How to use numba - 10 common examples

@cuda.jit
def gaussker_2d1_cuda(x, y, c, hx, hy, nf1, nf2, nspread, tau, real_ftau, imag_ftau ):
    """This kernel function for gauss grid 1d typ1, and it will be executed by a thread."""
    i  = cuda.grid(1)
    if i > x.shape[0]:
        return
    #do the 1d griding here
    xi = x[i] % (2 * np.pi) #x, shift the source point xj so that it lies in [0,2*pi]
    yi = y[i] % (2 * np.pi) #y, shift the source point yj so that it lies in [0,2*pi]
    mx = 1 + int(xi // hx) #index for the closest grid point
    my = 1 + int(yi // hy) #index for the closest grid point
    for mmx in range(-nspread, nspread): #mm index for all the spreading points
        for mmy in range(-nspread,nspread):
            #griding with g(x,y) = exp(-(x^2 + y^2) / 4*tau)
            #ftau[(mx + mmx) % nf1, (my + mmy) % nf2] +=
            tmp = c[i] * exp(-0.25 * (\
            (xi - hx * (mx + mmx)) ** 2 + \

@cuda.jit
def gaussker_3d1_fast_cuda(x, y, z, c, hx, hy, hz, nf1, nf2, nf3, nspread, tau, E3, real_ftau, imag_ftau ):
    """This kernel function for gauss grid 1d typ1, and it will be executed by a thread."""
    i     = cuda.grid(1)
    if i > c.shape[0]:
        return

    #read x, y, z values
    xi    = x[i] % (2 * np.pi) #x, shift the source point xj so that it lies in [0,2*pi]
    yi    = y[i] % (2 * np.pi) #y, shift the source point yj so that it lies in [0,2*pi]
    zi    = z[i] % (2 * np.pi) #z, shift the source point zj so that it lies in [0,2*pi]
    mx    = 1 + int(xi // hx) #index for the closest grid point
    my    = 1 + int(yi // hy) #index for the closest grid point
    mz    = 1 + int(zi // hz) #index for the closest grid point
    xi    = (xi - hx * mx) #offsets from the closest grid point
    yi    = (yi - hy * my) #offsets from the closest grid point
    zi    = (zi - hz * mz) #offsets from the closest grid point

def main():
    cu_discriminant = vectorize(['f4(f4, f4, f4)', 'f8(f8, f8, f8)'],
                                target='cuda')(poly.discriminant)

    N = 1e+8 // 2

    print('Data size', N)

    A, B, C = poly.generate_input(N, dtype=np.float32)
    D = np.empty(A.shape, dtype=A.dtype)

    stream = cuda.stream()

    print('== One')

    ts = time()

    with stream.auto_synchronize():

@jit
def increment1(value):
    return value + 1

# Parameters
    Nz = 2048
    Nr = 256
    rmax = 50.e-6
    m = 0

    # Initialize the random test_field
    interp_field_r = np.random.rand(Nz, Nr) + 1.j*np.random.rand(Nz, Nr)
    interp_field_t = np.random.rand(Nz, Nr) + 1.j*np.random.rand(Nz, Nr)
    d_interp_field_r = cuda.to_device( interp_field_r )
    d_interp_field_t = cuda.to_device( interp_field_t )
    # Initialize the field in spectral space
    spect_field_p = np.empty_like( interp_field_r )
    spect_field_m = np.empty_like( interp_field_t )
    d_spect_field_p = cuda.to_device( spect_field_p )
    d_spect_field_m = cuda.to_device( spect_field_m )
    # Initialize the field after back and forth transformation
    back_field_r = np.empty_like( interp_field_r )
    back_field_t = np.empty_like( interp_field_t )
    d_back_field_r = cuda.to_device( back_field_r )
    d_back_field_t = cuda.to_device( back_field_t )

    # ----------------
    # Scalar transform
    # ----------------
    print( '\n ### Scalar transform \n' )
    
    # Perform the transform on the CPU
    trans_cpu = SpectralTransformer( Nz, Nr, m, rmax )
    # Do a loop so as to get the fastest time
    # and remove compilation time
    tmin = 1.

def resdec(f):
        if not numbaexists:
            return f
        return jit(f)
    return resdec

@numba.jit(UniTuple(f8[:, :], 3)(f8[:, :], f8[:], f8[:]), nopython=True, nogil=True)
def positions_vector(position, orientation, radius_ts):
    """Center and shoulder positions"""
    x = np.cos(orientation)
    y = np.sin(orientation)
    t = np.stack((y, -x), axis=1)
    offset = t * radius_ts
    position_ls = position - offset
    position_rs = position + offset
    return position, position_ls, position_rs

@jit(u4(u4[:, :]), nopython=True, cache=True)
def true_num_ops(exponent_matrix):
    """
    without counting additions (just MUL & POW) and but WITH considering the coefficients (1 MUL per monomial)
    """
    num_ops = 0
    for monomial_nr in range(exponent_matrix.shape[0]):
        for dim in range(exponent_matrix.shape[1]):
            exp = exponent_matrix[monomial_nr, dim]
            if exp > 0:
                # per scalar factor 1 MUL operation is required
                num_ops += 1
                if exp >= 2:
                    # for scalar factors with exponent >= 2 additionally 1 POW operation is required
                    num_ops += 1

    return num_ops

@jit(float64(float64, float64),nopython=True)
def gb(X,Y):
    return Godunov.NumFlux(Burg,X,Y)

@numba.jit(nopython=True,nogil=True)
def i_will_win(state, last_move, player):
    """ Return true if I will win next step if the opponent don't have 4-in-a-row.
    Winning Conditions:
        1. 5 in a row.
        2. 4 in a row with both end open. (free 4)
        3. 4 in a row with one missing stone x 2 (hard 4 x 2)
     """
    r, c = last_move
    # try all 4 directions, the other 4 is equivalent
    directions = [(1,1), (1,0), (0,1), (1,-1)]
    n_hard_4 = 0 # number of hard 4s found
    for dr, dc in directions:
        line_length = 1 # last_move
        # try to extend in the positive direction (max 4 times)
        ext_r = r
        ext_c = c