text: // SPDX-License-Identifier: Apache-2.0
  // 
  // 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 uword method_id = in.aux_uword_a;
    
    const bool status = op_pinv::apply_direct(out, in.m, tol, method_id);
    
    if(status == false)
      {
      out.soft_reset();
      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 uword method_id)
    {
    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");
    
    // method_id = 0 -> default setting
    // method_id = 1 -> use standard algorithm
    // method_id = 2 -> use divide and conquer algorithm
    
    Mat<eT> A(expr.get_ref());
    
    const uword n_rows = A.n_rows;
    const uword n_cols = A.n_cols;
    
    if(A.is_empty())  { out.set_size(n_cols,n_rows); return true; }
    
    if(A.is_diagmat())
      {
      arma_extra_debug_print("op_pinv: detected diagonal matrix");
      
      out.zeros(n_cols, n_rows);
      
      const uword N = (std::min)(n_rows, n_cols);
      
      podarray<T> diag_abs_vals(N);
      
      T max_abs_Aii = T(0);
      
      for(uword i=0; i<N; ++i)
        {
        const eT     Aii = A.at(i,i);
        const  T abs_Aii = std::abs(Aii);
        
        if(arma_isnan(Aii))  { return false; }
        
        diag_abs_vals[i] = abs_Aii;
        
        max_abs_Aii = (abs_Aii > max_abs_Aii) ? abs_Aii : max_abs_Aii;
        }
      
      if(tol == T(0))  { tol = (std::max)(n_rows, n_cols) * max_abs_Aii * std::numeric_limits<T>::epsilon(); }
      
      for(uword i=0; i<N; ++i)
        {
        if(diag_abs_vals[i] >= tol)
          {
          const eT Aii = A.at(i,i);
          
          if(Aii != eT(0))  { out.at(i,i) = eT(eT(1) / Aii); }
          }
        }
      
      return true;
      }
      
    #if defined(ARMA_OPTIMISE_SYMPD)
      const bool try_sympd = (auxlib::crippled_lapack(A) == false) && (tol == T(0)) && (method_id == uword(0)) && sympd_helper::guess_sympd_anysize(A);
    #else
      const bool try_sympd = false;
    #endif
    
    if(try_sympd)
      {
      arma_extra_debug_print("op_pinv: attempting sympd optimisation");
      
      out = A;
      
      const T rcond_threshold = T((std::max)(uword(100), uword(A.n_rows))) * std::numeric_limits<T>::epsilon();
      
      const bool status = auxlib::inv_sympd_rcond(out, rcond_threshold);
      
      if(status)  { return true; }
      
      arma_extra_debug_print("op_pinv: sympd optimisation failed");
      // auxlib::inv_sympd_rcond() will fail if A isn't really positive definite or its rcond is below rcond_threshold
      }
    
    // economical SVD decomposition 
    Mat<eT> U;
    Col< T> s;
    Mat<eT> V;
    
    if(n_cols > n_rows)  { A = trans(A); }
    
    const bool status = ((method_id == uword(0)) || (method_id == uword(2))) ? auxlib::svd_dc_econ(U, s, V, A) : auxlib::svd_econ(U, s, V, A, 'b');
    
    if(status == false)  { 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)  { out.zeros(n_cols, n_rows); return true; }
    
    Col<T> s2(count, arma_nozeros_indicator());
    
    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] = (val > T(0)) ? T(T(1) / val) : T(0); ++count2; }
      }
    
    
    Mat<eT> tmp;
      
    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 );
      
      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 );
      
      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);
        }
      }
    
    return true;
    }
  
  
  
  //! @}
  