#include <topology/rips.h>
#include <topology/image-zigzag-persistence.h>
#include <utilities/types.h>
#include <utilities/containers.h>
#include <utilities/log.h>
#include <utilities/memory.h> // for report_memory()
#include <utilities/timer.h>
#include <geometry/l2distance.h> // for L2Distance and read_points()
#include <geometry/distances.h>
#include <map>
#include <cmath>
#include <fstream>
#include <stack>
#include <cstdlib>
#include <boost/tuple/tuple.hpp>
#include <boost/program_options.hpp>
#include <boost/progress.hpp>
#ifdef COUNTERS
static Counter* cComplexSize = GetCounter("rips/size");
static Counter* cOperations = GetCounter("rips/operations");
#endif // COUNTERS
typedef PairwiseDistances<PointContainer, L2Distance> PairDistances;
typedef PairDistances::DistanceType DistanceType;
typedef PairDistances::IndexType Vertex;
typedef Simplex<Vertex> Smplx;
typedef std::vector<Smplx> SimplexVector;
typedef std::list<Smplx> SimplexList;
typedef std::set<Smplx, Smplx::VertexDimensionComparison> SimplexSet;
typedef std::vector<Vertex> VertexVector;
typedef std::vector<DistanceType> EpsilonVector;
typedef std::vector<std::pair<Vertex, Vertex> > EdgeVector;
typedef Rips<PairDistances, Smplx> RipsGenerator;
typedef RipsGenerator::Evaluator SimplexEvaluator;
struct BirthInfo;
typedef ImageZigzagPersistence<BirthInfo> Zigzag;
typedef Zigzag::SimplexIndex Index;
typedef Zigzag::Death Death;
typedef std::map<Smplx, Index,
Smplx::VertexDimensionComparison> Complex;
typedef Zigzag::ZColumn Boundary;
// Information we need to know when a class dies
struct BirthInfo
{
BirthInfo(DistanceType dist = DistanceType(), Dimension dim = Dimension()):
distance(dist), dimension(dim) {}
DistanceType distance;
Dimension dimension;
};
// Forward declarations of auxilliary functions
void report_death(std::ofstream& out, Death d, DistanceType epsilon, Dimension skeleton_dimension);
void make_boundary(const Smplx& s, Complex& c, const Zigzag& zz, Boundary& b);
void show_image_betti(Zigzag& zz, Dimension skeleton);
std::ostream& operator<<(std::ostream& out, const BirthInfo& bi);
void process_command_line_options(int argc,
char* argv[],
unsigned& skeleton_dimension,
float& from_multiplier,
float& to_multiplier,
std::string& infilename,
std::string& outfilename);
int main(int argc, char* argv[])
{
#ifdef LOGGING
rlog::RLogInit(argc, argv);
stderrLog.subscribeTo( RLOG_CHANNEL("error") );
#endif
Timer total, remove, add, ec, vc;
total.start();
#if 0
SetFrequency(cOperations, 25000);
SetTrigger(cOperations, cComplexSize);
#endif
unsigned skeleton_dimension;
float from_multiplier, to_multiplier;
std::string infilename, outfilename;
process_command_line_options(argc, argv, skeleton_dimension, from_multiplier, to_multiplier, infilename, outfilename);
// Read in points
PointContainer points;
read_points(infilename, points);
// Create output file
std::ofstream out(outfilename.c_str());
// Create pairwise distances
PairDistances distances(points);
// Order vertices and epsilons (in maxmin fashion)
VertexVector vertices;
EpsilonVector epsilons;
EdgeVector edges;
{
EpsilonVector dist(distances.size(), Infinity);
vertices.push_back(distances.begin());
//epsilons.push_back(Infinity);
while (vertices.size() < distances.size())
{
for (Vertex v = distances.begin(); v != distances.end(); ++v)
dist[v] = std::min(dist[v], distances(v, vertices.back()));
EpsilonVector::const_iterator max = std::max_element(dist.begin(), dist.end());
vertices.push_back(max - dist.begin());
epsilons.push_back(*max);
}
epsilons.push_back(0);
}
rInfo("Point and epsilon ordering:");
for (unsigned i = 0; i < vertices.size(); ++i)
rInfo(" %4d: %4d - %f", i, vertices[i], epsilons[i]);
// Generate and sort all the edges
for (unsigned i = 0; i != vertices.size(); ++i)
for (unsigned j = i+1; j != vertices.size(); ++j)
{
Vertex u = vertices[i];
Vertex v = vertices[j];
if (distances(u,v) <= to_multiplier*epsilons[j-1])
edges.push_back(std::make_pair(u,v));
}
std::sort(edges.begin(), edges.end(), RipsGenerator::ComparePair(distances));
rInfo("Total participating edges: %d", edges.size());
for (EdgeVector::const_iterator cur = edges.begin(); cur != edges.end(); ++cur)
rDebug(" (%d, %d) %f", cur->first, cur->second, distances(cur->first, cur->second));
// Construct zigzag
Complex complex;
Zigzag zz;
RipsGenerator rips(distances);
SimplexEvaluator size(distances);
// Insert vertices
for (unsigned i = 0; i != vertices.size(); ++i)
{
// Add a vertex
Smplx sv; sv.add(vertices[i]);
rDebug("Adding %s", tostring(sv).c_str());
add.start();
complex.insert(std::make_pair(sv,
zz.add(Boundary(),
true, // vertex is always in the subcomplex
BirthInfo(0, 0)).first));
add.stop();
//rDebug("Newly born cycle order: %d", complex[sv]->low->order);
CountNum(cComplexSize, 0);
Count(cComplexSize);
Count(cOperations);
}
rInfo("Commencing computation");
boost::progress_display show_progress(vertices.size());
unsigned sce = 0, // index of the current one past last edge in the subcomplex
ce = 0; // index of the current one past last edge in the complex
for (unsigned stage = 0; stage != vertices.size() - 1; ++stage)
{
unsigned i = vertices.size() - 1 - stage;
rInfo("Current stage %d: %d %f: %f -> %f", stage,
vertices[i], epsilons[i-1],
from_multiplier*epsilons[i-1],
to_multiplier*epsilons[i-1]);
/* Increase epsilon */
// Record the cofaces of all the simplices that need to be removed and reinserted
SimplexSet cofaces;
rDebug(" Cofaces size: %d", cofaces.size());
while(sce < ce)
{
Vertex u,v;
boost::tie(u,v) = edges[sce];
if (distances(u,v) <= from_multiplier*epsilons[i-1])
++sce;
else
break;
// Skip an edge if any one of its vertices has been removed from the complex
bool skip_edge = false;
for (unsigned j = i+1; j != vertices.size(); ++j)
if (u == vertices[j] || v == vertices[j])
{
// Debug only: eventually remove
rDebug(" Skipping edge (%d, %d)", u, v);
Smplx s; s.add(u); s.add(v);
AssertMsg(complex.find(s) == complex.end(), "Simplex should not be in the complex.");
skip_edge = true;
break;
}
if (skip_edge) continue;
rDebug(" Generating cofaces for (%d, %d)", u, v);
ec.start();
rips.edge_cofaces(u, v,
skeleton_dimension,
to_multiplier*epsilons[i],
make_insert_functor(cofaces),
vertices.begin(),
vertices.begin() + i + 1);
ec.stop();
}
rDebug(" Recorded cofaces to remove");
rDebug(" Cofaces size: %d", cofaces.size());
// Remove all the cofaces
for (SimplexSet::const_reverse_iterator cur = cofaces.rbegin(); cur != (SimplexSet::const_reverse_iterator)cofaces.rend(); ++cur)
{
rDebug(" Removing %s", tostring(*cur).c_str());
Complex::iterator si = complex.find(*cur);
remove.start();
AssertMsg(!si->second->subcomplex, "We should not remove simplices already in the subcomplex when we increase epsilon");
Death d = zz.remove(si->second,
BirthInfo(epsilons[i-1], cur->dimension() - 1));
remove.stop();
complex.erase(si);
CountNumBy(cComplexSize, cur->dimension(), -1);
CountBy(cComplexSize, -1);
Count(cOperations);
AssertMsg(zz.check_consistency(), "Zigzag representation must be consistent after removing a simplex");
report_death(out, d, epsilons[i-1], skeleton_dimension);
}
rDebug(" Removed cofaces");
// Add anything else that needs to be inserted into the complex
while (ce < edges.size())
{
Vertex u,v;
boost::tie(u,v) = edges[ce];
if (distances(u,v) <= to_multiplier*epsilons[i-1])
++ce;
else
break;
rDebug(" Recording cofaces of edges[%d]=(%d, %d) with size=%f", (ce-1), u, v, distances(u,v));
ec.start();
rips.edge_cofaces(u, v,
skeleton_dimension,
to_multiplier*epsilons[i-1],
make_insert_functor(cofaces),
vertices.begin(),
vertices.begin() + i + 1);
ec.stop();
}
rDebug(" Recorded new cofaces to add");
// Progress sce
while (sce < ce)
{
Vertex u,v;
boost::tie(u,v) = edges[sce];
rDebug(" Progressing sce=%d over (%d, %d) %f", sce, u, v, distances(u,v));
if (distances(u,v) <= from_multiplier*epsilons[i-1])
++sce;
else
break;
}
rDebug(" Moved subcomplex index forward");
// Insert all the cofaces
rDebug(" Cofaces size: %d", cofaces.size());
for (SimplexSet::const_iterator cur = cofaces.begin(); cur != cofaces.end(); ++cur)
{
Index idx; Death d; Boundary b;
rDebug(" Adding %s, its size %f", tostring(*cur).c_str(), size(*cur));
make_boundary(*cur, complex, zz, b);
add.start();
boost::tie(idx, d) = zz.add(b,
size(*cur) <= from_multiplier*epsilons[i-1],
BirthInfo(epsilons[i-1], cur->dimension()));
add.stop();
//if (!d) rDebug("Newly born cycle order: %d", complex[*cur]->low->order);
CountNum(cComplexSize, cur->dimension());
Count(cComplexSize);
Count(cOperations);
AssertMsg(zz.check_consistency(), "Zigzag representation must be consistent after removing a simplex");
complex.insert(std::make_pair(*cur, idx));
report_death(out, d, epsilons[i-1], skeleton_dimension);
}
rInfo("Increased epsilon; complex size: %d", complex.size());
show_image_betti(zz, skeleton_dimension);
report_memory();
/* Remove the vertex */
cofaces.clear();
rDebug(" Cofaces size: %d", cofaces.size());
vc.start();
rips.vertex_cofaces(vertices[i],
skeleton_dimension,
to_multiplier*epsilons[i-1],
make_insert_functor(cofaces),
vertices.begin(),
vertices.begin() + i + 1);
vc.stop();
rDebug(" Computed cofaces of the vertex, their number: %d", cofaces.size());
for (SimplexSet::const_reverse_iterator cur = cofaces.rbegin(); cur != (SimplexSet::const_reverse_iterator)cofaces.rend(); ++cur)
{
rDebug(" Removing: %s", tostring(*cur).c_str());
Complex::iterator si = complex.find(*cur);
remove.start();
Death d = zz.remove(si->second,
BirthInfo(epsilons[i-1], cur->dimension() - 1));
remove.stop();
complex.erase(si);
CountNumBy(cComplexSize, cur->dimension(), -1);
CountBy(cComplexSize, -1);
Count(cOperations);
AssertMsg(zz.check_consistency(), "Zigzag representation must be consistent after removing a simplex");
report_death(out, d, epsilons[i-1], skeleton_dimension);
}
rInfo("Removed vertex; complex size: %d", complex.size());
for (Complex::const_iterator cur = complex.begin(); cur != complex.end(); ++cur)
rDebug(" %s", tostring(cur->first).c_str());
show_image_betti(zz, skeleton_dimension);
report_memory();
++show_progress;
}
// Remove the last vertex
AssertMsg(complex.size() == 1, "Only one vertex must remain");
remove.start();
Death d = zz.remove(complex.begin()->second, BirthInfo(epsilons[0], -1));
remove.stop();
complex.erase(complex.begin());
if (!d) AssertMsg(false, "The vertex must have died");
report_death(out, d, epsilons[0], skeleton_dimension);
CountNumBy(cComplexSize, 0, -1);
CountBy(cComplexSize, -1);
Count(cOperations);
rInfo("Removed vertex; complex size: %d", complex.size());
++show_progress;
total.stop();
remove.check("Remove timer ");
add.check ("Add timer ");
ec.check ("Edge coface timer ");
vc.check ("Vertex coface timer ");
total.check ("Total timer ");
}
void report_death(std::ofstream& out, Death d, DistanceType epsilon, Dimension skeleton_dimension)
{
if (d && ((d->distance - epsilon) != 0) && (d->dimension < skeleton_dimension))
out << d->dimension << " " << d->distance << " " << epsilon << std::endl;
}
void make_boundary(const Smplx& s, Complex& c, const Zigzag& zz, Boundary& b)
{
rDebug(" Boundary of <%s>", tostring(s).c_str());
for (Smplx::BoundaryIterator cur = s.boundary_begin(); cur != s.boundary_end(); ++cur)
{
b.append(c[*cur], zz.cmp);
rDebug(" %d (inL=%d)", c[*cur]->order, b.back()->subcomplex);
}
}
bool face_leaving_subcomplex(Complex::reverse_iterator si, const SimplexEvaluator& size, DistanceType after, DistanceType before)
{
const Smplx& s = si->first;
for (Smplx::VertexContainer::const_iterator v1 = s.vertices().begin(); v1 != s.vertices().end(); ++v1)
for (Smplx::VertexContainer::const_iterator v2 = boost::next(v1); v2 != s.vertices().end(); ++v2)
{
Smplx e; e.add(*v1); e.add(*v2);
if (size(e) > after && size(e) <= before)
return true;
}
return false;
}
void show_image_betti(Zigzag& zz, Dimension skeleton)
{
for (Zigzag::ZIndex cur = zz.image_begin(); cur != zz.image_end(); ++cur)
if (cur->low == zz.boundary_end() && cur->birth.dimension < skeleton)
rInfo("Class in the image of dimension: %d", cur->birth.dimension);
}
std::ostream& operator<<(std::ostream& out, const BirthInfo& bi)
{ return (out << bi.distance); }
void process_command_line_options(int argc,
char* argv[],
unsigned& skeleton_dimension,
float& from_multiplier,
float& to_multiplier,
std::string& infilename,
std::string& outfilename)
{
namespace po = boost::program_options;
po::options_description hidden("Hidden options");
hidden.add_options()
("input-file", po::value<std::string>(&infilename), "Point set whose Rips zigzag we want to compute")
("output-file", po::value<std::string>(&outfilename), "Location to save persistence pairs");
po::options_description visible("Allowed options", 100);
visible.add_options()
("help,h", "produce help message")
("skeleton-dimsnion,s", po::value<unsigned>(&skeleton_dimension)->default_value(2), "Dimension of the Rips complex we want to compute")
("from,f", po::value<float>(&from_multiplier)->default_value(4), "From multiplier for the epsilon (distance to next maxmin point) when computing the Rips complex")
("to,t", po::value<float>(&to_multiplier)->default_value(16), "To multiplier for the epsilon (distance to next maxmin point) when computing the Rips complex");
#if LOGGING
std::vector<std::string> log_channels;
visible.add_options()
("log,l", po::value< std::vector<std::string> >(&log_channels), "log channels to turn on (info, debug, etc)");
#endif
po::positional_options_description pos;
pos.add("input-file", 1);
pos.add("output-file", 2);
po::options_description all; all.add(visible).add(hidden);
po::variables_map vm;
po::store(po::command_line_parser(argc, argv).
options(all).positional(pos).run(), vm);
po::notify(vm);
#if LOGGING
for (std::vector<std::string>::const_iterator cur = log_channels.begin(); cur != log_channels.end(); ++cur)
stderrLog.subscribeTo( RLOG_CHANNEL(cur->c_str()) );
/**
* Interesting channels
* "info", "debug", "topology/persistence"
*/
#endif
if (vm.count("help") || !vm.count("input-file") || !vm.count("output-file"))
{
std::cout << "Usage: " << argv[0] << " [options] input-file output-file" << std::endl;
std::cout << visible << std::endl;
std::abort();
}
}