public override FunctionPoint FindMinimum(Vector startPoint)
{
// Find potential minimum with linear interpolation of derivative (so quadric interpolation of function)
// f'(x) = f'(x0) + f''(x0) * (x - x0) = 0
// dx = -f'(x0) / f''(x0)
double lastValue = Function(startPoint);
double newValue = lastValue;
Vector point = (Vector)startPoint.Clone();
FunctionPoint result;
do
{
double df = NumericalDerivative.First(Function, point, Direction);
double df2 = NumericalDerivative.Second(Function, point, Direction);
if (Math.Abs(df) < MaxError)
{
// We are at point f'(x) ~= 0
if (df2 > 0.0) // Ad we have minumum, so we're good
{
return(new FunctionPoint()
{
Point = point,
Value = Function(point)
});
}
else
{
// let's move a bit in arbitrary direction
df = 1.0;
}
}
else if (Math.Abs(df2) * 1000.0 < Math.Abs(df))
{
// We are at point f''(x) ~= 0, so we may assume function is linear (at least localy)
// If so it has no minima, so lets pick arbitrary step of -df
df2 = 1.0;
}
double dx = -df / df2;
if (dx > 0.0)
{
base.leftInt = point[Direction];
base.rightInt = point[Direction] + dx;
}
else
{
base.leftInt = point[Direction] + dx;
base.rightInt = point[Direction];
}
result = base.FindMinimum(point);
point = result.Point;
lastValue = newValue;
newValue = result.Value;
}while (Math.Abs(lastValue - newValue) > MaxError);
return(result);
}
public override FunctionPoint FindMinimum(Vector startPoint)
{
// Find potential minimum with linear interpolation of derivative (so quadric interpolation of function)
// f'(x) = f'(x0) + f''(x0) * (x - x0) = 0
// dx = -f'(x0) / f''(x0)
Vector point = (Vector)startPoint.Clone();
double lastPosition, lastValue;
int iteration = 0;
do
{
lastPosition = point[Direction];
lastValue = Function(point);
iteration++;
iterations1++;
double df = NumericalDerivative.First(Function, point, Direction, MaxError / 100);
double df2 = NumericalDerivative.Second(Function, point, Direction, MaxError / 100);
double step = Math.Abs(df / df2);
if (Math.Abs(df) < MaxError || step < MinPointChange)
{
// We are at point f'(x) ~= 0
double fhl = NumericalDerivative.fhLeft(Function, point, Direction, MaxError);
double fhr = NumericalDerivative.fhRight(Function, point, Direction, MaxError);
// We cound check if f''(x) > 0, but due to non-continous derivative of penalty function sometimes it may fail
if (fhl > lastValue && fhr > lastValue)
{
return(new FunctionPoint()
{
Point = point,
Value = lastValue
});
}
else if (!DisableModTwo)
{
// Most probably we are close to maximum and function is quite flat. To give it a kick lets use golden section.
point = useGoldenSection(point, lastValue, step, fhl, fhr);
}
}
else
{
if (Math.Abs(df2) < df2_error)
{
df2 = 1.0;
}
if (df > 0.0) // Move in direction which minimizes f(x)
{
point[Direction] -= Math.Abs(df / df2);
}
else
{
point[Direction] += Math.Abs(df / df2);
}
double newValue = Function(point);
throwOnInvalidValue(newValue, point, lastPosition, Direction);
}
}while (iteration < MaxIterations &&
(Math.Abs(lastValue - Function(point)) > MaxError ||
Math.Abs(lastPosition - point[Direction]) > MinPointChange));
if (iteration == MaxIterations)
{
// It doesnt converge
}
return(new FunctionPoint()
{
Point = point,
Value = Function(point)
});
}