97 lines
2.4 KiB
C++
97 lines
2.4 KiB
C++
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// Copyright (C) 2014-2015 National ICT Australia (NICTA)
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//
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// This Source Code Form is subject to the terms of the Mozilla Public
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// License, v. 2.0. If a copy of the MPL was not distributed with this
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// file, You can obtain one at http://mozilla.org/MPL/2.0/.
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// -------------------------------------------------------------------
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//
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// Written by Conrad Sanderson - http://conradsanderson.id.au
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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_extra_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.m; // force the evaluation of diagmat()
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arma_debug_check( (out.is_square() == false), "expmat(): given matrix must be square sized" );
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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)
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{
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out.at(i,i) = std::exp( out.at(i,i) );
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}
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}
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else
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{
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const unwrap<T1> tmp(expr.m);
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const Mat<eT>& A = tmp.M;
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arma_debug_check( (A.is_square() == false), "expmat(): given matrix must be square sized" );
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const T norm_val = arma::norm(A, "inf");
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const double log2_val = (norm_val > T(0)) ? double(eop_aux::log2(norm_val)) : double(0);
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int exponent = int(0); std::frexp(log2_val, &exponent);
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const uword s = uword( (std::max)(int(0), exponent + int(1)) );
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const Mat<eT> AA = 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(AA.n_rows, AA.n_rows, fill::eye); E += c * AA;
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Mat<eT> D(AA.n_rows, AA.n_rows, fill::eye); D -= c * AA;
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Mat<eT> X = AA;
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bool positive = true;
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const uword N = 6;
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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 = AA * 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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out = solve(D, E);
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for(uword i=0; i < s; ++i) { out = out * out; }
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}
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}
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//! @}
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