public static int general_driver(
Func <Func <double, vector, vector>, double,
vector, double, vector[]> stepper,
Func <double, vector, vector> f,
double a,
ref vector y,
double b,
double h, // Starting step size
double acc,
double eps,
List <double> ts = null,
List <vector> ys = null
)
{
// The current posistion, set to starting condition:
double t = a;
vector yt = y; // Not needed?
if (ts != null)
{
ts.Add(t);
}
if (ys != null)
{
ys.Add(yt);
}
vector err = new vector(y.size);
vector[] res;
// Step untill less than one step is needed:
int steps = 0;
while (t < b - h)
{
steps++;
//Write($"\nStep nr. {steps}, h = {h}\n");
// Do the step:
res = stepper(f, t, y, h);
yt = res[0];
err = res[1];
// Calculate the current step tolerance:
vector tau_is = (acc + eps * yt.abs()) * Sqrt(h / (b - a));
// Asses if the error of the step is within the tolerance
// and calculate the ratio of the tolerance and the error
// for each entry.
bool errAccepted = true;
vector tolRatios = new vector(err.size);
for (int i = 0; i < tau_is.size; i++)
{
if (Abs(err[i]) > Abs(tau_is[i]))
{
errAccepted = false;
}
tolRatios[i] = Abs(tau_is[i]) / Abs(err[i]);
}
// Is error estimate lower than tolerance?
// Then step is accepted, t and yt
if (errAccepted)
{
// Update t and y:
t += h;
y = yt;
if (ts != null)
{
ts.Add(t);
}
if (ys != null)
{
ys.Add(yt);
}
}
else
{
// Don't change t and yt.
}
// Update h: (vector.min() is a new method I implemented myself)
double h_factor = Pow(tolRatios.min(), 0.25) * 0.95;
h = (h_factor < 2)?h_factor * h:2 * h;
}
// Do the final step to reach b: (For now, there is a chance that
// the error gets too large in this step... But test this code
// first)
double h_final = b - t;
res = stepper(f, t, y, h_final);
yt = res[0];
err = res[1];
y = yt;
if (ts != null)
{
ts.Add(t + h_final);
}
if (ys != null)
{
ys.Add(yt);
}
return(steps);
}
