DenseGenComplexShiftSolve.h

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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 {

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:
    DenseGenComplexShiftSolve(ConstGenericMatrix& mat) :
        m_mat(mat), m_n(mat.rows())
    {
        if (mat.rows() != mat.cols())
            throw std::invalid_argument("DenseGenComplexShiftSolve: matrix must be square");
    }

    Index rows() const { return m_n; }
    Index cols() const { return m_n; }

    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();
    }

    // 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