def run_hylaa(self, predictions):
self.ha = None
self.predictions = None
self.modeList = []
self.initialState = None
self.ha = HybridAutomaton()
self.predictions = predictions
self.graphPredictions()
self.make_automaton()
initialBox = self.make_init(self.predictions[0][0])
core = Core(self.ha, self.settings)
profile.runctx(
'resultprof = self.run_hylaa_profile(initialBox, core)',
globals(),
locals(),
filename=
"/home/nvidia/f1racing/f110_ws/src/ppcm/reachability/scripts/profiler/prof/out_tmp.prof"
)
result = locals()['resultprof']
#result = core.run(initialBox)
reachsets = [
result.plot_data.get_verts_list(mode)[0] for mode in self.modeList
]
return reachsets
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_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 define_ha(limit):
'''make the hybrid automaton and return it'''
ha = HybridAutomaton()
mode = ha.new_mode('mode')
dynamics = loadmat('build.mat')
a_matrix = dynamics['A']
b_matrix = csc_matrix(dynamics['B'])
mode.set_dynamics(csr_matrix(a_matrix))
# 0.8 <= u1 <= 1.0
u_mat = [[1.0], [-1.0]]
u_rhs = [1.0, -0.8]
mode.set_inputs(b_matrix, u_mat, u_rhs)
error = ha.new_mode('error')
y1 = dynamics['C'][0]
mat = csr_matrix(y1, dtype=float)
trans1 = ha.new_transition(mode, error)
rhs = np.array([-limit], dtype=float) # safe
trans1.set_guard(mat, rhs) # y3 >= limit
return ha
def define_ha():
'''make the hybrid automaton'''
ha = HybridAutomaton(discrete=True)
a_matrix = [[1, T_const, -T_const], [0, 1, 0], [0, 0, 1]]
a_matrix_inv = np.linalg.inv(a_matrix)
b_mat = [[0.5 * T_const * T_const, -0.5 * T_const * T_const], [T_const, 0],
[0, T_const]]
# b_mat = [[0.5*T_const*T_const, -0.5*T_const*T_const, 1], [T_const, 0, 1], [0, T_const, 1]]
a_inv_b_mat = -1 * np.matmul(a_matrix_inv, b_mat)
# print(a_inv_b_mat)
b_constraints = [[1, 0], [-1, 0], [0, 1], [0, -1]]
b_rhs = [0.26, 0.46, 0.26, 0.47]
# b_constraints = [[1, 0, 0], [-1, 0, 0], [0, 1, 0], [0, -1, 0], [0, 0, 1], [0, 0, -1]]
# b_rhs = [0.26, 0.46, 0.26, 0.47, 0.005, 0.005]
mode = ha.new_mode('mode')
mode.set_dynamics(a_matrix_inv)
mode.set_inputs(a_inv_b_mat, b_constraints, b_rhs)
# error = ha.new_mode('error')
#
# trans1 = ha.new_transition(mode, error)
# trans1.set_guard([[-0, -1, -0], ], [-0.8, ])
return ha
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 make_automaton():
'make the hybrid automaton'
ha = HybridAutomaton()
# mode one: x' = y + u1, y' = -x + u2, c' = 1, a' = 0
m1 = ha.new_mode('m1')
m1.set_dynamics([[0, 1, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0]])
b_mat = [[1, 0], [0, 1], [0, 0], [0, 0]]
b_constraints = [[1, 0], [-1, 0], [0, 1], [0, -1]]
b_rhs = [0.5, 0.5, 0.5, 0.5]
m1.set_inputs(b_mat, b_constraints, b_rhs)
# mode two: x' = -y, y' = x, a' = 0
m2 = ha.new_mode('m2')
m2.set_dynamics([[0, -1], [1, 0]])
# m1 invariant: c <= pi/2
m1.set_invariant([[0, 0, 1, 0]], [math.pi / 2])
# guard: c >= pi/2
trans = ha.new_transition(m1, m2)
trans.set_guard([[0, 0, -1, 0]], [-math.pi / 2])
# Assign the reset to the transition
# y *= -1, also the reset is what is used to change the number of system variables (m1 has four vars, m2 has two)
reset_csr = [[1, 0, 0, 0], [0, -1, 0, 0]]
# no minkowski sum terms
trans.set_reset(reset_csr)
return ha
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 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 define_ha():
'''make the hybrid automaton'''
ha = HybridAutomaton()
# dynamics: x' = y, y' = -x
a_matrix = np.array([[0, 1], [-1, 0]], dtype=float)
a_csr = csr_matrix(a_matrix, dtype=float)
mode = ha.new_mode('mode')
mode.set_dynamics(a_csr)
return ha
def test_chull_one_step_inputs():
'test convex hull with one-step lpi for a system with inputs (bug where current vars was not set correctly)'
mode = HybridAutomaton().new_mode('mode_name')
step_size = math.pi/4
a_mat = np.array([[0, 1], [-1, 0]], dtype=float)
b_mat = [[1], [0]]
b_constraints = [[1], [-1]]
b_rhs = [0.2, 0.2]
mode.set_dynamics(a_mat)
mode.set_inputs(b_mat, b_constraints, b_rhs)
mode.init_time_elapse(step_size)
box = [[-5, -4], [0.0, 1.0]]
lpi = lputil.from_box(box, mode)
lpi_one_step = lpi.clone()
bm, ie_mat = mode.time_elapse.get_basis_matrix(1)
lputil.set_basis_matrix(lpi_one_step, bm)
lputil.add_input_effects_matrix(lpi_one_step, ie_mat, mode)
lpi_list = [lpi, lpi_one_step]
chull_lpi = lputil.aggregate_chull(lpi_list, mode)
# 2 current vars and 2 total input effect vars, so expected to be 4 from the end
assert chull_lpi.cur_vars_offset == chull_lpi.get_num_cols() - 4, "cur_vars in wrong place"
def test_guard_strengthening():
'simple 2-mode, 2-guard, 2d system with 1st guard A->B is x <= 2, 2nd guard A->B is y <= 2, and inv(B) is y <= 2'
ha = HybridAutomaton()
mode_a = ha.new_mode('A')
mode_a.set_dynamics(np.identity(2))
mode_b = ha.new_mode('B')
mode_b.set_dynamics(np.identity(2))
mode_b.set_invariant([[0, 1]], [2])
trans1 = ha.new_transition(mode_a, mode_b, 'first')
trans1.set_guard([[1, 0]], [2])
trans2 = ha.new_transition(mode_a, mode_b, 'second')
trans2.set_guard([[0, 1]], [2])
ha.do_guard_strengthening()
# trans1 should now have 2 conditions
assert (trans1.guard_csr.toarray() == np.array([[1, 0], [0, 1]], dtype=float)).all()
assert (trans1.guard_rhs == np.array([2, 2], dtype=float)).all()
# trans2 should still have 1 condition since invariant was redundant
assert (trans2.guard_csr.toarray() == np.array([[0, 1]], dtype=float)).all()
def make_automaton():
'make the hybrid automaton'
ha = HybridAutomaton()
# mode one: x' = 2, y' = 1, a' = 0
m1 = ha.new_mode('m1')
m1.set_dynamics([[0, 0, 2], [0, 0, 1], [0, 0, 0]])
# mode two: x' = 1, y' = 1, a' = 0
m2 = ha.new_mode('m2')
m2.set_dynamics([[0, 0, 1], [0, 0, 1], [0, 0, 0]])
# invariant: x <= 9.9
m1.set_invariant([[1, 0, 0]], [9.9])
# guard: x >= 9.9
trans = ha.new_transition(m1, m2, 'transition_name')
trans.set_guard([[-1, 0, 0]], [-9.9])
# Assign the reset to the transition:
#
# def set_reset(self, reset_csr=None, reset_minkowski_csr=None, reset_minkowski_constraints_csr=None,
# reset_minkowski_constraints_rhs=None):
# '''resets are of the form x' = Rx + My, Cy <= rhs, where y are fresh variables
# the reset_minowski variables can be None if no new variables are needed. If unassigned, the identity
# reset is assumed
#
# x' are the new variables
# x are the old variables
# reset_csr is R
# reset_minkowski_csr is M
# reset_minkowski_constraints_csr is C
# reset_minkowski_constraints_rhs is rhs
# '''
# we want the reset to set x' := [0, 1], y' := y - 10
reset_csr = [[0, 0, 0], [0, 1, 0], [0, 0, 1]]
# two new minkowski variables, y0 = [0, 1], y1 = [-10, -10]
minkowski_csr = [[1, 0], [0, 1], [0, 0]]
constraints_csr = [[1, 0], [-1, 0], [0, 1], [0, -1]]
constraints_rhs = [1, 0, -10, 10]
trans.set_reset(reset_csr, minkowski_csr, constraints_csr, constraints_rhs)
return ha
def test_add_curtime_constraints():
'tests add_curtime_constraints'
lpi = lputil.from_box([[-5, -4], [0, 1]],
HybridAutomaton().new_mode('mode_name'))
# new constraint to be added, x <= 3.14, y <= 10
csr_constraint = csr_matrix(np.array([[1, 0], [0, 1]], dtype=float))
rhs = np.array([3.14, 10], dtype=float)
lputil.add_curtime_constraints(lpi, csr_constraint, rhs)
mat = lpi.get_full_constraints()
vec = lpi.get_rhs()
types = lpi.get_types()
expected_mat = np.array([\
[1, 0, -1, 0], \
[0, 1, 0, -1], \
[-1, 0, 0, 0], \
[1, 0, 0, 0], \
[0, -1, 0, 0], \
[0, 1, 0, 0], \
[0, 0, 1, 0], \
[0, 0, 0, 1]], dtype=float)
expected_vec = np.array([0, 0, 5, -4, 0, 1, 3.14, 10], dtype=float)
fx = glpk.GLP_FX
up = glpk.GLP_UP
expected_types = [fx, fx, up, up, up, up, up, up]
assert np.allclose(vec, expected_vec)
assert types == expected_types
assert np.allclose(mat.toarray(), expected_mat)
def test_from_box():
'tests from_box'
lpi = lputil.from_box([[-5, -4], [0, 1]],
HybridAutomaton().new_mode('mode_name'))
assert lpi.basis_mat_pos == (0, 0)
assert lpi.dims == 2
mat = lpi.get_full_constraints()
types = lpi.get_types()
rhs = lpi.get_rhs()
names = lpi.get_names()
expected_mat = np.array([\
[1, 0, -1, 0], \
[0, 1, 0, -1], \
[-1, 0, 0, 0], \
[1, 0, 0, 0], \
[0, -1, 0, 0], \
[0, 1, 0, 0]], dtype=float)
expected_vec = np.array([0, 0, 5, -4, 0, 1], dtype=float)
fx = glpk.GLP_FX
up = glpk.GLP_UP
expected_types = [fx, fx, up, up, up, up]
expected_names = ["m0_i0", "m0_i1", "m0_c0", "m0_c1"]
assert np.allclose(rhs, expected_vec)
assert types == expected_types
assert np.allclose(mat.toarray(), expected_mat)
assert names == expected_names
def define_ha():
'''make the hybrid automaton'''
ha = HybridAutomaton(discrete=False)
a_matrix = [[0, 1], [-1, 0]]
b_mat = [[1], [0]]
b_constraints = [[1], [-1]]
b_rhs = [0.2, 0.2]
mode = ha.new_mode('mode')
mode.set_dynamics(a_matrix)
mode.set_inputs(b_mat, b_constraints, b_rhs)
return ha
def test_add_init_constraint():
'tests add_init_constraint on the harmonic oscillator example'
lpi = lputil.from_box([[-5, -4], [0, 1]],
HybridAutomaton().new_mode('mode_name'))
# update basis matrix
basis_mat = np.array([[0, 1], [-1, 0]], dtype=float)
lputil.set_basis_matrix(lpi, basis_mat)
# minimize y should give 4.0
miny = lpi.minimize([0, 1], columns=[lpi.cur_vars_offset + 1])[0]
assert abs(miny - 4.0) < 1e-6
# add constraint: y >= 4.5
direction = np.array([0, -1], dtype=float)
new_row = lputil.add_init_constraint(lpi, direction, -4.5)
assert new_row == 6, "new constraint should have been added in row index 6"
# minimize y should give 4.5
miny = lpi.minimize([0, 1], columns=[lpi.cur_vars_offset + 1])[0]
assert abs(miny - 4.5) < 1e-6
# check verts()
verts = lpplot.get_verts(lpi)
assert len(verts) == 5
assert [0.0, 5.0] in verts
assert [1.0, 5.0] in verts
assert [0.0, 4.5] in verts
assert [1.0, 4.5] in verts
assert verts[0] == verts[-1]
def test_get_box_center():
'test get_box_center'
lpi = lputil.from_box([[-5, -4], [0, 1]],
HybridAutomaton().new_mode('mode_name'))
pt = lputil.get_box_center(lpi)
assert len(pt) == 2
assert abs(pt[0] - (-4.5)) < 1e-4
assert abs(pt[1] - (0.5)) < 1e-4
basis = np.array([[0, 1], [-1, 0]], dtype=float)
lputil.set_basis_matrix(lpi, basis)
pt = lputil.get_box_center(lpi)
assert len(pt) == 2
assert abs(pt[0] - (0.5)) < 1e-4
assert abs(pt[1] - (4.5)) < 1e-4
# try it rotated 1/4 around the circle
a_mat = np.array([[0, 1], [-1, 0]], dtype=float)
bm = expm(a_mat * math.pi / 4)
lputil.set_basis_matrix(lpi, bm)
expected = np.dot(bm, np.array([[-4.5], [0.5]], dtype=float))
pt = lputil.get_box_center(lpi)
assert len(pt) == 2
assert abs(pt[0] - expected[0][0]) < 1e-4
assert abs(pt[1] - expected[1][0]) < 1e-4
def test_set_basis_matrix():
'tests lputil set_basis_matrix on harmonic oscillator example'
lpi = lputil.from_box([[-5, -4], [0, 1]],
HybridAutomaton().new_mode('mode_name'))
basis = np.array([[0, 1], [-1, 0]], dtype=float)
lputil.set_basis_matrix(lpi, basis)
assert np.allclose(lputil.get_basis_matrix(lpi), basis)
mat, vec = lpi.get_full_constraints(), lpi.get_rhs()
expected_mat = np.array([\
[0, 1, -1, 0], \
[-1, 0, 0, -1], \
[-1, 0, 0, 0], \
[1, 0, 0, 0], \
[0, -1, 0, 0], \
[0, 1, 0, 0]], dtype=float)
expected_vec = np.array([0, 0, 5, -4, 0, 1], dtype=float)
assert np.allclose(vec, expected_vec)
assert np.allclose(mat.toarray(), expected_mat)
def make_automaton():
'make the hybrid automaton'
ha = HybridAutomaton('Hylaa Output (hylaa_check.py)')
# mode one: x' = y + u1, y' = -x + + u1 + u2
# u1 in [-0.5, 0.5], u2 in [-1, 0]
m1 = ha.new_mode('m1')
m1.set_dynamics([[0, 1], [-1, 0]])
b_mat = [[1, 0], [1, 1]]
b_constraints = [[1, 0], [-1, 0], [0, 1], [0, -1]]
b_rhs = [0.5, 0.5, 0, 1]
m1.set_inputs(b_mat, b_constraints, b_rhs)
return ha
def test_box_aggregate3():
'tests box aggregation with 3 boxes'
mode = HybridAutomaton().new_mode('mode_name')
lpi1 = lputil.from_box([[-2, -1], [-0.5, 0.5]], mode)
lpi2 = lpi1.clone()
lpi3 = lpi1.clone()
basis2 = np.array([[0, 1], [-1, 0]], dtype=float)
lputil.set_basis_matrix(lpi2, basis2)
basis3 = np.array([[-1, 0], [0, -1]], dtype=float)
lputil.set_basis_matrix(lpi3, basis3)
plot_vecs = lpplot.make_plot_vecs(256, offset=0.1) # use an offset to prevent LP dir from being aligned with axis
# bounds for lpi1 should be [[-2, -1], [-0.5, 0.5]]
verts = lpplot.get_verts(lpi1, plot_vecs=plot_vecs)
assert_verts_is_box(verts, [[-2, -1], [-0.5, 0.5]])
# bounds for lpi2 should be [[-0.5, 0.5], [1, 2]]
verts = lpplot.get_verts(lpi2, plot_vecs=plot_vecs)
assert_verts_is_box(verts, [[-0.5, 0.5], [1, 2]])
# bounds for lpi3 should be [[2, 1], [-0.5, 0.5]]
verts = lpplot.get_verts(lpi3, plot_vecs=plot_vecs)
assert_verts_is_box(verts, [[2, 1], [-0.5, 0.5]])
# box aggregation, bounds should be [[-2, 2], [-0.5, 2]]
agg_dirs = np.identity(2)
lpi = lputil.aggregate([lpi1, lpi2, lpi3], agg_dirs, mode)
verts = lpplot.get_verts(lpi, plot_vecs=plot_vecs)
assert_verts_is_box(verts, [[-2, 2], [-0.5, 2]])
def test_box_aggregate2():
'tests box aggregation'
mode = HybridAutomaton().new_mode('mode_name')
lpi1 = lputil.from_box([[0, 1], [0, 1]], mode)
lpi2 = lputil.from_box([[1, 2], [1, 2]], mode)
agg_dirs = np.identity(2)
# box aggregation
lpi = lputil.aggregate([lpi1, lpi2], agg_dirs, mode)
verts = lpplot.get_verts(lpi)
assert_verts_is_box(verts, [[0, 2], [0, 2]])
# test setting basis matrix after aggregation
lputil.set_basis_matrix(lpi, np.identity(2))
verts = lpplot.get_verts(lpi)
assert_verts_is_box(verts, [[0, 2], [0, 2]])
lputil.set_basis_matrix(lpi, -1 * np.identity(2))
verts = lpplot.get_verts(lpi)
assert_verts_is_box(verts, [[-2, 0], [-2, 0]])
def test_rotated_aggregate():
'tests rotated aggregation'
mode = HybridAutomaton().new_mode('mode_name')
lpi1 = lputil.from_box([[0, 1], [0, 1]], mode)
lpi2 = lputil.from_box([[1, 2], [1, 2]], mode)
sq2 = math.sqrt(2) / 2.0
agg_dirs = np.array([[sq2, sq2], [sq2, -sq2]], dtype=float)
lpi = lputil.aggregate([lpi1, lpi2], agg_dirs, mode)
assert lputil.is_point_in_lpi([0, 0], lpi)
assert lputil.is_point_in_lpi([2, 2], lpi)
assert lputil.is_point_in_lpi([1, 2], lpi)
assert lputil.is_point_in_lpi([2, 1], lpi)
assert lputil.is_point_in_lpi([0, 1], lpi)
assert lputil.is_point_in_lpi([1, 0], lpi)
verts = lpplot.get_verts(lpi)
assert len(verts) == 5
for p in [(0.5, -0.5), (-0.5, 0.5), (2.5, 1.5), (1.5, 2.5)]:
assert pair_almost_in(p, verts)
assert verts[0] == verts[-1]
def test_aggregate_self():
'''
test aggregation on an identical set.
'''
mode = HybridAutomaton().new_mode('mode_name')
lpi1 = lputil.from_box([[-2, -1], [-10, 20], [100, 200]], mode)
lpi2 = lputil.from_box([[-2, -1], [-10, 20], [100, 200]], mode)
agg_dirs = np.identity(3)
# box aggregation
lpi = lputil.aggregate([lpi1, lpi2], agg_dirs, mode)
assert lpi.is_feasible()
verts = lpplot.get_verts(lpi, xdim=0, ydim=1)
assert_verts_is_box(verts, [[-2, -1], [-10, 20]])
verts = lpplot.get_verts(lpi, xdim=0, ydim=2)
assert_verts_is_box(verts, [[-2, -1], [100, 200]])
# make sure no extra variables in lp
names = lpi.get_names()
expected_names = ["m0_i0", "m0_i1", "m0_i2", "m0_c0", "m0_c1", "m0_c2"]
assert names == expected_names
assert lpi.get_num_rows() == 3 + 3*2
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 define_ha(unsafe_box):
'''make the hybrid automaton'''
ha = HybridAutomaton()
# dynamics: x' = y, y' = -x, t' == a
a_mat = [[0, 1, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0]]
one = ha.new_mode('one')
one.set_dynamics(a_mat)
one.set_invariant([[0, 0, 1, 0]], [math.pi - 1e-6]) # t <= pi
two = ha.new_mode('two')
two.set_dynamics([[0, 0, 0, 0], [0, 0, 0, -1], [0, 0, 0, 1], [0, 0, 0, 0]])
two.set_invariant([[0, -1, 0, 0]], [3]) # y >= -3
t = ha.new_transition(one, two)
t.set_guard_true()
error = ha.new_mode('error')
t = ha.new_transition(two, error)
unsafe_rhs = [
-unsafe_box[0][0], unsafe_box[0][1], -unsafe_box[1][0],
unsafe_box[1][1]
]
t.set_guard([[-1, 0, 0, 0], [1, 0, 0, 0], [0, -1, 0, 0], [0, 1, 0, 0]],
unsafe_rhs)
return ha
def test_verts():
'tests verts'
lpi = lputil.from_box([[-5, -4], [0, 1]],
HybridAutomaton().new_mode('mode_name'))
plot_vecs = lpplot.make_plot_vecs(4, offset=(math.pi / 4.0))
verts = lpplot.get_verts(lpi, plot_vecs=plot_vecs)
assert_verts_is_box(verts, [(-5, -4), (0, 1)])
def run_hylaa(self, predictions):
self.ha = None
self.predictions = None
self.modeList = []
self.initialState = None
self.ha = HybridAutomaton()
self.predictions = predictions
self.graphPredictions()
self.make_automaton()
initialBox = self.make_init(self.predictions[0][0])
core = Core(self.ha, self.settings)
result = core.run(initialBox)
reachsets = [
result.plot_data.get_verts_list(mode)[0] for mode in self.modeList
]
return reachsets
def define_ha():
'''make the hybrid automaton'''
ha = HybridAutomaton(discrete=True)
# dynamics: x' = y, y' = -x
a_matrix = np.array([[0.96065997, 0.1947354], [-0.1947354, 0.96065997]],
dtype=float)
a_csr = csr_matrix(a_matrix, dtype=float)
b_mat = [[1, 0], [0, 1]]
b_constraints = [[1, 0], [-1, 0], [0, 1], [0, -1]]
b_rhs = [0.39340481, -0.39340481, -0.03933961, 0.03933961]
mode = ha.new_mode('mode')
mode.set_dynamics(a_csr)
mode.set_inputs(b_mat, b_constraints, b_rhs, allow_constants=True)
return ha
def make_automaton(unsafe_box):
'make the hybrid automaton'
ha = HybridAutomaton('Deaggregation Example')
# x' = 2
m1 = ha.new_mode('mode0_right')
m1.set_dynamics([[0, 0, 2], [0, 0, 0], [0, 0, 0]])
m1.set_invariant([[1, 0, 0]], [3.5]) # x <= 3.5
# y' == 2
m2 = ha.new_mode('mode1_up')
m2.set_dynamics([[0, 0, 0], [0, 0, 2], [0, 0, 0]])
m2.set_invariant([0., 1., 0], [3.5]) # y <= 3.5
# x' == 2
m3 = ha.new_mode('mode2_right')
m3.set_dynamics([[0, 0, 2], [0, 0, -0], [0, 0, 0]])
m3.set_invariant([1., 0, 0], [7]) # x <= 7
t = ha.new_transition(m1, m2)
t.set_guard_true()
t = ha.new_transition(m2, m3)
t.set_guard_true()
error = ha.new_mode('error')
t = ha.new_transition(m3, error)
unsafe_rhs = [
-unsafe_box[0][0], unsafe_box[0][1], -unsafe_box[1][0],
unsafe_box[1][1]
]
# x >= 1.1 x <= 1.9, y >= 2.7, y <= 4.3
t.set_guard([[-1, 0, 0], [1, 0, 0], [0, -1, 0], [0, 1, 0]], unsafe_rhs)
t = ha.new_transition(m2, error)
# x >= 1.1 x <= 1.9, y >= 2.7, y <= 4.3
t.set_guard([[-1, 0, 0], [1, 0, 0], [0, -1, 0], [0, 1, 0]], unsafe_rhs)
return ha