def solve(self, refnode=gnd, period=1e-3, x0=None, timestep=1e-6, maxiterations=20):
self.period = period
toolkit = self.toolkit
irefnode = self.cir.get_node_index(refnode)
n = self.cir.n
dt = timestep
if x0 is None:
x = toolkit.zeros(n - 1) # currently without reference node !
else:
x = x0 # reference node not included !
# create vector with timepoints and a more fitting dt
times, dt = toolkit.linspace(0, period, num=int(period / dt), endpoint=True, retstep=True)
alpha = 1
def func(x):
x = self.solve_timestep(x, times[0], dt)
x0 = copy(x)
Jshoot = np.mat(toolkit.eye(n - 1))
C = copy(np.mat(self._C))
## Save C and transient jacobian for PAC analysis
self.Cvec = [copy(self._C)]
self.Jtvec = [copy(self._Jf)]
self.times = times
for t in times[1:]:
x = copy(self.solve_timestep(x, t, dt))
self.Cvec.append(copy(self._C))
self.Jtvec.append(copy(self._Jf))
Jshoot = np.mat(self._Jf).I * C * Jshoot
C = copy(np.mat(self._C))
residual = x0 - x
D = np.mat(toolkit.eye(n - 1))
return residual, D - alpha * Jshoot
## Find periodic steady state x-vector
x0_ss = analysis.fsolve(func, x, maxiter=maxiterations, toolkit=self.toolkit)
X = [x0_ss]
for t in times:
x = self.solve_timestep(X[-1], t, dt)
X.append(copy(x))
X = toolkit.array(X[1:]).T
# Insert reference node voltage
X = toolkit.concatenate((X[:irefnode], toolkit.zeros((1, len(times))), X[irefnode:]))
tpss = analysis.CircuitResult(self.cir, x=X, xdot=None, sweep_values=times, sweep_label="time", sweep_unit="s")
freqs, FX = freq_analysis(X[:, :-1], times[:-1])
fpss = analysis.CircuitResult(
self.cir, x=FX, xdot=None, sweep_values=freqs, sweep_label="freq", sweep_unit="Hz"
)
return InternalResultDict({"tpss": tpss, "fpss": fpss})
def solve_timestep(self, x0, t, dt, refnode=gnd):
toolkit = self.toolkit
concatenate, array = toolkit.concatenate, toolkit.array
n = self.cir.n
analysis_name = self.par.analysis
## Refer the voltages to the reference node by removing
## the rows and columns that corresponds to this node
irefnode = self.cir.get_node_index(refnode)
def func(x):
x = concatenate((x[:irefnode], array([0.0]), x[irefnode:]))
xlast = concatenate((x0[:irefnode], array([0.0]), x0[irefnode:]))
C = self.cir.C(x)
Geq = C / dt
ueq = -self.cir.q(xlast) / dt
f = self.cir.i(x) + self.cir.q(x) / dt + self.cir.u(
t, analysis=analysis_name) + ueq
J = self.cir.G(x) + Geq
(f, J, C) = remove_row_col((f, J, C), irefnode, self.toolkit)
self._Jf, self._C = J, C
return f, J
x = analysis.fsolve(func,
x0,
reltol=self.par.reltol,
toolkit=self.toolkit)
# Insert reference node voltage
#x = concatenate((x[:irefnode], array([0.0]), x[irefnode:]))
return x
def solve_timestep(self, x0, t, dt, refnode=gnd):
toolkit = self.toolkit
concatenate, array = toolkit.concatenate, toolkit.array
n = self.cir.n
analysis_name = self.par.analysis
## Refer the voltages to the reference node by removing
## the rows and columns that corresponds to this node
irefnode = self.cir.get_node_index(refnode)
def func(x):
x = concatenate((x[:irefnode], array([0.0]), x[irefnode:]))
xlast = concatenate((x0[:irefnode], array([0.0]), x0[irefnode:]))
C = self.cir.C(x)
Geq = C / dt
ueq = -self.cir.q(xlast) / dt
f = self.cir.i(x) + self.cir.q(x) / dt + self.cir.u(t, analysis=analysis_name) + ueq
J = self.cir.G(x) + Geq
(f, J, C) = remove_row_col((f, J, C), irefnode, self.toolkit)
self._Jf, self._C = J, C
return f, J
x = analysis.fsolve(func, x0, reltol=self.par.reltol, toolkit=self.toolkit)
# Insert reference node voltage
# x = concatenate((x[:irefnode], array([0.0]), x[irefnode:]))
return x
def solve(self,
refnode=gnd,
period=1e-3,
x0=None,
timestep=1e-6,
maxiterations=20):
self.period = period
toolkit = self.toolkit
irefnode = self.cir.get_node_index(refnode)
n = self.cir.n
dt = timestep
if x0 is None:
x = toolkit.zeros(n - 1) #currently without reference node !
else:
x = x0 # reference node not included !
#create vector with timepoints and a more fitting dt
times, dt = toolkit.linspace(0,
period,
num=int(period / dt),
endpoint=True,
retstep=True)
alpha = 1
def func(x):
x = self.solve_timestep(x, times[0], dt)
x0 = copy(x)
Jshoot = np.mat(toolkit.eye(n - 1))
C = copy(np.mat(self._C))
## Save C and transient jacobian for PAC analysis
self.Cvec = [copy(self._C)]
self.Jtvec = [copy(self._Jf)]
self.times = times
for t in times[1:]:
x = copy(self.solve_timestep(x, t, dt))
self.Cvec.append(copy(self._C))
self.Jtvec.append(copy(self._Jf))
Jshoot = np.mat(self._Jf).I * C * Jshoot
C = copy(np.mat(self._C))
residual = x0 - x
D = np.mat(toolkit.eye(n - 1))
return residual, D - alpha * Jshoot
## Find periodic steady state x-vector
x0_ss = analysis.fsolve(func,
x,
maxiter=maxiterations,
toolkit=self.toolkit)
X = [x0_ss]
for t in times:
x = self.solve_timestep(X[-1], t, dt)
X.append(copy(x))
X = toolkit.array(X[1:]).T
# Insert reference node voltage
X = toolkit.concatenate((X[:irefnode], toolkit.zeros(
(1, len(times))), X[irefnode:]))
tpss = analysis.CircuitResult(self.cir,
x=X,
xdot=None,
sweep_values=times,
sweep_label='time',
sweep_unit='s')
freqs, FX = freq_analysis(X[:, :-1], times[:-1])
fpss = analysis.CircuitResult(self.cir,
x=FX,
xdot=None,
sweep_values=freqs,
sweep_label='freq',
sweep_unit='Hz')
return InternalResultDict({'tpss': tpss, 'fpss': fpss})