N_BUCKETS = 9
CELL_SIZE = 8  # Each cell is 8x8 pixels
BLOCK_SIZE = 2  # Each block is 2x2 cells

def assign_bucket_vals(m, d, bucket_vals):
    left_bin = int(d / 20.)
    # Handle the case when the direction is between [160, 180)
    right_bin = (int(d / 20.) + 1) % N_BUCKETS
    assert 0 <= left_bin < right_bin < N_BUCKETS

    left_val= m * (right_bin * 20 - d) / 20
    right_val = m * (d - left_bin * 20) / 20
    bucket_vals[left_bin] += left_val
    bucket_vals[right_bin] += right_val

def get_magnitude_hist_cell(loc_x, loc_y):
    # (loc_x, loc_y) defines the top left corner of the target cell.
    cell_x = G_x[loc_x:loc_x + CELL_SIZE, loc_y:loc_y + CELL_SIZE]
    cell_y = G_y[loc_x:loc_x + CELL_SIZE, loc_y:loc_y + CELL_SIZE]
    magnitudes = np.sqrt(cell_x * cell_x + cell_y * cell_y)
    directions = np.abs(np.arctan(cell_y / cell_x) * 180 / np.pi)

    buckets = np.linspace(0, 180, N_BUCKETS + 1)
    bucket_vals = np.zeros(N_BUCKETS)
    map(
        lambda (m, d): assign_bucket_vals(m, d, bucket_vals), 
        zip(magnitudes.flatten(), directions.flatten())
    )
    return bucket_vals

def get_magnitude_hist_block(loc_x, loc_y):
    # (loc_x, loc_y) defines the top left corner of the target block.
    return reduce(
        lambda arr1, arr2: np.concatenate((arr1, arr2)),
        [get_magnitude_hist_cell(x, y) for x, y in zip(
            [loc_x, loc_x + CELL_SIZE, loc_x, loc_x + CELL_SIZE],
            [loc_y, loc_y, loc_y + CELL_SIZE, loc_y + CELL_SIZE],
        )]
    )