public static Ls_ret lsm(double[] x, double[] F, double fval, double alfa, int M, double[] lastfv, double eta, double fcnt, double bl, Type assembly)
{
int n = x.Length;
Ls_ret ls_ret = new Ls_ret();
double maxbl = 100;
double gamma = 1e-04;
double sigma1 = 0.1;
double sigma2 = 0.5;
double lam1 = 1;
double lam2 = 1;
double cbl = 0;
double fmax = double.NegativeInfinity;
for (int i = 0; i < lastfv.Length; i++)
{
fmax = Math.Max(fmax, lastfv[i]);
}
double[] xnew = new double[n];
double[] Fnew = new double[n];
while (cbl < maxbl)
{
double[] d = new double[n];
for (int i = 0; i < n; i++)
{
d[i] = -alfa * F[i];
}
xnew = new double[n];
for (int i = 0; i < n; i++)
{
xnew[i] = x[i] + lam1 * d[i];
}
Fnew = function(xnew, assembly);
fcnt++;
if (problem(Fnew))
{
ls_ret.xnew = null;
ls_ret.Fnew = null;
ls_ret.fcnt = fcnt;
ls_ret.bl = bl;
ls_ret.lsflag = 1;
ls_ret.fune = double.NaN;
return(ls_ret);
}
double fune1 = quad(Fnew);
if (fune1 <= (fmax + eta - (lam1 * lam1 * gamma * fval)))
{
if (cbl >= 1)
{
bl = bl + 1;
}
ls_ret.xnew = xnew;
ls_ret.Fnew = Fnew;
ls_ret.fcnt = fcnt;
ls_ret.bl = bl;
ls_ret.lsflag = 0;
ls_ret.fune = fune1;
return(ls_ret);
// return(list(xnew = xnew, Fnew = Fnew, fcnt = fcnt,
//bl = bl, lsflag = 0, fune = fune1))
}
for (int i = 0; i < n; i++)
{
xnew[i] = x[i] - lam2 * d[i];
}
Fnew = function(xnew, assembly);
fcnt++;
if (problem(Fnew))
{
ls_ret.xnew = null;
ls_ret.Fnew = null;
ls_ret.fcnt = fcnt;
ls_ret.bl = bl;
ls_ret.lsflag = 1;
ls_ret.fune = double.NaN;
return(ls_ret);
}
double fune2 = quad(Fnew);
if (fune2 <= (fmax + eta - (lam2 * lam2 * gamma * fval)))
{
if (cbl >= 1)
{
bl = bl + 1;
}
ls_ret.xnew = xnew;
ls_ret.Fnew = Fnew;
ls_ret.fcnt = fcnt;
ls_ret.bl = bl;
ls_ret.lsflag = 0;
ls_ret.fune = fune2;
return(ls_ret);
// return(list(xnew = xnew, Fnew = Fnew, fcnt = fcnt,
//bl = bl, lsflag = 0, fune = fune2))
}
double lamc = (2d * fval * lam1 * lam1) / (2d * (fune1 + (2d * lam1 - 1d) * fval));
double c1 = sigma1 * lam1;
double c2 = sigma2 * lam1;
if (lamc < c1)
{
lam1 = c1;
}
else if (lamc > c2)
{
lam1 = c2;
}
else
{
lam1 = lamc;
}
lamc = (2d * fval * lam2 * lam2) / (2d * (fune2 + (2d * lam2 - 1d) * fval));
c1 = sigma1 * lam2;
c2 = sigma2 * lam2;
if (lamc < c1)
{
lam2 = c1;
}
else if (lamc > c2)
{
lam2 = c2;
}
else
{
lam2 = lamc;
}
cbl = cbl + 1;
}
ls_ret.xnew = xnew;
ls_ret.Fnew = Fnew;
ls_ret.fcnt = fcnt;
ls_ret.bl = bl;
ls_ret.lsflag = 2;
ls_ret.fune = double.NaN; //TTH: set to NaN
return(ls_ret);
//return(list(xnew = xnew, Fnew = Fnew, fcnt = fcnt, bl = bl,
//lsflag = 2, fune = fune))
}
public static void Solve(double[] par, Type assembly)
{
//double[] x0 = new double[] { 0.3235007, 0.7100014, 0.4234151, 0.4153759, 0.1978808, 0.8531196, 0.4555675, 0.5234385, 0.2557746, 0.5328845 };
//Iteration: 0 ||F(x0)||: 0.08864655
//iteration: 10 ||F(xn)|| = 0.1041679
//iteration: 20 ||F(xn)|| = 0.02157386
//iteration: 30 ||F(xn)|| = 0.003530724
//iteration: 40 ||F(xn)|| = 8.22081e-05
//iteration: 50 ||F(xn)|| = 8.77939e-07
// ctrl <- list(maxit = 1500, M = 10, tol = 1e-07, trace = TRUE,
//triter = 10, noimp = 100, NM=FALSE, BFGS=FALSE)
string conv = "";
int method = 2;
int M = 10; //should be between 5-20, very hard stuff kan use > 20.
double maxit = 15000;
double tol = 1e-07;
bool trace = true;
double triter = 10; //when to print iterations
double noimp = 100; //when to stop (no improvement)
double n = par.Length;
double fcnt = 0;
int iter = 0;
double bl = 0;
double alfa = 1;
double eta = 1;
double eps = 1e-10;
double[] lastfv = new double[M];
double[] F = function(par, assembly);
fcnt++;
double F0 = Math.Sqrt(quad(F));
double normF = F0;
G.Writeln("Iteration 0, ||F(x0)||: " + F0 / Math.Sqrt(n));
double[] pbest = par;
double normF_best = normF;
lastfv[0] = normF * normF;
double flag = 0;
double knoimp = 0;
double alfa1 = 0;
double alfa2 = 0;
while (normF / Math.Sqrt(n) > tol && iter <= maxit)
{
if ((Math.Abs(alfa) <= eps) || (Math.Abs(alfa) >= 1 / eps))
{
if (normF > 1)
{
alfa = 1;
}
else if (normF >= 1e-05 && normF <= 1)
{
alfa = 1 / normF;
}
else if (normF < 1e-05)
{
alfa = 1e+05;
}
}
if (iter == 0)
{
alfa = Math.Min(1d / normF, 1d);
alfa1 = alfa;
alfa2 = alfa;
}
double temp = alfa2;
alfa2 = alfa;
if (normF <= 0.01)
{
alfa = alfa1; // retard scheme
}
alfa1 = temp;
Ls_ret ls_ret = lsm(par, F, normF * normF, alfa, M, lastfv, eta, fcnt, bl, assembly);
fcnt = ls_ret.fcnt;
bl = ls_ret.bl;
flag = ls_ret.lsflag;
if (flag > 0)
{
break;
}
double[] Fnew = ls_ret.Fnew;
double[] pnew = ls_ret.xnew;
double fune = ls_ret.fune;
double pF = 0;
double pp = 0;
double FF = 0;
for (int i = 0; i < n; i++)
{
pF += ((pnew[i] - par[i]) * (Fnew[i] - F[i]));
pp += ((pnew[i] - par[i]) * (pnew[i] - par[i]));
FF += ((Fnew[i] - F[i]) * (Fnew[i] - F[i]));
}
if (method == 1)
{
alfa = pp / pF;
}
else if (method == 2)
{
alfa = pF / FF;
}
else if (method == 3)
{
alfa = Math.Sign(pF) * Math.Sqrt(pp / FF);
}
if (double.IsNaN(alfa))
{
alfa = eps;
}
par = pnew;
F = Fnew;
double fun = fune;
normF = Math.Sqrt(fun);
if (normF < normF_best)
{
pbest = par;
normF_best = normF;
knoimp = 0;
}
else
{
knoimp = knoimp + 1;
}
iter++;
lastfv[(1 + iter % M) - 1] = fun;
eta = F0 / ((iter + 1) * (iter + 1));
G.Writeln("Iteration " + iter + " ||F(xn)||: " + normF);
if (knoimp == noimp)
{
flag = 3;
break;
}
if (flag == 0)
{
if (normF_best / Math.Sqrt(n) <= tol)
{
conv = "Successful convergence";
}
else if (iter > maxit)
{
conv = "Maximum limit for iterations exceeded";
}
else
{
conv = "Method stagnated";
}
}
else if (flag == 1)
{
conv = "Failure: Error in function evaluation";
}
else if (flag == 2)
{
conv = "Failure: Maximum limit on steplength reductions exceeded";
}
else if (flag == 3)
{
conv = "Lack of improvement in objective function";
}
}
G.Writeln(conv);
}