| | // 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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