262 lines
6.5 KiB
C++
262 lines
6.5 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_expmat
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//! @{
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//! implementation based on:
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//! Cleve Moler, Charles Van Loan.
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//! Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later.
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//! SIAM Review, Vol. 45, No. 1, 2003, pp. 3-49.
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//! http://dx.doi.org/10.1137/S00361445024180
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template<typename T1>
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inline
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void
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op_expmat::apply(Mat<typename T1::elem_type>& out, const Op<T1, op_expmat>& expr)
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{
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arma_debug_sigprint();
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const bool status = op_expmat::apply_direct(out, expr.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("expmat(): given matrix appears ill-conditioned");
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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_expmat::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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typedef typename T1::elem_type eT;
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typedef typename T1::pod_type T;
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if(is_op_diagmat<T1>::value)
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{
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out = expr.get_ref(); // force the evaluation of diagmat()
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arma_conform_check( (out.is_square() == false), "expmat(): given matrix must be square sized", [&](){ out.soft_reset(); } );
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const uword N = (std::min)(out.n_rows, out.n_cols);
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for(uword i=0; i<N; ++i) { out.at(i,i) = std::exp( out.at(i,i) ); }
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return true;
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}
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Mat<eT> A = expr.get_ref();
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arma_conform_check( (A.is_square() == false), "expmat(): given matrix must be square sized" );
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if(A.is_diagmat())
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{
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arma_debug_print("op_expmat: diag optimisation");
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const uword N = (std::min)(A.n_rows, A.n_cols);
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out.zeros(N,N);
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for(uword i=0; i<N; ++i) { out.at(i,i) = std::exp( A.at(i,i) ); }
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return true;
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}
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if( (arma_config::optimise_sym) && (auxlib::crippled_lapack(A) == false) && sym_helper::is_approx_sym(A) )
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{
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arma_debug_print("op_expmat: symmetric/hermitian optimisation");
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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, A, 'd', "expmat()");
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if(eig_status == false) { return false; }
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eigval = exp(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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// trace reduction
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const eT diag_shift = arma::trace(A) / T(A.n_rows);
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const eT exp_diag_shift = std::exp(diag_shift);
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const bool do_trace_reduction = arma_isfinite(diag_shift) && arma_isfinite(exp_diag_shift) && (exp_diag_shift != eT(0)) && ( (is_cx<eT>::yes) ? (std::abs(diag_shift) > T(0)) : (access::tmp_real(diag_shift) > T(0)) );
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if(do_trace_reduction)
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{
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arma_debug_print("op_expmat: diag_shift: ", diag_shift);
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A.diag() -= diag_shift;
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}
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const T norm_val = arma::norm(A, "inf");
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if(arma_isnonfinite(norm_val)) { return false; }
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int exponent = int(0); std::frexp(norm_val, &exponent);
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const uword s = (std::min)( uword( (std::max)(int(0), exponent) ), uword(1023) );
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arma_debug_print("op_expmat: s: ", s);
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A /= eT(eop_aux::pow(double(2), double(s)));
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T c = T(0.5);
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Mat<eT> E(A.n_rows, A.n_rows, fill::eye); E += c * A;
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Mat<eT> D(A.n_rows, A.n_rows, fill::eye); D -= c * A;
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Mat<eT> X = A;
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bool positive = true;
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const uword N = 8;
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for(uword i = 2; i <= N; ++i)
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{
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c = c * T(N - i + 1) / T(i * (2*N - i + 1));
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X = A * X;
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E += c * X;
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if(positive) { D += c * X; } else { D -= c * X; }
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positive = (positive) ? false : true;
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}
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if( (D.internal_has_nonfinite()) || (E.internal_has_nonfinite()) ) { return false; }
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const bool status = solve(out, D, E, solve_opts::no_approx);
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if(status == false) { return false; }
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for(uword i=0; i < s; ++i) { out = out * out; }
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// inverse trace reduction
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if(do_trace_reduction) { out *= exp_diag_shift; }
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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_expmat_sym::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_expmat_sym>& in)
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{
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arma_debug_sigprint();
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const bool status = op_expmat_sym::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("expmat_sym(): 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_expmat_sym::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::elem_type eT;
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typedef typename T1::pod_type T;
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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), "expmat_sym(): 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, "inv_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_expmat_sym: 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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out_ii = eT( std::exp(out_ii_real) );
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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', "expmat_sym()");
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if(status == false) { return false; }
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eigval = exp(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("expmat_sym(): 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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