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hscarbonexamples
Examples of Monte Carlo simulations written with Carbon
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README
Carbon
A Haskell framework for (parallel) montecarlo simulations.
What is it?
Carbon is an opensource, Haskell framework aiming to provide easy access to parallel Monte Carlo simulations by providing a simple, but powerful compositional method for building simulations, highlevel functions for running them, and efficient data structures for aggregating common data types.
Examples of simulations written in Carbon can be found at: https://github.com/icasperzen/hscarbonexamples
Features
Monadic Composition
Carbon allows users to quickly describe Monte Carlo simulations using monadic composition (similar to parser combinators).
For example, starting from a Carbon primitive action, randomR
, we can build a simulation which tests for membership in the unit circle.
mcSquareD :: RandomGen g => MonteCarlo g (Double,Double)
mcSquareD = liftM2 (,) (randomR (1,1)) (randomR (1,1))
inUnitCircle :: RandomGen g => MonteCarlo g Bool
inUnitCircle = do
(x,y) < mcSquareD
return $ x*x + y*y <= 1
We build mcSquareD
, which returns a random 2D coordinate in the unit square, from randomR
.
Next, we build inUnitCircle
using mcSquareD
, returning a Bool
if the sampled 2D point lies within the unit circle.
High Level Function
Carbon aims to capture common usage patterns in high level "skeletons". Currently, just one is provided (and its sequential equivalent):
experimentP :: (R.RandomGen g, Result s)
=> MonteCarlo g (Obs s) > Int > Int > g > s
For example, using inUnitCircle
, we can compute the value of pi.
let res = experimentP inUnitCircle noRuns chSize gen
pi = 4 * sampleMean res
Data Aggregation
Descriptions of simulations should be completely independent of the results desired.
Carbon enforces this separation of concerns by using type families.
Every simulation will require a type annotation describing the desired output.
The particular instance of the type family describes how data aggregation is to occur (what to do with each observation).
For example, the following two simulations use the same MonteCarlo
action, but deliver very different results.
let bl = experimentP inUnitCircle noRuns chnkSize gen :: [Bool]
let bs = experimentP inUnitCircle noRuns chnkSize gen :: BoolSumm
[Bool]
is a list containing every observation from the simulation.
This is inefficient, however, as it is rarely necessary to maintain each and every observation in memory.
Instead, we can fold it into a clever data structure.
BoolSumm
is a spaceefficient representation of binary observations.
The Result
typeclass captures this functionality.
Basic Statistics
Carbon provides functionality for computing basic statistics on some instances of Result
.
The Summary
typeclass is meant to capture some of the common statistical measures one might be interested in.
Creating new instances of Summary
is easy; and extra functions can be written for a Result
instance to capture even more complex statistical functionality.
Status
Updated: 2014/06/30
Version 0.1.0 released!
Current features:
 support for parallelism (using GpH Strategies)
 highlevel function for describing a simulation
 efficient data aggregation techniques