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// Copyright (C) 2016-2019 Yixuan Qiu <yixuan.qiu@cos.name>
//
// 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 https://mozilla.org/MPL/2.0/.
#ifndef SPARSE_GEN_REAL_SHIFT_SOLVE_H
#define SPARSE_GEN_REAL_SHIFT_SOLVE_H
#include <Eigen/Core>
#include <Eigen/SparseCore>
#include <Eigen/SparseLU>
#include <stdexcept>
namespace Spectra {
///
/// \ingroup MatOp
///
/// This class defines the shift-solve operation on a sparse real matrix \f$A\f$,
/// i.e., calculating \f$y=(A-\sigma I)^{-1}x\f$ for any real \f$\sigma\f$ and
/// vector \f$x\f$. It is mainly used in the GenEigsRealShiftSolver eigen solver.
///
template <typename Scalar,int Flags = 0, typename StorageIndex = int>
class SparseGenRealShiftSolve
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef Eigen::SparseMatrix<Scalar, Flags, StorageIndex> SparseMatrix;
typedef const Eigen::Ref<const SparseMatrix> ConstGenericSparseMatrix;
ConstGenericSparseMatrix m_mat;
const int m_n;
Eigen::SparseLU<SparseMatrix> m_solver;
public:
///
/// Constructor to create the matrix operation object.
///
/// \param mat An **Eigen** sparse matrix object, whose type can be
/// `Eigen::SparseMatrix<Scalar, ...>` or its mapped version
/// `Eigen::Map<Eigen::SparseMatrix<Scalar, ...> >`.
///
SparseGenRealShiftSolve(ConstGenericSparseMatrix& mat) :
m_mat(mat), m_n(mat.rows())
{
if(mat.rows() != mat.cols())
throw std::invalid_argument("SparseGenRealShiftSolve: matrix must be square");
}
///
/// Return the number of rows of the underlying matrix.
///
Index rows() const { return m_n; }
///
/// Return the number of columns of the underlying matrix.
///
Index cols() const { return m_n; }
///
/// Set the real shift \f$\sigma\f$.
///
void set_shift(Scalar sigma)
{
SparseMatrix I(m_n, m_n);
I.setIdentity();
m_solver.compute(m_mat - sigma * I);
if(m_solver.info() != Eigen::Success)
throw std::invalid_argument("SparseGenRealShiftSolve: factorization failed with the given shift");
}
///
/// Perform the shift-solve operation \f$y=(A-\sigma I)^{-1}x\f$.
///
/// \param x_in Pointer to the \f$x\f$ vector.
/// \param y_out Pointer to the \f$y\f$ vector.
///
// y_out = inv(A - sigma * I) * x_in
void perform_op(const Scalar* x_in, Scalar* y_out) const
{
MapConstVec x(x_in, m_n);
MapVec y(y_out, m_n);
y.noalias() = m_solver.solve(x);
}
};
} // namespace Spectra
#endif // SPARSE_GEN_REAL_SHIFT_SOLVE_H
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