522 lines
11 KiB
C++
522 lines
11 KiB
C++
// 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_sqrtmat
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//! @{
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//! implementation partly based on:
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//! N. J. Higham.
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//! A New sqrtm for Matlab.
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//! Numerical Analysis Report No. 336, January 1999.
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//! Department of Mathematics, University of Manchester.
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//! ISSN 1360-1725
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//! http://www.maths.manchester.ac.uk/~higham/narep/narep336.ps.gz
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template<typename T1>
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inline
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void
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op_sqrtmat::apply(Mat< std::complex<typename T1::elem_type> >& out, const mtOp<std::complex<typename T1::elem_type>,T1,op_sqrtmat>& in)
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{
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arma_extra_debug_sigprint();
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const bool status = op_sqrtmat::apply_direct(out, in.m);
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if(status == false)
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{
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arma_debug_warn_level(3, "sqrtmat(): given matrix is singular; may not have a square root");
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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_sqrtmat::apply_direct(Mat< std::complex<typename T1::elem_type> >& out, const Op<T1,op_diagmat>& expr)
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{
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arma_extra_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_debug_check( (P.n_rows != P.n_cols), "sqrtmat(): 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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bool singular = false;
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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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singular = (singular || (val == T(0)));
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out.at(i,i) = std::sqrt(val);
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}
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else
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{
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out.at(i,i) = std::sqrt( std::complex<T>(val) );
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}
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}
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return (singular) ? false : 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_sqrtmat::apply_direct(Mat< std::complex<typename T1::elem_type> >& out, const Base<typename T1::elem_type,T1>& expr)
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{
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arma_extra_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_debug_check( (A.is_square() == false), "sqrtmat(): 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::sqrt( 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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const uword N = A.n_rows;
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out.zeros(N,N); // aliasing can't happen as op_sqrtmat 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::sqrt(val);
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}
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else
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{
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out.at(i,i) = std::sqrt( 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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#if defined(ARMA_OPTIMISE_SYMPD)
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const bool try_sympd = sympd_helper::guess_sympd_anysize(A);
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#else
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const bool try_sympd = false;
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#endif
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if(try_sympd)
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{
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arma_extra_debug_print("op_sqrtmat: 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', "sqrtmat()");
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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 = sqrt(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_extra_debug_print("op_sqrtmat: sympd optimisation failed");
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// fallthrough if eigen decomposition failed or an eigenvalue is zero
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}
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Mat<out_T> U;
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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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const bool schur_ok = auxlib::schur(U,S);
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if(schur_ok == false)
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{
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arma_extra_debug_print("sqrtmat(): schur decomposition failed");
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out.soft_reset();
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return false;
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}
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const bool status = op_sqrtmat_cx::helper(S);
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const Mat<out_T> X = U*S;
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S.reset();
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out = X*U.t();
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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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void
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op_sqrtmat_cx::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_sqrtmat_cx>& in)
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{
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arma_extra_debug_sigprint();
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const bool status = op_sqrtmat_cx::apply_direct(out, in.m);
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if(status == false)
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{
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arma_debug_warn_level(3, "sqrtmat(): given matrix is singular; may not have a square root");
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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_sqrtmat_cx::apply_direct(Mat<typename T1::elem_type>& out, const Op<T1,op_diagmat>& expr)
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{
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arma_extra_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_sqrtmat_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_sqrtmat_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_sqrtmat_cx::apply_direct_noalias(Mat<typename T1::elem_type>& out, const diagmat_proxy<T1>& P)
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{
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arma_extra_debug_sigprint();
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typedef typename T1::elem_type eT;
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arma_debug_check( (P.n_rows != P.n_cols), "sqrtmat(): 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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const eT zero = eT(0);
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bool singular = false;
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for(uword i=0; i<N; ++i)
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{
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const eT val = P[i];
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singular = (singular || (val == zero));
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out.at(i,i) = std::sqrt(val);
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}
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return (singular) ? false : 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_sqrtmat_cx::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_extra_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> U;
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Mat<eT> S = expr.get_ref();
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arma_debug_check( (S.n_rows != S.n_cols), "sqrtmat(): 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::sqrt(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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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::sqrt( S.at(i,i) ); }
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return true;
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}
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#if defined(ARMA_OPTIMISE_SYMPD)
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const bool try_sympd = sympd_helper::guess_sympd_anysize(S);
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#else
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const bool try_sympd = false;
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#endif
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if(try_sympd)
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{
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arma_extra_debug_print("op_sqrtmat_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', "sqrtmat()");
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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 = sqrt(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_extra_debug_print("op_sqrtmat_cx: sympd optimisation failed");
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// fallthrough if eigen decomposition failed or an eigenvalue is zero
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}
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const bool schur_ok = auxlib::schur(U, S);
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if(schur_ok == false)
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{
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arma_extra_debug_print("sqrtmat(): schur decomposition failed");
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out.soft_reset();
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return false;
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}
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const bool status = op_sqrtmat_cx::helper(S);
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const Mat<eT> X = U*S;
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S.reset();
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out = X*U.t();
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return status;
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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_sqrtmat_cx::helper(Mat< std::complex<T> >& S)
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{
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typedef typename std::complex<T> eT;
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if(S.is_empty()) { return true; }
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const uword N = S.n_rows;
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const eT zero = eT(0);
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eT& S_00 = S[0];
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bool singular = (S_00 == zero);
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S_00 = std::sqrt(S_00);
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for(uword j=1; j < N; ++j)
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{
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eT* S_j = S.colptr(j);
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eT& S_jj = S_j[j];
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singular = (singular || (S_jj == zero));
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S_jj = std::sqrt(S_jj);
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for(uword ii=0; ii <= (j-1); ++ii)
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{
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const uword i = (j-1) - ii;
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const eT* S_i = S.colptr(i);
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//S_j[i] /= (S_i[i] + S_j[j]);
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S_j[i] /= (S_i[i] + S_jj);
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for(uword k=0; k < i; ++k)
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{
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S_j[k] -= S_i[k] * S_j[i];
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}
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}
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}
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return (singular) ? false : 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_sqrtmat_sympd::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_sqrtmat_sympd>& in)
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{
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arma_extra_debug_sigprint();
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const bool status = op_sqrtmat_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("sqrtmat_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_sqrtmat_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_extra_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_debug_check( (X.is_square() == false), "sqrtmat_sympd(): given matrix must be square sized" );
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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', "sqrtmat_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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if(all_pos == false) { return false; }
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eigval = sqrt(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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#else
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{
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arma_ignore(out);
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arma_ignore(expr);
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arma_stop_logic_error("sqrtmat_sympd(): use of LAPACK must be enabled");
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return false;
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}
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#endif
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}
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//! @}
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