573 lines
13 KiB
C++
573 lines
13 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 op_logmat
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//! @{
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// Partly based on algorithm 11.9 (inverse scaling and squaring algorithm with Schur decomposition) in:
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// Nicholas J. Higham.
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// Functions of Matrices: Theory and Computation.
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// SIAM, 2008.
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// ISBN 978-0-89871-646-7
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template<typename T1>
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inline
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void
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op_logmat::apply(Mat< std::complex<typename T1::elem_type> >& out, const mtOp<std::complex<typename T1::elem_type>,T1,op_logmat>& in)
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{
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arma_debug_sigprint();
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const bool status = op_logmat::apply_direct(out, in.m, in.aux_uword_a);
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if(status == false)
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{
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out.soft_reset();
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arma_stop_runtime_error("logmat(): transformation failed");
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}
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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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op_logmat::apply_direct(Mat< std::complex<typename T1::elem_type> >& out, const Op<T1,op_diagmat>& expr, const uword)
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{
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arma_debug_sigprint();
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typedef typename T1::elem_type T;
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const diagmat_proxy<T1> P(expr.m);
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arma_conform_check( (P.n_rows != P.n_cols), "logmat(): given matrix must be square sized" );
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const uword N = P.n_rows;
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out.zeros(N,N); // aliasing can't happen as op_logmat is defined as cx_mat = op(mat)
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for(uword i=0; i<N; ++i)
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{
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const T val = P[i];
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if(val >= T(0))
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{
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out.at(i,i) = std::log(val);
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}
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else
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{
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out.at(i,i) = std::log( std::complex<T>(val) );
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}
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}
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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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op_logmat::apply_direct(Mat< std::complex<typename T1::elem_type> >& out, const Base<typename T1::elem_type,T1>& expr, const uword n_iters)
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{
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arma_debug_sigprint();
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typedef typename T1::elem_type in_T;
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typedef typename std::complex<in_T> out_T;
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const quasi_unwrap<T1> expr_unwrap(expr.get_ref());
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const Mat<in_T>& A = expr_unwrap.M;
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arma_conform_check( (A.is_square() == false), "logmat(): given matrix must be square sized" );
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if(A.n_elem == 0)
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{
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out.reset();
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return true;
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}
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else
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if(A.n_elem == 1)
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{
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out.set_size(1,1);
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out[0] = std::log( std::complex<in_T>( A[0] ) );
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return true;
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}
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if(A.is_diagmat())
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{
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arma_debug_print("op_logmat: diag optimisation");
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const uword N = A.n_rows;
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out.zeros(N,N); // aliasing can't happen as op_logmat is defined as cx_mat = op(mat)
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for(uword i=0; i<N; ++i)
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{
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const in_T val = A.at(i,i);
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if(val >= in_T(0))
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{
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out.at(i,i) = std::log(val);
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}
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else
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{
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out.at(i,i) = std::log( out_T(val) );
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}
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}
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return true;
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}
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const bool try_sympd = arma_config::optimise_sym && sym_helper::guess_sympd(A);
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if(try_sympd)
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{
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arma_debug_print("op_logmat: attempting sympd optimisation");
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// if matrix A is sympd, all its eigenvalues are positive
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Col<in_T> eigval;
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Mat<in_T> eigvec;
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const bool eig_status = eig_sym_helper(eigval, eigvec, A, 'd', "logmat()");
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if(eig_status)
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{
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// ensure each eigenvalue is > 0
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const uword N = eigval.n_elem;
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const in_T* eigval_mem = eigval.memptr();
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bool all_pos = true;
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for(uword i=0; i<N; ++i) { all_pos = (eigval_mem[i] <= in_T(0)) ? false : all_pos; }
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if(all_pos)
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{
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eigval = log(eigval);
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out = conv_to< Mat<out_T> >::from( eigvec * diagmat(eigval) * eigvec.t() );
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return true;
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}
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}
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arma_debug_print("op_logmat: sympd optimisation failed");
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// fallthrough if eigen decomposition failed or an eigenvalue is <= 0
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}
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Mat<out_T> S(A.n_rows, A.n_cols, arma_nozeros_indicator());
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const in_T* Amem = A.memptr();
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out_T* Smem = S.memptr();
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const uword n_elem = A.n_elem;
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for(uword i=0; i<n_elem; ++i)
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{
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Smem[i] = std::complex<in_T>( Amem[i] );
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}
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return op_logmat_cx::apply_common(out, S, n_iters);
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}
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template<typename T1>
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inline
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void
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op_logmat_cx::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_logmat_cx>& in)
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{
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arma_debug_sigprint();
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const bool status = op_logmat_cx::apply_direct(out, in.m, in.aux_uword_a);
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if(status == false)
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{
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out.soft_reset();
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arma_stop_runtime_error("logmat(): transformation failed");
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}
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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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op_logmat_cx::apply_direct(Mat<typename T1::elem_type>& out, const Op<T1,op_diagmat>& expr, const uword)
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{
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arma_debug_sigprint();
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typedef typename T1::elem_type eT;
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const diagmat_proxy<T1> P(expr.m);
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bool status = false;
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if(P.is_alias(out))
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{
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Mat<eT> tmp;
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status = op_logmat_cx::apply_direct_noalias(tmp, P);
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out.steal_mem(tmp);
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}
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else
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{
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status = op_logmat_cx::apply_direct_noalias(out, P);
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}
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return status;
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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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op_logmat_cx::apply_direct_noalias(Mat<typename T1::elem_type>& out, const diagmat_proxy<T1>& P)
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{
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arma_debug_sigprint();
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arma_conform_check( (P.n_rows != P.n_cols), "logmat(): given matrix must be square sized" );
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const uword N = P.n_rows;
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out.zeros(N,N);
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for(uword i=0; i<N; ++i)
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{
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out.at(i,i) = std::log(P[i]);
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}
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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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op_logmat_cx::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type,T1>& expr, const uword n_iters)
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{
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arma_debug_sigprint();
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typedef typename T1::pod_type T;
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typedef typename T1::elem_type eT;
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Mat<eT> S = expr.get_ref();
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arma_conform_check( (S.n_rows != S.n_cols), "logmat(): given matrix must be square sized" );
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if(S.n_elem == 0)
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{
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out.reset();
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return true;
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}
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else
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if(S.n_elem == 1)
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{
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out.set_size(1,1);
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out[0] = std::log(S[0]);
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return true;
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}
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if(S.is_diagmat())
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{
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arma_debug_print("op_logmat_cx: diag optimisation");
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const uword N = S.n_rows;
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out.zeros(N,N); // aliasing can't happen as S is generated
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for(uword i=0; i<N; ++i) { out.at(i,i) = std::log( S.at(i,i) ); }
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return true;
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}
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const bool try_sympd = arma_config::optimise_sym && sym_helper::guess_sympd(S);
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if(try_sympd)
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{
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arma_debug_print("op_logmat_cx: attempting sympd optimisation");
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// if matrix S is sympd, all its eigenvalues are positive
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Col< T> eigval;
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Mat<eT> eigvec;
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const bool eig_status = eig_sym_helper(eigval, eigvec, S, 'd', "logmat()");
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if(eig_status)
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{
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// ensure each eigenvalue is > 0
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const uword N = eigval.n_elem;
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const T* eigval_mem = eigval.memptr();
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bool all_pos = true;
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for(uword i=0; i<N; ++i) { all_pos = (eigval_mem[i] <= T(0)) ? false : all_pos; }
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if(all_pos)
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{
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eigval = log(eigval);
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out = eigvec * diagmat(eigval) * eigvec.t();
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return true;
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}
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}
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arma_debug_print("op_logmat_cx: sympd optimisation failed");
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// fallthrough if eigen decomposition failed or an eigenvalue is <= 0
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}
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return op_logmat_cx::apply_common(out, S, n_iters);
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}
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template<typename T>
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inline
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bool
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op_logmat_cx::apply_common(Mat< std::complex<T> >& out, Mat< std::complex<T> >& S, const uword n_iters)
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{
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arma_debug_sigprint();
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typedef typename std::complex<T> eT;
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Mat<eT> U;
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const bool schur_ok = auxlib::schur(U,S);
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if(schur_ok == false) { arma_debug_print("logmat(): schur decomposition failed"); return false; }
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// NOTE: theta[0] and theta[1] not really used
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double theta[] = { 1.10e-5, 1.82e-3, 1.6206284795015624e-2, 5.3873532631381171e-2, 1.1352802267628681e-1, 1.8662860613541288e-1, 2.642960831111435e-1 };
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const uword N = S.n_rows;
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uword p = 0;
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uword m = 6;
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uword iter = 0;
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while(iter < n_iters)
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{
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const T tau = norm( (S - eye< Mat<eT> >(N,N)), 1 );
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if(tau <= theta[6])
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{
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p++;
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uword j1 = 0;
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uword j2 = 0;
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for(uword i=2; i<=6; ++i) { if( tau <= theta[i]) { j1 = i; break; } }
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for(uword i=2; i<=6; ++i) { if((tau/2.0) <= theta[i]) { j2 = i; break; } }
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// sanity check, for development purposes only
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arma_conform_check( (j2 > j1), "internal error: op_logmat::apply_direct(): j2 > j1" );
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if( ((j1 - j2) <= 1) || (p == 2) ) { m = j1; break; }
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}
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const bool sqrtmat_ok = op_sqrtmat_cx::apply_direct(S,S);
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if(sqrtmat_ok == false) { arma_debug_print("logmat(): sqrtmat() failed"); return false; }
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iter++;
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}
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if(iter >= n_iters) { arma_warn(2, "logmat(): reached max iterations without full convergence"); }
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S.diag() -= eT(1);
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if(m >= 1)
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{
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const bool helper_ok = op_logmat_cx::helper(S,m);
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if(helper_ok == false) { return false; }
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}
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out = U * S * U.t();
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out *= eT(eop_aux::pow(double(2), double(iter)));
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return true;
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}
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template<typename eT>
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inline
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bool
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op_logmat_cx::helper(Mat<eT>& A, const uword m)
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{
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arma_debug_sigprint();
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if(A.internal_has_nonfinite()) { return false; }
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const vec indices = regspace<vec>(1,m-1);
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mat tmp(m, m, arma_zeros_indicator());
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tmp.diag(-1) = indices / sqrt(square(2.0*indices) - 1.0);
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tmp.diag(+1) = indices / sqrt(square(2.0*indices) - 1.0);
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vec eigval;
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mat eigvec;
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const bool eig_ok = eig_sym_helper(eigval, eigvec, tmp, 'd', "logmat()");
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if(eig_ok == false) { arma_debug_print("logmat(): eig_sym() failed"); return false; }
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const vec nodes = (eigval + 1.0) / 2.0;
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const vec weights = square(eigvec.row(0).t());
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const uword N = A.n_rows;
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Mat<eT> B(N, N, arma_zeros_indicator());
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Mat<eT> X;
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for(uword i=0; i < m; ++i)
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{
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// B += weights(i) * solve( (nodes(i)*A + eye< Mat<eT> >(N,N)), A );
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//const bool solve_ok = solve( X, (nodes(i)*A + eye< Mat<eT> >(N,N)), A, solve_opts::fast );
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const bool solve_ok = solve( X, trimatu(nodes(i)*A + eye< Mat<eT> >(N,N)), A, solve_opts::no_approx );
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if(solve_ok == false) { arma_debug_print("logmat(): solve() failed"); return false; }
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B += weights(i) * X;
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}
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A = B;
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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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void
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op_logmat_sympd::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_logmat_sympd>& in)
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{
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arma_debug_sigprint();
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const bool status = op_logmat_sympd::apply_direct(out, in.m);
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if(status == false)
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{
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out.soft_reset();
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arma_stop_runtime_error("logmat_sympd(): transformation failed");
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}
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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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op_logmat_sympd::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type,T1>& expr)
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{
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arma_debug_sigprint();
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#if defined(ARMA_USE_LAPACK)
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{
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typedef typename T1::pod_type T;
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typedef typename T1::elem_type eT;
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const unwrap<T1> U(expr.get_ref());
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const Mat<eT>& X = U.M;
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arma_conform_check( (X.is_square() == false), "logmat_sympd(): given matrix must be square sized" );
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if((arma_config::check_conform) && (arma_config::warn_level > 0) && (is_cx<eT>::yes) && (sym_helper::check_diag_imag(X) == false))
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{
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arma_warn(1, "logmat_sympd(): imaginary components on diagonal are non-zero");
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}
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if(is_op_diagmat<T1>::value || X.is_diagmat())
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{
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arma_debug_print("op_logmat_sympd: diag optimisation");
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out = X;
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eT* colmem = out.memptr();
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const uword N = X.n_rows;
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for(uword i=0; i<N; ++i)
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{
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eT& out_ii = colmem[i];
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T out_ii_real = access::tmp_real(out_ii);
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if(out_ii_real <= T(0)) { return false; }
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out_ii = std::log(out_ii);
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colmem += N;
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}
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return true;
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}
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Col< T> eigval;
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Mat<eT> eigvec;
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const bool status = eig_sym_helper(eigval, eigvec, X, 'd', "logmat_sympd()");
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if(status == false) { return false; }
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const uword N = eigval.n_elem;
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const T* eigval_mem = eigval.memptr();
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bool all_pos = true;
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for(uword i=0; i<N; ++i) { all_pos = (eigval_mem[i] <= T(0)) ? false : all_pos; }
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|
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if(all_pos == false) { return false; }
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|
|
|
eigval = log(eigval);
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|
|
|
out = eigvec * diagmat(eigval) * eigvec.t();
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|
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|
return true;
|
|
}
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#else
|
|
{
|
|
arma_ignore(out);
|
|
arma_ignore(expr);
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|
arma_stop_logic_error("logmat_sympd(): use of LAPACK must be enabled");
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|
return false;
|
|
}
|
|
#endif
|
|
}
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|
|
|
|
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//! @}
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