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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_cond
//! @{
template<typename T1>
inline
typename T1::pod_type
op_cond::apply(const Base<typename T1::elem_type, T1>& X)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type eT;
typedef typename T1::pod_type T;
Mat<eT> A(X.get_ref());
if(A.n_elem == 0) { return T(0); }
if(is_op_diagmat<T1>::value || A.is_diagmat())
{
arma_extra_debug_print("op_cond::apply(): detected diagonal matrix");
return op_cond::apply_diag(A);
}
bool is_approx_sym = false;
bool is_approx_sympd = false;
sym_helper::analyse_matrix(is_approx_sym, is_approx_sympd, A);
const bool do_sym = (is_cx<eT>::no) ? (is_approx_sym) : (is_approx_sym && is_approx_sympd);
if(do_sym)
{
arma_extra_debug_print("op_cond: symmetric/hermitian optimisation");
return op_cond::apply_sym(A);
}
return op_cond::apply_gen(A);
}
template<typename eT>
inline
typename get_pod_type<eT>::result
op_cond::apply_diag(const Mat<eT>& A)
{
arma_extra_debug_sigprint();
typedef typename get_pod_type<eT>::result T;
const uword N = (std::min)(A.n_rows, A.n_cols);
T abs_min = Datum<T>::inf;
T abs_max = T(0);
for(uword i=0; i < N; ++i)
{
const T abs_val = std::abs(A.at(i,i));
if(arma_isnan(abs_val))
{
arma_debug_warn_level(3, "cond(): failed");
return Datum<T>::nan;
}
abs_min = (abs_val < abs_min) ? abs_val : abs_min;
abs_max = (abs_val > abs_max) ? abs_val : abs_max;
}
if((abs_min == T(0)) || (abs_max == T(0))) { return Datum<T>::inf; }
return T(abs_max / abs_min);
}
template<typename eT>
inline
typename get_pod_type<eT>::result
op_cond::apply_sym(Mat<eT>& A)
{
arma_extra_debug_sigprint();
typedef typename get_pod_type<eT>::result T;
Col<T> eigval;
const bool status = auxlib::eig_sym(eigval, A);
if(status == false)
{
arma_debug_warn_level(3, "cond(): failed");
return Datum<T>::nan;
}
if(eigval.n_elem == 0) { return T(0); }
const T* eigval_mem = eigval.memptr();
T abs_min = std::abs(eigval_mem[0]);
T abs_max = abs_min;
for(uword i=1; i < eigval.n_elem; ++i)
{
const T abs_val = std::abs(eigval_mem[i]);
abs_min = (abs_val < abs_min) ? abs_val : abs_min;
abs_max = (abs_val > abs_max) ? abs_val : abs_max;
}
if((abs_min == T(0)) || (abs_max == T(0))) { return Datum<T>::inf; }
return T(abs_max / abs_min);
}
template<typename eT>
inline
typename get_pod_type<eT>::result
op_cond::apply_gen(Mat<eT>& A)
{
arma_extra_debug_sigprint();
typedef typename get_pod_type<eT>::result T;
Col<T> S;
const bool status = auxlib::svd_dc(S, A);
if(status == false)
{
arma_debug_warn_level(3, "cond(): failed");
return Datum<T>::nan;
}
if(S.n_elem == 0) { return T(0); }
const T S_max = S[0];
const T S_min = S[S.n_elem-1];
if((S_max == T(0)) || (S_min == T(0))) { return Datum<T>::inf; }
return T(S_max / S_min);
}
//! @}
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