Ecosyste.ms: Awesome

An open API service indexing awesome lists of open source software.

Awesome Lists | Featured Topics | Projects

https://github.com/alexshtf/autodiff

A .NET library that provides fast, accurate and automatic differentiation (computes derivative / gradient) of mathematical functions.
https://github.com/alexshtf/autodiff

autodiff automatic-differentiation gradient math mathematical-modelling mathematics optimization

Last synced: 12 days ago
JSON representation

A .NET library that provides fast, accurate and automatic differentiation (computes derivative / gradient) of mathematical functions.

Awesome Lists containing this project

README 

        
| AppVeyor CI | NuGet Package |

|-------------|---------------|

|[![Build Status](https://ci.appveyor.com/api/projects/status/github/alexshtf/autodiff)](https://ci.appveyor.com/api/projects/status/github/alexshtf/autodiff) | [![NuGet](https://img.shields.io/nuget/dt/AutoDiff.svg?style=plastic)](https://www.nuget.org/packages/AutoDiff/) |



# Project Description

A library that provides moderately fast, accurate, and automatic differentiation (computes derivative /  gradient) of mathematical functions.



AutoDiff provides a simple and intuitive API for computing function gradients/derivatives along with a fast algorithm for performing the computation. Such computations are mainly useful in iterative numerical optimization scenarios.



# Code example

```c#

using AutoDiff;



class Program

{

    public static void Main(string[] args)

    {

            // define variables

            var x = new Variable();

            var y = new Variable();

            var z = new Variable();

    

            // define our function

            var func = (x + y) * TermBuilder.Exp(z + x * y);

    

            // prepare arrays needed for evaluation/differentiation

            Variable[] vars = { x, y, z };

            double[] values = {1, 2, -3 };

    

            // evaluate func at (1, 2, -3)

            double value = func.Evaluate(vars, values);

    

            // calculate the gradient at (1, 2, -3)

            double[] gradient = func.Differentiate(vars, values);

    

            // print results

            Console.WriteLine("The value at (1, 2, -3) is " + value);

            Console.WriteLine("The gradient at (1, 2, -3) is ({0}, {1}, {2})", gradient[0], gradient[1], gradient[2]);

    }

}

```



# Documentation

The [Documentation](docs/Readme.md) contains some basic tutorials, we have an [article](http://www.codeproject.com/KB/library/Automatic_Differentiation.aspx) on CodeProject, and finally source code contains some code examples in addition to the code of the library itself.



# Motivation

There are many open and commercial .NET libraries that have numeric optimization as one of their features (for example, [Microsoft Solver Foundation](http://msdn.microsoft.com/en-us/devlabs/hh145003.aspx),  [AlgLib](http://www.alglib.net),[Extreme Optimization](http://www.extremeoptimization.com/), [CenterSpace NMath](http://www.centerspace.net/)) . Most of them require the user to be able to evaluate the function and the function's gradient. This library tries to save the work in manually developing the function's gradient and coding it.

Once the developer defines his/her function, the AutoDiff library can automatically evaluate and differentiate this function at any point. This allows _easy development and prototyping_ of applications which require numerical optimization.



# Features

* Moderate execution speeds. We aim computing a _gradient_ within no more than 50 times the duration of _function evaluation_ by manually tuned code.

* Composition of functions using arithmetic operators, Exp, Log, Power and user-defined unary and binary functions.

* Function gradient evaluation at specified points

* Function value evaluation at specified points

* Computes gradients using Reverse-Mode AD algorithm in **linear time**, which is substantially faster than numerical gradient approximation for multivariate functions.



# **Using in research papers**



If you like the library and it helps you publish a research paper, please cite the paper I originally wrote the library for [geosemantic.bib](docs/Home_geosemantic.bib)



# Used by



* **Andreas Witsch,  Hendrik Skubch, Stefan Niemczyk, Kurt Geihs** [Using incomplete satisfiability modulo theories to determine robotic tasks](http://dx.doi.org/10.1109/IROS.2013.6697046) _Intelligent Robots and Systems (IROS), 2013 IEEE/RSJ International Conference_

* **Michael Kommenda, Michael Affenzeller, Gabriel Kronberger, Stephan M. Winkler** [Nonlinear Least Squares Optimization of Constants in Symbolic Regression](https://link.springer.com/chapter/10.1007/978-3-642-53856-8_53) _Revised Selected Papers of the 14th International Conference on Computer Aided Systems Theory - EUROCAST 2013 - Volume 8111_

* **Alex Shtof, Alexander Agathos, Yotam Gingold, Ariel Shamir, Daniel Cohen-Or** [Geosemantic Snapping for Sketch-Based Modeling](http://diglib.eg.org/handle/10.1111/v32i2pp245-253) _Eurographics 2013 proceedings_  ([code repository](https://bitbucket.org/alexshtf/sketchmodeller))

* **Michael Kommenda, Gabriel Kronberger, Stephan Winkler, Michael Affenzeller, Stefan Wagner** [Effects of constant optimization by nonlinear least squares minimization in symbolic regression](http://dl.acm.org/citation.cfm?id=2482691) _Proceeding of the fifteenth annual conference companion on Genetic and evolutionary computation conference companion_

* **Hendrik Skubch**, [Solving non-linear arithmetic constraints in soft realtime environments](http://dl.acm.org/citation.cfm?id=2245293) _Proceedings of the 27th Annual ACM Symposium on Applied Computing_

* [AlicaEngine](http://ros.org/wiki/AlicaEngine) - A cooperative planning engine for robotics. You can see it in action in this [video](http://www.youtube.com/watch?v=HhIrhU19PG4)

* [HeuristicsLab](http://dev.heuristiclab.com) - a framework for heuristic and evolutionary algorithms that is developed by members of the [Heuristic and Evolutionary Algorithms Laboratory (HEAL)](http://heal.heuristiclab.com/)