126 lines
4.0 KiB
C++
126 lines
4.0 KiB
C++
// Copyright (C) 2016-2022 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_DENSE_CHOLESKY_H
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#define SPECTRA_DENSE_CHOLESKY_H
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#include <Eigen/Core>
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#include <Eigen/Cholesky>
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#include <stdexcept>
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#include "../Util/CompInfo.h"
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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 the operations related to Cholesky decomposition on a
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/// positive definite matrix, \f$B=LL'\f$, where \f$L\f$ is a lower triangular
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/// matrix. It is mainly used in the SymGEigsSolver generalized eigen solver
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/// in the Cholesky decomposition 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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///
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template <typename Scalar_, int Uplo = Eigen::Lower, int Flags = Eigen::ColMajor>
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class DenseCholesky
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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 Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Flags>;
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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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const Index m_n;
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Eigen::LLT<Matrix, Uplo> m_decomp;
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CompInfo m_info; // status of the decomposition
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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** matrix object, whose type can be
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/// `Eigen::Matrix<Scalar, ...>` (e.g. `Eigen::MatrixXd` and
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/// `Eigen::MatrixXf`), or its mapped version
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/// (e.g. `Eigen::Map<Eigen::MatrixXd>`).
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///
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template <typename Derived>
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DenseCholesky(const Eigen::MatrixBase<Derived>& mat) :
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m_n(mat.rows()), m_info(CompInfo::NotComputed)
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{
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static_assert(
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static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(Matrix::IsRowMajor),
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"DenseCholesky: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
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if (m_n != mat.cols())
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throw std::invalid_argument("DenseCholesky: matrix must be square");
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m_decomp.compute(mat);
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m_info = (m_decomp.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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/// Returns 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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/// Returns 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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/// Performs the lower triangular solving operation \f$y=L^{-1}x\f$.
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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(L) * x_in
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void lower_triangular_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_decomp.matrixL().solve(x);
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}
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///
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/// Performs the upper triangular solving operation \f$y=(L')^{-1}x\f$.
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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(L') * x_in
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void upper_triangular_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_decomp.matrixU().solve(x);
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}
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};
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} // namespace Spectra
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#endif // SPECTRA_DENSE_CHOLESKY_H
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