# include <cppad/lu_solve.hpp>       // for CppAD::LuSolve
# include <cppad/near_equal.hpp>     // for CppAD::NearEqual
# include <cppad/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(j, 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;
}