// 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_spsolve
//! @{

//! Solve a system of linear equations, i.e., A*X = B, where X is unknown,
//! A is sparse, and B is dense.  X will be dense too.

template<typename T1, typename T2>
inline
bool
spsolve_helper
  (
           Mat<typename T1::elem_type>&     out,
  const SpBase<typename T1::elem_type, T1>& A,
  const   Base<typename T1::elem_type, T2>& B,
  const char*                          solver,
  const spsolve_opts_base&             settings,
  const typename arma_blas_type_only<typename T1::elem_type>::result* junk = 0
  )
  {
  arma_extra_debug_sigprint();
  arma_ignore(junk);
  
  typedef typename T1::pod_type   T;
  typedef typename T1::elem_type eT;
  
  const char sig = (solver != NULL) ? solver[0] : char(0);
  
  arma_debug_check( ((sig != 'l') && (sig != 's')), "spsolve(): unknown solver" );
  
  T rcond = T(0);
  
  bool status = false;
  
  superlu_opts superlu_opts_default;
  
  if(is_float <T>::value)  { superlu_opts_default.refine = superlu_opts::REF_SINGLE; }
  if(is_double<T>::value)  { superlu_opts_default.refine = superlu_opts::REF_DOUBLE; }
  
  const superlu_opts& opts = (settings.id == 1) ? static_cast<const superlu_opts&>(settings) : superlu_opts_default;
  
  arma_debug_check( ( (opts.pivot_thresh < double(0)) || (opts.pivot_thresh > double(1)) ), "spsolve(): pivot_thresh out of bounds" );
  
  if(sig == 's')  // SuperLU solver
    {
    if( (opts.equilibrate == false) && (opts.refine == superlu_opts::REF_NONE) )
      {
      status = sp_auxlib::spsolve_simple(out, A.get_ref(), B.get_ref(), opts);
      }
    else
      {
      status = sp_auxlib::spsolve_refine(out, rcond, A.get_ref(), B.get_ref(), opts);
      }
    }
  else
  if(sig == 'l')  // brutal LAPACK solver
    {
    if( (settings.id != 0) && ((opts.symmetric) || (opts.pivot_thresh != double(1.0))) )
      {
      arma_debug_warn("spsolve(): ignoring settings not applicable to LAPACK based solver");
      }
    
    Mat<eT> AA;
    
    bool conversion_ok = false;
    
    try
      {
      Mat<eT> tmp(A.get_ref());  // conversion from sparse to dense can throw std::bad_alloc
      
      AA.steal_mem(tmp);
      
      conversion_ok = true;
      }
    catch(std::bad_alloc&)
      {
      arma_debug_warn("spsolve(): not enough memory to use LAPACK based solver");
      }
    
    if(conversion_ok)
      {
      arma_debug_check( (AA.n_rows != AA.n_cols), "spsolve(): matrix A must be square sized" );
      
      uword flags = solve_opts::flag_none;
      
      if( (opts.equilibrate == false) && (opts.refine == superlu_opts::REF_NONE) )
        {
        flags |= solve_opts::flag_fast;
        }
      else
      if(opts.equilibrate == true)
        {
        flags |= solve_opts::flag_equilibrate;
        }
      
      if(opts.allow_ugly == true)
        {
        flags |= solve_opts::flag_allow_ugly;
        }
      
      status = glue_solve_gen::apply(out, AA, B.get_ref(), flags);
      }
    }
  
  
  if(status == false)
    {
    if(rcond > T(0))  { arma_debug_warn("spsolve(): system seems singular (rcond: ", rcond, ")"); }
    else              { arma_debug_warn("spsolve(): system seems singular");                      }
    
    out.soft_reset();
    }
  
  if( (status == true) && (rcond > T(0)) && (rcond <= (T(0.5)*std::numeric_limits<T>::epsilon())) )
    {
    arma_debug_warn("solve(): solution computed, but system seems singular to working precision (rcond: ", rcond, ")");
    }
  
  return status;
  }



template<typename T1, typename T2>
inline
bool
spsolve
  (
           Mat<typename T1::elem_type>&     out,
  const SpBase<typename T1::elem_type, T1>& A,
  const   Base<typename T1::elem_type, T2>& B,
  const char*                          solver   = "superlu",
  const spsolve_opts_base&             settings = spsolve_opts_none(),
  const typename arma_blas_type_only<typename T1::elem_type>::result* junk = 0
  )
  {
  arma_extra_debug_sigprint();
  arma_ignore(junk);
  
  const bool status = spsolve_helper(out, A.get_ref(), B.get_ref(), solver, settings);
  
  return status;
  }



template<typename T1, typename T2>
arma_warn_unused
inline
Mat<typename T1::elem_type>
spsolve
  (
  const SpBase<typename T1::elem_type, T1>& A,
  const   Base<typename T1::elem_type, T2>& B,
  const char*                          solver   = "superlu",
  const spsolve_opts_base&             settings = spsolve_opts_none(),
  const typename arma_blas_type_only<typename T1::elem_type>::result* junk = 0
  )
  {
  arma_extra_debug_sigprint();
  arma_ignore(junk);
  
  typedef typename T1::elem_type eT;
  
  Mat<eT> out;
  
  const bool status = spsolve_helper(out, A.get_ref(), B.get_ref(), solver, settings);
  
  if(status == false)
    {
    arma_stop_runtime_error("spsolve(): solution not found");
    }
  
  return out;
  }



//! @}