353 lines
9.2 KiB
C++
353 lines
9.2 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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//! \addtogroup fn_svds
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//! @{
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template<typename T1>
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inline
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bool
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svds_helper
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(
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Mat<typename T1::elem_type>& U,
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Col<typename T1::pod_type >& S,
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Mat<typename T1::elem_type>& V,
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const SpBase<typename T1::elem_type,T1>& X,
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const uword k,
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const typename T1::pod_type tol,
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const bool calc_UV,
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const typename arma_real_only<typename T1::elem_type>::result* junk = nullptr
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)
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{
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arma_extra_debug_sigprint();
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arma_ignore(junk);
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typedef typename T1::elem_type eT;
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typedef typename T1::pod_type T;
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arma_debug_check
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(
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( ((void*)(&U) == (void*)(&S)) || (&U == &V) || ((void*)(&S) == (void*)(&V)) ),
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"svds(): two or more output objects are the same object"
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);
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arma_debug_check( (tol < T(0)), "svds(): tol must be >= 0" );
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const unwrap_spmat<T1> tmp(X.get_ref());
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const SpMat<eT>& A = tmp.M;
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const uword kk = (std::min)( (std::min)(A.n_rows, A.n_cols), k );
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const T A_max = (A.n_nonzero > 0) ? T(max(abs(Col<eT>(const_cast<eT*>(A.values), A.n_nonzero, false)))) : T(0);
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if(A_max == T(0))
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{
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// TODO: use reset instead ?
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S.zeros(kk);
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if(calc_UV)
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{
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U.eye(A.n_rows, kk);
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V.eye(A.n_cols, kk);
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}
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}
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else
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{
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SpMat<eT> C( (A.n_rows + A.n_cols), (A.n_rows + A.n_cols) );
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SpMat<eT> B = A / A_max;
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SpMat<eT> Bt = B.t();
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C(0, A.n_rows, arma::size(B) ) = B;
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C(A.n_rows, 0, arma::size(Bt)) = Bt;
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Bt.reset();
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B.reset();
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Col<eT> eigval;
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Mat<eT> eigvec;
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eigs_opts opts;
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opts.tol = (tol / Datum<T>::sqrt2);
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const bool status = eigs_sym(eigval, eigvec, C, kk, "la", opts);
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if(status == false)
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{
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U.soft_reset();
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S.soft_reset();
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V.soft_reset();
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return false;
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}
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const T A_norm = max(eigval);
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const T tol2 = tol / Datum<T>::sqrt2 * A_norm;
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uvec indices = find(eigval > tol2);
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if(indices.n_elem > kk)
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{
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indices = indices.subvec(0,kk-1);
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}
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else
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if(indices.n_elem < kk)
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{
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const uvec indices2 = find(abs(eigval) <= tol2);
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const uword N_extra = (std::min)( indices2.n_elem, (kk - indices.n_elem) );
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if(N_extra > 0) { indices = join_cols(indices, indices2.subvec(0,N_extra-1)); }
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}
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const uvec sorted_indices = sort_index(eigval, "descend");
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S = eigval.elem(sorted_indices); S *= A_max;
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if(calc_UV)
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{
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uvec U_row_indices(A.n_rows, arma_nozeros_indicator()); for(uword i=0; i < A.n_rows; ++i) { U_row_indices[i] = i; }
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uvec V_row_indices(A.n_cols, arma_nozeros_indicator()); for(uword i=0; i < A.n_cols; ++i) { V_row_indices[i] = i + A.n_rows; }
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U = Datum<T>::sqrt2 * eigvec(U_row_indices, sorted_indices);
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V = Datum<T>::sqrt2 * eigvec(V_row_indices, sorted_indices);
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}
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}
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if(S.n_elem < k) { arma_debug_warn_level(1, "svds(): found fewer singular values than specified"); }
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return true;
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}
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template<typename T1>
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inline
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bool
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svds_helper
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(
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Mat<typename T1::elem_type>& U,
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Col<typename T1::pod_type >& S,
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Mat<typename T1::elem_type>& V,
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const SpBase<typename T1::elem_type,T1>& X,
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const uword k,
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const typename T1::pod_type tol,
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const bool calc_UV,
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const typename arma_cx_only<typename T1::elem_type>::result* junk = nullptr
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)
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{
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arma_extra_debug_sigprint();
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arma_ignore(junk);
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typedef typename T1::elem_type eT;
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typedef typename T1::pod_type T;
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if(arma_config::arpack == false)
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{
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arma_stop_logic_error("svds(): use of ARPACK must be enabled for decomposition of complex matrices");
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return false;
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}
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arma_debug_check
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(
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( ((void*)(&U) == (void*)(&S)) || (&U == &V) || ((void*)(&S) == (void*)(&V)) ),
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"svds(): two or more output objects are the same object"
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);
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arma_debug_check( (tol < T(0)), "svds(): tol must be >= 0" );
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const unwrap_spmat<T1> tmp(X.get_ref());
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const SpMat<eT>& A = tmp.M;
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const uword kk = (std::min)( (std::min)(A.n_rows, A.n_cols), k );
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const T A_max = (A.n_nonzero > 0) ? T(max(abs(Col<eT>(const_cast<eT*>(A.values), A.n_nonzero, false)))) : T(0);
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if(A_max == T(0))
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{
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// TODO: use reset instead ?
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S.zeros(kk);
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if(calc_UV)
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{
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U.eye(A.n_rows, kk);
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V.eye(A.n_cols, kk);
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}
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}
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else
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{
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SpMat<eT> C( (A.n_rows + A.n_cols), (A.n_rows + A.n_cols) );
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SpMat<eT> B = A / A_max;
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SpMat<eT> Bt = B.t();
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C(0, A.n_rows, arma::size(B) ) = B;
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C(A.n_rows, 0, arma::size(Bt)) = Bt;
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Bt.reset();
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B.reset();
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Col<eT> eigval_tmp;
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Mat<eT> eigvec;
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eigs_opts opts;
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opts.tol = (tol / Datum<T>::sqrt2);
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const bool status = eigs_gen(eigval_tmp, eigvec, C, kk, "lr", opts);
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if(status == false)
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{
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U.soft_reset();
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S.soft_reset();
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V.soft_reset();
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return false;
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}
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const Col<T> eigval = real(eigval_tmp);
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const T A_norm = max(eigval);
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const T tol2 = tol / Datum<T>::sqrt2 * A_norm;
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uvec indices = find(eigval > tol2);
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if(indices.n_elem > kk)
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{
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indices = indices.subvec(0,kk-1);
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}
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else
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if(indices.n_elem < kk)
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{
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const uvec indices2 = find(abs(eigval) <= tol2);
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const uword N_extra = (std::min)( indices2.n_elem, (kk - indices.n_elem) );
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if(N_extra > 0) { indices = join_cols(indices, indices2.subvec(0,N_extra-1)); }
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}
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const uvec sorted_indices = sort_index(eigval, "descend");
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S = eigval.elem(sorted_indices); S *= A_max;
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if(calc_UV)
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{
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uvec U_row_indices(A.n_rows, arma_nozeros_indicator()); for(uword i=0; i < A.n_rows; ++i) { U_row_indices[i] = i; }
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uvec V_row_indices(A.n_cols, arma_nozeros_indicator()); for(uword i=0; i < A.n_cols; ++i) { V_row_indices[i] = i + A.n_rows; }
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U = Datum<T>::sqrt2 * eigvec(U_row_indices, sorted_indices);
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V = Datum<T>::sqrt2 * eigvec(V_row_indices, sorted_indices);
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}
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}
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if(S.n_elem < k) { arma_debug_warn_level(1, "svds(): found fewer singular values than specified"); }
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return true;
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}
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//! find the k largest singular values and corresponding singular vectors of sparse matrix X
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template<typename T1>
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inline
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bool
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svds
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(
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Mat<typename T1::elem_type>& U,
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Col<typename T1::pod_type >& S,
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Mat<typename T1::elem_type>& V,
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const SpBase<typename T1::elem_type,T1>& X,
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const uword k,
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const typename T1::pod_type tol = 0.0,
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const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = nullptr
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)
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{
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arma_extra_debug_sigprint();
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arma_ignore(junk);
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const bool status = svds_helper(U, S, V, X.get_ref(), k, tol, true);
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if(status == false) { arma_debug_warn_level(3, "svds(): decomposition failed"); }
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return status;
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}
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//! find the k largest singular values of sparse matrix X
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template<typename T1>
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inline
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bool
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svds
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(
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Col<typename T1::pod_type >& S,
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const SpBase<typename T1::elem_type,T1>& X,
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const uword k,
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const typename T1::pod_type tol = 0.0,
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const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = nullptr
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)
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{
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arma_extra_debug_sigprint();
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arma_ignore(junk);
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Mat<typename T1::elem_type> U;
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Mat<typename T1::elem_type> V;
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const bool status = svds_helper(U, S, V, X.get_ref(), k, tol, false);
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if(status == false) { arma_debug_warn_level(3, "svds(): decomposition failed"); }
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return status;
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}
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//! find the k largest singular values of sparse matrix X
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template<typename T1>
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arma_warn_unused
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inline
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Col<typename T1::pod_type>
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svds
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(
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const SpBase<typename T1::elem_type,T1>& X,
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const uword k,
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const typename T1::pod_type tol = 0.0,
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const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = nullptr
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)
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{
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arma_extra_debug_sigprint();
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arma_ignore(junk);
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Col<typename T1::pod_type> S;
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Mat<typename T1::elem_type> U;
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Mat<typename T1::elem_type> V;
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const bool status = svds_helper(U, S, V, X.get_ref(), k, tol, false);
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if(status == false) { arma_stop_runtime_error("svds(): decomposition failed"); }
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return S;
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}
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//! @}
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