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https://github.com/ranjanan/MonteCarloIntegration.jl

A package for multi-dimensional integration using monte carlo methods
https://github.com/ranjanan/MonteCarloIntegration.jl

monte-carlo-integration numerical-integration

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A package for multi-dimensional integration using monte carlo methods

Host: GitHub
URL: https://github.com/ranjanan/MonteCarloIntegration.jl
Owner: ranjanan
License: mit
Created: 2019-05-14T18:39:03.000Z (about 5 years ago)
Default Branch: master
Last Pushed: 2023-11-02T18:49:08.000Z (8 months ago)
Last Synced: 2024-01-13T01:03:21.349Z (6 months ago)
Topics: monte-carlo-integration, numerical-integration
Language: Julia
Homepage:
Size: 48.8 KB
Stars: 33
Watchers: 4
Forks: 15
Open Issues: 9
Metadata Files:
- Readme: README.md
- License: LICENSE.txt

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awesome-sciml - ranjanan/MonteCarloIntegration.jl: A package for multi-dimensional integration using monte carlo methods

README

        # Monte Carlo Integration 

![CI](https://github.com/ranjanan/MonteCarloIntegration.jl/workflows/CI/badge.svg)

[![Coverage Status](https://coveralls.io/repos/github/ranjanan/MonteCarloIntegration.jl/badge.svg?branch=master)](https://coveralls.io/github/ranjanan/MonteCarloIntegration.jl?branch=master)

This package provides multidimensional integration 

algorithms based on monte carlo methods. The biggest

advantage of using monte carlo methods is that their

convergence rate is **independent of the dimension of

the integral**. 

Currently, this package only provides a routine 

called VEGAS: 

    vegas(f, st, en, kwargs...)

VEGAS is a Monte Carlo algorithm for 

multidimensional integration based on 

adaptive importance sampling. It divides

each dimension into bins and adaptively adjusts

bin widths so points are sampled from the

region where the function has highest magnitude. 

Arguments:

----------

- st: Array of starting values in each dimension. 

Defaults to zeros(2)

- end: Array of ending values in each dimension. 

Defaults to ones(2)

Kwargs:

------

- nbins: Number of bins in each dimension. 

Defaults to 100. 

- ncalls: Number of function calls per iteration. 

Defaults to 1000.

- maxiter: Maximum number of iterations. 

Defaults to 100.

- rtol: Relative tolerance required. 

Defaults to 1e-4.

- atol: Absolute tolerance required. 

Defaults to 1e-2.

- debug: Prints `abs(sd/I)` every 100 iterations. 

Defaults to false.

- batch: Whether `f` returns batches of function

evaluations. `f` is assumed to take one argument 

`pts`, an `ncalls × ndims` matrix. Each row

is a unique point and returns an `ncalls` length

vector of function evals. This argument defaults

to false. 

Output:

------

- Estimate for the integral 

- Standard deviation

- χ^2 / (numiter - 1): should be less than 1 

otherwise integral estimate should not be trusted. 

References:

-----------

- Lepage, G. Peter. "A new algorithm for adaptive 

multidimensional integration." Journal of 

Computational Physics 27.2 (1978): 192-203.

### Batch interface

Most of the computation time in an integration

algorithm is usually spent in function evaluations. 

The batch inteface allows users to provide 

batches of function evaluations, instead of supplying

a function directly to be integrated. Users can now

evaluate a number of points in parallel. 

### Roadmap 

- Supporting vector valued functions

- Other integration algorithms