# This (x, y) pair will be used in all the following examples
x = array([-2, 0, 2, 4])
y = 0.3 * x + 0.2

fig = figure()
# This xlim and ylim are explicitly set, and I expect them not to be altered unless I explicitly do so.
ax = fig.add_axes((0.1,0.1,0.8,0.8), xlim=(0,2), ylim=(0,1), autoscalex_on=False, autoscaley_on=False)
ax.plot(x, y, color='blue', lw=10)

fig = figure()
ax = fig.add_axes((0.1,0.1,0.8,0.8), xlim=(0,2), ylim=(0,1), autoscalex_on=False, autoscaley_on=False)
ax.plot(x, y, color='blue', lw=10)
ax = twinx(ax)
ax.plot(x, y, color='red', lw=5)
# I would expect the two lines to overlap, but they don't.
# Both xlim and ylim are changed.
# Note that the blue line and the red line are still "semantically" correct.

fig = figure()
ax = fig.add_axes((0.1,0.1,0.8,0.8), xlim=(0,2), ylim=(0,1), autoscalex_on=False, autoscaley_on=False)
ax.plot(x, y, color='blue', lw=10)
ax = twinx(ax)
ax.plot(x, y, color='red', lw=5)
ax.set_xlim((0,2))
# This one is acceptible, since the twinx axis has the same xlim as the original one,
# though I expected that this should be the default behavior (without manually setting xlim).

fig = figure()
ax = fig.add_axes((0.1,0.1,0.8,0.8), xlim=(0,2), ylim=(0,1), autoscalex_on=False, autoscaley_on=False)
ax.plot(x, y, color='blue', lw=10)
ax = twinx(ax)
ax.plot(x, y, color='red', lw=5)
ax.set_ylim((0,1))
# In this case the two lines overlap, but the original xlim is changed.

fig = figure()
ax = fig.add_axes((0.1,0.1,0.8,0.8), xlim=(0,2), ylim=(0,1), autoscalex_on=False, autoscaley_on=False)
ax.plot(x, y, color='blue', lw=10)
ax = twinx(ax)
ax.plot(x, y, color='red', lw=5)
ax.set_ylim((0,1))
ax.set_xlim((0,2))
# This is what I expected in the beginning.
# Basically, I do not expect the twinx to change the original xlim
# (and any other properties of the x axis).