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_invariants():
'test removing of redundant invariants'
ha = HybridAutomaton()
mode = ha.new_mode('mode')
# dynamics: x' = 1, y' = 1, a' = 0
mode.set_dynamics([[0, 0, 1], [0, 0, 1], [0, 0, 0]])
# invariant: x <= 2.5
mode.set_invariant([[1, 0, 0]], [2.5])
# initial set has x0 = [0, 1]
init_lpi = lputil.from_box([(0, 1), (0, 1), (1, 1)], mode)
init_list = [StateSet(init_lpi, mode)]
# settings, step size = 0.1
settings = HylaaSettings(0.1, 5.0)
settings.stdout = HylaaSettings.STDOUT_NONE
settings.plot.plot_mode = PlotSettings.PLOT_NONE
result = Core(ha, settings).run(init_list)
# check last cur_state to ensure redundant constraints were not added
assert result.last_cur_state.lpi.get_num_rows() == 3 + 2*3 + 1 # 3 for basis matrix, 2*3 for initial constraints
def test_init_outside_invariant():
'test when initial state is outside of the mode invariant'
ha = HybridAutomaton()
mode = ha.new_mode('mode')
mode.set_dynamics([[0, 0, 1], [0, 0, 1], [0, 0, 0]]) # x' = 1, y' = 1, a' = 0
# x <= 2.5
mode.set_invariant([[1, 0, 0]], [2.5])
# initial set, x = [3, 4]
init_lpi = lputil.from_box([(3, 4), (0, 1), (1, 1)], mode)
init_list = [StateSet(init_lpi, mode)]
# transition to error if x >= 10
error = ha.new_mode('error')
trans = ha.new_transition(mode, error)
trans.set_guard([[-1., 0, 0],], [-10])
# settings
settings = HylaaSettings(1.0, 5.0)
settings.stdout = HylaaSettings.STDOUT_VERBOSE
try:
Core(ha, settings).run(init_list)
assert False, "running with initial state outside of invariant did not raise RuntimeError"
except RuntimeError:
pass
def define_settings():
'''get the hylaa settings object
see hylaa/settings.py for a complete list of reachability settings'''
# step_size = 0.001, max_time = 0.75
settings = HylaaSettings(0.001, 0.15)
settings.plot.plot_mode = PlotSettings.PLOT_IMAGE # try PLOT_VIDEO (takes 10 minutes)
settings.plot.xdim_dir = 2
settings.plot.ydim_dir = 0
settings.plot.label.title = "Fuzzy PD Controller"
settings.plot.label.axes_limits = (-0.01, 0.3, -1.1, 1.1)
settings.stdout = HylaaSettings.STDOUT_VERBOSE
#settings.aggregation.require_same_path=False
#settings.aggregation.pop_strategy=AggregationSettings.POP_LARGEST_MAXTIME
#self.aggstrat = aggstrat.Aggregated()
# custom settings for video export
def make_video_writer():
'returns the Writer to create a video for export'
writer_class = animation.writers['ffmpeg']
return writer_class(fps=50, metadata=dict(artist='Me'), bitrate=1800)
settings.plot.make_video_writer_func = make_video_writer
return settings
def define_settings():
'''get the hylaa settings object
see hylaa/settings.py for a complete list of reachability settings'''
# step_size = 5.0E-4, max_time = 2.0
settings = HylaaSettings(5.0E-3, 2.0)
settings.stdout = HylaaSettings.STDOUT_VERBOSE
settings.plot.plot_mode = PlotSettings.PLOT_IMAGE
settings.plot.xdim_dir = 0 # [0, None, None]
#x0_dir = np.array([0, 0, 0, 0, 0, 0, 0.0833333333333333, 0, -1, 0, 0, 0, 0], dtype=float)
#settings.plot.ydim_dir = [2, 6, 8]
settings.plot.ydim_dir = 2
#settings.stop_on_error = False
#settings.plot.draw_stride = 5
#settings.plot.num_angles = 4096 * 128 # required for convex hull to show up correctly
#settings.aggregation.agg_mode = AggregationSettings.AGG_NONE
#def custom_pop_func(waiting_list):
# 'custom pop function for aggregation'
# mode = waiting_list[0].mode
# state_list = [state for state in waiting_list if state.mode == mode]
# num = 2 # performing clustering with this number of items
# return heapq.nsmallest(num, state_list, lambda s: s.cur_steps_since_start)
#settings.aggregation.custom_pop_func = custom_pop_func
settings.aggstrat.agg_type = Aggregated.AGG_CONVEX_HULL
return settings
def define_settings(unsafe_box):
'get the hylaa settings object'
step = math.pi / 6
max_time = 3 * math.pi
settings = HylaaSettings(step, max_time)
settings.process_urgent_guards = True
settings.aggstrat.deaggregate = True # use deaggregation
settings.aggstrat.deagg_preference = Aggregated.DEAGG_LEAVES_FIRST
settings.aggstrat.agg_type = Aggregated.AGG_CONVEX_HULL
plot_settings = settings.plot
plot_settings.plot_mode = PlotSettings.PLOT_IMAGE
plot_settings.xdim_dir = 0
plot_settings.ydim_dir = 1
plot_settings.label.x_label = '$x$'
plot_settings.label.y_label = '$y$'
cols = []
line = [(-10, -3), (10, -3)]
cols.append(
collections.LineCollection([line],
animated=True,
colors=('gray'),
linewidths=(2),
linestyle='dashed'))
line = []
line.append((unsafe_box[0][0], unsafe_box[1][0]))
line.append((unsafe_box[0][1], unsafe_box[1][0]))
line.append((unsafe_box[0][1], unsafe_box[1][1]))
line.append((unsafe_box[0][0], unsafe_box[1][1]))
line.append((unsafe_box[0][0], unsafe_box[1][0]))
cols.append(
collections.LineCollection([line],
animated=True,
colors=('red'),
linewidths=(2),
linestyle='dashed'))
settings.plot.extra_collections = cols
plot_settings.plot_mode = PlotSettings.PLOT_VIDEO
plot_settings.filename = 'ha_deagg.mp4'
plot_settings.video_fps = 4
plot_settings.video_extra_frames = 12 # extra frames at the end of a video so it doesn't end so abruptly
plot_settings.video_pause_frames = 2 # frames to render in video whenever a 'pause' occurs
plot_settings.label.axes_limits = [-6, 6, -4, 6]
plot_settings.label.y_label = '$y$'
plot_settings.label.x_label = '$x$'
plot_settings.label.title = 'Deaggregation Demo'
return settings
def test_agg_with_reset():
'test the aggregation of states with a reset'
# m1 dynamics: x' == 1, y' == 0, x0: [-3, -2], y0: [0, 1], step: 1.0
# m1 invariant: x + y <= 0
# m1 -> m2 guard: x + y >= 0 and y <= 0.5, reset = [[0, -1, 0], [1, 0, 0]] (x' = -y, y' = x, remove a)
# m2 dynamics: x' == 0, y' == 0
# time bound: 4
# expected result: last state is line (not box!) from (0, 0) to (-0.5, -0.5)
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
m2 = ha.new_mode('m2')
m2.set_dynamics([[0, 0], [0, 0]])
# invariant: x + y <= 0
m1.set_invariant([[1, 1, 0]], [0])
# guard: x + y == 0 & y <= 0.5
trans1 = ha.new_transition(m1, m2, 'trans1')
trans1.set_guard([[-1, -1, 0], [1, 1, 0], [0, 1, 0]], [0, 0, 0.5])
#trans1.set_reset(np.identity(3)[:2])
trans1.set_reset(np.array([[0, -1, 0], [1, 0, 0]], dtype=float))
# initial set has x0 = [-3, -2], y = [0, 1], a = 1
init_lpi = lputil.from_box([(-3, -2), (0, 1), (1, 1)], m1)
init_list = [StateSet(init_lpi, m1)]
# settings, step size = 1.0
settings = HylaaSettings(1.0, 4.0)
settings.stdout = HylaaSettings.STDOUT_NONE
settings.plot.plot_mode = PlotSettings.PLOT_NONE
# use agg_box
settings.aggstrat.agg_type = Aggregated.AGG_BOX
core = Core(ha, settings)
result = core.run(init_list)
lpi = result.last_cur_state.lpi
# 2 basis matrix rows, 4 init constraints rows, 6 rows from guard conditions (2 from each)
assert lpi.get_num_rows() == 2 + 4 + 6
verts = result.last_cur_state.verts(core.plotman)
assert len(verts) == 3
assert np.allclose(verts[0], verts[-1])
assert pair_almost_in((0, 0), verts)
assert pair_almost_in((-0.5, -0.5), verts)
def make_settings():
'make the reachability settings object'
# see hylaa.settings for a list of reachability settings
settings = HylaaSettings(1.0, 10.0) # step size = 1.0, time bound 10.0
settings.plot.plot_mode = PlotSettings.PLOT_IMAGE
settings.stdout = HylaaSettings.STDOUT_VERBOSE
settings.plot.filename = "demo_reset.png"
return settings
def test_transition():
'test a discrete transition'
ha = HybridAutomaton()
# mode one: x' = 1, t' = 1, a' = 0
m1 = ha.new_mode('m1')
m1.set_dynamics([[0, 0, 1], [0, 0, 1], [0, 0, 0]])
# mode two: x' = -1, t' = 1, a' = 0
m2 = ha.new_mode('m2')
m2.set_dynamics([[0, 0, -1], [0, 0, 1], [0, 0, 0]])
# invariant: t <= 2.5
m1.set_invariant([[0, 1, 0]], [2.5])
# guard: t >= 2.5
trans1 = ha.new_transition(m1, m2, 'trans1')
trans1.set_guard([[0, -1, 0]], [-2.5])
# error t >= 4.5
error = ha.new_mode('error')
trans2 = ha.new_transition(m2, error, "to_error")
trans2.set_guard([[0, -1, 0]], [-4.5])
# initial set has x0 = [0, 1], t = [0, 0.2], a = 1
init_lpi = lputil.from_box([(0, 1), (0, 0.2), (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.plot.store_plot_result = True
result = Core(ha, settings).run(init_list)
ce = result.counterexample
assert len(ce) == 2
assert ce[0].mode.name == 'm1'
assert ce[0].outgoing_transition.name == 'trans1'
assert ce[1].mode.name == 'm2'
assert ce[1].outgoing_transition.name == 'to_error'
assert ce[1].start[0] + 1e-9 >= 3.0
assert ce[1].end[0] - 1e-9 <= 2.0
polys = [obj[0] for obj in result.plot_data.mode_to_obj_list[0]['m1']]
assert len(polys) == 4
polys = [obj[0] for obj in result.plot_data.mode_to_obj_list[0]['m2']]
assert len(polys) == 3
assert result.last_cur_state.cur_steps_since_start[0] == 5
def test_agg_to_more_vars():
'test the aggregation of states with a reset to a mode with new variables'
ha = HybridAutomaton()
# mode one: x' = 1, a' = 0
m1 = ha.new_mode('m1')
m1.set_dynamics([[0, 1], [0, 0]])
# mode two: x' = 0, a' = 0, y' == 1
m2 = ha.new_mode('m2')
m2.set_dynamics([[0, 0, 0], [0, 0, 0], [0, 1, 0]])
# invariant: x <= 3.0
m1.set_invariant([[1, 0]], [3.0])
# guard: True
trans1 = ha.new_transition(m1, m2, 'trans1')
trans1.set_guard_true()
reset_mat = [[1, 0], [0, 1], [0, 0]]
reset_minkowski = [[0], [0], [1]]
reset_minkowski_constraints = [[1], [-1]]
reset_minkowski_rhs = [3, -3] # y0 == 3
trans1.set_reset(reset_mat, reset_minkowski, reset_minkowski_constraints, reset_minkowski_rhs)
# initial set has x0 = [0, 1], a = 1
init_lpi = lputil.from_box([(0, 1), (1, 1)], m1)
init_list = [StateSet(init_lpi, m1)]
# settings, step size = 1.0
settings = HylaaSettings(1.0, 4.0)
settings.stdout = HylaaSettings.STDOUT_DEBUG
settings.plot.plot_mode = PlotSettings.PLOT_NONE
settings.plot.store_plot_result = True
settings.plot.xdim_dir = 0
settings.plot.ydim_dir = {'m1': 1, 'm2': 2}
result = Core(ha, settings).run(init_list)
polys = [obj[0] for obj in result.plot_data.mode_to_obj_list[0]['m1']]
# 4 steps because invariant is allowed to be false for the final step
assert 4 <= len(polys) <= 5, "expected invariant to become false after 4/5 steps"
assert_verts_is_box(polys[0], [[0, 1], [1, 1]])
assert_verts_is_box(polys[1], [[1, 2], [1, 1]])
assert_verts_is_box(polys[2], [[2, 3], [1, 1]])
assert_verts_is_box(polys[3], [[3, 4], [1, 1]])
polys = [obj[0] for obj in result.plot_data.mode_to_obj_list[0]['m2']]
assert_verts_is_box(polys[0], [[1, 4], [3, 3]])
assert_verts_is_box(polys[1], [[1, 4], [4, 4]])
def make_settings():
'make the reachability settings object'
# see hylaa.settings for a list of reachability settings
settings = HylaaSettings(math.pi / 8,
math.pi) # step size = pi/8, time bound pi
settings.plot.plot_mode = PlotSettings.PLOT_IMAGE
settings.stdout = HylaaSettings.STDOUT_NORMAL
settings.plot.filename = "demo_inputs_reset.png"
return settings
def make_settings():
'make the reachability settings object'
# see hylaa.settings for a list of reachability settings
settings = HylaaSettings(math.pi / 4, math.pi) # step size = pi/4, time bound pi
settings.plot.plot_mode = PlotSettings.PLOT_IMAGE
settings.stdout = HylaaSettings.STDOUT_NORMAL
settings.plot.filename = "hylaa.png"
settings.plot.label.title_size = 18
settings.plot.plot_size = (6, 6)
return settings
def make_settings():
'make the reachability settings object'
# see hylaa.settings for a list of reachability settings
settings = HylaaSettings(0.1, 20.0) # step size = 0.1, time bound 20.0
settings.plot.plot_mode = PlotSettings.PLOT_NONE
settings.stdout = HylaaSettings.STDOUT_VERBOSE
settings.plot.filename = "space_station.png"
settings.plot.xdim_dir = None # x dimension will be time
dynamics = loadmat('iss.mat')
y3 = dynamics['C'][2]
settings.plot.ydim_dir = y3.toarray()[0] # use y3 for the y plot direction
return settings
def define_settings():
'get the hylaa settings object'
step = math.pi/16
max_time = 2*math.pi
settings = HylaaSettings(step, max_time)
settings.stdout = stdout = HylaaSettings.STDOUT_VERBOSE
plot_settings = settings.plot
plot_settings.plot_mode = PlotSettings.PLOT_IMAGE
plot_settings.xdim_dir = 0
plot_settings.ydim_dir = 1
#plot_settings.plot_mode = PlotSettings.PLOT_VIDEO
#plot_settings.filename = 'ha.mp4'
#plot_settings.video_fps = 2
#plot_settings.video_extra_frames = 10 # extra frames at the end of a video so it doesn't end so abruptly
#plot_settings.video_pause_frames = 5 # frames to render in video whenever a 'pause' occurs
plot_settings.label.y_label = '$y$'
plot_settings.label.x_label = '$x$'
plot_settings.label.title = 'Harmonic Oscillator'
return settings
def define_settings():
'get the hylaa settings object'
step = 1
max_time = 28
# max_time = 22
settings = HylaaSettings(step, max_time)
settings.stdout = stdout = HylaaSettings.STDOUT_VERBOSE
plot_settings = settings.plot
plot_settings.plot_mode = PlotSettings.PLOT_IMAGE
plot_settings.xdim_dir = 0
plot_settings.ydim_dir = 1
# plot_settings.plot_mode = PlotSettings.PLOT_VIDEO
# plot_settings.filename = 'tmpc.mp4'
plot_settings.video_fps = 1
plot_settings.video_extra_frames = 2 # extra frames at the end of a video so it doesn't end so abruptly
plot_settings.video_pause_frames = 2 # frames to render in video whenever a 'pause' occurs
plot_settings.label.y_label = '$y$'
plot_settings.label.x_label = '$x$'
plot_settings.label.title = 'TMPC mode 1 X vs Y'
return settings
def test_ha():
'test for the harmonic oscillator example with line initial set (from ARCH 2018 paper)'
ha = HybridAutomaton()
# with time and affine variable
mode = ha.new_mode('mode')
mode.set_dynamics([[0, 1, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0]])
error = ha.new_mode('error')
trans1 = ha.new_transition(mode, error)
trans1.set_guard([[1., 0, 0, 0], [-1., 0, 0, 0]], [4.0, -4.0])
# 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, 2*math.pi)
settings.stdout = HylaaSettings.STDOUT_VERBOSE
settings.plot.store_plot_result = True
settings.plot.plot_mode = PlotSettings.PLOT_NONE
core = Core(ha, settings)
result = core.run(init_list)
assert result.has_concrete_error
ce = result.counterexample[0]
# [-5.0, 0.6568542494923828, 0.0, 1.0] -> [4.0, 3.0710678118654737, 2.356194490192345, 1.0]
assert ce.mode == mode
assert np.allclose(ce.start, np.array([-5, 0.65685, 0, 1], dtype=float))
assert np.allclose(ce.end, np.array([4, 3.07106, 2.35619, 1], dtype=float))
# check the reachable state (should always have x <= 3.5)
obj_list = result.plot_data.mode_to_obj_list[0][mode.name]
for obj in obj_list:
verts = obj[0]
for vert in verts:
x, _ = vert
assert x <= 4.9
def test_unaggregation():
'test an unaggregated discrete transition'
ha = HybridAutomaton()
# mode one: x' = 1, t' = 1, a' = 0
m1 = ha.new_mode('m1')
m1.set_dynamics([[0, 0, 1], [0, 0, 1], [0, 0, 0]])
# mode two: x' = -1, t' = 1, a' = 0
m2 = ha.new_mode('m2')
m2.set_dynamics([[0, 0, -1], [0, 0, 1], [0, 0, 0]])
# invariant: t <= 2.5
m1.set_invariant([[0, 1, 0]], [2.5])
# guard: t >= 0.5
trans1 = ha.new_transition(m1, m2, 'trans1')
trans1.set_guard([[0, -1, 0]], [-0.5])
# error x >= 4.5
error = ha.new_mode('error')
trans2 = ha.new_transition(m2, error, "to_error")
trans2.set_guard([[-1, 0, 0]], [-4.5])
# initial set has x0 = [0, 0.2], t = [0, 0.2], a = 1
init_lpi = lputil.from_box([(0, 0.2), (0, 0.2), (1, 1)], m1)
init_list = [StateSet(init_lpi, m1)]
# settings, step size = 1.0
settings = HylaaSettings(1.0, 10.0)
settings.stdout = HylaaSettings.STDOUT_DEBUG
settings.plot.store_plot_result = True
settings.plot.plot_mode = PlotSettings.PLOT_NONE
settings.aggstrat = aggstrat.Unaggregated()
result = Core(ha, settings).run(init_list)
# expected no exception
# m2 should be reachable
polys = [obj[0] for obj in result.plot_data.mode_to_obj_list[0]['m2']]
assert len(polys) > 15
def define_settings(ha, limit):
'get the hylaa settings object'
step = 0.0025
max_time = 1.0
settings = HylaaSettings(step, max_time)
#settings.interval_guard_optimization = False
#settings.time_elapse.scipy_sim.max_step = 0.001
#settings.time_elapse.scipy_sim.rtol = 1e-9
#settings.time_elapse.scipy_sim.atol = 1e-12
settings.stdout = stdout = HylaaSettings.STDOUT_VERBOSE
plot_settings = settings.plot
plot_settings.plot_mode = PlotSettings.PLOT_IMAGE
#plot_settings.plot_mode = PlotSettings.PLOT_VIDEO
#plot_settings.filename = 'building.mp4'
plot_settings.xdim_dir = None
plot_settings.ydim_dir = ha.transitions[0].guard_csr[0].toarray()[0]
plot_settings.label.y_label = '$y_{1}$'
plot_settings.label.x_label = 'Time'
plot_settings.label.title = 'Building (Uncertain Inputs)'
#plot_settings.label.axes_limits = (0.4, 0.6, -0.0002, -0.0001)
plot_settings.plot_size = (12, 8)
plot_settings.label.big(size=36)
settings.stop_on_concrete_error = False
settings.make_counterexample = False
line = [(0.0, -limit), (max_time, -limit)]
lc = collections.LineCollection([line],
animated=True,
colors=('red'),
linewidths=(1),
linestyle='dashed')
plot_settings.extra_collections = [lc]
return settings
def test_agg_no_counterexample():
'test that aggregation to error does not create a counterexample'
# m1 dynamics: x' == 1, y' == 0, x0, y0: [0, 1], step: 1.0
# 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_DEBUG
settings.plot.plot_mode = PlotSettings.PLOT_NONE
result = Core(ha, settings).run(init_list)
assert not result.counterexample
def test_over_time_range():
'test plotting over time with aggergation (time range)'
ha = HybridAutomaton()
mode_a = ha.new_mode('A')
mode_b = ha.new_mode('B')
# dynamics: x' = a, a' = 0
mode_a.set_dynamics([[0, 1], [0, 0]])
mode_b.set_dynamics([[0, 1], [0, 0]])
# invariant: x <= 2.5
mode_a.set_invariant([[1, 0]], [2.5])
trans1 = ha.new_transition(mode_a, mode_b, 'first')
trans1.set_guard_true()
# initial set has x0 = [0, 0]
init_lpi = lputil.from_box([(0, 0), (1, 1)], mode_a)
init_list = [StateSet(init_lpi, mode_a)]
# settings, step size = 1.0
settings = HylaaSettings(1.0, 4.0)
settings.stdout = HylaaSettings.STDOUT_DEBUG
settings.process_urgent_guards = True
settings.plot.plot_mode = PlotSettings.PLOT_NONE
settings.plot.store_plot_result = True
settings.plot.xdim_dir = None
settings.plot.ydim_dir = 0
result = Core(ha, settings).run(init_list)
polys = [obj[0] for obj in result.plot_data.mode_to_obj_list[0][mode_b.name]]
# expected with aggegregation: [0, 2.5] -> [1, 3.5] -> [2, 4.5] -> [3, 5.5] -> [4, 6.5]
# 4 steps because invariant is allowed to be false for the final step
assert len(polys) == 5, "expected invariant to become false after 5 steps"
for i in range(5):
assert_verts_is_box(polys[i], [[i, i + 3.0], [i, i + 3.0]])
def test_tt_with_invstr():
'test time-triggered transitions combined with invariant strengthening'
ha = HybridAutomaton()
# mode one: x' = 1, a' = 0
m1 = ha.new_mode('m1')
m1.set_dynamics([[0, 1], [0, 0]])
m1.set_invariant([[1, 0]], [2.0]) # invariant: x <= 2.0
# mode two: x' = 1, a' = 0
m2 = ha.new_mode('m2')
m2.set_dynamics([[0, 1], [0, 0]])
m2.set_invariant([[1, 1]], [4.0]) # x + a <= 4.0
# guard: x >= 2.0
trans1 = ha.new_transition(m1, m2, 'trans1')
trans1.set_guard([[-1, 0]], [-2.0])
# error x >= 4.0
error = ha.new_mode('error')
trans2 = ha.new_transition(m2, error, "to_error")
trans2.set_guard([[-1, 0]], [-4.0])
# initial set has x0 = [0, 1]
init_lpi = lputil.from_box([(0, 1), (0, 1)], m1)
init_list = [StateSet(init_lpi, m1)]
# settings, step size = 0.1
settings = HylaaSettings(0.1, 5.0)
settings.stdout = HylaaSettings.STDOUT_VERBOSE
settings.plot.plot_mode = PlotSettings.PLOT_NONE
# run setup() only and check the result
core = Core(ha, settings)
core.setup(init_list)
assert trans1.time_triggered
assert not trans2.time_triggered # not time-triggered because invariant of m2 is True
def test_plot_over_time():
'test doing a plot over time'
ha = HybridAutomaton()
mode = ha.new_mode('mode')
mode.set_dynamics([[0, 1], [-1, 0]])
# initial set
init_lpi = lputil.from_box([(-5, -4), (0, 1)], mode)
init_list = [StateSet(init_lpi, mode)]
# settings
settings = HylaaSettings(math.pi/4, math.pi)
settings.stdout = HylaaSettings.STDOUT_VERBOSE
settings.plot.store_plot_result = True
settings.plot.plot_mode = PlotSettings.PLOT_NONE
settings.plot.ydim_dir = None # y dimension will be time
result = Core(ha, settings).run(init_list)
assert not result.has_aggregated_error and not result.has_concrete_error
# check the reachable state
# we would expect at the end that x = [4, 5], t = pi
obj_list = result.plot_data.mode_to_obj_list[0][mode.name]
for vert in obj_list[0][0]:
x, y = vert
assert abs(y) < 1e-6, "initial poly time is wrong"
assert abs(-5 - x) < 1e-6 or abs(-4 - x) < 1e-6
for vert in obj_list[-1][0]:
x, y = vert
assert abs(math.pi - y) < 1e-6, "final poly time is wrong"
assert abs(5 - x) < 1e-6 or abs(4 - x) < 1e-6
def test_init_unsat():
'initial region unsat with multiple invariant conditions'
ha = HybridAutomaton()
mode = ha.new_mode('A')
mode.set_dynamics(np.identity(2))
mode.set_invariant([[1, 0], [1, 0]], [2, 3]) # x <= 2 and x <= 3
# initial set
lpi1 = lputil.from_box([(10, 11), (0, 1)], mode)
lpi2 = lputil.from_box([(0, 1), (0, 1)], mode)
init_list = [StateSet(lpi1, mode), StateSet(lpi2, mode)]
# settings
settings = HylaaSettings(1, 5)
settings.stdout = HylaaSettings.STDOUT_VERBOSE
settings.plot.plot_mode = PlotSettings.PLOT_NONE
core = Core(ha, settings)
core.run(init_list) # expect no exception during running
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_multiple_init_states():
'test with multiple initial states in the same mode (should NOT do aggregation)'
ha = HybridAutomaton()
# with time and affine variable
mode = ha.new_mode('mode')
mode.set_dynamics([[0, 0], [0, 0]])
# initial set
init_lpi = lputil.from_box([(-5, -4), (0, 1)], mode)
init_lpi2 = lputil.from_box([(-5, -5), (2, 3)], mode)
init_list = [StateSet(init_lpi, mode), StateSet(init_lpi2, mode)]
# settings
settings = HylaaSettings(math.pi/4, math.pi)
settings.stdout = HylaaSettings.STDOUT_NONE
settings.plot.plot_mode = PlotSettings.PLOT_NONE
core = Core(ha, settings)
core.run(init_list)
def test_invariants():
'test invariant trimming'
ha = HybridAutomaton()
mode = ha.new_mode('mode')
# dynamics: x' = 1, y' = 1, a' = 0
mode.set_dynamics([[0, 0, 1], [0, 0, 1], [0, 0, 0]])
# invariant: x <= 2.5
mode.set_invariant([[1, 0, 0]], [2.5])
# initial set has x0 = [0, 1]
init_lpi = lputil.from_box([(0, 1), (0, 1), (1, 1)], mode)
init_list = [StateSet(init_lpi, mode)]
# settings, step size = 1.0
settings = HylaaSettings(1.0, 5.0)
settings.stdout = HylaaSettings.STDOUT_VERBOSE
settings.plot.store_plot_result = True
result = Core(ha, settings).run(init_list)
# check the reachable state
polys = [obj[0] for obj in result.plot_data.mode_to_obj_list[0][mode.name]]
# 4 steps because invariant is allowed to be false for the final step
assert len(polys) == 4, "expected invariant to become false after 4 steps"
assert_verts_is_box(polys[0], [[0, 1], [0, 1]])
assert_verts_is_box(polys[1], [[1, 2], [1, 2]])
assert_verts_is_box(polys[2], [[2, 3], [2, 3]])
assert_verts_is_box(polys[3], [[3, 3.5], [3, 4]])
def test_stateset_bad_init():
'test constructing a stateset with a basis matrix that is not the identity (should raise error)'
# this is from an issue reported by Mojtaba Zarei
ha = HybridAutomaton()
mode = ha.new_mode('mode')
mode.set_dynamics([[0, 1], [-1, 0]])
# initial set
init_lpi = lputil.from_box([(-5, -5), (0, 1)], mode)
init_list = [StateSet(init_lpi, mode)]
# settings
settings = HylaaSettings(math.pi/4, math.pi)
settings.stdout = HylaaSettings.STDOUT_NONE
settings.plot.store_plot_result = True
settings.plot.plot_mode = PlotSettings.PLOT_NONE
core = Core(ha, settings)
result = core.run(init_list)
# use last result
stateset = result.last_cur_state
mode = stateset.mode
lpi = stateset.lpi
try:
init_states = [StateSet(lpi, mode)]
settings = HylaaSettings(0.1, 0.1)
core = Core(ha, settings)
result = core.run(init_states)
assert False, "assertion should be raised if init basis matrix is not identity"
except RuntimeError:
pass
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_plain():
'test plain aggregation of states across discrete transitions'
# m1 dynamics: x' == 1, y' == 0, x0, y0: [0, 1], step: 1.0
# m1 invariant: x <= 3
# m1 -> m2 guard: True
# m2 dynamics: x' == 0, y' == 1
# time bound: 4
# excepted final states to be: x: [0, 4], y: [4,5]
# x is [1, 4] because no transitions are allowed at step 0 (simulation-equiv semantics) and a transition is
# allowed one step after the invariant becomes false
# y is [4,5] because after aggregation, the time elapsed for the aggregated set will be 0.0, the minimum
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(csr_matrix((0, 0)), [])
# 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, 4.0)
settings.stdout = HylaaSettings.STDOUT_DEBUG
settings.plot.plot_mode = PlotSettings.PLOT_NONE
settings.plot.store_plot_result = True
core = Core(ha, settings)
result = core.run(init_list)
# check history
state = result.last_cur_state
assert state.mode == m2
assert len(state.aggdag_op_list) > 1
op0 = state.aggdag_op_list[0]
op1 = state.aggdag_op_list[1]
assert isinstance(op0, OpTransition)
assert len(core.aggdag.roots) == 1
assert op0.child_node.stateset.mode is m2
assert op0.transition == trans1
assert op0.parent_node == core.aggdag.roots[0]
assert isinstance(op0.poststate, StateSet)
assert op0.step == 1
assert isinstance(op0.child_node, AggDagNode)
assert op0.child_node == op1.child_node
assert op0.child_node not in core.aggdag.roots
assert len(op0.parent_node.stateset.aggdag_op_list) == 1
assert op0.parent_node.stateset.aggdag_op_list[0] is None
# check polygons in m2
polys2 = [obj[0] for obj in result.plot_data.mode_to_obj_list[0]['m2']]
assert 4 <= len(polys2) <= 5
assert_verts_is_box(polys2[0], [[1, 4], [0, 1]])
assert_verts_is_box(polys2[1], [[1, 4], [1, 2]])
assert_verts_is_box(polys2[2], [[1, 4], [2, 3]])
assert_verts_is_box(polys2[3], [[1, 4], [3, 4]])
def test_tt_09():
'test time-triggered transition at 0.9 bug'
# this test is from an issue reported by Mojtaba Zarei
tt_time = 0.9
ha = HybridAutomaton()
# the test seems to be sensitive to the a_matrix... my guess is the LP is barely feasible at the tt_time
a_matrix = np.array(
[[6.037291088, -4.007840286, 2.870370645, 43.12729646, 10.06751155, 23.26084098, -0.001965587832, 0, 0],
[3.896645707, -0.03417905392, -9.564966476, 15.25894014, -21.57196438, 16.60548055, 0.03473846441, 0, 0],
[22.72995871, 14.12055097, -0.9315267908, 136.9851951, -71.66383111, 109.7143863, 0.1169799769, 0, 0],
[-38.16694597, 3.349061908, -9.10171149, -185.1866526, 9.210877185, -165.8086527, -0.06858712649, 0, 0],
[46.78596597, 27.7996521, 17.18120319, 285.4632424, -135.289626, 235.9427441, 0.228154713, 0, 0],
[-8.31135303, 3.243945466, -4.523811735, -39.26067436, -9.385678542, -36.63193931, -0.0008874747046, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=float)
mode1 = ha.new_mode('mode')
mode1.set_dynamics(a_matrix)
# time-triggered invariant: t <= tt_time
mat = np.array([[0, 0, 0, 0, 0, 0, 0, 1, 0]], dtype=float)
rhs = [tt_time]
mode1.set_invariant(mat, rhs)
mode2 = ha.new_mode('mode2')
mode2.set_dynamics(a_matrix)
# transition, guard: x >= -2 & y > 4 & t >= tt_time
# transition, guard: t >= 0.9
mat = np.array([[0, 0, 0, 0, 0, 0, 0, -1, 0]], dtype=float)
rhs = [-tt_time]
t = ha.new_transition(mode1, mode2)
t.set_guard(mat, rhs)
# initial set
init_box = np.array([[-0.1584, -0.1000],
[-0.0124, 0.0698],
[-0.3128, 0.0434],
[-0.0208, 0.0998],
[-0.4895, 0.1964],
[-0.0027, 0.0262],
[42.40, 42.5],
[0, 0], # t(0) = 0
[1, 1]]) # affine(0) = 1
init_lpi = lputil.from_box(init_box, mode1)
init_list = [StateSet(init_lpi, mode1)]
# settings
settings = HylaaSettings(0.05, 1.0)
settings.stdout = HylaaSettings.STDOUT_DEBUG
settings.plot.store_plot_result = True
settings.plot.plot_mode = PlotSettings.PLOT_NONE #INTERACTIVE
#settings.plot.xdim_dir = 7 #None
#settings.plot.ydim_dir = 0
core = Core(ha, settings)
result = core.run(init_list)
mode2_list = result.plot_data.mode_to_obj_list[0]['mode2']
assert len(mode2_list) == 3, f"mode2_list len was {len(mode2_list)}, expected 3 (0.9, 0.95, 1.0)"
