Multiple output and numba signatures

You can either use explicit declarations or string declaration :

Tuple with homogeneous types :

@nb.jit(nb.types.UniTuple(nb.float64[:],2)(nb.float64[:]),nopython=True)
def f(a) :
    return a,a

@nb.jit('UniTuple(float64[:], 2)(float64[:])',nopython=True)
def f(a) :
    return a,a

Tuple with heterogeneous types :

@nb.jit(nb.types.Tuple((nb.float64[:], nb.float64[:,:]))(nb.float64[:], nb.float64[:,:]),nopython=True)
def f(a, b) :
    return a, b

@nb.jit('Tuple((float64[:], float64[:,:]))(float64[:], float64[:,:])',nopython=True)
def f(a, b) :
    return a, b

Source : my own experiments, and the source code of Numba : https://github.com/numba/numba

Of course, the solution proposed by DavidW is an excellent workaround when you do not know the exact type :

@nb.jit(nb.typeof((1.0,1.0))(nb.double),nopython=True)
def f(a):
  return a,a