// 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 fn_as_scalar
//! @{



template<uword N>
struct as_scalar_redirect
  {
  template<typename T1>
  inline static typename T1::elem_type apply(const T1& X);
  };



template<>
struct as_scalar_redirect<2>
  {
  template<typename T1, typename T2>
  inline static typename T1::elem_type apply(const Glue<T1,T2,glue_times>& X);
  };


template<>
struct as_scalar_redirect<3>
  {
  template<typename T1, typename T2, typename T3>
  inline static typename T1::elem_type apply(const Glue< Glue<T1, T2, glue_times>, T3, glue_times>& X);
  };



template<uword N>
template<typename T1>
inline
typename T1::elem_type
as_scalar_redirect<N>::apply(const T1& X)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  const Proxy<T1> P(X);
  
  if(P.get_n_elem() != 1)
    {
    arma_debug_check(true, "as_scalar(): expression doesn't evaluate to exactly one element");
    
    return Datum<eT>::nan;
    }
  
  return (Proxy<T1>::use_at) ? P.at(0,0) : P[0];
  }



template<typename T1, typename T2>
inline
typename T1::elem_type
as_scalar_redirect<2>::apply(const Glue<T1, T2, glue_times>& X)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  // T1 must result in a matrix with one row
  // T2 must result in a matrix with one column
  
  const bool has_all_mat = (is_Mat<T1>::value || is_Mat_trans<T1>::value) && (is_Mat<T2>::value || is_Mat_trans<T2>::value);
  
  const bool use_at = (Proxy<T1>::use_at || Proxy<T2>::use_at);
  
  const bool do_partial_unwrap = (has_all_mat || use_at);
  
  if(do_partial_unwrap)
    {
    const partial_unwrap<T1> tmp1(X.A);
    const partial_unwrap<T2> tmp2(X.B);
    
    typedef typename partial_unwrap<T1>::stored_type TA;
    typedef typename partial_unwrap<T2>::stored_type TB;
    
    const TA& A = tmp1.M;
    const TB& B = tmp2.M;
    
    const uword A_n_rows = (tmp1.do_trans == false) ? (TA::is_row ? 1 : A.n_rows) : (TA::is_col ? 1 : A.n_cols);
    const uword A_n_cols = (tmp1.do_trans == false) ? (TA::is_col ? 1 : A.n_cols) : (TA::is_row ? 1 : A.n_rows);
    
    const uword B_n_rows = (tmp2.do_trans == false) ? (TB::is_row ? 1 : B.n_rows) : (TB::is_col ? 1 : B.n_cols);
    const uword B_n_cols = (tmp2.do_trans == false) ? (TB::is_col ? 1 : B.n_cols) : (TB::is_row ? 1 : B.n_rows);
    
    arma_debug_check( (A_n_rows != 1) || (B_n_cols != 1) || (A_n_cols != B_n_rows), "as_scalar(): incompatible dimensions" );
    
    const eT val = op_dot::direct_dot(A.n_elem, A.memptr(), B.memptr());
    
    return (tmp1.do_times || tmp2.do_times) ? (val * tmp1.get_val() * tmp2.get_val()) : val;
    }
  else
    {
    const Proxy<T1> PA(X.A);
    const Proxy<T2> PB(X.B);
    
    arma_debug_check
      (
      (PA.get_n_rows() != 1) || (PB.get_n_cols() != 1) || (PA.get_n_cols() != PB.get_n_rows()),
      "as_scalar(): incompatible dimensions"
      );
    
    return op_dot::apply_proxy(PA,PB);
    }
  }



template<typename T1, typename T2, typename T3>
inline
typename T1::elem_type
as_scalar_redirect<3>::apply(const Glue< Glue<T1, T2, glue_times>, T3, glue_times >& X)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  // T1 * T2 must result in a matrix with one row
  // T3 must result in a matrix with one column
  
  typedef typename strip_inv    <T2           >::stored_type T2_stripped_1;
  typedef typename strip_diagmat<T2_stripped_1>::stored_type T2_stripped_2;
  
  const strip_inv    <T2>            strip1(X.A.B);
  const strip_diagmat<T2_stripped_1> strip2(strip1.M);
  
  const bool tmp2_do_inv     = strip1.do_inv;
  const bool tmp2_do_diagmat = strip2.do_diagmat;
  
  if(tmp2_do_diagmat == false)
    {
    const Mat<eT> tmp(X);
    
    if(tmp.n_elem != 1)
      {
      arma_debug_check(true, "as_scalar(): expression doesn't evaluate to exactly one element");
      
      return Datum<eT>::nan;
      }
    
    return tmp[0];
    }
  else
    {
    const partial_unwrap<T1>            tmp1(X.A.A);
    const partial_unwrap<T2_stripped_2> tmp2(strip2.M);
    const partial_unwrap<T3>            tmp3(X.B);
    
    const Mat<eT>& A = tmp1.M;
    const Mat<eT>& B = tmp2.M;
    const Mat<eT>& C = tmp3.M;
    
    const uword A_n_rows = (tmp1.do_trans == false) ? A.n_rows : A.n_cols;
    const uword A_n_cols = (tmp1.do_trans == false) ? A.n_cols : A.n_rows;
    
    const bool B_is_vec = B.is_vec();
    
    const uword B_n_rows = (B_is_vec) ? B.n_elem : ( (tmp2.do_trans == false) ? B.n_rows : B.n_cols );
    const uword B_n_cols = (B_is_vec) ? B.n_elem : ( (tmp2.do_trans == false) ? B.n_cols : B.n_rows );
    
    const uword C_n_rows = (tmp3.do_trans == false) ? C.n_rows : C.n_cols;
    const uword C_n_cols = (tmp3.do_trans == false) ? C.n_cols : C.n_rows;
    
    const eT val = tmp1.get_val() * tmp2.get_val() * tmp3.get_val();
    
    arma_debug_check
      (
      (A_n_rows != 1)        ||
      (C_n_cols != 1)        ||
      (A_n_cols != B_n_rows) ||
      (B_n_cols != C_n_rows)
      ,
      "as_scalar(): incompatible dimensions"
      );
    
    
    if(B_is_vec)
      {
      if(tmp2_do_inv)
        {
        return val * op_dotext::direct_rowvec_invdiagvec_colvec(A.mem, B, C.mem);
        }
      else
        {
        return val * op_dot::direct_dot(A.n_elem, A.mem, B.mem, C.mem);
        }
      }
    else
      {
      if(tmp2_do_inv)
        {
        return val * op_dotext::direct_rowvec_invdiagmat_colvec(A.mem, B, C.mem);
        }
      else
        {
        return val * op_dotext::direct_rowvec_diagmat_colvec(A.mem, B, C.mem);
        }
      }
    }
  }



template<typename T1>
inline
typename T1::elem_type
as_scalar_diag(const Base<typename T1::elem_type,T1>& X)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  const unwrap<T1>   tmp(X.get_ref());
  const Mat<eT>& A = tmp.M;
  
  if(A.n_elem != 1)
    {
    arma_debug_check(true, "as_scalar(): expression doesn't evaluate to exactly one element");
    
    return Datum<eT>::nan;
    }
  
  return A.mem[0];
  }



template<typename T1, typename T2, typename T3>
inline
typename T1::elem_type
as_scalar_diag(const Glue< Glue<T1, T2, glue_times_diag>, T3, glue_times >& X)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  // T1 * T2 must result in a matrix with one row
  // T3 must result in a matrix with one column
  
  typedef typename strip_diagmat<T2>::stored_type T2_stripped;
  
  const strip_diagmat<T2> strip(X.A.B);
  
  const partial_unwrap<T1>          tmp1(X.A.A);
  const partial_unwrap<T2_stripped> tmp2(strip.M);
  const partial_unwrap<T3>          tmp3(X.B);
  
  const Mat<eT>& A = tmp1.M;
  const Mat<eT>& B = tmp2.M;
  const Mat<eT>& C = tmp3.M;
  
  
  const uword A_n_rows = (tmp1.do_trans == false) ? A.n_rows : A.n_cols;
  const uword A_n_cols = (tmp1.do_trans == false) ? A.n_cols : A.n_rows;
  
  const bool B_is_vec = B.is_vec();
  
  const uword B_n_rows = (B_is_vec) ? B.n_elem : ( (tmp2.do_trans == false) ? B.n_rows : B.n_cols );
  const uword B_n_cols = (B_is_vec) ? B.n_elem : ( (tmp2.do_trans == false) ? B.n_cols : B.n_rows );
  
  const uword C_n_rows = (tmp3.do_trans == false) ? C.n_rows : C.n_cols;
  const uword C_n_cols = (tmp3.do_trans == false) ? C.n_cols : C.n_rows;
  
  const eT val = tmp1.get_val() * tmp2.get_val() * tmp3.get_val();
  
  arma_debug_check
    (
    (A_n_rows != 1)        ||
    (C_n_cols != 1)        ||
    (A_n_cols != B_n_rows) ||
    (B_n_cols != C_n_rows)
    ,
    "as_scalar(): incompatible dimensions"
    );
  
  
  if(B_is_vec)
    {
    return val * op_dot::direct_dot(A.n_elem, A.mem, B.mem, C.mem);
    }
  else
    {
    return val * op_dotext::direct_rowvec_diagmat_colvec(A.mem, B, C.mem);
    }
  }



template<typename T1, typename T2>
arma_warn_unused
arma_inline
typename T1::elem_type
as_scalar(const Glue<T1, T2, glue_times>& X, const typename arma_not_cx<typename T1::elem_type>::result* junk = nullptr)
  {
  arma_extra_debug_sigprint();
  arma_ignore(junk);
  
  if(is_glue_times_diag<T1>::value == false)
    {
    const sword N_mat = 1 + depth_lhs< glue_times, Glue<T1,T2,glue_times> >::num;
    
    arma_extra_debug_print(arma_str::format("N_mat = %d") % N_mat);
    
    return as_scalar_redirect<N_mat>::apply(X);
    }
  else
    {
    return as_scalar_diag(X);
    }
  }



template<typename T1>
arma_warn_unused
inline
typename T1::elem_type
as_scalar(const Base<typename T1::elem_type,T1>& X)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  const Proxy<T1> P(X.get_ref());
  
  if(P.get_n_elem() != 1)
    {
    arma_debug_check(true, "as_scalar(): expression doesn't evaluate to exactly one element");
    
    return Datum<eT>::nan;
    }
  
  return (Proxy<T1>::use_at) ? P.at(0,0) : P[0];
  }


template<typename T1>
arma_warn_unused
inline
typename T1::elem_type
as_scalar(const Gen<T1, gen_randu>& X)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  if( (X.n_rows != 1) || (X.n_cols != 1) )
    {
    arma_debug_check(true, "as_scalar(): expression doesn't evaluate to exactly one element");
    
    return Datum<eT>::nan;
    }
  
  return eT(arma_rng::randu<eT>());
  }



template<typename T1>
arma_warn_unused
inline
typename T1::elem_type
as_scalar(const Gen<T1, gen_randn>& X)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  if( (X.n_rows != 1) || (X.n_cols != 1) )
    {
    arma_debug_check(true, "as_scalar(): expression doesn't evaluate to exactly one element");
    
    return Datum<eT>::nan;
    }
  
  return eT(arma_rng::randn<eT>());
  }



template<typename T1>
arma_warn_unused
inline
typename T1::elem_type
as_scalar(const BaseCube<typename T1::elem_type,T1>& X)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::elem_type eT;
  
  const ProxyCube<T1> P(X.get_ref());
  
  if(P.get_n_elem() != 1)
    {
    arma_debug_check(true, "as_scalar(): expression doesn't evaluate to exactly one element");
    
    return Datum<eT>::nan;
    }
  
  return (ProxyCube<T1>::use_at) ? P.at(0,0,0) : P[0];
  }



template<typename T>
arma_warn_unused
arma_inline
typename arma_scalar_only<T>::result
as_scalar(const T& x)
  {
  return x;
  }



template<typename T1>
arma_warn_unused
inline
typename T1::elem_type
as_scalar(const SpBase<typename T1::elem_type, T1>& X)
  {
  typedef typename T1::elem_type eT;
  
  const unwrap_spmat<T1>  tmp(X.get_ref());
  const SpMat<eT>& A    = tmp.M;
  
  if(A.n_elem != 1)
    {
    arma_debug_check(true, "as_scalar(): expression doesn't evaluate to exactly one element");
    
    return Datum<eT>::nan;
    }
  
  return A.at(0,0);
  }



//! @}
