firstapp.md

Getting started

Let us start by creating a new project, and adding a NuGet package reference to AutoDiff. Then, modify your program.cs file to have the following content:

using System;
using AutoDiff;

namespace MyFirstAutodiffProgram
{
    class Program
    {
        static void Main(string[] args)
        {
        }
    }
}

Defining a mathematical function

The main purpose of this library is to allow its user to compute gradients of mathematical functions, so let's see how simple it is. In the following example we will compute the gradient of the function:

f(x,y) = (x+y) * log(exp(x) + exp(y))

We begin by defining our function in code. Add the following lines of code to the Main method:

Variable x = new Variable();
Variable y = new Variable();
Term func = (x + y) * TermBuilder.Log(TermBuilder.Exp(x) + TermBuilder.Exp(y));

The first two lines of code create two objects x and y that represent the function's variables. The third line of code creates an object that represents our function.

The AutoDiff library uses the Term type to represent analytic terms (or expressions) that define our functions. Everything is a Term, even variables (x and y in this example). The class TermBuilder, as its name says, is used to construct new terms out of existing ones.

Now we can easily compute the value and the gradient at any given point. Let us compute the value and the gradient of this function at x = 2, y = -1. Add the following lines of code to the Main method:

var point = new double[] { 2, -1};
var variables = new Variable[] { x, y };
double value = func.Evaluate(variables, point);
double[] grad = func.Differentiate(variables, point);

As you can probably guess, the Evaluate method computes the value of the term func by assigning values to variables, and the Differentiate function computes the gradient. The first parameter to both functions is an array with all the function's variables. The second parameter is the assignment of values to those variables.

It is important to note that order does matter - the first variable in the variables array is assigned the first value in the values array, and so on. In addition, order matters for the gradient too. In our example, grad[0] is the partial derivative with respect to x because we provided x as the first element of the variables array, and similarly grad[1] is the partial derivative with respect to y.

Summary

This tutorial demonstrates the most basic usage of the AutoDiff library - defining functions and computing their values and gradients. Here are the key points:

• Objects of type Term are used to define functions analytically
• The Evaluate/Differentiate methods can be used to compute the value/gradient of a function given assignment of values to variables
• The order of variables given to the Evaluate and Differentiate methods matters