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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.

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]);
    }
}

The Documentation contains some basic tutorials, we have an article on CodeProject, and finally source code contains some code examples in addition to the code of the library itself.

There are many open and commercial .NET libraries that have numeric optimization as one of their features (for example, Microsoft Solver Foundation, AlgLib,Extreme Optimization, CenterSpace NMath) . 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.

• 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.

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

• Andreas Witsch, Hendrik Skubch, Stefan Niemczyk, Kurt Geihs Using incomplete satisfiability modulo theories to determine robotic tasks 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 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 Eurographics 2013 proceedings (code repository)
• Michael Kommenda, Gabriel Kronberger, Stephan Winkler, Michael Affenzeller, Stefan Wagner Effects of constant optimization by nonlinear least squares minimization in symbolic regression 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 Proceedings of the 27th Annual ACM Symposium on Applied Computing
• AlicaEngine - A cooperative planning engine for robotics. You can see it in action in this video
• HeuristicsLab - a framework for heuristic and evolutionary algorithms that is developed by members of the Heuristic and Evolutionary Algorithms Laboratory (HEAL)