forked from mirror/toddcox-faster
Make tc::Group an Eigen::Matrix (Schafli Matrix)
Makes tc::Group a direct subclass of Eigen::Matrix. Group should represent a Schlafli matrix. Added a note that tc::solve assumes the matrix to be for a coxeter group. In theory we could also implement the "normal" todd-coxeter and allow any Schlafli matrix as input.
This commit is contained in:
David Allemang
@@ -2,167 +2,150 @@
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#include "core.hpp"
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namespace tc {
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namespace tc::group {
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/**
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* Construct a group from a (simplified) Schlafli Symbol of the form [a, b, ..., c]
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* @param mults: The sequence of multiplicites between adjacent generators.
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* Universal Coxeter Group
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*/
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template<unsigned int Rank>
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Group <Rank> schlafli(const std::array<unsigned int, Rank - 1> &mults, const std::string &name) {
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Group<Rank> g(name);
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Group <Rank> U() {
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std::stringstream ss;
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ss << "U(" << Rank << ")";
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for (int i = 0; i < Rank - 1; i++) {
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g(i, i + 1) = mults[i];
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Group<Rank> res;
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res.name = ss.str();
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res.fill(2);
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return res;
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}
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/**
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* Simplex
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*/
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template<unsigned int Rank>
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Group <Rank> A() {
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std::stringstream ss;
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ss << "A(" << Rank << ")";
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if (Rank == 0) {
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Group<Rank> res;
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res.name = ss.str();
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return res;
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}
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std::array<unsigned int, Rank - 1> mults;
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mults.fill(3);
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return schlafli<Rank>(mults, ss.str());
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}
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/**
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* Cube, Orthoplex
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*/
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template<unsigned int Rank>
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Group <Rank> B() {
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std::stringstream ss;
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ss << "B(" << Rank << ")";
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tc::Symbol<Rank - 1> mults;
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mults.fill(3);
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mults(0) = 4;
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return schlafli<Rank>(mults, ss.str());
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}
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/**
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* Demicube, Orthoplex
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*/
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template<unsigned int Rank>
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Group <Rank> D() {
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std::stringstream ss;
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ss << "D(" << Rank << ")";
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tc::Symbol<Rank - 1> mults;
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mults.fill(3);
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mults(Rank - 2) = 2;
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Group<Rank> g = schlafli<Rank>(mults, ss.str());
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g(1, Rank - 1) = 3;
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g(Rank - 1, 1) = 3;
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return g;
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}
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/**
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* Construct a group from a (simplified) Schlafli Symbol of the form [a, b, ..., c]
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* @param mults: The sequence of multiplicites between adjacent generators.
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* E groups
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*/
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template<unsigned int Rank>
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Group <Rank> schlafli(const std::array<unsigned int, Rank - 1> &mults) {
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Group <Rank> E() {
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std::stringstream ss;
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ss << "[";
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if (Rank) {
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for (size_t i = 0; i < Rank - 2; ++i) {
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ss << mults[i] << ",";
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}
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ss << mults[Rank - 1];
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}
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ss << "]";
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ss << "E(" << Rank << ")";
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tc::Symbol<Rank - 1> mults;
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mults.fill(3);
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mults(Rank - 2) = 2;
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Group<Rank> g = schlafli<Rank>(mults, ss.str());
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g(2, Rank - 1) = 3;
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g(Rank - 1, 2) = 3;
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return g;
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}
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/**
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* 24 Cell
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*/
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Group<4> F4() {
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return schlafli<4>({3, 4, 3}, "F4");
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}
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/**
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* Hexagon
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*/
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Group<2> G2() {
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return schlafli<2>(tc::Symbol<1>(6), "G2");
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}
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/**
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* Icosahedron
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*/
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template<unsigned int Rank>
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Group <Rank> H() {
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std::stringstream ss;
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ss << "H(" << Rank << ")";
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tc::Symbol<Rank - 1> mults;
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mults.fill(3);
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mults(0) = 5;
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return schlafli<Rank>(mults, ss.str());
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}
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namespace group {
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/**
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* Simplex
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*/
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template<unsigned int Rank>
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Group <Rank> A() {
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std::stringstream ss;
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ss << "A(" << Rank << ")";
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/**
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* Polygonal
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*/
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Group<2> I2(unsigned int n) {
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std::stringstream ss;
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ss << "I2(" << n << ")";
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if (Rank == 0)
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return Group<Rank>(ss.str());
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return schlafli<2>(tc::Symbol<1>(n), ss.str());
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}
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std::array<unsigned int, Rank - 1> mults;
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mults.fill(3);
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/**
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* Toroidal. I2(n) * I2(m)
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*/
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Group<4> T(unsigned int n, unsigned int m) {
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std::stringstream ss;
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ss << "T(" << n << "," << m << ")";
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return schlafli<Rank>(mults, ss.str());
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}
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return schlafli<4>({n, 2, m}, ss.str());
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}
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/**
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* Cube, Orthoplex
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*/
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template<unsigned int Rank>
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Group <Rank> B() {
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std::stringstream ss;
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ss << "B(" << Rank << ")";
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/**
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* Toroidal. T(n, n)
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*/
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Group<4> T(unsigned int n) {
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std::stringstream ss;
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ss << "T(" << n << ")";
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std::array<unsigned int, Rank - 1> mults;
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mults.fill(3);
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mults[0] = 4;
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return schlafli<Rank>(mults, ss.str());
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}
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/**
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* Demicube, Orthoplex
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*/
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template<unsigned int Rank>
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Group <Rank> D() {
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std::stringstream ss;
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ss << "D(" << Rank << ")";
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std::array<unsigned int, Rank - 1> mults;
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mults.fill(3);
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mults[Rank - 2] = 2;
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Group<Rank> g = schlafli<Rank>(mults, ss.str());
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g(1, Rank - 1) = 3;
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return g;
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}
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/**
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* E groups
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*/
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template<unsigned int Rank>
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Group <Rank> E() {
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std::stringstream ss;
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ss << "E(" << Rank << ")";
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std::array<unsigned int, Rank - 1> mults;
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mults.fill(3);
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mults[Rank - 2] = 2;
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Group<Rank> g = schlafli<Rank>(mults, ss.str());
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g(2, Rank - 1) = 3;
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return g;
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}
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/**
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* 24 Cell
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*/
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Group<4> F4() {
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return schlafli<4>({3, 4, 3}, "F4");
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}
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/**
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* Hexagon
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*/
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Group<2> G2() {
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return schlafli<2>({6}, "G2");
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}
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/**
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* Icosahedron
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*/
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template<unsigned int Rank>
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Group <Rank> H() {
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std::stringstream ss;
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ss << "H(" << Rank << ")";
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std::array<unsigned int, Rank - 1> mults;
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mults.fill(3);
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mults[0] = 5;
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return schlafli<Rank>(mults, ss.str());
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}
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/**
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* Polygonal
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*/
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Group<2> I2(unsigned int n) {
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std::stringstream ss;
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ss << "I2(" << n << ")";
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return schlafli<2>({n}, ss.str());
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}
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/**
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* Toroidal. I2(n) * I2(m)
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*/
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Group<4> T(unsigned int n, unsigned int m) {
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std::stringstream ss;
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ss << "T(" << n << "," << m << ")";
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return schlafli<4>({n, 2, m}, ss.str());
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}
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/**
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* Toroidal. T(n, n)
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*/
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Group<4> T(unsigned int n) {
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std::stringstream ss;
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ss << "T(" << n << ")";
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return schlafli<4>({n, 2, n}, ss.str());
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}
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return schlafli<4>({n, 2, n}, ss.str());
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}
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}
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