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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_det
//! @{
template<typename T1>
inline
bool
op_det::apply_direct(typename T1::elem_type& out_val, const Base<typename T1::elem_type,T1>& expr)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type eT;
typedef typename T1::pod_type T;
if(strip_diagmat<T1>::do_diagmat)
{
const strip_diagmat<T1> strip(expr.get_ref());
out_val = op_det::apply_diagmat(strip.M);
return true;
}
if(strip_trimat<T1>::do_trimat)
{
const strip_trimat<T1> strip(expr.get_ref());
out_val = op_det::apply_trimat(strip.M);
return true;
}
Mat<eT> A(expr.get_ref());
arma_debug_check( (A.is_square() == false), "det(): given matrix must be square sized" );
const uword N = A.n_rows;
if(N == 0) { out_val = eT(1); return true; }
if(N == 1) { out_val = A[0]; return true; }
if((is_cx<eT>::no) && (N <= 3))
{
constexpr T det_min = std::numeric_limits<T>::epsilon();
constexpr T det_max = T(1) / std::numeric_limits<T>::epsilon();
eT det_val = eT(0);
if(N == 2) { det_val = op_det::apply_tiny_2x2(A); }
if(N == 3) { det_val = op_det::apply_tiny_3x3(A); }
const T abs_det_val = std::abs(det_val);
if((abs_det_val > det_min) && (abs_det_val < det_max)) { out_val = det_val; return true; }
// fallthrough if det_val is suspect
}
if(A.is_diagmat()) { out_val = op_det::apply_diagmat(A); return true; }
const bool is_triu = trimat_helper::is_triu(A);
const bool is_tril = is_triu ? false : trimat_helper::is_tril(A);
if(is_triu || is_tril) { out_val = op_det::apply_trimat(A); return true; }
return auxlib::det(out_val, A);
}
template<typename T1>
inline
typename T1::elem_type
op_det::apply_diagmat(const Base<typename T1::elem_type,T1>& expr)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type eT;
const diagmat_proxy<T1> A(expr.get_ref());
arma_debug_check( (A.n_rows != A.n_cols), "det(): given matrix must be square sized" );
const uword N = (std::min)(A.n_rows, A.n_cols);
eT val = eT(1);
for(uword i=0; i<N; ++i) { val *= A[i]; }
return val;
}
template<typename T1>
inline
typename T1::elem_type
op_det::apply_trimat(const Base<typename T1::elem_type,T1>& expr)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type eT;
const Proxy<T1> P(expr.get_ref());
const uword N = P.get_n_rows();
arma_debug_check( (N != P.get_n_cols()), "det(): given matrix must be square sized" );
eT val = eT(1);
for(uword i=0; i<N; ++i) { val *= P.at(i,i); }
return val;
}
template<typename eT>
inline
eT
op_det::apply_tiny_2x2(const Mat<eT>& X)
{
arma_extra_debug_sigprint();
const eT* Xm = X.memptr();
return ( Xm[pos<0,0>::n2]*Xm[pos<1,1>::n2] - Xm[pos<0,1>::n2]*Xm[pos<1,0>::n2] );
}
template<typename eT>
inline
eT
op_det::apply_tiny_3x3(const Mat<eT>& X)
{
arma_extra_debug_sigprint();
const eT* Xm = X.memptr();
// const double tmp1 = X.at(0,0) * X.at(1,1) * X.at(2,2);
// const double tmp2 = X.at(0,1) * X.at(1,2) * X.at(2,0);
// const double tmp3 = X.at(0,2) * X.at(1,0) * X.at(2,1);
// const double tmp4 = X.at(2,0) * X.at(1,1) * X.at(0,2);
// const double tmp5 = X.at(2,1) * X.at(1,2) * X.at(0,0);
// const double tmp6 = X.at(2,2) * X.at(1,0) * X.at(0,1);
// return (tmp1+tmp2+tmp3) - (tmp4+tmp5+tmp6);
const eT val1 = Xm[pos<0,0>::n3]*(Xm[pos<2,2>::n3]*Xm[pos<1,1>::n3] - Xm[pos<2,1>::n3]*Xm[pos<1,2>::n3]);
const eT val2 = Xm[pos<1,0>::n3]*(Xm[pos<2,2>::n3]*Xm[pos<0,1>::n3] - Xm[pos<2,1>::n3]*Xm[pos<0,2>::n3]);
const eT val3 = Xm[pos<2,0>::n3]*(Xm[pos<1,2>::n3]*Xm[pos<0,1>::n3] - Xm[pos<1,1>::n3]*Xm[pos<0,2>::n3]);
return ( val1 - val2 + val3 );
}
//! @}
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