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misc_pTop_funcs.cpp
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misc_pTop_funcs.cpp
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// LibQPEP: A Library for Globally Optimal Solving Quadratic Pose Estimation Problems,
// It also gives highly accurate uncertainty description of the solutions.
//
// Author: Jin Wu
// Affiliation: Hong Kong University of Science and Technology (HKUST)
// Emails: [email protected]; [email protected]
// Reference: Wu, J., et al. (2022) Quadratic Pose Estimation Problems:
// Globally Optimal Solutions,
// Solvability/Observability Analysis,
// and Uncertainty Description.
// IEEE Transactions on Robotics.
// https://doi.org/10.1109/TRO.2022.3155880
//
//
// misc_pTop_funcs.cpp: Functions for computation of Point-to-Plane registration problems
#include "misc_pTop_funcs.h"
Eigen::Vector3d
t_pTop_func(const Eigen::MatrixXd &pinvG, const Eigen::MatrixXd &coefs_tq, const Eigen::Quaterniond &q) {
double pinvG1_1 = pinvG(0, 0);
double pinvG1_2 = pinvG(0, 1);
double pinvG1_3 = pinvG(0, 2);
double pinvG2_1 = pinvG(1, 0);
double pinvG2_2 = pinvG(1, 1);
double pinvG2_3 = pinvG(1, 2);
double pinvG3_1 = pinvG(2, 0);
double pinvG3_2 = pinvG(2, 1);
double pinvG3_3 = pinvG(2, 2);
double coefs_tq1_1 = coefs_tq(0, 0);
double coefs_tq1_2 = coefs_tq(0, 1);
double coefs_tq1_3 = coefs_tq(0, 2);
double coefs_tq1_4 = coefs_tq(0, 3);
double coefs_tq1_5 = coefs_tq(0, 4);
double coefs_tq1_6 = coefs_tq(0, 5);
double coefs_tq1_7 = coefs_tq(0, 6);
double coefs_tq1_8 = coefs_tq(0, 7);
double coefs_tq1_9 = coefs_tq(0, 8);
double coefs_tq1_10 = coefs_tq(0, 9);
double coefs_tq1_11 = coefs_tq(0, 10);
double coefs_tq2_1 = coefs_tq(1, 0);
double coefs_tq2_2 = coefs_tq(1, 1);
double coefs_tq2_3 = coefs_tq(1, 2);
double coefs_tq2_4 = coefs_tq(1, 3);
double coefs_tq2_5 = coefs_tq(1, 4);
double coefs_tq2_6 = coefs_tq(1, 5);
double coefs_tq2_7 = coefs_tq(1, 6);
double coefs_tq2_8 = coefs_tq(1, 7);
double coefs_tq2_9 = coefs_tq(1, 8);
double coefs_tq2_10 = coefs_tq(1, 9);
double coefs_tq2_11 = coefs_tq(1, 10);
double coefs_tq3_1 = coefs_tq(2, 0);
double coefs_tq3_2 = coefs_tq(2, 1);
double coefs_tq3_3 = coefs_tq(2, 2);
double coefs_tq3_4 = coefs_tq(2, 3);
double coefs_tq3_5 = coefs_tq(2, 4);
double coefs_tq3_6 = coefs_tq(2, 5);
double coefs_tq3_7 = coefs_tq(2, 6);
double coefs_tq3_8 = coefs_tq(2, 7);
double coefs_tq3_9 = coefs_tq(2, 8);
double coefs_tq3_10 = coefs_tq(2, 9);
double coefs_tq3_11 = coefs_tq(2, 10);
double q0 = q.x();
double q1 = q.y();
double q2 = q.z();
double q3 = q.w();
Eigen::Vector3d t;
t(0) = (q0 * q0) * (coefs_tq1_1 * pinvG1_1 + coefs_tq2_1 * pinvG1_2 + coefs_tq3_1 * pinvG1_3) +
(q1 * q1) * (coefs_tq1_5 * pinvG1_1 + coefs_tq2_5 * pinvG1_2 + coefs_tq3_5 * pinvG1_3) +
(q2 * q2) * (coefs_tq1_8 * pinvG1_1 + coefs_tq2_8 * pinvG1_2 + coefs_tq3_8 * pinvG1_3) +
(q3 * q3) * (coefs_tq1_10 * pinvG1_1 + coefs_tq2_10 * pinvG1_2 + coefs_tq3_10 * pinvG1_3) +
coefs_tq1_11 * pinvG1_1 + coefs_tq2_11 * pinvG1_2 + coefs_tq3_11 * pinvG1_3 +
q0 * q1 * (coefs_tq1_2 * pinvG1_1 + coefs_tq2_2 * pinvG1_2 + coefs_tq3_2 * pinvG1_3) +
q0 * q2 * (coefs_tq1_3 * pinvG1_1 + coefs_tq2_3 * pinvG1_2 + coefs_tq3_3 * pinvG1_3) +
q0 * q3 * (coefs_tq1_4 * pinvG1_1 + coefs_tq2_4 * pinvG1_2 + coefs_tq3_4 * pinvG1_3) +
q1 * q2 * (coefs_tq1_6 * pinvG1_1 + coefs_tq2_6 * pinvG1_2 + coefs_tq3_6 * pinvG1_3) +
q1 * q3 * (coefs_tq1_7 * pinvG1_1 + coefs_tq2_7 * pinvG1_2 + coefs_tq3_7 * pinvG1_3) +
q2 * q3 * (coefs_tq1_9 * pinvG1_1 + coefs_tq2_9 * pinvG1_2 + coefs_tq3_9 * pinvG1_3);
t(1) = (q0 * q0) * (coefs_tq1_1 * pinvG2_1 + coefs_tq2_1 * pinvG2_2 + coefs_tq3_1 * pinvG2_3) +
(q1 * q1) * (coefs_tq1_5 * pinvG2_1 + coefs_tq2_5 * pinvG2_2 + coefs_tq3_5 * pinvG2_3) +
(q2 * q2) * (coefs_tq1_8 * pinvG2_1 + coefs_tq2_8 * pinvG2_2 + coefs_tq3_8 * pinvG2_3) +
(q3 * q3) * (coefs_tq1_10 * pinvG2_1 + coefs_tq2_10 * pinvG2_2 + coefs_tq3_10 * pinvG2_3) +
coefs_tq1_11 * pinvG2_1 + coefs_tq2_11 * pinvG2_2 + coefs_tq3_11 * pinvG2_3 +
q0 * q1 * (coefs_tq1_2 * pinvG2_1 + coefs_tq2_2 * pinvG2_2 + coefs_tq3_2 * pinvG2_3) +
q0 * q2 * (coefs_tq1_3 * pinvG2_1 + coefs_tq2_3 * pinvG2_2 + coefs_tq3_3 * pinvG2_3) +
q0 * q3 * (coefs_tq1_4 * pinvG2_1 + coefs_tq2_4 * pinvG2_2 + coefs_tq3_4 * pinvG2_3) +
q1 * q2 * (coefs_tq1_6 * pinvG2_1 + coefs_tq2_6 * pinvG2_2 + coefs_tq3_6 * pinvG2_3) +
q1 * q3 * (coefs_tq1_7 * pinvG2_1 + coefs_tq2_7 * pinvG2_2 + coefs_tq3_7 * pinvG2_3) +
q2 * q3 * (coefs_tq1_9 * pinvG2_1 + coefs_tq2_9 * pinvG2_2 + coefs_tq3_9 * pinvG2_3);
t(2) = (q0 * q0) * (coefs_tq1_1 * pinvG3_1 + coefs_tq2_1 * pinvG3_2 + coefs_tq3_1 * pinvG3_3) +
(q1 * q1) * (coefs_tq1_5 * pinvG3_1 + coefs_tq2_5 * pinvG3_2 + coefs_tq3_5 * pinvG3_3) +
(q2 * q2) * (coefs_tq1_8 * pinvG3_1 + coefs_tq2_8 * pinvG3_2 + coefs_tq3_8 * pinvG3_3) +
(q3 * q3) * (coefs_tq1_10 * pinvG3_1 + coefs_tq2_10 * pinvG3_2 + coefs_tq3_10 * pinvG3_3) +
coefs_tq1_11 * pinvG3_1 + coefs_tq2_11 * pinvG3_2 + coefs_tq3_11 * pinvG3_3 +
q0 * q1 * (coefs_tq1_2 * pinvG3_1 + coefs_tq2_2 * pinvG3_2 + coefs_tq3_2 * pinvG3_3) +
q0 * q2 * (coefs_tq1_3 * pinvG3_1 + coefs_tq2_3 * pinvG3_2 + coefs_tq3_3 * pinvG3_3) +
q0 * q3 * (coefs_tq1_4 * pinvG3_1 + coefs_tq2_4 * pinvG3_2 + coefs_tq3_4 * pinvG3_3) +
q1 * q2 * (coefs_tq1_6 * pinvG3_1 + coefs_tq2_6 * pinvG3_2 + coefs_tq3_6 * pinvG3_3) +
q1 * q3 * (coefs_tq1_7 * pinvG3_1 + coefs_tq2_7 * pinvG3_2 + coefs_tq3_7 * pinvG3_3) +
q2 * q3 * (coefs_tq1_9 * pinvG3_1 + coefs_tq2_9 * pinvG3_2 + coefs_tq3_9 * pinvG3_3);
return t;
}
std::vector<double> mon_J_pure_pTop_func(const Eigen::Quaterniond &q, const Eigen::Vector3d &t) {
double q0 = q.x();
double q1 = q.y();
double q2 = q.z();
double q3 = q.w();
double t1 = t(0);
double t2 = t(1);
double t3 = t(2);
double symobj[1][85];
std::memset(symobj, 0, 1 * 85 * sizeof(double));
symobj[0][0] = q0 * q0 * q0 * q0;
symobj[0][1] = (q0 * q0 * q0) * q1;
symobj[0][2] = (q0 * q0 * q0) * q2;
symobj[0][3] = (q0 * q0 * q0) * q3;
symobj[0][4] = (q0 * q0) * (q1 * q1);
symobj[0][5] = (q0 * q0) * q1 * q2;
symobj[0][6] = (q0 * q0) * q1 * q3;
symobj[0][7] = (q0 * q0) * (q2 * q2);
symobj[0][8] = (q0 * q0) * q2 * q3;
symobj[0][9] = (q0 * q0) * (q3 * q3);
symobj[0][10] = (q0 * q0) * t1;
symobj[0][11] = (q0 * q0) * t2;
symobj[0][12] = (q0 * q0) * t3;
symobj[0][13] = q0 * q0;
symobj[0][14] = q0 * (q1 * q1 * q1);
symobj[0][15] = q0 * (q1 * q1) * q2;
symobj[0][16] = q0 * (q1 * q1) * q3;
symobj[0][17] = q0 * q1 * (q2 * q2);
symobj[0][18] = q0 * q1 * q2 * q3;
symobj[0][19] = q0 * q1 * (q3 * q3);
symobj[0][20] = q0 * q1 * t1;
symobj[0][21] = q0 * q1 * t2;
symobj[0][22] = q0 * q1 * t3;
symobj[0][23] = q0 * q1;
symobj[0][24] = q0 * (q2 * q2 * q2);
symobj[0][25] = q0 * (q2 * q2) * q3;
symobj[0][26] = q0 * q2 * (q3 * q3);
symobj[0][27] = q0 * q2 * t1;
symobj[0][28] = q0 * q2 * t2;
symobj[0][29] = q0 * q2 * t3;
symobj[0][30] = q0 * q2;
symobj[0][31] = q0 * (q3 * q3 * q3);
symobj[0][32] = q0 * q3 * t1;
symobj[0][33] = q0 * q3 * t2;
symobj[0][34] = q0 * q3 * t3;
symobj[0][35] = q0 * q3;
symobj[0][36] = q1 * q1 * q1 * q1;
symobj[0][37] = (q1 * q1 * q1) * q2;
symobj[0][38] = (q1 * q1 * q1) * q3;
symobj[0][39] = (q1 * q1) * (q2 * q2);
symobj[0][40] = (q1 * q1) * q2 * q3;
symobj[0][41] = (q1 * q1) * (q3 * q3);
symobj[0][42] = (q1 * q1) * t1;
symobj[0][43] = (q1 * q1) * t2;
symobj[0][44] = (q1 * q1) * t3;
symobj[0][45] = q1 * q1;
symobj[0][46] = q1 * (q2 * q2 * q2);
symobj[0][47] = q1 * (q2 * q2) * q3;
symobj[0][48] = q1 * q2 * (q3 * q3);
symobj[0][49] = q1 * q2 * t1;
symobj[0][50] = q1 * q2 * t2;
symobj[0][51] = q1 * q2 * t3;
symobj[0][52] = q1 * q2;
symobj[0][53] = q1 * (q3 * q3 * q3);
symobj[0][54] = q1 * q3 * t1;
symobj[0][55] = q1 * q3 * t2;
symobj[0][56] = q1 * q3 * t3;
symobj[0][57] = q1 * q3;
symobj[0][58] = q2 * q2 * q2 * q2;
symobj[0][59] = (q2 * q2 * q2) * q3;
symobj[0][60] = (q2 * q2) * (q3 * q3);
symobj[0][61] = (q2 * q2) * t1;
symobj[0][62] = (q2 * q2) * t2;
symobj[0][63] = (q2 * q2) * t3;
symobj[0][64] = q2 * q2;
symobj[0][65] = q2 * (q3 * q3 * q3);
symobj[0][66] = q2 * q3 * t1;
symobj[0][67] = q2 * q3 * t2;
symobj[0][68] = q2 * q3 * t3;
symobj[0][69] = q2 * q3;
symobj[0][70] = q3 * q3 * q3 * q3;
symobj[0][71] = (q3 * q3) * t1;
symobj[0][72] = (q3 * q3) * t2;
symobj[0][73] = (q3 * q3) * t3;
symobj[0][74] = q3 * q3;
symobj[0][75] = t1 * t1;
symobj[0][76] = t1 * t2;
symobj[0][77] = t1 * t3;
symobj[0][78] = t1;
symobj[0][79] = t2 * t2;
symobj[0][80] = t2 * t3;
symobj[0][81] = t2;
symobj[0][82] = t3 * t3;
symobj[0][83] = t3;
symobj[0][84] = 1.0;
std::vector<double> tmp;
for (int i = 0; i < 1; ++i)
for (int j = 0; j < 85; ++j)
tmp.push_back(symobj[i][j]);
return tmp;
}
void eq_Jacob_pTop_func(Eigen::Matrix<double, 4, 1> &eq,
Eigen::Matrix<double, 4, 4> &Jacob,
const Eigen::MatrixXd &coef_f_q_sym,
const Eigen::Vector4d &q) {
double coef_f0_q_sym1 = coef_f_q_sym(0, 0);
double coef_f0_q_sym2 = coef_f_q_sym(0, 1);
double coef_f0_q_sym3 = coef_f_q_sym(0, 2);
double coef_f0_q_sym4 = coef_f_q_sym(0, 3);
double coef_f0_q_sym5 = coef_f_q_sym(0, 4);
double coef_f0_q_sym6 = coef_f_q_sym(0, 5);
double coef_f0_q_sym7 = coef_f_q_sym(0, 6);
double coef_f0_q_sym8 = coef_f_q_sym(0, 7);
double coef_f0_q_sym9 = coef_f_q_sym(0, 8);
double coef_f0_q_sym10 = coef_f_q_sym(0, 9);
double coef_f0_q_sym11 = coef_f_q_sym(0, 10);
double coef_f0_q_sym12 = coef_f_q_sym(0, 11);
double coef_f0_q_sym13 = coef_f_q_sym(0, 12);
double coef_f0_q_sym14 = coef_f_q_sym(0, 13);
double coef_f0_q_sym15 = coef_f_q_sym(0, 14);
double coef_f0_q_sym16 = coef_f_q_sym(0, 15);
double coef_f0_q_sym17 = coef_f_q_sym(0, 16);
double coef_f0_q_sym18 = coef_f_q_sym(0, 17);
double coef_f0_q_sym19 = coef_f_q_sym(0, 18);
double coef_f0_q_sym20 = coef_f_q_sym(0, 19);
double coef_f0_q_sym21 = coef_f_q_sym(0, 20);
double coef_f0_q_sym22 = coef_f_q_sym(0, 21);
double coef_f0_q_sym23 = coef_f_q_sym(0, 22);
double coef_f0_q_sym24 = coef_f_q_sym(0, 23);
double coef_f1_q_sym1 = coef_f_q_sym(1, 0);
double coef_f1_q_sym2 = coef_f_q_sym(1, 1);
double coef_f1_q_sym3 = coef_f_q_sym(1, 2);
double coef_f1_q_sym4 = coef_f_q_sym(1, 3);
double coef_f1_q_sym5 = coef_f_q_sym(1, 4);
double coef_f1_q_sym6 = coef_f_q_sym(1, 5);
double coef_f1_q_sym7 = coef_f_q_sym(1, 6);
double coef_f1_q_sym8 = coef_f_q_sym(1, 7);
double coef_f1_q_sym9 = coef_f_q_sym(1, 8);
double coef_f1_q_sym10 = coef_f_q_sym(1, 9);
double coef_f1_q_sym11 = coef_f_q_sym(1, 10);
double coef_f1_q_sym12 = coef_f_q_sym(1, 11);
double coef_f1_q_sym13 = coef_f_q_sym(1, 12);
double coef_f1_q_sym14 = coef_f_q_sym(1, 13);
double coef_f1_q_sym15 = coef_f_q_sym(1, 14);
double coef_f1_q_sym16 = coef_f_q_sym(1, 15);
double coef_f1_q_sym17 = coef_f_q_sym(1, 16);
double coef_f1_q_sym18 = coef_f_q_sym(1, 17);
double coef_f1_q_sym19 = coef_f_q_sym(1, 18);
double coef_f1_q_sym20 = coef_f_q_sym(1, 19);
double coef_f1_q_sym21 = coef_f_q_sym(1, 20);
double coef_f1_q_sym22 = coef_f_q_sym(1, 21);
double coef_f1_q_sym23 = coef_f_q_sym(1, 22);
double coef_f1_q_sym24 = coef_f_q_sym(1, 23);
double coef_f2_q_sym1 = coef_f_q_sym(2, 0);
double coef_f2_q_sym2 = coef_f_q_sym(2, 1);
double coef_f2_q_sym3 = coef_f_q_sym(2, 2);
double coef_f2_q_sym4 = coef_f_q_sym(2, 3);
double coef_f2_q_sym5 = coef_f_q_sym(2, 4);
double coef_f2_q_sym6 = coef_f_q_sym(2, 5);
double coef_f2_q_sym7 = coef_f_q_sym(2, 6);
double coef_f2_q_sym8 = coef_f_q_sym(2, 7);
double coef_f2_q_sym9 = coef_f_q_sym(2, 8);
double coef_f2_q_sym10 = coef_f_q_sym(2, 9);
double coef_f2_q_sym11 = coef_f_q_sym(2, 10);
double coef_f2_q_sym12 = coef_f_q_sym(2, 11);
double coef_f2_q_sym13 = coef_f_q_sym(2, 12);
double coef_f2_q_sym14 = coef_f_q_sym(2, 13);
double coef_f2_q_sym15 = coef_f_q_sym(2, 14);
double coef_f2_q_sym16 = coef_f_q_sym(2, 15);
double coef_f2_q_sym17 = coef_f_q_sym(2, 16);
double coef_f2_q_sym18 = coef_f_q_sym(2, 17);
double coef_f2_q_sym19 = coef_f_q_sym(2, 18);
double coef_f2_q_sym20 = coef_f_q_sym(2, 19);
double coef_f2_q_sym21 = coef_f_q_sym(2, 20);
double coef_f2_q_sym22 = coef_f_q_sym(2, 21);
double coef_f2_q_sym23 = coef_f_q_sym(2, 22);
double coef_f2_q_sym24 = coef_f_q_sym(2, 23);
double coef_f3_q_sym1 = coef_f_q_sym(3, 0);
double coef_f3_q_sym2 = coef_f_q_sym(3, 1);
double coef_f3_q_sym3 = coef_f_q_sym(3, 2);
double coef_f3_q_sym4 = coef_f_q_sym(3, 3);
double coef_f3_q_sym5 = coef_f_q_sym(3, 4);
double coef_f3_q_sym6 = coef_f_q_sym(3, 5);
double coef_f3_q_sym7 = coef_f_q_sym(3, 6);
double coef_f3_q_sym8 = coef_f_q_sym(3, 7);
double coef_f3_q_sym9 = coef_f_q_sym(3, 8);
double coef_f3_q_sym10 = coef_f_q_sym(3, 9);
double coef_f3_q_sym11 = coef_f_q_sym(3, 10);
double coef_f3_q_sym12 = coef_f_q_sym(3, 11);
double coef_f3_q_sym13 = coef_f_q_sym(3, 12);
double coef_f3_q_sym14 = coef_f_q_sym(3, 13);
double coef_f3_q_sym15 = coef_f_q_sym(3, 14);
double coef_f3_q_sym16 = coef_f_q_sym(3, 15);
double coef_f3_q_sym17 = coef_f_q_sym(3, 16);
double coef_f3_q_sym18 = coef_f_q_sym(3, 17);
double coef_f3_q_sym19 = coef_f_q_sym(3, 18);
double coef_f3_q_sym20 = coef_f_q_sym(3, 19);
double coef_f3_q_sym21 = coef_f_q_sym(3, 20);
double coef_f3_q_sym22 = coef_f_q_sym(3, 21);
double coef_f3_q_sym23 = coef_f_q_sym(3, 22);
double coef_f3_q_sym24 = coef_f_q_sym(3, 23);
double q0 = q.x();
double q1 = q.y();
double q2 = q.z();
double q3 = q.w();
double symobj[4][4];
std::memset(symobj, 0, 4 * 1 * sizeof(double));
symobj[0][0] = -coef_f1_q_sym1 * (q0 * q0 * q0 * q0) + coef_f0_q_sym12 * (q1 * q1 * q1 * q1) +
coef_f0_q_sym18 * (q1 * q1) - coef_f1_q_sym11 * (q0 * q0) + coef_f0_q_sym1 * (q0 * q0 * q0) * q1 +
coef_f0_q_sym5 * q0 * (q1 * q1 * q1) - coef_f1_q_sym2 * (q0 * q0 * q0) * q1 -
coef_f1_q_sym3 * (q0 * q0 * q0) * q2 + coef_f0_q_sym13 * (q1 * q1 * q1) * q2 -
coef_f1_q_sym4 * (q0 * q0 * q0) * q3 + coef_f0_q_sym14 * (q1 * q1 * q1) * q3 +
coef_f0_q_sym19 * q1 * (q2 * q2 * q2) + coef_f0_q_sym23 * q1 * (q3 * q3 * q3) -
coef_f1_q_sym12 * q0 * (q1 * q1 * q1) - coef_f1_q_sym19 * q0 * (q2 * q2 * q2) -
coef_f1_q_sym23 * q0 * (q3 * q3 * q3) + coef_f0_q_sym2 * (q0 * q0) * (q1 * q1) -
coef_f1_q_sym5 * (q0 * q0) * (q1 * q1) + coef_f0_q_sym15 * (q1 * q1) * (q2 * q2) -
coef_f1_q_sym8 * (q0 * q0) * (q2 * q2) + coef_f0_q_sym17 * (q1 * q1) * (q3 * q3) -
coef_f1_q_sym10 * (q0 * q0) * (q3 * q3) + coef_f0_q_sym11 * q0 * q1 + coef_f0_q_sym22 * q1 * q2 +
coef_f0_q_sym24 * q1 * q3 - coef_f1_q_sym18 * q0 * q1 - coef_f1_q_sym22 * q0 * q2 -
coef_f1_q_sym24 * q0 * q3 + coef_f0_q_sym3 * (q0 * q0) * q1 * q2 +
coef_f0_q_sym4 * (q0 * q0) * q1 * q3 + coef_f0_q_sym6 * q0 * (q1 * q1) * q2 +
coef_f0_q_sym7 * q0 * (q1 * q1) * q3 + coef_f0_q_sym8 * q0 * q1 * (q2 * q2) +
coef_f0_q_sym10 * q0 * q1 * (q3 * q3) - coef_f1_q_sym6 * (q0 * q0) * q1 * q2 -
coef_f1_q_sym7 * (q0 * q0) * q1 * q3 + coef_f0_q_sym16 * (q1 * q1) * q2 * q3 -
coef_f1_q_sym9 * (q0 * q0) * q2 * q3 + coef_f0_q_sym20 * q1 * (q2 * q2) * q3 +
coef_f0_q_sym21 * q1 * q2 * (q3 * q3) - coef_f1_q_sym13 * q0 * (q1 * q1) * q2 -
coef_f1_q_sym14 * q0 * (q1 * q1) * q3 - coef_f1_q_sym15 * q0 * q1 * (q2 * q2) -
coef_f1_q_sym17 * q0 * q1 * (q3 * q3) - coef_f1_q_sym20 * q0 * (q2 * q2) * q3 -
coef_f1_q_sym21 * q0 * q2 * (q3 * q3) + coef_f0_q_sym9 * q0 * q1 * q2 * q3 -
coef_f1_q_sym16 * q0 * q1 * q2 * q3;
symobj[1][0] =
coef_f0_q_sym19 * (q2 * q2 * q2 * q2) - coef_f2_q_sym1 * (q0 * q0 * q0 * q0) + coef_f0_q_sym22 * (q2 * q2) -
coef_f2_q_sym11 * (q0 * q0) + coef_f0_q_sym1 * (q0 * q0 * q0) * q2 + coef_f0_q_sym8 * q0 * (q2 * q2 * q2) +
coef_f0_q_sym12 * (q1 * q1 * q1) * q2 + coef_f0_q_sym15 * q1 * (q2 * q2 * q2) -
coef_f2_q_sym2 * (q0 * q0 * q0) * q1 + coef_f0_q_sym20 * (q2 * q2 * q2) * q3 -
coef_f2_q_sym3 * (q0 * q0 * q0) * q2 - coef_f2_q_sym4 * (q0 * q0 * q0) * q3 +
coef_f0_q_sym23 * q2 * (q3 * q3 * q3) - coef_f2_q_sym12 * q0 * (q1 * q1 * q1) -
coef_f2_q_sym19 * q0 * (q2 * q2 * q2) - coef_f2_q_sym23 * q0 * (q3 * q3 * q3) +
coef_f0_q_sym3 * (q0 * q0) * (q2 * q2) + coef_f0_q_sym13 * (q1 * q1) * (q2 * q2) +
coef_f0_q_sym21 * (q2 * q2) * (q3 * q3) - coef_f2_q_sym5 * (q0 * q0) * (q1 * q1) -
coef_f2_q_sym8 * (q0 * q0) * (q2 * q2) - coef_f2_q_sym10 * (q0 * q0) * (q3 * q3) +
coef_f0_q_sym11 * q0 * q2 + coef_f0_q_sym18 * q1 * q2 + coef_f0_q_sym24 * q2 * q3 -
coef_f2_q_sym18 * q0 * q1 - coef_f2_q_sym22 * q0 * q2 - coef_f2_q_sym24 * q0 * q3 +
coef_f0_q_sym2 * (q0 * q0) * q1 * q2 + coef_f0_q_sym5 * q0 * (q1 * q1) * q2 +
coef_f0_q_sym4 * (q0 * q0) * q2 * q3 + coef_f0_q_sym6 * q0 * q1 * (q2 * q2) +
coef_f0_q_sym9 * q0 * (q2 * q2) * q3 + coef_f0_q_sym10 * q0 * q2 * (q3 * q3) +
coef_f0_q_sym14 * (q1 * q1) * q2 * q3 + coef_f0_q_sym16 * q1 * (q2 * q2) * q3 +
coef_f0_q_sym17 * q1 * q2 * (q3 * q3) - coef_f2_q_sym6 * (q0 * q0) * q1 * q2 -
coef_f2_q_sym7 * (q0 * q0) * q1 * q3 - coef_f2_q_sym9 * (q0 * q0) * q2 * q3 -
coef_f2_q_sym13 * q0 * (q1 * q1) * q2 - coef_f2_q_sym14 * q0 * (q1 * q1) * q3 -
coef_f2_q_sym15 * q0 * q1 * (q2 * q2) - coef_f2_q_sym17 * q0 * q1 * (q3 * q3) -
coef_f2_q_sym20 * q0 * (q2 * q2) * q3 - coef_f2_q_sym21 * q0 * q2 * (q3 * q3) +
coef_f0_q_sym7 * q0 * q1 * q2 * q3 - coef_f2_q_sym16 * q0 * q1 * q2 * q3;
symobj[2][0] =
coef_f0_q_sym24 * (q3 * q3) + coef_f0_q_sym23 * (q3 * q3 * q3 * q3) - coef_f3_q_sym1 * (q0 * q0 * q0 * q0) -
coef_f3_q_sym11 * (q0 * q0) + coef_f0_q_sym1 * (q0 * q0 * q0) * q3 + coef_f0_q_sym10 * q0 * (q3 * q3 * q3) +
coef_f0_q_sym12 * (q1 * q1 * q1) * q3 + coef_f0_q_sym17 * q1 * (q3 * q3 * q3) +
coef_f0_q_sym19 * (q2 * q2 * q2) * q3 + coef_f0_q_sym21 * q2 * (q3 * q3 * q3) -
coef_f3_q_sym2 * (q0 * q0 * q0) * q1 - coef_f3_q_sym3 * (q0 * q0 * q0) * q2 -
coef_f3_q_sym4 * (q0 * q0 * q0) * q3 - coef_f3_q_sym12 * q0 * (q1 * q1 * q1) -
coef_f3_q_sym19 * q0 * (q2 * q2 * q2) - coef_f3_q_sym23 * q0 * (q3 * q3 * q3) +
coef_f0_q_sym4 * (q0 * q0) * (q3 * q3) + coef_f0_q_sym14 * (q1 * q1) * (q3 * q3) +
coef_f0_q_sym20 * (q2 * q2) * (q3 * q3) - coef_f3_q_sym5 * (q0 * q0) * (q1 * q1) -
coef_f3_q_sym8 * (q0 * q0) * (q2 * q2) - coef_f3_q_sym10 * (q0 * q0) * (q3 * q3) +
coef_f0_q_sym11 * q0 * q3 + coef_f0_q_sym18 * q1 * q3 + coef_f0_q_sym22 * q2 * q3 -
coef_f3_q_sym18 * q0 * q1 - coef_f3_q_sym22 * q0 * q2 - coef_f3_q_sym24 * q0 * q3 +
coef_f0_q_sym2 * (q0 * q0) * q1 * q3 + coef_f0_q_sym3 * (q0 * q0) * q2 * q3 +
coef_f0_q_sym5 * q0 * (q1 * q1) * q3 + coef_f0_q_sym7 * q0 * q1 * (q3 * q3) +
coef_f0_q_sym8 * q0 * (q2 * q2) * q3 + coef_f0_q_sym9 * q0 * q2 * (q3 * q3) +
coef_f0_q_sym13 * (q1 * q1) * q2 * q3 + coef_f0_q_sym15 * q1 * (q2 * q2) * q3 +
coef_f0_q_sym16 * q1 * q2 * (q3 * q3) - coef_f3_q_sym6 * (q0 * q0) * q1 * q2 -
coef_f3_q_sym7 * (q0 * q0) * q1 * q3 - coef_f3_q_sym9 * (q0 * q0) * q2 * q3 -
coef_f3_q_sym13 * q0 * (q1 * q1) * q2 - coef_f3_q_sym14 * q0 * (q1 * q1) * q3 -
coef_f3_q_sym15 * q0 * q1 * (q2 * q2) - coef_f3_q_sym17 * q0 * q1 * (q3 * q3) -
coef_f3_q_sym20 * q0 * (q2 * q2) * q3 - coef_f3_q_sym21 * q0 * q2 * (q3 * q3) +
coef_f0_q_sym6 * q0 * q1 * q2 * q3 - coef_f3_q_sym16 * q0 * q1 * q2 * q3;
symobj[3][0] = q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3 - 1.0;
for (int i = 0; i < 4; ++i)
for (int j = 0; j < 1; ++j)
eq(i, j) = symobj[i][j];
std::memset(symobj, 0, 4 * 4 * sizeof(double));
symobj[0][0] = coef_f0_q_sym11 * q1 - coef_f1_q_sym11 * q0 * 2.0 - coef_f1_q_sym18 * q1 - coef_f1_q_sym22 * q2 -
coef_f1_q_sym24 * q3 + coef_f0_q_sym5 * (q1 * q1 * q1) - coef_f1_q_sym1 * (q0 * q0 * q0) * 4.0 -
coef_f1_q_sym12 * (q1 * q1 * q1) - coef_f1_q_sym19 * (q2 * q2 * q2) -
coef_f1_q_sym23 * (q3 * q3 * q3) + coef_f0_q_sym1 * (q0 * q0) * q1 * 3.0 +
coef_f0_q_sym2 * q0 * (q1 * q1) * 2.0 + coef_f0_q_sym6 * (q1 * q1) * q2 +
coef_f0_q_sym7 * (q1 * q1) * q3 + coef_f0_q_sym8 * q1 * (q2 * q2) -
coef_f1_q_sym2 * (q0 * q0) * q1 * 3.0 + coef_f0_q_sym10 * q1 * (q3 * q3) -
coef_f1_q_sym3 * (q0 * q0) * q2 * 3.0 - coef_f1_q_sym5 * q0 * (q1 * q1) * 2.0 -
coef_f1_q_sym4 * (q0 * q0) * q3 * 3.0 - coef_f1_q_sym8 * q0 * (q2 * q2) * 2.0 -
coef_f1_q_sym10 * q0 * (q3 * q3) * 2.0 - coef_f1_q_sym13 * (q1 * q1) * q2 -
coef_f1_q_sym14 * (q1 * q1) * q3 - coef_f1_q_sym15 * q1 * (q2 * q2) -
coef_f1_q_sym17 * q1 * (q3 * q3) - coef_f1_q_sym20 * (q2 * q2) * q3 -
coef_f1_q_sym21 * q2 * (q3 * q3) + coef_f0_q_sym3 * q0 * q1 * q2 * 2.0 +
coef_f0_q_sym4 * q0 * q1 * q3 * 2.0 + coef_f0_q_sym9 * q1 * q2 * q3 -
coef_f1_q_sym6 * q0 * q1 * q2 * 2.0 - coef_f1_q_sym7 * q0 * q1 * q3 * 2.0 -
coef_f1_q_sym9 * q0 * q2 * q3 * 2.0 - coef_f1_q_sym16 * q1 * q2 * q3;
symobj[0][1] = coef_f0_q_sym11 * q0 + coef_f0_q_sym18 * q1 * 2.0 + coef_f0_q_sym22 * q2 + coef_f0_q_sym24 * q3 -
coef_f1_q_sym18 * q0 + coef_f0_q_sym1 * (q0 * q0 * q0) - coef_f1_q_sym2 * (q0 * q0 * q0) +
coef_f0_q_sym12 * (q1 * q1 * q1) * 4.0 + coef_f0_q_sym19 * (q2 * q2 * q2) +
coef_f0_q_sym23 * (q3 * q3 * q3) + coef_f0_q_sym2 * (q0 * q0) * q1 * 2.0 +
coef_f0_q_sym3 * (q0 * q0) * q2 + coef_f0_q_sym5 * q0 * (q1 * q1) * 3.0 +
coef_f0_q_sym4 * (q0 * q0) * q3 + coef_f0_q_sym8 * q0 * (q2 * q2) +
coef_f0_q_sym10 * q0 * (q3 * q3) + coef_f0_q_sym13 * (q1 * q1) * q2 * 3.0 -
coef_f1_q_sym5 * (q0 * q0) * q1 * 2.0 + coef_f0_q_sym14 * (q1 * q1) * q3 * 3.0 +
coef_f0_q_sym15 * q1 * (q2 * q2) * 2.0 - coef_f1_q_sym6 * (q0 * q0) * q2 -
coef_f1_q_sym7 * (q0 * q0) * q3 + coef_f0_q_sym17 * q1 * (q3 * q3) * 2.0 +
coef_f0_q_sym20 * (q2 * q2) * q3 + coef_f0_q_sym21 * q2 * (q3 * q3) -
coef_f1_q_sym12 * q0 * (q1 * q1) * 3.0 - coef_f1_q_sym15 * q0 * (q2 * q2) -
coef_f1_q_sym17 * q0 * (q3 * q3) + coef_f0_q_sym6 * q0 * q1 * q2 * 2.0 +
coef_f0_q_sym7 * q0 * q1 * q3 * 2.0 + coef_f0_q_sym9 * q0 * q2 * q3 +
coef_f0_q_sym16 * q1 * q2 * q3 * 2.0 - coef_f1_q_sym13 * q0 * q1 * q2 * 2.0 -
coef_f1_q_sym14 * q0 * q1 * q3 * 2.0 - coef_f1_q_sym16 * q0 * q2 * q3;
symobj[0][2] = coef_f0_q_sym22 * q1 - coef_f1_q_sym22 * q0 - coef_f1_q_sym3 * (q0 * q0 * q0) +
coef_f0_q_sym13 * (q1 * q1 * q1) + coef_f0_q_sym3 * (q0 * q0) * q1 +
coef_f0_q_sym6 * q0 * (q1 * q1) - coef_f1_q_sym6 * (q0 * q0) * q1 +
coef_f0_q_sym15 * (q1 * q1) * q2 * 2.0 + coef_f0_q_sym16 * (q1 * q1) * q3 -
coef_f1_q_sym8 * (q0 * q0) * q2 * 2.0 + coef_f0_q_sym19 * q1 * (q2 * q2) * 3.0 -
coef_f1_q_sym9 * (q0 * q0) * q3 + coef_f0_q_sym21 * q1 * (q3 * q3) -
coef_f1_q_sym13 * q0 * (q1 * q1) - coef_f1_q_sym19 * q0 * (q2 * q2) * 3.0 -
coef_f1_q_sym21 * q0 * (q3 * q3) + coef_f0_q_sym8 * q0 * q1 * q2 * 2.0 +
coef_f0_q_sym9 * q0 * q1 * q3 + coef_f0_q_sym20 * q1 * q2 * q3 * 2.0 -
coef_f1_q_sym15 * q0 * q1 * q2 * 2.0 - coef_f1_q_sym16 * q0 * q1 * q3 -
coef_f1_q_sym20 * q0 * q2 * q3 * 2.0;
symobj[0][3] = coef_f0_q_sym24 * q1 - coef_f1_q_sym24 * q0 - coef_f1_q_sym4 * (q0 * q0 * q0) +
coef_f0_q_sym14 * (q1 * q1 * q1) + coef_f0_q_sym4 * (q0 * q0) * q1 +
coef_f0_q_sym7 * q0 * (q1 * q1) - coef_f1_q_sym7 * (q0 * q0) * q1 +
coef_f0_q_sym16 * (q1 * q1) * q2 + coef_f0_q_sym17 * (q1 * q1) * q3 * 2.0 -
coef_f1_q_sym9 * (q0 * q0) * q2 + coef_f0_q_sym20 * q1 * (q2 * q2) +
coef_f0_q_sym23 * q1 * (q3 * q3) * 3.0 - coef_f1_q_sym10 * (q0 * q0) * q3 * 2.0 -
coef_f1_q_sym14 * q0 * (q1 * q1) - coef_f1_q_sym20 * q0 * (q2 * q2) -
coef_f1_q_sym23 * q0 * (q3 * q3) * 3.0 + coef_f0_q_sym9 * q0 * q1 * q2 +
coef_f0_q_sym10 * q0 * q1 * q3 * 2.0 + coef_f0_q_sym21 * q1 * q2 * q3 * 2.0 -
coef_f1_q_sym16 * q0 * q1 * q2 - coef_f1_q_sym17 * q0 * q1 * q3 * 2.0 -
coef_f1_q_sym21 * q0 * q2 * q3 * 2.0;
symobj[1][0] = coef_f0_q_sym11 * q2 - coef_f2_q_sym11 * q0 * 2.0 - coef_f2_q_sym18 * q1 - coef_f2_q_sym22 * q2 -
coef_f2_q_sym24 * q3 + coef_f0_q_sym8 * (q2 * q2 * q2) - coef_f2_q_sym1 * (q0 * q0 * q0) * 4.0 -
coef_f2_q_sym12 * (q1 * q1 * q1) - coef_f2_q_sym19 * (q2 * q2 * q2) -
coef_f2_q_sym23 * (q3 * q3 * q3) + coef_f0_q_sym1 * (q0 * q0) * q2 * 3.0 +
coef_f0_q_sym3 * q0 * (q2 * q2) * 2.0 + coef_f0_q_sym5 * (q1 * q1) * q2 +
coef_f0_q_sym6 * q1 * (q2 * q2) + coef_f0_q_sym9 * (q2 * q2) * q3 +
coef_f0_q_sym10 * q2 * (q3 * q3) - coef_f2_q_sym2 * (q0 * q0) * q1 * 3.0 -
coef_f2_q_sym3 * (q0 * q0) * q2 * 3.0 - coef_f2_q_sym5 * q0 * (q1 * q1) * 2.0 -
coef_f2_q_sym4 * (q0 * q0) * q3 * 3.0 - coef_f2_q_sym8 * q0 * (q2 * q2) * 2.0 -
coef_f2_q_sym10 * q0 * (q3 * q3) * 2.0 - coef_f2_q_sym13 * (q1 * q1) * q2 -
coef_f2_q_sym14 * (q1 * q1) * q3 - coef_f2_q_sym15 * q1 * (q2 * q2) -
coef_f2_q_sym17 * q1 * (q3 * q3) - coef_f2_q_sym20 * (q2 * q2) * q3 -
coef_f2_q_sym21 * q2 * (q3 * q3) + coef_f0_q_sym2 * q0 * q1 * q2 * 2.0 +
coef_f0_q_sym4 * q0 * q2 * q3 * 2.0 + coef_f0_q_sym7 * q1 * q2 * q3 -
coef_f2_q_sym6 * q0 * q1 * q2 * 2.0 - coef_f2_q_sym7 * q0 * q1 * q3 * 2.0 -
coef_f2_q_sym9 * q0 * q2 * q3 * 2.0 - coef_f2_q_sym16 * q1 * q2 * q3;
symobj[1][1] = coef_f0_q_sym18 * q2 - coef_f2_q_sym18 * q0 + coef_f0_q_sym15 * (q2 * q2 * q2) -
coef_f2_q_sym2 * (q0 * q0 * q0) + coef_f0_q_sym2 * (q0 * q0) * q2 + coef_f0_q_sym6 * q0 * (q2 * q2) +
coef_f0_q_sym12 * (q1 * q1) * q2 * 3.0 + coef_f0_q_sym13 * q1 * (q2 * q2) * 2.0 +
coef_f0_q_sym16 * (q2 * q2) * q3 + coef_f0_q_sym17 * q2 * (q3 * q3) -
coef_f2_q_sym5 * (q0 * q0) * q1 * 2.0 - coef_f2_q_sym6 * (q0 * q0) * q2 -
coef_f2_q_sym7 * (q0 * q0) * q3 - coef_f2_q_sym12 * q0 * (q1 * q1) * 3.0 -
coef_f2_q_sym15 * q0 * (q2 * q2) - coef_f2_q_sym17 * q0 * (q3 * q3) +
coef_f0_q_sym5 * q0 * q1 * q2 * 2.0 + coef_f0_q_sym7 * q0 * q2 * q3 +
coef_f0_q_sym14 * q1 * q2 * q3 * 2.0 - coef_f2_q_sym13 * q0 * q1 * q2 * 2.0 -
coef_f2_q_sym14 * q0 * q1 * q3 * 2.0 - coef_f2_q_sym16 * q0 * q2 * q3;
symobj[1][2] = coef_f0_q_sym11 * q0 + coef_f0_q_sym18 * q1 + coef_f0_q_sym22 * q2 * 2.0 + coef_f0_q_sym24 * q3 -
coef_f2_q_sym22 * q0 + coef_f0_q_sym1 * (q0 * q0 * q0) + coef_f0_q_sym12 * (q1 * q1 * q1) +
coef_f0_q_sym19 * (q2 * q2 * q2) * 4.0 - coef_f2_q_sym3 * (q0 * q0 * q0) +
coef_f0_q_sym23 * (q3 * q3 * q3) + coef_f0_q_sym2 * (q0 * q0) * q1 +
coef_f0_q_sym3 * (q0 * q0) * q2 * 2.0 + coef_f0_q_sym5 * q0 * (q1 * q1) +
coef_f0_q_sym4 * (q0 * q0) * q3 + coef_f0_q_sym8 * q0 * (q2 * q2) * 3.0 +
coef_f0_q_sym10 * q0 * (q3 * q3) + coef_f0_q_sym13 * (q1 * q1) * q2 * 2.0 +
coef_f0_q_sym14 * (q1 * q1) * q3 + coef_f0_q_sym15 * q1 * (q2 * q2) * 3.0 +
coef_f0_q_sym17 * q1 * (q3 * q3) + coef_f0_q_sym20 * (q2 * q2) * q3 * 3.0 +
coef_f0_q_sym21 * q2 * (q3 * q3) * 2.0 - coef_f2_q_sym6 * (q0 * q0) * q1 -
coef_f2_q_sym8 * (q0 * q0) * q2 * 2.0 - coef_f2_q_sym9 * (q0 * q0) * q3 -
coef_f2_q_sym13 * q0 * (q1 * q1) - coef_f2_q_sym19 * q0 * (q2 * q2) * 3.0 -
coef_f2_q_sym21 * q0 * (q3 * q3) + coef_f0_q_sym6 * q0 * q1 * q2 * 2.0 +
coef_f0_q_sym7 * q0 * q1 * q3 + coef_f0_q_sym9 * q0 * q2 * q3 * 2.0 +
coef_f0_q_sym16 * q1 * q2 * q3 * 2.0 - coef_f2_q_sym15 * q0 * q1 * q2 * 2.0 -
coef_f2_q_sym16 * q0 * q1 * q3 - coef_f2_q_sym20 * q0 * q2 * q3 * 2.0;
symobj[1][3] = coef_f0_q_sym24 * q2 - coef_f2_q_sym24 * q0 + coef_f0_q_sym20 * (q2 * q2 * q2) -
coef_f2_q_sym4 * (q0 * q0 * q0) + coef_f0_q_sym4 * (q0 * q0) * q2 + coef_f0_q_sym9 * q0 * (q2 * q2) +
coef_f0_q_sym14 * (q1 * q1) * q2 + coef_f0_q_sym16 * q1 * (q2 * q2) +
coef_f0_q_sym21 * (q2 * q2) * q3 * 2.0 + coef_f0_q_sym23 * q2 * (q3 * q3) * 3.0 -
coef_f2_q_sym7 * (q0 * q0) * q1 - coef_f2_q_sym9 * (q0 * q0) * q2 -
coef_f2_q_sym10 * (q0 * q0) * q3 * 2.0 - coef_f2_q_sym14 * q0 * (q1 * q1) -
coef_f2_q_sym20 * q0 * (q2 * q2) - coef_f2_q_sym23 * q0 * (q3 * q3) * 3.0 +
coef_f0_q_sym7 * q0 * q1 * q2 + coef_f0_q_sym10 * q0 * q2 * q3 * 2.0 +
coef_f0_q_sym17 * q1 * q2 * q3 * 2.0 - coef_f2_q_sym16 * q0 * q1 * q2 -
coef_f2_q_sym17 * q0 * q1 * q3 * 2.0 - coef_f2_q_sym21 * q0 * q2 * q3 * 2.0;
symobj[2][0] = coef_f0_q_sym11 * q3 - coef_f3_q_sym11 * q0 * 2.0 - coef_f3_q_sym18 * q1 - coef_f3_q_sym22 * q2 -
coef_f3_q_sym24 * q3 + coef_f0_q_sym10 * (q3 * q3 * q3) - coef_f3_q_sym1 * (q0 * q0 * q0) * 4.0 -
coef_f3_q_sym12 * (q1 * q1 * q1) - coef_f3_q_sym19 * (q2 * q2 * q2) -
coef_f3_q_sym23 * (q3 * q3 * q3) + coef_f0_q_sym1 * (q0 * q0) * q3 * 3.0 +
coef_f0_q_sym4 * q0 * (q3 * q3) * 2.0 + coef_f0_q_sym5 * (q1 * q1) * q3 +
coef_f0_q_sym7 * q1 * (q3 * q3) + coef_f0_q_sym8 * (q2 * q2) * q3 + coef_f0_q_sym9 * q2 * (q3 * q3) -
coef_f3_q_sym2 * (q0 * q0) * q1 * 3.0 - coef_f3_q_sym3 * (q0 * q0) * q2 * 3.0 -
coef_f3_q_sym5 * q0 * (q1 * q1) * 2.0 - coef_f3_q_sym4 * (q0 * q0) * q3 * 3.0 -
coef_f3_q_sym8 * q0 * (q2 * q2) * 2.0 - coef_f3_q_sym10 * q0 * (q3 * q3) * 2.0 -
coef_f3_q_sym13 * (q1 * q1) * q2 - coef_f3_q_sym14 * (q1 * q1) * q3 -
coef_f3_q_sym15 * q1 * (q2 * q2) - coef_f3_q_sym17 * q1 * (q3 * q3) -
coef_f3_q_sym20 * (q2 * q2) * q3 - coef_f3_q_sym21 * q2 * (q3 * q3) +
coef_f0_q_sym2 * q0 * q1 * q3 * 2.0 + coef_f0_q_sym3 * q0 * q2 * q3 * 2.0 +
coef_f0_q_sym6 * q1 * q2 * q3 - coef_f3_q_sym6 * q0 * q1 * q2 * 2.0 -
coef_f3_q_sym7 * q0 * q1 * q3 * 2.0 - coef_f3_q_sym9 * q0 * q2 * q3 * 2.0 -
coef_f3_q_sym16 * q1 * q2 * q3;
symobj[2][1] = coef_f0_q_sym18 * q3 - coef_f3_q_sym18 * q0 + coef_f0_q_sym17 * (q3 * q3 * q3) -
coef_f3_q_sym2 * (q0 * q0 * q0) + coef_f0_q_sym2 * (q0 * q0) * q3 + coef_f0_q_sym7 * q0 * (q3 * q3) +
coef_f0_q_sym12 * (q1 * q1) * q3 * 3.0 + coef_f0_q_sym14 * q1 * (q3 * q3) * 2.0 +
coef_f0_q_sym15 * (q2 * q2) * q3 + coef_f0_q_sym16 * q2 * (q3 * q3) -
coef_f3_q_sym5 * (q0 * q0) * q1 * 2.0 - coef_f3_q_sym6 * (q0 * q0) * q2 -
coef_f3_q_sym7 * (q0 * q0) * q3 - coef_f3_q_sym12 * q0 * (q1 * q1) * 3.0 -
coef_f3_q_sym15 * q0 * (q2 * q2) - coef_f3_q_sym17 * q0 * (q3 * q3) +
coef_f0_q_sym5 * q0 * q1 * q3 * 2.0 + coef_f0_q_sym6 * q0 * q2 * q3 +
coef_f0_q_sym13 * q1 * q2 * q3 * 2.0 - coef_f3_q_sym13 * q0 * q1 * q2 * 2.0 -
coef_f3_q_sym14 * q0 * q1 * q3 * 2.0 - coef_f3_q_sym16 * q0 * q2 * q3;
symobj[2][2] = coef_f0_q_sym22 * q3 - coef_f3_q_sym22 * q0 + coef_f0_q_sym21 * (q3 * q3 * q3) -
coef_f3_q_sym3 * (q0 * q0 * q0) + coef_f0_q_sym3 * (q0 * q0) * q3 + coef_f0_q_sym9 * q0 * (q3 * q3) +
coef_f0_q_sym13 * (q1 * q1) * q3 + coef_f0_q_sym16 * q1 * (q3 * q3) +
coef_f0_q_sym19 * (q2 * q2) * q3 * 3.0 + coef_f0_q_sym20 * q2 * (q3 * q3) * 2.0 -
coef_f3_q_sym6 * (q0 * q0) * q1 - coef_f3_q_sym8 * (q0 * q0) * q2 * 2.0 -
coef_f3_q_sym9 * (q0 * q0) * q3 - coef_f3_q_sym13 * q0 * (q1 * q1) -
coef_f3_q_sym19 * q0 * (q2 * q2) * 3.0 - coef_f3_q_sym21 * q0 * (q3 * q3) +
coef_f0_q_sym6 * q0 * q1 * q3 + coef_f0_q_sym8 * q0 * q2 * q3 * 2.0 +
coef_f0_q_sym15 * q1 * q2 * q3 * 2.0 - coef_f3_q_sym15 * q0 * q1 * q2 * 2.0 -
coef_f3_q_sym16 * q0 * q1 * q3 - coef_f3_q_sym20 * q0 * q2 * q3 * 2.0;
symobj[2][3] = coef_f0_q_sym11 * q0 + coef_f0_q_sym18 * q1 + coef_f0_q_sym22 * q2 + coef_f0_q_sym24 * q3 * 2.0 -
coef_f3_q_sym24 * q0 + coef_f0_q_sym1 * (q0 * q0 * q0) + coef_f0_q_sym12 * (q1 * q1 * q1) +
coef_f0_q_sym19 * (q2 * q2 * q2) + coef_f0_q_sym23 * (q3 * q3 * q3) * 4.0 -
coef_f3_q_sym4 * (q0 * q0 * q0) + coef_f0_q_sym2 * (q0 * q0) * q1 + coef_f0_q_sym3 * (q0 * q0) * q2 +
coef_f0_q_sym5 * q0 * (q1 * q1) + coef_f0_q_sym4 * (q0 * q0) * q3 * 2.0 +
coef_f0_q_sym8 * q0 * (q2 * q2) + coef_f0_q_sym10 * q0 * (q3 * q3) * 3.0 +
coef_f0_q_sym13 * (q1 * q1) * q2 + coef_f0_q_sym14 * (q1 * q1) * q3 * 2.0 +
coef_f0_q_sym15 * q1 * (q2 * q2) + coef_f0_q_sym17 * q1 * (q3 * q3) * 3.0 +
coef_f0_q_sym20 * (q2 * q2) * q3 * 2.0 + coef_f0_q_sym21 * q2 * (q3 * q3) * 3.0 -
coef_f3_q_sym7 * (q0 * q0) * q1 - coef_f3_q_sym9 * (q0 * q0) * q2 -
coef_f3_q_sym10 * (q0 * q0) * q3 * 2.0 - coef_f3_q_sym14 * q0 * (q1 * q1) -
coef_f3_q_sym20 * q0 * (q2 * q2) - coef_f3_q_sym23 * q0 * (q3 * q3) * 3.0 +
coef_f0_q_sym6 * q0 * q1 * q2 + coef_f0_q_sym7 * q0 * q1 * q3 * 2.0 +
coef_f0_q_sym9 * q0 * q2 * q3 * 2.0 + coef_f0_q_sym16 * q1 * q2 * q3 * 2.0 -
coef_f3_q_sym16 * q0 * q1 * q2 - coef_f3_q_sym17 * q0 * q1 * q3 * 2.0 -
coef_f3_q_sym21 * q0 * q2 * q3 * 2.0;
symobj[3][0] = q0 * 2.0;
symobj[3][1] = q1 * 2.0;
symobj[3][2] = q2 * 2.0;
symobj[3][3] = q3 * 2.0;
for (int i = 0; i < 4; ++i)
for (int j = 0; j < 4; ++j)
Jacob(i, j) = symobj[i][j];
}
void v_func_pTop(Eigen::Matrix<double, 28, 1> &v,
const Eigen::Vector4d &q) {
v(0, 0) = (q(0) * q(0) * q(0)) * q(1);
v(1, 0) = (q(0) * q(0) * q(0)) * q(2);
v(2, 0) = (q(0) * q(0) * q(0)) * q(3);
v(3, 0) = q(0) * (q(1) * q(1) * q(1));
v(4, 0) = q(0) * (q(1) * q(1)) * q(2);
v(5, 0) = q(0) * (q(1) * q(1)) * q(3);
v(6, 0) = q(0) * q(1) * (q(2) * q(2));
v(7, 0) = q(0) * q(1) * q(2) * q(3);
v(8, 0) = q(0) * q(1) * (q(3) * q(3));
v(9, 0) = q(0) * (q(2) * q(2) * q(2));
v(10, 0) = q(0) * (q(2) * q(2)) * q(3);
v(11, 0) = q(0) * q(2) * (q(3) * q(3));
v(12, 0) = q(0) * (q(3) * q(3) * q(3));
v(13, 0) = q(1) * q(1) * q(1) * q(1);
v(14, 0) = (q(1) * q(1) * q(1)) * q(2);
v(15, 0) = (q(1) * q(1) * q(1)) * q(3);
v(16, 0) = (q(1) * q(1)) * (q(2) * q(2));
v(17, 0) = (q(1) * q(1)) * q(2) * q(3);
v(18, 0) = (q(1) * q(1)) * (q(3) * q(3));
v(19, 0) = q(1) * (q(2) * q(2) * q(2));
v(20, 0) = q(1) * (q(2) * q(2)) * q(3);
v(21, 0) = q(1) * q(2) * (q(3) * q(3));
v(22, 0) = q(1) * (q(3) * q(3) * q(3));
v(23, 0) = q(2) * q(2) * q(2) * q(2);
v(24, 0) = (q(2) * q(2) * q(2)) * q(3);
v(25, 0) = (q(2) * q(2)) * (q(3) * q(3));
v(26, 0) = q(2) * (q(3) * q(3) * q(3));
v(27, 0) = q(3) * q(3) * q(3) * q(3);
}
void y_func_pTop(Eigen::Matrix<double, 9, 1> &y,
const Eigen::Vector4d &q) {
y(0, 0) = q(0) * q(1);
y(1, 0) = q(0) * q(2);
y(2, 0) = q(0) * q(3);
y(3, 0) = q(1) * q(1);
y(4, 0) = q(1) * q(2);
y(5, 0) = q(1) * q(3);
y(6, 0) = q(2) * q(2);
y(7, 0) = q(2) * q(3);
y(8, 0) = q(3) * q(3);
}
void jv_func_pTop(Eigen::MatrixXd &jv,
const Eigen::Vector4d &q) {
jv(0, 0) = (q(0) * q(0)) * q(1) * 3.0;
jv(0, 1) = q(0) * q(0) * q(0);
jv(1, 0) = (q(0) * q(0)) * q(2) * 3.0;
jv(1, 2) = q(0) * q(0) * q(0);
jv(2, 0) = (q(0) * q(0)) * q(3) * 3.0;
jv(2, 3) = q(0) * q(0) * q(0);
jv(3, 0) = q(1) * q(1) * q(1);
jv(3, 1) = q(0) * (q(1) * q(1)) * 3.0;
jv(4, 0) = (q(1) * q(1)) * q(2);
jv(4, 1) = q(0) * q(1) * q(2) * 2.0;
jv(4, 2) = q(0) * (q(1) * q(1));
jv(5, 0) = (q(1) * q(1)) * q(3);
jv(5, 1) = q(0) * q(1) * q(3) * 2.0;
jv(5, 3) = q(0) * (q(1) * q(1));
jv(6, 0) = q(1) * (q(2) * q(2));
jv(6, 1) = q(0) * (q(2) * q(2));
jv(6, 2) = q(0) * q(1) * q(2) * 2.0;
jv(7, 0) = q(1) * q(2) * q(3);
jv(7, 1) = q(0) * q(2) * q(3);
jv(7, 2) = q(0) * q(1) * q(3);
jv(7, 3) = q(0) * q(1) * q(2);
jv(8, 0) = q(1) * (q(3) * q(3));
jv(8, 1) = q(0) * (q(3) * q(3));
jv(8, 3) = q(0) * q(1) * q(3) * 2.0;
jv(9, 0) = q(2) * q(2) * q(2);
jv(9, 2) = q(0) * (q(2) * q(2)) * 3.0;
jv(10, 0) = (q(2) * q(2)) * q(3);
jv(10, 2) = q(0) * q(2) * q(3) * 2.0;
jv(10, 3) = q(0) * (q(2) * q(2));
jv(11, 0) = q(2) * (q(3) * q(3));
jv(11, 2) = q(0) * (q(3) * q(3));
jv(11, 3) = q(0) * q(2) * q(3) * 2.0;
jv(12, 0) = q(3) * q(3) * q(3);
jv(12, 3) = q(0) * (q(3) * q(3)) * 3.0;
jv(13, 1) = (q(1) * q(1) * q(1)) * 4.0;
jv(14, 1) = (q(1) * q(1)) * q(2) * 3.0;
jv(14, 2) = q(1) * q(1) * q(1);
jv(15, 1) = (q(1) * q(1)) * q(3) * 3.0;
jv(15, 3) = q(1) * q(1) * q(1);
jv(16, 1) = q(1) * (q(2) * q(2)) * 2.0;
jv(16, 2) = (q(1) * q(1)) * q(2) * 2.0;
jv(17, 1) = q(1) * q(2) * q(3) * 2.0;
jv(17, 2) = (q(1) * q(1)) * q(3);
jv(17, 3) = (q(1) * q(1)) * q(2);
jv(18, 1) = q(1) * (q(3) * q(3)) * 2.0;
jv(18, 3) = (q(1) * q(1)) * q(3) * 2.0;
jv(19, 1) = q(2) * q(2) * q(2);
jv(19, 2) = q(1) * (q(2) * q(2)) * 3.0;
jv(20, 1) = (q(2) * q(2)) * q(3);
jv(20, 2) = q(1) * q(2) * q(3) * 2.0;
jv(20, 3) = q(1) * (q(2) * q(2));
jv(21, 1) = q(2) * (q(3) * q(3));
jv(21, 2) = q(1) * (q(3) * q(3));
jv(21, 3) = q(1) * q(2) * q(3) * 2.0;
jv(22, 1) = q(3) * q(3) * q(3);
jv(22, 3) = q(1) * (q(3) * q(3)) * 3.0;
jv(23, 2) = (q(2) * q(2) * q(2)) * 4.0;
jv(24, 2) = (q(2) * q(2)) * q(3) * 3.0;
jv(24, 3) = q(2) * q(2) * q(2);
jv(25, 2) = q(2) * (q(3) * q(3)) * 2.0;
jv(25, 3) = (q(2) * q(2)) * q(3) * 2.0;
jv(26, 2) = q(3) * q(3) * q(3);
jv(26, 3) = q(2) * (q(3) * q(3)) * 3.0;
jv(27, 3) = (q(3) * q(3) * q(3)) * 4.0;
}
void jy_func_pTop(Eigen::MatrixXd &jy,
const Eigen::Vector4d &q) {
jy(0, 0) = q(1);
jy(0, 1) = q(0);
jy(1, 0) = q(2);
jy(1, 2) = q(0);
jy(2, 0) = q(3);
jy(2, 3) = q(0);
jy(3, 1) = q(1) * 2.0;
jy(4, 1) = q(2);
jy(4, 2) = q(1);
jy(5, 1) = q(3);
jy(5, 3) = q(1);
jy(6, 2) = q(2) * 2.0;
jy(7, 2) = q(3);
jy(7, 3) = q(2);
jy(8, 3) = q(3) * 2.0;
}