void Stir::step() {
omega = __q(angle - _robot->angle());
move->set(speed_x, speed_y, ratio * omega);
move->step();
}
void
hankel_transition()
{
auto sign = [](int s, int r){return (s + r) % 2 == 1 ? -1 : +1; };
using rational = _Tp;
std::cout.precision(std::numeric_limits<_Tp>::digits10);
auto width = std::cout.precision() + 6;
__gnu_cxx::_Polynomial<int> poo({0, -2});
std::vector<__gnu_cxx::_Polynomial<int>> phi;
std::vector<__gnu_cxx::_Polynomial<int>> psi;
phi.push_back(__gnu_cxx::_Polynomial<int>(1));
phi.push_back(__gnu_cxx::_Polynomial<int>(0));
phi.push_back(__gnu_cxx::_Polynomial<int>({0, -2}));
psi.push_back(__gnu_cxx::_Polynomial<int>(0));
psi.push_back(__gnu_cxx::_Polynomial<int>(-1));
psi.push_back(__gnu_cxx::_Polynomial<int>(0));
for (int s = 3; s <= 18; ++s)
{
phi.push_back(poo * phi[s - 2] -2 * (s - 2) * phi[s - 3]);
psi.push_back(poo * psi[s - 2] -2 * (s - 2) * psi[s - 3]);
}
std::cout << "\nphi polynomial\n";
for (const auto& p : phi)
std::cout << p << '\n';
std::cout << "\npsi polynomial\n";
for (const auto& p : psi)
std::cout << p << '\n';
std::vector<__gnu_cxx::_Polynomial<rational>> A(6);
std::vector<__gnu_cxx::_Polynomial<rational>> B(6);
for (int s = 0; s < 6; ++s)
{
for (int r = 0; r <= s; ++r)
A[s] += phi[2 * s + r] * __gnu_cxx::_Polynomial<rational>(sign(r, s), r);
std::cout << "A_" << s << ": " << A[s] << '\n';
for (int r = 0; r <= s; ++r)
B[s] += psi[2 * s + r] * __gnu_cxx::_Polynomial<rational>(sign(r, s), r);
std::cout << "B_" << s << ": " << B[s] << '\n';
}
std::vector<__gnu_cxx::_Polynomial<__gnu_cxx::_Rational<long long>>>
P
{
{{1, 1}},
{{}, {-1, 5}},
{{}, {}, {3, 35}, {}, {}, {-9, 100}},
{{-1, 225}, {}, {}, {-173, 3150}, {}, {}, {957, 7000}},
{{}, {947, 346500}, {}, {}, {5903, 138600}, {}, {}, {-23573, 147000}, {}, {}, {27, 20000}}
};
std::vector<__gnu_cxx::_Polynomial<__gnu_cxx::_Rational<long long>>>
Q
{
{{}, {}, {3, 10}},
{{1, 70}, {}, {}, {-17, 70}},
{{}, {-37, 3150}, {}, {}, {611, 3150}, {}, {}, {-9, 1000}},
{{}, {}, {79, 12375}, {}, {}, {-110767, 693000}, {}, {}, {549, 28000}}
};
std::vector<__gnu_cxx::_Polynomial<__gnu_cxx::_Rational<long long>>>
R
{
{{1, 1}},
{{}, {-4, 5}},
{{}, {}, {57, 70}, {}, {}, {-9, 100}},
{{23, 3150}, {}, {}, {-2617, 3150}, {}, {}, {699, 3500}},
{{}, {-1159, 115500}, {}, {}, {3889, 4620}, {}, {}, {-46631, 147000}, {}, {}, {27, 20000}}
};
std::vector<__gnu_cxx::_Polynomial<__gnu_cxx::_Rational<long long>>>
S
{
{{-1, 5}, {}, {}, {3, 5}},
{{}, {1, 5}, {}, {}, {-131, 140}},
{{}, {}, {-593, 3150}, {}, {}, {5437, 4500}, {}, {}, {-9, 500}},
{{947, 346500}, {}, {}, {31727, 173250}, {}, {}, {-999443, 693000}, {}, {}, {369, 7000}}
};
std::cout << "\nP polynomial\n";
for (const auto& p : P)
std::cout << p << '\n';
std::cout << "\nP values\n";
for (int i = -100; i <= +100; ++i)
{
auto z = _Tp{0.01Q} * i;
std::cout << std::setw(width) << z;
for (const auto& p : P)
std::cout << std::setw(width) << p(z);
std::cout << '\n';
}
std::cout << "\nQ polynomial\n";
for (const auto& q : Q)
std::cout << q << '\n';
std::cout << "\nQ values\n";
for (int i = -100; i <= +100; ++i)
{
auto z = _Tp{0.01Q} * i;
std::cout << std::setw(width) << z;
for (const auto& q : Q)
std::cout << std::setw(width) << q(z);
std::cout << '\n';
}
std::cout << "\nR polynomial\n";
for (const auto& r : R)
std::cout << r << '\n';
std::cout << "\nR values\n";
for (int i = -100; i <= +100; ++i)
{
auto z = _Tp{0.01Q} * i;
std::cout << std::setw(width) << z;
for (const auto& r : R)
std::cout << std::setw(width) << r(z);
std::cout << '\n';
}
std::cout << "\nS polynomial\n";
for (const auto& s : S)
std::cout << s << '\n';
std::cout << "\nS values\n";
for (int i = -100; i <= +100; ++i)
{
auto z = _Tp{0.01Q} * i;
std::cout << std::setw(width) << z;
for (const auto& s : S)
std::cout << std::setw(width) << s(z);
std::cout << '\n';
}
auto __nu = _Tp{20};
const auto _S_2p13 = _Tp{1.259921049894873164767210607278228350570Q};
const auto _S_2p23 = _Tp{1.587401051968199474751705639272308260393Q};
const auto _S_2p43 = _Tp{2.519842099789746329534421214556456701140Q};
const auto _S_2p53 = _Tp{3.174802103936398949503411278544616520785Q};
const auto _S_pi = _Tp{3.141592653589793238462643383279502884195Q};
const auto __nu13 = std::pow(__nu, _Tp{1} / _Tp{3});
const auto __nu23 = __nu13 * __nu13;
const auto __nu43 = __nu23 * __nu23;
std::cout << "\n\nTransition region Bessel functions: J_\\nu(\\nu + a\\nu^{1/3})\n";
std::cout << "\nnu = " << __nu << "\n"
<< std::setw(width) << "a"
<< std::setw(width) << "J_\\nu"
<< std::setw(width) << "N_\\nu"
<< std::setw(width) << "J'_\\nu"
<< std::setw(width) << "N'_\\nu"
<< '\n';
for (int __i = -100; __i <= +100; ++__i)
{
auto __a = _Tp{0.005Q} * __i;
const auto __airy_arg = -_S_2p13 * __a;
_Tp _Ai, _Bi, _Aip, _Bip;
std::__detail::__airy(__airy_arg, _Ai, _Bi, _Aip, _Bip);
auto __num2k3 = _Tp{1};
auto _Jsum1 = _Tp{0};
auto _Nsum1 = _Tp{0};
__num2k3 = _Tp{1};
for (const auto& __p : P)
{
_Jsum1 += __p(__a) * __num2k3;
_Nsum1 += __p(__a) * __num2k3;
__num2k3 /= __nu23;
}
auto _Jsum2 = _Tp{0};
auto _Nsum2 = _Tp{0};
__num2k3 = _Tp{1};
for (const auto& __q : Q)
{
_Jsum2 += __q(__a) * __num2k3;
_Nsum2 += __q(__a) * __num2k3;
__num2k3 /= __nu23;
}
const auto _Jt = _S_2p13 * _Ai * _Jsum1 / __nu13
+ _S_2p23 * _Aip * _Jsum2 / __nu;
const auto _Nt = -_S_2p13 * _Bi * _Nsum1 / __nu13
- _S_2p23 * _Bip * _Nsum2 / __nu;
auto _Jpsum1 = _Tp{0};
auto _Npsum1 = _Tp{0};
__num2k3 = _Tp{1};
for (const auto& __r : R)
{
_Jpsum1 += __r(__a) * __num2k3;
_Npsum1 += __r(__a) * __num2k3;
__num2k3 /= __nu23;
}
auto _Jpsum2 = _Tp{0};
auto _Npsum2 = _Tp{0};
__num2k3 = _Tp{1};
for (const auto& __s : S)
{
_Jpsum2 += __s(__a) * __num2k3;
_Npsum2 += __s(__a) * __num2k3;
__num2k3 /= __nu23;
}
const auto _Jtp = -_S_2p23 * _Aip * _Jpsum1 / __nu23
+ _S_2p13 * _Ai * _Jpsum2 / __nu43;
const auto _Ntp = _S_2p23 * _Bip * _Npsum1 / __nu23
- _S_2p13 * _Bi * _Npsum2 / __nu43;
std::cout << std::setw(width) << __a
<< std::setw(width) << _Jt
<< std::setw(width) << _Nt
<< std::setw(width) << _Jtp
<< std::setw(width) << _Ntp
<< std::setw(width) << '\n';
}
const auto __mipi3 = std::polar(-_S_pi / _Tp{3});
const auto __pipi3 = std::polar(+_S_pi / _Tp{3});
std::cout << "\n\nTransition region Bessel functions: J_\\nu(\\nu + a\\nu^{1/3})\n";
std::cout << "\nnu = " << __nu << "\n"
<< std::setw(2*width) << "a"
<< std::setw(2*width) << "J_\\nu"
<< std::setw(2*width) << "N_\\nu"
<< std::setw(2*width) << "J'_\\nu"
<< std::setw(2*width) << "N'_\\nu"
<< '\n';
const auto __eps = std::numeric_limits<_Tp>::epsilon();
for (int __i = -100; __i <= +100; ++__i)
{
auto __a = _Tp{0.005Q} * __i;
const std::complex<_Tp> __airy_argm = _S_2p13 * __a * __mipi3;
std::complex<_Tp> _Ami, _Bmi, _Amip, _Bmip;
std::__detail::__airy(__airy_argm, __eps, _Ami, _Bmi, _Amip, _Bmip);
const std::complex<_Tp> __airy_argp = _S_2p13 * __a * __pipi3;
std::complex<_Tp> _Api, _Bpi, _Apip, _Bpip;
std::__detail::__airy(__airy_argp, __eps, _Api, _Bpi, _Apip, _Bpip);
auto __num2k3 = _Tp{1};
auto _H1sum1 = _Tp{0};
auto _H2sum1 = _Tp{0};
__num2k3 = _Tp{1};
for (const auto& __p : P)
{
_H1sum1 += __p(__a) * __num2k3;
_H2sum1 += __p(__a) * __num2k3;
__num2k3 /= __nu23;
}
auto _H1sum2 = _Tp{0};
auto _H2sum2 = _Tp{0};
__num2k3 = _Tp{1};
for (const auto& __q : Q)
{
_H1sum2 += __q(__a) * __num2k3;
_H2sum2 += __q(__a) * __num2k3;
__num2k3 /= __nu23;
}
const auto _H1t = _S_2p43 * __mipi3 * _Ami * _H1sum1 / __nu13
+ _S_2p53 * __mipi3 * _Amip * _H1sum2 / __nu;
const auto _H2t = _S_2p43 * __pipi3 * _Api * _H2sum1 / __nu13
+ _S_2p53 * __pipi3 * _Apip * _H2sum2 / __nu;
auto _H1psum1 = _Tp{0};
auto _H2psum1 = _Tp{0};
__num2k3 = _Tp{1};
for (const auto& __r : R)
{
_H1psum1 += __r(__a) * __num2k3;
_H2psum1 += __r(__a) * __num2k3;
__num2k3 /= __nu23;
}
auto _H1psum2 = _Tp{0};
auto _H2psum2 = _Tp{0};
__num2k3 = _Tp{1};
for (const auto& __s : S)
{
_H1psum2 += __s(__a) * __num2k3;
_H2psum2 += __s(__a) * __num2k3;
__num2k3 /= __nu23;
}
const auto _H1pt = -_S_2p53 * __mipi3 * _Amip * _H1psum1 / __nu23
+ _S_2p43 * __mipi3 * _Ami * _H1psum2 / __nu43;
const auto _H2pt = -_S_2p53 * __pipi3 * _Apip * _H2psum1 / __nu23
+ _S_2p43 * __pipi3 * _Api * _H2psum2 / __nu43;
std::cout << std::setw(2*width) << __a
<< std::setw(2*width) << _H1t
<< std::setw(2*width) << _H2t
<< std::setw(2*width) << _H1pt
<< std::setw(2*width) << _H2pt
<< std::setw(2*width) << '\n';
}
}
