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QPEP_lm_single.cpp
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QPEP_lm_single.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
//
//
// QPEP_lm_single.cpp: Refines QPEPs by Levenberg-Marquardt algorithm (LMA)
#include "QPEP_lm_single.h"
#include "utils.h"
#include "linearLeastSquares.h"
#include "rt_nonfinite.h"
#include "xnrm2.h"
#include "xzlarf.h"
#include "xzlarfg.h"
#include <cmath>
typedef bool boolean_T;
double rtInf = std::numeric_limits<double>::max();
double rtNaN = NAN;
static int div_nde_s32_floor(int numerator, int denominator)
{
int b_numerator;
if (((numerator < 0) != (denominator < 0)) &&
(numerator % denominator != 0)) {
b_numerator = -1;
} else {
b_numerator = 0;
}
return numerator / denominator + b_numerator;
}
void xzlarf(int m, int n, int iv0, double tau, double C[45], int ic0,
double work[5])
{
int i;
int ia;
int lastc;
int lastv;
if (tau != 0.0) {
boolean_T exitg2;
lastv = m;
i = iv0 + m;
while ((lastv > 0) && (C[i - 2] == 0.0)) {
lastv--;
i--;
}
lastc = n - 1;
exitg2 = false;
while ((!exitg2) && (lastc + 1 > 0)) {
int exitg1;
i = ic0 + lastc * 9;
ia = i;
do {
exitg1 = 0;
if (ia <= (i + lastv) - 1) {
if (C[ia - 1] != 0.0) {
exitg1 = 1;
} else {
ia++;
}
} else {
lastc--;
exitg1 = 2;
}
} while (exitg1 == 0);
if (exitg1 == 1) {
exitg2 = true;
}
}
} else {
lastv = 0;
lastc = -1;
}
if (lastv > 0) {
double c;
int b_i;
int iac;
if (lastc + 1 != 0) {
if (0 <= lastc) {
std::memset(&work[0], 0, (lastc + 1) * sizeof(double));
}
b_i = ic0 + 9 * lastc;
for (iac = ic0; iac <= b_i; iac += 9) {
c = 0.0;
i = (iac + lastv) - 1;
for (ia = iac; ia <= i; ia++) {
c += C[ia - 1] * C[((iv0 + ia) - iac) - 1];
}
i = div_nde_s32_floor(iac - ic0, 9);
work[i] += c;
}
}
if (!(-tau == 0.0)) {
i = ic0;
for (iac = 0; iac <= lastc; iac++) {
if (work[iac] != 0.0) {
c = work[iac] * -tau;
b_i = lastv + i;
for (ia = i; ia < b_i; ia++) {
C[ia - 1] += C[((iv0 + ia) - i) - 1] * c;
}
}
i += 9;
}
}
}
}
double xnrm2(int n, const double x[45], int ix0)
{
double scale;
double y;
int kend;
y = 0.0;
scale = 3.3121686421112381E-170;
kend = (ix0 + n) - 1;
for (int k{ix0}; k <= kend; k++) {
double absxk;
absxk = std::abs(x[k - 1]);
if (absxk > scale) {
double t;
t = scale / absxk;
y = y * t * t + 1.0;
scale = absxk;
} else {
double t;
t = absxk / scale;
y += t * t;
}
}
return scale * std::sqrt(y);
}
static double rt_hypotd_snf(double u0, double u1)
{
double a;
double y;
a = std::abs(u0);
y = std::abs(u1);
if (a < y) {
a /= y;
y *= std::sqrt(a * a + 1.0);
} else if (a > y) {
y /= a;
y = a * std::sqrt(y * y + 1.0);
} else if (!std::isnan(y)) {
y = a * 1.4142135623730951;
}
return y;
}
double xzlarfg(int n, double *alpha1, double x[45], int ix0)
{
double tau;
double xnorm;
tau = 0.0;
xnorm = xnrm2(n - 1, x, ix0);
if (xnorm != 0.0) {
double beta1;
beta1 = rt_hypotd_snf(*alpha1, xnorm);
if (*alpha1 >= 0.0) {
beta1 = -beta1;
}
if (std::abs(beta1) < 1.0020841800044864E-292) {
int i;
int k;
int knt;
knt = -1;
i = (ix0 + n) - 2;
do {
knt++;
for (k = ix0; k <= i; k++) {
x[k - 1] *= 9.9792015476736E+291;
}
beta1 *= 9.9792015476736E+291;
*alpha1 *= 9.9792015476736E+291;
} while (!(std::abs(beta1) >= 1.0020841800044864E-292));
beta1 = rt_hypotd_snf(*alpha1, xnrm2(n - 1, x, ix0));
if (*alpha1 >= 0.0) {
beta1 = -beta1;
}
tau = (beta1 - *alpha1) / beta1;
xnorm = 1.0 / (*alpha1 - beta1);
for (k = ix0; k <= i; k++) {
x[k - 1] *= xnorm;
}
for (k = 0; k <= knt; k++) {
beta1 *= 1.0020841800044864E-292;
}
*alpha1 = beta1;
} else {
int i;
tau = (beta1 - *alpha1) / beta1;
xnorm = 1.0 / (*alpha1 - beta1);
i = (ix0 + n) - 2;
for (int k{ix0}; k <= i; k++) {
x[k - 1] *= xnorm;
}
*alpha1 = beta1;
}
}
return tau;
}
namespace coder {
namespace optim {
namespace coder {
namespace levenbergMarquardt {
void linearLeastSquares(double lhs[45], double rhs[9], double dx[5])
{
double jpvt[5];
double tau[5];
double vn1[5];
double vn2[5];
double work[5];
double d;
double temp;
int b_i;
int i;
int ii;
int ix;
int iy;
int j;
int k;
int nfxd;
int temp_tmp;
for (i = 0; i < 5; i++) {
jpvt[i] = 0.0;
}
nfxd = -1;
for (j = 0; j < 5; j++) {
if (jpvt[j] != 0.0) {
nfxd++;
if (j + 1 != nfxd + 1) {
ix = j * 9;
iy = nfxd * 9;
for (k = 0; k < 9; k++) {
temp_tmp = ix + k;
temp = lhs[temp_tmp];
b_i = iy + k;
lhs[temp_tmp] = lhs[b_i];
lhs[b_i] = temp;
}
jpvt[j] = jpvt[nfxd];
jpvt[nfxd] = static_cast<double>(j) + 1.0;
} else {
jpvt[j] = static_cast<double>(j) + 1.0;
}
} else {
jpvt[j] = static_cast<double>(j) + 1.0;
}
tau[j] = 0.0;
work[j] = 0.0;
}
for (i = 0; i <= nfxd; i++) {
ii = i * 9 + i;
temp = lhs[ii];
d = xzlarfg(9 - i, &temp, lhs, ii + 2);
tau[i] = d;
lhs[ii] = temp;
if (i + 1 < 5) {
temp = lhs[ii];
lhs[ii] = 1.0;
xzlarf(9 - i, 4 - i, ii + 1, d, lhs, ii + 10, work);
lhs[ii] = temp;
}
}
if (nfxd + 1 < 5) {
for (i = 0; i < 5; i++) {
work[i] = 0.0;
vn1[i] = 0.0;
vn2[i] = 0.0;
}
b_i = nfxd + 2;
for (j = b_i; j < 6; j++) {
d = xnrm2(8 - nfxd, lhs, (nfxd + (j - 1) * 9) + 2);
vn1[j - 1] = d;
vn2[j - 1] = d;
}
for (i = b_i; i < 6; i++) {
double s;
int ip1;
ip1 = i + 1;
j = (i - 1) * 9;
ii = (j + i) - 1;
iy = 6 - i;
nfxd = -1;
if (6 - i > 1) {
temp = std::abs(vn1[i - 1]);
for (k = 2; k <= iy; k++) {
s = std::abs(vn1[(i + k) - 2]);
if (s > temp) {
nfxd = k - 2;
temp = s;
}
}
}
iy = i + nfxd;
if (iy + 1 != i) {
ix = iy * 9;
for (k = 0; k < 9; k++) {
temp_tmp = ix + k;
temp = lhs[temp_tmp];
nfxd = j + k;
lhs[temp_tmp] = lhs[nfxd];
lhs[nfxd] = temp;
}
temp = jpvt[iy];
jpvt[iy] = jpvt[i - 1];
jpvt[i - 1] = temp;
vn1[iy] = vn1[i - 1];
vn2[iy] = vn2[i - 1];
}
temp = lhs[ii];
d = xzlarfg(10 - i, &temp, lhs, ii + 2);
tau[i - 1] = d;
lhs[ii] = temp;
if (i < 5) {
temp = lhs[ii];
lhs[ii] = 1.0;
xzlarf(10 - i, 5 - i, ii + 1, d, lhs, ii + 10,
work);
lhs[ii] = temp;
}
for (j = ip1; j < 6; j++) {
iy = i + (j - 1) * 9;
d = vn1[j - 1];
if (d != 0.0) {
temp = std::abs(lhs[iy - 1]) / d;
temp = 1.0 - temp * temp;
if (temp < 0.0) {
temp = 0.0;
}
s = d / vn2[j - 1];
s = temp * (s * s);
if (s <= 1.4901161193847656E-8) {
d = xnrm2(9 - i, lhs, iy + 1);
vn1[j - 1] = d;
vn2[j - 1] = d;
} else {
vn1[j - 1] = d * std::sqrt(temp);
}
}
}
}
}
for (j = 0; j < 5; j++) {
if (tau[j] != 0.0) {
temp = rhs[j];
b_i = j + 2;
for (i = b_i; i < 10; i++) {
temp += lhs[(i + 9 * j) - 1] * rhs[i - 1];
}
temp *= tau[j];
if (temp != 0.0) {
rhs[j] -= temp;
for (i = b_i; i < 10; i++) {
rhs[i - 1] -= lhs[(i + 9 * j) - 1] * temp;
}
}
}
}
for (i = 0; i < 5; i++) {
dx[i] = rhs[i];
}
for (j = 4; j >= 0; j--) {
iy = j + j * 9;
dx[j] /= lhs[iy];
for (i = 0; i < j; i++) {
ix = (j - i) - 1;
dx[ix] -= dx[j] * lhs[(iy - i) - 1];
}
}
for (b_i = 0; b_i < 5; b_i++) {
tau[b_i] = dx[b_i];
}
for (b_i = 0; b_i < 5; b_i++) {
dx[static_cast<int>(jpvt[b_i]) - 1] = tau[b_i];
}
}
} // namespace levenbergMarquardt
} // namespace coder
} // namespace optim
} // namespace coder
// Function Declarations
static void anon(const double W[256], const double Q[16], const double x[5],
double varargout_1[4], double varargout_2[20]);
// Function Definitions
//
// Arguments : const double W[256]
// const double Q[16]
// const double x[5]
// double varargout_1[4]
// double varargout_2[20]
// Return Type : void
//
static void anon(const double W[256], const double Q[16], const double x[5],
double varargout_1[4], double varargout_2[20])
{
static const signed char b[16]{1, 0, 0, 0, 0, 1, 0, 0,
0, 0, 1, 0, 0, 0, 0, 1};
double b_b[64];
double K[16];
double varargout_2_tmp;
int i1;
int kidx;
kidx = -1;
for (i1 = 0; i1 < 4; i1++) {
K[kidx + 1] = x[i1] * x[0];
K[kidx + 2] = x[i1] * x[1];
K[kidx + 3] = x[i1] * x[2];
K[kidx + 4] = x[i1] * x[3];
kidx += 4;
}
kidx = -1;
for (i1 = 0; i1 < 4; i1++) {
for (int i2{0}; i2 < 16; i2++) {
b_b[(kidx + i2) + 1] = x[i1] * K[i2];
}
kidx += 16;
}
for (kidx = 0; kidx < 16; kidx++) {
K[kidx] = Q[kidx] - x[4] * static_cast<double>(b[kidx]);
}
for (kidx = 0; kidx < 4; kidx++) {
varargout_2_tmp = 0.0;
for (i1 = 0; i1 < 64; i1++) {
varargout_2_tmp += W[kidx + (i1 << 2)] * b_b[i1];
}
varargout_1[kidx] =
varargout_2_tmp -
(((K[kidx] * x[0] + K[kidx + 4] * x[1]) + K[kidx + 8] * x[2]) +
K[kidx + 12] * x[3]);
}
double ab_varargout_2_tmp;
double ac_varargout_2_tmp;
double ad_varargout_2_tmp;
double b_varargout_2_tmp;
double bb_varargout_2_tmp;
double bc_varargout_2_tmp;
double bd_varargout_2_tmp;
double c_varargout_2_tmp;
double cb_varargout_2_tmp;
double cc_varargout_2_tmp;
double cd_varargout_2_tmp;
double d_varargout_2_tmp;
double db_varargout_2_tmp;
double dc_varargout_2_tmp;
double dd_varargout_2_tmp;
double e_varargout_2_tmp;
double eb_varargout_2_tmp;
double ec_varargout_2_tmp;
double ed_varargout_2_tmp;
double f_varargout_2_tmp;
double fb_varargout_2_tmp;
double fc_varargout_2_tmp;
double fd_varargout_2_tmp;
double g_varargout_2_tmp;
double gb_varargout_2_tmp;
double gc_varargout_2_tmp;
double gd_varargout_2_tmp;
double h_varargout_2_tmp;
double hb_varargout_2_tmp;
double hc_varargout_2_tmp;
double i_varargout_2_tmp;
double ib_varargout_2_tmp;
double ic_varargout_2_tmp;
double j_varargout_2_tmp;
double jb_varargout_2_tmp;
double jc_varargout_2_tmp;
double k_varargout_2_tmp;
double kb_varargout_2_tmp;
double kc_varargout_2_tmp;
double l_varargout_2_tmp;
double lb_varargout_2_tmp;
double lc_varargout_2_tmp;
double m_varargout_2_tmp;
double mb_varargout_2_tmp;
double mc_varargout_2_tmp;
double n_varargout_2_tmp;
double nb_varargout_2_tmp;
double nc_varargout_2_tmp;
double o_varargout_2_tmp;
double ob_varargout_2_tmp;
double oc_varargout_2_tmp;
double p_varargout_2_tmp;
double pb_varargout_2_tmp;
double pc_varargout_2_tmp;
double q_varargout_2_tmp;
double qb_varargout_2_tmp;
double qc_varargout_2_tmp;
double r_varargout_2_tmp;
double rb_varargout_2_tmp;
double rc_varargout_2_tmp;
double s_varargout_2_tmp;
double sb_varargout_2_tmp;
double sc_varargout_2_tmp;
double t_varargout_2_tmp;
double tb_varargout_2_tmp;
double tc_varargout_2_tmp;
double u_varargout_2_tmp;
double ub_varargout_2_tmp;
double uc_varargout_2_tmp;
double v_varargout_2_tmp;
double vb_varargout_2_tmp;
double vc_varargout_2_tmp;
double w_varargout_2_tmp;
double wb_varargout_2_tmp;
double wc_varargout_2_tmp;
double x_varargout_2_tmp;
double xb_varargout_2_tmp;
double xc_varargout_2_tmp;
double y_varargout_2_tmp;
double yb_varargout_2_tmp;
double yc_varargout_2_tmp;
varargout_2_tmp = x[1] * x[1];
b_varargout_2_tmp = x[2] * x[2];
c_varargout_2_tmp = x[3] * x[3];
d_varargout_2_tmp = x[0] * x[0];
varargout_2[0] =
(((((((((((((((((((((((((((((((((((((-Q[0] + x[4]) +
W[0] * d_varargout_2_tmp * 3.0) +
W[20] * varargout_2_tmp) +
W[40] * b_varargout_2_tmp) +
W[60] * c_varargout_2_tmp) +
W[68] * varargout_2_tmp) +
W[80] * varargout_2_tmp) +
W[136] * b_varargout_2_tmp) +
W[160] * b_varargout_2_tmp) +
W[204] * c_varargout_2_tmp) +
W[240] * c_varargout_2_tmp) +
x[0] * W[4] * x[1] * 2.0) +
x[0] * W[8] * x[2] * 2.0) +
x[0] * W[16] * x[1] * 2.0) +
x[0] * W[12] * x[3] * 2.0) +
x[1] * W[24] * x[2]) +
x[0] * W[32] * x[2] * 2.0) +
x[1] * W[28] * x[3]) +
x[1] * W[36] * x[2]) +
x[0] * W[48] * x[3] * 2.0) +
x[2] * W[44] * x[3]) +
x[1] * W[52] * x[3]) +
x[0] * W[64] * x[1] * 2.0) +
x[2] * W[56] * x[3]) +
x[1] * W[72] * x[2]) +
x[1] * W[76] * x[3]) +
x[1] * W[96] * x[2]) +
x[1] * W[112] * x[3]) +
x[0] * W[128] * x[2] * 2.0) +
x[1] * W[132] * x[2]) +
x[1] * W[144] * x[2]) +
x[2] * W[140] * x[3]) +
x[2] * W[176] * x[3]) +
x[0] * W[192] * x[3] * 2.0) +
x[1] * W[196] * x[3]) +
x[2] * W[200] * x[3]) +
x[1] * W[208] * x[3]) +
x[2] * W[224] * x[3];
varargout_2[1] =
((((((((((((((((((((((((((((((((((((-Q[1] +
W[1] * d_varargout_2_tmp * 3.0) +
W[21] * varargout_2_tmp) +
W[41] * b_varargout_2_tmp) +
W[61] * c_varargout_2_tmp) +
W[69] * varargout_2_tmp) +
W[81] * varargout_2_tmp) +
W[137] * b_varargout_2_tmp) +
W[161] * b_varargout_2_tmp) +
W[205] * c_varargout_2_tmp) +
W[241] * c_varargout_2_tmp) +
x[0] * W[5] * x[1] * 2.0) +
x[0] * W[9] * x[2] * 2.0) +
x[0] * W[17] * x[1] * 2.0) +
x[0] * W[13] * x[3] * 2.0) +
x[1] * W[25] * x[2]) +
x[0] * W[33] * x[2] * 2.0) +
x[1] * W[29] * x[3]) +
x[1] * W[37] * x[2]) +
x[0] * W[49] * x[3] * 2.0) +
x[2] * W[45] * x[3]) +
x[1] * W[53] * x[3]) +
x[0] * W[65] * x[1] * 2.0) +
x[2] * W[57] * x[3]) +
x[1] * W[73] * x[2]) +
x[1] * W[77] * x[3]) +
x[1] * W[97] * x[2]) +
x[1] * W[113] * x[3]) +
x[0] * W[129] * x[2] * 2.0) +
x[1] * W[133] * x[2]) +
x[1] * W[145] * x[2]) +
x[2] * W[141] * x[3]) +
x[2] * W[177] * x[3]) +
x[0] * W[193] * x[3] * 2.0) +
x[1] * W[197] * x[3]) +
x[2] * W[201] * x[3]) +
x[1] * W[209] * x[3]) +
x[2] * W[225] * x[3];
varargout_2[2] =
((((((((((((((((((((((((((((((((((((-Q[2] +
W[2] * d_varargout_2_tmp * 3.0) +
W[22] * varargout_2_tmp) +
W[42] * b_varargout_2_tmp) +
W[62] * c_varargout_2_tmp) +
W[70] * varargout_2_tmp) +
W[82] * varargout_2_tmp) +
W[138] * b_varargout_2_tmp) +
W[162] * b_varargout_2_tmp) +
W[206] * c_varargout_2_tmp) +
W[242] * c_varargout_2_tmp) +
x[0] * W[6] * x[1] * 2.0) +
x[0] * W[10] * x[2] * 2.0) +
x[0] * W[18] * x[1] * 2.0) +
x[0] * W[14] * x[3] * 2.0) +
x[1] * W[26] * x[2]) +
x[0] * W[34] * x[2] * 2.0) +
x[1] * W[30] * x[3]) +
x[1] * W[38] * x[2]) +
x[0] * W[50] * x[3] * 2.0) +
x[2] * W[46] * x[3]) +
x[1] * W[54] * x[3]) +
x[0] * W[66] * x[1] * 2.0) +
x[2] * W[58] * x[3]) +
x[1] * W[74] * x[2]) +
x[1] * W[78] * x[3]) +
x[1] * W[98] * x[2]) +
x[1] * W[114] * x[3]) +
x[0] * W[130] * x[2] * 2.0) +
x[1] * W[134] * x[2]) +
x[1] * W[146] * x[2]) +
x[2] * W[142] * x[3]) +
x[2] * W[178] * x[3]) +
x[0] * W[194] * x[3] * 2.0) +
x[1] * W[198] * x[3]) +
x[2] * W[202] * x[3]) +
x[1] * W[210] * x[3]) +
x[2] * W[226] * x[3];
varargout_2[3] =
((((((((((((((((((((((((((((((((((((-Q[3] +
W[3] * d_varargout_2_tmp * 3.0) +
W[23] * varargout_2_tmp) +
W[43] * b_varargout_2_tmp) +
W[63] * c_varargout_2_tmp) +
W[71] * varargout_2_tmp) +
W[83] * varargout_2_tmp) +
W[139] * b_varargout_2_tmp) +
W[163] * b_varargout_2_tmp) +
W[207] * c_varargout_2_tmp) +
W[243] * c_varargout_2_tmp) +
x[0] * W[7] * x[1] * 2.0) +
x[0] * W[11] * x[2] * 2.0) +
x[0] * W[19] * x[1] * 2.0) +
x[0] * W[15] * x[3] * 2.0) +
x[1] * W[27] * x[2]) +
x[0] * W[35] * x[2] * 2.0) +
x[1] * W[31] * x[3]) +
x[1] * W[39] * x[2]) +
x[0] * W[51] * x[3] * 2.0) +
x[2] * W[47] * x[3]) +
x[1] * W[55] * x[3]) +
x[0] * W[67] * x[1] * 2.0) +
x[2] * W[59] * x[3]) +
x[1] * W[75] * x[2]) +
x[1] * W[79] * x[3]) +
x[1] * W[99] * x[2]) +
x[1] * W[115] * x[3]) +
x[0] * W[131] * x[2] * 2.0) +
x[1] * W[135] * x[2]) +
x[1] * W[147] * x[2]) +
x[2] * W[143] * x[3]) +
x[2] * W[179] * x[3]) +
x[0] * W[195] * x[3] * 2.0) +
x[1] * W[199] * x[3]) +
x[2] * W[203] * x[3]) +
x[1] * W[211] * x[3]) +
x[2] * W[227] * x[3];
e_varargout_2_tmp = x[0] * W[24];
f_varargout_2_tmp = x[0] * W[36];
g_varargout_2_tmp = x[0] * W[72];
h_varargout_2_tmp = x[0] * W[96];
i_varargout_2_tmp = x[0] * W[132];
j_varargout_2_tmp = x[0] * W[144];
k_varargout_2_tmp = x[0] * W[28];
l_varargout_2_tmp = x[0] * W[52];
m_varargout_2_tmp = x[0] * W[76];
n_varargout_2_tmp = x[0] * W[112];
o_varargout_2_tmp = x[0] * W[196];
p_varargout_2_tmp = x[0] * W[208];
varargout_2[4] =
((((((((((((((((((((((((((((((((((((-Q[4] + W[4] * d_varargout_2_tmp) +
W[16] * d_varargout_2_tmp) +
W[64] * d_varargout_2_tmp) +
W[84] * varargout_2_tmp * 3.0) +
W[104] * b_varargout_2_tmp) +
W[124] * c_varargout_2_tmp) +
W[152] * b_varargout_2_tmp) +
W[164] * b_varargout_2_tmp) +
W[220] * c_varargout_2_tmp) +
W[244] * c_varargout_2_tmp) +
x[0] * W[20] * x[1] * 2.0) +
e_varargout_2_tmp * x[2]) +
k_varargout_2_tmp * x[3]) +
f_varargout_2_tmp * x[2]) +
l_varargout_2_tmp * x[3]) +
x[0] * W[68] * x[1] * 2.0) +
g_varargout_2_tmp * x[2]) +
x[0] * W[80] * x[1] * 2.0) +
m_varargout_2_tmp * x[3]) +
x[1] * W[88] * x[2] * 2.0) +
h_varargout_2_tmp * x[2]) +
x[1] * W[92] * x[3] * 2.0) +
x[1] * W[100] * x[2] * 2.0) +
n_varargout_2_tmp * x[3]) +
x[2] * W[108] * x[3]) +
x[1] * W[116] * x[3] * 2.0) +
x[2] * W[120] * x[3]) +
i_varargout_2_tmp * x[2]) +
j_varargout_2_tmp * x[2]) +
x[1] * W[148] * x[2] * 2.0) +
x[2] * W[156] * x[3]) +
x[2] * W[180] * x[3]) +
o_varargout_2_tmp * x[3]) +
p_varargout_2_tmp * x[3]) +
x[1] * W[212] * x[3] * 2.0) +
x[2] * W[216] * x[3]) +
x[2] * W[228] * x[3];
q_varargout_2_tmp = x[0] * W[25];
r_varargout_2_tmp = x[0] * W[37];
s_varargout_2_tmp = x[0] * W[73];
t_varargout_2_tmp = x[0] * W[97];
u_varargout_2_tmp = x[0] * W[133];
v_varargout_2_tmp = x[0] * W[145];
w_varargout_2_tmp = x[0] * W[29];
x_varargout_2_tmp = x[0] * W[53];
y_varargout_2_tmp = x[0] * W[77];
ab_varargout_2_tmp = x[0] * W[113];
bb_varargout_2_tmp = x[0] * W[197];
cb_varargout_2_tmp = x[0] * W[209];
varargout_2[5] =
(((((((((((((((((((((((((((((((((((((-Q[5] + x[4]) +
W[5] * d_varargout_2_tmp) +
W[17] * d_varargout_2_tmp) +
W[65] * d_varargout_2_tmp) +
W[85] * varargout_2_tmp * 3.0) +
W[105] * b_varargout_2_tmp) +
W[125] * c_varargout_2_tmp) +
W[153] * b_varargout_2_tmp) +
W[165] * b_varargout_2_tmp) +
W[221] * c_varargout_2_tmp) +
W[245] * c_varargout_2_tmp) +
x[0] * W[21] * x[1] * 2.0) +
q_varargout_2_tmp * x[2]) +
w_varargout_2_tmp * x[3]) +
r_varargout_2_tmp * x[2]) +
x_varargout_2_tmp * x[3]) +
x[0] * W[69] * x[1] * 2.0) +
s_varargout_2_tmp * x[2]) +
x[0] * W[81] * x[1] * 2.0) +
y_varargout_2_tmp * x[3]) +
x[1] * W[89] * x[2] * 2.0) +
t_varargout_2_tmp * x[2]) +
x[1] * W[93] * x[3] * 2.0) +
x[1] * W[101] * x[2] * 2.0) +
ab_varargout_2_tmp * x[3]) +
x[2] * W[109] * x[3]) +
x[1] * W[117] * x[3] * 2.0) +
x[2] * W[121] * x[3]) +
u_varargout_2_tmp * x[2]) +
v_varargout_2_tmp * x[2]) +
x[1] * W[149] * x[2] * 2.0) +
x[2] * W[157] * x[3]) +
x[2] * W[181] * x[3]) +
bb_varargout_2_tmp * x[3]) +
cb_varargout_2_tmp * x[3]) +
x[1] * W[213] * x[3] * 2.0) +
x[2] * W[217] * x[3]) +
x[2] * W[229] * x[3];
db_varargout_2_tmp = x[0] * W[26];
eb_varargout_2_tmp = x[0] * W[38];
fb_varargout_2_tmp = x[0] * W[74];
gb_varargout_2_tmp = x[0] * W[98];
hb_varargout_2_tmp = x[0] * W[134];
ib_varargout_2_tmp = x[0] * W[146];
jb_varargout_2_tmp = x[0] * W[30];
kb_varargout_2_tmp = x[0] * W[54];
lb_varargout_2_tmp = x[0] * W[78];
mb_varargout_2_tmp = x[0] * W[114];
nb_varargout_2_tmp = x[0] * W[198];
ob_varargout_2_tmp = x[0] * W[210];
varargout_2[6] =
((((((((((((((((((((((((((((((((((((-Q[6] + W[6] * d_varargout_2_tmp) +
W[18] * d_varargout_2_tmp) +
W[66] * d_varargout_2_tmp) +
W[86] * varargout_2_tmp * 3.0) +
W[106] * b_varargout_2_tmp) +
W[126] * c_varargout_2_tmp) +
W[154] * b_varargout_2_tmp) +
W[166] * b_varargout_2_tmp) +
W[222] * c_varargout_2_tmp) +
W[246] * c_varargout_2_tmp) +
x[0] * W[22] * x[1] * 2.0) +
db_varargout_2_tmp * x[2]) +
jb_varargout_2_tmp * x[3]) +
eb_varargout_2_tmp * x[2]) +
kb_varargout_2_tmp * x[3]) +
x[0] * W[70] * x[1] * 2.0) +
fb_varargout_2_tmp * x[2]) +
x[0] * W[82] * x[1] * 2.0) +
lb_varargout_2_tmp * x[3]) +
x[1] * W[90] * x[2] * 2.0) +
gb_varargout_2_tmp * x[2]) +
x[1] * W[94] * x[3] * 2.0) +
x[1] * W[102] * x[2] * 2.0) +
mb_varargout_2_tmp * x[3]) +
x[2] * W[110] * x[3]) +
x[1] * W[118] * x[3] * 2.0) +
x[2] * W[122] * x[3]) +
hb_varargout_2_tmp * x[2]) +
ib_varargout_2_tmp * x[2]) +
x[1] * W[150] * x[2] * 2.0) +
x[2] * W[158] * x[3]) +
x[2] * W[182] * x[3]) +
nb_varargout_2_tmp * x[3]) +
ob_varargout_2_tmp * x[3]) +
x[1] * W[214] * x[3] * 2.0) +
x[2] * W[218] * x[3]) +
x[2] * W[230] * x[3];
pb_varargout_2_tmp = x[0] * W[27];
qb_varargout_2_tmp = x[0] * W[39];
rb_varargout_2_tmp = x[0] * W[75];
sb_varargout_2_tmp = x[0] * W[99];
tb_varargout_2_tmp = x[0] * W[135];
ub_varargout_2_tmp = x[0] * W[147];
vb_varargout_2_tmp = x[0] * W[31];
wb_varargout_2_tmp = x[0] * W[55];
xb_varargout_2_tmp = x[0] * W[79];
yb_varargout_2_tmp = x[0] * W[115];
ac_varargout_2_tmp = x[0] * W[199];
bc_varargout_2_tmp = x[0] * W[211];
varargout_2[7] =
((((((((((((((((((((((((((((((((((((-Q[7] + W[7] * d_varargout_2_tmp) +
W[19] * d_varargout_2_tmp) +
W[67] * d_varargout_2_tmp) +
W[87] * varargout_2_tmp * 3.0) +
W[107] * b_varargout_2_tmp) +
W[127] * c_varargout_2_tmp) +
W[155] * b_varargout_2_tmp) +
W[167] * b_varargout_2_tmp) +
W[223] * c_varargout_2_tmp) +
W[247] * c_varargout_2_tmp) +
x[0] * W[23] * x[1] * 2.0) +
pb_varargout_2_tmp * x[2]) +
vb_varargout_2_tmp * x[3]) +
qb_varargout_2_tmp * x[2]) +
wb_varargout_2_tmp * x[3]) +
x[0] * W[71] * x[1] * 2.0) +
rb_varargout_2_tmp * x[2]) +
x[0] * W[83] * x[1] * 2.0) +
xb_varargout_2_tmp * x[3]) +
x[1] * W[91] * x[2] * 2.0) +
sb_varargout_2_tmp * x[2]) +
x[1] * W[95] * x[3] * 2.0) +
x[1] * W[103] * x[2] * 2.0) +
yb_varargout_2_tmp * x[3]) +
x[2] * W[111] * x[3]) +
x[1] * W[119] * x[3] * 2.0) +
x[2] * W[123] * x[3]) +
tb_varargout_2_tmp * x[2]) +
ub_varargout_2_tmp * x[2]) +
x[1] * W[151] * x[2] * 2.0) +
x[2] * W[159] * x[3]) +
x[2] * W[183] * x[3]) +
ac_varargout_2_tmp * x[3]) +
bc_varargout_2_tmp * x[3]) +
x[1] * W[215] * x[3] * 2.0) +
x[2] * W[219] * x[3]) +
x[2] * W[231] * x[3];
cc_varargout_2_tmp = x[0] * W[44];
dc_varargout_2_tmp = x[0] * W[56];
ec_varargout_2_tmp = x[1] * W[108];
fc_varargout_2_tmp = x[1] * W[120];
gc_varargout_2_tmp = x[0] * W[140];
hc_varargout_2_tmp = x[1] * W[156];
ic_varargout_2_tmp = x[0] * W[176];
jc_varargout_2_tmp = x[1] * W[180];
kc_varargout_2_tmp = x[0] * W[200];
lc_varargout_2_tmp = x[1] * W[216];
mc_varargout_2_tmp = x[0] * W[224];
nc_varargout_2_tmp = x[1] * W[228];
varargout_2[8] =
((((((((((((((((((((((((((((((((((((-Q[8] + W[8] * d_varargout_2_tmp) +
W[32] * d_varargout_2_tmp) +
W[88] * varargout_2_tmp) +
W[100] * varargout_2_tmp) +
W[128] * d_varargout_2_tmp) +
W[148] * varargout_2_tmp) +
W[168] * b_varargout_2_tmp * 3.0) +
W[188] * c_varargout_2_tmp) +
W[236] * c_varargout_2_tmp) +
W[248] * c_varargout_2_tmp) +
e_varargout_2_tmp * x[1]) +
f_varargout_2_tmp * x[1]) +
x[0] * W[40] * x[2] * 2.0) +
cc_varargout_2_tmp * x[3]) +
dc_varargout_2_tmp * x[3]) +
g_varargout_2_tmp * x[1]) +
h_varargout_2_tmp * x[1]) +
x[1] * W[104] * x[2] * 2.0) +
ec_varargout_2_tmp * x[3]) +
fc_varargout_2_tmp * x[3]) +
i_varargout_2_tmp * x[1]) +
x[0] * W[136] * x[2] * 2.0) +
j_varargout_2_tmp * x[1]) +
gc_varargout_2_tmp * x[3]) +
x[1] * W[152] * x[2] * 2.0) +
x[0] * W[160] * x[2] * 2.0) +
hc_varargout_2_tmp * x[3]) +
x[1] * W[164] * x[2] * 2.0) +
ic_varargout_2_tmp * x[3]) +
x[2] * W[172] * x[3] * 2.0) +
jc_varargout_2_tmp * x[3]) +
x[2] * W[184] * x[3] * 2.0) +
kc_varargout_2_tmp * x[3]) +
lc_varargout_2_tmp * x[3]) +
mc_varargout_2_tmp * x[3]) +
nc_varargout_2_tmp * x[3]) +
x[2] * W[232] * x[3] * 2.0;
e_varargout_2_tmp = x[0] * W[45];
f_varargout_2_tmp = x[0] * W[57];
g_varargout_2_tmp = x[1] * W[109];
h_varargout_2_tmp = x[1] * W[121];
i_varargout_2_tmp = x[0] * W[141];
j_varargout_2_tmp = x[1] * W[157];
oc_varargout_2_tmp = x[0] * W[177];
pc_varargout_2_tmp = x[1] * W[181];
qc_varargout_2_tmp = x[0] * W[201];
rc_varargout_2_tmp = x[1] * W[217];
sc_varargout_2_tmp = x[0] * W[225];
tc_varargout_2_tmp = x[1] * W[229];
varargout_2[9] =
((((((((((((((((((((((((((((((((((((-Q[9] + W[9] * d_varargout_2_tmp) +
W[33] * d_varargout_2_tmp) +
W[89] * varargout_2_tmp) +
W[101] * varargout_2_tmp) +
W[129] * d_varargout_2_tmp) +
W[149] * varargout_2_tmp) +
W[169] * b_varargout_2_tmp * 3.0) +
W[189] * c_varargout_2_tmp) +
W[237] * c_varargout_2_tmp) +
W[249] * c_varargout_2_tmp) +
q_varargout_2_tmp * x[1]) +
r_varargout_2_tmp * x[1]) +
x[0] * W[41] * x[2] * 2.0) +
e_varargout_2_tmp * x[3]) +
f_varargout_2_tmp * x[3]) +
s_varargout_2_tmp * x[1]) +
t_varargout_2_tmp * x[1]) +
x[1] * W[105] * x[2] * 2.0) +
g_varargout_2_tmp * x[3]) +
h_varargout_2_tmp * x[3]) +
u_varargout_2_tmp * x[1]) +
x[0] * W[137] * x[2] * 2.0) +
v_varargout_2_tmp * x[1]) +
i_varargout_2_tmp * x[3]) +
x[1] * W[153] * x[2] * 2.0) +
x[0] * W[161] * x[2] * 2.0) +
j_varargout_2_tmp * x[3]) +
x[1] * W[165] * x[2] * 2.0) +
oc_varargout_2_tmp * x[3]) +
x[2] * W[173] * x[3] * 2.0) +
pc_varargout_2_tmp * x[3]) +
x[2] * W[185] * x[3] * 2.0) +
qc_varargout_2_tmp * x[3]) +
rc_varargout_2_tmp * x[3]) +
sc_varargout_2_tmp * x[3]) +
tc_varargout_2_tmp * x[3]) +
x[2] * W[233] * x[3] * 2.0;
q_varargout_2_tmp = x[0] * W[46];
r_varargout_2_tmp = x[0] * W[58];
s_varargout_2_tmp = x[1] * W[110];