110 lines
4.2 KiB
C++
110 lines
4.2 KiB
C++
// SPDX-License-Identifier: Apache-2.0
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//
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// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
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// Copyright 2008-2016 National ICT Australia (NICTA)
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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// ------------------------------------------------------------------------
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namespace newarp
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{
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//! This class implements the eigen solver for general real matrices.
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template<typename eT, int SelectionRule, typename OpType>
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class GenEigsSolver
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{
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protected:
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const OpType& op; // object to conduct matrix operation, eg. matrix-vector product
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const uword nev; // number of eigenvalues requested
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Col< std::complex<eT> > ritz_val; // ritz values
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// Sort the first nev Ritz pairs in decreasing magnitude order
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// This is used to return the final results
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virtual void sort_ritzpair();
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private:
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const uword dim_n; // dimension of matrix A
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const uword ncv; // number of ritz values
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uword nmatop; // number of matrix operations called
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uword niter; // number of restarting iterations
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Mat<eT> fac_V; // V matrix in the Arnoldi factorisation
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Mat<eT> fac_H; // H matrix in the Arnoldi factorisation
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Col<eT> fac_f; // residual in the Arnoldi factorisation
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Mat< std::complex<eT> > ritz_vec; // ritz vectors
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Col< std::complex<eT> > ritz_est; // last row of ritz_vec
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std::vector<bool> ritz_conv; // indicator of the convergence of ritz values
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const eT eps; // the machine precision
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// eg. ~= 1e-16 for double type
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const eT approx0; // a number that is approximately zero
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// approx0 = eps^(2/3)
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// used to test the orthogonality of vectors,
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// and in convergence test, tol*approx0 is
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// the absolute tolerance
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std::mt19937_64 local_rng; // local random number generator
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inline void fill_rand(eT* dest, const uword N, const uword seed_val);
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// Arnoldi factorisation starting from step-k
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inline void factorise_from(uword from_k, uword to_m, const Col<eT>& fk);
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// Implicitly restarted Arnoldi factorisation
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inline void restart(uword k);
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// Calculate the number of converged Ritz values
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inline uword num_converged(eT tol);
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// Return the adjusted nev for restarting
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inline uword nev_adjusted(uword nconv);
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// Retrieve and sort ritz values and ritz vectors
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inline void retrieve_ritzpair();
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public:
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//! Constructor to create a solver object.
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inline GenEigsSolver(const OpType& op_, uword nev_, uword ncv_);
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//! Providing the initial residual vector for the algorithm.
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inline void init(eT* init_resid);
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//! Providing a random initial residual vector.
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inline void init();
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//! Conducting the major computation procedure.
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inline uword compute(uword maxit = 1000, eT tol = 1e-10);
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//! Returning the number of iterations used in the computation.
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inline int num_iterations() { return niter; }
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//! Returning the number of matrix operations used in the computation.
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inline int num_operations() { return nmatop; }
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//! Returning the converged eigenvalues.
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inline Col< std::complex<eT> > eigenvalues();
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//! Returning the eigenvectors associated with the converged eigenvalues.
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inline Mat< std::complex<eT> > eigenvectors(uword nvec);
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//! Returning all converged eigenvectors.
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inline Mat< std::complex<eT> > eigenvectors() { return eigenvectors(nev); }
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};
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} // namespace newarp
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