236 lines
6.7 KiB
C++
236 lines
6.7 KiB
C++
// 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" );
|
|
|
|
if((A.n_rows <= 4) && is_cx<eT>::no)
|
|
{
|
|
constexpr T det_min = std::numeric_limits<T>::epsilon();
|
|
constexpr T det_max = T(1) / std::numeric_limits<T>::epsilon();
|
|
|
|
const eT det_val = op_det::apply_tiny(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>
|
|
arma_cold
|
|
inline
|
|
eT
|
|
op_det::apply_tiny(const Mat<eT>& X)
|
|
{
|
|
arma_extra_debug_sigprint();
|
|
|
|
// NOTE: assuming matrix X is square sized
|
|
|
|
const uword N = X.n_rows;
|
|
const eT* Xm = X.memptr();
|
|
|
|
if(N == 0) { return eT(1); }
|
|
|
|
if(N == 1) { return Xm[0]; }
|
|
|
|
if(N == 2)
|
|
{
|
|
return ( Xm[pos<0,0>::n2]*Xm[pos<1,1>::n2] - Xm[pos<0,1>::n2]*Xm[pos<1,0>::n2] );
|
|
}
|
|
|
|
if(N == 3)
|
|
{
|
|
// 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 );
|
|
}
|
|
|
|
if(N == 4)
|
|
{
|
|
const eT val_03_12 = Xm[pos<0,3>::n4] * Xm[pos<1,2>::n4];
|
|
const eT val_02_13 = Xm[pos<0,2>::n4] * Xm[pos<1,3>::n4];
|
|
const eT val_03_11 = Xm[pos<0,3>::n4] * Xm[pos<1,1>::n4];
|
|
|
|
const eT val_01_13 = Xm[pos<0,1>::n4] * Xm[pos<1,3>::n4];
|
|
const eT val_02_11 = Xm[pos<0,2>::n4] * Xm[pos<1,1>::n4];
|
|
const eT val_01_12 = Xm[pos<0,1>::n4] * Xm[pos<1,2>::n4];
|
|
|
|
const eT val_03_10 = Xm[pos<0,3>::n4] * Xm[pos<1,0>::n4];
|
|
const eT val_00_13 = Xm[pos<0,0>::n4] * Xm[pos<1,3>::n4];
|
|
const eT val_02_10 = Xm[pos<0,2>::n4] * Xm[pos<1,0>::n4];
|
|
const eT val_00_12 = Xm[pos<0,0>::n4] * Xm[pos<1,2>::n4];
|
|
|
|
const eT val_01_10 = Xm[pos<0,1>::n4] * Xm[pos<1,0>::n4];
|
|
const eT val_00_11 = Xm[pos<0,0>::n4] * Xm[pos<1,1>::n4];
|
|
|
|
const eT val_21_30 = Xm[pos<2,1>::n4] * Xm[pos<3,0>::n4];
|
|
const eT val_22_30 = Xm[pos<2,2>::n4] * Xm[pos<3,0>::n4];
|
|
const eT val_23_30 = Xm[pos<2,3>::n4] * Xm[pos<3,0>::n4];
|
|
|
|
const eT val_20_31 = Xm[pos<2,0>::n4] * Xm[pos<3,1>::n4];
|
|
const eT val_22_31 = Xm[pos<2,2>::n4] * Xm[pos<3,1>::n4];
|
|
const eT val_23_31 = Xm[pos<2,3>::n4] * Xm[pos<3,1>::n4];
|
|
|
|
const eT val_20_32 = Xm[pos<2,0>::n4] * Xm[pos<3,2>::n4];
|
|
const eT val_21_32 = Xm[pos<2,1>::n4] * Xm[pos<3,2>::n4];
|
|
const eT val_23_32 = Xm[pos<2,3>::n4] * Xm[pos<3,2>::n4];
|
|
|
|
const eT val_20_33 = Xm[pos<2,0>::n4] * Xm[pos<3,3>::n4];
|
|
const eT val_21_33 = Xm[pos<2,1>::n4] * Xm[pos<3,3>::n4];
|
|
const eT val_22_33 = Xm[pos<2,2>::n4] * Xm[pos<3,3>::n4];
|
|
|
|
const eT val = \
|
|
val_03_12 * val_21_30 \
|
|
- val_02_13 * val_21_30 \
|
|
- val_03_11 * val_22_30 \
|
|
+ val_01_13 * val_22_30 \
|
|
+ val_02_11 * val_23_30 \
|
|
- val_01_12 * val_23_30 \
|
|
- val_03_12 * val_20_31 \
|
|
+ val_02_13 * val_20_31 \
|
|
+ val_03_10 * val_22_31 \
|
|
- val_00_13 * val_22_31 \
|
|
- val_02_10 * val_23_31 \
|
|
+ val_00_12 * val_23_31 \
|
|
+ val_03_11 * val_20_32 \
|
|
- val_01_13 * val_20_32 \
|
|
- val_03_10 * val_21_32 \
|
|
+ val_00_13 * val_21_32 \
|
|
+ val_01_10 * val_23_32 \
|
|
- val_00_11 * val_23_32 \
|
|
- val_02_11 * val_20_33 \
|
|
+ val_01_12 * val_20_33 \
|
|
+ val_02_10 * val_21_33 \
|
|
- val_00_12 * val_21_33 \
|
|
- val_01_10 * val_22_33 \
|
|
+ val_00_11 * val_22_33 \
|
|
;
|
|
|
|
return val;
|
|
}
|
|
|
|
return eT(0);
|
|
}
|
|
|
|
|
|
|
|
//! @}
|