//returns the point which axproximates the zero inside the interval
public Vector2D Solve(double inf, double sup)
{
double a = inf, b = sup, x = 0;
double fa = function(a), fb = function(b), fx = 0;
bool success = false;
//check if the interval is valid
if (fa * fb > 0)
{
throw new CalculationException("Not valid interval", function);
}
//first iteration is used for providing a reference estimation
x = (a + b) / 2;
fx = function(x);
if (fx * fa < 0)
{
b = x;
fb = fx;
}
else if (fx * fb < 0)
{
a = x;
fa = fx;
}
stoppingCriteria.SetCriteria(new Vector2D(x, fx));
for (int k = 0; k < maxIterations; k++)
{
x = (a + b) / 2;
fx = function(x);
if (stoppingCriteria.FullfilCriteria(new Vector2D(x, fx)))
{
success = true;
break;
}
if (fx * fa < 0)
{
b = x;
fb = fx;
}
else if (fx * fb < 0)
{
a = x;
fa = fx;
}
}
if (!success)
{
throw new CalculationException("No convergence to the solution (exceded the maximum number of iterations)", function);
}
return(new Vector2D(x, fx));
}
public Vector2D Solve(double initialEstimation, int multiplicity = 1)
{
if (multiplicity < 1)
{
throw new ArgumentOutOfRangeException("multiplicity", "the multiplicity of the root must be equal or greater than 1");
}
double xn = initialEstimation;
double fn = 0;
double dfn = 0;
bool success = false;
stoppingCriteria.SetCriteria(new Vector2D(xn, function(xn)));
for (int k = 0; k < maxIterations; k++)
{
fn = function(xn);
dfn = derivative(xn);
if (dfn == 0 && fn != 0)
{
throw new CalculationException("Cannot continue calculation, the function derivative is 0 in " + xn, function);
}
if (stoppingCriteria.FullfilCriteria(new Vector2D(xn, fn)))
{
success = true;
break;
}
xn = xn - multiplicity * fn / dfn;
}
if (!success)
{
throw new CalculationException("No convergence to the solution (exceded the maximum number of iterations)", function);
}
return(new Vector2D(xn, fn));
}
public Vector2D Solve(double x0, double x1)
{
double xn1 = x1, xn0 = x0, x = 0;
double fn1 = function(xn1), fn0 = function(xn0);
bool success = false;
stoppingCriteria.SetCriteria(new Vector2D(xn1, function(fn1)));
for (int k = 0; k < maxIterations; k++)
{
double d = (fn1 - fn0) / (xn1 - xn0);
x = xn1 - fn1 / d;
if (!x.IsFinite())
{
throw new CalculationException("Found a non finite point in the succession to the root", function);
}
fn0 = fn1;
xn0 = xn1;
fn1 = function(x);
xn1 = x;
if (stoppingCriteria.FullfilCriteria(new Vector2D(xn1, fn1)))
{
success = true;
break;
}
}
if (!success)
{
throw new CalculationException("No convergence to the solution (exceded the maximum number of iterations)", function);
}
return(new Vector2D(xn1, fn1));
}