| // 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/. |
| // SPDX-FileCopyrightText: The Eigen Authors |
| // SPDX-License-Identifier: MPL-2.0 |
| |
| #ifndef EIGEN_STRUCTURED_MATRICES_MODULE_H |
| #define EIGEN_STRUCTURED_MATRICES_MODULE_H |
| |
| #include "../../Eigen/Core" |
| #include "../../Eigen/Eigenvalues" |
| #include "../../Eigen/LU" |
| #include "../../Eigen/SVD" |
| #include "../../Eigen/IterativeLinearSolvers" |
| #include "FFT" |
| |
| namespace Eigen { |
| |
| /** |
| * \defgroup StructuredMatrices_Module StructuredMatrices module |
| * |
| * This module provides lightweight operator types for displacement-structured |
| * matrices together with fast matrix-vector products and direct solvers: |
| * - \c Circulant : a circulant matrix, diagonalized by the DFT; |
| * - \c Toeplitz : a (possibly rectangular) Toeplitz matrix, multiplied in |
| * O(n log n) via circulant embedding; |
| * - \c Hankel : a (possibly rectangular) Hankel matrix -- a column-reversed |
| * Toeplitz matrix -- with the same O(n log n) products, and square solves |
| * through the Toeplitz equivalent; |
| * - \c KroneckerOperator : the Kronecker product of two dense or diagonal |
| * matrices as an implicit operator; products, solves, least squares, |
| * eigendecomposition, SVD, inverse and determinant all factor through the |
| * operands, and diagonal (in particular identity) factors are stored and |
| * applied in diagonal form; |
| * - \c DiagonalPlusLowRank : a diagonal matrix plus a rank-k correction, with |
| * O(nk) products and O(nk^2) Woodbury solves, closed under inversion; |
| * - \c Vandermonde : a Vandermonde matrix stored as its nodes, with Horner |
| * products and O(n^2) Björck-Pereyra primal/dual solves |
| * (\c BjorckPereyra). |
| * |
| * The operator types derive from \c EigenBase and store only compact generators |
| * or factors. The FFT-backed operators (\c Circulant, \c Toeplitz and \c Hankel) |
| * also keep a precomputed DFT symbol that every product reuses. |
| * The operator types derive from \c EigenBase and store only their generating |
| * vectors; the FFT-backed operators (\c Circulant, \c Toeplitz, \c Bccb) also |
| * keep a precomputed DFT symbol that every product reuses. |
| * Because they expose \c operator* returning an Eigen product expression, they |
| * also plug directly into the matrix-free iterative solvers |
| * (\c ConjugateGradient, \c GMRES, \c MINRES, ...) without forming the dense |
| * matrix; and since they hook into the evaluator system, they can be assigned |
| * to a dense matrix when an explicit representation is needed. Like every |
| * matrix-free operator, they carry no coefficient storage the default |
| * preconditioners could read, so the iterative solvers must be instantiated |
| * with \c IdentityPreconditioner. |
| * |
| * All operator types are closed under transposition (\c transpose(), |
| * \c conjugate(), \c adjoint() return operators of the same kind, the FFT-based |
| * ones reusing the cached symbol), which in particular feeds the least-squares |
| * solvers \c LSMR and \c LeastSquaresConjugateGradient (again with |
| * \c IdentityPreconditioner). |
| * The \c Circulant, \c Toeplitz and \c Hankel operators are closed under |
| * transposition (\c transpose(), |
| * \c conjugate(), \c adjoint() return operators of the same kind, reusing the |
| * cached symbol), which in particular feeds the least-squares solvers \c LSMR |
| * and \c LeastSquaresConjugateGradient (again with \c IdentityPreconditioner). |
| * \c Circulant additionally exposes its closed-form eigendecomposition and SVD |
| * in the Fourier basis, a pseudo-inverse (minimum-norm least-squares) solve, |
| * \c rank(), \c inverse() and \c determinant(). |
| * |
| * \code |
| * #include <unsupported/Eigen/StructuredMatrices> |
| * \endcode |
| */ |
| |
| } // namespace Eigen |
| |
| #include "../../Eigen/src/Core/util/DisableStupidWarnings.h" |
| |
| // IWYU pragma: begin_exports |
| #include "src/StructuredMatrices/StructuredMatrixUtils.h" |
| #include "src/StructuredMatrices/Circulant.h" |
| #include "src/StructuredMatrices/Toeplitz.h" |
| #include "src/StructuredMatrices/LookAheadLevinson.h" |
| #include "src/StructuredMatrices/Hankel.h" |
| #include "src/StructuredMatrices/KroneckerOperator.h" |
| #include "src/StructuredMatrices/DiagonalPlusLowRank.h" |
| #include "src/StructuredMatrices/Vandermonde.h" |
| // IWYU pragma: end_exports |
| |
| #include "../../Eigen/src/Core/util/ReenableStupidWarnings.h" |
| |
| #endif // EIGEN_STRUCTURED_MATRICES_MODULE_H |
