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DOPRI8_symmetrical_plot.cpp
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DOPRI8_symmetrical_plot.cpp
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#include "parameters.h"
#include "vector.h"
#include <QVector>
#include <QDebug>
//nu1, nu2, nu3, x, y, theta
Vector<6> rightpart(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;
rez[0] = (parameters::symmetrical::m * x[1] * x[2] / parameters::symmetrical::Lambda + parameters::c1 * (u[0] / 2 - u[1] + u[2] / 2) / parameters::symmetrical::r
- 3 * parameters::c2 * x[0] / 2 / parameters::symmetrical::r / parameters::symmetrical::r) / parameters::symmetrical::A1;
rez[1] = (- parameters::symmetrical::m * x[0] * x[2] / parameters::symmetrical::Lambda + parameters::c1 * sqrt(3) * (u[0] - u[2]) / 2 / parameters::symmetrical::r
- 3 * parameters::c2 * x[1] / 2 / parameters::symmetrical::r / parameters::symmetrical::r) / parameters::symmetrical::A2;
rez[2] = (parameters::c1 * parameters::symmetrical::rho * (u[0] + u[1] + u[2]) / parameters::symmetrical::Lambda / parameters::symmetrical::r
- 3 * parameters::c2 * parameters::symmetrical::rho * parameters::symmetrical::rho * x[2]
/ (parameters::symmetrical::Lambda * parameters::symmetrical::Lambda) / parameters::symmetrical::r / parameters::symmetrical::r) / parameters::symmetrical::A3;
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::symmetrical::Lambda;
return rez;
}
Vector<6> DOPRI8_symmetrical_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, QVector<double> &u1_vec, QVector<double> &u2_vec,
QVector<double> &u3_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]);
Vector<3> u;
if (tl < t_sw)
u = control_minus;
else
u = control_plus;
u1_vec.append(u[0]);
u2_vec.append(u[1]);
u3_vec.append(u[2]);
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(tl, xl, control_minus, control_plus, t_sw);
k2 = rightpart(tl + h / 18, xl + h * k1 / 18, control_minus, control_plus, t_sw);
k3 = rightpart(tl + h / 12, xl + h * (k1 / 48 + k2 / 16) , control_minus, control_plus, t_sw);
k4 = rightpart(tl + h / 8, xl + h * (k1 / 32 + k3 * 3 / 32) , control_minus, control_plus, t_sw);
k5 = rightpart(tl + h * 5 / 16, xl + h * (k1 * 5 / 16 + k3 * (-75) / 64 + k4 * 75 / 64) , control_minus, control_plus, t_sw);
k6 = rightpart(tl + h * 3 / 8, xl + h * (k1 * 3 / 80 + k4 * 3 / 16 + k5 * 3 / 20) , control_minus, control_plus, t_sw);
k7 = rightpart(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(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(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(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(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(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(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]);
if (tl < t_sw)
u = control_minus;
else
u = control_plus;
u1_vec.append(u[0]);
u2_vec.append(u[1]);
u3_vec.append(u[2]);
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]);
if (tl < t_sw)
u = control_minus;
else
u = control_plus;
u1_vec.append(u[0]);
u2_vec.append(u[1]);
u3_vec.append(u[2]);
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;
}