def simulate(self, Tend, nIntervals, gridWidth):
problem = Explicit_Problem(self.rhs, self.y0)
problem.name = 'CVode'
# solver.rhs = self.right_hand_side
problem.handle_result = self.handle_result
problem.state_events = self.state_events
problem.handle_event = self.handle_event
problem.time_events = self.time_events
problem.finalize = self.finalize
simulation = CVode(problem)
# Change multistep method: 'adams' or 'VDF'
if self.discr == 'Adams':
simulation.discr = 'Adams'
simulation.maxord = 12
else:
simulation.discr = 'BDF'
simulation.maxord = 5
# Change iteration algorithm: functional(FixedPoint) or newton
if self.iter == 'FixedPoint':
simulation.iter = 'FixedPoint'
else:
simulation.iter = 'Newton'
# Sets additional parameters
simulation.atol = self.atol
simulation.rtol = self.rtol
simulation.verbosity = self.verbosity
if hasattr(simulation, 'continuous_output'):
simulation.continuous_output = False # default 0, if one step approach should be used
elif hasattr(simulation, 'report_continuously'):
simulation.report_continuously = False # default 0, if one step approach should be used
# '''Initialize problem '''
# self.t_cur = self.t0
# self.y_cur = self.y0
# Calculate nOutputIntervals:
if gridWidth <> None:
nOutputIntervals = int((Tend - self.t0) / gridWidth)
else:
nOutputIntervals = nIntervals
# Check for feasible input parameters
if nOutputIntervals == 0:
print 'Error: gridWidth too high or nIntervals set to 0! Continue with nIntervals=1'
nOutputIntervals = 1
# Perform simulation
simulation.simulate(
Tend, nOutputIntervals
) # to get the values: t_new, y_new = simulation.simulate
def simulate(self, Tend, nIntervals, gridWidth):
problem = Explicit_Problem(self.rhs, self.y0)
problem.name = 'CVode'
# solver.rhs = self.right_hand_side
problem.handle_result = self.handle_result
problem.state_events = self.state_events
problem.handle_event = self.handle_event
problem.time_events = self.time_events
problem.finalize = self.finalize
simulation = CVode(problem)
# Change multistep method: 'adams' or 'VDF'
if self.discr == 'Adams':
simulation.discr = 'Adams'
simulation.maxord = 12
else:
simulation.discr = 'BDF'
simulation.maxord = 5
# Change iteration algorithm: functional(FixedPoint) or newton
if self.iter == 'FixedPoint':
simulation.iter = 'FixedPoint'
else:
simulation.iter = 'Newton'
# Sets additional parameters
simulation.atol = self.atol
simulation.rtol = self.rtol
simulation.verbosity = self.verbosity
if hasattr(simulation, 'continuous_output'):
simulation.continuous_output = False # default 0, if one step approach should be used
elif hasattr(simulation, 'report_continuously'):
simulation.report_continuously = False # default 0, if one step approach should be used
# '''Initialize problem '''
# self.t_cur = self.t0
# self.y_cur = self.y0
# Calculate nOutputIntervals:
if gridWidth <> None:
nOutputIntervals = int((Tend - self.t0) / gridWidth)
else:
nOutputIntervals = nIntervals
# Check for feasible input parameters
if nOutputIntervals == 0:
print 'Error: gridWidth too high or nIntervals set to 0! Continue with nIntervals=1'
nOutputIntervals = 1
# Perform simulation
simulation.simulate(Tend, nOutputIntervals) # to get the values: t_new, y_new = simulation.simulate
def test_switches(self):
"""
This tests that the switches are actually turned when override.
"""
f = lambda t,x,sw: N.array([1.0])
state_events = lambda t,x,sw: N.array([x[0]-1.])
def handle_event(solver, event_info):
solver.sw = [False] #Override the switches to point to another instance
mod = Explicit_Problem(f,[0.0])
mod.sw0 = [True]
mod.state_events = state_events
mod.handle_event = handle_event
sim = CVode(mod)
assert sim.sw[0] == True
sim.simulate(3)
assert sim.sw[0] == False
def test_switches(self):
"""
This tests that the switches are actually turned when override.
"""
f = lambda t,x,sw: N.array([1.0])
state_events = lambda t,x,sw: N.array([x[0]-1.])
def handle_event(solver, event_info):
solver.sw = [False] #Override the switches to point to another instance
mod = Explicit_Problem(f,[0.0])
mod.sw0 = [True]
mod.state_events = state_events
mod.handle_event = handle_event
sim = Radau5ODE(mod)
assert sim.sw[0] == True
sim.simulate(3)
assert sim.sw[0] == False
m = 0.145 # Initial conditions. The vector X0 is passed into the solver v0 = 45 theta = 30 theta = np.radians(theta) X0 = np.array([0, v0 * np.cos(theta), 1, v0 * np.sin(theta)]) # Time at start of simulation t0 = 0.0 # Create a model object with our equations and initial conditions model = Explicit_Problem(no_drag, X0, t0) # Bind event functions to model model.state_events = events model.handle_event = handle_event # Create simulation object sim = CVode(model) # Run simulation t, X = sim.simulate(5, 100) print(X.shape) #print(t[-1], X[-1, :]) # Plot results plt.plot(X[:, 0], X[:, 2], '.') plt.show()
def create_model():
def pendulum(t, X, sw):
"""
The ODE to be simulated. The parameter sw should be fixed during
the simulation and only be changed during the event handling.
"""
#X = X.copy()
g = 9.81
x = X[0]
vx = X[2]
vy = X[3]
return np.array([vx, vy, -(np.pi**2)*x, -g, 1.0])
def state_events(t, X, sw):
"""
This is our function that keep track of our events, when the sign
of any of the events has changed, we have an event.
"""
x = X[0]
y = X[1]
return [x - y]
#return np.array([x - y])
def handle_event(solver, event_info):
"""
Event handling. This functions is called when Assimulo finds an event as
specified by the event functions.
"""
state_info = event_info[0] #We are only interested in state events info
if state_info[0] != 0: #Check if the first event function have been triggered
if solver.sw[0]: #If the switch is True the pendulum bounces
X = solver.y
X[1] = X[0] + 1e-3
X[3] = 0.9*(X[2] - X[3])
#solver.sw[0] = not solver.sw[0] #Change event function
#Initial values
phi = 1.0241592; Y0 = -13.0666666; A = 2.0003417; w = np.pi
y0 = [A*np.sin(phi), 1+A*np.sin(phi), A*w*np.cos(phi), Y0 - A*w*np.cos(phi)-1, 0] #Initial states
t0 = 0.0 #Initial time
switches0 = [True] #Initial switches
#Create an Assimulo Problem
mod = Explicit_Problem(pendulum, y0, t0, sw0=switches0)
mod.state_events = state_events #Sets the state events to the problem
mod.handle_event = handle_event #Sets the event handling to the problem
mod.name = 'Bouncing Ball on Sonusoidal Platform' #Sets the name of the problem
#Create an Assimulo solver (CVode)
sim = CVode(mod)
#sim = LSODAR(mod)
sim.options['verbosity'] = 40
#Specifies options
sim.discr = 'Adams' #Sets the discretization method
sim.iter = 'FixedPoint' #Sets the iteration method
sim.rtol = 1.e-8 #Sets the relative tolerance
sim.atol = 1.e-6 #Sets the absolute tolerance
return sim
def create_model():
def nav(t, X, sw):
"""
The ODE to be simulated. The parameter sw should be fixed during
the simulation and only be changed during the event handling.
"""
A, b = get_dyn(sw2mode(sw))
return np.dot(A, X) + b
def state_events(t, X, sw):
"""
This is our function that keep track of our events, when the sign
of any of the events has changed, we have an event.
"""
#TODO: is this the best way?
mode = sw2mode(sw)
g = get_guard_vals(X, mode)
G = [g[0], g[1], g[2], g[3]] # y == 0
if debug:
print(mode)
print('G =', G)
return G
def handle_event(solver, event_info):
"""
Event handling. This functions is called when Assimulo finds an event as
specified by the event functions.
"""
state_info = event_info[
0] #We are only interested in state events info
if debug:
print('############### EVENT DETECTED')
g = state_info
if g[0] <= 0 or g[1] <= 0 or g[2] <= 0 or g[3] <= 0:
mode = sw2mode(solver.sw)
mode_ = new_mode(g, mode)
if debug:
print('############### new_mode =', mode_)
solver.sw = mode2sw(mode_)
#Initial values
y0 = [0., 0., 0., 0.] #Initial states
t0 = 5.0 #Initial time
switches0 = [False] * NUM_MODES #Initial switches
# Without the below statemment, it hits an error
switches0[79] = True
#Create an Assimulo Problem
mod = Explicit_Problem(nav, y0, t0, sw0=switches0)
mod.state_events = state_events #Sets the state events to the problem
mod.handle_event = handle_event #Sets the event handling to the problem
mod.name = 'nav30' #Sets the name of the problem
#Create an Assimulo solver (CVode)
sim = CVode(mod)
#sim = LSODAR(mod)
#sim = RungeKutta34(mod)
#sim.options['verbosity'] = 20 #LOUD
#sim.options['verbosity'] = 40 #WHISPER
sim.verbosity = 40 #WHISPER
#sim.display_progress = True
#sim.options['minh'] = 1e-4
#sim.options['rtol'] = 1e-3
# #Specifies options
# sim.discr = 'Adams' #Sets the discretization method
# sim.iter = 'FixedPoint' #Sets the iteration method
# sim.rtol = 1.e-8 #Sets the relative tolerance
# sim.atol = 1.e-6 #Sets the absolute tolerance
return sim
def create_model():
def pendulum(t, X, sw):
"""
The ODE to be simulated. The parameter sw should be fixed during
the simulation and only be changed during the event handling.
"""
g = 1
Y = X.copy()
Y[0] = X[2] #x_dot
Y[1] = X[3] #y_dot
Y[2] = 0 #vx_dot
Y[3] = -g #vy_dot
return Y
def state_events(t, X, sw):
"""
This is our function that keep track of our events, when the sign
of any of the events has changed, we have an event.
"""
return [X[1]] # y == 0
def handle_event(solver, event_info):
"""
Event handling. This functions is called when Assimulo finds an event as
specified by the event functions.
"""
state_info = event_info[
0] #We are only interested in state events info
if state_info[
0] != 0: #Check if the first event function have been triggered
if solver.sw[0]:
X = solver.y
if X[3] < 0: # if the ball is falling (vy < 0)
# bounce!
#X[1] = 1e-5 # used with CVode
X[1] = 1e-3 # gives better results with Dopri
X[3] = -0.75 * X[3]
#solver.sw[0] = not solver.sw[0] #Change event function
#Initial values
y0 = [0., 0., 0., 0.] #Initial states
t0 = 0.0 #Initial time
switches0 = [True] #Initial switches
#Create an Assimulo Problem
mod = Explicit_Problem(pendulum, y0, t0, sw0=switches0)
mod.state_events = state_events #Sets the state events to the problem
mod.handle_event = handle_event #Sets the event handling to the problem
mod.name = 'Bouncing Ball in X-Y' #Sets the name of the problem
#Create an Assimulo solver (CVode)
# leaks memory!!
#sim = CVode(mod)
# hands and possibly leaks memory
#sim = LSODAR(mod)
#sim = RungeKutta34(mod)
sim = Dopri5(mod)
#sim.options['verbosity'] = 20 #LOUD
sim.verbosity = 40 #WHISPER
#sim.display_progress = False
#sim.options['minh'] = 1e-4
#sim.options['rtol'] = 1e-3
# What is time_limit?
sim.time_limit = 1
# #Specifies options
# sim.discr = 'Adams' #Sets the discretization method
# sim.iter = 'FixedPoint' #Sets the iteration method
# sim.rtol = 1.e-8 #Sets the relative tolerance
# sim.atol = 1.e-6 #Sets the absolute tolerance
return sim
def create_model():
def pendulum(t, X, sw):
"""
The ODE to be simulated. The parameter sw should be fixed during
the simulation and only be changed during the event handling.
"""
X = X.copy()
X[0] = X[1]
X[1] = -1 + 0.04 * (X[1]**2) * np.sin(X[1])
X[2] = 1
return X
def state_events(t, X, sw):
"""
This is our function that keep track of our events, when the sign
of any of the events has changed, we have an event.
"""
return [X[0] - np.sin(X[2])]
def handle_event(solver, event_info):
"""
Event handling. This functions is called when Assimulo finds an event as
specified by the event functions.
"""
state_info = event_info[
0] #We are only interested in state events info
if state_info[
0] != 0: #Check if the first event function have been triggered
if solver.sw[0]: #If the switch is True the pendulum bounces
X = solver.y
if X[1] - np.cos(X[2]) < 0:
X[1] = -0.9 * X[1] + 1.9 * np.cos(X[2])
#solver.sw[0] = not solver.sw[0] #Change event function
#Initial values
y0 = [0, 0, 0] #Initial states
t0 = 0.0 #Initial time
switches0 = [True] #Initial switches
#Create an Assimulo Problem
mod = Explicit_Problem(pendulum, y0, t0, sw0=switches0)
mod.state_events = state_events #Sets the state events to the problem
mod.handle_event = handle_event #Sets the event handling to the problem
mod.name = 'Bouncing Ball on Sonusoidal Platform' #Sets the name of the problem
#Create an Assimulo solver (CVode)
sim = CVode(mod)
#sim = LSODAR(mod)
#sim.options['verbosity'] = 20 #LOUD
sim.options['verbosity'] = 40 #WHISPER
#sim.options['minh'] = 1e-4
#sim.options['rtol'] = 1e-3
#Specifies options
sim.discr = 'Adams' #Sets the discretization method
sim.iter = 'FixedPoint' #Sets the iteration method
sim.rtol = 1.e-8 #Sets the relative tolerance
sim.atol = 1.e-6 #Sets the absolute tolerance
return sim
def create_model():
def pendulum(t, X, sw):
"""
The ODE to be simulated. The parameter sw should be fixed during
the simulation and only be changed during the event handling.
"""
X = X.copy()
X[0] = X[1]
X[1] = -1 + 0.04 * (X[1]**2) * np.sin(X[1])
X[2] = 1
return X
def state_events(t, X, sw):
"""
This is our function that keep track of our events, when the sign
of any of the events has changed, we have an event.
"""
return [X[0] - np.sin(X[2])]
def handle_event(solver, event_info):
"""
Event handling. This functions is called when Assimulo finds an event as
specified by the event functions.
"""
state_info = event_info[0] #We are only interested in state events info
if state_info[0] != 0: #Check if the first event function have been triggered
if solver.sw[0]: #If the switch is True the pendulum bounces
X = solver.y
if X[1] - np.cos(X[2]) < 0:
X[1] = -0.9*X[1] + 1.9*np.cos(X[2])
#solver.sw[0] = not solver.sw[0] #Change event function
#Initial values
y0 = [0, 0, 0] #Initial states
t0 = 0.0 #Initial time
switches0 = [True] #Initial switches
#Create an Assimulo Problem
mod = Explicit_Problem(pendulum, y0, t0, sw0=switches0)
mod.state_events = state_events #Sets the state events to the problem
mod.handle_event = handle_event #Sets the event handling to the problem
mod.name = 'Bouncing Ball on Sonusoidal Platform' #Sets the name of the problem
#Create an Assimulo solver (CVode)
sim = CVode(mod)
#sim = LSODAR(mod)
#sim.options['verbosity'] = 20 #LOUD
sim.options['verbosity'] = 40 #WHISPER
#sim.options['minh'] = 1e-4
#sim.options['rtol'] = 1e-3
#Specifies options
sim.discr = 'Adams' #Sets the discretization method
sim.iter = 'FixedPoint' #Sets the iteration method
sim.rtol = 1.e-8 #Sets the relative tolerance
sim.atol = 1.e-6 #Sets the absolute tolerance
return sim
def run_example():
def pendulum(t,y,sw):
"""
The ODE to be simulated. The parameter sw should be fixed during
the simulation and only be changed during the event handling.
"""
l=1.0
g=9.81
yd_0 = y[1]
yd_1 = -g/l*N.sin(y[0])
return N.array([yd_0, yd_1])
def state_events(t,y,sw):
"""
This is our function that keep track of our events, when the sign
of any of the events has changed, we have an event.
"""
if sw[0]:
e_0 = y[0]+N.pi/4.
else:
e_0 = y[0]
return N.array([e_0])
def handle_event(solver, event_info):
"""
Event handling. This functions is called when Assimulo finds an event as
specified by the event functions.
"""
state_info = event_info[0] #We are only interested in state events info
if state_info[0] != 0: #Check if the first event function have been triggered
if solver.sw[0]: #If the switch is True the pendulum bounces
solver.y[1] = -0.9*solver.y[1] #Change the velocity and lose energy
solver.sw[0] = not solver.sw[0] #Change event function
#Initial values
y0 = [N.pi/2.0, 0.0] #Initial states
t0 = 0.0 #Initial time
switches0 = [True] #Initial switches
#Create an Assimulo Problem
mod = Explicit_Problem(pendulum, y0, t0, sw0=switches0)
mod.state_events = state_events #Sets the state events to the problem
mod.handle_event = handle_event #Sets the event handling to the problem
mod.name = 'Pendulum with events' #Sets the name of the problem
#Create an Assimulo solver (CVode)
sim = CVode(mod)
#Specifies options
sim.discr = 'Adams' #Sets the discretization method
sim.iter = 'FixedPoint' #Sets the iteration method
sim.rtol = 1.e-8 #Sets the relative tolerance
sim.atol = 1.e-6 #Sets the absolute tolerance
#Simulation
ncp = 200 #Number of communication points
tfinal = 10.0 #Final time
t,y = sim.simulate(tfinal, ncp) #Simulate
#Print event information
sim.print_event_data()
#Plot
P.plot(t,y)
P.show()
def create_model():
def pendulum(t, X, sw):
"""
The ODE to be simulated. The parameter sw should be fixed during
the simulation and only be changed during the event handling.
"""
g = 1
Y = X.copy()
Y[0] = X[2] #x_dot
Y[1] = X[3] #y_dot
Y[2] = 0 #vx_dot
Y[3] = -g #vy_dot
return Y
def state_events(t, X, sw):
"""
This is our function that keep track of our events, when the sign
of any of the events has changed, we have an event.
"""
return [X[1]] # y == 0
def handle_event(solver, event_info):
"""
Event handling. This functions is called when Assimulo finds an event as
specified by the event functions.
"""
state_info = event_info[0] #We are only interested in state events info
if state_info[0] != 0: #Check if the first event function have been triggered
if solver.sw[0]:
X = solver.y
if X[3] < 0: # if the ball is falling (vy < 0)
# bounce!
X[1] = 1e-5
X[3] = -0.75*X[3]
#solver.sw[0] = not solver.sw[0] #Change event function
#Initial values
y0 = [0., 0., 0., 0.] #Initial states
t0 = 0.0 #Initial time
switches0 = [True] #Initial switches
#Create an Assimulo Problem
mod = Explicit_Problem(pendulum, y0, t0, sw0=switches0)
mod.state_events = state_events #Sets the state events to the problem
mod.handle_event = handle_event #Sets the event handling to the problem
mod.name = 'Bouncing Ball in X-Y' #Sets the name of the problem
#Create an Assimulo solver (CVode)
sim = CVode(mod)
#sim = LSODAR(mod)
#sim = RungeKutta34(mod)
#sim.options['verbosity'] = 20 #LOUD
sim.verbosity = 40 #WHISPER
#sim.display_progress = True
#sim.options['minh'] = 1e-4
#sim.options['rtol'] = 1e-3
# #Specifies options
# sim.discr = 'Adams' #Sets the discretization method
# sim.iter = 'FixedPoint' #Sets the iteration method
# sim.rtol = 1.e-8 #Sets the relative tolerance
# sim.atol = 1.e-6 #Sets the absolute tolerance
return sim
def create_model():
def pendulum(t, X, sw):
"""
The ODE to be simulated. The parameter sw should be fixed during
the simulation and only be changed during the event handling.
"""
#X = X.copy()
g = 9.81
x = X[0]
vx = X[2]
vy = X[3]
return np.array([vx, vy, -(np.pi**2) * x, -g, 1.0])
def state_events(t, X, sw):
"""
This is our function that keep track of our events, when the sign
of any of the events has changed, we have an event.
"""
x = X[0]
y = X[1]
return [x - y]
#return np.array([x - y])
def handle_event(solver, event_info):
"""
Event handling. This functions is called when Assimulo finds an event as
specified by the event functions.
"""
state_info = event_info[
0] #We are only interested in state events info
if state_info[
0] != 0: #Check if the first event function have been triggered
if solver.sw[0]: #If the switch is True the pendulum bounces
X = solver.y
X[1] = X[0] + 1e-3
X[3] = 0.9 * (X[2] - X[3])
#solver.sw[0] = not solver.sw[0] #Change event function
#Initial values
phi = 1.0241592
Y0 = -13.0666666
A = 2.0003417
w = np.pi
y0 = [
A * np.sin(phi), 1 + A * np.sin(phi), A * w * np.cos(phi),
Y0 - A * w * np.cos(phi) - 1, 0
] #Initial states
t0 = 0.0 #Initial time
switches0 = [True] #Initial switches
#Create an Assimulo Problem
mod = Explicit_Problem(pendulum, y0, t0, sw0=switches0)
mod.state_events = state_events #Sets the state events to the problem
mod.handle_event = handle_event #Sets the event handling to the problem
mod.name = 'Bouncing Ball on Sonusoidal Platform' #Sets the name of the problem
#Create an Assimulo solver (CVode)
sim = CVode(mod)
#sim = LSODAR(mod)
sim.options['verbosity'] = 40
#Specifies options
sim.discr = 'Adams' #Sets the discretization method
sim.iter = 'FixedPoint' #Sets the iteration method
sim.rtol = 1.e-8 #Sets the relative tolerance
sim.atol = 1.e-6 #Sets the absolute tolerance
return sim
if solver.sw[0]: #If the switch is True the pendulum bounces
solver.y[1] = -0.9*solver.y[1] #Change the velocity and lose energy
solver.sw[0] = not solver.sw[0] #Change event function
#Initial values
y0 = [N.pi/2.0, 0.0] #Initial states
t0 = 0.0 #Initial time
switches0 = [True] #Initial switches
#Create an Assimulo Problem
mod = Explicit_Problem(pendulum, y0, t0, sw0=switches0)
mod.state_events = state_events #Sets the state events to the problem
mod.handle_event = handle_event #Sets the event handling to the problem
mod.name = 'Pendulum with events' #Sets the name of the problem
#Create an Assimulo solver (CVode)
sim = CVode(mod)
#Specifies options
sim.discr = 'Adams' #Sets the discretization method
sim.iter = 'FixedPoint' #Sets the iteration method
sim.rtol = 1.e-8 #Sets the relative tolerance
sim.atol = 1.e-6 #Sets the absolute tolerance
#Simulation
ncp = 200 #Number of communication points