| // This file is part of Eigen, a lightweight C++ template library |
| // for linear algebra. |
| // |
| // This Source Code Form is subject to the terms of the Mozilla |
| // Public License v. 2.0. If a copy of the MPL was not distributed |
| // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. |
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| /** |
| * \defgroup OrderingMethods_Module OrderingMethods module |
| * |
| * This module is currently for internal use only |
| * |
| * It defines various built-in and external ordering methods for sparse matrices. |
| * They are typically used to reduce the number of elements during |
| * the sparse matrix decomposition (LLT, LU, QR). |
| * Precisely, in a preprocessing step, a permutation matrix P is computed using |
| * those ordering methods and applied to the columns of the matrix. |
| * Using for instance the sparse Cholesky decomposition, it is expected that |
| * the nonzeros elements in LLT(A*P) will be much smaller than that in LLT(A). |
| * |
| * |
| * Usage : |
| * \code |
| * |
| * \endcode |
| * |
| * A simple usage is as a template parameter in the sparse decomposition classes : |
| * |
| * \code |
| * SparseLU<MatrixType, COLAMDOrdering<int> > solver; |
| * \endcode |
| * |
| * \code |
| * SparseQR<MatrixType, COLAMDOrdering<int> > solver; |
| * \endcode |
| * |
| * It is possible as well to call directly a particular ordering method for your own purpose, |
| * \code |
| * AMDOrdering<int> ordering; |
| * PermutationMatrix<Dynamic, Dynamic, int> perm; |
| * SparseMatrix<double> A; |
| * //Fill the matrix ... |
| * |
| * ordering(A, perm); // Call AMD |
| * \endcode |
| * |
| * \note Some of these methods (like AMD or METIS), need the sparsity pattern |
| * of the input matrix to be symmetric. When the matrix is structurally unsymmetric, |
| * Eigen computes internally the pattern of \f$A^T*A\f$ before calling the method. |
| * If your matrix is already symmetric (at leat in structure), you can avoid that |
| * by calling the method with a SelfAdjointView type. |
| * |
| * \code |
| * // Call the ordering on the pattern of the lower triangular matrix A |
| * ordering(A.selfadjointView<Lower>(), perm); |
| * \endcode |
| */ |
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