// Copyright (C) 2008-2010 NICTA (www.nicta.com.au)
// Copyright (C) 2008-2010 Conrad Sanderson
// 
// This file is part of the Armadillo C++ library.
// It is provided without any warranty of fitness
// for any purpose. You can redistribute this file
// and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published
// by the Free Software Foundation, either version 3
// of the License or (at your option) any later version.
// (see http://www.opensource.org/licenses for more info)


//! \addtogroup glue_times
//! @{



template<u32 N>
template<typename T1, typename T2>
inline
void
glue_times_redirect<N>::apply(Mat<typename T1::elem_type>& out, const Glue<T1,T2,glue_times>& X)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  const partial_unwrap_check<T1> tmp1(X.A, out);
  const partial_unwrap_check<T2> tmp2(X.B, out);
  
  const Mat<eT>& A = tmp1.M;
  const Mat<eT>& B = tmp2.M;
  
  const bool do_trans_A = tmp1.do_trans;
  const bool do_trans_B = tmp2.do_trans;

  const bool use_alpha = tmp1.do_times | tmp2.do_times;
  const eT       alpha = use_alpha ? (tmp1.val * tmp2.val) : eT(0);
  
  glue_times::apply(out, A, B, alpha, do_trans_A, do_trans_B, use_alpha);
  }



template<typename T1, typename T2, typename T3>
inline
void
glue_times_redirect<3>::apply(Mat<typename T1::elem_type>& out, const Glue< Glue<T1,T2,glue_times>, T3, glue_times>& X)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  // there is exactly 3 objects
  // hence we can safely expand X as X.A.A, X.A.B and X.B
  
  const partial_unwrap_check<T1> tmp1(X.A.A, out);
  const partial_unwrap_check<T2> tmp2(X.A.B, out);
  const partial_unwrap_check<T3> tmp3(X.B,   out);
  
  const Mat<eT>& A = tmp1.M;
  const Mat<eT>& B = tmp2.M;
  const Mat<eT>& C = tmp3.M;
  
  const bool do_trans_A = tmp1.do_trans;
  const bool do_trans_B = tmp2.do_trans;
  const bool do_trans_C = tmp3.do_trans;
  
  const bool use_alpha = tmp1.do_times | tmp2.do_times | tmp3.do_times;
  const eT       alpha = use_alpha ? (tmp1.val * tmp2.val * tmp3.val) : eT(0);
  
  glue_times::apply(out, A, B, C, alpha, do_trans_A, do_trans_B, do_trans_C, use_alpha);
  }



template<typename T1, typename T2, typename T3, typename T4>
inline
void
glue_times_redirect<4>::apply(Mat<typename T1::elem_type>& out, const Glue< Glue< Glue<T1,T2,glue_times>, T3, glue_times>, T4, glue_times>& X)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  // there is exactly 4 objects
  // hence we can safely expand X as X.A.A.A, X.A.A.B, X.A.B and X.B
  
  const partial_unwrap_check<T1> tmp1(X.A.A.A, out);
  const partial_unwrap_check<T2> tmp2(X.A.A.B, out);
  const partial_unwrap_check<T3> tmp3(X.A.B,   out);
  const partial_unwrap_check<T4> tmp4(X.B,     out);
  
  const Mat<eT>& A = tmp1.M;
  const Mat<eT>& B = tmp2.M;
  const Mat<eT>& C = tmp3.M;
  const Mat<eT>& D = tmp4.M;
  
  const bool do_trans_A = tmp1.do_trans;
  const bool do_trans_B = tmp2.do_trans;
  const bool do_trans_C = tmp3.do_trans;
  const bool do_trans_D = tmp4.do_trans;
  
  const bool use_alpha = tmp1.do_times | tmp2.do_times | tmp3.do_times | tmp4.do_times;
  const eT       alpha = use_alpha ? (tmp1.val * tmp2.val * tmp3.val * tmp4.val) : eT(0);
  
  glue_times::apply(out, A, B, C, D, alpha, do_trans_A, do_trans_B, do_trans_C, do_trans_D, use_alpha);
  }



template<typename T1, typename T2>
inline
void
glue_times::apply(Mat<typename T1::elem_type>& out, const Glue<T1,T2,glue_times>& X)
  {
  arma_extra_debug_sigprint();

  typedef typename T1::elem_type eT;

  const s32 N_mat = 1 + depth_lhs< glue_times, Glue<T1,T2,glue_times> >::num;

  arma_extra_debug_print(arma_boost::format("N_mat = %d") % N_mat);

  glue_times_redirect<N_mat>::apply(out, X);
  }



template<typename T1>
inline
void
glue_times::apply_inplace(Mat<typename T1::elem_type>& out, const T1& X)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  const unwrap_check<T1> tmp(X, out);
  const Mat<eT>& B     = tmp.M;
  
  arma_debug_assert_mul_size(out, B, "matrix multiply");
  
  if(out.n_cols == B.n_cols)
    {
    podarray<eT> tmp(out.n_cols);
    eT* tmp_rowdata = tmp.memptr();
    
    for(u32 out_row=0; out_row < out.n_rows; ++out_row)
      {
      for(u32 out_col=0; out_col < out.n_cols; ++out_col)
        {
        tmp_rowdata[out_col] = out.at(out_row,out_col);
        }
      
      for(u32 B_col=0; B_col < B.n_cols; ++B_col)
        {
        const eT* B_coldata = B.colptr(B_col);
        
        eT val = eT(0);
        for(u32 i=0; i < B.n_rows; ++i)
          {
          val += tmp_rowdata[i] * B_coldata[i];
          }
        
        out.at(out_row,B_col) = val;
        }
      }
    
    }
  else
    {
    const Mat<eT> tmp(out);
    glue_times::apply(out, tmp, B, eT(1), false, false, false);
    }
  
  }



template<typename T1, typename T2>
arma_hot
inline
void
glue_times::apply_inplace_plus(Mat<typename T1::elem_type>& out, const Glue<T1, T2, glue_times>& X, const s32 sign)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  const partial_unwrap_check<T1> tmp1(X.A, out);
  const partial_unwrap_check<T2> tmp2(X.B, out);
  
  const Mat<eT>& A     = tmp1.M;
  const Mat<eT>& B     = tmp2.M;
  const eT       alpha = tmp1.val * tmp2.val * ( (sign > s32(0)) ? eT(1) : eT(-1) );
  
  const bool do_trans_A = tmp1.do_trans;
  const bool do_trans_B = tmp2.do_trans;
  const bool use_alpha  = tmp1.do_times | tmp2.do_times | (sign < s32(0));
  
  arma_debug_assert_mul_size(A, B, do_trans_A, do_trans_B, "matrix multiply");
  
  const u32 result_n_rows = (do_trans_A == false) ? A.n_rows : A.n_cols;
  const u32 result_n_cols = (do_trans_B == false) ? B.n_cols : B.n_rows;
  
  arma_assert_same_size(out.n_rows, out.n_cols, result_n_rows, result_n_cols, "matrix addition");
  
  if( (do_trans_A == false) && (do_trans_B == false) && (use_alpha == false) )
    {
    if(A.n_rows == 1)
      {
      gemv<true,         false, true>::apply(out.memptr(), B, A.memptr(), alpha, eT(1));
      }
    else
    if(B.n_cols == 1)
      {
      gemv<false,        false, true>::apply(out.memptr(), A, B.memptr(), alpha, eT(1));
      }
    else
      {
      gemm<false, false, false, true>::apply(out, A, B, alpha, eT(1));
      }
    }
  else
  if( (do_trans_A == false) && (do_trans_B == false) && (use_alpha == true) )
    {
    if(A.n_rows == 1)
      {
      gemv<true,         true, true>::apply(out.memptr(), B, A.memptr(), alpha, eT(1));
      }
    else
    if(B.n_cols == 1)
      {
      gemv<false,        true, true>::apply(out.memptr(), A, B.memptr(), alpha, eT(1));
      }
    else
      {
      gemm<false, false, true, true>::apply(out, A, B, alpha, eT(1));
      }
    }
  else
  if( (do_trans_A == true) && (do_trans_B == false) && (use_alpha == false) )
    {
    if(A.n_cols == 1)
      {
      gemv<true,        false, true>::apply(out.memptr(), B, A.memptr(), alpha, eT(1));
      }
    else
    if(B.n_cols == 1)
      {
      gemv<true,        false, true>::apply(out.memptr(), A, B.memptr(), alpha, eT(1));
      }
    else
      {
      gemm<true, false, false, true>::apply(out, A, B, alpha, eT(1));
      }
    }
  else
  if( (do_trans_A == true) && (do_trans_B == false) && (use_alpha == true) )
    {
    if(A.n_cols == 1)
      {
      gemv<true,        true, true>::apply(out.memptr(), B, A.memptr(), alpha, eT(1));
      }
    else
    if(B.n_cols == 1)
      {
      gemv<true,        true, true>::apply(out.memptr(), A, B.memptr(), alpha, eT(1));
      }
    else
      {
      gemm<true, false, true, true>::apply(out, A, B, alpha, eT(1));
      }
    }
  else
  if( (do_trans_A == false) && (do_trans_B == true) && (use_alpha == false) )
    {
    if(A.n_rows == 1)
      {
      gemv<false,       false, true>::apply(out.memptr(), B, A.memptr(), alpha, eT(1));
      }
    else
    if(B.n_rows == 1)
      {
      gemv<false,       false, true>::apply(out.memptr(), A, B.memptr(), alpha, eT(1));
      }
    else
      {
      gemm<false, true, false, true>::apply(out, A, B, alpha, eT(1));
      }
    }
  else
  if( (do_trans_A == false) && (do_trans_B == true) && (use_alpha == true) )
    {
    if(A.n_rows == 1)
      {
      gemv<false,       true, true>::apply(out.memptr(), B, A.memptr(), alpha, eT(1));
      }
    else
    if(B.n_rows == 1)
      {
      gemv<false,       true, true>::apply(out.memptr(), A, B.memptr(), alpha, eT(1));
      }
    else
      {
      gemm<false, true, true, true>::apply(out, A, B, alpha, eT(1));
      }
    }
  else
  if( (do_trans_A == true) && (do_trans_B == true) && (use_alpha == false) )
    {
    if(A.n_cols == 1)
      {
      gemv<false,      false, true>::apply(out.memptr(), B, A.memptr(), alpha, eT(1));
      }
    else
    if(B.n_rows == 1)
      {
      gemv<true,       false, true>::apply(out.memptr(), A, B.memptr(), alpha, eT(1));
      }
    else
      {
      gemm<true, true, false, true>::apply(out, A, B, alpha, eT(1));
      }
    }
  else
  if( (do_trans_A == true) && (do_trans_B == true) && (use_alpha == true) )
    {
    if(A.n_cols == 1)
      {
      gemv<false,      true, true>::apply(out.memptr(), B, A.memptr(), alpha, eT(1));
      }
    else
    if(B.n_rows == 1)
      {
      gemv<true,       true, true>::apply(out.memptr(), A, B.memptr(), alpha, eT(1));
      }
    else
      {
      gemm<true, true, true, true>::apply(out, A, B, alpha, eT(1));
      }
    }
  
  
  }



template<typename eT>
arma_inline
u32
glue_times::mul_storage_cost(const Mat<eT>& A, const Mat<eT>& B, const bool do_trans_A, const bool do_trans_B)
  {
  const u32 final_A_n_rows = (do_trans_A == false) ? A.n_rows : A.n_cols;
  const u32 final_B_n_cols = (do_trans_B == false) ? B.n_cols : B.n_rows;
  
  return final_A_n_rows * final_B_n_cols;
  }



template<typename eT>
arma_hot
inline
void
glue_times::apply
  (
        Mat<eT>& out,
  const Mat<eT>& A,
  const Mat<eT>& B,
  const eT       alpha,
  const bool     do_trans_A,
  const bool     do_trans_B,
  const bool     use_alpha
  )
  {
  arma_extra_debug_sigprint();
  
  arma_debug_assert_mul_size(A, B, do_trans_A, do_trans_B, "matrix multiply");
  
  const u32 final_n_rows = (do_trans_A == false) ? A.n_rows : A.n_cols;
  const u32 final_n_cols = (do_trans_B == false) ? B.n_cols : B.n_rows;
  
  out.set_size(final_n_rows, final_n_cols);
  
  // TODO: thoroughly test all combinations
  
  if( (do_trans_A == false) && (do_trans_B == false) && (use_alpha == false) )
    {
    if(A.n_rows == 1)
      {
      gemv<true,         false, false>::apply(out.memptr(), B, A.memptr());
      }
    else
    if(B.n_cols == 1)
      {
      gemv<false,        false, false>::apply(out.memptr(), A, B.memptr());
      }
    else
      {
      gemm<false, false, false, false>::apply(out, A, B);
      }
    }
  else
  if( (do_trans_A == false) && (do_trans_B == false) && (use_alpha == true) )
    {
    if(A.n_rows == 1)
      {
      gemv<true,         true, false>::apply(out.memptr(), B, A.memptr(), alpha);
      }
    else
    if(B.n_cols == 1)
      {
      gemv<false,        true, false>::apply(out.memptr(), A, B.memptr(), alpha);
      }
    else
      {
      gemm<false, false, true, false>::apply(out, A, B, alpha);
      }
    }
  else
  if( (do_trans_A == true) && (do_trans_B == false) && (use_alpha == false) )
    {
    if(A.n_cols == 1)
      {
      gemv<true,        false, false>::apply(out.memptr(), B, A.memptr());
      }
    else
    if(B.n_cols == 1)
      {
      gemv<true,        false, false>::apply(out.memptr(), A, B.memptr());
      }
    else
      {
      gemm<true, false, false, false>::apply(out, A, B);
      }
    }
  else
  if( (do_trans_A == true) && (do_trans_B == false) && (use_alpha == true) )
    {
    if(A.n_cols == 1)
      {
      gemv<true,        true, false>::apply(out.memptr(), B, A.memptr(), alpha);
      }
    else
    if(B.n_cols == 1)
      {
      gemv<true,        true, false>::apply(out.memptr(), A, B.memptr(), alpha);
      }
    else
      {
      gemm<true, false, true, false>::apply(out, A, B, alpha);
      }
    }
  else
  if( (do_trans_A == false) && (do_trans_B == true) && (use_alpha == false) )
    {
    if(A.n_rows == 1)
      {
      gemv<false,       false, false>::apply(out.memptr(), B, A.memptr());
      }
    else
    if(B.n_rows == 1)
      {
      gemv<false,       false, false>::apply(out.memptr(), A, B.memptr());
      }
    else
      {
      gemm<false, true, false, false>::apply(out, A, B);
      }
    }
  else
  if( (do_trans_A == false) && (do_trans_B == true) && (use_alpha == true) )
    {
    if(A.n_rows == 1)
      {
      gemv<false,       true, false>::apply(out.memptr(), B, A.memptr(), alpha);
      }
    else
    if(B.n_rows == 1)
      {
      gemv<false,       true, false>::apply(out.memptr(), A, B.memptr(), alpha);
      }
    else
      {
      gemm<false, true, true, false>::apply(out, A, B, alpha);
      }
    }
  else
  if( (do_trans_A == true) && (do_trans_B == true) && (use_alpha == false) )
    {
    if(A.n_cols == 1)
      {
      gemv<false,      false, false>::apply(out.memptr(), B, A.memptr());
      }
    else
    if(B.n_rows == 1)
      {
      gemv<true,       false, false>::apply(out.memptr(), A, B.memptr());
      }
    else
      {
      gemm<true, true, false, false>::apply(out, A, B);
      }
    }
  else
  if( (do_trans_A == true) && (do_trans_B == true) && (use_alpha == true) )
    {
    if(A.n_cols == 1)
      {
      gemv<false,      true, false>::apply(out.memptr(), B, A.memptr(), alpha);
      }
    else
    if(B.n_rows == 1)
      {
      gemv<true,       true, false>::apply(out.memptr(), A, B.memptr(), alpha);
      }
    else
      {
      gemm<true, true, true, false>::apply(out, A, B, alpha);
      }
    }
  }



template<typename eT>
inline
void
glue_times::apply
  (
        Mat<eT>& out,
  const Mat<eT>& A,
  const Mat<eT>& B,
  const Mat<eT>& C,
  const eT       alpha,
  const bool     do_trans_A,
  const bool     do_trans_B,
  const bool     do_trans_C,
  const bool     use_alpha
  )
  {
  arma_extra_debug_sigprint();
  
  Mat<eT> tmp;
  
  if( glue_times::mul_storage_cost(A, B, do_trans_A, do_trans_B) <= glue_times::mul_storage_cost(B, C, do_trans_B, do_trans_C) )
    {
    // out = (A*B)*C
    glue_times::apply(tmp, A,   B, alpha, do_trans_A, do_trans_B, use_alpha);
    glue_times::apply(out, tmp, C, eT(0), false,      do_trans_C, false    );
    }
  else
    {
    // out = A*(B*C)
    glue_times::apply(tmp, B, C,   alpha, do_trans_B, do_trans_C, use_alpha);
    glue_times::apply(out, A, tmp, eT(0), do_trans_A, false,      false    );
    }
  }



template<typename eT>
inline
void
glue_times::apply
  (
        Mat<eT>& out,
  const Mat<eT>& A,
  const Mat<eT>& B,
  const Mat<eT>& C,
  const Mat<eT>& D,
  const eT       alpha,
  const bool     do_trans_A,
  const bool     do_trans_B,
  const bool     do_trans_C,
  const bool     do_trans_D,
  const bool     use_alpha
  )
  {
  arma_extra_debug_sigprint();
  
  Mat<eT> tmp;
  
  if( glue_times::mul_storage_cost(A, C, do_trans_A, do_trans_C) <= glue_times::mul_storage_cost(B, D, do_trans_B, do_trans_D) )
    {
    // out = (A*B*C)*D
    glue_times::apply(tmp, A, B, C, alpha, do_trans_A, do_trans_B, do_trans_C, use_alpha);
    
    glue_times::apply(out, tmp, D, eT(0), false, do_trans_D, false);
    }
  else
    {
    // out = A*(B*C*D)
    glue_times::apply(tmp, B, C, D, alpha, do_trans_B, do_trans_C, do_trans_D, use_alpha);
    
    glue_times::apply(out, A, tmp, eT(0), do_trans_A, false, false);
    }
  }



//
// glue_times_diag


template<typename T1, typename T2>
arma_hot
inline
void
glue_times_diag::apply(Mat<typename T1::elem_type>& out, const Glue<T1, T2, glue_times_diag>& X)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  const strip_diagmat<T1> S1(X.A);
  const strip_diagmat<T2> S2(X.B);
  
  typedef typename strip_diagmat<T1>::stored_type T1_stripped;
  typedef typename strip_diagmat<T2>::stored_type T2_stripped;
  
  if( (S1.do_diagmat == true) && (S2.do_diagmat == false) )
    {
    const diagmat_proxy_check<T1_stripped> A(S1.M, out);
    
    const unwrap_check<T2> tmp(X.B, out);
    const Mat<eT>& B     = tmp.M;
    
    arma_debug_assert_mul_size(A.n_elem, A.n_elem, B.n_rows, B.n_cols, "matrix multiply");
    
    out.set_size(A.n_elem, B.n_cols);
    
    for(u32 col=0; col<B.n_cols; ++col)
      {
            eT* out_coldata = out.colptr(col);
      const eT* B_coldata   = B.colptr(col);
      
      for(u32 row=0; row<B.n_rows; ++row)
        {
        out_coldata[row] = A[row] * B_coldata[row];
        }
      }
    }
  else
  if( (S1.do_diagmat == false) && (S2.do_diagmat == true) )
    {
    const unwrap_check<T1> tmp(X.A, out);
    const Mat<eT>& A     = tmp.M;
    
    const diagmat_proxy_check<T2_stripped> B(S2.M, out);
    
    arma_debug_assert_mul_size(A.n_rows, A.n_cols, B.n_elem, B.n_elem, "matrix multiply");
    
    out.set_size(A.n_rows, B.n_elem);
    
    for(u32 col=0; col<A.n_cols; ++col)
      {
      const eT  val = B[col];
      
            eT* out_coldata = out.colptr(col);
      const eT*   A_coldata =   A.colptr(col);
    
      for(u32 row=0; row<A.n_rows; ++row)
        {
        out_coldata[row] = A_coldata[row] * val;
        }
      }
    }
  else
  if( (S1.do_diagmat == true) && (S2.do_diagmat == true) )
    {
    const diagmat_proxy_check<T1_stripped> A(S1.M, out);
    const diagmat_proxy_check<T2_stripped> B(S2.M, out);
    
    arma_debug_assert_mul_size(A.n_elem, A.n_elem, B.n_elem, B.n_elem, "matrix multiply");
    
    out.zeros(A.n_elem, A.n_elem);
    
    for(u32 i=0; i<A.n_elem; ++i)
      {
      out.at(i,i) = A[i] * B[i];
      }
    }
  }



//! @}
