SymGEigsCayleyOp.h

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// Copyright (C) 2020-2025 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 SPECTRA_SYM_GEIGS_CAYLEY_OP_H
#define SPECTRA_SYM_GEIGS_CAYLEY_OP_H
 
#include <Eigen/Core>
 
#include "../SymShiftInvert.h"
#include "../SparseSymMatProd.h"
 
namespace Spectra {
 
template <typename OpType = SymShiftInvert<double>,
          typename BOpType = SparseSymMatProd<double>>
class SymGEigsCayleyOp
{
public:
    using Scalar = typename OpType::Scalar;
 
private:
    using Index = Eigen::Index;
    using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
    using MapConstVec = Eigen::Map<const Vector>;
    using MapVec = Eigen::Map<Vector>;
 
    OpType& m_op;
    const BOpType& m_Bop;
    mutable Vector m_cache;  // temporary working space
    Scalar m_sigma;
 
public:
    SymGEigsCayleyOp(OpType& op, const BOpType& Bop) :
        m_op(op), m_Bop(Bop), m_cache(op.rows())
    {}
 
    SymGEigsCayleyOp(SymGEigsCayleyOp&& other) :
        m_op(other.m_op), m_Bop(other.m_Bop), m_sigma(other.m_sigma)
    {
        // We emulate the move constructor for Vector using Vector::swap()
        m_cache.swap(other.m_cache);
    }
 
    Index rows() const { return m_op.rows(); }
    Index cols() const { return m_op.rows(); }
 
    void set_shift(const Scalar& sigma)
    {
        m_op.set_shift(sigma);
        m_sigma = sigma;
    }
 
    // y_out = inv(A - sigma * B) * (A + sigma * B) * x_in
    void perform_op(const Scalar* x_in, Scalar* y_out) const
    {
        //   inv(A - sigma * B) * (A + sigma * B) * x
        // = inv(A - sigma * B) * (A - sigma * B + 2 * sigma * B) * x
        // = x + 2 * sigma * inv(A - sigma * B) * B * x
        m_Bop.perform_op(x_in, m_cache.data());
        m_op.perform_op(m_cache.data(), y_out);
        MapConstVec x(x_in, this->rows());
        MapVec y(y_out, this->rows());
        y.noalias() = x + (Scalar(2) * m_sigma) * y;
    }
};
 
}  // namespace Spectra
 
#endif  // SPECTRA_SYM_GEIGS_CAYLEY_OP_H