373 lines
13 KiB
MQL5
373 lines
13 KiB
MQL5
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//+------------------------------------------------------------------+
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//| 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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//+------------------------------------------------------------------+
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//| math functions |
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//+------------------------------------------------------------------+
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enum EnMathFunction
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{
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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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//+------------------------------------------------------------------+
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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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{
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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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{
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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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{
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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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{
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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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{
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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;
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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;
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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;
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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;
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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;
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case Josephine:
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result=GenerateFunctionDataFixedSize(x_size,y_size,data,-200.0,+200.0,-200.0,+200.0,JosephineFunction);
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break;
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case Screw:
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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);
|
||
|
|
}
|
||
|
|
//+------------------------------------------------------------------+
|