text: // 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 op_pinv
  //! @{
  
  
  
  template<typename T1>
  inline
  void
  op_pinv::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_pinv>& in)
    {
    arma_extra_debug_sigprint();
    
    typedef typename T1::pod_type T;
    
    const T tol = access::tmp_real(in.aux);
    
    const bool use_divide_and_conquer = (in.aux_uword_a == 1);
    
    const bool status = op_pinv::apply_direct(out, in.m, tol, use_divide_and_conquer);
    
    if(status == false)
      {
      arma_stop_runtime_error("pinv(): svd failed");
      }
    }
  
  
  
  template<typename T1>
  inline
  bool
  op_pinv::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type,T1>& expr, typename T1::pod_type tol, const bool use_divide_and_conquer)
    {
    arma_extra_debug_sigprint();
    
    typedef typename T1::elem_type eT;
    typedef typename T1::pod_type   T;
    
    arma_debug_check((tol < T(0)), "pinv(): tolerance must be >= 0");
    
    const Proxy<T1> P(expr.get_ref());
    
    const uword n_rows = P.get_n_rows();
    const uword n_cols = P.get_n_cols();
    
    if( (n_rows*n_cols) == 0 )
      {
      out.set_size(n_cols,n_rows);
      return true;
      }
    
    
    // economical SVD decomposition 
    Mat<eT> U;
    Col< T> s;
    Mat<eT> V;
    
    bool status = false;
    
    if(use_divide_and_conquer)
      {
      status = (n_cols > n_rows) ? auxlib::svd_dc_econ(U, s, V, trans(P.Q)) : auxlib::svd_dc_econ(U, s, V, P.Q);
      }
    else
      {
      status = (n_cols > n_rows) ? auxlib::svd_econ(U, s, V, trans(P.Q), 'b') : auxlib::svd_econ(U, s, V, P.Q, 'b');
      }
    
    if(status == false)
      {
      out.soft_reset();
      return false;
      }
    
    const uword s_n_elem = s.n_elem;
    const T*    s_mem    = s.memptr();
    
    // set tolerance to default if it hasn't been specified
    if( (tol == T(0)) && (s_n_elem > 0) )
      {
      tol = (std::max)(n_rows, n_cols) * s_mem[0] * std::numeric_limits<T>::epsilon();
      }
    
    
    uword count = 0;
    
    for(uword i = 0; i < s_n_elem; ++i)
      {
      count += (s_mem[i] >= tol) ? uword(1) : uword(0);
      }
    
    
    if(count > 0)
      {
      Col<T> s2(count);
      
      T* s2_mem = s2.memptr();
      
      uword count2 = 0;
      
      for(uword i=0; i < s_n_elem; ++i)
        {
        const T val = s_mem[i];
        
        if(val >= tol)  {  s2_mem[count2] = T(1) / val;  ++count2; }
        }
      
      
      if(n_rows >= n_cols)
        {
        // out = ( (V.n_cols > count) ? V.cols(0,count-1) : V ) * diagmat(s2) * trans( (U.n_cols > count) ? U.cols(0,count-1) : U );
        
        Mat<eT> tmp;
        
        if(count < V.n_cols)
          {
          tmp = V.cols(0,count-1) * diagmat(s2);
          }
        else
          {
          tmp = V * diagmat(s2);
          }
        
        if(count < U.n_cols)
          {
          out = tmp * trans(U.cols(0,count-1));
          }
        else
          {
          out = tmp * trans(U);
          }
        }
      else
        {
        // out = ( (U.n_cols > count) ? U.cols(0,count-1) : U ) * diagmat(s2) * trans( (V.n_cols > count) ? V.cols(0,count-1) : V );
        
        Mat<eT> tmp;
        
        if(count < U.n_cols)
          {
          tmp = U.cols(0,count-1) * diagmat(s2);
          }
        else
          {
          tmp = U * diagmat(s2);
          }
        
        if(count < V.n_cols)
          {
          out = tmp * trans(V.cols(0,count-1));
          }
        else
          {
          out = tmp * trans(V);
          }
        }
      }
    else
      {
      out.zeros(n_cols, n_rows);
      }
    
    return true;
    }
  
  
  
  //! @}
  