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 make_init(ha):
'''returns list of initial states'''
bounds_list = []
dims = list(ha.modes.values())[0].a_csr.shape[0]
for dim in range(dims):
if dim < 10:
lb = 0.0002
ub = 0.00025
elif dim == 25:
lb = -0.0001
ub = 0.0001
else:
lb = ub = 0
bounds_list.append((lb, ub))
mode = ha.modes['mode']
init_lpi = lputil.from_box(bounds_list, mode)
init_list = [StateSet(init_lpi, mode)]
return init_list
def make_op_transition(self, t, t_lpi, state, parent_node):
'make an OpTransition object, can return null if lp solving fails'
step_in_mode = state.cur_step_in_mode
steps_since_start = state.cur_steps_since_start
is_concrete = state.is_concrete
successor_has_inputs = t.to_mode.b_csr is not None
op = OpTransition(step_in_mode, parent_node, None, t, None)
succeeded = self.settings.aggstrat.pretransition(t, t_lpi, op)
if not succeeded:
self.core.print_verbose(
f"Warning: aggstrat.pretransition returned None (LP solving failed)"
)
op = None
else:
lputil.add_reset_variables(t_lpi, t.to_mode.mode_id, t.transition_index, \
reset_csr=t.reset_csr, minkowski_csr=t.reset_minkowski_csr, \
minkowski_constraints_csr=t.reset_minkowski_constraints_csr, \
minkowski_constraints_rhs=t.reset_minkowski_constraints_rhs, successor_has_inputs=successor_has_inputs)
if not t_lpi.is_feasible():
raise RuntimeError(
"cur_state became infeasible after reset was applied")
op_list = [op]
state = StateSet(t_lpi, t.to_mode, steps_since_start, op_list,
is_concrete)
op.poststate = state
return op
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 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_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_init(ha):
'make the initial states'
mode = ha.modes['mode0_right']
init_lpi = lputil.from_box([(0, 1), (0, 1.0), (1.0, 1.0)], mode)
init_list = [StateSet(init_lpi, mode)]
return init_list
def make_init(ha):
'''returns list of initial states'''
mode = ha.modes['mode']
init_lpi = lputil.from_box([[0.4, 5.0], [-0.2, 0.5], [-0.2, 0.5]], mode)
init_list = [StateSet(init_lpi, mode)]
return init_list
def make_init(ha):
'make the initial states'
p2 = ha.modes['Far']
init_lpi = lputil.from_box([(-925.0, -875.0), (-425.0, -375.0), (0.0, 0.0),
(0.0, 0.0), (0.0, 0.0), (1.0, 1.0)], p2)
init_list = [StateSet(init_lpi, p2)]
return init_list
def make_init(ha):
'''returns list of initial states'''
mode = ha.modes['mode']
# init states: x in [-5, -4], y in [0, 1]
init_lpi = lputil.from_box([[-6, -5], [0, 1]], mode)
init_list = [StateSet(init_lpi, mode)]
return init_list
def make_init(ha):
'make the initial states'
# initial set has x0 = [-5, -4], y = [0, 1], c = 0, a = 1
mode = ha.modes['m1']
init_lpi = lputil.from_box([(-5, -4), (0, 1), (0, 0), (1, 1)], mode)
init_list = [StateSet(init_lpi, mode)]
return init_list
def make_init(ha):
'''returns list of initial states'''
mode = ha.modes['mode']
init_lpi = lputil.from_box([[0.53, 10], [0.2, 0.6], [0.2, 0.6]], mode)
# print(init_lpi.get_full_constraints().toarray(), init_lpi.get_rhs(), init_lpi.get_types())
init_list = [StateSet(init_lpi, mode)]
return init_list
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 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 make_init(ha):
'make the initial states'
# initial set has every variable as [-0.0001, 0.0001]
mode = ha.modes['mode']
dims = mode.a_csr.shape[0]
init_box = dims * [[-0.0001, 0.0001]]
init_lpi = lputil.from_box(init_box, mode)
init_list = [StateSet(init_lpi, mode)]
return init_list
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_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 make_init(ha):
'make the initial states'
p2 = ha.modes['Far']
box = [[-925.0, -875.0], [-425.0, -375.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [1.0, 1.0]]
# move init y up 300
#box[0][0] += 400
#box[0][1] += 400
init_lpi = lputil.from_box(box, p2)
init_list = [StateSet(init_lpi, p2)]
return init_list
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 define_init_states(ha):
'''returns a list of StateSet objects'''
# Variable ordering: [x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, t, affine]
rv = []
mode = ha.modes['negAngleInit']
#X_0 = {center + alpha * generator, alpha in [-1, 1]}
center = [-0.0432, -11, 0, 30, 0, 30, 360, -0.0013, 30, -0.0013, 30, 0, 1]
generator = [0.0056, 4.67, 0, 10, 0, 10, 120, 0.0006, 10, 0.0006, 10, 0, 0]
lpi = lputil.from_zonotope(center, [generator], mode)
rv.append(StateSet(lpi, mode))
return rv
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 make_init(ha, box):
'make the initial states'
mode = ha.modes['move_free']
# px==-0.0165 & py==0.003 & vx==0 & vy==0 & I==0 & affine==1.0
init_lpi = lputil.from_box(box, mode)
#init_lpi = lputil.from_box([(-0.02, -0.02), (-0.005, -0.003), (0, 0), (0, 0), (0, 0), (1.0, 1.0)], mode)
#start = [-0.02, -0.004213714568273684, 0.0, 0.0, 0.0, 1.0]
#tol = 1e-7
#init_lpi = lputil.from_box([(x - tol, x + tol) if i < 2 else (x, x) for i, x in enumerate(start)], mode)
init_list = [StateSet(init_lpi, mode)]
# why does 0.003-0.005 reach an error with i=30 for roots first but not leaves first?
return init_list
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 aggregate_chull(agg_list, op_list, print_func):
'''
perform template-based aggregation on the passed-in list of states
Currently, this can either use box template directions or arnoldi (+box) template directions
'''
min_step = min([state.cur_steps_since_start[0] for state in agg_list])
max_step = max([state.cur_steps_since_start[1] for state in agg_list])
step_interval = [min_step, max_step]
print_func("Convex hull aggregation time step interval: {}".format(step_interval))
postmode = agg_list[0].mode
lpi_list = [state.lpi for state in agg_list]
new_lpi = lputil.aggregate_chull(lpi_list, postmode)
return StateSet(new_lpi, agg_list[0].mode, step_interval, op_list, is_concrete=False)
def make_init(ha):
'make the initial states'
p2 = ha.modes['P2']
box = [(-925.0, -875.0), (-425.0, -375.0), (0.0, 0.0), (0.0, 0.0),
(0.0, 0.0), (1.0, 1.0)]
init_lpi = lputil.from_box(box, p2)
init_list = [StateSet(init_lpi, p2)]
#corners = [[(box[0][0], box[0][0]), (box[1][0], box[1][0]), (0, 0), (0, 0), (0, 0), (1, 1)], \
# [(box[0][1], box[0][1]), (box[1][0], box[1][0]), (0, 0), (0, 0), (0, 0), (1, 1)], \
# [(box[0][1], box[0][1]), (box[1][1], box[1][1]), (0, 0), (0, 0), (0, 0), (1, 1)], \
# [(box[0][0], box[0][0]), (box[1][0], box[1][0]), (0, 0), (0, 0), (0, 0), (1, 1)]]
#init_list = [StateSet(lputil.from_box(c, p2), p2) for c in corners]
return init_list
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_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_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_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()