# Untitled

May 24th, 2020
168
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1. #define _CRT_SECURE_NO_WARNINGS
2. #include <stdio.h>
3. #include <stdlib.h>
4. #define _USE_MATH_DEFINES
5. #include <math.h>
6. #include <time.h>
7. #include <string.h>
8.
9. double func(double x, double y) {
10.     return sin(x) - cos(2 * y);
11. }
12.
14.     return cos(x);
15. }
17.     return 2 * sin(2 * y);
18. }
19.
20. double calcVx(double x) {
21.     return cos(x) / sin(x);
22. }
23.
24. double calcVy(double y) {
25.     return -0.5 * tan(2 * y);
26. }
27.
28. double randOnRange(double min, double max) {
29.     double f = (double)rand() / RAND_MAX;
30.     return min + f * (max - min);
31. };
32.
35. }
36.
37. int main() {
38.     puts("Really minimum f(x,y) = sin(x)-cos(2y) is -2");
39.     srand(time(0));
40.     double arrX[100] = { 0 };
41.     double arrY[100] = { 0 };
42.     double eps = 0.01;
43.     double t = 0;
44.     double count = 0;
45.     for (int i = 0; i < 100; i++) {
46.         arrX[i] = randOnRange(-10, 10);
47.         arrY[i] = randOnRange(-10, 10);
48.     }
49.
50.     for (int i = 0; i < 100; i++) {
51.         double x = arrX[i];
52.         double y = arrY[i];
53.         for (; sqrt(pow(gradientX(x), 2) + pow(gradientY(y), 2) > eps); ) {
54.             if (gradientX(x) * calcVx(x) + gradientY(y) * calcVy(y) > 0) {
55.                 t = -1;
56.             }
57.             else {
58.                 t = 1;
59.             }
60.             while (func(x + t * calcVx(x), y + t * calcVy(y)) >= func(x, y) + 3 / 4 * t * (gradientX(x) * calcVx(x) + gradientY(y) * calcVy(y))) {
61.                 t /= 2;
62.             }
63.             x = x + t * calcVx(x);
64.             y = y + t * calcVy(y);
65.         }
66.         arrX[i] = x;
67.         arrY[i] = y;
68.     }
69.     for (int i = 0; i < 100; i++) {
70.         count += func(arrX[i], arrY[i])- func(3 / 2 * M_PI, 0);
71.     }
72.     printf("Average accuracy: %.6lf\n", count/100);
73.
74.     return 0;
75. }