// 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 operator_times
//! @{



//! Base * scalar
template<typename T1>
arma_inline
typename enable_if2< is_arma_type<T1>::value, const eOp<T1, eop_scalar_times> >::result
operator*
(const T1& X, const typename T1::elem_type k)
  {
  arma_extra_debug_sigprint();
  
  return eOp<T1, eop_scalar_times>(X,k);
  }



//! scalar * Base
template<typename T1>
arma_inline
typename enable_if2< is_arma_type<T1>::value, const eOp<T1, eop_scalar_times> >::result
operator*
(const typename T1::elem_type k, const T1& X)
  {
  arma_extra_debug_sigprint();
  
  return eOp<T1, eop_scalar_times>(X,k);  // NOTE: order is swapped
  }



//! non-complex Base * complex scalar
template<typename T1>
arma_inline
typename
enable_if2
  <
  (is_arma_type<T1>::value && is_cx<typename T1::elem_type>::no),
  const mtOp<typename std::complex<typename T1::pod_type>, T1, op_cx_scalar_times>
  >::result
operator*
  (
  const T1&                                  X,
  const std::complex<typename T1::pod_type>& k
  )
  {
  arma_extra_debug_sigprint();
  
  return mtOp<typename std::complex<typename T1::pod_type>, T1, op_cx_scalar_times>('j', X, k);
  }



//! complex scalar * non-complex Base
template<typename T1>
arma_inline
typename
enable_if2
  <
  (is_arma_type<T1>::value && is_cx<typename T1::elem_type>::no),
  const mtOp<typename std::complex<typename T1::pod_type>, T1, op_cx_scalar_times>
  >::result
operator*
  (
  const std::complex<typename T1::pod_type>& k,
  const T1&                                  X
  )
  {
  arma_extra_debug_sigprint();
  
  return mtOp<typename std::complex<typename T1::pod_type>, T1, op_cx_scalar_times>('j', X, k);
  }



//! scalar * trans(T1)
template<typename T1>
arma_inline
const Op<T1, op_htrans2>
operator*
(const typename T1::elem_type k, const Op<T1, op_htrans>& X)
  {
  arma_extra_debug_sigprint();
  
  return Op<T1, op_htrans2>(X.m, k);
  }



//! trans(T1) * scalar
template<typename T1>
arma_inline
const Op<T1, op_htrans2>
operator*
(const Op<T1, op_htrans>& X, const typename T1::elem_type k)
  {
  arma_extra_debug_sigprint();
  
  return Op<T1, op_htrans2>(X.m, k);
  }



//! Base * diagmat
template<typename T1, typename T2>
arma_inline
typename
enable_if2
  <
  (is_arma_type<T1>::value && is_same_type<typename T1::elem_type, typename T2::elem_type>::value),
  const Glue<T1, Op<T2, op_diagmat>, glue_times_diag>
  >::result
operator*
(const T1& X, const Op<T2, op_diagmat>& Y)
  {
  arma_extra_debug_sigprint();
  
  return Glue<T1, Op<T2, op_diagmat>, glue_times_diag>(X, Y);
  }



//! diagmat * Base
template<typename T1, typename T2>
arma_inline
typename
enable_if2
  <
  (is_arma_type<T2>::value && is_same_type<typename T1::elem_type, typename T2::elem_type>::value),
  const Glue<Op<T1, op_diagmat>, T2, glue_times_diag>
  >::result
operator*
(const Op<T1, op_diagmat>& X, const T2& Y)
  {
  arma_extra_debug_sigprint();
  
  return Glue<Op<T1, op_diagmat>, T2, glue_times_diag>(X, Y);
  }



//! diagmat * diagmat
template<typename T1, typename T2>
inline
Mat< typename promote_type<typename T1::elem_type, typename T2::elem_type>::result >
operator*
(const Op<T1, op_diagmat>& X, const Op<T2, op_diagmat>& Y)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT1;
  typedef typename T2::elem_type eT2;
  
  typedef typename promote_type<eT1,eT2>::result out_eT;
  
  promote_type<eT1,eT2>::check();
  
  const diagmat_proxy<T1> A(X.m);
  const diagmat_proxy<T2> B(Y.m);
  
  arma_debug_assert_mul_size(A.n_rows, A.n_cols, B.n_rows, B.n_cols, "matrix multiplication");
  
  Mat<out_eT> out(A.n_rows, B.n_cols, fill::zeros);
  
  const uword A_length = (std::min)(A.n_rows, A.n_cols);
  const uword B_length = (std::min)(B.n_rows, B.n_cols);
  
  const uword N = (std::min)(A_length, B_length);
  
  for(uword i=0; i<N; ++i)
    {
    out.at(i,i) = upgrade_val<eT1,eT2>::apply( A[i] ) * upgrade_val<eT1,eT2>::apply( B[i] );
    }
  
  return out;
  }



//! multiplication of Base objects with same element type
template<typename T1, typename T2>
arma_inline
typename
enable_if2
  <
  is_arma_type<T1>::value && is_arma_type<T2>::value && is_same_type<typename T1::elem_type, typename T2::elem_type>::value,
  const Glue<T1, T2, glue_times>
  >::result
operator*
(const T1& X, const T2& Y)
  {
  arma_extra_debug_sigprint();
  
  return Glue<T1, T2, glue_times>(X, Y);
  }



//! multiplication of Base objects with different element types
template<typename T1, typename T2>
inline
typename
enable_if2
  <
  (is_arma_type<T1>::value && is_arma_type<T2>::value && (is_same_type<typename T1::elem_type, typename T2::elem_type>::no)),
  const mtGlue< typename promote_type<typename T1::elem_type, typename T2::elem_type>::result, T1, T2, glue_mixed_times >
  >::result
operator*
  (
  const T1& X,
  const T2& Y
  )
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT1;
  typedef typename T2::elem_type eT2;
  
  typedef typename promote_type<eT1,eT2>::result out_eT;
  
  promote_type<eT1,eT2>::check();
  
  return mtGlue<out_eT, T1, T2, glue_mixed_times>( X, Y );
  }



//! sparse multiplied by scalar
template<typename T1>
inline
typename
enable_if2
  <
  is_arma_sparse_type<T1>::value,
  SpOp<T1,spop_scalar_times>
  >::result
operator*
  (
  const T1& X,
  const typename T1::elem_type k
  )
  {
  arma_extra_debug_sigprint();
  
  return SpOp<T1,spop_scalar_times>(X, k);
  }



template<typename T1>
inline
typename
enable_if2
  <
  is_arma_sparse_type<T1>::value,
  SpOp<T1,spop_scalar_times>
  >::result
operator*
  (
  const typename T1::elem_type k,
  const T1& X
  )
  {
  arma_extra_debug_sigprint();
  
  return SpOp<T1,spop_scalar_times>(X, k);
  }



//! multiplication of two sparse objects
template<typename T1, typename T2>
inline
arma_hot
typename
enable_if2
  <
  (is_arma_sparse_type<T1>::value && is_arma_sparse_type<T2>::value && is_same_type<typename T1::elem_type, typename T2::elem_type>::value),
  const SpGlue<T1,T2,spglue_times>
  >::result
operator*
  (
  const T1& x,
  const T2& y
  )
  {
  arma_extra_debug_sigprint();

  return SpGlue<T1,T2,spglue_times>(x, y);
  }



//! convert "(sparse + sparse) * scalar" to specialised operation "scalar * (sparse + sparse)"
template<typename T1, typename T2>
inline
const SpGlue<T1,T2,spglue_plus2>
operator*
  (
  const SpGlue<T1,T2,spglue_plus>& X,
  const typename T1::elem_type k
  )
  {
  arma_extra_debug_sigprint();
  
  return SpGlue<T1,T2,spglue_plus2>(X.A, X.B, k);
  }



//! convert "scalar * (sparse + sparse)" to specialised operation 
template<typename T1, typename T2>
inline
const SpGlue<T1,T2,spglue_plus2>
operator*
  (
  const typename T1::elem_type k,
  const SpGlue<T1,T2,spglue_plus>& X
  )
  {
  arma_extra_debug_sigprint();
  
  return SpGlue<T1,T2,spglue_plus2>(X.A, X.B, k);
  }



//! convert "(sparse - sparse) * scalar" to specialised operation "scalar * (sparse - sparse)"
template<typename T1, typename T2>
inline
const SpGlue<T1,T2,spglue_minus2>
operator*
  (
  const SpGlue<T1,T2,spglue_minus>& X,
  const typename T1::elem_type k
  )
  {
  arma_extra_debug_sigprint();
  
  return SpGlue<T1,T2,spglue_minus2>(X.A, X.B, k);
  }



//! convert "scalar * (sparse - sparse)" to specialised operation 
template<typename T1, typename T2>
inline
const SpGlue<T1,T2,spglue_minus2>
operator*
  (
  const typename T1::elem_type k,
  const SpGlue<T1,T2,spglue_minus>& X
  )
  {
  arma_extra_debug_sigprint();
  
  return SpGlue<T1,T2,spglue_minus2>(X.A, X.B, k);
  }



//! convert "(sparse*sparse) * scalar" to specialised operation "scalar * (sparse*sparse)"
template<typename T1, typename T2>
inline
const SpGlue<T1,T2,spglue_times2>
operator*
  (
  const SpGlue<T1,T2,spglue_times>& X,
  const typename T1::elem_type k
  )
  {
  arma_extra_debug_sigprint();
  
  return SpGlue<T1,T2,spglue_times2>(X.A, X.B, k);
  }



//! convert "scalar * (sparse*sparse)" to specialised operation
template<typename T1, typename T2>
inline
const SpGlue<T1,T2,spglue_times2>
operator*
  (
  const typename T1::elem_type k,
  const SpGlue<T1,T2,spglue_times>& X
  )
  {
  arma_extra_debug_sigprint();
  
  return SpGlue<T1,T2,spglue_times2>(X.A, X.B, k);
  }



//! convert "(scalar*sparse) * sparse" to specialised operation "scalar * (sparse*sparse)"
template<typename T1, typename T2>
inline
typename
enable_if2
  <
  is_arma_sparse_type<T2>::value,
  const SpGlue<T1,T2,spglue_times2>
  >::result
operator*
  (
  const SpOp<T1,spop_scalar_times>& X,
  const T2& Y
  )
  {
  arma_extra_debug_sigprint();
  
  return SpGlue<T1,T2,spglue_times2>(X.m, Y, X.aux);
  }



//! convert "sparse * (scalar*sparse)" to specialised operation "scalar * (sparse*sparse)"
template<typename T1, typename T2>
inline
typename
enable_if2
  <
  is_arma_sparse_type<T1>::value,
  const SpGlue<T1,T2,spglue_times2>
  >::result
operator*
  (
  const T1& X,
  const SpOp<T2,spop_scalar_times>& Y
  )
  {
  arma_extra_debug_sigprint();
  
  return SpGlue<T1,T2,spglue_times2>(X, Y.m, Y.aux);
  }



//! multiplication of one sparse and one dense object
template<typename T1, typename T2>
inline
typename
enable_if2
  <
  (is_arma_sparse_type<T1>::value && is_arma_type<T2>::value && is_same_type<typename T1::elem_type, typename T2::elem_type>::value),
  Mat<typename T1::elem_type>
  >::result
operator*
  (
  const T1& x,
  const T2& y
  )
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  const SpProxy<T1> pa(x);
  const   Proxy<T2> pb(y);
  
  arma_debug_assert_mul_size(pa.get_n_rows(), pa.get_n_cols(), pb.get_n_rows(), pb.get_n_cols(), "matrix multiplication");
  
  Mat<eT> result(pa.get_n_rows(), pb.get_n_cols());
  result.zeros();
  
  if( (pa.get_n_nonzero() > 0) && (pb.get_n_elem() > 0) )
    {
    typename SpProxy<T1>::const_iterator_type x_it     = pa.begin();
    typename SpProxy<T1>::const_iterator_type x_it_end = pa.end();
    
    const uword result_n_cols = result.n_cols;
      
    while(x_it != x_it_end)
      {
      const eT    x_it_val = (*x_it);
      const uword x_it_row = x_it.row();
      const uword x_it_col = x_it.col();
      
      for(uword col = 0; col < result_n_cols; ++col)
        {
        result.at(x_it_row, col) += x_it_val * pb.at(x_it_col, col);
        }
      
      ++x_it;
      }
    }
  
  return result;
  }



//! multiplication of one dense and one sparse object
template<typename T1, typename T2>
inline
typename
enable_if2
  <
  (is_arma_type<T1>::value && is_arma_sparse_type<T2>::value && is_same_type<typename T1::elem_type, typename T2::elem_type>::value),
  Mat<typename T1::elem_type>
  >::result
operator*
  (
  const T1& x,
  const T2& y
  )
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  const   Proxy<T1> pa(x);
  const SpProxy<T2> pb(y);
  
  arma_debug_assert_mul_size(pa.get_n_rows(), pa.get_n_cols(), pb.get_n_rows(), pb.get_n_cols(), "matrix multiplication");
  
  Mat<eT> result(pa.get_n_rows(), pb.get_n_cols());
  result.zeros();
  
  if( (pa.get_n_elem() > 0) && (pb.get_n_nonzero() > 0) )
    {
    typename SpProxy<T2>::const_iterator_type y_it     = pb.begin();
    typename SpProxy<T2>::const_iterator_type y_it_end = pb.end();
    
    const uword result_n_rows = result.n_rows;
    
    while(y_it != y_it_end)
      {
      const eT    y_it_val = (*y_it);
      const uword y_it_col = y_it.col();
      const uword y_it_row = y_it.row();
      
      for(uword row = 0; row < result_n_rows; ++row)
        {
        result.at(row, y_it_col) += pa.at(row, y_it_row) * y_it_val;
        }
      
      ++y_it;
      }
    }
  
  return result;
  }



//! @}
