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