136 lines
4.6 KiB
C++
136 lines
4.6 KiB
C++
// Copyright (C) 2017-2022 Yixuan Qiu <yixuan.qiu@cos.name>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at https://mozilla.org/MPL/2.0/.
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#ifndef SPECTRA_SPARSE_REGULAR_INVERSE_H
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#define SPECTRA_SPARSE_REGULAR_INVERSE_H
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#include <Eigen/Core>
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#include <Eigen/SparseCore>
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#include <Eigen/IterativeLinearSolvers>
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#include <stdexcept>
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namespace Spectra {
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///
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/// \ingroup MatOp
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///
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/// This class defines matrix operations required by the generalized eigen solver
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/// in the regular inverse mode. For a sparse and positive definite matrix \f$B\f$,
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/// it implements the matrix-vector product \f$y=Bx\f$ and the linear equation
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/// solving operation \f$y=B^{-1}x\f$.
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///
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/// This class is intended to be used with the SymGEigsSolver generalized eigen solver
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/// in the regular inverse mode.
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///
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/// \tparam Scalar_ The element type of the matrix, for example,
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/// `float`, `double`, and `long double`.
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/// \tparam Uplo Either `Eigen::Lower` or `Eigen::Upper`, indicating which
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/// triangular part of the matrix is used.
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/// \tparam Flags Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
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/// the storage format of the input matrix.
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/// \tparam StorageIndex The type of the indices for the sparse matrix.
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///
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template <typename Scalar_, int Uplo = Eigen::Lower, int Flags = Eigen::ColMajor, typename StorageIndex = int>
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class SparseRegularInverse
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{
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public:
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///
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/// Element type of the matrix.
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///
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using Scalar = Scalar_;
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private:
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using Index = Eigen::Index;
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using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
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using MapConstVec = Eigen::Map<const Vector>;
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using MapVec = Eigen::Map<Vector>;
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using SparseMatrix = Eigen::SparseMatrix<Scalar, Flags, StorageIndex>;
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using ConstGenericSparseMatrix = const Eigen::Ref<const SparseMatrix>;
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ConstGenericSparseMatrix m_mat;
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const Index m_n;
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Eigen::ConjugateGradient<SparseMatrix> m_cg;
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mutable CompInfo m_info;
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public:
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///
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/// Constructor to create the matrix operation object.
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///
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/// \param mat An **Eigen** sparse matrix object, whose type can be
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/// `Eigen::SparseMatrix<Scalar, ...>` or its mapped version
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/// `Eigen::Map<Eigen::SparseMatrix<Scalar, ...> >`.
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///
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template <typename Derived>
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SparseRegularInverse(const Eigen::SparseMatrixBase<Derived>& mat) :
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m_mat(mat), m_n(mat.rows())
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{
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static_assert(
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static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(SparseMatrix::IsRowMajor),
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"SparseRegularInverse: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
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if (mat.rows() != mat.cols())
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throw std::invalid_argument("SparseRegularInverse: matrix must be square");
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m_cg.compute(mat);
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m_info = (m_cg.info() == Eigen::Success) ?
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CompInfo::Successful :
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CompInfo::NumericalIssue;
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}
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///
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/// Return the number of rows of the underlying matrix.
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///
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Index rows() const { return m_n; }
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///
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/// Return the number of columns of the underlying matrix.
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///
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Index cols() const { return m_n; }
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///
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/// Returns the status of the computation.
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/// The full list of enumeration values can be found in \ref Enumerations.
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///
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CompInfo info() const { return m_info; }
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///
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/// Perform the solving operation \f$y=B^{-1}x\f$.
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///
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/// \param x_in Pointer to the \f$x\f$ vector.
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/// \param y_out Pointer to the \f$y\f$ vector.
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///
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// y_out = inv(B) * x_in
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void solve(const Scalar* x_in, Scalar* y_out) const
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{
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MapConstVec x(x_in, m_n);
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MapVec y(y_out, m_n);
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y.noalias() = m_cg.solve(x);
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m_info = (m_cg.info() == Eigen::Success) ?
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CompInfo::Successful :
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CompInfo::NotConverging;
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if (m_info != CompInfo::Successful)
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throw std::runtime_error("SparseRegularInverse: CG solver does not converge");
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}
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///
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/// Perform the matrix-vector multiplication operation \f$y=Bx\f$.
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///
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/// \param x_in Pointer to the \f$x\f$ vector.
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/// \param y_out Pointer to the \f$y\f$ vector.
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///
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// y_out = B * x_in
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void perform_op(const Scalar* x_in, Scalar* y_out) const
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{
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MapConstVec x(x_in, m_n);
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MapVec y(y_out, m_n);
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y.noalias() = m_mat.template selfadjointView<Uplo>() * x;
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}
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};
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} // namespace Spectra
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#endif // SPECTRA_SPARSE_REGULAR_INVERSE_H
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