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