mirror of https://github.com/CGAL/cgal
135 lines
4.9 KiB
Plaintext
135 lines
4.9 KiB
Plaintext
namespace CGAL {
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/*!
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\mainpage User Manual
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\anchor Chapter_CGAL_and_Solvers
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\anchor chapterSolvers
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\cgalAutoToc
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\authors Simon Giraudot, Pierre Alliez, Frédéric Cazals, Gaël Guennebaud, Bruno Lévy, Marc Pouget, Laurent Saboret, and Liangliang Nan
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Several \cgal packages have to solve linear systems with dense or
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sparse matrices, linear integer programs. This package provides
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concepts and models for that purpose.
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For linear systems, we generally provide models using the
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\ref thirdpartyEigen library. Wrappers for the Eigen classes
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`Eigen_matrix` and `Eigen_vector` are also provided when needed.
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It is straightforward to develop equivalent models for
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other solvers, for example those found in the <a
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href="https://software.intel.com/en-us/mkl">Intel Math Kernel
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Library (MKL)</a>.
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For mixed integer programs (either constrained or unconstrained),
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we provide models using \ref thirdpartySCIP and \ref thirdpartyGLPK
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libraries. It is also possible to derive new models from other
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high performance libraries, e.g.,
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<a href = "https://projects.coin-or.org/Cbc"> CBC </a>,
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<a href = "http://www.gurobi.com/"> Gurobi </a>.
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\section SectionSolverDiagonalize Matrix Diagonalization
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The concept `DiagonalizeTraits<T,dim>` defines an interface for the
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diagonalization and computation of eigenvectors and eigenvalues of a
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symmetric matrix. `T` is the number type and `dim` is the dimension of
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the matrices and vector (set to 3 by default). We provide the model
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`Eigen_diagonalize_traits<T,dim>` that uses the \ref thirdpartyEigen library.
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This is an example of an eigen decomposition of a matrix using this
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class:
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\cgalExample{Solver_interface/diagonalize_matrix.cpp}
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\section SectionSolverSVD Singular Value Decomposition
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The concept `SvdTraits` defines an interface for solving in the least
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square sense a linear system with a singular value decomposition. The
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field type is `double`. We provide the model `Eigen_svd` that uses the
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\ref thirdpartyEigen library.
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Here is a simple example that shows how to handle matrices, vectors
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and this solver:
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\cgalExample{Solver_interface/singular_value_decomposition.cpp}
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\section SectionSolverSparse Sparse Solvers
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We define 3 concepts for sparse linear algebra:
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- `SparseLinearAlgebraTraits_d`
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- `SparseLinearAlgebraWithFactorTraits_d`
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- `NormalEquationSparseLinearAlgebraTraits_d`
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An interface to the sparse solvers from the \ref thirdpartyEigen
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library is provided as a model for these 3 concepts through the class
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`Eigen_solver_traits<T>`. This solver traits class can be used for an
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iterative or a direct, symmetric or general sparse solvers. The
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specific solver to be used must be given as template parameter.
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Each \cgal package using a sparse solver specifies which type of matrix
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and solver is required:
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\code{.cpp}
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typedef CGAL::Eigen_sparse_matrix<double>::EigenType EigenMatrix;
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//iterative general solver
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typedef CGAL::Eigen_solver_traits< Eigen::BiCGSTAB<EigenMatrix> > Iterative_general_solver;
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//iterative symmetric solver
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typedef CGAL::Eigen_solver_traits< Eigen::ConjugateGradient<EigenMatrix> > Iterative_symmetric_solver;
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//direct symmetric solver
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typedef CGAL::Eigen_solver_traits< Eigen::SimplicialCholesky<EigenMatrix> > Direct_symmetric_solver;
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\endcode
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Here is an example that shows how to fill the sparse matrix and call
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the solver:
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\cgalExample{Solver_interface/sparse_solvers.cpp}
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\section SectionMIPSolver Mixed Integer Program Solvers
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The concept `MixedIntegerProgramTraits` defines an interface for
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formulating and solving (constrained or unconstrained) mixed integer
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programs. It can also be used for general linear programs.
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The field type is `double`. We provide two models of this concept:
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`CGAL::GLPK_mixed_integer_program_traits` using \ref thirdpartyGLPK and
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`CGAL::SCIP_mixed_integer_program_traits` using \ref thirdpartySCIP.
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Here is an example that shows how to formulate and solve a simple
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mixed integer program using this solver.
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\cgalExample{Solver_interface/mixed_integer_program.cpp}
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\section SolversHistory Implementation History
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This package is the result of the increasing needs for linear solvers
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in \cgal. The first packages that introduced the solver concepts were
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\ref PkgSurfaceMeshParameterization, \ref PkgPoissonSurfaceReconstruction3
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and \ref PkgJetFitting3. At that time, these packages were relying
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on \sc{Taucs}, \sc{LAPACK}, \sc{BLAS} and \sc{OpenNL}. Gaël Guennebaud
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then introduced new models using the \ref thirdpartyEigen library that
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became the only supported models by \cgal. Later on the packages \ref
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PkgSurfaceMeshSkeletonization and \ref PkgSurfaceMeshDeformation
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extended the existing concepts. Liangliang Nan introduced the concept
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`MixedIntegerProgramTraits` and two models for solving mixed integer
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programs when implementing the \ref PkgPolygonalSurfaceReconstruction
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package.
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Simon Giraudot was responsible for gathering all concepts and classes, and also wrote this user manual
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with the help of Andreas Fabri.
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*/
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} /* namespace CGAL */
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