253 lines
6.9 KiB
C++
253 lines
6.9 KiB
C++
// SPDX-License-Identifier: Apache-2.0
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//
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// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
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// Copyright 2008-2016 National ICT Australia (NICTA)
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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// ------------------------------------------------------------------------
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//! \addtogroup op_det
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//! @{
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template<typename T1>
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inline
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bool
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op_det::apply_direct(typename T1::elem_type& out_val, const Base<typename T1::elem_type,T1>& expr)
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{
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arma_extra_debug_sigprint();
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typedef typename T1::elem_type eT;
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typedef typename T1::pod_type T;
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if(strip_diagmat<T1>::do_diagmat)
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{
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const strip_diagmat<T1> strip(expr.get_ref());
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out_val = op_det::apply_diagmat(strip.M);
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return true;
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}
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if(strip_trimat<T1>::do_trimat)
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{
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const strip_trimat<T1> strip(expr.get_ref());
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out_val = op_det::apply_trimat(strip.M);
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return true;
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}
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Mat<eT> A(expr.get_ref());
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arma_debug_check( (A.is_square() == false), "det(): given matrix must be square sized" );
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const uword N = A.n_rows;
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if(N == 0) { out_val = eT(1); return true; }
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if(N == 1) { out_val = A[0]; return true; }
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if((is_cx<eT>::no) && (N <= 4))
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{
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constexpr T det_min = std::numeric_limits<T>::epsilon();
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constexpr T det_max = T(1) / std::numeric_limits<T>::epsilon();
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eT det_val = eT(0);
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if(N == 2) { det_val = op_det::apply_tiny_2x2(A); }
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if(N == 3) { det_val = op_det::apply_tiny_3x3(A); }
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if(N == 4) { det_val = op_det::apply_tiny_4x4(A); }
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const T abs_det_val = std::abs(det_val);
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if((abs_det_val > det_min) && (abs_det_val < det_max)) { out_val = det_val; return true; }
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// fallthrough if det_val is suspect
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}
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if(A.is_diagmat()) { out_val = op_det::apply_diagmat(A); return true; }
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const bool is_triu = trimat_helper::is_triu(A);
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const bool is_tril = is_triu ? false : trimat_helper::is_tril(A);
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if(is_triu || is_tril) { out_val = op_det::apply_trimat(A); return true; }
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return auxlib::det(out_val, A);
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}
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template<typename T1>
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inline
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typename T1::elem_type
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op_det::apply_diagmat(const Base<typename T1::elem_type,T1>& expr)
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{
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arma_extra_debug_sigprint();
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typedef typename T1::elem_type eT;
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const diagmat_proxy<T1> A(expr.get_ref());
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arma_debug_check( (A.n_rows != A.n_cols), "det(): given matrix must be square sized" );
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const uword N = (std::min)(A.n_rows, A.n_cols);
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eT val = eT(1);
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for(uword i=0; i<N; ++i) { val *= A[i]; }
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return val;
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}
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template<typename T1>
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inline
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typename T1::elem_type
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op_det::apply_trimat(const Base<typename T1::elem_type,T1>& expr)
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{
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arma_extra_debug_sigprint();
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typedef typename T1::elem_type eT;
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const Proxy<T1> P(expr.get_ref());
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const uword N = P.get_n_rows();
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arma_debug_check( (N != P.get_n_cols()), "det(): given matrix must be square sized" );
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eT val = eT(1);
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for(uword i=0; i<N; ++i) { val *= P.at(i,i); }
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return val;
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}
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template<typename eT>
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inline
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eT
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op_det::apply_tiny_2x2(const Mat<eT>& X)
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{
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arma_extra_debug_sigprint();
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const eT* Xm = X.memptr();
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return ( Xm[pos<0,0>::n2]*Xm[pos<1,1>::n2] - Xm[pos<0,1>::n2]*Xm[pos<1,0>::n2] );
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}
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template<typename eT>
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inline
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eT
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op_det::apply_tiny_3x3(const Mat<eT>& X)
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{
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arma_extra_debug_sigprint();
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const eT* Xm = X.memptr();
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// const double tmp1 = X.at(0,0) * X.at(1,1) * X.at(2,2);
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// const double tmp2 = X.at(0,1) * X.at(1,2) * X.at(2,0);
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// const double tmp3 = X.at(0,2) * X.at(1,0) * X.at(2,1);
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// const double tmp4 = X.at(2,0) * X.at(1,1) * X.at(0,2);
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// const double tmp5 = X.at(2,1) * X.at(1,2) * X.at(0,0);
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// const double tmp6 = X.at(2,2) * X.at(1,0) * X.at(0,1);
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// return (tmp1+tmp2+tmp3) - (tmp4+tmp5+tmp6);
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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]);
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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]);
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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]);
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return ( val1 - val2 + val3 );
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}
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template<typename eT>
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inline
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eT
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op_det::apply_tiny_4x4(const Mat<eT>& X)
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{
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arma_extra_debug_sigprint();
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const eT* Xm = X.memptr();
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const eT val_03_12 = Xm[pos<0,3>::n4] * Xm[pos<1,2>::n4];
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const eT val_02_13 = Xm[pos<0,2>::n4] * Xm[pos<1,3>::n4];
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const eT val_03_11 = Xm[pos<0,3>::n4] * Xm[pos<1,1>::n4];
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const eT val_01_13 = Xm[pos<0,1>::n4] * Xm[pos<1,3>::n4];
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const eT val_02_11 = Xm[pos<0,2>::n4] * Xm[pos<1,1>::n4];
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const eT val_01_12 = Xm[pos<0,1>::n4] * Xm[pos<1,2>::n4];
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const eT val_03_10 = Xm[pos<0,3>::n4] * Xm[pos<1,0>::n4];
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const eT val_00_13 = Xm[pos<0,0>::n4] * Xm[pos<1,3>::n4];
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const eT val_02_10 = Xm[pos<0,2>::n4] * Xm[pos<1,0>::n4];
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const eT val_00_12 = Xm[pos<0,0>::n4] * Xm[pos<1,2>::n4];
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const eT val_01_10 = Xm[pos<0,1>::n4] * Xm[pos<1,0>::n4];
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const eT val_00_11 = Xm[pos<0,0>::n4] * Xm[pos<1,1>::n4];
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const eT val_21_30 = Xm[pos<2,1>::n4] * Xm[pos<3,0>::n4];
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const eT val_22_30 = Xm[pos<2,2>::n4] * Xm[pos<3,0>::n4];
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const eT val_23_30 = Xm[pos<2,3>::n4] * Xm[pos<3,0>::n4];
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const eT val_20_31 = Xm[pos<2,0>::n4] * Xm[pos<3,1>::n4];
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const eT val_22_31 = Xm[pos<2,2>::n4] * Xm[pos<3,1>::n4];
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const eT val_23_31 = Xm[pos<2,3>::n4] * Xm[pos<3,1>::n4];
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const eT val_20_32 = Xm[pos<2,0>::n4] * Xm[pos<3,2>::n4];
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const eT val_21_32 = Xm[pos<2,1>::n4] * Xm[pos<3,2>::n4];
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const eT val_23_32 = Xm[pos<2,3>::n4] * Xm[pos<3,2>::n4];
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const eT val_20_33 = Xm[pos<2,0>::n4] * Xm[pos<3,3>::n4];
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const eT val_21_33 = Xm[pos<2,1>::n4] * Xm[pos<3,3>::n4];
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const eT val_22_33 = Xm[pos<2,2>::n4] * Xm[pos<3,3>::n4];
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const eT val = \
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val_03_12 * val_21_30 \
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- val_02_13 * val_21_30 \
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- val_03_11 * val_22_30 \
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+ val_01_13 * val_22_30 \
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+ val_02_11 * val_23_30 \
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- val_01_12 * val_23_30 \
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- val_03_12 * val_20_31 \
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+ val_02_13 * val_20_31 \
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+ val_03_10 * val_22_31 \
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- val_00_13 * val_22_31 \
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- val_02_10 * val_23_31 \
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+ val_00_12 * val_23_31 \
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+ val_03_11 * val_20_32 \
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- val_01_13 * val_20_32 \
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- val_03_10 * val_21_32 \
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+ val_00_13 * val_21_32 \
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+ val_01_10 * val_23_32 \
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- val_00_11 * val_23_32 \
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- val_02_11 * val_20_33 \
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+ val_01_12 * val_20_33 \
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+ val_02_10 * val_21_33 \
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- val_00_12 * val_21_33 \
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- val_01_10 * val_22_33 \
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+ val_00_11 * val_22_33 \
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;
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return val;
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}
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//! @}
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