def test_zero_dynamics():
'test a system with zero dynamic (only should process one frame)'
ha = HybridAutomaton()
# with time and affine variable
mode = ha.new_mode('mode')
mode.set_dynamics([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]])
# initial set
init_lpi = lputil.from_box([(-5, -5), (0, 1), (0, 0), (1, 1)], mode)
init_list = [StateSet(init_lpi, mode)]
# settings
settings = HylaaSettings(math.pi/4, 20*math.pi)
settings.stdout = HylaaSettings.STDOUT_VERBOSE
settings.plot.plot_mode = PlotSettings.PLOT_NONE
core = Core(ha, settings)
core.setup(init_list)
core.do_step() # pop
core.do_step() # propagate and remove
assert core.aggdag.get_cur_state() is None, "cur state should be none, since mode dynamics were zero"
def test_redundant_inv_transition():
'test removing of redundant invariants with a transition'
ha = HybridAutomaton()
mode1 = ha.new_mode('mode1')
# dynamics: x' = 1, y' = 1, a' = 0
mode1.set_dynamics([[0, 0, 1], [0, 0, 1], [0, 0, 0]])
# invariant: x <= 2.5
mode1.set_invariant([[1, 0, 0]], [2.5])
mode2 = ha.new_mode('mode2')
mode2.set_dynamics([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
ha.new_transition(mode1, mode2).set_guard([[-1, 0, 0]], [-2.5]) # x >= 2.5
# initial set has x0 = [0, 1]
init_lpi = lputil.from_box([(0, 1), (0, 1), (1, 1)], mode1)
init_list = [StateSet(init_lpi, mode1)]
# settings, step size = 0.1
settings = HylaaSettings(0.1, 5.0)
settings.stdout = HylaaSettings.STDOUT_DEBUG
settings.plot.plot_mode = PlotSettings.PLOT_NONE
core = Core(ha, settings)
core.setup(init_list)
for _ in range(20):
core.do_step()
assert core.result.last_cur_state.lpi.get_num_rows() == 3 + 2*3 + 1 # 3 for basis matrix, 2*3 for init constraints
assert len(core.aggdag.waiting_list) > 2
core.plotman.run_to_completion()
def test_agg_ha():
'test aggregation with the harmonic oscillator dynamics'
ha = HybridAutomaton('Deaggregation Example')
m1 = ha.new_mode('green')
m1.set_dynamics([[0, 1], [-1, 0]])
m2 = ha.new_mode('cyan')
m2.set_dynamics([[0, 0, 0], [0, 0, -2], [0, 0, 0]])
t1 = ha.new_transition(m1, m2)
t1.set_guard_true()
reset_mat = [[1, 0], [0, 1], [0, 0]]
t1.set_reset(reset_mat, [[0], [0], [1]], [[1], [-1]], [1, -1]) # create 3rd variable with a0 = 1
mode = ha.modes['green']
init_lpi = lputil.from_box([(-5, -4), (-0.5, 0.5)], mode)
init_list = [StateSet(init_lpi, mode)]
step = math.pi/4
settings = HylaaSettings(step, 2*step)
settings.process_urgent_guards = True
settings.plot.plot_mode = PlotSettings.PLOT_NONE
settings.stdout = HylaaSettings.STDOUT_DEBUG
core = Core(ha, settings)
core.setup(init_list)
core.do_step() # pop
#xs, ys = zip(*core.cur_state.verts(core.plotman))
#plt.plot(xs, ys, 'k-')
core.do_step() # 0
#xs, ys = zip(*core.cur_state.verts(core.plotman))
#plt.plot(xs, ys, 'k-')
core.do_step() # 1
#xs, ys = zip(*core.cur_state.verts(core.plotman))
#plt.plot(xs, ys, 'k-')
core.do_step() # 2
assert len(core.aggdag.waiting_list) > 1
#for state in core.waiting_list:
# xs, ys = zip(*state.verts(core.plotman))
# plt.plot(xs, ys, 'k-')
core.do_step() # pop
assert not core.aggdag.waiting_list
lpi = core.aggdag.get_cur_state().lpi
# 3 constraints from basis matrix
# 2 aggregation directions from premode arnoldi, +1 from null space
# + 2 more aggregation directions from box (3rd is omited since it's exactly the same as null space direction)
#print(lpi)
#xs, ys = zip(*core.cur_state.verts(core.plotman))
#plt.plot(xs, ys, 'r--')
#plt.show()
assert lpi.get_num_rows() == 3 + 2 * (5)
assert lputil.is_point_in_lpi((-5, 2, 1), lpi)
def test_inputs_reset():
'test a system with both inputs and a reset'
# 2-d system with one input
# x' = x, y' = u, u \in [1, 1]
# x0 = 1, y0 = 0
# inv1: y <= 2.5
# guard: y >= 2.5
# reset: x := 1, y += 2 [should go from (e^3, 3.0) -> (1, 5.0)]
# mode2:
# x' = 2x, y' = Bu, u \in [1, 2], B = 2
# (1, 5.0) -> (e^2, [7, 9]) -> (e^4, [9, 13])
# mode2 -> error y >= 13
ha = HybridAutomaton()
m1 = ha.new_mode('m1')
m1.set_dynamics([[1, 0], [0, 0]])
m1.set_inputs([[0], [1]], [[1], [-1]], [1, -1], allow_constants=True)
m1.set_invariant([[0, 1]], [2.5])
m2 = ha.new_mode('m2')
m2.set_dynamics([[2, 0], [0, 0]])
m2.set_inputs([[0], [2]], [[1], [-1]], [2, -1])
error = ha.new_mode('error')
t1 = ha.new_transition(m1, m2)
t1.set_guard([[0, -1]], [-2.5]) # y >= 2.5
reset_mat = [[0, 0], [0, 1]]
min_mat = np.identity(2)
min_cons = [[1, 0], [-1, 0], [0, 1], [0, -1]]
min_rhs = [1, -1, 2, -2]
t1.set_reset(reset_mat, min_mat, min_cons, min_rhs)
t2 = ha.new_transition(m2, error)
t2.set_guard([0, -1], [-13]) # y >= 13
init_box = [[1, 1], [0, 0]]
lpi = lputil.from_box(init_box, m1)
settings = HylaaSettings(1.0, 10.0)
settings.stdout = HylaaSettings.STDOUT_VERBOSE
settings.plot.store_plot_result = True
settings.plot.plot_mode = PlotSettings.PLOT_NONE
core = Core(ha, settings)
init_list = [StateSet(lpi, m1)]
core.setup(init_list)
core.do_step() # pop
core.do_step() # continuous_post() to time 1
lpi = core.result.last_cur_state.lpi
assert lpi.get_names() == ['m0_i0', 'm0_i1', 'm0_c0', 'm0_c1', 'm0_ti0', 'm0_ti1', 'm0_I0']
assert_verts_is_box(lpplot.get_verts(lpi), [[math.exp(1), math.exp(1)], [1, 1]])
core.do_step() # continuous_post() to time 2
assert_verts_is_box(lpplot.get_verts(core.result.last_cur_state.lpi), [[math.exp(2), math.exp(2)], [2, 2]])
core.do_step() # continuous_post() to time 3
assert_verts_is_box(lpplot.get_verts(core.result.last_cur_state.lpi), [[math.exp(3), math.exp(3)], [3, 3]])
core.do_step() # trim to invariant
assert core.aggdag.get_cur_state() is None
assert len(core.aggdag.waiting_list) == 1
core.run_to_completion()
result = core.result
# reset: x := 1, y += 2 [should go from (e^3, 3.0) -> (1, 5.0)]
# (1, 5.0) -> (e^2, [7, 9]) -> (e^4, [9, 13])
polys2 = [obj[0] for obj in result.plot_data.mode_to_obj_list[0]['m2']]
assert_verts_is_box(polys2[0], [[1, 1], [5, 5]])
assert_verts_is_box(polys2[1], [[math.exp(2), math.exp(2)], [7, 9]])
assert_verts_is_box(polys2[2], [[math.exp(4), math.exp(4)], [9, 13]])
assert len(polys2) == 3
# check counterexamples
assert len(result.counterexample) == 2
c1 = result.counterexample[0]
assert c1.mode == m1
assert c1.outgoing_transition == t1
assert np.allclose(c1.start, [1, 0])
assert np.allclose(c1.end, [math.exp(3), 3])
assert len(c1.reset_minkowski_vars) == 2
assert abs(c1.reset_minkowski_vars[0] - 1) < 1e-9
assert abs(c1.reset_minkowski_vars[1] - 2) < 1e-9
assert len(c1.inputs) == 3
for i in c1.inputs:
assert len(i) == 1
assert abs(i[0] - 1) < 1e-9
c2 = result.counterexample[1]
assert c2.mode == m2
assert c2.outgoing_transition == t2
assert np.allclose(c2.start, [1, 5])
assert np.allclose(c2.end, [math.exp(4), 13])
assert not c2.reset_minkowski_vars
assert len(c2.inputs) == 2
for i in c2.inputs:
assert len(i) == 1
assert abs(i[0] - 2) < 1e-9
def fail_deagg_counterexample():
'test that aggregation with a counterexample'
# init: x0, y0 \in [0, 1], step = 1.0
#
# m1 dynamics: x' == 1, y' == 0,
# m1 invariant: x <= 3
# m1 -> m2 guard: True
# m2 dynamics: x' == 0, y' == 1
# m2 -> error: y >= 3
ha = HybridAutomaton()
# mode one: x' = 1, y' = 0, a' = 0
m1 = ha.new_mode('m1')
m1.set_dynamics([[0, 0, 1], [0, 0, 0], [0, 0, 0]])
# mode two: x' = 0, y' = 1, a' = 0
m2 = ha.new_mode('m2')
m2.set_dynamics([[0, 0, 0], [0, 0, 1], [0, 0, 0]])
# invariant: x <= 3.0
m1.set_invariant([[1, 0, 0]], [3.0])
# guard: True
trans1 = ha.new_transition(m1, m2, 'trans1')
trans1.set_guard_true()
error = ha.new_mode('error')
trans2 = ha.new_transition(m2, error, 'trans2')
trans2.set_guard([[0, -1, 0]], [-3]) # y >= 3
# initial set has x0 = [0, 1], t = [0, 1], a = 1
init_lpi = lputil.from_box([(0, 1), (0, 1), (1, 1)], m1)
init_list = [StateSet(init_lpi, m1)]
# settings, step size = 1.0
settings = HylaaSettings(1.0, 10.0)
settings.stdout = HylaaSettings.STDOUT_VERBOSE
settings.plot.plot_mode = PlotSettings.PLOT_NONE
settings.aggregation.deaggregation = True
core = Core(ha, settings)
core.setup(init_list)
core.do_step() # pop
assert core.aggdag.cur_node is not None
for _ in range(5): # 4 + 1 step to leave invariant
core.do_step() # continuous post in m1
core.do_step() # pop
# at this point, the state should be aggregated, but we should maintain one concrete state that's feasible
cur_node = core.aggdag.cur_node
assert cur_node.aggregated_state == core.aggdag.get_cur_state()
assert cur_node.concrete_state is not None
assert len(core.aggdag.roots) == 1
root = core.aggdag.roots[0]
assert root.op_list
assert isinstance(
root.op_list[0],
OpTransition) and root.op_list[0].step == 1 # transition from x=[1, 2]
assert isinstance(
root.op_list[1],
OpTransition) and root.op_list[1].step == 2 # transition from x=[2, 3]
assert isinstance(
root.op_list[2],
OpTransition) and root.op_list[2].step == 3 # transition from x=[3, 4]
assert isinstance(
root.op_list[3],
OpTransition) and root.op_list[3].step == 4 # transition from x=[4, 5]
for s in range(4):
assert root.op_list[s].transition == trans1 and root.op_list[
s].poststate.is_concrete
assert isinstance(root.op_list[4], OpInvIntersect)
op4 = root.op_list[4]
assert op4.step == 5 and op4.node == root and op4.i_index == 0 and not op4.is_stronger
assert isinstance(
root.op_list[5],
OpTransition) and root.op_list[5].step == 5 # transition from x=[4, 4]
assert isinstance(root.op_list[6], OpInvIntersect)
op6 = root.op_list[6]
assert op6.step == 6 and op6.node == root and op6.i_index == 0 and op6.is_stronger
assert len(root.op_list) == 7
core.run_to_completion()
assert root.op_list[0].child_node == cur_node
assert root.op_list[3].child_node == cur_node