static void Main(string[] args)
{
// we will use a function of two variables
Variable x = new Variable();
Variable y = new Variable();
// func(x, y) = (x + y) * exp(x - y)
var func = (x + y) * TermBuilder.Exp(x - y);
// create compiled term and use it for many gradient/value evaluations
var compiledFunc = func.Compile(x, y);
// we can now efficiently compute the gradient of "func" 64 times with different inputs.
// compilation helps when we need many evaluations of the same function.
for (int i = 0; i < 64; ++i)
{
var xVal = i / 64.0;
var yVal = 1 + i / 128.0;
var diffResult = compiledFunc.Differentiate(xVal, yVal);
var gradient = diffResult.Item1;
var value = diffResult.Item2;
Console.WriteLine("The value of func at x = {0}, y = {1} is {2} and the gradient is ({3}, {4})",
xVal, yVal, value, gradient[0], gradient[1]);
}
}
static void Main(string[] args)
{
Variable x = new Variable();
// f(x) = e^(-x) + x - 2
// it has two roots. See plot.png image attached to this project.
var func = TermBuilder.Exp(-x) + x - 2;
// find the root near 2
var root1 = RootFinder.NewtonRaphson(func, x, 2);
// find the root near -1
var root2 = RootFinder.NewtonRaphson(func, x, -1);
Console.WriteLine("The equation e^(-x) + x - 2 = 0 has two solutions:\nx = {0}\nx = {1}", root1, root2);
}
static void Main(string[] args)
{
// we will use a function of two variables
Variable x = new Variable();
Variable y = new Variable();
// func(x, y) = (x + y) * exp(x - y)
var func = (x + y) * TermBuilder.Exp(x - y);
// define the ordering of variables, and a point where the function will be evaluated/differentiated
Variable[] vars = { x, y };
double[] point = { 1, -2 };
// calculate the value and the gradient at the point (x, y) = (1, -2)
double eval = func.Evaluate(vars, point);
double[] gradient = func.Differentiate(vars, point);
// write the results
Console.WriteLine("f(1, -2) = " + eval);
Console.WriteLine("Gradient of f at (1, -2) = ({0}, {1})", gradient[0], gradient[1]);
}
public void ExpContract()
{
Assert.Throws <ArgumentNullException>(() => TermBuilder.Exp(null));
Assert.IsType <Exp>(TermBuilder.Exp(x));
}