768 lines
20 KiB
C++
768 lines
20 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_diagmat
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//! @{
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template<typename T1>
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inline
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void
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op_diagmat::apply(Mat<typename T1::elem_type>& out, const Op<T1, op_diagmat>& X)
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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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if(is_Mat<T1>::value)
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{
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// allow detection of in-place operation
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const unwrap<T1> U(X.m);
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const Mat<eT>& A = U.M;
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if(&out != &A) // no aliasing
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{
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const Proxy< Mat<eT> > P(A);
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op_diagmat::apply(out, P);
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}
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else // we have aliasing
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{
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const uword n_rows = out.n_rows;
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const uword n_cols = out.n_cols;
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if((n_rows == 1) || (n_cols == 1)) // create diagonal matrix from vector
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{
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const eT* out_mem = out.memptr();
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const uword N = out.n_elem;
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Mat<eT> tmp(N,N, arma_zeros_indicator());
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for(uword i=0; i<N; ++i) { tmp.at(i,i) = out_mem[i]; }
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out.steal_mem(tmp);
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}
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else // create diagonal matrix from matrix
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{
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const uword N = (std::min)(n_rows, n_cols);
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for(uword i=0; i < n_cols; ++i)
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{
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if(i < N)
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{
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eT& out_ii = out.at(i,i);
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const eT val = out_ii;
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arrayops::fill_zeros(out.colptr(i), n_rows);
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out_ii = val;
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}
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else
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{
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arrayops::fill_zeros(out.colptr(i), n_rows);
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}
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}
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}
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}
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}
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else
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{
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const Proxy<T1> P(X.m);
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if(P.is_alias(out))
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{
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Mat<eT> tmp;
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op_diagmat::apply(tmp, P);
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out.steal_mem(tmp);
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}
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else
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{
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op_diagmat::apply(out, P);
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}
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}
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}
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template<typename T1>
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inline
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void
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op_diagmat::apply(Mat<typename T1::elem_type>& out, const Proxy<T1>& P)
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{
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arma_extra_debug_sigprint();
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const uword n_rows = P.get_n_rows();
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const uword n_cols = P.get_n_cols();
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const uword n_elem = P.get_n_elem();
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if(n_elem == 0) { out.reset(); return; }
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const bool P_is_vec = (T1::is_row) || (T1::is_col) || (n_rows == 1) || (n_cols == 1);
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if(P_is_vec)
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{
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out.zeros(n_elem, n_elem);
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if(Proxy<T1>::use_at == false)
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{
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typename Proxy<T1>::ea_type Pea = P.get_ea();
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for(uword i=0; i < n_elem; ++i) { out.at(i,i) = Pea[i]; }
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}
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else
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{
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if(n_rows == 1)
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{
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for(uword i=0; i < n_elem; ++i) { out.at(i,i) = P.at(0,i); }
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}
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else
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{
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for(uword i=0; i < n_elem; ++i) { out.at(i,i) = P.at(i,0); }
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}
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}
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}
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else // P represents a matrix
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{
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out.zeros(n_rows, n_cols);
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const uword N = (std::min)(n_rows, n_cols);
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for(uword i=0; i<N; ++i) { out.at(i,i) = P.at(i,i); }
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}
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}
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template<typename T1, typename T2>
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inline
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void
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op_diagmat::apply(Mat<typename T1::elem_type>& out, const Op< Glue<T1,T2,glue_times>, op_diagmat>& X)
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{
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arma_extra_debug_sigprint();
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op_diagmat::apply_times(out, X.m.A, X.m.B);
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}
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template<typename T1, typename T2>
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inline
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void
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op_diagmat::apply_times(Mat<typename T1::elem_type>& actual_out, const T1& X, const T2& Y, const typename arma_not_cx<typename T1::elem_type>::result* junk)
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{
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arma_extra_debug_sigprint();
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arma_ignore(junk);
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typedef typename T1::elem_type eT;
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const partial_unwrap<T1> UA(X);
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const partial_unwrap<T2> UB(Y);
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const typename partial_unwrap<T1>::stored_type& A = UA.M;
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const typename partial_unwrap<T2>::stored_type& B = UB.M;
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arma_debug_assert_trans_mul_size< partial_unwrap<T1>::do_trans, partial_unwrap<T2>::do_trans >(A.n_rows, A.n_cols, B.n_rows, B.n_cols, "matrix multiplication");
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const bool use_alpha = partial_unwrap<T1>::do_times || partial_unwrap<T2>::do_times;
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const eT alpha = use_alpha ? (UA.get_val() * UB.get_val()) : eT(0);
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const uword A_n_rows = A.n_rows;
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const uword A_n_cols = A.n_cols;
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const uword B_n_rows = B.n_rows;
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const uword B_n_cols = B.n_cols;
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// check if the multiplication results in a vector
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if( (partial_unwrap<T1>::do_trans == false) && (partial_unwrap<T2>::do_trans == false) )
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{
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if((A_n_rows == 1) || (B_n_cols == 1))
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{
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arma_extra_debug_print("trans_A = false; trans_B = false; vector result");
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const Mat<eT> C = A*B;
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const eT* C_mem = C.memptr();
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const uword N = C.n_elem;
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actual_out.zeros(N,N);
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for(uword i=0; i<N; ++i) { actual_out.at(i,i) = (use_alpha) ? eT(alpha * C_mem[i]) : eT(C_mem[i]); }
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return;
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}
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}
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else
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if( (partial_unwrap<T1>::do_trans == true ) && (partial_unwrap<T2>::do_trans == false) )
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{
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if((A_n_cols == 1) || (B_n_cols == 1))
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{
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arma_extra_debug_print("trans_A = true; trans_B = false; vector result");
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const Mat<eT> C = trans(A)*B;
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const eT* C_mem = C.memptr();
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const uword N = C.n_elem;
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actual_out.zeros(N,N);
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for(uword i=0; i<N; ++i) { actual_out.at(i,i) = (use_alpha) ? eT(alpha * C_mem[i]) : eT(C_mem[i]); }
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return;
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}
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}
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else
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if( (partial_unwrap<T1>::do_trans == false) && (partial_unwrap<T2>::do_trans == true ) )
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{
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if((A_n_rows == 1) || (B_n_rows == 1))
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{
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arma_extra_debug_print("trans_A = false; trans_B = true; vector result");
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const Mat<eT> C = A*trans(B);
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const eT* C_mem = C.memptr();
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const uword N = C.n_elem;
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actual_out.zeros(N,N);
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for(uword i=0; i<N; ++i) { actual_out.at(i,i) = (use_alpha) ? eT(alpha * C_mem[i]) : eT(C_mem[i]); }
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return;
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}
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}
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else
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if( (partial_unwrap<T1>::do_trans == true ) && (partial_unwrap<T2>::do_trans == true ) )
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{
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if((A_n_cols == 1) || (B_n_rows == 1))
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{
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arma_extra_debug_print("trans_A = true; trans_B = true; vector result");
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const Mat<eT> C = trans(A)*trans(B);
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const eT* C_mem = C.memptr();
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const uword N = C.n_elem;
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actual_out.zeros(N,N);
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for(uword i=0; i<N; ++i) { actual_out.at(i,i) = (use_alpha) ? eT(alpha * C_mem[i]) : eT(C_mem[i]); }
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return;
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}
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}
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// if we got to this point, the multiplication results in a matrix
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const bool is_alias = (UA.is_alias(actual_out) || UB.is_alias(actual_out));
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Mat<eT> tmp;
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Mat<eT>& out = (is_alias) ? tmp : actual_out;
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if( (partial_unwrap<T1>::do_trans == false) && (partial_unwrap<T2>::do_trans == false) )
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{
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arma_extra_debug_print("trans_A = false; trans_B = false; matrix result");
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out.zeros(A_n_rows, B_n_cols);
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const uword N = (std::min)(A_n_rows, B_n_cols);
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for(uword k=0; k < N; ++k)
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{
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eT acc1 = eT(0);
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eT acc2 = eT(0);
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const eT* B_colptr = B.colptr(k);
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// condition: A_n_cols = B_n_rows
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uword j;
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for(j=1; j < A_n_cols; j+=2)
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{
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const uword i = (j-1);
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const eT tmp_i = B_colptr[i];
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const eT tmp_j = B_colptr[j];
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acc1 += A.at(k, i) * tmp_i;
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acc2 += A.at(k, j) * tmp_j;
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}
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const uword i = (j-1);
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if(i < A_n_cols)
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{
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acc1 += A.at(k, i) * B_colptr[i];
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}
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const eT acc = acc1 + acc2;
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out.at(k,k) = (use_alpha) ? eT(alpha * acc) : eT(acc);
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}
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}
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else
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if( (partial_unwrap<T1>::do_trans == true ) && (partial_unwrap<T2>::do_trans == false) )
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{
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arma_extra_debug_print("trans_A = true; trans_B = false; matrix result");
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out.zeros(A_n_cols, B_n_cols);
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const uword N = (std::min)(A_n_cols, B_n_cols);
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for(uword k=0; k < N; ++k)
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{
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const eT* A_colptr = A.colptr(k);
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const eT* B_colptr = B.colptr(k);
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// condition: A_n_rows = B_n_rows
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const eT acc = op_dot::direct_dot(A_n_rows, A_colptr, B_colptr);
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out.at(k,k) = (use_alpha) ? eT(alpha * acc) : eT(acc);
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}
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}
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else
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if( (partial_unwrap<T1>::do_trans == false) && (partial_unwrap<T2>::do_trans == true ) )
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{
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arma_extra_debug_print("trans_A = false; trans_B = true; matrix result");
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out.zeros(A_n_rows, B_n_rows);
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const uword N = (std::min)(A_n_rows, B_n_rows);
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for(uword k=0; k < N; ++k)
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{
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eT acc = eT(0);
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// condition: A_n_cols = B_n_cols
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for(uword i=0; i < A_n_cols; ++i)
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{
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acc += A.at(k,i) * B.at(k,i);
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}
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out.at(k,k) = (use_alpha) ? eT(alpha * acc) : eT(acc);
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}
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}
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else
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if( (partial_unwrap<T1>::do_trans == true ) && (partial_unwrap<T2>::do_trans == true ) )
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{
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arma_extra_debug_print("trans_A = true; trans_B = true; matrix result");
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out.zeros(A_n_cols, B_n_rows);
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const uword N = (std::min)(A_n_cols, B_n_rows);
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for(uword k=0; k < N; ++k)
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{
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eT acc = eT(0);
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const eT* A_colptr = A.colptr(k);
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// condition: A_n_rows = B_n_cols
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for(uword i=0; i < A_n_rows; ++i)
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{
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acc += A_colptr[i] * B.at(k,i);
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}
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out.at(k,k) = (use_alpha) ? eT(alpha * acc) : eT(acc);
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}
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}
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if(is_alias) { actual_out.steal_mem(tmp); }
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}
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template<typename T1, typename T2>
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inline
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void
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op_diagmat::apply_times(Mat<typename T1::elem_type>& actual_out, const T1& X, const T2& Y, const typename arma_cx_only<typename T1::elem_type>::result* junk)
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{
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arma_extra_debug_sigprint();
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arma_ignore(junk);
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typedef typename T1::pod_type T;
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typedef typename T1::elem_type eT;
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const partial_unwrap<T1> UA(X);
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const partial_unwrap<T2> UB(Y);
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const typename partial_unwrap<T1>::stored_type& A = UA.M;
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const typename partial_unwrap<T2>::stored_type& B = UB.M;
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arma_debug_assert_trans_mul_size< partial_unwrap<T1>::do_trans, partial_unwrap<T2>::do_trans >(A.n_rows, A.n_cols, B.n_rows, B.n_cols, "matrix multiplication");
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const bool use_alpha = partial_unwrap<T1>::do_times || partial_unwrap<T2>::do_times;
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const eT alpha = use_alpha ? (UA.get_val() * UB.get_val()) : eT(0);
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const uword A_n_rows = A.n_rows;
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const uword A_n_cols = A.n_cols;
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const uword B_n_rows = B.n_rows;
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const uword B_n_cols = B.n_cols;
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// check if the multiplication results in a vector
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if( (partial_unwrap<T1>::do_trans == false) && (partial_unwrap<T2>::do_trans == false) )
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{
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if((A_n_rows == 1) || (B_n_cols == 1))
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{
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arma_extra_debug_print("trans_A = false; trans_B = false; vector result");
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const Mat<eT> C = A*B;
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const eT* C_mem = C.memptr();
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const uword N = C.n_elem;
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actual_out.zeros(N,N);
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for(uword i=0; i<N; ++i) { actual_out.at(i,i) = (use_alpha) ? eT(alpha * C_mem[i]) : eT(C_mem[i]); }
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return;
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}
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}
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else
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if( (partial_unwrap<T1>::do_trans == true ) && (partial_unwrap<T2>::do_trans == false) )
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{
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if((A_n_cols == 1) || (B_n_cols == 1))
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{
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arma_extra_debug_print("trans_A = true; trans_B = false; vector result");
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const Mat<eT> C = trans(A)*B;
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const eT* C_mem = C.memptr();
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const uword N = C.n_elem;
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actual_out.zeros(N,N);
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for(uword i=0; i<N; ++i) { actual_out.at(i,i) = (use_alpha) ? eT(alpha * C_mem[i]) : eT(C_mem[i]); }
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return;
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}
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}
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else
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if( (partial_unwrap<T1>::do_trans == false) && (partial_unwrap<T2>::do_trans == true ) )
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{
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if((A_n_rows == 1) || (B_n_rows == 1))
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{
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arma_extra_debug_print("trans_A = false; trans_B = true; vector result");
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const Mat<eT> C = A*trans(B);
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const eT* C_mem = C.memptr();
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const uword N = C.n_elem;
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actual_out.zeros(N,N);
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for(uword i=0; i<N; ++i) { actual_out.at(i,i) = (use_alpha) ? eT(alpha * C_mem[i]) : eT(C_mem[i]); }
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return;
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}
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}
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else
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if( (partial_unwrap<T1>::do_trans == true ) && (partial_unwrap<T2>::do_trans == true ) )
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{
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if((A_n_cols == 1) || (B_n_rows == 1))
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{
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arma_extra_debug_print("trans_A = true; trans_B = true; vector result");
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const Mat<eT> C = trans(A)*trans(B);
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const eT* C_mem = C.memptr();
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const uword N = C.n_elem;
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actual_out.zeros(N,N);
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for(uword i=0; i<N; ++i) { actual_out.at(i,i) = (use_alpha) ? eT(alpha * C_mem[i]) : eT(C_mem[i]); }
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return;
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}
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}
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|
// if we got to this point, the multiplication results in a matrix
|
|
|
|
const bool is_alias = (UA.is_alias(actual_out) || UB.is_alias(actual_out));
|
|
|
|
Mat<eT> tmp;
|
|
Mat<eT>& out = (is_alias) ? tmp : actual_out;
|
|
|
|
if( (partial_unwrap<T1>::do_trans == false) && (partial_unwrap<T2>::do_trans == false) )
|
|
{
|
|
arma_extra_debug_print("trans_A = false; trans_B = false; matrix result");
|
|
|
|
out.zeros(A_n_rows, B_n_cols);
|
|
|
|
const uword N = (std::min)(A_n_rows, B_n_cols);
|
|
|
|
for(uword k=0; k < N; ++k)
|
|
{
|
|
T acc_real = T(0);
|
|
T acc_imag = T(0);
|
|
|
|
const eT* B_colptr = B.colptr(k);
|
|
|
|
// condition: A_n_cols = B_n_rows
|
|
|
|
for(uword i=0; i < A_n_cols; ++i)
|
|
{
|
|
// acc += A.at(k, i) * B_colptr[i];
|
|
|
|
const std::complex<T>& xx = A.at(k, i);
|
|
const std::complex<T>& yy = B_colptr[i];
|
|
|
|
const T a = xx.real();
|
|
const T b = xx.imag();
|
|
|
|
const T c = yy.real();
|
|
const T d = yy.imag();
|
|
|
|
acc_real += (a*c) - (b*d);
|
|
acc_imag += (a*d) + (b*c);
|
|
}
|
|
|
|
const eT acc = std::complex<T>(acc_real, acc_imag);
|
|
|
|
out.at(k,k) = (use_alpha) ? eT(alpha * acc) : eT(acc);
|
|
}
|
|
}
|
|
else
|
|
if( (partial_unwrap<T1>::do_trans == true) && (partial_unwrap<T2>::do_trans == false) )
|
|
{
|
|
arma_extra_debug_print("trans_A = true; trans_B = false; matrix result");
|
|
|
|
out.zeros(A_n_cols, B_n_cols);
|
|
|
|
const uword N = (std::min)(A_n_cols, B_n_cols);
|
|
|
|
for(uword k=0; k < N; ++k)
|
|
{
|
|
T acc_real = T(0);
|
|
T acc_imag = T(0);
|
|
|
|
const eT* A_colptr = A.colptr(k);
|
|
const eT* B_colptr = B.colptr(k);
|
|
|
|
// condition: A_n_rows = B_n_rows
|
|
|
|
for(uword i=0; i < A_n_rows; ++i)
|
|
{
|
|
// acc += std::conj(A_colptr[i]) * B_colptr[i];
|
|
|
|
const std::complex<T>& xx = A_colptr[i];
|
|
const std::complex<T>& yy = B_colptr[i];
|
|
|
|
const T a = xx.real();
|
|
const T b = xx.imag();
|
|
|
|
const T c = yy.real();
|
|
const T d = yy.imag();
|
|
|
|
// take into account the complex conjugate of xx
|
|
|
|
acc_real += (a*c) + (b*d);
|
|
acc_imag += (a*d) - (b*c);
|
|
}
|
|
|
|
const eT acc = std::complex<T>(acc_real, acc_imag);
|
|
|
|
out.at(k,k) = (use_alpha) ? eT(alpha * acc) : eT(acc);
|
|
}
|
|
}
|
|
else
|
|
if( (partial_unwrap<T1>::do_trans == false) && (partial_unwrap<T2>::do_trans == true) )
|
|
{
|
|
arma_extra_debug_print("trans_A = false; trans_B = true; matrix result");
|
|
|
|
out.zeros(A_n_rows, B_n_rows);
|
|
|
|
const uword N = (std::min)(A_n_rows, B_n_rows);
|
|
|
|
for(uword k=0; k < N; ++k)
|
|
{
|
|
T acc_real = T(0);
|
|
T acc_imag = T(0);
|
|
|
|
// condition: A_n_cols = B_n_cols
|
|
|
|
for(uword i=0; i < A_n_cols; ++i)
|
|
{
|
|
// acc += A.at(k,i) * std::conj(B.at(k,i));
|
|
|
|
const std::complex<T>& xx = A.at(k, i);
|
|
const std::complex<T>& yy = B.at(k, i);
|
|
|
|
const T a = xx.real();
|
|
const T b = xx.imag();
|
|
|
|
const T c = yy.real();
|
|
const T d = -yy.imag(); // take the conjugate
|
|
|
|
acc_real += (a*c) - (b*d);
|
|
acc_imag += (a*d) + (b*c);
|
|
}
|
|
|
|
const eT acc = std::complex<T>(acc_real, acc_imag);
|
|
|
|
out.at(k,k) = (use_alpha) ? eT(alpha * acc) : eT(acc);
|
|
}
|
|
}
|
|
else
|
|
if( (partial_unwrap<T1>::do_trans == true) && (partial_unwrap<T2>::do_trans == true) )
|
|
{
|
|
arma_extra_debug_print("trans_A = true; trans_B = true; matrix result");
|
|
|
|
out.zeros(A_n_cols, B_n_rows);
|
|
|
|
const uword N = (std::min)(A_n_cols, B_n_rows);
|
|
|
|
for(uword k=0; k < N; ++k)
|
|
{
|
|
T acc_real = T(0);
|
|
T acc_imag = T(0);
|
|
|
|
const eT* A_colptr = A.colptr(k);
|
|
|
|
// condition: A_n_rows = B_n_cols
|
|
|
|
for(uword i=0; i < A_n_rows; ++i)
|
|
{
|
|
// acc += std::conj(A_colptr[i]) * std::conj(B.at(k,i));
|
|
|
|
const std::complex<T>& xx = A_colptr[i];
|
|
const std::complex<T>& yy = B.at(k, i);
|
|
|
|
const T a = xx.real();
|
|
const T b = -xx.imag(); // take the conjugate
|
|
|
|
const T c = yy.real();
|
|
const T d = -yy.imag(); // take the conjugate
|
|
|
|
acc_real += (a*c) - (b*d);
|
|
acc_imag += (a*d) + (b*c);
|
|
}
|
|
|
|
const eT acc = std::complex<T>(acc_real, acc_imag);
|
|
|
|
out.at(k,k) = (use_alpha) ? eT(alpha * acc) : eT(acc);
|
|
}
|
|
}
|
|
|
|
if(is_alias) { actual_out.steal_mem(tmp); }
|
|
}
|
|
|
|
|
|
|
|
//
|
|
//
|
|
//
|
|
|
|
|
|
|
|
template<typename T1>
|
|
inline
|
|
void
|
|
op_diagmat2::apply(Mat<typename T1::elem_type>& out, const Op<T1, op_diagmat2>& X)
|
|
{
|
|
arma_extra_debug_sigprint();
|
|
|
|
typedef typename T1::elem_type eT;
|
|
|
|
const uword row_offset = X.aux_uword_a;
|
|
const uword col_offset = X.aux_uword_b;
|
|
|
|
const Proxy<T1> P(X.m);
|
|
|
|
if(P.is_alias(out))
|
|
{
|
|
Mat<eT> tmp;
|
|
|
|
op_diagmat2::apply(tmp, P, row_offset, col_offset);
|
|
|
|
out.steal_mem(tmp);
|
|
}
|
|
else
|
|
{
|
|
op_diagmat2::apply(out, P, row_offset, col_offset);
|
|
}
|
|
}
|
|
|
|
|
|
|
|
template<typename T1>
|
|
inline
|
|
void
|
|
op_diagmat2::apply(Mat<typename T1::elem_type>& out, const Proxy<T1>& P, const uword row_offset, const uword col_offset)
|
|
{
|
|
arma_extra_debug_sigprint();
|
|
|
|
const uword n_rows = P.get_n_rows();
|
|
const uword n_cols = P.get_n_cols();
|
|
const uword n_elem = P.get_n_elem();
|
|
|
|
if(n_elem == 0) { out.reset(); return; }
|
|
|
|
const bool P_is_vec = (T1::is_row) || (T1::is_col) || (n_rows == 1) || (n_cols == 1);
|
|
|
|
if(P_is_vec)
|
|
{
|
|
const uword n_pad = (std::max)(row_offset, col_offset);
|
|
|
|
out.zeros(n_elem + n_pad, n_elem + n_pad);
|
|
|
|
if(Proxy<T1>::use_at == false)
|
|
{
|
|
typename Proxy<T1>::ea_type Pea = P.get_ea();
|
|
|
|
for(uword i=0; i < n_elem; ++i) { out.at(row_offset + i, col_offset + i) = Pea[i]; }
|
|
}
|
|
else
|
|
{
|
|
if(n_rows == 1)
|
|
{
|
|
for(uword i=0; i < n_elem; ++i) { out.at(row_offset + i, col_offset + i) = P.at(0,i); }
|
|
}
|
|
else
|
|
{
|
|
for(uword i=0; i < n_elem; ++i) { out.at(row_offset + i, col_offset + i) = P.at(i,0); }
|
|
}
|
|
}
|
|
}
|
|
else // P represents a matrix
|
|
{
|
|
arma_debug_check_bounds
|
|
(
|
|
((row_offset > 0) && (row_offset >= n_rows)) || ((col_offset > 0) && (col_offset >= n_cols)),
|
|
"diagmat(): requested diagonal out of bounds"
|
|
);
|
|
|
|
out.zeros(n_rows, n_cols);
|
|
|
|
const uword N = (std::min)(n_rows - row_offset, n_cols - col_offset);
|
|
|
|
for(uword i=0; i<N; ++i)
|
|
{
|
|
const uword row = i + row_offset;
|
|
const uword col = i + col_offset;
|
|
|
|
out.at(row,col) = P.at(row,col);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
|
|
//! @}
|