def make_T_Testing(self):
'''Generate the approximating transfer function using the identified
poles of the transfer function.
'''
self.T_testing = Potapov.get_Potapov(self.T,self.roots,self.vecs)
return
def make_vecs(self):
'''Generate an ordered list of vectors representing the form of the
Potapov factors.
'''
self.vecs = Potapov.get_Potapov_vecs(self.T,self.roots)
return
def time_sim(Example, omega = 0., t1=150, dt=0.05, freq=None,
port_in = 0, port_out = [0,1], kind='FP',
):
'''
takes an example and simulates it up to t1 increments of dt.
freq indicates the maximum frequency where we look for modes
omega indicates the frequency of driving. omega = 0 is DC.
port_in and port_out are where the system is driven.
'''
E = Example(max_freq = freq) if freq != None else Example()
E.run_Potapov()
T,T_testing,poles,vecs = E.get_outputs()
print "number of poles is ", len(poles)
num = len(poles)
[A,B,C,D] = Potapov.get_Potapov_ABCD(poles,vecs)
y0 = np.matrix([[0]]*A.shape[1])
t0 = 0
force_func = lambda t: np.cos(omega*t)
r = ode(f).set_integrator('zvode', method='bdf')
r.set_initial_value(y0, t0).set_f_params(A,B,force_func,port_in)
Y = [C*y0+D*force_func(t0)]
while r.successful() and r.t < t1:
r.integrate(r.t+dt)
#print r.t, r.y
u = force_func(r.t)
Y.append(C*r.y+D*u)
time = np.linspace(t0,t1,len(Y))
plot_time(time,Y,port_out,port_in,num=num,kind=kind)
return
def make_commensurate_vecs(self,):
self.commensurate_vecs = Potapov.get_Potapov_vecs(
self.T,self.commensurate_roots)
self.vecs = map(
lambda i: self.commensurate_vecs[self.map_root_to_commensurate_index[i]],
range(len(self.roots)) )
return
def make_vecs(self):
'''Generate an ordered list of vectors representing the form of the
Potapov factors.
'''
self.vecs = Potapov.get_Potapov_vecs(self.T, self.roots)
return
def make_T_Testing(self):
'''Generate the approximating transfer function using the identified
poles of the transfer function.
'''
self.T_testing = Potapov.get_Potapov(self.T, self.roots, self.vecs)
return
def make_commensurate_vecs(self, ):
self.commensurate_vecs = Potapov.get_Potapov_vecs(
self.T, self.commensurate_roots)
self.vecs = map(
lambda i: self.
commensurate_vecs[self.map_root_to_commensurate_index[i]],
range(len(self.roots)))
return
def get_Potapov_ABCD(self,z=0.,doubled=False):
'''
Find the ABCD matrices from the Time_Delay_Network.
Args:
z (optional [complex number]): location where to estimate D.
Return:
(tuple of matrices):
A,B,C,D matrices.
'''
A,B,C,D = Potapov.get_Potapov_ABCD(self.roots,self.vecs,self.T,z=z)
if not doubled:
return A,B,C,D
else:
A_d,C_d,D_d = map(double_up,(A,C,D))
B_d = -double_up(C.H)
return A_d,B_d,C_d,D_d
def time_sim(
Example,
omega=0.,
t1=150,
dt=0.05,
freq=None,
port_in=0,
port_out=[0, 1],
kind='FP',
):
'''
takes an example and simulates it up to t1 increments of dt.
freq indicates the maximum frequency where we look for modes
omega indicates the frequency of driving. omega = 0 is DC.
port_in and port_out are where the system is driven.
'''
E = Example(max_freq=freq) if freq != None else Example()
E.run_Potapov()
T, T_testing, poles, vecs = E.get_outputs()
print "number of poles is ", len(poles)
num = len(poles)
[A, B, C, D] = Potapov.get_Potapov_ABCD(poles, vecs)
y0 = np.matrix([[0]] * A.shape[1])
t0 = 0
force_func = lambda t: np.cos(omega * t)
r = ode(f).set_integrator('zvode', method='bdf')
r.set_initial_value(y0, t0).set_f_params(A, B, force_func, port_in)
Y = [C * y0 + D * force_func(t0)]
while r.successful() and r.t < t1:
r.integrate(r.t + dt)
#print r.t, r.y
u = force_func(r.t)
Y.append(C * r.y + D * u)
time = np.linspace(t0, t1, len(Y))
plot_time(time, Y, port_out, port_in, num=num, kind=kind)
return
def get_Potapov_ABCD(self, z=0., doubled=False):
'''
Find the ABCD matrices from the Time_Delay_Network.
Args:
z (optional [complex number]): location where to estimate D.
Return:
(tuple of matrices):
A,B,C,D matrices.
'''
A, B, C, D = Potapov.get_Potapov_ABCD(self.roots,
self.vecs,
self.T,
z=z)
if not doubled:
return A, B, C, D
else:
A_d, C_d, D_d = map(double_up, (A, C, D))
B_d = -double_up(C.H)
return A_d, B_d, C_d, D_d