--- /dev/null
+#ifndef simplicialcomplex_h_nealaezeojeeChuh
+#define simplicialcomplex_h_nealaezeojeeChuh
+
+#include <stdint.h>
+#include <cstdlib>
+#include <cstring>
+#include <algorithm>
+#include <vector>
+#include <limits>
+
+#include <iostream>
+
+#include "booleanmatrix.h"
+
+
+namespace libstick {
+
+/** A simplicial complex is a std::vector of simplices such that each face is
+ * also part of the complex. Every simplex has dimension at most MAXDIM. The
+ * indices of simplices resp. their faces are of type IT. To each simplex a
+ * value is assigend, which is of type VT. When a simplicial_complex is
+ * instantiated, a single (-1) dimensional simplex is automatically created.
+ * Each 0-dimensional simplex automatically has this simplex as its face.
+ * Consequently, the innner class simplex_order gives the extended boundary
+ * matrix. */
+template<int MAXDIM, class IT, class VT>
+class simplicial_complex {
+
+ public:
+ /** The type of this class. */
+ typedef simplicial_complex<MAXDIM, IT, VT> simplcompltype;
+ /** Type of indices of simplices. */
+ typedef IT index_type;
+ /** To every simplex a function value is assigned according to which a
+ * filtration is considered. This is the value type of the function. */
+ typedef VT value_type;
+
+ /** A simplex of the complex. */
+ struct simplex {
+ /** Dimension of the simplex. */
+ int dim;
+ /** The indices of the faces of the simplex. */
+ index_type faces[MAXDIM+1];
+ /** The value of the simplex. */
+ value_type value;
+
+ /** Create a new simplex with dimension 'dim', (dim+1)-faces and
+ * its value. If simpley is 0-dimensional, its face is
+ * automatically set to one (-1)-dimensional simplex. */
+ static simplex create(int dim, index_type* faces, value_type value) {
+ assert(0 <= dim && dim <= MAXDIM);
+
+ simplex s;
+ s.dim = dim;
+ s.value = value;
+
+ if (dim > 0)
+ memcpy(s.faces, faces, face_count_bydim(dim)*sizeof(index_type));
+ else
+ s.faces[0] = 0;
+
+ return s;
+ }
+
+ /** Create a (-1)-dimensional simplex. It has the lowest possible value. */
+ static simplex create_minusonedim_simplex() {
+ simplex s;
+
+ s.dim = -1;
+ s.faces[0] = 0;
+ s.value = std::numeric_limits<VT>::has_infinity
+ ? -std::numeric_limits<VT>::infinity()
+ : std::numeric_limits<VT>::min();
+
+ return s;
+ }
+
+ /** Get number of faces. */
+ size_t face_count() const {
+ return face_count_bydim(dim);
+ }
+
+ /** Get number of faces of a dim-dimensional simplex. */
+ static size_t face_count_bydim(int dim) {
+ assert(-1 <= dim && dim <= MAXDIM);
+ return dim + 1;
+ }
+ };
+
+ /** An order of the simplices of complex c. An order can be interpreted
+ * as a permuation of the complex's std::vector of simplices. */
+ class simplex_order {
+
+ public:
+ typedef boolean_colmatrix<IT> boundary_matrix;
+
+ /** Create a standard order of the complex c, i.e., the identity permutation. */
+ simplex_order(const simplcompltype &c) :
+ c(c)
+ {
+ reset();
+ }
+
+ /** Reset order to the identity permutation of the complex's simplices. */
+ void reset() {
+ order.clear();
+ for (unsigned i=0; i < c.size(); ++i)
+ order.push_back(i);
+ revorder = order;
+ }
+
+ /** Return number of simplices. */
+ size_t size() const {
+ assert(order.size() == revorder.size());
+ return order.size();
+ }
+
+ /** Get i-th simplex in the simplex order. */
+ const simplex& get_simplex(index_type i) const {
+ assert(0 <= i && i < size());
+ return c.simplices[order.at(i)];
+ }
+
+ const simplcompltype& get_complex() const {
+ return c;
+ }
+
+ /** Returns true iff the faces of simplex i are before i in this order. */
+ bool is_filtration() const {
+ assert(size() == c.size());
+
+ for (unsigned i=0; i < size(); ++i)
+ for (unsigned f=0; f < get_simplex(i).face_count(); ++f)
+ if (revorder[get_simplex(i).faces[f]] >= i)
+ return false;
+
+ return true;
+ }
+
+ /** Returns true iff is_filtration() gives true and values of simplices
+ * are monotone w.r.t. this order of simplices. */
+ bool is_monotone() const {
+ assert(size() == c.size());
+
+ for (unsigned i=1; i < size(); ++i)
+ if (get_simplex(i-1).value > get_simplex(i).value)
+ return false;
+
+ return is_filtration();
+ }
+
+ /** Randomize order. It has hardly any impact on runtime, but
+ * it makes cycles "nicer" when the simplice's function values
+ * are constant.
+ * */
+ void randomize_order() {
+ std::random_shuffle(order.begin(), order.end());
+ restore_revorder_from_order();
+ }
+
+ /** Sort simplices such that is_monotone() gives true. This
+ * requires that the complex's is_monotone() gave true
+ * beforehand.*/
+ void make_monotone_filtration() {
+ assert(c.is_monotone());
+
+ std::sort(order.begin(), order.end(), cmp_monotone_filtration(c));
+ restore_revorder_from_order();
+
+ assert(c.is_monotone());
+ assert(is_filtration());
+ assert(is_monotone());
+ }
+
+ /** Get the boundary matrix of the complex according to this order. */
+ boundary_matrix get_boundary_matrix() const {
+ boundary_matrix mat(size());
+
+ for (unsigned c=0; c < size(); ++c)
+ for(unsigned r=0; r < get_simplex(c).face_count(); ++r)
+ mat.set(revorder[get_simplex(c).faces[r]], c, true);
+
+ return mat;
+ }
+
+ private:
+ /** Reconstruct 'revorder' by inverting the permutation given by 'order'. */
+ void restore_revorder_from_order() {
+ // Make revorder * order the identity permutation
+ for (unsigned i=0; i < size(); ++i)
+ revorder[order[i]] = i;
+ }
+
+ /** The complex of which we consider a simplex order. */
+ const simplcompltype &c;
+
+ /** The i-th simplex in order is the order[i]-th simplex of the
+ * complex. 'order' can be seen as a permutation of the
+ * simplices saved in 'c'. */
+ std::vector<index_type> order;
+
+ /** The i-th simplex in the complex is the revorder[i]-th
+ * simplex in order. 'revorder' can be seen as the inverse
+ * permutation saved in 'order'. */
+ std::vector<index_type> revorder;
+ };
+
+ public:
+ simplicial_complex() {
+ // Add the one minus-one dimensional simplex
+ add_simplex(simplex::create_minusonedim_simplex());
+ }
+
+ /** Remove all simplices except the dummy simplex */
+ void clear() {
+ simplices.resize(1);
+ }
+
+ /** Return number of simplices. */
+ size_t size() const {
+ return simplices.size();
+ }
+
+ /** Add a simplex to the complex. The dimension of the faces must be
+ * dim-1, and they must already be part of the complex. Returns the
+ * index of the added simplex. */
+ index_type add_simplex(int dim, index_type* faces, value_type value) {
+ return add_simplex(simplex::create(dim, faces, value));
+ }
+
+ /** Add a simplex to the complex of at least dimension 1. The dimension
+ * of the faces must be dim-1, and they must already be part of the
+ * complex. The value of the simplex is set to the maximum value of its
+ * faces. Returns the index of the added simplex. */
+ index_type add_simplex(int dim, index_type* faces) {
+ assert(dim >= 1);
+
+ // Get max value of its faces
+ VT value = simplices[faces[0]].value;
+ for (size_t i=0; i < simplex::face_count_bydim(dim); ++i)
+ value = std::max(value, simplices[faces[i]].value);
+
+ return add_simplex(dim, faces, value);
+ }
+
+ /** Add a simplex to the complex. The dimension of the faces must be
+ * dim-1, and they must already be part of the complex. Returns the
+ * index of the added simplex. */
+ index_type add_simplex(simplex s) {
+ // Check requirements for faces
+ for (unsigned i=0; i < s.face_count(); ++i) {
+ // Faces are already in complex.
+ assert(s.faces[i] < size());
+ // Faces have dimension dim-1
+ assert(simplices[s.faces[i]].dim == s.dim-1);
+ }
+
+ // index_type must be large enough
+ assert(simplices.size() < std::numeric_limits<IT>::max());
+
+ index_type idx = simplices.size();
+ simplices.push_back(s);
+ return idx;
+ }
+
+ /** Add an array of simplices */
+ void add_simplices(simplex* sarray, size_t count) {
+ for (unsigned i=0; i < count; ++i)
+ add_simplex(sarray[i]);
+ }
+
+ /** Return true iff for each simplex i with dimension dim it holds that
+ * the faces of i are contained in the complex and have dimension dim-1. */
+ bool is_complex() const {
+ for (unsigned i=0; i < size(); ++i) {
+
+ const simplex &s = simplices[i];
+ for (unsigned f=0; f < s.face_count(); ++f) {
+
+ if (s.faces[f] >= size())
+ return false;
+
+ const simplex &face = simplices[s.faces[f]];
+ if (face.dim != s.dim-1)
+ return false;
+ }
+ }
+ return true;
+ }
+
+ /** Returns true iff simplex's values are monotone w.r.t.
+ * face-inclusion, i.e., for each simplex its value is not smaller than
+ * the values of its faces. Requires that is_complex() gives true. */
+ bool is_monotone() const {
+ assert(is_complex());
+
+ typename std::vector<simplex>::const_iterator it = ++simplices.begin();
+ for (; it != simplices.end(); ++it)
+ for (unsigned f=0; f < it->face_count(); ++f)
+ if (simplices[it->faces[f]].value > it->value)
+ return false;
+
+ return true;
+ }
+
+ private:
+ /** Compares (operator<) two simplices (i.e. indices) in a
+ * simplex_order w.r.t. lexicographical order on (value,
+ * dimension)-tuples. */
+ struct cmp_monotone_filtration {
+ const simplicial_complex &c;
+
+ cmp_monotone_filtration(const simplicial_complex &c) :
+ c(c){
+ }
+
+ bool operator()(index_type i, index_type j) {
+ const simplex& si = c.simplices[i];
+ const simplex& sj = c.simplices[j];
+
+ if (si.value < sj.value)
+ return true;
+ else if (si.value == sj.value)
+ return si.dim < sj.dim;
+ else
+ return false;
+ }
+ };
+
+ public:
+ /** A list of simplices */
+ std::vector<simplex> simplices;
+};
+
+}
+
+
+#endif
projects / libstick.git / blobdiff