public static vector newton(Func <vector, vector> f, vector x, double eps = 1e-3, double dx = 1e-7)
{
int n = x.size;
vector fx = f(x), z, fz;
while (true)
{
matrix J = jacobi(f, fx, x);
matrix R = new matrix(n, n);
QR.qr_gs_decomp(J, R);
matrix B = QR.qr_gs_inverse(J, R);
//B.print("inverse B");
vector del_x = -B * fx;
double lambda = 1;
while (true)
{
z = x + lambda * del_x;
fz = f(z);
if (fz.norm() < (1 - lambda / 2) * fx.norm())
{
break;
}
else if (lambda < 1.0 / 64)
{
break;
}
else
{
lambda /= 2;
}
}
x = z;
fx = fz;
if (fx.norm() < eps)
{
break;
}
else if (x.norm() < dx)
{
break;
}
}
return(x);
}