// Copyright (C) 2009-2011 NICTA (www.nicta.com.au)
// Copyright (C) 2009-2011 Conrad Sanderson
// Copyright (C) 2009-2010 Dimitrios Bouzas
// Copyright (C) 2011 Stanislav Funiak
// 
// 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 op_pinv
//! @{



template<typename eT>
inline
void
op_pinv::direct_pinv(Mat<eT>& out, const Mat<eT>& A, eT tol)
  {
  arma_extra_debug_sigprint();
  
  const u32 n_rows = A.n_rows;
  const u32 n_cols = A.n_cols;
  
  // SVD decomposition 
  Mat<eT> U;
  Col<eT> s;
  Mat<eT> V;
  
  const bool status   = (n_cols > n_rows) ? auxlib::svd(U,s,V,trans(A)) : auxlib::svd(U,s,V,A);
  const u32  s_n_elem = s.n_elem;
  
  if(status == false)
    {
    out.reset();
    arma_bad("pinv(): svd failed");
    return;
    }
  
  // set tolerance to default if it hasn't been specified as an argument
  if( (tol == eT(0)) && (s_n_elem > 0) )
    {
    tol = (std::max)(n_rows,n_cols) * eop_aux::direct_eps(max(s));
    }
  
  // count non zero valued elements in s
  
  u32 count = 0;
  
  for(u32 i=0; i < s_n_elem; ++i)
    {
    if(s[i] > tol)
      {
      ++count;
      }
    }
  
  
  if(count != 0)
    {
    // reduce the length of s in order to contain only the values above tolerance
    if(count < s_n_elem)
      {
      //s = s.rows(0,count-1);
      s.shed_rows(count, s_n_elem-1);
      }
    
    // set the elements of s equal to their reciprocals
    s = eT(1) / s;
    
    if(A.n_cols <= A.n_rows)
      {
      out = ( V.n_cols > count ? V.cols(0,count-1) : V ) * diagmat(s) * trans( U.n_cols > count ? U.cols(0,count-1) : U );
      }
    else
      {
      out = ( U.n_cols > count ? U.cols(0,count-1) : U ) * diagmat(s) * trans( V.n_cols > count ? V.cols(0,count-1) : V );
      }
    }
  else
    {
    out.zeros(n_cols, n_rows);
    }
  }



template<typename T>
inline
void
op_pinv::direct_pinv(Mat< std::complex<T> >& out, const Mat< std::complex<T> >& A, T tol)
  {
  arma_extra_debug_sigprint();
  
  const u32 n_rows = A.n_rows;
  const u32 n_cols = A.n_cols;
  
  typedef typename std::complex<T> eT;
  
  // SVD decomposition 
  Mat<eT> U;
  Col< T> s;
  Mat<eT> V;
  
  const bool status  = (n_cols > n_rows) ? auxlib::svd(U,s,V,trans(A)) : auxlib::svd(U,s,V,A);
  const u32 s_n_elem = s.n_elem;
  
  if(status == false)
    {
    out.reset();
    arma_bad("pinv(): svd failed");
    return;
    }
 
  // set tolerance to default if it hasn't been specified as an argument 
  if( (tol == T(0)) && (s_n_elem > 0) )
    {
    tol = (std::max)(n_rows,n_cols) * eop_aux::direct_eps(max(s));
    }
  
  
  // count non zero valued elements in s
  
  u32 count = 0;
  
  for(u32 i = 0; i < s_n_elem; ++i)
    {
    if(s[i] > tol)
      {
      ++count;
      }
    }
  
  if(count != 0)
    {
    // reduce the length of s in order to contain only the values above tolerance
    if(count < s_n_elem)
      {
      // s = s.rows(0,count-1);
      s.shed_rows(count, s_n_elem-1);
      }

    // set the elements of s equal to their reciprocals
    s = T(1) / s;
    
    if(n_rows >= n_cols)
      {
      out = ( V.n_cols > count ? V.cols(0,count-1) : V ) * diagmat(s) * trans( U.n_cols > count ? U.cols(0,count-1) : U );
      }
    else
      {
      out = ( U.n_cols > count ? U.cols(0,count-1) : U ) * diagmat(s) * trans( V.n_cols > count ? V.cols(0,count-1) : V );
      }
    }
  else
    {
    out.zeros(n_cols, n_rows);
    }
  }



template<typename T1>
inline
void
op_pinv::apply(Mat<typename T1::pod_type>& out, const Op<T1,op_pinv>& in)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::pod_type eT;
  
  const eT tol = in.aux; 
  
  arma_debug_check((tol < eT(0)), "pinv(): tolerance must be >= 0");
  
  const unwrap<T1>   tmp(in.m);
  const Mat<eT>& A = tmp.M;
  
  op_pinv::direct_pinv(out, A, tol);
  }



template<typename T1>
inline
void
op_pinv::apply(Mat< std::complex<typename T1::pod_type> >& out, const Op<T1,op_pinv>& in)
  {
  arma_extra_debug_sigprint();
  
  typedef typename T1::pod_type     T;
  typedef typename std::complex<T> eT;
  
  const T tol = in.aux.real();
  
  arma_debug_check((tol < T(0)), "pinv(): tolerance must be >= 0");
  
  const unwrap<T1>   tmp(in.m);
  const Mat<eT>& A = tmp.M;
  
  op_pinv::direct_pinv(out, A, tol);
  }



//! @}
