Спецификация программы:
double d_left; //левый край интервала
double d_right; //правый край интервала
double d_startPoint=0; //начальная точка
double d_step; //шаг
double d_nextPoint; //следующая точка
double d_previousPoint; //предыдущая точка
double d_number; //номер числа Фибоначи
double E=0.00001; //точность
double xmed; //минимум по Фибоначи
double func(double x); //заданая функция
void Svenn(); //метод Свенна
double GetFib(double d_number); //получение числа Фибоначи по номеру double GetFibNumber(double Fn); //получение порядкового номера числа Фибоначи double DevisSvennKempi(); // метод ДСК
Текст программы:
#include<iostream.h>
#include <conio.h>
#include <math.h>
double d_left;
double d_right;
double d_startPoint=0;
double d_step;
double d_nextPoint;
double d_previousPoint;
double d_number;
double E=0.00001;
double xmed;
double func(double x)
{
double res=2*x*x+3*exp(-x);
return res;
}
void Svenn()
{
if(d_startPoint==0)
d_step=0.01;
else
d_step=0.01*fabs(d_startPoint);
d_nextPoint=d_startPoint+d_step;
if(func(d_startPoint)<func(d_nextPoint))
{
d_step=-d_step;
d_nextPoint=d_startPoint+d_step;
}
while(func(d_nextPoint)<func(d_startPoint))
{
d_previousPoint=d_startPoint;
d_startPoint=d_nextPoint;
d_nextPoint=d_startPoint+d_step;
d_step=2*d_step;
}
d_left=d_previousPoint;
d_right=d_nextPoint;
}
void Localization()
{
int k = 0;
double d_alfaPoint, d_muPoint;
while( fabs( d_right - d_left ) > E )
{
d_alfaPoint = d_left + ( d_right - d_left) / 4;
d_muPoint = d_right - ( d_right - d_left) / 4;
if ( func ( d_alfaPoint ) < func ( d_muPoint ))
d_right = d_muPoint;
else
d_left = d_alfaPoint;
k++;
}
double d_Xmin = ( d_left + d_right ) / 2;
cout<<"Iteration ="<<k<<endl;
cout<<"Min ="<<d_Xmin<<endl;
}
double GetFib(double d_number) //1 1 2 3 5 8 13... - числа Фиб
{
double F0=1,F1=1,F2;
if((d_number==1)||(d_number==2)) //для получения 1-го или 2-го числа Фиб
return 1;
for(double i=3; i<=d_number; i++)
{
F2=F0+F1;
F0=F1;
F1=F2;
}
return F2;
}
double GetFibNumber(double Fn) // функция, вычисляющая номер заданного числа Фиббоначи
{
double F0=1,F1=1,F2,d_number=2;
do
{
F2=F0+F1;
F0=F1;
F1=F2;
d_number++;
}while(F2<Fn);
return d_number;
}
double Fib()
{
double Ln=0.00001;
double L1=0;
double Fn;
double d_alfaPoint=0;
double d_muPoint=0;
int k;
cout<<d_left<<"----"<<d_right;
L1=fabs(d_right-d_left);
do
{
Fn=GetFib(d_number);
d_number=GetFibNumber(Fn);
d_number++;
}while(Fn<(L1/Ln));
d_alfaPoint=d_left+(GetFib(d_number-2)/Fn)*L1;
d_muPoint=d_left+(GetFib(d_number-1)/Fn)*L1;
k=1;
while(k!=(d_number-1))
{
d_muPoint=d_alfaPoint+E;
if(func(d_startPoint)<func(d_nextPoint))
{
xmed=(d_left+d_muPoint)/2;
d_left=d_left;
d_right=d_muPoint;
d_muPoint=d_alfaPoint;
d_alfaPoint=d_left+(GetFib(d_number-k-2)/(GetFib(d_number-k)))*L1;
}
else
{
xmed=(d_right+d_alfaPoint)/2;
d_right=d_right;
d_left=d_alfaPoint;
d_alfaPoint=d_muPoint;
d_muPoint=d_left+(GetFib(d_number-k-1)/(GetFib(d_number-k)))*L1;
}
k++;
}
return xmed;
}
double DevisSvennKempi()
{
double a;
double b;
double c;
double d;
if(d_startPoint==0)
d_step=0.01;
else
d_step=0.01*fabs(d_startPoint);
d_nextPoint=d_startPoint+d_step;
while(1)
{
if(func(d_startPoint)<func(d_nextPoint))
{
d_step=-d_step;
d_nextPoint=d_startPoint+d_step;
}
do
{
d_startPoint=d_nextPoint;
d_nextPoint=d_startPoint+d_step;
d_step=2*d_step;
}
while(func(d_nextPoint)>func(d_startPoint));
d_previousPoint=(d_startPoint+d_nextPoint)/2;
if(d_previousPoint<d_startPoint)
{
a=d_startPoint;
b=d_previousPoint;
c=d_nextPoint;
}
else
{
a=d_startPoint-0.5*d_step;
b=d_startPoint;
c=d_previousPoint;
}
double if1,if2;
d=b+0.5*((b-a)*(func(a)-func(c)))/(func(a)-2*func(b)+func(c));
if1=fabs((d-b)/b);
if2=fabs((func(d)-func(b))/func(b));
if(if1<=E && if2<=E)
return (b+d)/2;
else
{
if(func(b)<func(d))
d_startPoint=b;
else
{
d_startPoint=d;
d_step=d_step/2;
}
}
}
}
void main()
{
double db_startPoint=d_startPoint;
Svenn();
Localization();
Fib();
cout<<endl<<"Minimum="<<DevisSvennKempi();
getch();
}