# include <cppad/utility/lu_solve.hpp>       // for CppAD::LuSolve
# include <cppad/utility/near_equal.hpp>     // for CppAD::NearEqual
# include <cppad/utility/vector.hpp>  // for CppAD::vector
# include <complex>               // for std::complex

typedef std::complex<double> Complex;    // define the Complex type
bool LuSolve(void)
{     bool  ok = true;
     using namespace CppAD;

     size_t   n = 3;           // number rows in A and B
     size_t   m = 2;           // number columns in B, X and S

     // A is an n by n matrix, B, X, and S are n by m matrices
     CppAD::vector<Complex> A(n * n), B(n * m), X(n * m) , S(n * m);

     Complex  logdet;          // log of determinant of A
     int      signdet;         // zero if A is singular
     Complex  det;             // determinant of A
     size_t   i, j, k;         // some temporary indices

     // set A equal to the n by n Hilbert Matrix
     for(i = 0; i < n; i++)
          for(j = 0; j < n; j++)
               A[i * n + j] = 1. / (double) (i + j + 1);

     // set S to the solution of the equation we will solve
     for(j = 0; j < n; j++)
          for(k = 0; k < m; k++)
               S[ j * m + k ] = Complex(double(j), double(j + k));

     // set B = A * S
     size_t ik;
     Complex sum;
     for(k = 0; k < m; k++)
     {     for(i = 0; i < n; i++)
          {     sum = 0.;
               for(j = 0; j < n; j++)
                    sum += A[i * n + j] * S[j * m + k];
               B[i * m + k] = sum;
          }
     }

     // solve the equation A * X = B and compute determinant of A
     signdet = CppAD::LuSolve(n, m, A, B, X, logdet);
     det     = Complex( signdet ) * exp( logdet );

     double cond  = 4.62963e-4;       // condition number of A when n = 3
     double determinant = 1. / 2160.; // determinant of A when n = 3
     double delta = 1e-14 / cond;     // accuracy expected in X

     // check determinant
     ok &= CppAD::NearEqual(det, determinant, delta, delta);

     // check solution
     for(ik = 0; ik < n * m; ik++)
          ok &= CppAD::NearEqual(X[ik], S[ik], delta, delta);

     return ok;
}