86 lines
3.4 KiB
C++
86 lines
3.4 KiB
C++
// Copyright (C) 2016-2022 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_GEN_EIGS_REAL_SHIFT_SOLVER_H
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#define SPECTRA_GEN_EIGS_REAL_SHIFT_SOLVER_H
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#include <Eigen/Core>
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#include "GenEigsBase.h"
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#include "Util/SelectionRule.h"
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#include "MatOp/DenseGenRealShiftSolve.h"
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namespace Spectra {
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///
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/// \ingroup EigenSolver
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///
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/// This class implements the eigen solver for general real matrices with
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/// a real shift value in the **shift-and-invert mode**. The background
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/// knowledge of the shift-and-invert mode can be found in the documentation
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/// of the SymEigsShiftSolver class.
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///
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/// \tparam OpType The name of the matrix operation class. Users could either
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/// use the wrapper classes such as DenseGenRealShiftSolve and
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/// SparseGenRealShiftSolve, or define their own that implements the type
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/// definition `Scalar` and all the public member functions as in
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/// DenseGenRealShiftSolve.
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///
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template <typename OpType = DenseGenRealShiftSolve<double>>
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class GenEigsRealShiftSolver : public GenEigsBase<OpType, IdentityBOp>
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{
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private:
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using Scalar = typename OpType::Scalar;
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using Index = Eigen::Index;
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using Complex = std::complex<Scalar>;
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using ComplexArray = Eigen::Array<Complex, Eigen::Dynamic, 1>;
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using Base = GenEigsBase<OpType, IdentityBOp>;
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using Base::m_nev;
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using Base::m_ritz_val;
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const Scalar m_sigma;
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// First transform back the Ritz values, and then sort
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void sort_ritzpair(SortRule sort_rule) override
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{
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// The eigenvalues we get from the iteration is nu = 1 / (lambda - sigma)
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// So the eigenvalues of the original problem is lambda = 1 / nu + sigma
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m_ritz_val.head(m_nev) = Scalar(1) / m_ritz_val.head(m_nev).array() + m_sigma;
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Base::sort_ritzpair(sort_rule);
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}
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public:
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///
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/// Constructor to create a eigen solver object using the shift-and-invert mode.
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///
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/// \param op The matrix operation object that implements
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/// the shift-solve operation of \f$A\f$: calculating
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/// \f$(A-\sigma I)^{-1}v\f$ for any vector \f$v\f$. Users could either
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/// create the object from the wrapper class such as DenseGenRealShiftSolve, or
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/// define their own that implements all the public members
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/// as in DenseGenRealShiftSolve.
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/// \param nev Number of eigenvalues requested. This should satisfy \f$1\le nev \le n-2\f$,
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/// where \f$n\f$ is the size of matrix.
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/// \param ncv Parameter that controls the convergence speed of the algorithm.
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/// Typically a larger `ncv` means faster convergence, but it may
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/// also result in greater memory use and more matrix operations
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/// in each iteration. This parameter must satisfy \f$nev+2 \le ncv \le n\f$,
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/// and is advised to take \f$ncv \ge 2\cdot nev + 1\f$.
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/// \param sigma The real-valued shift.
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///
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GenEigsRealShiftSolver(OpType& op, Index nev, Index ncv, const Scalar& sigma) :
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Base(op, IdentityBOp(), nev, ncv),
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m_sigma(sigma)
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{
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op.set_shift(m_sigma);
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}
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};
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} // namespace Spectra
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#endif // SPECTRA_GEN_EIGS_REAL_SHIFT_SOLVER_H
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