public static T FindMin(IFunctional <T> functional, IParametricFunction <T> function, IVector <T> s, IVector <T> p, T eps)
{
var la = LinearAlgebra.Value;
var a = la.Cast(0);
var b = la.Cast(1e2);
var x = la.Sum(a, la.Mult(la.Mult(la.Cast(0.5), la.Sub(la.Cast(3), la.Sqrt(la.Cast(5.0)))), (la.Sub(b, a))));
var y = la.Sum(la.Sub(b, x), a);
var fx = function.Bind(s.AddWithCloning(p.MultWithCloning(la.Mult(x, la.Cast(-1)))));
var fy = function.Bind(s.AddWithCloning(p.MultWithCloning(la.Mult(y, la.Cast(-1)))));
var valueX = functional.Value(fx);
var valueY = functional.Value(fy);
while (la.Compare(la.Abs(la.Sub(b, a)), la.Cast(1e-5)) == 1)
{
if (la.Compare(valueX, valueY) == -1)
{
b = y;
y = x;
fy = fx;
valueY = valueX;
x = la.Sub(la.Sum(b, a), y);
fx = function.Bind(s.AddWithCloning(p.MultWithCloning(la.Mult(x, la.Cast(-1)))));
valueX = functional.Value(fx);
}
else
{
a = x;
x = y;
fx = fy;
valueX = valueY;
y = la.Sub(la.Sum(b, a), x);
fy = function.Bind(s.AddWithCloning(p.MultWithCloning(la.Mult(y, la.Cast(-1)))));
valueY = functional.Value(fy);
}
}
return(la.Div(la.Sum(a, b), la.Cast(2)));
}
public IVector <T> Minimize(IFunctional <T> objective, IParametricFunction <T> function, IVector <T> initialParameters, IVector <T> minimumParameters = default,
IVector <T> maximumParameters = default)
{
var k = 0;
var la = LinearAlgebra.Value;
IVector <T> xPrev = initialParameters.Clone() as IVector <T>;
IVector <T> xNew = initialParameters.Clone() as IVector <T>;
var normalDist = new Normal(Mean, StdDev);
T prevValue = objective.Value(function.Bind(xPrev));
do
{
var t = 20d / Math.Log(k, Math.E);
for (int i = 0; i < xPrev.Count; i++)
{
var nR = normalDist.Sample() * t;
xNew[i] = la.Sum(xPrev[i], la.Cast(nR));
}
this.ApplyMinimumAndMaximumValues(minimumParameters, maximumParameters, xNew, la);
var newValue = objective.Value(function.Bind(xNew));
var sub = la.Sub(newValue, prevValue);
if (la.Compare(sub, la.GetZeroValue()) == -1) // || la.Exp(la.Mult(la.Cast(-1/t), sub)) >= rand.NextDouble())
{
prevValue = newValue;
xPrev = xNew.Clone() as IVector <T>;
}
} while ((MaxIter.HasValue && MaxIter > k++ && la.Compare(prevValue, Eps) == 1) || (!MaxIter.HasValue && la.Compare(prevValue, Eps) == 1));
return(xPrev);
}