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);
| |||
}
| |||
//+------------------------------------------------------------------+
|