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+// SPDX-License-Identifier: Apache-2.0
+//
+// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
+// Copyright 2008-2016 National ICT Australia (NICTA)
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+// ------------------------------------------------------------------------
+
+
+
+//! \addtogroup op_expmat
+//! @{
+
+
+//! implementation based on:
+//! Cleve Moler, Charles Van Loan.
+//! Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later.
+//! SIAM Review, Vol. 45, No. 1, 2003, pp. 3-49.
+//! http://dx.doi.org/10.1137/S00361445024180
+
+
+template<typename T1>
+inline
+void
+op_expmat::apply(Mat<typename T1::elem_type>& out, const Op<T1, op_expmat>& expr)
+ {
+ arma_extra_debug_sigprint();
+
+ const bool status = op_expmat::apply_direct(out, expr.m);
+
+ if(status == false)
+ {
+ out.soft_reset();
+ arma_stop_runtime_error("expmat(): given matrix appears ill-conditioned");
+ }
+ }
+
+
+
+template<typename T1>
+inline
+bool
+op_expmat::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type, T1>& expr)
+ {
+ arma_extra_debug_sigprint();
+
+ typedef typename T1::elem_type eT;
+ typedef typename T1::pod_type T;
+
+ if(is_op_diagmat<T1>::value)
+ {
+ out = expr.get_ref(); // force the evaluation of diagmat()
+
+ arma_debug_check( (out.is_square() == false), "expmat(): given matrix must be square sized", [&](){ out.soft_reset(); } );
+
+ const uword N = (std::min)(out.n_rows, out.n_cols);
+
+ for(uword i=0; i<N; ++i) { out.at(i,i) = std::exp( out.at(i,i) ); }
+
+ return true;
+ }
+
+ Mat<eT> A = expr.get_ref();
+
+ arma_debug_check( (A.is_square() == false), "expmat(): given matrix must be square sized" );
+
+ if(A.is_diagmat())
+ {
+ arma_extra_debug_print("op_expmat: detected diagonal matrix");
+
+ const uword N = (std::min)(A.n_rows, A.n_cols);
+
+ out.zeros(N,N);
+
+ for(uword i=0; i<N; ++i) { out.at(i,i) = std::exp( A.at(i,i) ); }
+
+ return true;
+ }
+
+ bool do_sym = false;
+
+ if( (arma_config::optimise_sym) && (auxlib::crippled_lapack(A) == false) )
+ {
+ bool is_approx_sym = false;
+ bool is_approx_sympd = false;
+
+ sym_helper::analyse_matrix(is_approx_sym, is_approx_sympd, A);
+
+ do_sym = ((is_cx<eT>::no) ? (is_approx_sym) : (is_approx_sym && is_approx_sympd));
+ }
+
+ if(do_sym)
+ {
+ arma_extra_debug_print("op_expmat: symmetric/hermitian optimisation");
+
+ Col< T> eigval;
+ Mat<eT> eigvec;
+
+ const bool eig_status = eig_sym_helper(eigval, eigvec, A, 'd', "expmat()");
+
+ if(eig_status == false) { return false; }
+
+ eigval = exp(eigval);
+
+ out = eigvec * diagmat(eigval) * eigvec.t();
+
+ return true;
+ }
+
+ const T norm_val = arma::norm(A, "inf");
+
+ if(arma_isfinite(norm_val) == false) { return false; }
+
+ const double log2_val = (norm_val > T(0)) ? double(eop_aux::log2(norm_val)) : double(0);
+
+ int exponent = int(0); std::frexp(log2_val, &exponent);
+
+ const uword s = uword( (std::max)(int(0), exponent + int(1)) );
+
+ A /= eT(eop_aux::pow(double(2), double(s)));
+
+ T c = T(0.5);
+
+ Mat<eT> E(A.n_rows, A.n_rows, fill::eye); E += c * A;
+ Mat<eT> D(A.n_rows, A.n_rows, fill::eye); D -= c * A;
+
+ Mat<eT> X = A;
+
+ bool positive = true;
+
+ const uword N = 6;
+
+ for(uword i = 2; i <= N; ++i)
+ {
+ c = c * T(N - i + 1) / T(i * (2*N - i + 1));
+
+ X = A * X;
+
+ E += c * X;
+
+ if(positive) { D += c * X; } else { D -= c * X; }
+
+ positive = (positive) ? false : true;
+ }
+
+ if( (D.internal_has_nonfinite()) || (E.internal_has_nonfinite()) ) { return false; }
+
+ const bool status = solve(out, D, E, solve_opts::no_approx);
+
+ if(status == false) { return false; }
+
+ for(uword i=0; i < s; ++i) { out = out * out; }
+
+ return true;
+ }
+
+
+
+template<typename T1>
+inline
+void
+op_expmat_sym::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_expmat_sym>& in)
+ {
+ arma_extra_debug_sigprint();
+
+ const bool status = op_expmat_sym::apply_direct(out, in.m);
+
+ if(status == false)
+ {
+ out.soft_reset();
+ arma_stop_runtime_error("expmat_sym(): transformation failed");
+ }
+ }
+
+
+
+template<typename T1>
+inline
+bool
+op_expmat_sym::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type,T1>& expr)
+ {
+ arma_extra_debug_sigprint();
+
+ #if defined(ARMA_USE_LAPACK)
+ {
+ typedef typename T1::elem_type eT;
+ typedef typename T1::pod_type T;
+
+ const unwrap<T1> U(expr.get_ref());
+ const Mat<eT>& X = U.M;
+
+ arma_debug_check( (X.is_square() == false), "expmat_sym(): given matrix must be square sized" );
+
+ if((arma_config::debug) && (arma_config::warn_level > 0) && (is_cx<eT>::yes) && (sym_helper::check_diag_imag(X) == false))
+ {
+ arma_debug_warn_level(1, "inv_sympd(): imaginary components on diagonal are non-zero");
+ }
+
+ if(is_op_diagmat<T1>::value || X.is_diagmat())
+ {
+ arma_extra_debug_print("op_expmat_sym: detected diagonal matrix");
+
+ out = X;
+
+ eT* colmem = out.memptr();
+
+ const uword N = X.n_rows;
+
+ for(uword i=0; i<N; ++i)
+ {
+ eT& out_ii = colmem[i];
+ T out_ii_real = access::tmp_real(out_ii);
+
+ out_ii = eT( std::exp(out_ii_real) );
+
+ colmem += N;
+ }
+
+ return true;
+ }
+
+ Col< T> eigval;
+ Mat<eT> eigvec;
+
+ const bool status = eig_sym_helper(eigval, eigvec, X, 'd', "expmat_sym()");
+
+ if(status == false) { return false; }
+
+ eigval = exp(eigval);
+
+ out = eigvec * diagmat(eigval) * eigvec.t();
+
+ return true;
+ }
+ #else
+ {
+ arma_ignore(out);
+ arma_ignore(expr);
+ arma_stop_logic_error("expmat_sym(): use of LAPACK must be enabled");
+ return false;
+ }
+ #endif
+ }
+
+
+
+//! @}