def __find_bounds(self, dir_vec, ptope, bund):
'Find the generator of the parallelotope.'
genFun = ptope.getGeneratorRep()
'Create subsitutions tuples.'
var_sub = []
for var_ind, var in enumerate(self.vars):
var_sub.append((var, genFun[var_ind]))
#print(f"Variable Sub for {dir_vec}: {var_sub}")
Timer.start('Functional Composition')
fog = [func.subs(var_sub, simultaneous=True) for func in self.f]
Timer.stop('Functional Composition')
'Perform functional composition with exact transformation from unitbox to parallelotope.'
bound_polyu = 0
for coeff_idx, coeff in enumerate(dir_vec):
bound_polyu += coeff * fog[coeff_idx]
'Calculate min/max Bernstein coefficients.'
Timer.start('Bound Computation')
ub, lb = OptProd(bound_polyu, bund).getBounds()
Timer.stop('Bound Computation')
return ub, -1 * lb
def getGeneratorRep(self):
Timer.start('Generator Procedure')
base_vertex = self._computeBaseVertex()
gen_list = self._computeGenerators(base_vertex)
'Create list representing the linear transformation q + \sum_{j} a_j* g_j'
expr_list = base_vertex
for var_ind, var in enumerate(self.vars):
for i in range(self.dim):
expr_list[i] += gen_list[var_ind][i] * var
Timer.stop('Generator Procedure')
return expr_list
def plot2DPhase(self, x, y, separate=False, lims=None):
assert len(
self.flowpipes
) != 0, "Plot Object must have at least one flowpipe to plot for 2DPhase."
Timer.start('Phase')
dim = self.model.dim
figure = plt.figure(figsize=PlotSettings.fig_size)
phase_ax = figure.add_subplot(1, 2, 1)
vol_ax = figure.add_subplot(1, 2, 2)
for flow_idx, (flow_label, flowpipe) in enumerate(self.flowpipes):
self.__halfspace_inter_plot(flowpipe, flow_idx, flow_label, x, y,
phase_ax, separate)
#self.__support_plot(flowpipe, flow_idx, flow_label, x, y, ax)
self.__plot_trajs(x, y, phase_ax)
self.__phase_plot_legend(x, y, phase_ax, lims)
'Add volume data'
self.__plot_volume(vol_ax)
figure_name = "Kaa{}Phase{}.png".format(flowpipe.model.name,
self.__create_var_str([x, y]))
self.__plot_figure(figure, figure_name)
phase_time = Timer.stop('Phase')
print("Plotting phase for dimensions {}, {} done -- Time Spent: {}".
format(x_var, y_var, phase_time))
def plot2DPhase(self, x, y):
Timer.start('Phase')
x_var, y_var = self.vars[x], self.vars[y]
'Define the following projected normal vectors.'
norm_vecs = np.zeros([6, self.dim_sys])
norm_vecs[0][x] = 1
norm_vecs[1][y] = 1
norm_vecs[2][x] = -1
norm_vecs[3][y] = -1
norm_vecs[4][x] = 1
norm_vecs[4][y] = 1
norm_vecs[5][x] = -1
norm_vecs[5][y] = -1
fig, ax = plt.subplots(1)
comple_dim = [i for i in range(self.dim_sys) if i not in [x, y]]
'Initialize objective function for Chebyshev intersection LP routine.'
c = [0 for _ in range(self.dim_sys + 1)]
c[-1] = 1
for bund in self.flowpipe:
bund_A, bund_b = bund.getIntersect()
'Compute the normal vector offsets'
bund_off = np.empty([len(norm_vecs), 1])
for i in range(len(norm_vecs)):
bund_off[i] = minLinProg(np.negative(norm_vecs[i]), bund_A,
bund_b).fun
'Remove irrelevant dimensions. Mostly doing this to make HalfspaceIntersection happy.'
phase_intersect = np.hstack((norm_vecs, bund_off))
phase_intersect = np.delete(phase_intersect, comple_dim, axis=1)
'Compute Chebyshev center of intersection.'
row_norm = np.reshape(np.linalg.norm(norm_vecs, axis=1),
(norm_vecs.shape[0], 1))
center_A = np.hstack((norm_vecs, row_norm))
neg_bund_off = np.negative(bund_off)
center_pt = maxLinProg(c, center_A, list(neg_bund_off.flat)).x
center_pt = np.asarray(
[b for b_i, b in enumerate(center_pt) if b_i in [x, y]])
'Run scipy.spatial.HalfspaceIntersection.'
hs = HalfspaceIntersection(phase_intersect, center_pt)
inter_x, inter_y = zip(*hs.intersections)
ax.set_xlabel('{}'.format(x_var))
ax.set_ylabel('{}'.format(y_var))
ax.fill(inter_x, inter_y, 'b')
fig.show()
phase_time = Timer.stop('Phase')
print("Plotting phase for dimensions {}, {} done -- Time Spent: {}".
format(x_var, y_var, phase_time))
def get2DProj(self, var_ind):
pipe_len = len(self.flowpipe)
Timer.start('Proj')
curr_var = self.vars[var_ind]
'Vector of minimum and maximum points of the polytope represented by parallelotope bundle.'
y_min, y_max = np.empty(pipe_len), np.empty(pipe_len)
'Initialize objective function'
y_obj = [0 for _ in self.vars]
y_obj[var_ind] = 1
'Calculate the minimum and maximum points through LPs for every iteration of the bundle.'
for bund_ind, bund in enumerate(self.flowpipe):
bund_sys = bund.getIntersect()
y_min[bund_ind] = bund_sys.max_opt(y_obj).fun
y_max[bund_ind] = bund_sys.min_opt(y_obj).fun
Timer.stop("Proj")
return y_min, y_max
def computeReachSet(self, time_steps):
initial_set = self.model.bund
transformer = BundleTransformer(self.model.f)
flowpipe = [initial_set]
for ind in range(time_steps):
Timer.start('Reachable Set Computation')
trans_bund = transformer.transform(flowpipe[ind])
reach_time = Timer.stop('Reachable Set Computation')
print("Computed Step {0} -- Time Elapsed: {1} sec".format(
ind, reach_time))
flowpipe.append(trans_bund)
return FlowPipe(flowpipe, self.model.vars)
def plot2DProj(self, *vars_tup):
num_var = len(vars_tup)
pipe_len = len(self.flowpipe)
fig, ax = plt.subplots(1, num_var)
ax = [ax] if num_var == 1 else ax
'Time step vector for plotting'
t = np.arange(0, pipe_len, 1)
for ax_ind, var_ind in enumerate(vars_tup):
Timer.start('Proj')
curr_var = self.vars[var_ind]
'Vector of minimum and maximum points of the polytope represented by parallelotope bundle.'
y_min, y_max = np.empty(pipe_len), np.empty(pipe_len)
'Initialize objective function'
y_obj = [0 for _ in self.vars]
y_obj[var_ind] = 1
'Calculate the minimum and maximum points through LPs for every iteration of the bundle.'
for bund_ind, bund in enumerate(self.flowpipe):
bund_A, bund_b = bund.getIntersect()
y_min[bund_ind] = minLinProg(y_obj, bund_A, bund_b).fun
y_max[bund_ind] = maxLinProg(y_obj, bund_A, bund_b).fun
ax[ax_ind].fill_between(t, y_min, y_max)
ax[ax_ind].set_xlabel("t: time steps")
ax[ax_ind].set_ylabel("Reachable Set for {}".format(curr_var))
plot_time = Timer.stop('Proj')
print(
"Plotting projection for dimension {} done -- Time Spent: {}".
format(curr_var, plot_time))
fig.show()
def computeReachSet(self,
time_steps,
tempstrat=None,
transmode=BundleMode.AFO):
initial_set = self.model.bund
transformer = BundleTransformer(self.model, transmode)
strat = tempstrat if tempstrat is not None else DefaultStrat(
self.model)
flowpipe = [initial_set]
for ind in range(time_steps):
Timer.start('Reachable Set Computation')
starting_bund = copy.deepcopy(flowpipe[ind])
#print("Open: L: {} \n T: {}".format(starting_bund.L, starting_bund.T))
#print("Open: Offu: {} \n Offl{}".format(starting_bund.offu, starting_bund.offl))
strat.open_strat(starting_bund)
trans_bund = transformer.transform(starting_bund)
strat.close_strat(trans_bund)
#print("Close: L: {} \n T: {}".format(trans_bund.L, trans_bund.T))
#print("Close: Offu: {} Offl{}".format(trans_bund.offu, trans_bund.offl))
reach_time = Timer.stop('Reachable Set Computation')
'TODO: Revamp Kaa.log to be output sink handling all output formatting.'
if not KaaSettings.SuppressOutput:
print("Computed Step {} -- Time Elapsed: {} sec".format(
bolden(ind), bolden(reach_time)))
flowpipe.append(trans_bund)
return FlowPipe(flowpipe, self.model, strat)