-
Notifications
You must be signed in to change notification settings - Fork 0
/
DOPRI8_final_plot.cpp
203 lines (149 loc) · 7.97 KB
/
DOPRI8_final_plot.cpp
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
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
#include "parameters.h"
#include "vector.h"
#include <array>
#include <QVector>
#include <QDebug>
#include <cassert>
#include "custom_functions.h"
//nu1, nu2, nu3, x, y, theta
Vector<6> rightpart_final(double t, Vector<6> x, Vector<3> control_minus, Vector<3> control_plus, double t_sw)
{
Vector<6> rez;
Vector<3> u;
if (t < t_sw)
u = control_minus;
else
u = control_plus;
const auto A_rev = matr_rev(A_matr(parameters::final::alpha, parameters::final::beta,
parameters::final::delta, parameters::final::Delta, parameters::final::Lambda));
const auto Sigma = Sigma_matr(parameters::final::alpha, parameters::final::beta,
parameters::final::delta, parameters::final::Delta, parameters::final::Lambda);
auto second_matr = scal_mult(matr_mult(A_rev, matr_T(Sigma)), parameters::c1);
auto third_matr = scal_mult(matr_mult(A_rev, matr_mult(matr_T(Sigma), Sigma)), -parameters::c2);
auto rightpart_expr = vec_mult(A_rev, {x[1] * x[2] / parameters::final::Lambda,
- x[0] * x[2] / parameters::final::Lambda, 0}) +
vec_mult(second_matr, u) + vec_mult(third_matr, {x[0], x[1], x[2]});
rez[0] = rightpart_expr[0];
rez[1] = rightpart_expr[1];
rez[2] = rightpart_expr[2];
rez[3] = x[0] * cos(x[5]) - x[1] * sin(x[5]);
rez[4] = x[0] * sin(x[5]) + x[1] * cos(x[5]);
rez[5] = x[2] / parameters::final::Lambda;
return rez;
}
Vector<6> DOPRI8_final_plot(double t_left, double t_right, Vector<6> initial_values,
Vector<3> control_minus, Vector<3> control_plus, double t_sw,
QVector<double> &t_vec, QVector<double> &nu1_vec, QVector<double> &nu2_vec,
QVector<double> &nu3_vec, QVector<double> &x_vec, QVector<double> &y_vec,
QVector<double> &theta_vec)
{
double h = (t_right - t_left) / 1e7;
double h_new;
bool switch_flag = false;
bool last_flag = false;
double tl = t_left;
Vector<6> xl = initial_values;
Vector<6> stepx;
Vector<6> errx;
double err, coef;
double coefmax = 5;
Vector<6> k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13;
t_vec.append(tl);
nu1_vec.append(xl[0]);
nu2_vec.append(xl[1]);
nu3_vec.append(xl[2]);
x_vec.append(xl[3]);
y_vec.append(xl[4]);
theta_vec.append(xl[5]);
while (tl + h < t_right || last_flag)
{
//switch point
if (tl < t_sw && tl + h > t_sw && !switch_flag)
{
h = t_sw - tl;
switch_flag = true;
}
k1 = rightpart_final(tl, xl, control_minus, control_plus, t_sw);
k2 = rightpart_final(tl + h / 18, xl + h * k1 / 18, control_minus, control_plus, t_sw);
k3 = rightpart_final(tl + h / 12, xl + h * (k1 / 48 + k2 / 16) , control_minus, control_plus, t_sw);
k4 = rightpart_final(tl + h / 8, xl + h * (k1 / 32 + k3 * 3 / 32) , control_minus, control_plus, t_sw);
k5 = rightpart_final(tl + h * 5 / 16, xl + h * (k1 * 5 / 16 + k3 * (-75) / 64 + k4 * 75 / 64) , control_minus, control_plus, t_sw);
k6 = rightpart_final(tl + h * 3 / 8, xl + h * (k1 * 3 / 80 + k4 * 3 / 16 + k5 * 3 / 20) , control_minus, control_plus, t_sw);
k7 = rightpart_final(tl + h * 59. / 400., xl + h * (k1 * (29443841. / 614563906.) + k4 * (77736538. / 692538347.) + k5 * ((-28693883.) / 1125000000.) +
k6 * (23124283. / 1800000000.) ), control_minus, control_plus, t_sw);
k8 = rightpart_final(tl + h * 93. / 200., xl + h * (k1 * (16016141. / 946692911.) + k4 * (61564180. / 158732637.) + k5 * (22789713. / 633445777.) +
k6 * (545815736. / 2771057229.) + k7 * ((-180193667.) / 1043307555.) ), control_minus, control_plus, t_sw);
k9 = rightpart_final(tl + h * (5490023248. / 9719169821.), xl + h * (k1 * (39632708. / 573591083.) + k4 * ((-433636366.) / 683701615.) + k5 * ((-421739975.) / 2616292301.) +
k6 * (100302831. / 723423059.) + k7 * (790204164. / 839813087.) + k8 * (800635310. / 3783071287.) ), control_minus, control_plus, t_sw);
k10 = rightpart_final(tl + h * 13 / 20, xl + h * (k1 * (246121993. / 1340847787.) + k4 * ((-37695042795.) / 15268766246.) + k5 * ((-309121744.) / 1061227803.) +
k6 * ((-12992083.) / 490766935.) + k7 * (6005943493. / 2108947869.) + k8 * (393006217. / 1396673457) + k9 * (123872331. / 1001029789.) ), control_minus, control_plus, t_sw);
k11 = rightpart_final(tl + h * (1201146811. / 1299019798.), xl + h * (k1 * ((-1028468189.) / 846180014.) + k4 * (8478235783. / 508512852.) + k5 * (1311729495. / 1432422823.) +
k6 * ((-10304129995.) / 1701304382.) + k7 * ((-48777925059.) / 3047939560.) + k8 * (15336726248. / 1032824649.) + k9 * ((-45442868181.) / 3398467696.) +
k10 * (3065993473. / 597172653.) ), control_minus, control_plus, t_sw);
k12 = rightpart_final(tl + h, xl + h * (k1 * (185892177. / 718116043.) + k4 * ((-3185094517.) / 667107341.) + k5 * ((-477755414.) / 1098053517.) +
k6 * ((-703635378.) / 230739211.) + k7 * (5731566787. / 1027545527.) + k8 * (5232866602. / 850066563.) + k9 * ((-4093664535.) / 808688257.) +
k10 * (3962137247. / 1805957418.) + k11 * (65686358. / 487910083.) ), control_minus, control_plus, t_sw);
k13 = rightpart_final(tl + h, xl + h * (k1 * (403863854. / 491063109.) + k4 * ((-5068492393.) / 434740067.) + k5 * ((-411421997.) / 543043805.) +
k6 * (652783627. / 914296604.) + k7 * (11173962825. / 925320556.) + k8 * ((-13158990841.) / 6184727034.) + k9 * (3936647629. / 1978049680.) +
k10 * ((-160528059.) / 685178525.) + k11 * (248638103. / 1413531060.) ), control_minus, control_plus, t_sw);
stepx = h * (k1 * (14005451. / 335480064.) + k6 * ((-59238493.) / 1068277825.) + k7 * (181606767. / 758867731.) + k8 * (561292985. / 797845732.) +
k9 * ((-1041891430.) / 1371343529.) + k10 * (760417239. / 1151165299.) + k11 * (118820643. / 751138087.) + k12 * ((-528747749.) / 2220607170.) + k13 / 4 );
errx = h * (k1 * (13451932. / 455176623.) + k6 * ((-808719846.) / 976000145.) + k7 * (1757004468. / 5645159321.) + k8 * (656045339. / 265891186.) +
k9 * ((-3867574721.) / 1518517206.) + k10 * (465885868. / 322736535.) + k11 * (53011238. / 667516719.) + k12 * 2 / 45 );
err = (stepx - errx).euclidDistance();
//step correction section
if (err < 1e-15)
{
tl += h;
xl += stepx;
t_vec.append(tl);
nu1_vec.append(xl[0]);
nu2_vec.append(xl[1]);
nu3_vec.append(xl[2]);
x_vec.append(xl[3]);
y_vec.append(xl[4]);
theta_vec.append(xl[5]);
coefmax = 5;
h *= 2;
}
else
{
coef = pow(precision::DOPRI8_error_EPS / err, 1.0 / (8 + 1));
if (coef > coefmax)
coef = coefmax;
else if (coef < 0.2)
coef = 0.2;
h_new = 0.9 * h * coef;
if (precision::DOPRI8_error_EPS > err)
{
tl += h;
xl += stepx;
t_vec.append(tl);
nu1_vec.append(xl[0]);
nu2_vec.append(xl[1]);
nu3_vec.append(xl[2]);
x_vec.append(xl[3]);
y_vec.append(xl[4]);
theta_vec.append(xl[5]);
coefmax = 5;
}
else
coefmax = 1;
h = h_new;
}
//for correct plotting; there could be too few points
if (h > (t_right - t_left) / 100)
{
h = (t_right - t_left) / 100;
}
//last step correction
if (tl + h >= t_right && last_flag == false)
{
h = t_right - tl;
last_flag = true;
}
else
last_flag = false;
}
return xl;
}