5. Исходный текст программы.

//---------------------------------------------------------------------------

#include <vcl.h>

#pragma hdrstop

#include <conio.h>

#include <math.h>

#include <stdio.h>

//---------------------------------------------------------------------------

class myVector

{

public:

double x,y; //default Constructor

myVector(double x0=0, double y0=0){

x=x0;

y=y0;

} //basic operators

myVector operator + (const myVector &mV) { //sum of two Vectors

return myVector(x+mV.x,y+mV.y);

}

myVector &operator -(){ //unary minus

this->x = - this->x;

this->y = - this->y;

return *this;

}

myVector operator -(const myVector &mV) { //difference of two vectors

return myVector(x-mV.x,y-mV.y);

}

myVector operator *(const double i) { //multiply by Num postfix

return myVector(x*i,y*i);

}

double operator *(const myVector &mV){ //Scalar Multiply

return (this->x * mV.x + this->y * mV.y);

}

};

//---------------------------------------------------------------------------

//our function f

double fun(const myVector &mV){

return (-12*mV.y+4*mV.x*mV.x+4*mV.y*mV.y-4*mV.x*mV.y);

}

//gradient in point grad(point)

inline myVector gradient(const myVector &point){

return myVector(8*point.x-4*point.y,-12+8*point.y-4*point.x);

}

//gradient in point multiply by direction = f'(grad,line)

double d_fun(const myVector &point,const myVector &line){

return gradient(point)*line;

}

//---------------------------------------------------------------------------

//algorith Swann-4

bool Swann4(const myVector &start_point, myVector &line,

double &a,double &b, myVector &answer){

double y1,y2,alfa=300000000;

int k=0;

myVector x1,x2;

y1 = d_fun(start_point,line);

if (y1>0) -line;

x1= start_point;

a=0;

do {

x2 = x1 + line*alfa;

y2 = d_fun(x2,line);

b = alfa;

alfa = 2*alfa;

k++;

if (!y2) {answer=x2; printf("Count steps Swann4= %d\n",k); return true;}

if (y1*y2<0) break; else {y1=y2; x1 = x2; a=b;}

} while (true);

printf("Count steps Swann4= %d\n",k);

return false;

}

//---------------------------------------------------------------------------

//algorith Boltsano

bool Boltsano( myVector &start_point, myVector &line, double &a,double &b, myVector &answer){

double eps=0.000001, y,c;

int k=1;

myVector x;

c=(a+b)/2;

x = start_point + line*c;

y = d_fun(x,line);

while (fabs(y)>eps && y){

if (y>0) b=c; else a=c;

c=(a+b)/2;

x = start_point+line*c;

y = d_fun(x,line);

k++;

}

answer = x;

printf("Count steps Boltsano= %d\n",k);

if (y) return false; else {b=c; return true;}

}

//---------------------------------------------------------------------------

//algorith Davidona

void Davidon(myVector &start_point, myVector &line, double &a,double &b, myVector &answer){

double eps=0.0000001,y, alfa0,r,z,w;

myVector x1,x2,x;

int k=0;

alfa0=a;

b=b-alfa0;

a=0;

do {

x1 = start_point + line*a;

x2 = start_point + line*b;

z = d_fun(x1,line)+ d_fun(x2,line)+3*(fun(x1)-fun(x2))/b;

w = sqrt(z*z-d_fun(x1,line)*d_fun(x2,line));

r = b* (w - d_fun(x1,line)+z)/(2*w-d_fun(x1,line)+d_fun(x2,line));

x = x1 + line*r;

y = d_fun(x,line);

k++;

if (fabs(y)<=eps) break;

else if (y<0) {b=b-r;a=0;alfa0+=r;} else b=r;

} while (true);

if (y) x = x1 + d_fun(r+alfa0,line);

answer = x;

b = a+r;

printf("Count steps Davidon= %d\n",k);

}

//---------------------------------------------------------------------------

int main()

{

myVector st_p(-0.5,1),line(1,0),x;

double a,b,y;

printf("___WELCOME TO LAB 3: METHODS OF LINE SEARCHING___ \n\n");

if (!Swann4(st_p,line,a,b,x)) {

if (!Boltsano(st_p,line,a,b,x)) {

Davidon(st_p,line,a,b,x);

printf("Davidon gave answer\n x*=(%.3f,%.3f) \n and f(x*)= %.3f \n and alfa = %.3f\n",x.x,x.y,fun(x),b);

} else printf("The answer was found Boltsano,\n x*=(%.3f,%.3f),\n and f(x*)= %.3f \n and alfa = %.3f",x.x,x.y,fun(x),b);

} else printf("The answer was found Swann4,\n x*=(%.3f,%.3f),\n and f(x*)= %.3f \n and alfa = %.3f",x.x,x.y,fun(x),b);

printf("\n\n<<PRESS ANY KEY TO EXIT>>");

getch();

}

//---------------------------------------------------------------------------