1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
|
#include "roots.h"
#include <math.h>
#include <stdio.h>
char root_ok = 1;
// функция для проверки того, успешно ли выполнилась последняя функция
char is_root_ok(void) {
return root_ok;
}
// метод дихтомии
double sol_binsr(f_t f, double a, double b, double ex, double ey) {
if (copysign(1.0, f(a)) == copysign(1.0, f(b))) {
root_ok = 0;
return NAN;
}
double mid;
do {
mid = (a + b) / 2;
if (copysign(1.0, f(a)) != copysign(1.0, f(mid))) b = mid;
else a = mid;
} while (f(mid) > ey || (b-a) > ex);
root_ok = 1;
return mid;
}
// метод хорд
double sol_chord(f_t f, double a, double b, double ex, double ey) {
if (copysign(1.0, f(a)) == copysign(1.0, f(b))) {
root_ok = 0;
return NAN;
}
double mid = a + fabs( f(a) / (f(b)-f(a)) ) * (b-a);
double diff = mid;
while (f(mid) > ey || fabs(diff - mid) > ex) {
diff = mid;
mid = a + fabs( f(a) / (f(b)-f(a)) ) * (b-a);
if (copysign(1.0, f(a)) != copysign(1.0, f(mid))) b = mid;
else a = mid;
}
root_ok = 1;
return mid;
}
// метод касательных (Ньютона)
double sol_newtn(f_t f, double x0, double ex, double ey) {
const double dx = 1e-6;
double diff = x0+2*ex;
// check for divergence
double d2x0 = (f(x0 + 2*dx) - 2*f(x0 + dx) + f(x0))/(dx*dx);
if (copysign(1.0, d2x0) != copysign(1.0, f(x0))) {
root_ok = 0;
return NAN;
}
while ((fabs(diff - x0) > ex || f(x0) > ey)) {
double fx0 = f(x0);
double dx0 = (f(x0+dx) - fx0) / dx;
diff = x0;
x0 -= fx0/dx0;
if (isinf(x0) || isnan(x0)) {
root_ok = 0;
return NAN;
}
}
root_ok = 1;
return x0;
}
// метод итераций
double sol_itern(f_t f, double x0, double ex, double ey) {
const double dx = 1e-6;
double diff = x0 + 2*ex;
do {
double dx0 = (f(x0+dx) - f(x0))/dx;
if (fabs(dx0) > 1.0) {
root_ok = 0;
return NAN;
}
diff = x0;
x0 = f(x0);
printf("x0=%lf, f(x0)=%lf\n", x0, f(x0));
getchar();
} while (fabs(diff - x0) > ex || fabs(f(x0) - x0) > ey);
root_ok = 1;
return x0;
}
|
