677 lines
16 KiB
C++
677 lines
16 KiB
C++
// 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 fn_trace
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//! @{
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template<typename T1>
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arma_warn_unused
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inline
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typename T1::elem_type
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trace(const Base<typename T1::elem_type, T1>& 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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const Proxy<T1> P(X.get_ref());
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const uword N = (std::min)(P.get_n_rows(), P.get_n_cols());
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eT val1 = eT(0);
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eT val2 = eT(0);
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uword i,j;
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for(i=0, j=1; j<N; i+=2, j+=2)
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{
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val1 += P.at(i,i);
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val2 += P.at(j,j);
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}
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if(i < N)
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{
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val1 += P.at(i,i);
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}
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return val1 + val2;
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}
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template<typename T1>
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arma_warn_unused
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inline
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typename T1::elem_type
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trace(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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const diagmat_proxy<T1> A(X.m);
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const uword N = (std::min)(A.n_rows, A.n_cols);
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eT val = eT(0);
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for(uword i=0; i<N; ++i)
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{
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val += A[i];
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}
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return val;
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}
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//! speedup for trace(A*B); non-complex elements
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template<typename T1, typename T2>
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arma_warn_unused
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inline
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typename enable_if2< is_cx<typename T1::elem_type>::no, typename T1::elem_type>::result
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trace(const Glue<T1, T2, glue_times>& 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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const partial_unwrap<T1> tmp1(X.A);
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const partial_unwrap<T2> tmp2(X.B);
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const typename partial_unwrap<T1>::stored_type& A = tmp1.M;
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const typename partial_unwrap<T2>::stored_type& B = tmp2.M;
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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 ? (tmp1.get_val() * tmp2.get_val()) : eT(0);
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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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if( (A.n_elem == 0) || (B.n_elem == 0) )
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{
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return eT(0);
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}
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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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eT acc = eT(0);
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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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const uword N = (std::min)(A_n_rows, B_n_cols);
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eT acc1 = eT(0);
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eT acc2 = eT(0);
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for(uword k=0; k < N; ++k)
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{
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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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}
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acc = (acc1 + acc2);
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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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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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acc += op_dot::direct_dot(A_n_rows, A_colptr, B_colptr);
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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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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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// 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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}
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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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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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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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}
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}
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return (use_alpha) ? (alpha * acc) : acc;
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}
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//! speedup for trace(A*B); complex elements
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template<typename T1, typename T2>
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arma_warn_unused
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inline
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typename enable_if2< is_cx<typename T1::elem_type>::yes, typename T1::elem_type>::result
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trace(const Glue<T1, T2, glue_times>& X)
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{
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arma_extra_debug_sigprint();
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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> tmp1(X.A);
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const partial_unwrap<T2> tmp2(X.B);
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const typename partial_unwrap<T1>::stored_type& A = tmp1.M;
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const typename partial_unwrap<T2>::stored_type& B = tmp2.M;
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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 ? (tmp1.get_val() * tmp2.get_val()) : eT(0);
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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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if( (A.n_elem == 0) || (B.n_elem == 0) )
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{
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return eT(0);
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}
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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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eT acc = eT(0);
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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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const uword N = (std::min)(A_n_rows, B_n_cols);
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T acc_real = T(0);
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T acc_imag = T(0);
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for(uword k=0; k < N; ++k)
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{
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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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for(uword i=0; i < A_n_cols; ++i)
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{
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// acc += A.at(k, i) * B_colptr[i];
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const std::complex<T>& xx = A.at(k, i);
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const std::complex<T>& yy = B_colptr[i];
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const T a = xx.real();
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const T b = xx.imag();
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const T c = yy.real();
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const T d = yy.imag();
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acc_real += (a*c) - (b*d);
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acc_imag += (a*d) + (b*c);
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}
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}
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acc = std::complex<T>(acc_real, acc_imag);
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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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const uword N = (std::min)(A_n_cols, B_n_cols);
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T acc_real = T(0);
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T acc_imag = T(0);
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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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for(uword i=0; i < A_n_rows; ++i)
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{
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// acc += std::conj(A_colptr[i]) * B_colptr[i];
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const std::complex<T>& xx = A_colptr[i];
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const std::complex<T>& yy = B_colptr[i];
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const T a = xx.real();
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const T b = xx.imag();
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const T c = yy.real();
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const T d = yy.imag();
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// take into account the complex conjugate of xx
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acc_real += (a*c) + (b*d);
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acc_imag += (a*d) - (b*c);
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}
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}
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acc = std::complex<T>(acc_real, acc_imag);
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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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const uword N = (std::min)(A_n_rows, B_n_rows);
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T acc_real = T(0);
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T acc_imag = T(0);
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for(uword k=0; k < N; ++k)
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{
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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) * std::conj(B.at(k,i));
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const std::complex<T>& xx = A.at(k, i);
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const std::complex<T>& yy = B.at(k, i);
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const T a = xx.real();
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const T b = xx.imag();
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const T c = yy.real();
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const T d = -yy.imag(); // take the conjugate
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acc_real += (a*c) - (b*d);
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acc_imag += (a*d) + (b*c);
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}
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}
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acc = std::complex<T>(acc_real, acc_imag);
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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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const uword N = (std::min)(A_n_cols, B_n_rows);
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T acc_real = T(0);
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T acc_imag = T(0);
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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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// 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 += std::conj(A_colptr[i]) * std::conj(B.at(k,i));
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const std::complex<T>& xx = A_colptr[i];
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const std::complex<T>& yy = B.at(k, i);
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const T a = xx.real();
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const T b = -xx.imag(); // take the conjugate
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const T c = yy.real();
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const T d = -yy.imag(); // take the conjugate
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acc_real += (a*c) - (b*d);
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acc_imag += (a*d) + (b*c);
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}
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}
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acc = std::complex<T>(acc_real, acc_imag);
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}
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return (use_alpha) ? eT(alpha * acc) : eT(acc);
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}
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//! trace of sparse object; generic version
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template<typename T1>
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arma_warn_unused
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inline
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typename T1::elem_type
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trace(const SpBase<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 SpProxy<T1> P(expr.get_ref());
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const uword N = (std::min)(P.get_n_rows(), P.get_n_cols());
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eT acc = eT(0);
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if( (is_SpMat<typename SpProxy<T1>::stored_type>::value) && (P.get_n_nonzero() >= 5*N) )
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{
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const unwrap_spmat<typename SpProxy<T1>::stored_type> U(P.Q);
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const SpMat<eT>& X = U.M;
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for(uword i=0; i < N; ++i)
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{
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acc += X.at(i,i); // use binary search
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}
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}
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else
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{
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typename SpProxy<T1>::const_iterator_type it = P.begin();
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const uword P_n_nz = P.get_n_nonzero();
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for(uword i=0; i < P_n_nz; ++i)
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{
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if(it.row() == it.col()) { acc += (*it); }
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++it;
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}
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}
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return acc;
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}
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//! trace of sparse object; speedup for trace(A + B)
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template<typename T1, typename T2>
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arma_warn_unused
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inline
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typename T1::elem_type
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trace(const SpGlue<T1, T2, spglue_plus>& expr)
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{
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arma_extra_debug_sigprint();
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const unwrap_spmat<T1> UA(expr.A);
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const unwrap_spmat<T2> UB(expr.B);
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arma_debug_assert_same_size(UA.M.n_rows, UA.M.n_cols, UB.M.n_rows, UB.M.n_cols, "addition");
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return (trace(UA.M) + trace(UB.M));
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}
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//! trace of sparse object; speedup for trace(A - B)
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template<typename T1, typename T2>
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arma_warn_unused
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inline
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typename T1::elem_type
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trace(const SpGlue<T1, T2, spglue_minus>& expr)
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{
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arma_extra_debug_sigprint();
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const unwrap_spmat<T1> UA(expr.A);
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const unwrap_spmat<T2> UB(expr.B);
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arma_debug_assert_same_size(UA.M.n_rows, UA.M.n_cols, UB.M.n_rows, UB.M.n_cols, "subtraction");
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return (trace(UA.M) - trace(UB.M));
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}
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//! trace of sparse object; speedup for trace(A % B)
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template<typename T1, typename T2>
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arma_warn_unused
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inline
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typename T1::elem_type
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trace(const SpGlue<T1, T2, spglue_schur>& 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 unwrap_spmat<T1> UA(expr.A);
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const unwrap_spmat<T2> UB(expr.B);
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const SpMat<eT>& A = UA.M;
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const SpMat<eT>& B = UB.M;
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arma_debug_assert_same_size(A.n_rows, A.n_cols, B.n_rows, B.n_cols, "element-wise multiplication");
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const uword N = (std::min)(A.n_rows, A.n_cols);
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eT acc = eT(0);
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for(uword i=0; i<N; ++i)
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{
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acc += A.at(i,i) * B.at(i,i);
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}
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return acc;
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}
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//! trace of sparse object; speedup for trace(A*B)
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template<typename T1, typename T2>
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arma_warn_unused
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inline
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typename T1::elem_type
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trace(const SpGlue<T1, T2, spglue_times>& 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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// better-than-nothing implementation
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const unwrap_spmat<T1> UA(expr.A);
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const unwrap_spmat<T2> UB(expr.B);
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const SpMat<eT>& A = UA.M;
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const SpMat<eT>& B = UB.M;
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arma_debug_assert_mul_size(A.n_rows, A.n_cols, B.n_rows, B.n_cols, "matrix multiplication");
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if( (A.n_nonzero == 0) || (B.n_nonzero == 0) )
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{
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return eT(0);
|
|
}
|
|
|
|
const uword N = (std::min)(A.n_rows, B.n_cols);
|
|
|
|
eT acc = eT(0);
|
|
|
|
// TODO: the threshold may need tuning for complex matrices
|
|
if( (A.n_nonzero >= 5*N) || (B.n_nonzero >= 5*N) )
|
|
{
|
|
for(uword k=0; k < N; ++k)
|
|
{
|
|
typename SpMat<eT>::const_col_iterator B_it = B.begin_col_no_sync(k);
|
|
typename SpMat<eT>::const_col_iterator B_it_end = B.end_col_no_sync(k);
|
|
|
|
while(B_it != B_it_end)
|
|
{
|
|
const eT B_val = (*B_it);
|
|
const uword i = B_it.row();
|
|
|
|
acc += A.at(k,i) * B_val;
|
|
|
|
++B_it;
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
const SpMat<eT> AB = A * B;
|
|
|
|
acc = trace(AB);
|
|
}
|
|
|
|
return acc;
|
|
}
|
|
|
|
|
|
|
|
//! trace of sparse object; speedup for trace(A.t()*B); non-complex elements
|
|
template<typename T1, typename T2>
|
|
arma_warn_unused
|
|
inline
|
|
typename enable_if2< is_cx<typename T1::elem_type>::no, typename T1::elem_type>::result
|
|
trace(const SpGlue<SpOp<T1, spop_htrans>, T2, spglue_times>& expr)
|
|
{
|
|
arma_extra_debug_sigprint();
|
|
|
|
typedef typename T1::elem_type eT;
|
|
|
|
const unwrap_spmat<T1> UA(expr.A.m);
|
|
const unwrap_spmat<T2> UB(expr.B);
|
|
|
|
const SpMat<eT>& A = UA.M;
|
|
const SpMat<eT>& B = UB.M;
|
|
|
|
// NOTE: deliberately swapped A.n_rows and A.n_cols to take into account the requested transpose operation
|
|
arma_debug_assert_mul_size(A.n_cols, A.n_rows, B.n_rows, B.n_cols, "matrix multiplication");
|
|
|
|
if( (A.n_nonzero == 0) || (B.n_nonzero == 0) )
|
|
{
|
|
return eT(0);
|
|
}
|
|
|
|
const uword N = (std::min)(A.n_cols, B.n_cols);
|
|
|
|
eT acc = eT(0);
|
|
|
|
if( (A.n_nonzero >= 5*N) || (B.n_nonzero >= 5*N) )
|
|
{
|
|
for(uword k=0; k < N; ++k)
|
|
{
|
|
typename SpMat<eT>::const_col_iterator B_it = B.begin_col_no_sync(k);
|
|
typename SpMat<eT>::const_col_iterator B_it_end = B.end_col_no_sync(k);
|
|
|
|
while(B_it != B_it_end)
|
|
{
|
|
const eT B_val = (*B_it);
|
|
const uword i = B_it.row();
|
|
|
|
acc += A.at(i,k) * B_val;
|
|
|
|
++B_it;
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
const SpMat<eT> AtB = A.t() * B;
|
|
|
|
acc = trace(AtB);
|
|
}
|
|
|
|
return acc;
|
|
}
|
|
|
|
|
|
|
|
//! trace of sparse object; speedup for trace(A.t()*B); complex elements
|
|
template<typename T1, typename T2>
|
|
arma_warn_unused
|
|
inline
|
|
typename enable_if2< is_cx<typename T1::elem_type>::yes, typename T1::elem_type>::result
|
|
trace(const SpGlue<SpOp<T1, spop_htrans>, T2, spglue_times>& expr)
|
|
{
|
|
arma_extra_debug_sigprint();
|
|
|
|
typedef typename T1::elem_type eT;
|
|
|
|
const unwrap_spmat<T1> UA(expr.A.m);
|
|
const unwrap_spmat<T2> UB(expr.B);
|
|
|
|
const SpMat<eT>& A = UA.M;
|
|
const SpMat<eT>& B = UB.M;
|
|
|
|
// NOTE: deliberately swapped A.n_rows and A.n_cols to take into account the requested transpose operation
|
|
arma_debug_assert_mul_size(A.n_cols, A.n_rows, B.n_rows, B.n_cols, "matrix multiplication");
|
|
|
|
if( (A.n_nonzero == 0) || (B.n_nonzero == 0) )
|
|
{
|
|
return eT(0);
|
|
}
|
|
|
|
const uword N = (std::min)(A.n_cols, B.n_cols);
|
|
|
|
eT acc = eT(0);
|
|
|
|
// TODO: the threshold may need tuning for complex matrices
|
|
if( (A.n_nonzero >= 5*N) || (B.n_nonzero >= 5*N) )
|
|
{
|
|
for(uword k=0; k < N; ++k)
|
|
{
|
|
typename SpMat<eT>::const_col_iterator B_it = B.begin_col_no_sync(k);
|
|
typename SpMat<eT>::const_col_iterator B_it_end = B.end_col_no_sync(k);
|
|
|
|
while(B_it != B_it_end)
|
|
{
|
|
const eT B_val = (*B_it);
|
|
const uword i = B_it.row();
|
|
|
|
acc += std::conj(A.at(i,k)) * B_val;
|
|
|
|
++B_it;
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
const SpMat<eT> AtB = A.t() * B;
|
|
|
|
acc = trace(AtB);
|
|
}
|
|
|
|
return acc;
|
|
}
|
|
|
|
|
|
|
|
//! @}
|