static void Main(string[] args)
{
// create function factory for arctangent
var arctan = UnaryFunc.Factory(
x => Math.Atan(x), // evaluate
x => 1 / (1 + x * x)); // derivative of atan
// create function factory for atan2
var atan2 = BinaryFunc.Factory(
(x, y) => Math.Atan2(y, x),
(x, y) => Tuple.Create(
-y / (x * x + y * y), // d/dx (from wikipedia)
x / (x * x + y * y))); // d/dy (from wikipedia)
// define variables
var u = new Variable();
var v = new Variable();
var w = new Variable();
// create and compile a term
var term = atan2(u, v) - arctan(w) * atan2(v, w);
var compiled = term.Compile(u, v, w);
// compute value + gradient
var diff = compiled.Differentiate(1, 2, -2);
Console.WriteLine("The value at (1, 2, -2) is {0}", diff.Item2);
Console.WriteLine("The gradient at (1, 2, -2) is ({0}, {1}, {2})",
diff.Item1[0],
diff.Item1[1],
diff.Item1[2]);
}
public void TestBinaryFuncSimple()
{
var v = Vec(new Variable(), new Variable());
var func = BinaryFunc.Factory(
(x, y) => x * x - x * y,
(x, y) => Tuple.Create(2 * x - y, -x));
var term = func(v[0], v[1]);
var y1 = term.Evaluate(v, NumVec(1, 0)); // 1 - 0 = 1
var y2 = term.Evaluate(v, NumVec(0, 1)); // 0 - 0 = 0
var y3 = term.Evaluate(v, NumVec(1, 2)); // 1 - 2 = -1
Assert.Equal(1.0, y1);
Assert.Equal(0.0, y2);
Assert.Equal(-1.0, y3);
}
public void TestBinaryFuncComplex()
{
var v = Vec(new Variable(), new Variable());
var func = BinaryFunc.Factory(
(x, y) => x * x - x * y,
(x, y) => Tuple.Create(2 * x - y, -x));
// f(x, y) = x² - xy - y² + xy = x² - y²
var term = func(v[0], v[1]) - func(v[1], v[0]);
var y1 = term.Evaluate(v, NumVec(1, 0)); // 1 - 0 = 1
var y2 = term.Evaluate(v, NumVec(0, 1)); // 0 - 1 = -1
var y3 = term.Evaluate(v, NumVec(2, 1)); // 4 - 1 = 3
Assert.Equal(1.0, y1);
Assert.Equal(-1.0, y2);
Assert.Equal(3.0, y3);
}
public void DiffBinaryComplex()
{
var v = Vec(new Variable(), new Variable());
var func = BinaryFunc.Factory(
(x, y) => x * x - x * y,
(x, y) => Tuple.Create(2 * x - y, -x));
// f(x, y) = x² - xy - y² + xy = x² - y²
// df/dx = 2x
// df/dy = -2y
var term = func(v[0], v[1]) - func(v[1], v[0]);
var y1 = term.Differentiate(v, Vec(1.0, 0.0)); // (2, 0)
var y2 = term.Differentiate(v, Vec(0.0, 1.0)); // (0, -2)
var y3 = term.Differentiate(v, Vec(2.0, 1.0)); // (4, -2)
Assert.Equal(Vec(2.0, 0.0), y1);
Assert.Equal(Vec(0.0, -2.0), y2);
Assert.Equal(Vec(4.0, -2.0), y3);
}
public void DiffBinarySimple()
{
var v = Vec(new Variable(), new Variable());
var func = BinaryFunc.Factory(
(x, y) => x * x - x * y,
(x, y) => Tuple.Create(2 * x - y, -x));
// f(x, y) = x² - xy
// df/dx = 2x - y
// df/dy = -x
var term = func(v[0], v[1]);
var y1 = term.Differentiate(v, Vec(1.0, 0.0)); // (2, -1)
var y2 = term.Differentiate(v, Vec(0.0, 1.0)); // (-1, 0)
var y3 = term.Differentiate(v, Vec(1.0, 2.0)); // (0, -1)
Assert.Equal(Vec(2.0, -1.0), y1);
Assert.Equal(Vec(-1.0, 0.0), y2);
Assert.Equal(Vec(0.0, -1.0), y3);
}