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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_roots
//! @{
template<typename T1>
inline
void
op_roots::apply(Mat< std::complex<typename T1::pod_type> >& out, const mtOp<std::complex<typename T1::pod_type>, T1, op_roots>& expr)
{
arma_extra_debug_sigprint();
const bool status = op_roots::apply_direct(out, expr.m);
if(status == false)
{
out.soft_reset();
arma_stop_runtime_error("roots(): eigen decomposition failed");
}
}
template<typename T1>
inline
bool
op_roots::apply_direct(Mat< std::complex<typename T1::pod_type> >& out, const Base<typename T1::elem_type, T1>& X)
{
arma_extra_debug_sigprint();
typedef std::complex<typename T1::pod_type> out_eT;
const quasi_unwrap<T1> U(X.get_ref());
bool status = false;
if(U.is_alias(out))
{
Mat<out_eT> tmp;
status = op_roots::apply_noalias(tmp, U.M);
out.steal_mem(tmp);
}
else
{
status = op_roots::apply_noalias(out, U.M);
}
return status;
}
template<typename eT>
inline
bool
op_roots::apply_noalias(Mat< std::complex<typename get_pod_type<eT>::result> >& out, const Mat<eT>& X)
{
arma_extra_debug_sigprint();
typedef typename get_pod_type<eT>::result T;
typedef std::complex<typename get_pod_type<eT>::result> out_eT;
arma_debug_check( (X.is_vec() == false), "roots(): given object must be a vector" );
if(X.internal_has_nonfinite()) { return false; }
// treat X as a column vector
const Col<eT> Y( const_cast<eT*>(X.memptr()), X.n_elem, false, false);
const T Y_max = (Y.is_empty() == false) ? T(max(abs(Y))) : T(0);
if(Y_max == T(0)) { out.set_size(1,0); return true; }
const uvec indices = find( Y / Y_max );
const uword n_tail_zeros = (indices.n_elem > 0) ? uword( (Y.n_elem-1) - indices[indices.n_elem-1] ) : uword(0);
const Col<eT> Z = Y.subvec( indices[0], indices[indices.n_elem-1] );
if(Z.n_elem >= uword(2))
{
Mat<eT> tmp;
if(Z.n_elem == uword(2))
{
tmp.set_size(1,1);
tmp[0] = -Z[1] / Z[0];
}
else
{
tmp = diagmat(ones< Col<eT> >(Z.n_elem - 2), -1);
tmp.row(0) = strans(-Z.subvec(1, Z.n_elem-1) / Z[0]);
}
Mat<out_eT> junk;
const bool status = auxlib::eig_gen(out, junk, false, tmp);
if(status == false) { return false; }
if(n_tail_zeros > 0)
{
out.resize(out.n_rows + n_tail_zeros, 1);
}
}
else
{
out.zeros(n_tail_zeros,1);
}
return true;
}
//! @}
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