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// SPDX-License-Identifier: Apache-2.0
//
// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
// Copyright 2008-2016 National ICT Australia (NICTA)
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// ------------------------------------------------------------------------
namespace newarp
{
//! This class implements the eigen solver for real symmetric matrices.
template<typename eT, int SelectionRule, typename OpType>
class SymEigsSolver
{
protected:
const OpType& op; // object to conduct matrix operation, eg. matrix-vector product
const uword nev; // number of eigenvalues requested
Col<eT> ritz_val; // ritz values
// Sort the first nev Ritz pairs in ascending algebraic order
// This is used to return the final results
virtual void sort_ritzpair();
private:
const uword dim_n; // dimension of matrix A
const uword ncv; // number of ritz values
uword nmatop; // number of matrix operations called
uword niter; // number of restarting iterations
Mat<eT> fac_V; // V matrix in the Arnoldi factorisation
Mat<eT> fac_H; // H matrix in the Arnoldi factorisation
Col<eT> fac_f; // residual in the Arnoldi factorisation
Mat<eT> ritz_vec; // ritz vectors
Col<eT> ritz_est; // last row of ritz_vec
std::vector<bool> ritz_conv; // indicator of the convergence of ritz values
const eT eps; // the machine precision
// eg. ~= 1e-16 for double type
const eT eps23; // eps^(2/3), used in convergence test
// tol*eps23 is the absolute tolerance
const eT near0; // a very small value, but 1/near0 does not overflow
std::mt19937_64 local_rng; // local random number generator
inline void fill_rand(eT* dest, const uword N, const uword seed_val);
// Arnoldi factorisation starting from step-k
inline void factorise_from(uword from_k, uword to_m, const Col<eT>& fk);
// Implicitly restarted Arnoldi factorisation
inline void restart(uword k);
// Calculate the number of converged Ritz values
inline uword num_converged(eT tol);
// Return the adjusted nev for restarting
inline uword nev_adjusted(uword nconv);
// Retrieve and sort ritz values and ritz vectors
inline void retrieve_ritzpair();
public:
//! Constructor to create a solver object.
inline SymEigsSolver(const OpType& op_, uword nev_, uword ncv_);
//! Providing the initial residual vector for the algorithm.
inline void init(eT* init_resid);
//! Providing a random initial residual vector.
inline void init();
//! Conducting the major computation procedure.
inline uword compute(uword maxit = 1000, eT tol = 1e-10);
//! Returning the number of iterations used in the computation.
inline uword num_iterations() { return niter; }
//! Returning the number of matrix operations used in the computation.
inline uword num_operations() { return nmatop; }
//! Returning the converged eigenvalues.
inline Col<eT> eigenvalues();
//! Returning the eigenvectors associated with the converged eigenvalues.
inline Mat<eT> eigenvectors(uword nvec);
//! Returning all converged eigenvectors.
inline Mat<eT> eigenvectors() { return eigenvectors(nev); }
};
} // namespace newarp
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