/// <summary>
/// Implementation of the actual code to search for the zeroes of
/// the <see cref="IObjectiveFunction"/>.
/// </summary>
/// <remarks>
/// It assumes that:
/// <list type="bullet">
/// <item>
/// <description>
/// <see cref="Solver1D.XMin"/> and <see cref="Solver1D.XMax"/> form a valid bracket;
/// </description>
/// </item>
/// <item>
/// <description>
/// <see cref="Solver1D.FXMin"/> and <see cref="Solver1D.FXMax"/> contain the values of the
/// function in <see cref="Solver1D.XMin"/> and <see cref="Solver1D.XMax"/>;
/// </description>
/// </item>
/// <item>
/// <description>
/// <see cref="Solver1D.Root"/> was initialized to a valid initial guess.
/// </description>
/// </item>
/// </list>
/// </remarks>
/// <param name="objectiveFunction">The <see cref="IObjectiveFunction"/>.</param>
/// <param name="xAccuracy">Given accuracy.</param>
/// <returns>The zero of the objective function.</returns>
/// <exception cref="ApplicationException">
/// Thrown when a bracket is not found after the maximum
/// number of evaluations (see <see cref="Solver1D.MaxEvaluations"/>).
/// </exception>
/// <exception cref="NotImplementedException">
/// Thrown by the <see cref="ObjectiveFunction"/> base class
/// when the function's derivative has not been implemented.
/// </exception>
protected override double SolveImpl(IObjectiveFunction objectiveFunction,
double xAccuracy)
{
while (EvaluationNumber++ < MaxEvaluations)
{
double froot = objectiveFunction.Value(Root);
double dfroot = objectiveFunction.Derivative(Root);
double dx = froot / dfroot;
Root -= dx;
// jumped out of brackets, switch to NewtonSafe
if ((XMin - Root) * (Root - XMax) < 0.0)
{
ISolver1D newtonSafe = new NewtonSafe();
newtonSafe.MaxEvaluations -= EvaluationNumber;
return(newtonSafe.Solve(objectiveFunction, xAccuracy,
Root + dx, XMin, XMax));
}
if (Math.Abs(dx) < xAccuracy)
{
return(Root);
}
}
throw new ApplicationException("SlvMaxEval");
}
/// <summary>
/// Implementation of the actual code to search for the zeroes of
/// the <see cref="IObjectiveFunction"/>.
/// </summary>
/// <remarks>
/// It assumes that:
/// <list type="bullet">
/// <item>
/// <description>
/// <see cref="Solver1D.XMin"/> and <see cref="Solver1D.XMax"/> form a valid bracket;
/// </description>
/// </item>
/// <item>
/// <description>
/// <see cref="Solver1D.FXMin"/> and <see cref="Solver1D.FXMax"/> contain the values of the
/// function in <see cref="Solver1D.XMin"/> and <see cref="Solver1D.XMax"/>;
/// </description>
/// </item>
/// <item>
/// <description>
/// <see cref="Solver1D.Root"/> was initialized to a valid initial guess.
/// </description>
/// </item>
/// </list>
/// </remarks>
/// <param name="objectiveFunction">The <see cref="IObjectiveFunction"/>.</param>
/// <param name="xAccuracy">Given accuracy.</param>
/// <returns>The zero of the objective function.</returns>
/// <exception cref="ApplicationException">
/// Thrown when a bracket is not found after the maximum
/// number of evaluations (see <see cref="Solver1D.MaxEvaluations"/>).
/// </exception>
/// <exception cref="NotImplementedException">
/// Thrown by the <see cref="ObjectiveFunction"/> base class
/// when the function's derivative has not been implemented.
/// </exception>
protected override double SolveImpl(IObjectiveFunction objectiveFunction,
double xAccuracy)
{
// Orient the search so that f(xl) < 0
double xh, xl;
if (FXMin < 0.0)
{
xl = XMin; xh = XMax;
}
else
{
xh = XMin; xl = XMax;
}
// the "stepsize before last"
double dxold = XMax - XMin;
// it was dxold=QL_FABS(_xMax_-_xMin_); in Numerical Recipes
// here (_xMax_-_xMin_ > 0) is verified in the constructor
// and the last step
double dx = dxold;
double froot = objectiveFunction.Value(Root);
double dfroot = objectiveFunction.Derivative(Root);
// the objectiveFunction throws System.NotImplementedException
while (++EvaluationNumber < MaxEvaluations)
{
// Bisect if (out of range || not decreasing fast enough)
if ((((Root - xh) * dfroot - froot) * ((Root - xl) * dfroot - froot) > 0.0) ||
(Math.Abs(2.0 * froot) > Math.Abs(dxold * dfroot)))
{
dxold = dx;
dx = (xh - xl) / 2.0;
Root = xl + dx;
}
else
{
dxold = dx;
dx = froot / dfroot;
Root -= dx;
}
// Convergence criterion
if (Math.Abs(dx) < xAccuracy)
{
return(Root);
}
froot = objectiveFunction.Value(Root);
dfroot = objectiveFunction.Derivative(Root);
if (froot < 0.0)
{
xl = Root;
}
else
{
xh = Root;
}
}
throw new ApplicationException(String.Format(
"SlvMaxEval")
);
}