qr factorization

Optimal_bounding_box/include/CGAL/Optimal_bounding_box/linear_algebra.h

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+// Copyright (c) 2018 GeometryFactory (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+// You can redistribute it and/or modify it under the terms of the GNU
+// General Public License as published by the Free Software Foundation,
+// either version 3 of the License, or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0+
+//
+//
+// Author(s)     : Konstantinos Katrioplas
+
+#ifndef CGAL_OPTIMAL_BOUNDING_BOX_H
+#define CGAL_OPTIMAL_BOUNDING_BOX_H
+
+
+#include <Eigen/QR>
+
+
+namespace CGAL {
+namespace Optimal_bounding_box {
+
+
+template<typename EigenMatrix>
+void qr_factorization(EigenMatrix& A, EigenMatrix& Q)
+{
+  Eigen::HouseholderQR<EigenMatrix> qr(A);
+  Q = qr.householderQ();
+}
+
+
+
+}}
+
+
+
+
+
+
+#endif //CGAL_OPTIMAL_BOUNDING_BOX_H
+
+

Optimal_bounding_box/test/Optimal_bounding_box/CMakeLists.txt

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+# Created by the script cgal_create_CMakeLists
+# This is the CMake script for compiling a set of CGAL applications.
+
+project( Optimal_bounding_box_Tests )
+
+
+cmake_minimum_required(VERSION 2.6.2)
+if("${CMAKE_MAJOR_VERSION}.${CMAKE_MINOR_VERSION}" VERSION_GREATER 2.6)
+  if("${CMAKE_MAJOR_VERSION}.${CMAKE_MINOR_VERSION}.${CMAKE_PATCH_VERSION}" VERSION_GREATER 2.8.3)
+    cmake_policy(VERSION 2.8.4)
+  else()
+    cmake_policy(VERSION 2.6)
+  endif()
+endif()
+
+
+# CGAL and its components
+find_package( CGAL QUIET COMPONENTS  )
+
+if ( NOT CGAL_FOUND )
+
+  message(STATUS "This project requires the CGAL library, and will not be compiled.")
+  return()  
+
+endif()
+
+# include helper file
+include( ${CGAL_USE_FILE} )
+
+
+# Boost and its components
+find_package( Boost REQUIRED )
+
+if ( NOT Boost_FOUND )
+
+  message(STATUS "This project requires the Boost library, and will not be compiled.")
+
+  return()  
+
+endif()
+
+# include for local directory
+
+# include for local package
+include_directories( BEFORE ../../include )
+
+find_package(Eigen3 3.2.0) #(requires 3.2.0 or greater)
+
+find_package( TBB )
+
+include( CGAL_CreateSingleSourceCGALProgram )
+if (EIGEN3_FOUND)
+  include( ${EIGEN3_USE_FILE} )
+
+  create_single_source_cgal_program("test_linear_algebra_functions.cpp")
+  
+endif(EIGEN3_FOUND)
+
+

Optimal_bounding_box/test/Optimal_bounding_box/test_linear_algebra_functions.cpp

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+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Surface_mesh.h>
+
+#include <CGAL/Optimal_bounding_box/linear_algebra.h>
+
+#include <iostream>
+#include <fstream>
+
+#include <Eigen/Dense>
+
+//typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
+//typedef CGAL::Surface_mesh<K::Point_3> Surface_mesh;
+
+typedef Eigen::MatrixXf MatrixXf;
+
+
+bool assert_doubles(double d1, double d2, double epsilon)
+{
+  return (d1 < d2 + epsilon && d1 > d2 - epsilon) ? true : false;
+}
+
+
+void test_qr_factorization()
+{
+
+  MatrixXf A(3, 3);
+  A << 0.3011944, 0.9932761, 0.5483701,
+       0.5149142, 0.5973263, 0.5162336,
+       0.0039213, 0.0202949, 0.9240308;
+
+  MatrixXf Q;
+  CGAL::Optimal_bounding_box::qr_factorization(A, Q);
+
+  double epsilon = 1e-6;
+  CGAL_assertion(assert_doubles(Q(0,0), -0.504895, epsilon));
+  CGAL_assertion(assert_doubles(Q(0,1), 0.862834, epsilon));
+  CGAL_assertion(assert_doubles(Q(0,2), -0.024447, epsilon));
+  CGAL_assertion(assert_doubles(Q(1,0), -0.863156, epsilon));
+  CGAL_assertion(assert_doubles(Q(1,1), -0.504894, epsilon));
+  CGAL_assertion(assert_doubles(Q(1,2), 0.006687, epsilon));
+  CGAL_assertion(assert_doubles(Q(2,0), -0.006573, epsilon));
+  CGAL_assertion(assert_doubles(Q(2,1), 0.024478, epsilon));
+  CGAL_assertion(assert_doubles(Q(2,2), 0.999679, epsilon));
+
+
+}
+
+
+
+
+
+int main()
+{
+
+  test_qr_factorization();
+
+  return 0;
+}