Лабораторные работы 1-5 / LABA3 / LABA3
.DOC
#include <math.h>
#include <conio.h>
#include <iostream.h>
/**********************************Strukturi*********************************/
struct Dot
{
double x1,x2;
};
struct Vek
{
double x1,x2,len;
};
Dot x;
Vek p;
/******************************Celevaya funkciya*****************************/
double f(double k)
{
return (x.x1+k*p.x1)*(x.x1+k*p.x1)+3*(x.x2+k*p.x2)*(x.x2+k*p.x2)+2*(x.x1+k*p.x1)*(x.x2+k*p.x2);
}
/**********************************Ee proizvodnaya***************************/
double df(double k)
{
return (2*(x.x1+k*p.x1)+2*(x.x2+k*p.x2))*p.x1+(6*(x.x2+k*p.x2)+2*(x.x1+k*p.x1))*p.x2;
}
/*********************************Metod Swenna*******************************/
void swann(double* a,double* b)
{
float h1,x1;
h1=0.01;
x1=h1;
if(f(0)<f(x1))
{
h1=-h1;
x1=h1;
}
do
{
h1=2*h1;
x1=x1+h1;
}
while(f(x1-h1)>f(x1));
*a=x1-1.5*h1;
*b=x1;
}
/***********************Metod Zolotogo Se4eniya 2****************************/
double zs_2(double a,double b)
{
double e,x1,x2;
int k=0;
e=0.001;
x1=a+0.618*fabs(b-a);
do
{
x2=a+b-x1;
if((x1<x2)&&(f(x1)<f(x2)))
b=x2;
if((x1<x2)&&(f(x1)>=f(x2)))
{
a=x1;
x1=x2;
}
if((x1>x2)&&(f(x1)<f(x2)))
a=x2;
if((x1>x2)&&(f(x1)>=f(x2)))
{
b=x1;
x1=x2;
}
k++;
}
while(k<5);
return (a+b)/2;
}
/*******************************Metod Devidona*******************************/
double david()
{
int k=1;
double e=0.000000001,dfun,a,b,n,h,r,z,w,a0;
dfun=df(0);
h=0.000001;
if(dfun>0)
{
p.x1=-p.x1;
p.x2=-p.x2;
dfun=df(0);
}
do
{
h=h+2*h;
}
while(dfun*df(h)<0);
a=h/3;
b=h;
do
{
z=df(a)+df(b)+3*(f(a)-f(b))/(b-a);
w=sqrt(z*z-df(a)*df(b));
r=(w-df(a)+z)/(2*w-df(a)+df(b));
r*=(b-a);
if(df(r)<=e) return r;
if(df(r)>0) b=r;
else a=r;
}
while(k<10);
return r;
}
/********************************Osnovnaya programma*************************/
void main()
{
double a,b,n,kmin;
Dot min;
clrscr();
cout<<"\n-Laboratornaya rabota 3. Issledovanie metodov lineynogo poiska.-";
cout<<"\n-------------------------Variant 1------------------------------";
cout<<"\n----------------------MZS -> Devidona---------------------------";
cout<<"\n-------------- Vipolnila: Nikitina T., gr. 2375 ----------------";
cout<<"\n\n\nCelevaya funkciya: x1^2+3*x2^2+2*x1*x2";
cout<<"\nVvedite koordinati na4al'noy to4ki poiska: "<<'\n';
cin>>x.x1>>x.x2;
cout<<"\nZadayte napravlenie poiska: "<<'\n';
cin>>p.x1>>p.x2;
p.len=sqrt(p.x1*p.x1+p.x2*p.x2);
p.x1=p.x1/p.len;
p.x2=p.x2/p.len;
p.len=1;
swann(&a,&b);
if(a>b)
{
n=a;
a=b;
b=n;
}
kmin=zs_2(a,b);
x.x1=x.x1+kmin*p.x1;
x.x2=x.x2+kmin*p.x2;
kmin=david();
min.x1=x.x1+kmin*p.x1;
min.x2=x.x2+kmin*p.x2;
cout<<"\nNaydenaya to4ka minimuma: ("<<min.x1<<" "<<min.x2<<")"<<'\n';
getch();
}
/*****************************************************************************/