// This method shows how to use root finding.
// A method y = Foo(x) is given and we want to find x such that Foo(x) = 7.
private void FindRoot()
{
var debugRenderer = GraphicsScreen.DebugRenderer2D;
debugRenderer.DrawText("----- RootFinding Example:");
// Create a new instance of a root finder class.
// The Newton-Raphson root finding method uses the function and the first-order
// derivative of the function where we want to find solutions. If the derivate
// is not known, other root finding classes can be used, like the BisectionMethod
// or RegulaFalsiMethod classes.
var rootFinder = new ImprovedNewtonRaphsonMethodF(Foo, FooDerived);
// Several x could result in Foo(x) = 7. So we need to define an x interval
// that contains the desired x solution.
// We decide to look for a solution near x = 0 and let the rootFinder approximate
// an x interval that contains the result.
float x0 = 0;
float x1 = 0;
// Find an interval [x0, x1] that contains an x such that Foo(x) = 7.
rootFinder.ExpandBracket(ref x0, ref x1, 7);
// Now we use the root finder to find an x within [x0, x1] such that Foo(x) = 7.
float x = rootFinder.FindRoot(x0, x1, 7);
// Lets check the result.
float y = Foo(x);
// Important note: We use Numeric.AreEqual() to safely compare floating-point numbers.
if (Numeric.AreEqual(y, 7))
{
debugRenderer.DrawText("Solution is correct.\n");
}
else
{
debugRenderer.DrawText("Solution is wrong.\n");
}
}
public GetParameterHelper2F()
{
_rootFinder = new ImprovedNewtonRaphsonMethodF(GetLength, GetTangentLength);
}
public GetParameterHelper1F()
{
_rootFinder = new ImprovedNewtonRaphsonMethodF(GetPoint, GetTangent);
}
public void FindRootTest1()
{
Func <float, float> polynomial = x => (x - 1) * (x - 10) * (x - 18);
Func <float, float> computeDerivative = x => 3 * x * x - 58 * x + 208;
ImprovedNewtonRaphsonMethodF rootFinder = new ImprovedNewtonRaphsonMethodF(polynomial, computeDerivative);
rootFinder.EpsilonX = Numeric.EpsilonF / 100;
float xRoot = rootFinder.FindRoot(0, 2);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(4, 10);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(10, 4);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(10, 12);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(2, 0);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(0, 3);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(3, 0);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(-6, 2);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(-1, 1);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(-1, 1);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(0.9f, 9.9f);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(2, 3);
Assert.IsTrue(float.IsNaN(xRoot));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(3, 2);
Assert.IsTrue(float.IsNaN(xRoot));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
rootFinder.MaxNumberOfIterations = 1;
xRoot = rootFinder.FindRoot(0, 1000);
Assert.IsTrue(float.IsNaN(xRoot));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
}
public void FindRootTest1()
{
Func<float, float> polynomial = x => (x - 1)*(x - 10)*(x - 18);
Func<float, float> computeDerivative = x => 3 * x * x - 58 * x + 208;
ImprovedNewtonRaphsonMethodF rootFinder = new ImprovedNewtonRaphsonMethodF(polynomial, computeDerivative);
rootFinder.EpsilonX = Numeric.EpsilonF / 100;
float xRoot = rootFinder.FindRoot(0, 2);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(4, 10);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(10, 4);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(10, 12);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(2, 0);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(0, 3);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(3, 0);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(-6, 2);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(-1, 1);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(-1, 1);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(0.9f, 9.9f);
Assert.IsTrue(Numeric.AreEqual(0, polynomial(xRoot)));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(2, 3);
Assert.IsTrue(float.IsNaN(xRoot));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
xRoot = rootFinder.FindRoot(3, 2);
Assert.IsTrue(float.IsNaN(xRoot));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
rootFinder.MaxNumberOfIterations = 1;
xRoot = rootFinder.FindRoot(0, 1000);
Assert.IsTrue(float.IsNaN(xRoot));
Console.WriteLine("NumberOfIterations: {0}", rootFinder.NumberOfIterations);
}
