372 lines
13 KiB
MQL5
372 lines
13 KiB
MQL5
//+------------------------------------------------------------------+
|
|
//| Functions.mqh |
|
|
//| Copyright 2000-2025, MetaQuotes Ltd. |
|
|
//| https://www.mql5.com |
|
|
//+------------------------------------------------------------------+
|
|
|
|
//--- custom function y=f(x,y)
|
|
typedef double(*MathFunction)(double,double);
|
|
|
|
//+------------------------------------------------------------------+
|
|
//| math functions |
|
|
//+------------------------------------------------------------------+
|
|
enum EnMathFunction
|
|
{
|
|
Peaks=0,
|
|
Chomolungma=1,
|
|
ClimberDream=2,
|
|
Granite=3,
|
|
Hedgehog=4,
|
|
Hill=5,
|
|
Josephine=6,
|
|
Screw=7,
|
|
DoubleScrew=8,
|
|
MultiExtremalScrew=9,
|
|
Sink=10,
|
|
Skin=11,
|
|
Trapfall=12,
|
|
};
|
|
//+------------------------------------------------------------------+
|
|
//| Names of the math functions |
|
|
//+------------------------------------------------------------------+
|
|
const string ExtFunctionsNames[]=
|
|
{
|
|
"Peaks",
|
|
"Chomolungma",
|
|
"Climber Dream",
|
|
"Granite",
|
|
"Hedgehog",
|
|
"Hill",
|
|
"Josephine",
|
|
"Screw",
|
|
"Double Screw",
|
|
"Multi Extremal Screw",
|
|
"Sinc",
|
|
"Skin",
|
|
"Trapfall"
|
|
};
|
|
//+------------------------------------------------------------------+
|
|
//| Function Peaks |
|
|
//+------------------------------------------------------------------+
|
|
double PeaksFunction(double x,double y)
|
|
{
|
|
double res = 3*MathPow((1-x),2)*MathExp(-x*x-(y+1)*(y+1))-10*(0.2*x-MathPow(x,3)-MathPow(y,5))*MathExp(-x*x-y*y)-1/3*MathExp(-(x+1)*(x+1)-y*y);
|
|
//---
|
|
return(res);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Function Chomolungma |
|
|
//+------------------------------------------------------------------+
|
|
double ChomolungmaFunction(double x,double y)
|
|
{
|
|
double a= MathCos(x*x)+MathCos(y*y);
|
|
double b= MathPow(MathCos(5*x*y),5);
|
|
double c=1.0/MathPow(2,b);
|
|
//--- calculate result
|
|
double res=a-c;
|
|
//---
|
|
return(res);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Function ClimberDream |
|
|
//+------------------------------------------------------------------+
|
|
double ClimberDreamFunction(double x,double y)
|
|
{
|
|
double a= MathSin(MathSqrt(MathAbs(x - 1.3) + MathAbs(y)));
|
|
double b= MathCos(MathSqrt(MathAbs(MathSin(x))) + MathSqrt(MathAbs(MathSin(y))));
|
|
double f=a+b;
|
|
//--- calculate result
|
|
double res=MathPow(f,4);
|
|
//---
|
|
return(res);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Function Granite |
|
|
//+------------------------------------------------------------------+
|
|
double GraniteFunction(double x,double y)
|
|
{
|
|
double a= MathPow(MathSin(MathSqrt(MathAbs(x)+MathAbs(y))),2);
|
|
double b= MathPow(MathCos(MathSqrt(MathAbs(x)+MathAbs(y))),2);
|
|
//--- calculate result
|
|
double res=a*b;
|
|
//---
|
|
return(res);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Function Hedgehog |
|
|
//+------------------------------------------------------------------+
|
|
double HedgehogFunction(double x,double y)
|
|
{
|
|
double a1=MathSin(MathSqrt(MathAbs(x-2)+MathAbs(y)));
|
|
double a2=MathCos(MathSqrt(MathAbs(MathSin(x)))+MathSqrt(MathAbs(MathSin(y))));
|
|
//--- calculate result
|
|
double res=a1+a2;
|
|
//---
|
|
return(res);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Function Hill |
|
|
//+------------------------------------------------------------------+
|
|
double HillFunction(double x,double y)
|
|
{
|
|
//--- calculate result
|
|
double res=MathExp(-x*x-y*y);
|
|
//---
|
|
return(res);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Function Josephine |
|
|
//+------------------------------------------------------------------+
|
|
double JosephineFunction(double x,double y)
|
|
{
|
|
double a= MathSin(MathPow(MathAbs(x)+MathAbs(y),0.5));
|
|
double b= MathCos(MathPow(MathAbs(x),0.5)+MathPow(MathAbs(y),0.5));
|
|
//--- calculate function
|
|
double res=a+b;
|
|
//---
|
|
return(res);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Function Screw |
|
|
//+------------------------------------------------------------------+
|
|
double ScrewFunction(double x,double y)
|
|
{
|
|
double a=(y==0)?0:((x*y<0)?MathArctan(x/y):MathArctan(x/y)+M_PI);
|
|
double b=x*x+y*y;
|
|
double f=MathSin(b+a);
|
|
//--- calculate result
|
|
double res=(f*f);
|
|
//---
|
|
return(res);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Function DoubleScrew |
|
|
//+------------------------------------------------------------------+
|
|
double DoubleScrewFunction(double x,double y)
|
|
{
|
|
double a=(y==0)?0:((x*y<0)?MathArctan(x/y):MathArctan(x/y)+M_PI);
|
|
double b=x*x+y*y;
|
|
double res1=MathCos(b/2+a*3);
|
|
res1=((res1*res1)/sqrt(b+1)-0.2);
|
|
double res2=MathCos(b/2-a*3);
|
|
res2=((res2*res2)/sqrt(b+1)-0.2);
|
|
double f=fmax(res1,res2);
|
|
//--- calculate result
|
|
double res=(f>0)?f:0;
|
|
//---
|
|
return(res);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Function MultiExtremalScrew |
|
|
//+------------------------------------------------------------------+
|
|
double MultiExtremalScrewFunction(double x,double y)
|
|
{
|
|
double a=(y==0)?0:((x*y<0)?MathArctan(x/y):MathArctan(x/y)+M_PI);
|
|
double b=x*x+y*y;
|
|
double res1=MathCos(b/2+a*3);
|
|
res1=((res1*res1)/sqrt(b+1)-0.2);
|
|
double res2=MathCos(b/2-a*3);
|
|
res2=((res2*res2)/sqrt(b+1)-0.2);
|
|
//--- calculate function
|
|
double res=fmin(res1,res2);
|
|
//---
|
|
return(res);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Function Sink |
|
|
//+------------------------------------------------------------------+
|
|
double SinkFunction(double x,double y)
|
|
{
|
|
static double k=5.0;
|
|
static double p=6.0;
|
|
//--- calculate result
|
|
double res=MathSin(x*x+y*y)+k*MathExp(-p*x*x-p*y*y);
|
|
//---
|
|
return(res);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Function Skin |
|
|
//+------------------------------------------------------------------+
|
|
double SkinFunction(double x,double y)
|
|
{
|
|
double a1=2*x*x;
|
|
double a2=2*y*y;
|
|
double b1=MathCos(a1)-1.1;
|
|
b1=b1*b1;
|
|
double c1=MathSin(0.5*x)-1.2;
|
|
c1=c1*c1;
|
|
double d1=MathCos(a2)-1.1;
|
|
d1=d1*d1;
|
|
double e1=MathSin(0.5*y)-1.2;
|
|
e1=e1*e1;
|
|
//--- calculate result
|
|
double res=b1+c1-d1+e1;
|
|
//---
|
|
return(res);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Function Trapfall |
|
|
//+------------------------------------------------------------------+
|
|
double TrapfallFunction(double x,double y)
|
|
{
|
|
double a1=MathSqrt(MathAbs(MathSin(x-1.0)));
|
|
double b1=MathSqrt(MathAbs(MathSin(y+2.0)));
|
|
//--- calculate result
|
|
double res=-MathSqrt(MathAbs(MathSin(MathSin(a1+b1))));
|
|
//---
|
|
return(res);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| GenerateFunctionData |
|
|
//+------------------------------------------------------------------+
|
|
void GenerateFunctionData(double &data[],int &x_size,int &y_size,double x_min,double x_max,double y_min,double y_max,MathFunction function)
|
|
{
|
|
double dx = 0.1;
|
|
double dy = 0.1;
|
|
//---
|
|
x_size = (int)((x_max - x_min)/dx) + 1;
|
|
y_size = (int)((y_max - y_min)/dy) + 1;
|
|
ArrayResize(data,x_size*y_size);
|
|
//---
|
|
for(int j = 0; j < y_size; j++)
|
|
{
|
|
for(int i = 0; i < x_size; i++)
|
|
{
|
|
double x = x_min + i*dx;
|
|
double y = y_min + j*dy;
|
|
data[j*x_size + i] = function(x,y);
|
|
}
|
|
}
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| GenerateData |
|
|
//+------------------------------------------------------------------+
|
|
void GenerateData(EnMathFunction function_id,double &data[],int &x_size,int &y_size)
|
|
{
|
|
//---
|
|
switch(function_id)
|
|
{
|
|
case Peaks:
|
|
GenerateFunctionData(data,x_size,y_size,-3.0,+3.0,-3.0,+3.0,PeaksFunction);
|
|
break;
|
|
case Chomolungma:
|
|
GenerateFunctionData(data,x_size,y_size,-2.0,+2.0,-2.0,+2.0,ChomolungmaFunction);
|
|
break;
|
|
case ClimberDream:
|
|
GenerateFunctionData(data,x_size,y_size,-10.0,+10.0,-10.0,+10.0,ClimberDreamFunction);
|
|
break;
|
|
case Granite:
|
|
GenerateFunctionData(data,x_size,y_size,-4.0,+4.0,-4.0,+4.0,GraniteFunction);
|
|
break;
|
|
case Hedgehog:
|
|
GenerateFunctionData(data,x_size,y_size,-10.0,+10.0,-10.0,+10.0,HedgehogFunction);
|
|
break;
|
|
case Hill:
|
|
GenerateFunctionData(data,x_size,y_size,-1.5,+1.5,-1.5,+1.5,HillFunction);
|
|
break;
|
|
case Josephine:
|
|
GenerateFunctionData(data,x_size,y_size,-200.0,+200.0,-200.0,+200.0,JosephineFunction);
|
|
break;
|
|
case Screw:
|
|
GenerateFunctionData(data,x_size,y_size,-3.0,+3.0,-3.0,+3.0,ScrewFunction);
|
|
break;
|
|
case DoubleScrew:
|
|
GenerateFunctionData(data,x_size,y_size,-3.0,+3.0,-3.0,+3.0,DoubleScrewFunction);
|
|
break;
|
|
case MultiExtremalScrew:
|
|
GenerateFunctionData(data,x_size,y_size,-3.0,+3.0,-3.0,+3.0,MultiExtremalScrewFunction);
|
|
break;
|
|
case Sink:
|
|
GenerateFunctionData(data,x_size,y_size,-3.0,+3.0,-3.0,+3.0,SinkFunction);
|
|
break;
|
|
case Skin:
|
|
GenerateFunctionData(data,x_size,y_size,-5.0,+5.0,-5.0,+5.0,SkinFunction);
|
|
break;
|
|
case Trapfall:
|
|
GenerateFunctionData(data,x_size,y_size,-5.0,+5.0,-5.0,+5.0,TrapfallFunction);
|
|
break;
|
|
}
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| GenerateFunctionDataFixedSize |
|
|
//+------------------------------------------------------------------+
|
|
bool GenerateFunctionDataFixedSize(int x_size,int y_size,double &data[],double x_min,double x_max,double y_min,double y_max,MathFunction function)
|
|
{
|
|
if(x_size<2 || y_size<2)
|
|
{
|
|
PrintFormat("Error in data sizes: x_size=%d,y_size=%d",x_size,y_size);
|
|
return(false);
|
|
}
|
|
double dx = (x_max - x_min)/(x_size-1);
|
|
double dy = (y_max - y_min)/(y_size-1);
|
|
ArrayResize(data,x_size*y_size);
|
|
//---
|
|
for(int j = 0; j < y_size; j++)
|
|
{
|
|
for(int i = 0; i < x_size; i++)
|
|
{
|
|
double x = x_min + i*dx;
|
|
double y = y_min + j*dy;
|
|
data[j*x_size + i] = function(x,y);
|
|
}
|
|
}
|
|
return(true);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| GenerateDataFixedSize |
|
|
//+------------------------------------------------------------------+
|
|
bool GenerateDataFixedSize(int x_size,int y_size,EnMathFunction function_id,double &data[])
|
|
{
|
|
if(x_size<2 || y_size<2)
|
|
{
|
|
PrintFormat("Error in data sizes: x_size=%d,y_size=%d",x_size,y_size);
|
|
return(false);
|
|
}
|
|
bool result=false;
|
|
//---
|
|
switch(function_id)
|
|
{
|
|
case Peaks:
|
|
result=GenerateFunctionDataFixedSize(x_size,y_size,data,-3.0,+3.0,-3.0,+3.0,PeaksFunction);
|
|
break;
|
|
case Chomolungma:
|
|
result=GenerateFunctionDataFixedSize(x_size,y_size,data,-2.0,+2.0,-2.0,+2.0,ChomolungmaFunction);
|
|
break;
|
|
case ClimberDream:
|
|
result=GenerateFunctionDataFixedSize(x_size,y_size,data,-10.0,+10.0,-10.0,+10.0,ClimberDreamFunction);
|
|
break;
|
|
case Granite:
|
|
result=GenerateFunctionDataFixedSize(x_size,y_size,data,-4.0,+4.0,-4.0,+4.0,GraniteFunction);
|
|
break;
|
|
case Hedgehog:
|
|
result=GenerateFunctionDataFixedSize(x_size,y_size,data,-10.0,+10.0,-10.0,+10.0,HedgehogFunction);
|
|
break;
|
|
case Hill:
|
|
result=GenerateFunctionDataFixedSize(x_size,y_size,data,-1.5,+1.5,-1.5,+1.5,HillFunction);
|
|
break;
|
|
case Josephine:
|
|
result=GenerateFunctionDataFixedSize(x_size,y_size,data,-200.0,+200.0,-200.0,+200.0,JosephineFunction);
|
|
break;
|
|
case Screw:
|
|
result=GenerateFunctionDataFixedSize(x_size,y_size,data,-3.0,+3.0,-3.0,+3.0,ScrewFunction);
|
|
break;
|
|
case DoubleScrew:
|
|
result=GenerateFunctionDataFixedSize(x_size,y_size,data,-3.0,+3.0,-3.0,+3.0,DoubleScrewFunction);
|
|
break;
|
|
case MultiExtremalScrew:
|
|
result=GenerateFunctionDataFixedSize(x_size,y_size,data,-3.0,+3.0,-3.0,+3.0,MultiExtremalScrewFunction);
|
|
break;
|
|
case Sink:
|
|
result=GenerateFunctionDataFixedSize(x_size,y_size,data,-3.0,+3.0,-3.0,+3.0,SinkFunction);
|
|
break;
|
|
case Skin:
|
|
result=GenerateFunctionDataFixedSize(x_size,y_size,data,-5.0,+5.0,-5.0,+5.0,SkinFunction);
|
|
break;
|
|
case Trapfall:
|
|
result=GenerateFunctionDataFixedSize(x_size,y_size,data,-5.0,+5.0,-5.0,+5.0,TrapfallFunction);
|
|
break;
|
|
}
|
|
//---
|
|
return(result);
|
|
}
|
|
//+------------------------------------------------------------------+
|