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#include "stdafx.h"
#include<cstdio>
#include<iostream>
#include<math.h>
double f(double x,double y){return log(1+x*x+y*y)+sin(0.1*x+0.2*y);}
double dx(double x,double y){return (2*x)/(1+x*x+y*y) +0.1*cos(0.1*x+0.2*y);}
double dy(double x,double y){return (2*y)/(1+x*x+y*y) +0.2*cos(0.1*x+0.2*y);}
double dxdx(double x,double y){return (2*(1-x*x+y*y))/(pow(1+x*x+y*y,2))- 0.01*sin(0.1*x+0.2*y);}
double dydy(double x,double y){return (2*(1+x*x-y*y))/(pow(1+x*x+y*y,2))- 0.04*sin(0.1*x+0.2*y);}
double dxdy(double x,double y){return (4*x*y)/(pow(1+x*x+y*y,2))- 0.02*sin(0.1*x+0.2*y);}
double max(double x1, double x2) {return dx(x1, x2) > dy(x1, x2) ? dx(x1, x2) : dy(x1, x2);}
double finddirection(double x, double y) {
return (-(dx(x,y)*dx(x,y))-(dy(x,y)*dy(x,y)))/
(dxdx(x,y)*(dx(x,y)*dx(x,y)) + 2*dxdy(x,y)*dx(x,y)*dy(x,y) + dydy(x,y)*(dy(x,y)*dy(x,y)));
}
double descent(double x, double y,double e){
double x1 = x, y1 = y, x2, y2, t;
int count = 1;
while(true) {
t = finddirection(x1, y1);
x2 = x1-t*dx(x1,y1);
y2 = y1-t*dy(x1,y1);
if (max(x2, y2) <= 0.001) {
printf("i = %d\t", count);
printf("x = %f, y = %f \t", x1, y1);
return f(x1,y1);
}
printf("i = %d\t", count);
printf("x = %f, y = %f \t", x1, y1);
printf("f(x,y) = %f\n",f(x1,y1));
x1 = x2;
y1 = y2;
count++;
}
}
int main(){
double x = 1, y = 2, eps = 0.001;
printf("f(x,y) = %f\n",descent(x,y,eps));
return 0;
}