159 lines
3.8 KiB
C++
159 lines
3.8 KiB
C++
// Copyright (C) 2018-2022 Yixuan Qiu <yixuan.qiu@cos.name>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at https://mozilla.org/MPL/2.0/.
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#ifndef SPECTRA_ARNOLDI_OP_H
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#define SPECTRA_ARNOLDI_OP_H
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#include <Eigen/Core>
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#include <cmath> // std::sqrt
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namespace Spectra {
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///
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/// \ingroup Internals
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/// @{
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///
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///
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/// \defgroup Operators Operators
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///
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/// Different types of operators.
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///
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///
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/// \ingroup Operators
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///
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/// Operators used in the Arnoldi factorization.
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///
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template <typename Scalar, typename OpType, typename BOpType>
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class ArnoldiOp
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{
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private:
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using Index = Eigen::Index;
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using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
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const OpType& m_op;
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const BOpType& m_Bop;
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mutable Vector m_cache;
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public:
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ArnoldiOp(const OpType& op, const BOpType& Bop) :
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m_op(op), m_Bop(Bop), m_cache(op.rows())
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{}
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// Move constructor
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ArnoldiOp(ArnoldiOp&& other) :
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m_op(other.m_op), m_Bop(other.m_Bop)
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{
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// We emulate the move constructor for Vector using Vector::swap()
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m_cache.swap(other.m_cache);
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}
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inline Index rows() const { return m_op.rows(); }
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// In generalized eigenvalue problem Ax=lambda*Bx, define the inner product to be <x, y> = x'By.
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// For regular eigenvalue problems, it is the usual inner product <x, y> = x'y
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// Compute <x, y> = x'By
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// x and y are two vectors
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template <typename Arg1, typename Arg2>
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Scalar inner_product(const Arg1& x, const Arg2& y) const
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{
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m_Bop.perform_op(y.data(), m_cache.data());
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return x.dot(m_cache);
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}
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// Compute res = <X, y> = X'By
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// X is a matrix, y is a vector, res is a vector
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template <typename Arg1, typename Arg2>
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void trans_product(const Arg1& x, const Arg2& y, Eigen::Ref<Vector> res) const
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{
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m_Bop.perform_op(y.data(), m_cache.data());
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res.noalias() = x.transpose() * m_cache;
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}
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// B-norm of a vector, ||x||_B = sqrt(x'Bx)
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template <typename Arg>
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Scalar norm(const Arg& x) const
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{
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using std::sqrt;
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return sqrt(inner_product<Arg, Arg>(x, x));
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}
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// The "A" operator to generate the Krylov subspace
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inline void perform_op(const Scalar* x_in, Scalar* y_out) const
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{
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m_op.perform_op(x_in, y_out);
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}
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};
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///
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/// \ingroup Operators
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///
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/// Placeholder for the B-operator when \f$B = I\f$.
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///
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class IdentityBOp
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{};
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///
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/// \ingroup Operators
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///
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/// Partial specialization for the case \f$B = I\f$.
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///
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template <typename Scalar, typename OpType>
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class ArnoldiOp<Scalar, OpType, IdentityBOp>
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{
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private:
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using Index = Eigen::Index;
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using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
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const OpType& m_op;
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public:
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ArnoldiOp(const OpType& op, const IdentityBOp& /*Bop*/) :
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m_op(op)
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{}
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inline Index rows() const { return m_op.rows(); }
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// Compute <x, y> = x'y
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// x and y are two vectors
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template <typename Arg1, typename Arg2>
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Scalar inner_product(const Arg1& x, const Arg2& y) const
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{
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return x.dot(y);
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}
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// Compute res = <X, y> = X'y
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// X is a matrix, y is a vector, res is a vector
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template <typename Arg1, typename Arg2>
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void trans_product(const Arg1& x, const Arg2& y, Eigen::Ref<Vector> res) const
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{
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res.noalias() = x.transpose() * y;
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}
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// B-norm of a vector. For regular eigenvalue problems it is simply the L2 norm
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template <typename Arg>
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Scalar norm(const Arg& x) const
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{
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return x.norm();
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}
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// The "A" operator to generate the Krylov subspace
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inline void perform_op(const Scalar* x_in, Scalar* y_out) const
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{
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m_op.perform_op(x_in, y_out);
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}
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};
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///
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/// @}
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///
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} // namespace Spectra
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#endif // SPECTRA_ARNOLDI_OP_H
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