std::vector<std::vector<T>> group(std::vector<T> v, F similar) {
UnionFind uf(v.size());
for (size_t i = 0; i < v.size(); ++i) {
for (size_t j = i + 1; j < v.size(); ++j) {
if (similar(v[i], v[j])) {
uf.join(i, j);
}
}
}
std::vector<int> idxmap(v.size(), -1);
std::vector<std::vector<T>> vs;
for (size_t i = 0; i < v.size(); ++i) {
size_t set = uf.find(i);
int group = idxmap[set];
if (group < 0) {
idxmap[set] = vs.size();
vs.emplace_back(1, v[i]);
} else {
vs[group].push_back(v[i]);
}
}
return vs;
}
void KNDdeTorusCollocation::Save(const char* dat, const char* idx, const KNVector& in)
{
// writing to file for plotting
std::ofstream ff(dat);
for (size_t i2 = 0; i2 < nint2; i2++)
{
for (size_t j2 = 0; j2 < ndeg2; j2++)
{
for (size_t i1 = 0; i1 < nint1; i1++)
{
for (size_t j1 = 0; j1 < ndeg1; j1++)
{
const size_t idx1 = idxmap(j1, j2, i1, i2);
for (size_t p = 0; p < NDIM; p++)
{
ff << in(p + NDIM*idx1) << "\t";
}
}
}
ff << "\n";
}
}
std::ofstream gg(idx);
for (size_t i1 = 0; i1 < nint1; i1++)
{
for (size_t j1 = 0; j1 < ndeg1; j1++)
{
const double t1 = (mesh1(j1) + i1) / ((double)nint1);
gg << t1 << "\t";
}
}
gg << "\n";
for (size_t i2 = 0; i2 < nint2; i2++)
{
for (size_t j2 = 0; j2 < ndeg2; j2++)
{
const double t2 = (mesh2(j2) + i2) / ((double)nint2);
gg << t2 << "\t";
}
}
gg << "\n";
}
void KNDdeTorusCollocation::importSolution(KNVector& out, KNVector& in)
{
for (size_t i2 = 0; i2 < nint2; i2++)
{
for (size_t i1 = 0; i1 < nint1; i1++)
{
for (size_t j2 = 0; j2 < ndeg2; j2++)
{
for (size_t j1 = 0; j1 < ndeg1; j1++)
{
const size_t idx1 = idxmap(j1, j2, i1, i2);
for (size_t p = 0; p < NDIM; p++)
{
out(p + NDIM*idx1) = in(p + NDIM * (j1 + i1 * ndeg1));
}
}
}
}
}
}
void KNDdeTorusCollocation::init(const KNVector& sol, const KNVector& par)
{
double* t1 = new double[NTAU+1];
double* t2 = new double[NTAU+1];
for (size_t i2 = 0; i2 < nint2; i2++)
{
for (size_t i1 = 0; i1 < nint1; i1++)
{
for (size_t j2 = 0; j2 < ndeg2; j2++)
{
for (size_t j1 = 0; j1 < ndeg1; j1++)
{
const size_t idx = idxmap(j1, j2, i1, i2); // this is a unique
time1(idx) = ((double)i1 + col1(j1)) / nint1;
time2(idx) = ((double)i2 + col2(j2)) / nint2;
}
}
}
}
sys->p_tau(p_tau, time1, par);
p_xx.clear();
for (size_t idx = 0; idx < time1.size(); ++idx)
{
t1[0] = time1(idx);
t2[0] = time2(idx);
for (size_t k = 0; k < NTAU; k++)
{
t1[1+k] = (t1[0] - p_tau(k,idx) / par(0)) - floor(t1[0] - p_tau(k,idx) / par(0));
t2[1+k] = (t2[0] - par(RHO) * p_tau(k,idx) / par(0)) - floor(t2[0] - par(RHO) * p_tau(k,idx) / par(0));
}
for (size_t k = 0; k < NTAU + 1; k++)
{
size_t i1 = static_cast<size_t>(floor(nint1 * t1[k]));
size_t i2 = static_cast<size_t>(floor(nint2 * t2[k]));
// some error checking
if ((t1[k] > 1.0) || (t2[k] > 1.0) ||
(t1[k] < 0.0) || (t2[k] < 0.0)) std::cout << "Er ";
if ((i1 >= nint1) || (i2 >= nint2)) std::cout << "Ei ";
// end error checking
for (size_t j2 = 0; j2 < ndeg2 + 1; j2++)
{
for (size_t j1 = 0; j1 < ndeg1 + 1; j1++)
{
const size_t idxKK = idxkk(j1, j2, k);
kk(idxKK,idx) = idxmap(j1, j2, i1, i2);
ee(idxKK,idx) = idxKK;
}
}
}
// sorting
comp aa(kk.pointer(0,idx));
std::sort(ee.pointer(0,idx), ee.pointer(0,idx) + (NTAU + 1)*(ndeg1 + 1)*(ndeg2 + 1), aa);
// filtering same indices
rr(ee(0,idx),idx) = 0;
size_t nz = 0;
for (size_t i = 1; i < (NTAU + 1)*(ndeg1 + 1)*(ndeg2 + 1); i++)
{
if (kk(ee(i-1,idx),idx) != kk(ee(i,idx),idx)) nz++;
rr(ee(i,idx),idx) = nz;
}
// interpolate the solution
for (size_t k = 1; k < NTAU + 1; k++)
{
const double c1 = nint1 * t1[k] - floor(nint1 * t1[k]);
const double c2 = nint2 * t2[k] - floor(nint2 * t2[k]);
for (size_t j2 = 0; j2 < ndeg2 + 1; j2++)
{
for (size_t j1 = 0; j1 < ndeg1 + 1; j1++)
{
const size_t idxKK = idxkk(j1, j2, k);
const double cf = poly_lgr_eval(mesh1, j1, c1) * poly_lgr_eval(mesh2, j2, c2);
for (size_t p = 0; p < NDIM; p++)
{
p_xx(p, k - 1, idx) += cf * sol(p + NDIM * kk(idxKK, idx));
}
}
}
}
// derivatives at all delays
for (size_t k = 0; k < NTAU + 1; k++)
{
const double c1 = nint1 * t1[k] - floor(nint1 * t1[k]);
const double c2 = nint2 * t2[k] - floor(nint2 * t2[k]);
for (size_t j2 = 0; j2 < ndeg2 + 1; j2++)
{
for (size_t j1 = 0; j1 < ndeg1 + 1; j1++)
{
const size_t idxKK = idxkk(j1, j2, k);
const double cf1 = poly_dlg_eval(mesh1, j1, c1) * nint1 * poly_lgr_eval(mesh2, j2, c2);
const double cf2 = poly_lgr_eval(mesh1, j1, c1) * poly_dlg_eval(mesh2, j2, c2) * nint2;
for (size_t p = 0; p < NDIM; p++)
{
p_xx(p, NTAU + 2*k, idx) += cf1 * sol(p + NDIM * kk(idxKK, idx));
p_xx(p, NTAU + 2*k + 1, idx) += cf2 * sol(p + NDIM * kk(idxKK, idx));
}
}
}
}
}
// for (int idx = 0; idx < time1.size(); ++idx) std::cout<<p_xx(0, NTAU, idx)<<"\t";
// std::cout<<"\np_xx(0,...) was\n";
delete[] t2;
delete[] t1;
}
