Relative barmode in PGFPlotsX.jl

How about:

@pgf Axis(
    {ybar_stacked},
    Plot(Coordinates([(1,   1),   (2,  4), (3,  9),   (4, 16)])),
    Plot(Coordinates([(1,   6),   (2, -8), (3, -4.5), (4,  8)])),
    Plot(Coordinates([(1, -15),   (2, -3), (3,  4.5), (4, -8)])),
    Plot(Coordinates([(1,  -1),   (2,  3), (3, -3),   (4, -4)])),
)

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