106 lines
3.1 KiB
C
106 lines
3.1 KiB
C
|
// Copyright (C) 2020-2022 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 {
|
||
|
|
|
||
|
|
///
|
||
|
|
/// \ingroup Operators
|
||
|
|
///
|
||
|
|
/// This class defines the matrix operation for generalized eigen solver in the
|
||
|
|
/// Cayley mode. It computes \f$y=(A-\sigma B)^{-1}(A+\sigma B)x\f$ for any
|
||
|
|
/// vector \f$x\f$, where \f$A\f$ is a symmetric matrix, \f$B\f$ is positive definite,
|
||
|
|
/// and \f$\sigma\f$ is a real shift.
|
||
|
|
/// This class is intended for internal use.
|
||
|
|
///
|
||
|
|
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:
|
||
|
|
///
|
||
|
|
/// Constructor to create the matrix operation object.
|
||
|
|
///
|
||
|
|
/// \param op The \f$(A-\sigma B)^{-1}\f$ matrix operation object.
|
||
|
|
/// \param Bop The \f$B\f$ matrix operation object.
|
||
|
|
///
|
||
|
|
SymGEigsCayleyOp(OpType& op, const BOpType& Bop) :
|
||
|
|
m_op(op), m_Bop(Bop), m_cache(op.rows())
|
||
|
|
{}
|
||
|
|
|
||
|
|
///
|
||
|
|
/// Move constructor.
|
||
|
|
///
|
||
|
|
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);
|
||
|
|
}
|
||
|
|
|
||
|
|
///
|
||
|
|
/// Return the number of rows of the underlying matrix.
|
||
|
|
///
|
||
|
|
Index rows() const { return m_op.rows(); }
|
||
|
|
///
|
||
|
|
/// Return the number of columns of the underlying matrix.
|
||
|
|
///
|
||
|
|
Index cols() const { return m_op.rows(); }
|
||
|
|
|
||
|
|
///
|
||
|
|
/// Set the real shift \f$\sigma\f$.
|
||
|
|
///
|
||
|
|
void set_shift(const Scalar& sigma)
|
||
|
|
{
|
||
|
|
m_op.set_shift(sigma);
|
||
|
|
m_sigma = sigma;
|
||
|
|
}
|
||
|
|
|
||
|
|
///
|
||
|
|
/// Perform the matrix operation \f$y=(A-\sigma B)^{-1}(A+\sigma B)x\f$.
|
||
|
|
///
|
||
|
|
/// \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 * 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
|