A = np.column_stack((2. * p[:,0], 2. * p[:,1], [-1,-1,-1]))

b = np.sum(p**2, axis=1)

# Normalizing the vectors

norm = np.sqrt(np.sum(A*A, axis=1))

An = np.transpose(A.T / norm)

bn = b / norm

# Solving the system

M = GaussElimination(An,bn)

M.solve()

sol = M.sol

# Calculating determinant of a 3x3 matrix

det = An[0,0] * An[1,1] * An[2,2] + An[0,1] * An[1,2] * An[2,0] + \

An[0,2] * An[1,0] * An[2,1] - An[0,2] * An[1,1] * An[2,0] - \

An[0,1] * An[1,0] * An[2,2] - An[0,0] * An[1,2] * An[2,1]

r = np.sqrt(sol[0]**2 + sol[1]**2 - sol[2])

eps = np.finfo(float).eps

if np.abs(det) < eps:

print "System does not have a solution (det=0)"

elif np.abs(det) < tol:

print "System is ill conditioned: |det| = {0}".format(np.abs(det))

else:

print "System has a determined solution: det = {0}".format(det)

print "Solution is x = {0:.5f}, y={1:.5f} and r={2:.5f}".format(sol[0],

sol[1],r)