256 lines
6.0 KiB
C++
256 lines
6.0 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_powmat
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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_powmat::apply(Mat<typename T1::elem_type>& out, const Op<T1, op_powmat>& expr)
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{
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arma_extra_debug_sigprint();
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const uword y = expr.aux_uword_a;
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const bool y_neg = (expr.aux_uword_b == uword(1));
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const bool status = op_powmat::apply_direct(out, expr.m, y, y_neg);
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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("powmat(): 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_powmat::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type,T1>& X, const uword y, const bool y_neg)
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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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if(y_neg)
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{
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if(y == uword(1))
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{
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return op_inv::apply_direct(out, X.get_ref(), "powmat()");
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}
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else
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{
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Mat<eT> X_inv;
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const bool inv_status = op_inv::apply_direct(X_inv, X.get_ref(), "powmat()");
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if(inv_status == false) { return false; }
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op_powmat::apply_direct_positive(out, X_inv, y);
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}
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}
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else
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{
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const quasi_unwrap<T1> U(X.get_ref());
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arma_debug_check( (U.M.is_square() == false), "powmat(): given matrix must be square sized" );
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op_powmat::apply_direct_positive(out, U.M, y);
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}
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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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void
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op_powmat::apply_direct_positive(Mat<eT>& out, const Mat<eT>& X, const uword y)
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{
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arma_extra_debug_sigprint();
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const uword N = X.n_rows;
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if(y == uword(0)) { out.eye(N,N); return; }
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if(y == uword(1)) { out = X; return; }
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if(X.is_diagmat())
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{
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podarray<eT> tmp(N); // use temporary array in case we have aliasing
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for(uword i=0; i<N; ++i) { tmp[i] = eop_aux::pow(X.at(i,i), int(y)); }
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out.zeros(N,N);
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for(uword i=0; i<N; ++i) { out.at(i,i) = tmp[i]; }
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}
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else
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{
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if(y == uword(2)) { out = X*X; }
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else if(y == uword(3)) { const Mat<eT> tmp = X*X; out = X*tmp; }
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else if(y == uword(4)) { const Mat<eT> tmp = X*X; out = tmp*tmp; }
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else if(y == uword(5)) { const Mat<eT> tmp = X*X; out = X*tmp*tmp; }
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else
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{
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Mat<eT> tmp = X;
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out = X;
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uword z = y-1;
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while(z > 0)
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{
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if(z & 1) { out = tmp * out; }
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z /= uword(2);
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if(z > 0) { tmp = tmp * tmp; }
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}
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}
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}
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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_powmat_cx::apply(Mat< std::complex<typename T1::pod_type> >& out, const mtOp<std::complex<typename T1::pod_type>,T1,op_powmat_cx>& expr)
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{
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arma_extra_debug_sigprint();
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typedef typename T1::pod_type in_T;
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const in_T y = std::real(expr.aux_out_eT);
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const bool status = op_powmat_cx::apply_direct(out, expr.m, y);
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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("powmat(): 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_powmat_cx::apply_direct(Mat< std::complex<typename T1::pod_type> >& out, const Base<typename T1::elem_type,T1>& X, const typename T1::pod_type y)
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{
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arma_extra_debug_sigprint();
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typedef typename T1::elem_type in_eT;
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typedef typename T1::pod_type in_T;
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typedef std::complex<in_T> out_eT;
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if( y == in_T(int(y)) )
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{
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arma_extra_debug_print("op_powmat_cx::apply_direct(): integer exponent detected; redirecting to op_powmat");
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const uword y_val = (y < int(0)) ? uword(-y) : uword(y);
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const bool y_neg = (y < int(0));
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Mat<in_eT> tmp;
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const bool status = op_powmat::apply_direct(tmp, X.get_ref(), y_val, y_neg);
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if(status == false) { return false; }
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out = conv_to< Mat<out_eT> >::from(tmp);
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return true;
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}
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const quasi_unwrap<T1> U(X.get_ref());
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const Mat<in_eT>& A = U.M;
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arma_debug_check( (A.is_square() == false), "powmat(): given matrix must be square sized" );
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const uword N = A.n_rows;
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if(A.is_diagmat())
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{
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podarray<out_eT> tmp(N); // use temporary array in case we have aliasing
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for(uword i=0; i<N; ++i) { tmp[i] = eop_aux::pow( std::complex<in_T>(A.at(i,i)), y) ; }
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out.zeros(N,N);
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for(uword i=0; i<N; ++i) { out.at(i,i) = tmp[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(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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Col<in_T> eigval;
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Mat<in_eT> eigvec;
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const bool eig_status = eig_sym(eigval, eigvec, A);
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if(eig_status)
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{
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eigval = pow(eigval, y);
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const Mat<in_eT> tmp = diagmat(eigval) * eigvec.t();
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out = conv_to< Mat<out_eT> >::from(eigvec * tmp);
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return true;
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}
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// fallthrough
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}
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bool powmat_status = false;
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Col<out_eT> eigval;
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Mat<out_eT> eigvec;
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const bool eig_status = eig_gen(eigval, eigvec, A);
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if(eig_status)
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{
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eigval = pow(eigval, y);
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Mat<out_eT> eigvec_t = trans(eigvec);
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Mat<out_eT> tmp = diagmat(conj(eigval)) * eigvec_t;
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const bool solve_status = auxlib::solve_square_fast(out, eigvec_t, tmp);
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if(solve_status) { out = trans(out); powmat_status = true; }
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}
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return powmat_status;
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}
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//! @}
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