Math.lab4

#include <stdio.h>
#include <math.h>
#define EPS 0.0001

void newton(float x0, float y0);
void check(float x, float y);
float F(float x, float y);
float fx(float x, float y);
float fy(float x, float y);
float G(float x, float y);

int main()
{
    printf("\nf(x,y) = sin(x+y) - 1.2x - 0.2\ng(x,y) = x^2 + y^2 - 1\n\n");
    printf("\n==================================\n");
    printf("1st pair of roots:\n");
    newton(-1, -1);
    printf("\n==================================\n");
    printf("2nd pair of roots:\n");
    newton(1, 1);

    return 0;
}

void newton(float x, float y)
{
    float A, B, J;
    float x0, y0, x1 = x, y1 = y;

    do {
        x0 = x1;
        y0 = y1;

        A = F(x0,y0) * 2*y - fy(x0,y0) * G(x0,y0);
        B = fx(x0,y0) * G(x0,y0) - F(x0,y0) * 2*x;
        J = fx(x0,y0) * 2*y - fy(x0,y0) * 2*x;

        if (J == 0) {
            printf("Jacobian is equal to zero!\n");
            break;
        }

        x1 = x0 - A / J;
        y1 = y0 - B / J;
    } while ((fabs(x1 - x0) >= EPS) && (fabs(y1 - y0) >= EPS));

    printf("\nx = %f\ty = %f\n", x1, y1);
    check(x1,y1);
}

void check(float x, float y)
{
    float f = sin(x+y) - 1.2*x - 0.2;
    float g = x*x + y*y - 1;
    printf("\nChecking...\n\n");
    printf("f(%f,%f) = %f\n\n",x,y,f);
    printf("g(%f,%f) = %f\n\n",x,y,g);
}

float F(float x, float y)
{
    float sinxy = sin(x+y);
    return (sinxy - 1.2*x - 0.2);
}

float fx(float x, float y)
{
    return (cos(x+y) - 1.2);
}

float fy(float x, float y)
{
    return cos(x+y);
}

float G(float x, float y)
{
    return (x*x + y*y - 1);
}