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Project Description

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

Getting AutoDiff

Using NuGet:
Install Autodiff Image

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

What is it for?

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

Code example

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]);


In the Documentation tab right now we have some basic tutorials, and some others are under construction. We also have an article on CodeProject. In addition, the binary distribution contains XML comments for all public methods and a help file you can view with your favorite help viewer. And finally, the source control contains some code examples in addition to the library's code.


There are many open and commercial .NET libraries that have numeric optimization as one of their features (for example, Microsoft Solver Foundation, AlgLib, Microsoft Research SHO 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 based on numeric optimization.


  • Fast! See 0.5 vs 0.3 benchmark and 0.3 benchmark.
  • 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
  • Uses Code Contracts for specifying valid parameters and return values
  • Computes gradients using Reverse-Mode AD algorithm in linear time!
    • Yes, it's faster than numeric approximation for multivariate functions
    • You get both high accuracy and speed!

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Last edited Jan 8, 2014 at 12:51 PM by alexshtf, version 60