def precompute_redfield_tensor_finegrid(self, t_init, t_final, dt,
integrator):
if self.is_verbose:
print("\n--- Precomputing the Redfield tensor on a fine RK4 grid")
int_order = integrator.order
c = integrator.c
n_timesteps = int((t_final - t_init) / dt + 1)
self.redfield_tensor_ni = []
cost = []
rate_file = open('rate_%s.dat' % (self.method), 'w')
for n in range(n_timesteps):
self.redfield_tensor_ni.append([])
for i in range(int_order):
t = t_init + n * dt + c[i] * dt
self.make_redfield_tensor(t)
self.redfield_tensor_ni[n].append(self.redfield_tensor)
cost.append(
utils.tensor_diff(self.redfield_tensor,
self.redfield_tensor_ni[n - 1][i]))
if n > 0 and cost[n] < self.markov_tol * np.std(cost):
if self.is_verbose:
print("\n--- Tensor has stopped changing at t ="), t
self.n_markov = n
rate_file.close()
break
if n > 0 and t >= self.markov_time:
if self.is_verbose:
print("\n--- Tensor calculation stopped at t ="), t
self.n_markov = n
rate_file.close()
break
rate_file.write('%0.6f ' % (t))
for row in self.redfield_tensor:
for R in row:
rate_file.write('%0.6f %0.6f ' % (R.real, R.imag))
rate_file.write('\n')
self.n_markov = n
rate_file.close()
if self.is_verbose:
print("\n--- Done precomputing the Redfield tensor")
def precompute_redfield_tensor_finegrid(self, t_init, t_final, dt, integrator):
if self.is_verbose:
print "\n--- Precomputing the Redfield tensor on a fine RK4 grid"
int_order = integrator.order
c = integrator.c
n_timesteps = int( (t_final-t_init)/dt + 1 )
self.redfield_tensor_ni = []
cost = []
rate_file = open('rate_%s.dat'%(self.method),'w')
for n in range(n_timesteps):
self.redfield_tensor_ni.append([])
for i in range(int_order):
t = t_init + n*dt + c[i]*dt
self.make_redfield_tensor(t)
self.redfield_tensor_ni[n].append(self.redfield_tensor)
cost.append( utils.tensor_diff( self.redfield_tensor,
self.redfield_tensor_ni[n-1][i] ) )
if n > 0 and cost[n] < self.markov_tol*np.std(cost):
if self.is_verbose:
print "\n--- Tensor has stopped changing at t =", t
self.n_markov = n
rate_file.close()
break
if n > 0 and t >= self.markov_time:
if self.is_verbose:
print "\n--- Tensor calculation stopped at t =", t
self.n_markov = n
rate_file.close()
break
rate_file.write('%0.6f '%(t))
for row in self.redfield_tensor:
for R in row:
rate_file.write('%0.6f %0.6f '%(R.real, R.imag))
rate_file.write('\n')
self.n_markov = n
rate_file.close()
if self.is_verbose:
print "\n--- Done precomputing the Redfield tensor"
def precompute_redfield_tensor(self, t_init, t_final, dt):
"""Precompute the time-dependent Redfield-like tensor, store in array.
Parameters
----------
t_init : float
Initial time at which to start precomputing.
f_final : float
Final time at which to stop precomputing.
dt : float
Timestep for precomputing.
integrator : Integrator
An instance of the pyrho Integrator class.
Notes
-----
The tensor is stored on a coarse grid which is ignorant to the
Integrator grid (e.g. RK4).
"""
if self.is_verbose:
print "\n--- Precomputing the Redfield tensor"
n_timesteps = int( (t_final-t_init)/dt + 1 )
self.redfield_tensor_n = []
redfield_tensor_integral_n = []
cost = []
if self.method == 'TCL2':
redfield_tensor_n = []
for time in np.arange(0.0, t_init, dt):
self.make_redfield_tensor(time)
redfield_tensor_n.append(self.redfield_tensor)
redfield_tensor_integral_0_t_init = np.trapz(redfield_tensor_n, dx=dt, axis=0)
for n in range(n_timesteps):
time = t_init + n*dt
self.make_redfield_tensor(time)
self.redfield_tensor_n.append(self.redfield_tensor)
# Collect running integral for TCL2
if self.method == 'TCL2':
redfield_tensor_integral_n.append(redfield_tensor_integral_0_t_init
+ np.trapz(self.redfield_tensor_n[:n+1], dx=dt, axis=0) )
cost.append( utils.tensor_diff( self.redfield_tensor,
self.redfield_tensor_n[n-1] ) )
if n > 0 and cost[n] < self.markov_tol*np.std(cost):
if self.is_verbose:
print "\n--- Tensor has stopped changing at t =", time
self.n_markov = n
break
if n > 0 and time >= self.markov_time:
if self.is_verbose:
print "\n--- Tensor calculation stopped at t =", time
self.n_markov = n
break
self.n_markov = n
if self.method == 'TCL2':
self.redfield_tensor_n = redfield_tensor_integral_n
if self.is_verbose:
print "\n--- Done precomputing the Redfield tensor"
cost_file = open('cost_%s.dat'%(self.method),'w')
rate_file = open('rate_%s.dat'%(self.method),'w')
for n in range(self.n_markov):
time = t_init + n*dt
cost_file.write('%0.6f %0.6f %0.6f %0.6f\n'
%(time, cost[n], np.std(cost[:n+1]), self.markov_tol))
rate_file.write('%0.6f '%(time))
for row in self.redfield_tensor_n[n]:
for R in row:
rate_file.write('%0.6f %0.6f '%(R.real, R.imag))
rate_file.write('\n')
cost_file.close()
rate_file.close()
def precompute_redfield_tensor(self, t_init, t_final, dt):
"""Precompute the time-dependent Redfield-like tensor, store in array.
Parameters
----------
t_init : float
Initial time at which to start precomputing.
f_final : float
Final time at which to stop precomputing.
dt : float
Timestep for precomputing.
integrator : Integrator
An instance of the pyrho Integrator class.
Notes
-----
The tensor is stored on a coarse grid which is ignorant to the
Integrator grid (e.g. RK4).
"""
if self.is_verbose:
print "\n--- Precomputing the Redfield tensor"
n_timesteps = int( (t_final-t_init)/dt + 1 )
self.redfield_tensor_n = []
redfield_tensor_integral_n = []
cost = []
for n in range(n_timesteps):
t = t_init + n*dt
self.make_redfield_tensor(t)
self.redfield_tensor_n.append(self.redfield_tensor)
# Collect running integral for TCL2
if self.method == 'TCL2':
redfield_tensor_integral_n.append(
np.trapz(self.redfield_tensor_n[:n+1], dx=dt, axis=0) )
cost.append( utils.tensor_diff( self.redfield_tensor,
self.redfield_tensor_n[n-1] ) )
if n > 0 and cost[n] < self.markov_tol*np.std(cost):
if self.is_verbose:
print "\n--- Tensor has stopped changing at t =", t
self.n_markov = n
break
if n > 0 and t >= self.markov_time:
if self.is_verbose:
print "\n--- Tensor calculation stopped at t =", t
self.n_markov = n
break
self.n_markov = n
if self.method == 'TCL2':
self.redfield_tensor_n = redfield_tensor_integral_n
if self.is_verbose:
print "\n--- Done precomputing the Redfield tensor"
cost_file = open('cost_%s.dat'%(self.method),'w')
rate_file = open('rate_%s.dat'%(self.method),'w')
for n in range(self.n_markov):
t = t_init + n*dt
cost_file.write('%0.6f %0.6f %0.6f %0.6f\n'
%(t, cost[n], np.std(cost[:n+1]), self.markov_tol))
rate_file.write('%0.6f '%(t))
for row in self.redfield_tensor_n[n]:
for R in row:
rate_file.write('%0.6f %0.6f '%(R.real, R.imag))
rate_file.write('\n')
cost_file.close()
rate_file.close()
