1 files changed, 77 insertions, 0 deletions
diff --git a/src/Coxeter_triangulation/include/gudhi/Coxeter_triangulation.h b/src/Coxeter_triangulation/include/gudhi/Coxeter_triangulation.h
new file mode 100644
index 00000000..de68acb6
--- /dev/null
+++ b/src/Coxeter_triangulation/include/gudhi/Coxeter_triangulation.h
@@ -0,0 +1,77 @@
+/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+ *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+ *    Author(s):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2019 Inria
+ *
+ *    Modification(s):
+ *      - YYYY/MM Author: Description of the modification
+ */
+
+#ifndef COXETER_TRIANGULATION_H_
+#define COXETER_TRIANGULATION_H_
+
+#include <vector>
+#include <cmath>  // for std::sqrt
+
+#include <boost/range/iterator_range.hpp>
+#include <boost/graph/graph_traits.hpp>
+#include <boost/graph/adjacency_list.hpp>
+
+#include <Eigen/Eigenvalues>
+#include <Eigen/Sparse>
+#include <Eigen/SVD>
+
+#include <gudhi/Freudenthal_triangulation.h>
+#include <gudhi/Permutahedral_representation.h>
+
+namespace Gudhi {
+
+namespace coxeter_triangulation {
+
+/**
+ * \class Coxeter_triangulation
+ * \brief A class that stores Coxeter triangulation of type \f$\tilde{A}_d\f$.
+ * This triangulation has the greatest simplex quality out of all linear transformations
+ * of the Freudenthal-Kuhn triangulation.
+ *
+ * \ingroup coxeter_triangulation
+ *
+ * \tparam Permutahedral_representation_ Type of a simplex given by a permutahedral representation.
+ *  Needs to be a model of SimplexInCoxeterTriangulation.
+ */
+template <class Permutahedral_representation_ =
+              Permutahedral_representation<std::vector<int>, std::vector<std::vector<std::size_t> > > >
+class Coxeter_triangulation : public Freudenthal_triangulation<Permutahedral_representation_> {
+  using Matrix = Eigen::MatrixXd;
+
+  Matrix root_matrix(unsigned d) {
+    Matrix cartan(Matrix::Identity(d, d));
+    for (unsigned i = 1; i < d; i++) {
+      cartan(i - 1, i) = -0.5;
+      cartan(i, i - 1) = -0.5;
+    }
+    Eigen::SelfAdjointEigenSolver<Matrix> saes(cartan);
+    Eigen::VectorXd sqrt_diag(d);
+    for (unsigned i = 0; i < d; ++i) sqrt_diag(i) = std::sqrt(saes.eigenvalues()[i]);
+
+    Matrix lower(Matrix::Ones(d, d));
+    lower = lower.triangularView<Eigen::Lower>();
+
+    Matrix result = (lower * saes.eigenvectors() * sqrt_diag.asDiagonal()).inverse();
+    return result;
+  }
+
+ public:
+  /** \brief Constructor of Coxeter triangulation of a given dimension.
+   * @param[in] dimension The dimension of the triangulation.
+   */
+  Coxeter_triangulation(std::size_t dimension)
+      : Freudenthal_triangulation<Permutahedral_representation_>(dimension, root_matrix(dimension)) {}
+};
+
+}  // namespace coxeter_triangulation
+
+}  // namespace Gudhi
+
+#endif