riemann 1.0.0a1

A package for computing Riemann summations in n-dimensional space

riemann

Riemann, a pure-Python package for computing Riemann sums of functions of several real variables.

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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 $[0, 1]$ using 10 partitions along the $x$ axis.

>>> import riemann
>>> from riemann import Interval
>>> f = lambda x: x ** 2
>>> intervals = [Interval(0, 1, 10)]
>>> methods = [riemann.LEFT]
>>> riemann.rsum(f, intervals, methods)
Decimal('0.285')

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 $x \in [0, 1], y \in [0, 1]$ using 10 partitions along the $x$ axis and 10 partitions along the $y$ axis.

>>> import riemann
>>> from riemann import Interval
>>> f = lambda x, y: x ** 2 + y ** 2
>>> intervals = [Interval(0, 1, 10), Interval(0, 1, 10)]
>>> methods = [riemann.LEFT, riemann.LEFT]
>>> riemann.rsum(f, intervals, methods)
Decimal('0.57')

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.

Requirements

Riemann requires Python 3.5+. This project does not require any additional dependencies.

Installation

$ pip install riemann

Documentation

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