def create_lpi(self, ce_object):
longest_ce_lpi = LpInstance(self.num_dims, self.num_dims)
longest_ce_lpi.update_basis_matrix(self.init_star.basis_matrix)
prev_node_state = ce_object.patch[ce_object.start_index].state
basis_centers = []
while True:
if isinstance(prev_node_state.parent, InitParent) or isinstance(
prev_node_state.parent.star.parent, InitParent):
break
elif isinstance(prev_node_state.parent.star.parent,
DiscretePostParent):
basis_centers.append(
prev_node_state.parent.star.parent.prestar_basis_center)
prev_node_state = prev_node_state.parent.star.parent.prestar
for idx in range(ce_object.start_index, ce_object.end_index + 1, 1):
node = ce_object.patch[idx]
if node.state.mode.name != prev_node_state.mode.name:
basis_centers.append(
node.state.parent.star.parent.prestar_basis_center)
prev_node_state = node.state
usafe_basis_preds = self.compute_usafe_set_pred_in_star_basis(
node.state)
for pred in usafe_basis_preds:
for basis_center in basis_centers[::-1]:
pred = self.convert_usafe_basis_pred_in_basis_center(
pred, basis_center)
longest_ce_lpi.add_basis_constraint(pred.vector, pred.value)
for pred in self.init_star.constraint_list:
longest_ce_lpi.add_basis_constraint(pred.vector, pred.value)
return longest_ce_lpi
def test_underconstrained(self):
'test an underconstrained case (fails for cvxopt)'
a_ub = [[1.0, 0.0], [-1.0, 0.0]]
b_ub = [1.0, 1.0]
c = [1.0, 0.0]
num_vars = 2
lp = LpInstance(num_vars, num_vars)
orthonormal_basis = [[
1.0 if d == index else 0.0 for d in xrange(num_vars)
] for index in xrange(num_vars)]
lp.update_basis_matrix(np.array(orthonormal_basis, dtype=float))
# add each constraint
for row in xrange(len(b_ub)):
vec = np.matrix(a_ub[row], dtype=float)
val = b_ub[row]
lp.add_basis_constraint(vec, val)
res_glpk = np.zeros(num_vars)
lp.minimize(np.array(c, dtype=float), res_glpk)
self.assertAlmostEqual(res_glpk[0], -1)
def compute_ce_vector(self,
simulation,
usafe_set_constraint_list,
direction=None,
sim_start_time=0,
current_mode_idx=0):
usafe_points = []
ce_vector = []
for time in self.error_time_steps[current_mode_idx]:
point = simulation[int(time) - sim_start_time]
usafe_lpi = LpInstance(self.num_dims, self.num_dims)
identity_matrix = np.identity(self.num_dims)
usafe_lpi.update_basis_matrix(np.identity(self.num_dims))
for dim in range(identity_matrix.ndim):
lc = LinearConstraint(identity_matrix[dim], point[dim])
usafe_lpi.add_basis_constraint(lc.vector, lc.value)
lc = LinearConstraint(-1 * identity_matrix[dim], -point[dim])
usafe_lpi.add_basis_constraint(lc.vector, lc.value)
for constraints in usafe_set_constraint_list:
usafe_lpi.add_basis_constraint(constraints.vector,
constraints.value)
direction = np.zeros(self.num_dims)
usafe_point = np.zeros(self.num_dims)
is_feasible = usafe_lpi.minimize(direction,
usafe_point,
error_if_infeasible=False)
usafe_points.append(usafe_point)
if is_feasible:
ce_vector.append(1)
else:
ce_vector.append(0)
return ce_vector
def test_ha(self):
'test based on harmonic oscillator dynamics'
lp = LpInstance(2, 2)
basis = np.array([[0, -1], [1, 0]], dtype=float)
lp.update_basis_matrix(basis)
# x == 1
lp.add_basis_constraint(np.array([1, 0], dtype=float), 1.0)
lp.add_basis_constraint(np.array([-1, 0], dtype=float), -1.0)
# y == 0
lp.add_basis_constraint(np.array([0, 1], dtype=float), 0)
lp.add_basis_constraint(np.array([0, -1], dtype=float), -0)
res = -np.ones(4)
lp.minimize(np.array([0, 0], dtype=float), res)
# result should be [0, -1] (standard basis) and [1, 0] (star basis)
self.assertAlmostEqual(res[0], 0.0)
self.assertAlmostEqual(res[1], -1.0)
# star constraints
self.assertAlmostEqual(res[2], 1.0)
self.assertAlmostEqual(res[3], 0.0)
def compute_longest_sequence(self,
ce_vector,
init_star,
direction,
current_mode_idx=0):
usafe_lpi = LpInstance(init_star.num_dims, init_star.num_dims)
length = 0
# First value is the length of the subsequence
# Second and third values are the indices of the subsequence in the ce_vector
time_step_indices = [0, 0, 0]
start_index = 0
end_index = 0
index = [0, 0]
max_len = 0
current_index = 0
while (current_index < len(ce_vector)):
if ce_vector[current_index] == 1:
if length == 0:
usafe_lpi = LpInstance(init_star.num_dims,
init_star.num_dims)
usafe_lpi.update_basis_matrix(init_star.basis_matrix)
for lc in init_star.constraint_list:
usafe_lpi.add_basis_constraint(lc.vector, lc.value)
start_index = current_index
usafe_basis_predicates = self.usafe_basis_predicates[
current_mode_idx][current_index]
result = np.zeros(init_star.num_dims)
for usafe_basis_predicate in usafe_basis_predicates:
usafe_lpi.add_basis_constraint(
usafe_basis_predicate.vector,
usafe_basis_predicate.value)
is_feasible = usafe_lpi.minimize(direction,
result,
error_if_infeasible=False)
if is_feasible:
length = length + 1
end_index = current_index
else:
current_index = start_index + 1
length = 0
if max_len < length:
max_len = length
index[0] = start_index
index[1] = end_index
else:
length = 0
current_index = current_index + 1
time_step_indices[1] = self.error_time_steps[current_mode_idx][
index[0]]
time_step_indices[2] = self.error_time_steps[current_mode_idx][
index[1]]
time_step_indices[0] = time_step_indices[2] - time_step_indices[1] + 1
return time_step_indices
def make_no_input_lpi(self, basis_matrix=None):
'''make the lpi object for the input-free star, using the current star's basis matrix'''
if basis_matrix is None:
basis_matrix = np.zeros((self.star.num_dims, self.star.num_dims))
rv = LpInstance(self.star.num_dims, self.star.num_dims)
rv.update_basis_matrix(basis_matrix)
for lc in self.star.constraint_list:
rv.add_basis_constraint(lc.vector, lc.value)
return rv
def compare_opt(self, a_ub, b_ub, c):
'compare cvx opt versus our glpk interface'
# make sure we're using floats not ints
a_ub = [[float(x) for x in row] for row in a_ub]
b_ub = [float(x) for x in b_ub]
c = [float(x) for x in c]
num_vars = len(a_ub[0])
# solve it with cvxopt
options = {'show_progress': False}
sol = cvxopt.solvers.lp(cvxopt.matrix(c),
cvxopt.matrix(a_ub).T,
cvxopt.matrix(b_ub),
options=options)
#if sol['status'] == 'primal infeasible':
# res_cvxopt = None
if sol['status'] != 'optimal':
raise RuntimeError("cvxopt LP failed: {}".format(sol['status']))
res_cvxopt = [float(n) for n in sol['x']]
#print "cvxopt value = {}, result = {}".format(np.dot(res_cvxopt, c), repr(res_cvxopt))
# solve it with the glpk <-> hylaa interface
lp = LpInstance(num_vars, num_vars)
orthonormal_basis = [[
1.0 if d == index else 0.0 for d in xrange(num_vars)
] for index in xrange(num_vars)]
lp.update_basis_matrix(np.array(orthonormal_basis, dtype=float))
# add each constraint
for row in xrange(len(b_ub)):
vec = np.matrix(a_ub[row], dtype=float)
val = b_ub[row]
lp.add_basis_constraint(vec, val)
res_glpk = np.zeros(num_vars)
lp.minimize(np.array(c, dtype=float), res_glpk)
#print "glpk interface value = {}, result = {}".format(np.dot(res_glpk, c), repr(res_glpk))
self.assertEqual(num_vars, len(res_cvxopt))
self.assertAlmostEqual(np.dot(res_glpk, c),
np.dot(res_cvxopt, c),
places=5)
def test_damping(self):
'test based on damping dynamics'
lp = LpInstance(1, 1)
basis = np.array([[0.5]], dtype=float)
lp.update_basis_matrix(basis)
lp.add_basis_constraint(np.array([1.0], dtype=float), 1.0)
lp.add_basis_constraint(np.array([-1.0], dtype=float), -1.0)
res = np.zeros(2)
lp.minimize(np.array([0], dtype=float), res)
self.assertLess(res[0], 1.0)
def make_input_lpi(self, basis_matrix=None):
'make the lpi object for the input star'
rv = None
if self.star.mode.num_inputs > 0:
rv = LpInstance(self.star.num_dims, self.star.mode.num_inputs)
if basis_matrix is None:
basis_matrix = np.zeros(
(self.star.mode.num_inputs, self.star.num_dims))
rv.update_basis_matrix(basis_matrix)
for i in range(self.star.mode.u_constraints_b.shape[0]):
rv.add_basis_constraint(self.star.mode.u_constraints_a[i, :],
self.star.mode.u_constraints_b[i])
return rv
def get_lpi(self):
'get (maybe create) the LpInstance object for this star + inputs, and return it'
rv = self._star_lpi
if rv is None:
rv = LpInstance(self.num_dims, self.num_dims)
rv.update_basis_matrix(self.basis_matrix)
for lc in self.constraint_list:
rv.add_basis_constraint(lc.vector, lc.value)
# add the influence of the inputs
if self.input_stars is not None:
for input_star in self.input_stars:
rv.add_input_star(input_star.a_matrix_t, input_star.b_vector, input_star.input_basis_matrix)
self._star_lpi = rv
return rv
def compute_sequence_in_a_mode(self, error_star_list, direction, compute_intersection):
usafe_basis_preds_list = self.compute_usafe_basis_pred_in_star_basis_in_star_list(error_star_list, compute_intersection)
valid_ids_for_all_indices = []
feasible_points = []
for idx_i in range(len(error_star_list)):
valid_ids_for_current_index = []
## Create an LP instance
usafe_lpi = LpInstance(self.num_dims, self.num_dims)
usafe_lpi.update_basis_matrix(error_star_list[0].parent.star.basis_matrix)
all_preds = []
for pred in usafe_basis_preds_list[idx_i]:
all_preds.append(pred.clone())
for pred in error_star_list[0].parent.star.constraint_list:
all_preds.append(pred.clone())
for pred in all_preds:
usafe_lpi.add_basis_constraint(pred.vector, pred.value)
result = np.zeros(self.num_dims)
usafe_lpi.minimize(direction, result, error_if_infeasible=False)
feasible_point = np.dot(error_star_list[0].parent.star.basis_matrix, result)
valid_ids_for_current_index.append(idx_i)
for idx_j in range(idx_i-1, -1, -1):
for pred in usafe_basis_preds_list[idx_j]:
usafe_lpi.add_basis_constraint(pred.vector, pred.value)
result = np.zeros(self.num_dims)
is_feasible = usafe_lpi.minimize(direction, result, error_if_infeasible=False)
if not is_feasible:
break
valid_ids_for_current_index.append(idx_j)
feasible_point = np.dot(self.init_star.basis_matrix, result)
valid_ids_for_all_indices.append(valid_ids_for_current_index)
feasible_points.append(feasible_point)
return valid_ids_for_all_indices, feasible_points
def check_if_feasible(self, usafe_basis_preds, usafe_basis_preds_list_in_first_mode, start_index, end_index, direction):
## Create an LP instance
usafe_lpi = LpInstance(self.num_dims, self.num_dims)
usafe_lpi.update_basis_matrix(self.init_star.basis_matrix)
for pred in usafe_basis_preds:
usafe_lpi.add_basis_constraint(pred.vector, pred.value)
for idx in range(len(usafe_basis_preds_list_in_first_mode)):
if idx >= start_index and idx <= end_index:
for pred in usafe_basis_preds_list_in_first_mode[idx]:
usafe_lpi.add_basis_constraint(pred.vector, pred.value)
for pred in self.init_star.constraint_list:
usafe_lpi.add_basis_constraint(pred.vector, pred.value)
result = np.zeros(self.num_dims)
is_feasible = usafe_lpi.minimize(direction, result, error_if_infeasible=False)
return is_feasible
def make_combined_lpi(self, automaton_transition=None, skip_inputs=False):
'create one lpi per guard, which will have both the star and input effects, as well as the guard condition'
lpi = LpInstance(self.star.num_dims, self.star.num_dims)
lpi.update_basis_matrix(self.star.basis_matrix)
for lc in self.star.constraint_list:
lpi.add_basis_constraint(lc.vector, lc.value)
# add standard basis guard constraints
if automaton_transition is not None:
for lc in automaton_transition.condition_list:
lpi.add_standard_constraint(lc.vector, lc.value)
# add any input star constraints
mode = self.star.mode
if not skip_inputs and self.star.input_stars is not None:
for input_star in self.star.input_stars:
lpi.add_input_star(mode.u_constraints_a_t,
mode.u_constraints_b,
input_star.input_basis_matrix)
return lpi
def check_path_feasibility(self, node, direction, basis_centers,
constraints_list):
current_constraints_list = []
current_basis_centers = []
for constraint in constraints_list:
current_constraints_list.append(constraint)
for basis_center in basis_centers:
current_basis_centers.append(basis_center)
if node.error is False:
print("Non-error node at '{}' in location '{}'".format(
node.state.total_steps, node.state.mode.name))
if node.cont_transition is not None:
print(
" -- has a continuous transition at '{}' to location '{}'".
format(node.cont_transition.succ_node.state.total_steps,
node.cont_transition.succ_node.state.mode.name))
self.check_path_feasibility(node.cont_transition.succ_node,
direction, current_basis_centers,
current_constraints_list)
if len(node.disc_transitions) > 0 and node.disc_transitions[
0].succ_node.cont_transition is not None:
print(" -- has a discrete transition at '{}' to location '{}'".
format(
node.disc_transitions[0].succ_node.state.total_steps,
node.disc_transitions[0].succ_node.state.mode.name))
basis_centers.append(node.state.center)
self.check_path_feasibility(node.disc_transitions[0].succ_node,
direction, current_basis_centers,
current_constraints_list)
if node.cont_transition is None and len(
node.disc_transitions) == 0:
print(" -- has no transition. Returning to previous node")
else:
print("Error node at '{}' in location '{}'".format(
node.state.total_steps, node.state.mode.name))
# print "basis centers '{}'".format(basis_centers)
usafe_lpi = LpInstance(self.num_dims, self.num_dims)
usafe_lpi.update_basis_matrix(self.init_star.basis_matrix)
for constraint in current_constraints_list:
usafe_lpi.add_basis_constraint(constraint.vector,
constraint.value)
usafe_basis_preds = self.compute_usafe_set_pred_in_star_basis(
node.state)
for pred in usafe_basis_preds:
for basis_center in current_basis_centers[::-1]:
pred = self.convert_usafe_basis_pred_in_basis_center(
pred, basis_center)
usafe_lpi.add_basis_constraint(pred.vector, pred.value)
current_constraints_list.append(pred)
if isinstance(node.state.parent.star.parent, DiscretePostParent):
for pred in node.state.parent.star.constraint_list:
for basis_center in current_basis_centers[::-1]:
pred = self.convert_usafe_basis_pred_in_basis_center(
pred, basis_center)
usafe_lpi.add_basis_constraint(pred.vector, pred.value)
current_constraints_list.append(pred)
result = np.zeros(self.num_dims)
is_feasible = usafe_lpi.minimize(direction,
result,
error_if_infeasible=False)
if is_feasible:
feasible_point = np.dot(self.init_star.basis_matrix, result)
print("feasible point is '{}' at the time step '{}'".format(
feasible_point, node.state.total_steps))
if node.cont_transition is None and len(
node.disc_transitions) is 0:
print("-- has no transition. Returning to previous node")
if node.cont_transition is not None:
print(
" -- has a continuous transition at '{}' to location '{}'".
format(node.cont_transition.succ_node.state.total_steps,
node.cont_transition.succ_node.state.mode.name))
self.check_path_feasibility(node.cont_transition.succ_node,
direction, current_basis_centers,
current_constraints_list)
if len(node.disc_transitions) > 0 and node.disc_transitions[
0].succ_node.cont_transition is not None:
print(
" -- '{}' in location '{}' has a discrete transition at '{}' to location '{}'"
.format(
node.state.total_steps, node.state.mode.name,
node.disc_transitions[0].succ_node.state.total_steps,
node.disc_transitions[0].succ_node.state.mode.name))
current_basis_centers.append(
node.disc_transitions[0].succ_node.state.parent.
prestar_basis_center)
self.check_path_feasibility(
node.disc_transitions[0].succ_node.cont_transition.
succ_node, direction, current_basis_centers,
current_constraints_list)
def compute_robust_ce_old(self):
Timers.tic('Robust counter-example generation time')
ce_object = self.compute_longest_ce()
robust_points_in_initial_star = []
patch = ce_object.patch[1:len(ce_object.patch) - 1]
for node in patch:
usafe_lpi = LpInstance(self.num_dims, self.num_dims)
usafe_lpi.update_basis_matrix(node.state.basis_matrix)
error_std_preds = self.convert_star_pred_in_standard_pred(
node.state)
for pred in error_std_preds:
usafe_lpi.add_standard_constraint(pred.vector, pred.value)
for pred in self.usafe_set_constraint_list:
usafe_lpi.add_standard_constraint(pred.vector, pred.value)
directions = np.identity(self.num_dims, dtype=float)
avg_points = []
for index in range(self.num_dims):
direction = directions[index]
result = np.ones(self.num_dims)
is_feasible = usafe_lpi.minimize(direction,
result,
error_if_infeasible=False)
if is_feasible:
basis_matrix = np.identity(self.num_dims, dtype=float)
point1 = np.dot(basis_matrix, result)
result = np.ones(self.num_dims)
is_feasible = usafe_lpi.minimize(-1 * direction,
result,
error_if_infeasible=False)
if is_feasible:
basis_matrix = np.identity(self.num_dims, dtype=float)
point2 = np.dot(basis_matrix, result)
avg_point = (point1 + point2) / 2
avg_points.append(avg_point)
robust_point_in_star = np.zeros(self.num_dims, dtype=float)
for point in avg_points:
robust_point_in_star += point
robust_point_in_star = robust_point_in_star / len(avg_points)
# print "robust point in star {}".format(robust_point_in_star)
basis_centers = []
prev_node_state = node.state
while True:
if isinstance(
prev_node_state.parent, InitParent) or isinstance(
prev_node_state.parent.star.parent, InitParent):
break
elif isinstance(prev_node_state.parent.star.parent,
DiscretePostParent):
basis_centers.append(prev_node_state.parent.star.parent.
prestar_basis_center)
prev_node_state = prev_node_state.parent.star.parent.prestar
error_star_state = node.state.point_to_star_basis(
robust_point_in_star)
for basis_center in basis_centers[::-1]:
error_star_state = error_star_state - basis_center
robust_points_in_initial_star.append(
np.dot(self.init_star.basis_matrix.T, error_star_state))
robust_point = 0.0
for point in robust_points_in_initial_star:
robust_point += point
robust_point = robust_point / len(robust_points_in_initial_star)
print("Robust point: '{}'".format(robust_point))
Timers.toc('Robust counter-example generation time')
return robust_point
def compute_deepest_ce(self, direction):
start_node = self.reach_tree.nodes[0]
node_queue = [start_node]
depth = None
deepest_node = None
deepest_point = None
Timers.tic("Deepest counter-example generation time")
while len(node_queue) is not 0:
node = node_queue[0]
node_queue = node_queue[1:]
if node.error is True:
usafe_lpi = LpInstance(self.num_dims, self.num_dims)
# usafe_lpi.update_basis_matrix(np.identity(self.num_dims))
usafe_lpi.update_basis_matrix(node.state.basis_matrix)
error_std_preds = self.convert_star_pred_in_standard_pred(
node.state)
for pred in error_std_preds:
usafe_lpi.add_standard_constraint(pred.vector, pred.value)
for pred in self.usafe_set_constraint_list:
usafe_lpi.add_standard_constraint(pred.vector, pred.value)
# usafe_basis_preds = self.compute_usafe_set_pred_in_star_basis(node.state)
# for pred in node.state.constraint_list:
# usafe_lpi.add_basis_constraint(pred.vector, pred.value)
# for pred in usafe_basis_preds:
# usafe_lpi.add_basis_constraint(pred.vector, pred.value)
result = np.ones(self.num_dims)
is_feasible = usafe_lpi.minimize(-1 * direction,
result,
error_if_infeasible=False)
if is_feasible:
# basis_matrix = node.state.basis_matrix
basis_matrix = np.identity(self.num_dims, dtype=float)
point = np.dot(basis_matrix, result)
current_depth = np.dot(direction, point)
# print("Current depth {}".format(current_depth))
# print ("depth for the point {} at time {} in loc {} is : {}".format(point, node.state.total_steps,
# node.state.mode.name, current_depth))
if depth is None or current_depth >= depth:
depth = current_depth
deepest_node = node
deepest_point = point
if node.cont_transition is not None:
node_queue.append(node.cont_transition.succ_node)
if len(node.disc_transitions) > 0 and node.disc_transitions[
0].succ_node.cont_transition is not None:
node_queue.append(node.disc_transitions[0].succ_node.
cont_transition.succ_node)
print("deepest point is '{}' in location '{}' with depth '{}'".format(
deepest_point, deepest_node.state.mode.name,
np.dot(abs(direction), deepest_point)))
basis_centers = []
# basis_matrices = []
prev_node_state = deepest_node.state
while True:
if isinstance(prev_node_state.parent, InitParent) or isinstance(
prev_node_state.parent.star.parent, InitParent):
break
elif isinstance(prev_node_state.parent.star.parent,
DiscretePostParent):
basis_centers.append(
prev_node_state.parent.star.parent.prestar_basis_center)
# basis_matrices.append(prev_node_state.parent.star.parent.prestar.basis_matrix)
prev_node_state = prev_node_state.parent.star.parent.prestar
print("Basis centers: {}".format(basis_centers))
# usafe_lpi = LpInstance(self.num_dims, self.num_dims)
# usafe_lpi.update_basis_matrix(self.init_star.basis_matrix)
# error_star_state = self.convert_std_state_in_star_state(deepest_point, deepest_node.state)
error_star_state = deepest_node.state.point_to_star_basis(
deepest_point)
# for index in range(len(basis_centers)-1, -1, -1):
# print "Index is {}".format(index)
# basis_center = basis_centers[index]
# basis_matrix = basis_matrices[index]
# basis_center_coeffs = np.dot(inv(basis_matrix.T),basis_center)
# error_star_state = error_star_state - basis_center_coeffs
for basis_center in basis_centers[::-1]:
error_star_state = error_star_state - basis_center
deepest_ce = np.dot(self.init_star.basis_matrix.T, error_star_state)
ce_depth = float(np.dot(abs(direction), deepest_point))
ce_object = CeObject(ce=deepest_ce, ce_depth=ce_depth)
print("The deepest ce is '{}' with depth '{}'".format(
deepest_ce, ce_depth))
Timers.toc("Deepest counter-example generation time")
return ce_object
def compute_longest_ce_in_a_path(self, path):
# longest_ce_lpi = None
direction = np.ones(self.num_dims)
prev_time_step = path[0].state.total_steps - 1
continuous_patches = []
current_patch = []
for node in path:
if node.state.total_steps == prev_time_step + 1:
current_patch.append(node)
# print(node.state.mode.name, node.state.total_steps)
else:
continuous_patches.append(current_patch)
current_patch = [node]
prev_time_step = node.state.total_steps
# print('Loc {} time step {}\n'.format(node.state.mode.name, node.state.total_steps))
if len(current_patch) is not 0:
continuous_patches.append(current_patch)
# ce_length = 0
# ce = None
ce_object = None
for patch in continuous_patches:
# current_ce_length = 0
# ce = None
for idx_i in range(len(patch)):
usafe_lpi = LpInstance(self.num_dims, self.num_dims)
usafe_lpi.update_basis_matrix(self.init_star.basis_matrix)
prev_node_state = patch[idx_i].state
basis_centers = []
current_ce_length = 0
while True:
if isinstance(prev_node_state.parent,
InitParent) or isinstance(
prev_node_state.parent.star.parent,
InitParent):
break
elif isinstance(prev_node_state.parent.star.parent,
DiscretePostParent):
basis_centers.append(prev_node_state.parent.star.
parent.prestar_basis_center)
prev_node_state = prev_node_state.parent.star.parent.prestar
# TO CHECK Reverse the basis_centers list here?
prev_node_state = patch[idx_i].state
for idx_j in range(idx_i, len(patch), 1):
node = patch[idx_j]
if node.state.mode.name != prev_node_state.mode.name:
basis_centers.append(
node.state.parent.star.parent.prestar_basis_center)
prev_node_state = node.state
usafe_basis_preds = self.compute_usafe_set_pred_in_star_basis(
node.state)
for pred in usafe_basis_preds:
for basis_center in basis_centers[::-1]:
pred = self.convert_usafe_basis_pred_in_basis_center(
pred, basis_center)
usafe_lpi.add_basis_constraint(pred.vector, pred.value)
for pred in self.init_star.constraint_list:
usafe_lpi.add_basis_constraint(pred.vector, pred.value)
# TO CHECK is this a redundant step?
# if isinstance(node.state.parent.star.parent, DiscretePostParent):
# for pred in node.state.parent.star.constraint_list:
# for basis_center in basis_centers[::-1]:
# pred = self.convert_usafe_basis_pred_in_basis_center(pred, basis_center)
# usafe_lpi.add_basis_constraint(pred.vector, pred.value)
result = np.zeros(self.num_dims)
is_feasible = usafe_lpi.minimize(direction,
result,
error_if_infeasible=False)
if is_feasible:
feasible_point = np.dot(self.init_star.basis_matrix,
result)
current_ce_length = current_ce_length + 1
current_ce = feasible_point
# print "Counterexample is '{}' of length '{}' for node '{}' at time '{}'".format(current_ce,
# current_ce_length, node.state.mode.name, node.state.total_steps)
else:
# print "Node '{}' at time '{}' is not feasible with existing states".format(
# node.state.mode.name, node.state.total_steps)
break
if ce_object is None or current_ce_length >= ce_object.ce_length:
ce_object = CeObject(current_ce, current_ce_length,
usafe_lpi, 0, patch,
patch[idx_i].state.total_steps,
patch[idx_j].state.total_steps)
# longest_ce_lpi = usafe_lpi
# print "This counterexample starts from index '{}' in location '{}'".format(
# patch[idx_i].state.total_steps, patch[idx_i].state.mode.name)
# print "This counterexample ends at index '{}' in location '{}'".format(
# node.state.total_steps, node.state.mode.name)
return ce_object
class GuardOptData(Freezable):
'Guard optimization data'
def __init__(self, star, mode, transition_index):
assert isinstance(mode, LinearAutomatonMode)
self.settings = star.settings
self.mode = mode
self.inputs = star.inputs
self.star = star
self.transition = mode.transitions[transition_index]
self.num_output_vars = self.transition.guard_matrix_csr.shape[1]
self.key_dir_offset = 0
if self.settings.plot.plot_mode != PlotSettings.PLOT_NONE:
if self.settings.plot.xdim_dir is not None:
self.key_dir_offset += 1
if self.settings.plot.ydim_dir is not None:
self.key_dir_offset += 1
self.lpi = LpInstance(self.num_output_vars, star.num_init_vars,
self.inputs)
self.lpi.set_init_constraints(star.init_mat, star.init_rhs)
self.lpi.set_output_constraints(self.transition.guard_matrix_csr,
self.transition.guard_rhs)
if star.inputs > 0:
self.lpi.set_input_constraints_csc(
csc_matrix(star.mode.u_constraints_csr),
star.mode.u_constraints_rhs)
self.optimized_lp_solution = None
self.freeze_attrs()
def update_full_lp(self):
'''update the LP solution and, if it's feasible, get its solution, for GUARD_FULL_LP'''
cur_basis_mat = self.star.time_elapse.cur_basis_mat
# start and end rows of key-dir matrices
start = self.key_dir_offset
end = self.key_dir_offset + self.num_output_vars
self.lpi.update_basis_matrix(cur_basis_mat[start:end])
# add input effects for the current step (if it exists)
if self.star.time_elapse.cur_input_effects_matrix is not None:
input_effects_mat = self.star.time_elapse.cur_input_effects_matrix
self.lpi.add_input_effects_matrix(input_effects_mat[start:end])
result_len = self.num_output_vars + self.star.num_init_vars
result_len += self.num_output_vars # total input effect
result_len += self.inputs * (self.star.time_elapse.next_step - 1
) # inputs at each step
result = np.zeros((result_len), dtype=float)
direction = np.zeros((self.num_output_vars, ), dtype=float)
is_feasible = self.lpi.minimize(direction,
result,
error_if_infeasible=False)
return result if is_feasible else None
def get_guard_lpi(self):
'''get the current full lp instance for this guard'''
return self.lpi
def get_optimized_lp_solution(self):
'''gets the lp solution without calling an lp solver
this is only possible if the initial set has only range conditions for each initial dimension,
and the output-space has only a single condition
This returns either an lp solution (np.ndarray) or None if infeasible
'''
Timers.tic('get_optimized_lp_solution')
init_ranges = self.star.init_range_tuples
basis_mat = self.star.time_elapse.cur_basis_mat
input_effects_mat = self.star.time_elapse.cur_input_effects_matrix
assert len(init_ranges) == basis_mat.shape[1]
assert len(self.transition.guard_rhs) == 1
assert self.num_output_vars == 1
assert self.transition.guard_matrix_csr.shape == (1, 1)
guard_multiplier = self.transition.guard_matrix_csr[0, 0]
if self.optimized_lp_solution is None:
# +1 for output +1 for total input effects
self.optimized_lp_solution = [0.0] * (len(init_ranges) + 1 + 1)
result = self.optimized_lp_solution
total_output_index = len(init_ranges)
total_input_index = len(init_ranges) + 1
guard_threshold = self.transition.guard_rhs[0]
noinput_effect = 0
Timers.tic("noinput_effects")
for init_index in xrange(len(init_ranges)):
basis_val = basis_mat[0, init_index]
min_init = init_ranges[init_index][0]
max_init = init_ranges[init_index][1]
mult = basis_val * guard_multiplier
val1 = min_init * mult
val2 = max_init * mult
# take the minimum of val1 and val2, since guard is CONDITION <= RHS
if val1 < val2:
noinput_effect += val1
result[init_index] = min_init
else:
noinput_effect += val2
result[init_index] = max_init
Timers.toc("noinput_effects")
# add input effects if they exist
if input_effects_mat is not None:
Timers.tic("input_effects")
input_ranges = self.star.mode.u_range_tuples
for input_index in xrange(len(input_ranges)):
basis_val = input_effects_mat[0][input_index]
min_input = input_ranges[input_index][0]
max_input = input_ranges[input_index][1]
val1 = min_input * basis_val * guard_multiplier
val2 = max_input * basis_val * guard_multiplier
# take the minimum of val1 and val2, since guard is CONDITION <= RHS
if val1 < val2:
result[total_input_index] += val1
result.append(min_input)
else:
result[total_input_index] += val2
result.append(max_input)
Timers.toc("input_effects")
result[total_output_index] = noinput_effect + result[total_input_index]
rv = np.array(
result, dtype=float
) if result[total_output_index] <= guard_threshold else None
Timers.toc('get_optimized_lp_solution')
return rv
def get_updated_lp_solution(self):
'''update the LP solution and, if it's feasible, get its solution'''
if self.star.settings.interval_guard_optimization and self.star.init_range_tuples is not None and \
(self.star.inputs == 0 or self.star.mode.u_range_tuples is not None) and self.num_output_vars == 1:
# LP can be decomposed column-by-column (optimization)
rv = self.get_optimized_lp_solution()
else:
rv = self.update_full_lp()
return rv
def compute_sequence_in_a_mode_wrt_init_mode(self, error_star_list, direction, compute_intersection):
basis_center = error_star_list[0].parent.star.parent.prestar_basis_center
usafe_basis_preds_list = self.compute_usafe_basis_pred_in_star_basis_in_star_list(error_star_list,
compute_intersection)
valid_ids_for_all_indices = []
feasible_points = []
basis_matrix = error_star_list[0].parent.star.parent.prestar.parent.star.basis_matrix
for idx_i in range(len(error_star_list)):
valid_ids_for_current_index = []
## Create an LP instance
usafe_lpi = LpInstance(self.num_dims, self.num_dims)
usafe_lpi.update_basis_matrix(basis_matrix)
#if idx_i == 0:
# with open("constraints_before", 'w+') as f:
# f.write('uasfe_basis_preds\n')
# for pred in usafe_basis_preds_list[idx_i]:
# f.write('{},{};\n'.format(pred.vector, pred.value))
# f.write('parent.star.constraint_list\n')
# for pred in error_star_list[0].parent.star.constraint_list:
# f.write('{},{};\n'.format(pred.vector, pred.value))
# f.write('Initial mode predicates\n')
# for pred in error_star_list[0].parent.star.parent.prestar.parent.star.constraint_list:
# f.write('{},{};\n'.format(pred.vector, pred.value))
all_preds = []
for pred in usafe_basis_preds_list[idx_i]:
all_preds.append(self.convert_usafe_basis_pred_in_basis_center(pred, basis_center))
for pred in error_star_list[0].parent.star.constraint_list:
all_preds.append(self.convert_usafe_basis_pred_in_basis_center(pred, basis_center))
## adding constraints from the previous mode initial star (P)
for pred in error_star_list[0].parent.star.parent.prestar.parent.star.constraint_list:
all_preds.append(pred.clone())
for pred in all_preds:
usafe_lpi.add_basis_constraint(pred.vector, pred.value)
#if idx_i == 0:
# with open("constraints_after", 'w+') as f:
# for pred in all_preds:
# f.write('{},{};\n'.format(pred.vector, pred.value))
result = np.zeros(self.num_dims)
usafe_lpi.minimize(direction, result, error_if_infeasible=False)
feasible_point = np.dot(basis_matrix, result)
valid_ids_for_current_index.append(idx_i)
for idx_j in range(idx_i - 1, -1, -1):
for pred in usafe_basis_preds_list[idx_j]:
new_pred = self.convert_usafe_basis_pred_in_basis_center(pred, basis_center)
usafe_lpi.add_basis_constraint(new_pred.vector, new_pred.value)
result = np.zeros(self.num_dims)
is_feasible = usafe_lpi.minimize(direction, result, error_if_infeasible=False)
if not is_feasible:
break
valid_ids_for_current_index.append(idx_j)
feasible_point = np.dot(basis_matrix, result)
valid_ids_for_all_indices.append(valid_ids_for_current_index)
feasible_points.append(feasible_point)
#print "valid ids for current mode: '{}'".format(valid_ids_for_all_indices)
#print "feasible points: '{}'".format(feasible_points)
return valid_ids_for_all_indices, feasible_points
def compute_sequences_in_two_modes(self, error_star_list_per_mode, direction, compute_intersection=False):
error_star_list_second_mode = error_star_list_per_mode[1]
error_star_list_first_mode = []
for index in range(len(error_star_list_per_mode[0])):
if (error_star_list_per_mode[0][index].total_steps < error_star_list_second_mode[0].total_steps):
error_star_list_first_mode.append(error_star_list_per_mode[0][index].clone())
else:
break
usafe_basis_preds_list_first_mode = self.compute_usafe_basis_pred_in_star_basis_in_star_list(error_star_list_first_mode, compute_intersection)
usafe_basis_preds_list_second_mode = self.compute_usafe_basis_pred_in_star_basis_in_star_list(error_star_list_second_mode, compute_intersection)
## compute_sequence_in_a_mode() returns the indices of the feasible stars for each star scanning from left to right
sequences_in_second_mode, feasible_pts_in_second_mode = self.compute_sequence_in_a_mode_wrt_init_mode(error_star_list_second_mode, direction, compute_intersection)
sequences_in_first_mode, feasible_pts_in_first_mode = self.compute_sequence_in_a_mode(error_star_list_first_mode, direction, compute_intersection)
len_of_longest_seq_in_first_mode = 0
longest_ce_in_first_mode = None
longest_seq_in_first_mode = [0, 0]
ce_length_in_first_mode = 0
for index in range(len(sequences_in_first_mode)):
valid_ids = sequences_in_first_mode[index]
cur_seq_len = (valid_ids[0]-valid_ids[len(valid_ids)-1])
if len_of_longest_seq_in_first_mode < cur_seq_len:
len_of_longest_seq_in_first_mode = cur_seq_len
longest_seq_in_first_mode[1] = valid_ids[0]
longest_seq_in_first_mode[0] = valid_ids[len(valid_ids)-1]
ce_length_in_first_mode = longest_seq_in_first_mode[1] - longest_seq_in_first_mode[0] + 1
longest_ce_in_first_mode = feasible_pts_in_first_mode[index]
len_of_longest_seq_in_second_mode = 0
longest_seq_in_second_mode = [0, 0]
longest_ce_in_second_mode = None
ce_length_in_second_mode = 0
for index in range(len(sequences_in_second_mode)):
valid_ids = sequences_in_second_mode[index]
cur_seq_len = (valid_ids[0] - valid_ids[len(valid_ids)-1])
if len_of_longest_seq_in_second_mode < cur_seq_len:
len_of_longest_seq_in_second_mode = cur_seq_len
longest_seq_in_second_mode[1] = valid_ids[0]
longest_seq_in_second_mode[0] = valid_ids[len(valid_ids) - 1]
ce_length_in_second_mode = longest_seq_in_second_mode[1] - longest_seq_in_second_mode[0] + 1
longest_ce_in_second_mode = feasible_pts_in_second_mode[index]
## Compute indices - Compute longest sequence in first mode for each star in the next mode
## The sequence is represented as start and end index. If there is none, both start and end indices are -1
first_mode_seq_for_each_second_mode_stars = []
#usafe_basis_preds_list_in_first_mode = self.compute_usafe_basis_pred_in_star_basis_in_star_list(
# error_star_list_per_mode[0], compute_intersection)
for index in range(len(error_star_list_second_mode)):
usafe_basis_preds_for_current_star_in_current_mode = self.compute_usafe_basis_pred_in_star_basis(
error_star_list_second_mode[index], compute_intersection)
basis_center = error_star_list_second_mode[0].parent.star.parent.prestar_basis_center
new_usafe_basis_preds = []
for pred in usafe_basis_preds_for_current_star_in_current_mode:
new_usafe_basis_preds.append(self.convert_usafe_basis_pred_in_basis_center(pred, basis_center))
indices = self.compute_indices(new_usafe_basis_preds, usafe_basis_preds_list_first_mode, 0,
len(usafe_basis_preds_list_first_mode) - 1, direction)
first_mode_seq_for_each_second_mode_stars.append(self.perform_pruning(indices))
final_seqs_for_first_mode = []
final_seqs_for_second_mode = []
feasible_ces = []
basis_center = error_star_list_second_mode[0].parent.star.parent.prestar_basis_center
for valid_ids_for_current_index in sequences_in_second_mode:
start = 0
end = len(valid_ids_for_current_index) - 1
feasible_point = None
while True:
## Create an LP instance
usafe_lpi = LpInstance(self.num_dims, self.num_dims)
usafe_lpi.update_basis_matrix(self.init_star.basis_matrix)
for pred in self.init_star.constraint_list:
usafe_lpi.add_basis_constraint(pred.vector, pred.value)
sequence_1 = first_mode_seq_for_each_second_mode_stars[valid_ids_for_current_index[start]] ## Merging it with same sequence gives the same seq
for idx in range(start, end, 1 ):
sequence_1 = self.compute_sequences_intersection(sequence_1, first_mode_seq_for_each_second_mode_stars[valid_ids_for_current_index[idx]])
if sequence_1[1] != -1:
for pred in usafe_basis_preds_list_second_mode[valid_ids_for_current_index[idx]]:
lc = self.convert_usafe_basis_pred_in_basis_center(pred, basis_center)
usafe_lpi.add_basis_constraint(lc.vector, lc.value)
#sequence_1 = self.compute_sequences_intersection(sequence_1, first_mode_seq_for_each_second_mode_stars[valid_ids_for_current_index[idx]])
if sequence_1[1] == -1:
break
for idx in range(len(sequence_1)):
for pred in usafe_basis_preds_list_first_mode[idx]:
usafe_lpi.add_basis_constraint(pred.vector, pred.value)
result = np.zeros(self.num_dims)
is_feasible = usafe_lpi.minimize(direction, result, error_if_infeasible=False)
feasible_point = np.dot(self.init_star.basis_matrix, result)
if is_feasible:
break
else:
end = end - 1
valid_ids = valid_ids_for_current_index[start:end+1] #end+1 for including the last value
sequence_2 = [-1,-1]
sequence_2[1] = valid_ids[0]
sequence_2[0] = valid_ids[len(valid_ids) - 1]
if sequence_1[1] != -1:
final_seqs_for_second_mode.append(sequence_2)
final_seqs_for_first_mode.append(sequence_1)
feasible_ces.append(feasible_point)
combined_max_ce_length = 0
start_idx_first_mode = -1
start_idx_sec_mode = -1
end_idx_first_mode = -1
end_idx_sec_mode = -1
longest_ce = None
for index in range(len(final_seqs_for_second_mode)):
current_ce_length = final_seqs_for_first_mode[index][1] - final_seqs_for_first_mode[index][0] + 1
current_ce_length = current_ce_length + (final_seqs_for_second_mode[index][1] - final_seqs_for_second_mode[index][0] + 1)
if current_ce_length > combined_max_ce_length:
start_idx_first_mode = final_seqs_for_first_mode[index][0]
end_idx_first_mode = final_seqs_for_first_mode[index][1]
start_idx_sec_mode = final_seqs_for_second_mode[index][0]
end_idx_sec_mode = final_seqs_for_second_mode[index][1]
combined_max_ce_length = current_ce_length
longest_ce = feasible_ces[index]
if combined_max_ce_length < ce_length_in_first_mode:
combined_max_ce_length = ce_length_in_first_mode
longest_ce = longest_ce_in_first_mode
start_idx_first_mode = longest_ce_in_first_mode[0]
end_idx_first_mode = longest_ce_in_first_mode[1]
start_idx_sec_mode = end_idx_sec_mode = -1
if combined_max_ce_length < ce_length_in_second_mode:
combined_max_ce_length = ce_length_in_second_mode
longest_ce = longest_ce_in_second_mode
start_idx_sec_mode = longest_seq_in_second_mode[0]
end_idx_sec_mode = longest_seq_in_second_mode[1]
start_idx_first_mode = end_idx_first_mode = -1
final_indices = []
final_indices.append(combined_max_ce_length)
final_indices.append(start_idx_first_mode)
final_indices.append(end_idx_first_mode)
final_indices.append(start_idx_sec_mode)
final_indices.append(end_idx_sec_mode)
return final_indices, longest_ce
def compute_deepest_ce(self, depth_direction):
compute_intersection = True
Timers.tic('Deepest counter-example')
points = []
for error_star in self.error_stars:
usafe_lpi = LpInstance(self.num_dims, self.num_dims)
usafe_lpi.update_basis_matrix(error_star.basis_matrix)
for pred in self.usafe_set_constraint_list:
usafe_lpi.add_standard_constraint(pred.vector, pred.value)
for pred in error_star.constraint_list:
usafe_lpi.add_basis_constraint(pred.vector, pred.value)
result = np.zeros(self.num_dims)
is_feasible = usafe_lpi.minimize(-1 * depth_direction, result, error_if_infeasible=False)
if is_feasible:
usafe_set_basis_matrix = np.identity(self.num_dims, dtype=float)
points.append(np.dot(usafe_set_basis_matrix, result))
if len(points) is 0:
print("Result (Deepest counter-example): No solution exists in this direction.")
Timers.toc('Deepest counter-example')
return
# Find the index of the error_star corresponding to the max_depth
max_depth = np.dot(depth_direction, points[0])
max_depth_error_star = self.error_stars[0].clone()
max_point = points[0]
for index in range(len(points)):
point = points[index]
depth = np.dot(depth_direction, point)
if depth > max_depth:
max_depth = depth
max_depth_error_star = self.error_stars[index].clone()
max_point = point
print("The deepest point is: '{}' with max_depth '{}'".format(max_point, max_depth))
#print "Max error star: '{}'".format(max_depth_error_star)
#max_depth_error_star = self.error_stars[max_depth_index].clone()
feasible_point = None
if max_depth_error_star.mode.name == self.init_star.mode.name:
basis_matrix = max_depth_error_star.parent.star.basis_matrix
usafe_lpi = LpInstance(self.num_dims, self.num_dims)
usafe_lpi.update_basis_matrix(basis_matrix)
usafe_basis_preds = self.compute_point_as_star_basis(max_point, max_depth_error_star)
#usafe_basis_preds = self.compute_usafe_basis_pred_in_star_basis(max_depth_error_star, False)
for pred in usafe_basis_preds:
usafe_lpi.add_basis_constraint(pred.vector, pred.value)
for pred in max_depth_error_star.parent.star.constraint_list:
usafe_lpi.add_basis_constraint(pred.vector, pred.value)
result = np.zeros(self.num_dims)
is_feasible = usafe_lpi.minimize(-1 * depth_direction, result, error_if_infeasible=False)
if is_feasible:
feasible_point = np.dot(basis_matrix, result)
print("CounterExample: '{}' with depth '{}' in the given direction".format(feasible_point, max_depth))
Timers.toc('Deepest counter-example')
else:
basis_center = max_depth_error_star.parent.star.parent.prestar_basis_center
usafe_basis_preds = self.compute_usafe_basis_pred_in_star_basis(max_depth_error_star, compute_intersection)
#print "Usafe Basis predicates: {}".format(usafe_basis_preds)
#usafe_basis_preds = self.compute_point_as_star_basis(max_point, max_depth_error_star)
basis_matrix = max_depth_error_star.parent.star.parent.prestar.parent.star.basis_matrix
usafe_lpi = LpInstance(self.num_dims, self.num_dims)
usafe_lpi.update_basis_matrix(basis_matrix)
all_preds = []
for pred in usafe_basis_preds:
all_preds.append(self.convert_usafe_basis_pred_in_basis_center(pred, basis_center))
#for pred in max_depth_error_star.parent.star.constraint_list:
# all_preds.append(self.convert_usafe_basis_pred_in_basis_center(pred, basis_center))
## adding constraints from the previous mode initial star (P)
for pred in max_depth_error_star.parent.star.parent.prestar.parent.star.constraint_list:
all_preds.append(pred.clone())
for pred in all_preds:
usafe_lpi.add_basis_constraint(pred.vector, pred.value)
result = np.zeros(self.num_dims)
is_feasible = usafe_lpi.minimize(-1 * depth_direction, result, error_if_infeasible=False)
if is_feasible:
feasible_point = np.dot(basis_matrix, result)
print("CounterExample: '{}' with depth '{}' in the given direction".format(feasible_point, max_depth))
Timers.toc('Deepest counter-example')
return feasible_point
def compute_counter_examples(self, direction):
## Populate error stars info
error_star_steps = []
error_star_modes = []
for error_star in self.error_stars:
error_star_steps.append(error_star.total_steps)
error_star_modes.append(error_star.mode)
# List of feasible solutions/initial points
initial_points = []
usafe_basis_predicates_list = []
## Iterate over the stars which intersect with the unsafe set
## Eventually there is going to be just one star at a particular
## time step that user is interested in.
for index in range(len(self.error_stars)):
#basis_matrix = error_star_basis_matrices[index]
#basis_center = error_star_centers[index]
error_star = self.error_stars[index]
usafe_basis_predicates = self.compute_usafe_basis_pred_in_star_basis(error_star)
## List of predicates for each time step where our standard star intersects with the unsafe set
## To be used while computing the longest subsequence.
usafe_basis_predicates_list.append(usafe_basis_predicates)
## Create an LP instance
usafe_lpi = LpInstance(self.num_dims, self.num_dims)
## Update the basis matrix
usafe_lpi.update_basis_matrix(self.init_star.basis_matrix)
for predicate in usafe_basis_predicates:
usafe_lpi.add_basis_constraint(predicate.vector, predicate.value)
## Add init star basis constraints to the usafe linear constraints list
for lc in self.init_star.constraint_list:
usafe_lpi.add_basis_constraint(lc.vector, lc.value)
result = np.zeros(self.num_dims)
is_feasible = usafe_lpi.minimize(direction, result, error_if_infeasible=False)
## This gives us a point, if any, in the initial set which leads to an unsafe point at a given time step.
if is_feasible:
initial_points.append(np.dot(self.init_star.basis_matrix, result))
counterExamples = []
unique_initial_points = []
for index_i in range(len(initial_points)):
not_unique = False
for index_u in range(len(unique_initial_points)):
out = np.zeros(self.num_dims)
if (np.subtract(unique_initial_points[index_u], initial_points[index_i]) == out).all():
not_unique = True
break
if not not_unique:
counterExample = CounterExample(initial_points[index_i], usafe_basis_predicates_list, error_star_steps,
error_star_modes, self.num_dims)
counterExamples.append(counterExample)
unique_initial_points.append(initial_points[index_i])
return counterExamples