/** Method: Try steffensen acceleration (if error, return -1)
* f - function
* x - independent variable
* min - min value of the interval
* max - max value of the interval
* val - value to add (0 if pure root search)
* iterations - number of iterations */
internal double TrySteffensenAcceleration(function f, derivative d, double x, double val, double iterations)
{
double gx = f(x) - val;
int i = 0;
double xi = -1;
double xiMin1 = -1;
double xiMin2 = -1;
while (Math.Abs(gx) > epsilon)
{
if (d(x) == 0)
{
return(0);
}
if (i < 4 || i % 2 == 0 || xi - 2 * xiMin1 + xiMin2 == 0)
{
x = x - gx / d(x);
}
else
{
x = GetAitkenIteration(xiMin2, xiMin1, xi);
}
gx = f(x) - val;
xiMin2 = xiMin1;
xiMin1 = xi;
xi = x;
i++;
if (i > maxIterations)
{
throw new Exception("Exceed maximun iterations");
}
}
iterations = i;
return(x);
}
//Расчёт значения производной в точке
public double GetDerivative(derivative function, int k, uint round = 0)
{
if (round != 0)
{
return(Math.Round(function(points[0, k], points[1, k]), (int)round));
}
else
{
return(function(points[0, k], points[1, k]));
}
}
/** Method: Bisection root search numerical method
* f - function
* d - first derivative
* min - min value of the interval
* max - max value of the interval
* val - value to add (0 if pure root search)
* eps - epsilon for solution validation
* maxIt - maximum of iterations */
internal double MonotoneBisection(function f, derivative d, double min, double max, double val, double eps, ref int it, int maxIt)
{
double dMin = d(min);
double dMax = d(max);
if (dMin * dMax < 0)
{
throw new ArgumentException("This method is only for monotone intervals");
}
return(MonotoneBisectionRec(f, min, max, val, (dMin > 0), eps, ref it, maxIt));
}
/** Method:
* Metodo Steffenson, que es una forma mas rapida de encontrar una raiz o cero de una función
* Si va es cero entonces encuantra la raiz de la funcion
* si no, encuentra la inversa de la función
* f - function
* d - first derivative
* x - independent variable
* val - Valor para el cual se desea buscar la inversa de la función */
internal double SteffensenAcceleration(function f, derivative d, double x, double val)
{
double gxAnt = double.MaxValue;
epsilon = 0.005;
double gx = f(x) - val;
int i = 0;
double xi = -1;
double xiMin1 = -1;
double xiMin2 = -1;
while (Math.Abs(gx) > epsilon)
{
if (d(x) == 0)
{
return(0);
}
if (i < 4 || i % 2 == 0 || xi - 2 * xiMin1 + xiMin2 == 0)
{
x = x - gx / d(x);
}
else
{
x = GetAitkenIteration(xiMin2, xiMin1, xi);
}
gx = f(x) - val;
if (Math.Abs(gx) > Math.Abs(gxAnt))
{
return(xi);
}
gxAnt = gx;
xiMin2 = xiMin1;
xiMin1 = xi;
xi = x;
i++;
if (i > maxIterations)
{
return(0);
}
}
iterations = i;
return(x);
}
/** Method:
* Metodo Newton Raphson para encontrar una raiz o cero de una función</para>
* Si val es cero entonces encuantra la raiz de la funcion,
* si no, encuentra la inversa de la función
* f - function
* d - first derivative
* x - independent variable
* val - Valor para el cual se desea buscar la inversa de la función */
internal double NewtonRaphson(function f, derivative d, double x, double val)
{
int i = 0;
double gx = f(x) - val;
while (Math.Abs(gx) > epsilon)
{
if (d(x) == 0)
{
return(0);
}
x = x - gx / d(x);
gx = f(x) - val;
i++;
if (i > maxIterations)
{
throw new Exception("Exceed the maximun iterations");
}
}
return(x);
}
/** Method:
* Metodo Newton Raphson para encontrar una raiz o cero de una función
* Si val es cero entonces encuantra la raiz de la funcion
* si no, encuentra la inversa de la función <paramref name="f"/> en val
* f - function
* d - first derivative
* d2 - second derivative
* min - min value of the interval
* max - max value of the interval
* val - value to add (0 if pure root search)
* eps - epsilon for solution validation
* maxIt - maximum of iterations */
internal double NewtonRaphsonOneRoot(function f, derivative d, derivative2 d2, double min, double max, double val)
{
if ((f(min) - val) * f(max) - val > 0)
{
throw new ArgumentException("No zero between these values");
}
double nr = 0;
double x;
int i = 0;
while (nr == 0)
{
x = GetFourierValue(f, d2, min, max, val);
nr = NewtonRaphson(f, d, x, val);
if (i > maxIterations)
{
throw new Exception("Exceed the maximun iterations");
}
i++;
}
return(nr);
}
/** Method:
* Metodo Steffenson, que es una forma mas rapida de encontrar una raiz o cero de una función
* Si val es cero entonces encuantra la raiz de la funcion
* si no, encuentra la inversa de la función
* f - function
* d - first derivative
* d2 - second derivative
* min - min value of the interval
* max - max value of the interval
* val - value to add (0 if pure root search)
* maxIterations - maximum of iterations */
internal double SteffensenAccOneRoot(function f, derivative d, derivative2 d2, double min, double max, double val, int maxIterations)
{
if ((f(min) - val) * f(max) - val > 0)
{
throw new Exception("No zero between these values");
}
double st = 0;
double x;
int i = 0;
while (st == 0)
{
x = GetFourierValue(f, d2, min, max, val);
st = SteffensenAcceleration(f, d, x, val);
i++;
if (i > maxIterations)
{
throw new Exception("Exceed maximun iterations");
}
}
//Console.WriteLine("val = " + val + " , st = " + st + " , it = " + i);
return(st);
}
static void Main(string[] args)
{
Func <double, double, double> func = (x1, x2) => (100 * Math.Pow(x1, 2) + Math.Pow(x2, 2));
derivative[] masDerivatives = new derivative[2];
masDerivatives[0] = ((x1, x2) => (200 * x1));
masDerivatives[1] = ((x1, x2) => (2 * x2));
secondDerivative[,] masSecondDerivatives = new secondDerivative[2, 2];
masSecondDerivatives[0, 0] = ((x1, x2) => (200));
masSecondDerivatives[0, 1] = ((x1, x2) => (0));
masSecondDerivatives[1, 0] = ((x1, x2) => (0));
masSecondDerivatives[1, 1] = ((x1, x2) => (2));
double[,] points = new double[2, 12];
points[0, 0] = 0; points[1, 0] = 1;
Gradient gradient1 = new Gradient(points, 0.1, 0.15, 10, 0.5, 3, masDerivatives, masSecondDerivatives, 3, func);
Gradient gradient2 = new Gradient(points, 0.1, 0.15, 10, 0.5, 3, masDerivatives, masSecondDerivatives, 3, func);
Gradient gradient3 = new Gradient(points, 0.1, 0.15, 10, 0.5, 3, masDerivatives, masSecondDerivatives, 3, func);
//gradient1.RegisterHandler(func);
//gradient2.RegisterHandler(func);
//gradient3.RegisterHandler(func);
Console.WriteLine("Метод Ньютона: ");
Console.WriteLine();
gradient1.SearchMinNyuton();
Console.WriteLine();
Console.WriteLine();
Console.WriteLine("Метод сопряжённых градиентов: ");
Console.WriteLine();
gradient2.SearchMinConjugateGradients();
Console.WriteLine();
Console.WriteLine();
Console.WriteLine("Метод наискорейшего градиентного спуска: ");
Console.WriteLine();
gradient3.SearchMinFast();
}
//Расчёт значения производной в точке
public double GetDerivative(derivative function, int k)
{
return(function(points[0, k], points[1, k]));
}
