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Introduce complex solvers

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This commit is contained in:
David Allemang
2021-11-12 15:06:29 -05:00
parent fa13493569
commit bdecf40345
10 changed files with 363 additions and 23 deletions
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include/tc/complex.hpp Normal file
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#pragma once
#include <tc/group.hpp>
#include <tc/solver.hpp>
#include <cmath>
#include <optional>
#include <numeric>
#include <iostream>
namespace tc {
std::vector<Symbol> combinations(const Symbol &symbol, size_t srank) {
size_t rank = symbol.size();
std::vector<bool> mask(rank, false);
std::fill_n(mask.begin(), srank, true);
std::vector<Symbol> combos;
combos.reserve(choose(rank, srank));
Symbol row(srank);
do {
for (int j = 0, k = 0; j < rank; ++j) {
if (mask[j]) {
row(k++) = symbol(j);
}
}
combos.emplace_back(row);
} while (std::prev_permutation(mask.begin(), mask.end()));
return combos;
}
/**
* An primitive stage N indices.
* @tparam N
*/
template<unsigned N>
struct Primitive {
static_assert(N > 0, "Primitives must contain at least one point. Primitive<0> or lower is impossible.");
std::array<unsigned, N> inds;
Primitive() = default;
Primitive(const Primitive<N> &) = default;
Primitive(const Primitive<N - 1> &sub, unsigned root) {
std::copy(sub.inds.begin(), sub.inds.end(), inds.begin());
inds[N - 1] = root;
}
~Primitive() = default;
inline void flip() {
if (N > 1) std::swap(inds[0], inds[1]);
}
void apply(const tc::Cosets &table, unsigned int gen) {
for (auto &ind: inds) {
ind = table.get(ind, gen);
}
flip();
}
};
/**
* Produce a list of all generators for the group context. The range [0..group.rank).
*/
std::vector<unsigned int> generators(const tc::Group &context) {
std::vector<unsigned int> g_gens(context.rank());
std::iota(g_gens.begin(), g_gens.end(), 0);
return g_gens;
}
/**
* Determine whether the orientation of the group sg_gens is reversed from the group g_gens within group context
*/
int get_parity(
const tc::Group &context,
const Symbol &g_gens,
const Symbol &sg_gens
) {
if (g_gens.size() != sg_gens.size() + 1) return 0;
const auto proper_sg_gens = recontext_gens(context.rank(), g_gens, sg_gens);
int i = 0;
for (; i < sg_gens.size(); ++i) {
if (proper_sg_gens[i] != i) {
break;
}
}
return i & 1;
}
/**
* Apply some context transformation to all primitives of this mesh.
*/
template<unsigned N>
std::vector<Primitive<N>> apply(std::vector<Primitive<N>> prims, const tc::Cosets &table, unsigned int gen) {
for (auto &prim: prims) {
prim.apply(table, gen);
}
return prims;
}
/**
* Reverse the orientation of all primitives in this mesh.
*/
template<unsigned N>
void flip(std::vector<Primitive<N>> prims) {
for (auto &prim: prims) {
prim.flip();
}
}
/**
* Convert the indexes of this mesh to those of a different context, using g_gens to build the parent context and sg_gens to build this context.
*/
template<unsigned N>
[[nodiscard]]
std::vector<Primitive<N>> recontext(
std::vector<Primitive<N>> prims,
const tc::Group &context,
const Symbol &g_gens,
const Symbol &sg_gens
) {
const auto proper_sg_gens = recontext_gens(context.rank(), g_gens, sg_gens);
const auto table = solve(context, g_gens, Symbol(0));
const auto path = solve(context, sg_gens, Symbol(0)).path();
auto map = path.walk(0U, proper_sg_gens, [&table](auto coset, auto gen) {
return table.get(coset, gen);
});
std::vector<Primitive<N>> res(prims);
for (Primitive<N> &prim: res) {
for (auto &ind: prim.inds) {
ind = map[ind];
}
}
if (get_parity(context, g_gens, sg_gens) == 1)
flip(res);
return res;
}
/**
* Union several meshes of the same dimension
*/
template<unsigned N>
std::vector<Primitive<N>> merge(const std::vector<std::vector<Primitive<N>>> &meshes) {
size_t size = 0;
for (const auto &mesh: meshes) {
size += mesh.size();
}
std::vector<Primitive<N>> res;
res.reserve(size);
for (const auto &mesh: meshes) {
res.insert(res.end(), mesh.begin(), mesh.end());
}
return res;
}
template<unsigned N>
[[nodiscard]]
std::vector<std::vector<Primitive<N>>> each_tile(
std::vector<Primitive<N>> prims,
const tc::Group &context,
const Symbol &g_gens,
const Symbol &sg_gens
) {
std::vector<Primitive<N>> base = recontext(prims, context, g_gens, sg_gens);
const auto table = solve(context, g_gens, Symbol(0));
const auto path = solve(context, g_gens, sg_gens).path();
auto _gens = generators(context);
auto res = path.walk(base, _gens, [&table](auto from, auto gen){
return apply(from, table, gen);
});
return res;
}
template<unsigned N>
[[nodiscard]]
std::vector<Primitive<N>> tile(
std::vector<Primitive<N>> prims,
const tc::Group &context,
const Symbol &g_gens,
const Symbol &sg_gens
) {
auto res = each_tile<N>(prims, context, g_gens, sg_gens);
return merge(res);
}
/**
* Produce a mesh of higher dimension by fanning a single point to all primitives in this mesh.
*/
template<unsigned N>
[[nodiscard]]
std::vector<Primitive<N + 1>> fan(std::vector<Primitive<N>> prims, int root) {
std::vector<Primitive<N + 1>> res(prims.size());
std::transform(prims.begin(), prims.end(), res.begin(),
[root](const Primitive<N> &prim) {
return Primitive<N + 1>(prim, root);
}
);
return res;
}
/**
* Produce a mesh of primitives that fill out the volume of the subgroup generated by generators g_gens within the group context
*/
template<unsigned N>
std::vector<Primitive<N>> triangulate(
const tc::Group &context,
const Symbol &g_gens
) {
if (g_gens.size() + 1 != N) // todo make static assert
throw std::logic_error("g_gens size must be one less than N");
const auto &combos = combinations(g_gens, g_gens.size() - 1);
std::vector<std::vector<Primitive<N>>> meshes;
for (const auto &sg_gens: combos) {
auto base = triangulate<N - 1>(context, sg_gens);
auto raised = tile(base, context, g_gens, sg_gens);
raised.erase(raised.begin(), raised.begin() + base.size());
meshes.push_back(fan(raised, 0));
}
return merge(meshes);
}
/**
* Single-index primitives should not be further triangulated.
*/
template<>
std::vector<Primitive<1>> triangulate(
const tc::Group &context,
const Symbol &g_gens
) {
if (g_gens.size() != 0) // todo make static assert
throw std::logic_error("g_gens must be empty for a trivial Mesh");
std::vector<Primitive<1>> res;
res.emplace_back();
return res;
}
template<unsigned N, class T>
auto hull(const tc::Group &group, T all_sg_gens, const std::vector<Symbol> &exclude) {
std::vector<std::vector<Primitive<N>>> parts;
auto g_gens = group.gens;
for (const Symbol &sg_gens: all_sg_gens) {
bool excluded = false;
for (const auto &test: exclude) {
if (sg_gens == test) {
excluded = true;
break;
}
}
if (excluded) continue;
const auto &base = triangulate<N>(group, sg_gens);
const auto &tiles = each_tile(base, group, g_gens, sg_gens);
for (const auto &tile: tiles) {
parts.push_back(tile);
}
}
return parts;
}
}