def tauLeap(model, tmax, tau=1, track=False, silent=False, propagate=False, **kwargs) :
# Initialisation ##########################################################
# If user requested to propagate old results, don't build the model
if not propagate :
model.build(silent=True) # initialise model
# Time array
t = [0]
# Initialise the trace
trace = model.X[:]
# Timestep and tracking indices
idx = 0
tracking_idx = -1;
# Start the progress bar
if not silent :
helpers.progBarStart()
# Preallocate array of tracked reactions
if track :
tracked_trans_array = np.zeros((model.N_events,1)) #int(tmax/tau)))
counter = 0
# Which transitions need to be capped ?
cappedEvents = -(model.transition * (model.transition < 0))
# Simulation loop #########################################################
while t[-1] < tmax :
# Compute a rates vector
rates = [rate(model.X, t[-1]) for rate in model.rates]
# Ensure all rates are valid
if np.any(np.array(rates) < 0) :
raise helpers.SimulationError("Negative rates found.")
# Ensure there are possible events to continue with
if not np.any(np.array(rates) > 0) :
if not silent :
print "No more possible events, stopping early !"
return (t, trace) if not track else (t, trace, tracked_trans_array)
def gillespie(model, tmax, track=False, silent=False, propagate=False, **kwargs) :
# Initialise ##############################################################
# Generate this many random uniforms at once, for speed
randsize = 1000
# Timestep at which random numbers were last updated
tlast = 0
# Time array
t = [0]
# If user requested to propagate old results, don't build the model
if not propagate :
model.build(silent=True) # initialise model
# Initialise the trace
trace = []
trace.append(model.X[:].astype(int))
# Preallocate array of tracked reactions
if track :
tracked_trans_array = []
# Pregenerate some random numbers
rand = np.random.uniform(size=1000)
rcount = 0
# Start the progress bar
if not silent :
helpers.progBarStart()
# Simulation loop #########################################################
while t[-1] < tmax :
# Compute a rates vector
rates = [rate(model.X, t[-1]) for rate in model.rates]
# Ensure all rates are statistically valid
if np.any(np.array(rates) < 0) :
raise helpers.SimulationError("Negative rates found.")
# Ensure there are possible events to continue with
if not np.any(np.array(rates) > 0) :
if not silent :
print("No more possible events, stopping early !")
out = [t, np.array(trace)]
if track :
out.append(np.array(tracked_trans_array))
return out
# Draw a waiting time
t.append(t[-1] + np.random.exponential(1./np.sum(rates)))
# Select which transition occurs
trans = np.where(np.random.uniform() < \
np.cumsum(rates / np.sum(rates)))[0][0]
# Update the state space
model.X += model.transition[:, trans].astype(int)
# If we're tracking, keep track of the transition
if track :
currentevent = np.zeros(model.N_events)
currentevent[trans] = 1
tracked_trans_array.append(currentevent)
"""
tracked_trans_array[trans, tcount] = 1
tcount += 1
if tcount >= tracked_trans_array.shape[1] :
tracked_trans_array = np.hstack((tracked_trans_array, \
np.zeros((model.N_events,randsize))))
"""
# At the end of randsize iterations, update randsize "adaptively"
rcount += 1
if rcount == randsize :
rcount = 0
randsize = max(1000, randsize * tmax / (tlast - t[-1]) - 1)
rand = np.random.uniform(size=randsize)
tlast = t[-1]
# Append new state space to trace
trace.append(list(model.X))
# Update progress bar
if not silent :
helpers.progBarUpdate(t[-2:], tmax)
# Termination #############################################################
# Reset state space
if not propagate :
model.X = np.array([model.initconds[x] for x in model.states],
dtype=int)
# Return
out = [t, np.array(trace)]
if track :
out.append(np.array(tracked_trans_array))
return out
def tauLeap(model, tmax, tau=1, track=False, silent=False, propagate=False, noNegStatesAllowed = True, **kwargs) :
# Initialisation ##########################################################
# If user requested to propagate old results, don't build the model
if not propagate :
model.build(silent=True) # initialise model
# Time array
t = [0]
# Initialise the trace
trace = []
trace.append(model.X[:].astype(int))
# Timestep and tracking indices
idx = 0
# Start the progress bar
if not silent :
helpers.progBarStart()
# Array of tracked reactions
if track :
tracked_trans_array = []#np.zeros((model.N_events,1)) #int(tmax/tau)))
# Simulation loop #########################################################
while t[-1] < tmax :
# Compute a rates vector
rates = [rate(model.X, t[-1]) for rate in model.rates]
# Ensure all rates are valid
if np.any(np.array(rates) < 0) :
print(t[-1])
print(rates)
print(model.X)
raise helpers.SimulationError("Negative rates found.")
# Ensure there are possible events to continue with
if not np.any(np.array(rates) > 0) :
if not silent :
print("No more possible events, stopping early !")
# Return
out = [t, np.array(trace)]
if track :
out.append(np.array(tracked_trans_array))
return out
#Estimate the total number of events per transition
estEvents = np.array([np.random.poisson(rate * tau) \
for rate in rates], dtype=int)
# Calculate transitions by statespace
#tempTransitions_array = model.transition * estEvents
# Create array of state space values to test against transitions
#tempStateSpace = np.tile(model.X.reshape([model.N_states,1]), model.N_events)
# Calculate net transitions by statespace
tempTransitions = np.sum(model.transition * estEvents, axis=1).astype(int)
# Calculate negative transitions by statespace
negTransitions = deepcopy(model.transition)
negTransitions[model.transition>=0] =0
tempNegTransitions = np.sum(negTransitions * estEvents, axis=1).astype(int)
# If tracking is on, check if there are any total negative transitions that go below the number
# individuals in the statespace
if track :
if noNegStatesAllowed & np.any(model.X + tempNegTransitions <0) :
# create blank new transitions vector
tempNewNegTransitions = np.zeros(model.N_states)
#create new Events vector
newEvents = np.zeros(model.N_events)
# initiate tempEvents vector as estEvents
tempEvents = deepcopy(estEvents)
while np.all(model.X + tempNewNegTransitions >0) :
#randomly pick an event from est Events
newEventIdx = np.random.choice(model.N_events,None,True, tempEvents.astype(float)/np.sum(tempEvents))
newEvents[newEventIdx] +=1
tempEvents[newEventIdx]-=1
#create vector of new negative transitions
tempNewNegTransitions = np.sum(negTransitions * newEvents, axis=1).astype(int)
diff = estEvents-newEvents
reductionRatio = min(1-diff[diff>0]/estEvents[diff>0])
#reductionRatio = max(newEvents/estEvents)
model.X += np.sum(model.transition*newEvents, axis=1).astype(int)
t.append(t[idx]+reductionRatio*tau)
tracked_trans_array.append(newEvents)
else :
model.X += np.sum(model.transition*estEvents, axis=1).astype(int)
t.append(t[idx]+tau)
tracked_trans_array.append(estEvents)
else :
#Check if negative states exist and if they are allowed
if noNegStatesAllowed & np.any(model.X + tempTransitions < 0) :
#if negative states exist but are not allowed, find where they are
tempNewModelStates =model.X + tempTransitions
negidx= np.where(tempNewModelStates<0)
#calculate ratio by which to reduce all transitions (max ratio of differences in events)
reductionRatio = min(1-tempNewModelStates[negidx]/tempTransitions[negidx])
#Adjust number of events done down by ratio
estEvents_new = reductionRatio*estEvents
# Update the state space
model.X += np.sum(model.transition * estEvents_new, axis=1).astype(int)
#update t by adjusted tau
t.append(t[idx] + tau * reductionRatio)
else :
# Otherwise, add a full tau increment to the time array
t.append(t[idx] + tau)
# Update the state space
model.X += np.sum(model.transition * estEvents, axis=1).astype(int)
#check for negative
# randomly until go negative -- keep track of new events vs est events -- that is ratio
# #check if there are negative transitions
# # check it total number of negative transitions goes below 0
# if noNegStatesAllowed & np.any((tempStateSpace + tempTransitions_array )<0) :
# #if negative states exist but are not allowed, find where they are
# tempNewStateSpaceChanges = (tempStateSpace+tempTransitions_array)
# negidx = np.where(tempNewStateSpaceChanges <0)
# #calculate ratio by which to reduce all transitions (max ratio of differences in events)
# reductionRatio = min(1-tempNewStateSpaceChanges[negidx]/tempTransitions_array[negidx])
# #Adjust number of events done down by ratio
# estEvents_new = reductionRatio*estEvents
# # Update the state space
# model.X += np.sum(model.transition * estEvents_new, axis=1).astype(int)
# if track :
# tracked_trans_array.append(estEvents_new)
# print("time idx is")
# print(idx)
# print("time is")
# print(t[idx])
# print("estEvents_new are")
# print(estEvents_new)
# print("time idx is")
# print(idx)
# print("time is")
# print(t[idx])
# #update t by adjusted tau
# t.append(t[idx] + tau * reductionRatio)
# else :
# # Otherwise, add a full tau increment to the time array
# t.append(t[idx] + tau)
# if track :
# tracked_trans_array.append(estEvents)
# print("time idx is")
# print(idx)
# print("time is")
# print(t[idx])
# print("estEvents are")
# print(estEvents)
# # Update the state space
# model.X += np.sum(model.transition * estEvents, axis=1).astype(int)
# Append new state space to trace, increment timestep index
idx += 1
trace.append(list(model.X))
# Update progress bar
if not silent :
helpers.progBarUpdate(t[idx:(idx+1)],len(t))
# Record tracked reactions
#if track :
# tracked_trans_array.append(estEvents)
# Termination #############################################################
# Reset state space unless the user wants to carry it forward
if not propagate :
model.X = np.array([model.initconds[x] for x in model.states], dtype=int)
# Return
out = [t, np.array(trace)]
if track :
out.append(np.array(tracked_trans_array))
return out
def tauLeap(model, tmax, tau=1, track=False, silent=False, propagate=False, **kwargs) :
# Initialisation ##########################################################
# If user requested to propagate old results, don't build the model
if not propagate :
model.build(silent=True) # initialise model
# Time array
t = [0]
# Initialise the trace
trace = model.X[:]
# Timestep and tracking indices
idx = 0
tracking_idx = -1;
# Start the progress bar
if not silent :
helpers.progBarStart()
# Preallocate array of tracked reactions
if track :
tracked_trans_array = np.zeros((model.N_events,int(tmax/tau)))
counter = 0
# Which transitions need to be capped ?
cappedEvents = -(model.transition * (model.transition < 0))
# Simulation loop #########################################################
while t[-1] < tmax :
# Compute a rates vector
rates = [rate(model.X, t[-1]) for rate in model.rates]
# Ensure all rates are valid
if np.any(np.array(rates) < 0) :
raise helpers.SimulationError("Negative rates found.")
# Ensure there are possible events to continue with
if not np.any(np.array(rates) > 0) :
if not silent :
print "No more possible events, stopping early !"
return (t, trace) if not track else (t, trace, tracked_trans_array)
# What the hell was this madness ?
# It's here for book-keeping until next update, but
# serves no purpose... Too much caffeine ?!
"""
# Determine which events occurred after ensuring that there's
# a valid transition, and update the state space
if np.sum(rates) <= 0 :
if not silent :
print "Stopping early - no valid transitions !"
trace = np.delete(trace,range(idx+1,int(tmax/tau)+1),0)
t = np.delete(t,range(idx+1,int(tmax/tau)+1),0)
if track:
tracked_trans_array = np.delete(tracked_trans_array,range(idx+1,int(tmax/tau)+1),1)
break
"""
# Estimate the total number of events per transition
estEvents = np.array([np.random.poisson(rate * tau) \
for rate in rates], dtype=int)
# Find the maximum number of removals from a state that can occur
maxEvents = (cappedEvents * estEvents).sum(1)
# If we want more removals than are possible from that state :
if np.any((model.X - maxEvents) < 0) :
# Find the largest discrepancy
discrepancy = np.argmin(model.X - maxEvents)
# Adjust done events
estEvents = np.floor(estEvents * \
model.X[discrepancy] / float(maxEvents[discrepancy])).astype(int)
else :
# Otherwise, there's no discrepancy between our estimate and the possible max
discrepancy = -1
# If there's at least one event but we can't do them all :
if (discrepancy > -1) and np.sum(estEvents) > 0 :
# Then we do fewer events, so adjust time increment accordingly
t.append(t[idx] + tau * model.X[discrepancy] / float(maxEvents[discrepancy]))
else :
# Otherwise, add a full tau increment to the time array
t.append(t[idx] + tau)
# Update the state space
model.X += np.sum(model.transition * estEvents, axis=1).astype(int)
# Append new state space to trace, increment timestep index
idx += 1
trace = np.vstack((trace, model.X))
# Record tracked reactions
if track :
tracked_trans_array[:, idx] = estEvents
# Update progress bar
if not silent :
helpers.progBarUpdate(t[idx:(idx+1)], len(t))
# Termination #############################################################
# Reset state space unless the user wants to carry it forward
if not propagate :
model.X = np.array([model.initconds[x] for x in model.states], dtype=int)
# Return
return (t, trace, tracked_trans_array) if track else (t, trace)
def sample(self, T, trajectories=100, bootstraps=500, tvals=1000, alpha=0.95, silent=False, **kwargs) :
"""
t, means, CI_low, CI_high = scotch.model.sample(T, trajectories=100, bootstraps=500, tvals=1000, alpha=0.95)
------------------------------------------------------------------------------------------------------------
Return summary statistics.
T is the time until which the system is simulated.
trajectories is the number of realisations to simulate.
bootstraps is the number of bootstrap samples to draw to
compute the confidence intervals.
bootstraps=0 means CI_low and CI_high are not returned;
only the mean trajectory is calculated.
tvals is the number of time values to interpolate over to compute
means and confidence intervals, and the number of time values
returned to the user.
alpha is the level at which confidence intervals are computed.
The default, alpha=0.95, returns 95% confidence intervals around
the mean of the trajectories.
A number of optional arguments can be passed to this function.
algorithm="gillespie", algorithm="tauLeap"
Use the exact Gillespie Stochastic Simulation Algorithm, or
a tau-leaping approximation for speed. More algorithms to come.
If algorithm="tauLeap", you may want to specify
tau=delta_t, where delta_t is the timestep at which tau-leaping
should be done.
By default, tau=1.
If no algorithm is passed, we use the default algorithm as
defined in the model. If none is set, it defaults to Gillespie.
silent=False, silent=True
If silent, don't use progress bars or return warnings.
By default, silent=False.
propagate=False, propagate=True
If propagate, don't rebuild the model to initial conditions
every time this is run; carry forward the last state space.
By default, propagate=False.
track=False, track=True,
If track, we track all transitions as they occur and return
these as a third output variable.
By default, track=False. Tracking slows simulations considerably.
"""
# Sample repeatedly from the model and return summary statistics only
all_t = []
all_trace = []
if not silent :
print("Sampling trajectories.")
helpers.progBarStart()
# For each trajectory index :
for traj in range(trajectories) :
if not silent :
helpers.progBarUpdate([traj-1, traj], trajectories)
# Simulate the model
t, trace = self.simulate(T, silent=True, **kwargs)
# Append the time and traces to our arrays
all_t.append(t)
all_trace.append(trace)
if not silent :
print("\n")
# For each state variable, interpolate
int_t = np.linspace(0, T, tvals)
int_trace = {}
for dim_num, dim in enumerate(self.states) :
int_trace[dim] = []
for x, y in zip(all_t, all_trace) :
t = np.append(x, T)
trace = np.append(y[:, dim_num], np.nan)
int_trace[dim].append(interp1d(t, trace)(int_t))
int_trace[dim] = np.array(int_trace[dim])
# Calculate the mean
m = { dim : np.nanmean(int_trace[dim], axis=0) for dim in self.states }
if bootstraps :
# Bootstrap some 95% confidence intervals :
means = {}
# Draw a number of realisations with replacement
idx = np.random.randint(0, trajectories, (bootstraps, trajectories))
if not silent :
print("Bootstrapping.")
helpers.progBarStart()
# For each dimension in the state space
for dimidx, dim in enumerate(self.states) :
means[dim] = []
# and for each bootstrap iteration
for iidx, i in enumerate(idx) :
# Calculate the means of this iteration
means[dim].append(np.nanmean(int_trace[dim][i], axis=0))
if not silent :
helpers.progBarUpdate([dimidx*(iidx-1), dimidx*iidx], len(self.states)*bootstraps)
# After doing all iterations, sort the means
means[dim] = np.sort(np.array(means[dim]), axis=0)
# Extract intervals
ci_low = { dim : means[dim][int((1-alpha)*bootstraps/2.)] for dim in self.states }
ci_high = { dim : means[dim][int(1.-(1-alpha)*bootstraps/2.)] for dim in self.states }
# Return everything
return int_t, m, ci_low, ci_high
else :
return int_t, m