/// <summary>
/// Integrates a given function within the given integral.
/// </summary>
/// <param name="f">The function to integrate.</param>
/// <param name="a">The lower limit.</param>
/// <param name="b">The higher limit.</param>
/// <returns>
/// The integral of <paramref name="function"/> over the interval from <paramref name="a"/> to <paramref name="b"/>
/// </returns>
public float Integrate(MathFunctions.FloatUnaryFunction f, float a, float b)
{
if (a > b)
{
return(-Integrate(f, b, a));
}
float sum = 0;
float stepSize = (float)((b - a) / _stepsNumber);
float stepSizeDiv3 = stepSize / 3.0f;
for (int i = 0; i < _stepsNumber; i = i + 2)
{
sum += (f(a + i * stepSize) + 4.0f * f(a + (i + 1) * stepSize) + f(a + (i + 2) * stepSize)) * stepSizeDiv3;
}
return(sum);
}
/// <summary>
/// Integrates a given function within the given integral.
/// </summary>
/// <param name="f">The function to integrate.</param>
/// <param name="a">The lower limit.</param>
/// <param name="b">The higher limit.</param>
/// <returns>
/// The integral of <paramref name="function"/> over the interval from <paramref name="a"/> to <paramref name="b"/>
/// </returns>
public float Integrate(MathFunctions.FloatUnaryFunction f, float a, float b)
{
// Check the _romD field is initialized correctly.
if ((_romF == null) || (_romF.GetLength(1) == _order))
{
_romF = new float[1, _order];
}
if (a > b)
{
return(Integrate(f, b, a));
}
float h = (b - a);
_romF[0, 0] = 0.5f * h * (f(a) + f(b));
for (int i = 2, ipower = 1; i <= _order; i++, ipower *= 2, h /= 2)
{
// Approximation using the trapezoid rule.
float sum = 0;
for (int j = 1; j <= ipower; j++)
{
sum += f(a + h * (j - 0.5f));
}
// Richardson extrapolation
_romF[1, 0] = 0.5f * (_romF[0, 0] + (h * sum));
for (int k = 1, kpower = 4; i < i; k++, kpower *= 4)
{
_romF[1, k] = (kpower * _romF[1, k - 1] - _romF[0, k - 1]) / (kpower - 1);
}
// Save the extrapolated values for the next iteration
for (int j = 0; j < i; j++)
{
_romF[0, j] = _romF[1, j];
}
}
return(_romF[0, _order - 1]);
}
/// <summary>
/// Initializes a new instance of the <see cref="FloatUnaryFunction"/> class.
/// </summary>
/// <param name="f">A function delegate that takes a float value as a parameter and returns a float value.</param>
/// <param name="d">The <see cref="IDifferentiator"/> to use.</param>
/// <param name="i">The <see cref="IIntegrator"/> to use.</param>
public FloatUnaryFunction(MathFunctions.FloatUnaryFunction f, IDifferentiator d, IIntegrator i)
{
_function = f;
_differentiator = d;
_integrator = i;
}
/// <summary>
/// Initializes a new instance of the <see cref="FloatUnaryFunction"/> class.
/// </summary>
/// <param name="f">
/// A function delegate that takes a float value as a parameter and returns a float value.
/// </param>
public FloatUnaryFunction(MathFunctions.FloatUnaryFunction f)
{
_function = f;
_differentiator = null;
_integrator = null;
}
/// <summary>
/// Initializes a new instance of the <see cref="FloatUnaryFunction"/> class.
/// </summary>
/// <param name="f">A function delegate that takes a float value as a parameter and returns a float value.</param>
/// <param name="d">The <see cref="IDifferentiator"/> to use.</param>
/// <param name="i">The <see cref="IIntegrator"/> to use.</param>
public FloatUnaryFunction(MathFunctions.FloatUnaryFunction f, IDifferentiator d, IIntegrator i)
{
_function = f;
_differentiator = d;
_integrator = i;
}
/// <summary>
/// Initializes a new instance of the <see cref="FloatUnaryFunction"/> class.
/// </summary>
/// <param name="f">
/// A function delegate that takes a float value as a parameter and returns a float value.
/// </param>
public FloatUnaryFunction(MathFunctions.FloatUnaryFunction f)
{
_function = f;
_differentiator = null;
_integrator = null;
}
