# C# Root Finding Example

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```using System;

using CenterSpace.NMath.Core;
using CenterSpace.NMath.Analysis;

namespace CenterSpace.NMath.Analysis.Examples.CSharp
{
class RootFindingExample
{
/// <summary>
/// A .NET example in C# showing how to find a root of a univariate function
/// using the secant and Newton-Raphson methods.
/// </summary>
static void Main( string[] args )
{
Console.WriteLine();

// Find a root of the function 4x^3 + 0.4x - 9 in the interval
// -1000 < x < 1000 using the secant method.
var finder1 = new SecantRootFinder();
double root = finder1.Find( function, -1000, 1000 );
Console.Write( "Secant root finder found a root at " + root );
Console.WriteLine( " in " + finder1.Iterations + " iterations." );
Console.WriteLine();

// Function evaluated at the root is within tolerance of zero.
Console.WriteLine( "The function evaluated at the root: " + function.Evaluate( root ) );
Console.WriteLine();

// If you know the derivative of the function, you can use the
// Newton-Raphson root finder.
var finder2 = new NewtonRaphsonRootFinder();
root = finder2.Find( function, derivative, -1000, 1000 );
Console.Write( "Newton-Raphson root finder found the root" );
Console.WriteLine( " in " + finder2.Iterations + " iterations." );
Console.WriteLine();

// Reducing the tolerance speeds up the calculation.
finder2.Tolerance = 0.1;
root = finder2.Find( function, derivative, -1000, 1000 );
Console.Write( "Newton-Raphson root finder found the root" );
Console.WriteLine( " in " + finder2.Iterations + " iterations." );
Console.WriteLine();

// A negative tolerance causes the root finder to run until the maximum
// number of iterations is reached.
finder2.Tolerance = -1;
root = finder2.Find( function, derivative, -1000, 1000 );
Console.Write( "Newton-Raphson root finder found the root" );
Console.WriteLine( " in " + finder2.Iterations + " iterations." );
Console.WriteLine();

Console.WriteLine();
Console.WriteLine( "Press Enter Key" );
}

private static OneVariableFunction function = new OneVariableFunction( new Func<double, double>( F ) );

private static OneVariableFunction derivative = new OneVariableFunction( new Func<double, double>( DF ) );

private static double F( double x )
{
return 4 * Math.Pow( x, 3 ) + ( 0.4 * x ) - 9;
}

private static double DF( double x )
{
return 12 * Math.Pow( x, 2 ) + 0.4;
}

} // class

} // namespace

```
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