def _set_optimization_variables_lower_bounds(self, umin, qmin, xmin, x0):
umin_user_provided = umin
umin = inputchecks.check_controls_data(umin, \
self._discretization.system.nu, 1)
if umin_user_provided is None:
umin = -np.inf * np.ones(umin.shape)
Umin = ci.repmat(umin, 1, \
self._discretization.optimization_variables["U"].shape[1])
qmin_user_provided = qmin
qmin = inputchecks.check_constant_controls_data(qmin, \
self._discretization.system.nq)
if qmin_user_provided is None:
qmin = -np.inf * np.ones(qmin.shape)
Qmin = qmin
xmin_user_provided = xmin
xmin = inputchecks.check_states_data(xmin, \
self._discretization.system.nx, 0)
if xmin_user_provided is None:
xmin = -np.inf * np.ones(xmin.shape)
Xmin = ci.repmat(xmin, 1, \
self._discretization.optimization_variables["X"].shape[1])
Xmin[:,0] = x0
self._optimization_variables_lower_bounds = ci.veccat([ \
Umin,
Qmin,
Xmin,
])
def _set_optimization_variables_lower_bounds(self, umin, qmin, xmin, x0):
umin_user_provided = umin
umin = inputchecks.check_controls_data(umin, \
self._discretization.system.nu, 1)
if umin_user_provided is None:
umin = -np.inf * np.ones(umin.shape)
Umin = ci.repmat(umin, 1, \
self._discretization.optimization_variables["U"].shape[1])
qmin_user_provided = qmin
qmin = inputchecks.check_constant_controls_data(qmin, \
self._discretization.system.nq)
if qmin_user_provided is None:
qmin = -np.inf * np.ones(qmin.shape)
Qmin = qmin
xmin_user_provided = xmin
xmin = inputchecks.check_states_data(xmin, \
self._discretization.system.nx, 0)
if xmin_user_provided is None:
xmin = -np.inf * np.ones(xmin.shape)
Xmin = ci.repmat(xmin, 1, \
self._discretization.optimization_variables["X"].shape[1])
Xmin[:,0] = x0
self._optimization_variables_lower_bounds = ci.veccat([ \
Umin,
Qmin,
Xmin,
])
def _set_optimization_variables_upper_bounds(self, umax, qmax, xmax, x0):
umax_user_provided = umax
umax = inputchecks.check_controls_data(umax, \
self._discretization.system.nu, 1)
if umax_user_provided is None:
umax = np.inf * np.ones(umax.shape)
Umax = ci.repmat(umax, 1, \
self._discretization.optimization_variables["U"].shape[1])
qmax_user_provided = qmax
qmax = inputchecks.check_constant_controls_data(qmax, \
self._discretization.system.nq)
if qmax_user_provided is None:
qmax = -np.inf * np.ones(qmax.shape)
Qmax = qmax
xmax_user_provided = xmax
xmax = inputchecks.check_states_data(xmax, \
self._discretization.system.nx, 0)
if xmax_user_provided is None:
xmax = np.inf * np.ones(xmax.shape)
Xmax = ci.repmat(xmax, 1, \
self._discretization.optimization_variables["X"].shape[1])
Xmax[:,0] = x0
self._optimization_variables_upper_bounds = ci.veccat([ \
Umax,
Xmax,
])
def _set_optimization_variables_upper_bounds(self, umax, qmax, xmax, x0):
umax_user_provided = umax
umax = inputchecks.check_controls_data(umax, \
self._discretization.system.nu, 1)
if umax_user_provided is None:
umax = np.inf * np.ones(umax.shape)
Umax = ci.repmat(umax, 1, \
self._discretization.optimization_variables["U"].shape[1])
qmax_user_provided = qmax
qmax = inputchecks.check_constant_controls_data(qmax, \
self._discretization.system.nq)
if qmax_user_provided is None:
qmax = -np.inf * np.ones(qmax.shape)
Qmax = qmax
xmax_user_provided = xmax
xmax = inputchecks.check_states_data(xmax, \
self._discretization.system.nx, 0)
if xmax_user_provided is None:
xmax = np.inf * np.ones(xmax.shape)
Xmax = ci.repmat(xmax, 1, \
self._discretization.optimization_variables["X"].shape[1])
Xmax[:,0] = x0
self._optimization_variables_upper_bounds = ci.veccat([ \
Umax,
Xmax,
])
def _set_optimization_variables_initials(self, pinit, xinit):
xinit = inputchecks.check_states_data(xinit, \
self._discretization.system.nx, \
self._discretization.number_of_intervals)
repretitions_xinit = \
self._discretization.optimization_variables["X"][:,:-1].shape[1] / \
self._discretization.number_of_intervals
Xinit = ci.repmat(xinit[:, :-1], repretitions_xinit, 1)
Xinit = ci.horzcat([ \
Xinit.reshape((self._discretization.system.nx, \
Xinit.size() / self._discretization.system.nx)),
xinit[:, -1],
])
pinit = inputchecks.check_parameter_data(pinit, \
self._discretization.system.np)
Pinit = pinit
Vinit = np.zeros(self._discretization.optimization_variables["V"].shape)
EPS_Uinit = np.zeros( \
self._discretization.optimization_variables["EPS_U"].shape)
self._optimization_variables_initials = ci.veccat([ \
Pinit,
Xinit,
EPS_Uinit,
Vinit,
])
def _set_optimization_variables_initials(self, qinit, x0, uinit):
self.simulation = Simulation(self._discretization.system, \
self._pdata, qinit)
self.simulation.run_system_simulation(x0, \
self._discretization.time_points, uinit, print_status = False)
xinit = self.simulation.simulation_results
repretitions_xinit = \
self._discretization.optimization_variables["X"][:,:-1].shape[1] / \
self._discretization.number_of_intervals
Xinit = ci.repmat(xinit[:, :-1], repretitions_xinit, 1)
Xinit = ci.horzcat([ \
Xinit.reshape((self._discretization.system.nx, \
Xinit.size() / self._discretization.system.nx)),
xinit[:, -1],
])
uinit = inputchecks.check_controls_data(uinit, \
self._discretization.system.nu, \
self._discretization.number_of_intervals)
Uinit = uinit
qinit = inputchecks.check_constant_controls_data(qinit, \
self._discretization.system.nq)
Qinit = qinit
self._optimization_variables_initials = ci.veccat([ \
Uinit,
Qinit,
Xinit,
])
def _set_optimization_variables_initials(self, qinit, x0, uinit):
self.simulation = Simulation(self._discretization.system, \
self._pdata, qinit)
self.simulation.run_system_simulation(x0, \
self._discretization.time_points, uinit, print_status = False)
xinit = self.simulation.simulation_results
repretitions_xinit = \
self._discretization.optimization_variables["X"][:,:-1].shape[1] / \
self._discretization.number_of_intervals
Xinit = ci.repmat(xinit[:, :-1], repretitions_xinit, 1)
Xinit = ci.horzcat([ \
Xinit.reshape((self._discretization.system.nx, \
Xinit.numel() / self._discretization.system.nx)),
xinit[:, -1],
])
uinit = inputchecks.check_controls_data(uinit, \
self._discretization.system.nu, \
self._discretization.number_of_intervals)
Uinit = uinit
qinit = inputchecks.check_constant_controls_data(qinit, \
self._discretization.system.nq)
Qinit = qinit
self._optimization_variables_initials = ci.veccat([ \
Uinit,
Qinit,
Xinit,
])
def _set_optimization_variables_initials(self, pinit, xinit):
xinit = inputchecks.check_states_data(xinit, \
self._discretization.system.nx, \
self._discretization.number_of_intervals)
repretitions_xinit = \
self._discretization.optimization_variables["X"][:,:-1].shape[1] / \
self._discretization.number_of_intervals
Xinit = ci.repmat(xinit[:, :-1], repretitions_xinit, 1)
Xinit = ci.horzcat([ \
Xinit.reshape((self._discretization.system.nx, \
Xinit.numel() / self._discretization.system.nx)),
xinit[:, -1],
])
pinit = inputchecks.check_parameter_data(pinit, \
self._discretization.system.np)
Pinit = pinit
Vinit = np.zeros(
self._discretization.optimization_variables["V"].shape)
EPS_Uinit = np.zeros( \
self._discretization.optimization_variables["EPS_U"].shape)
self._optimization_variables_initials = ci.veccat([ \
Pinit,
Xinit,
Vinit,
EPS_Uinit,
])
def _plot_confidence_ellipsoids(self, pdata, properties = "initial"):
if properties == "initial":
covariance_matrix = {"initial": self.covariance_matrix_initial}
elif properties == "optimized":
covariance_matrix = {"optimized": self.covariance_matrix_optimized}
elif properties == "all":
covariance_matrix = {"initial" : self._covariance_matrix_initial, \
"optimized" : self._covariance_matrix_optimized}
else:
raise ValueError('''
Input-value not supported, choose either "initial", "final", or "all".
''')
plotting_directory = "confidence_ellipsoids_" + \
os.path.basename(__main__.__file__).strip(".py")
try:
os.mkdir(plotting_directory)
except OSError:
if not os.path.isdir(plotting_directory):
raise OSError('''
Plotting directory "confidence_ellipsoids_{0}"
does not yet exist, but could not be created.
Do you have write access within your working folder, or is
some file with this name already present within your working folder?
'''.format(plotting_directory))
xy = np.array([np.cos(np.linspace(0, 2*np.pi, 100)),
np.sin(np.linspace(0, 2*np.pi, 100))])
for p1 in range(pdata.size):
for p2 in range(pdata.size)[p1+1:]:
plt.figure()
for prop, cm in covariance_matrix.iteritems():
covariance_matrix_p1p2 = np.array([ \
[cm[p1, p1], cm[p1, p2]], \
[cm[p2, p1], cm[p2, p2]]
])
w, v = np.linalg.eig(covariance_matrix_p1p2)
ellipsoid = ci.repmat(np.array([pdata[p1], pdata[p2]]), 1, 100) + \
ci.mul([v, ci.diag(w), xy])
plt.plot(ellipsoid[0,:].T, ellipsoid[1,:].T, label = \
"p_" + str(p1) + ", p_" + str(p2) + " " + prop)
plt.scatter(pdata[p1], pdata[p2], color = "k")
plt.legend(loc="upper right")
plt.savefig(plotting_directory + "/p_" + str(p1) + \
"-p_" + str(p2) + "-" + properties + ".png", bbox_inches='tight')
plt.close()
def _plot_confidence_ellipsoids(self, pdata, properties = "initial"):
if properties == "initial":
covariance_matrix = {"initial": self.covariance_matrix_initial}
elif properties == "optimized":
covariance_matrix = {"optimized": self.covariance_matrix_optimized}
elif properties == "all":
covariance_matrix = {"initial" : self._covariance_matrix_initial, \
"optimized" : self._covariance_matrix_optimized}
else:
raise ValueError('''
Input-value not supported, choose either "initial", "final", or "all".
''')
plotting_directory = "confidence_ellipsoids_" + \
os.path.basename(__main__.__file__).strip(".py")
try:
os.mkdir(plotting_directory)
except OSError:
if not os.path.isdir(plotting_directory):
raise OSError('''
Plotting directory "confidence_ellipsoids_{0}"
does not yet exist, but could not be created.
Do you have write access within your working folder, or is
some file with this name already present within your working folder?
'''.format(plotting_directory))
xy = np.array([np.cos(np.linspace(0, 2*np.pi, 100)),
np.sin(np.linspace(0, 2*np.pi, 100))])
for p1 in range(pdata.size):
for p2 in range(pdata.size)[p1+1:]:
plt.figure()
for prop, cm in covariance_matrix.iteritems():
covariance_matrix_p1p2 = np.array([ \
[cm[p1, p1], cm[p1, p2]], \
[cm[p2, p1], cm[p2, p2]]
])
w, v = np.linalg.eig(covariance_matrix_p1p2)
ellipsoid = ci.repmat(np.array([pdata[p1], pdata[p2]]), 1, 100) + \
ci.mul([v, ci.diag(w), xy])
plt.plot(ellipsoid[0,:].T, ellipsoid[1,:].T, label = \
"p_" + str(p1) + ", p_" + str(p2) + " " + prop)
plt.scatter(pdata[p1], pdata[p2], color = "k")
plt.legend(loc="upper right")
plt.savefig(plotting_directory + "/p_" + str(p1) + \
"-p_" + str(p2) + "-" + properties + ".png", bbox_inches='tight')
plt.close()