// Nelder-Mead algorithm
public Object Solve(Func <Object> f, string[] vars, string pos)
{
Kerbulator.DebugLine("Entering solver");
int N = vars.Length;
if (N == 0)
{
return (Object) new Object[] {}
}
;
// Stopping criteria
int maxiter = this.maxiter == 0 ? 200 * N : this.maxiter;
int maxfev = this.maxfev == 0 ? 200 * N : this.maxfev;
int iterations = 1;
int fcalls = 1;
// Some parameters
double rho = 1.0;
double chi = 2.0;
double psi = 0.5;
double sigma = 0.5;
// Variables that keep track of the current simplex
double[][] sim = new double[N + 1][];
double[] fsim = new double[N + 1];
// Initialize best vertex of current simplex
sim[0] = new double[N];
for (int i = 0; i < N; i++)
{
if (func.IsLocalDefined(vars[i]))
{
Object o = func.GetVar(vars[i], pos);
if (o.GetType() != typeof(double))
{
throw new Exception(pos + "solver cannot optimize variables of type list");
}
sim[0][i] = (double)o;
}
else
{
sim[0][i] = 0.0;
}
}
fsim[0] = CallFunc(f, vars, sim[0], pos);
fcalls++;
// Initialize other vertices of current simplex
double nonzdelt = 1.05;
double zdelt = 0.00025;
for (int k = 0; k < N; k++)
{
double[] y = (double[])sim[0].Clone();
if (y[k] == 0.0)
{
y[k] = zdelt;
}
else
{
y[k] = sim[0][k] * nonzdelt;
}
sim[k + 1] = y;
fsim[k + 1] = CallFunc(f, vars, y, pos);
fcalls++;
}
// Sort vertices
SortVertices(sim, fsim);
double[] xbar = new double[N];
double[] xr = new double[N];
double[] xe = new double[N];
double[] xc = new double[N];
double[] xcc = new double[N];
while (fcalls < maxfev && iterations < maxiter)
{
Kerbulator.DebugLine("Iteration " + iterations);
PrintVertices(sim, fsim);
// Test stopping criterium
double xmax = 0;
double fmax = 0;
for (int i = 1; i < N + 1; i++)
{
for (int j = 1; j < N; j++)
{
double xdiff = Math.Abs(sim[i][j] - sim[0][j]);
if (xdiff > xmax)
{
xmax = xdiff;
}
}
double fdiff = Math.Abs(fsim[i] - fsim[0]);
if (fdiff > fmax)
{
fmax = fdiff;
}
}
if (xmax <= xtol && fmax < ftol)
{
Kerbulator.DebugLine("Stopping criterium reached. (" + xmax + ", " + fmax + ")");
break;
}
else
{
Kerbulator.DebugLine("Continue. (" + xmax + ", " + fmax + ")");
}
for (int i = 0; i < N; i++)
{
xbar[i] = 0.0;
for (int j = 0; j < N; j++)
{
xbar[i] += sim[j][i];
}
xbar[i] /= N;
}
for (int i = 0; i < N; i++)
{
xr[i] = (1 + rho) * xbar[i] - rho * sim[sim.Length - 1][i];
}
double fxr = CallFunc(f, vars, xr, pos);
fcalls++;
bool doshrink = false;
if (fxr < fsim[0])
{
for (int i = 0; i < N; i++)
{
xe[i] = (1 + rho * chi) * xbar[i] - rho * chi * sim[sim.Length - 1][i];
}
double fxe = CallFunc(f, vars, xe, pos);
fcalls++;
if (fxe < fxr)
{
for (int i = 0; i < N; i++)
{
sim[sim.Length - 1][i] = xe[i];
}
fsim[fsim.Length - 1] = fxe;
}
else
{
for (int i = 0; i < N; i++)
{
sim[sim.Length - 1][i] = xr[i];
}
fsim[fsim.Length - 1] = fxr;
}
}
else // fsim[0] <= fxr
{
if (fxr < fsim[fsim.Length - 2])
{
for (int i = 0; i < N; i++)
{
sim[sim.Length - 1][i] = xr[i];
}
fsim[fsim.Length - 1] = fxr;
}
else // fxr >= fsim[-2]
// Perform contraction
{
if (fxr < fsim[fsim.Length - 1])
{
for (int i = 0; i < N; i++)
{
xc[i] = (1 + psi * rho) * xbar[i] - psi * rho * sim[sim.Length - 1][i];
}
double fxc = CallFunc(f, vars, xc, pos);
fcalls++;
if (fxc <= fxr)
{
for (int i = 0; i < N; i++)
{
sim[sim.Length - 1][i] = xc[i];
}
fsim[fsim.Length - 1] = fxc;
}
else
{
doshrink = true;
}
}
else
{
// Perform an inside contraction
for (int i = 0; i < N; i++)
{
xcc[i] = (1 - psi) * xbar[i] + psi * sim[sim.Length - 1][i];
}
double fxcc = CallFunc(f, vars, xcc, pos);
fcalls++;
if (fxcc < fsim[fsim.Length - 1])
{
for (int i = 0; i < N; i++)
{
sim[sim.Length - 1][i] = xcc[i];
}
fsim[fsim.Length - 1] = fxcc;
}
else
{
doshrink = true;
}
}
if (doshrink)
{
for (int j = 1; j < N + 1; j++)
{
for (int i = 0; i < N; i++)
{
sim[j][i] = sim[0][i] + sigma * (sim[j][i] - sim[0][i]);
}
fsim[j] = CallFunc(f, vars, sim[j], pos);
fcalls++;
}
}
}
}
SortVertices(sim, fsim);
iterations++;
}
Kerbulator.DebugLine("Leaving solver");
// Copy the locals of interest to the output
if (vars.Length == 1)
{
return(func.GetVar(vars[0], pos));
}
else
{
List <Object> outs = new List <Object>(vars.Length);
foreach (string id in vars)
{
outs.Add(func.GetVar(id, pos));
}
return((Object)outs.ToArray());
}
}
