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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 DENSE_GEN_COMPLEX_SHIFT_SOLVE_H
#define DENSE_GEN_COMPLEX_SHIFT_SOLVE_H
#include <Eigen/Core>
#include <Eigen/LU>
#include <stdexcept>
namespace Spectra {
///
/// \ingroup MatOp
///
/// This class defines the complex shift-solve operation on a general real matrix \f$A\f$,
/// i.e., calculating \f$y=\mathrm{Re}\{(A-\sigma I)^{-1}x\}\f$ for any complex-valued
/// \f$\sigma\f$ and real-valued vector \f$x\f$. It is mainly used in the
/// GenEigsComplexShiftSolver eigen solver.
///
template <typename Scalar>
class DenseGenComplexShiftSolve
{
private:
typedef Eigen::Index Index;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
typedef Eigen::Map<const Vector> MapConstVec;
typedef Eigen::Map<Vector> MapVec;
typedef const Eigen::Ref<const Matrix> ConstGenericMatrix;
typedef std::complex<Scalar> Complex;
typedef Eigen::Matrix<Complex, Eigen::Dynamic, Eigen::Dynamic> ComplexMatrix;
typedef Eigen::Matrix<Complex, Eigen::Dynamic, 1> ComplexVector;
typedef Eigen::PartialPivLU<ComplexMatrix> ComplexSolver;
ConstGenericMatrix m_mat;
const Index m_n;
ComplexSolver m_solver;
ComplexVector m_x_cache;
public:
///
/// Constructor to create the matrix operation object.
///
/// \param mat An **Eigen** matrix object, whose type can be
/// `Eigen::Matrix<Scalar, ...>` (e.g. `Eigen::MatrixXd` and
/// `Eigen::MatrixXf`), or its mapped version
/// (e.g. `Eigen::Map<Eigen::MatrixXd>`).
///
DenseGenComplexShiftSolve(ConstGenericMatrix& mat) :
m_mat(mat), m_n(mat.rows())
{
if(mat.rows() != mat.cols())
throw std::invalid_argument("DenseGenComplexShiftSolve: 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 complex shift \f$\sigma\f$.
///
/// \param sigmar Real part of \f$\sigma\f$.
/// \param sigmai Imaginary part of \f$\sigma\f$.
///
void set_shift(Scalar sigmar, Scalar sigmai)
{
m_solver.compute(m_mat.template cast<Complex>() - Complex(sigmar, sigmai) * ComplexMatrix::Identity(m_n, m_n));
m_x_cache.resize(m_n);
m_x_cache.setZero();
}
///
/// Perform the complex shift-solve operation
/// \f$y=\mathrm{Re}\{(A-\sigma I)^{-1}x\}\f$.
///
/// \param x_in Pointer to the \f$x\f$ vector.
/// \param y_out Pointer to the \f$y\f$ vector.
///
// y_out = Re( inv(A - sigma * I) * x_in )
void perform_op(const Scalar* x_in, Scalar* y_out)
{
m_x_cache.real() = MapConstVec(x_in, m_n);
MapVec y(y_out, m_n);
y.noalias() = m_solver.solve(m_x_cache).real();
}
};
} // namespace Spectra
#endif // DENSE_GEN_COMPLEX_SHIFT_SOLVE_H
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