemann sum of a function over a closed interval. The below code snippet computes the Riemann sum of $f(x) = x^{2}$ over the interval $[0, 2]$ using 10 partitions along the $x$ axis.

>>> import riemann
>>> from riemann import Dimension
>>> f = lambda x: x ** 2
>>> dim_x = Dimension(0, 2, 10, riemann.LOWER)
>>> dim_x
Dimension(a=0, b=2, n=10, method=Method(name='lower'))
>>> riemann.rsum(f, dim_x)
Decimal('2.28')

However, Riemann is not restricted to computing Riemann sums only over one dimension. A similar syntax can be used to calculate the Riemann sum of a function of several real variables over a closed multi-dimensional interval. The below code snippet computes the Riemann sum of $f(x, y) = x^{2} y^{2}$ over the interval $x \in [0, 2], y \in [0, 4]$ using 10 partitions along the $x$ axis and 10 partitions along the $y$ axis.

>>> import riemann
>>> from riemann import Dimension
>>> f = lambda x, y: (x ** 2) * (y ** 2)
>>> dim_x = Dimension(0, 2, 10, riemann.MIDDLE)
>>> dim_x
Dimension(a=0, b=2, n=10, method=Method(name='middle'))
>>> dim_y = Dimension(0, 4, 10, riemann.MIDDLE)
>>> dim_y
Dimension(a=0, b=4, n=10, method=Method(name='middle'))
>>> riemann.rsum(f, dim_x, dim_y)
Decimal('56.6048')

The sole requirement is that the number of parameters taken by the function passed as the func argument to riemann.rsum equals the number of riemann.Dimension objects passed.

Features

• Fast computation of Riemann sum.
• Support for computation of multi-dimensional Riemann sum.
• Built-in support for left, middle, and right Riemann sum methods.
• Support for custom Riemann sum methods (using the :py:class:riemann.Method class).

Requirements

Riemann requires Python 3.7+. This project does not require any additional dependencies.

Installation

$ pip install riemann

Documentation

The documentation for this project is available on Read the Docs.