# include <complex>
# include <vector>

# include <cppad/core/cppad_assert.hpp>
# include <cppad/utility/check_simple_vector.hpp>
# include <cppad/utility/check_numeric_type.hpp>

namespace CppAD { // BEGIN CppAD namespace

// AbsGeq
template <typename Float>
inline bool AbsGeq(const Float &x, const Float &y)
{     Float xabs = x;
     if( xabs <= Float(0) )
          xabs = - xabs;
     Float yabs = y;
     if( yabs <= Float(0) )
          yabs = - yabs;
     return xabs >= yabs;
}
inline bool AbsGeq(
     const std::complex<double> &x,
     const std::complex<double> &y)
{     double xsq = x.real() * x.real() + x.imag() * x.imag();
     double ysq = y.real() * y.real() + y.imag() * y.imag();

     return xsq >= ysq;
}
inline bool AbsGeq(
     const std::complex<float> &x,
     const std::complex<float> &y)
{     float xsq = x.real() * x.real() + x.imag() * x.imag();
     float ysq = y.real() * y.real() + y.imag() * y.imag();

     return xsq >= ysq;
}

// Lines that are different from code in cppad/core/lu_ratio.hpp end with //
template <class SizeVector, class FloatVector>                          //
int LuFactor(SizeVector &ip, SizeVector &jp, FloatVector &LU)           //
{
     // type of the elements of LU                                   //
     typedef typename FloatVector::value_type Float;                 //

     // check numeric type specifications
     CheckNumericType<Float>();

     // check simple vector class specifications
     CheckSimpleVector<Float, FloatVector>();
     CheckSimpleVector<size_t, SizeVector>();

     size_t  i, j;          // some temporary indices
     const Float zero( 0 ); // the value zero as a Float object
     size_t  imax;          // row index of maximum element
     size_t  jmax;          // column indx of maximum element
     Float    emax;         // maximum absolute value
     size_t  p;             // count pivots
     int     sign;          // sign of the permutation
     Float   etmp;          // temporary element
     Float   pivot;         // pivot element

     // -------------------------------------------------------
     size_t n = ip.size();
     CPPAD_ASSERT_KNOWN(
          size_t(jp.size()) == n,
          "Error in LuFactor: jp must have size equal to n"
     );
     CPPAD_ASSERT_KNOWN(
          size_t(LU.size()) == n * n,
          "Error in LuFactor: LU must have size equal to n * m"
     );
     // -------------------------------------------------------

     // initialize row and column order in matrix not yet pivoted
     for(i = 0; i < n; i++)
     {     ip[i] = i;
          jp[i] = i;
     }
     // initialize the sign of the permutation
     sign = 1;
     // ---------------------------------------------------------

     // Reduce the matrix P to L * U using n pivots
     for(p = 0; p < n; p++)
     {     // determine row and column corresponding to element of
          // maximum absolute value in remaining part of P
          imax = jmax = n;
          emax = zero;
          for(i = p; i < n; i++)
          {     for(j = p; j < n; j++)
               {     CPPAD_ASSERT_UNKNOWN(
                         (ip[i] < n) & (jp[j] < n)
                    );
                    etmp = LU[ ip[i] * n + jp[j] ];

                    // check if maximum absolute value so far
                    if( AbsGeq (etmp, emax) )
                    {     imax = i;
                         jmax = j;
                         emax = etmp;
                    }
               }
          }
          CPPAD_ASSERT_KNOWN(
          (imax < n) & (jmax < n) ,
          "LuFactor can't determine an element with "
          "maximum absolute value.\n"
          "Perhaps original matrix contains not a number or infinity.\n"
          "Perhaps your specialization of AbsGeq is not correct."
          );
          if( imax != p )
          {     // switch rows so max absolute element is in row p
               i        = ip[p];
               ip[p]    = ip[imax];
               ip[imax] = i;
               sign     = -sign;
          }
          if( jmax != p )
          {     // switch columns so max absolute element is in column p
               j        = jp[p];
               jp[p]    = jp[jmax];
               jp[jmax] = j;
               sign     = -sign;
          }
          // pivot using the max absolute element
          pivot   = LU[ ip[p] * n + jp[p] ];

          // check for determinant equal to zero
          if( pivot == zero )
          {     // abort the mission
               return   0;
          }

          // Reduce U by the elementary transformations that maps
          // LU( ip[p], jp[p] ) to one.  Only need transform elements
          // above the diagonal in U and LU( ip[p] , jp[p] ) is
          // corresponding value below diagonal in L.
          for(j = p+1; j < n; j++)
               LU[ ip[p] * n + jp[j] ] /= pivot;

          // Reduce U by the elementary transformations that maps
          // LU( ip[i], jp[p] ) to zero. Only need transform elements
          // above the diagonal in U and LU( ip[i], jp[p] ) is
          // corresponding value below diagonal in L.
          for(i = p+1; i < n; i++ )
          {     etmp = LU[ ip[i] * n + jp[p] ];
               for(j = p+1; j < n; j++)
               {     LU[ ip[i] * n + jp[j] ] -=
                         etmp * LU[ ip[p] * n + jp[j] ];
               }
          }
     }
     return sign;
}
} // END CppAD namespace