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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 fn_hess
//! @{
template<typename T1>
inline
bool
hess
(
Mat<typename T1::elem_type>& H,
const Base<typename T1::elem_type,T1>& X,
const typename arma_blas_type_only<typename T1::elem_type>::result* junk = nullptr
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
typedef typename T1::elem_type eT;
Col<eT> tao;
const bool status = auxlib::hess(H, X.get_ref(), tao);
if(H.n_rows > 2)
{
for(uword i=0; i < H.n_rows-2; ++i)
{
H(span(i+2, H.n_rows-1), i).zeros();
}
}
if(status == false)
{
H.soft_reset();
arma_debug_warn_level(3, "hess(): decomposition failed");
}
return status;
}
template<typename T1>
arma_warn_unused
inline
Mat<typename T1::elem_type>
hess
(
const Base<typename T1::elem_type,T1>& X,
const typename arma_blas_type_only<typename T1::elem_type>::result* junk = nullptr
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
typedef typename T1::elem_type eT;
Mat<eT> H;
Col<eT> tao;
const bool status = auxlib::hess(H, X.get_ref(), tao);
if(H.n_rows > 2)
{
for(uword i=0; i < H.n_rows-2; ++i)
{
H(span(i+2, H.n_rows-1), i).zeros();
}
}
if(status == false)
{
H.soft_reset();
arma_stop_runtime_error("hess(): decomposition failed");
}
return H;
}
template<typename T1>
inline
bool
hess
(
Mat<typename T1::elem_type>& U,
Mat<typename T1::elem_type>& H,
const Base<typename T1::elem_type,T1>& X,
const typename arma_blas_type_only<typename T1::elem_type>::result* junk = nullptr
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
arma_debug_check( void_ptr(&U) == void_ptr(&H), "hess(): 'U' is an alias of 'H'" );
typedef typename T1::elem_type eT;
Col<eT> tao;
const bool status = auxlib::hess(H, X.get_ref(), tao);
if(H.n_rows == 0)
{
U.reset();
}
else
if(H.n_rows == 1)
{
U.ones(1, 1);
}
else
if(H.n_rows == 2)
{
U.eye(2, 2);
}
else
{
U.eye(size(H));
Col<eT> v;
for(uword i=0; i < H.n_rows-2; ++i)
{
// TODO: generate v in a more efficient manner;
// TODO: the .ones() operation is an overkill, as most of v is overwritten afterwards
v.ones(H.n_rows-i-1);
v(span(1, H.n_rows-i-2)) = H(span(i+2, H.n_rows-1), i);
U(span::all, span(i+1, H.n_rows-1)) -= tao(i) * (U(span::all, span(i+1, H.n_rows-1)) * v * v.t());
}
U(span::all, H.n_rows-1) = U(span::all, H.n_rows-1) * (eT(1) - tao(H.n_rows-2));
for(uword i=0; i < H.n_rows-2; ++i)
{
H(span(i+2, H.n_rows-1), i).zeros();
}
}
if(status == false)
{
U.soft_reset();
H.soft_reset();
arma_debug_warn_level(3, "hess(): decomposition failed");
}
return status;
}
//! @}
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