# GridDensities

This packages allows users to define a piecewise uniform density over a hypergrid and draw samples from it.

The figure below shows an example defined on a two-dimensional grid. The left half of the figure shows a plot of the probability density function (pdf) and the right half of the figure shows a two-dimensional histogram of 1,000,000 samples. Darker colors indicate higher values.

## Installation

Start Julia and run the following command:

`Pkg.add("GridDensities")`

## Usage

To use the GridDensities module, begin your code with

`using GridDensities`

## Defining a Grid Density

A grid density is defined by calling `d = GridDensity(data, lo, hi, bins)`

where `data`

is the relative density within each grid cell (does not need to be normalized), `lo`

is a vector of lower bounds for each dimension, `hi`

is a vector of upper bounds for each dimension, and `bins`

is a vector containing the number of bins for each dimension. The following line will create the density shown in the figure above.

`d = GridDensity(collect(1:8), [0.0, 0.0], [2.0, 4.0], [2, 4])`

## Evaluating the Probability Density Function (PDF)

To evaluate the probability density function of grid density `d`

and at point `x`

, run:

`prob_density = pdf(d, x)`

## Sampling

To draw a sample from the distribution for grid density `d`

, run:

`sample = rand(d)`

To draw `n`

samples from the distribution for grid density `d`

, run:

`samples = rand(d, n)`

## Credits

Contributors to this package include Mykel Kochenderfer and Sydney Katz.