def runSecSim(self, tMainSim):
params = self.params
# Define the parameters
eqns_params = {'k1':params.k1,
'k2':params.k2,
'k3':params.k3,
's1_in':params.s1_in,
's2_in':params.s2_in,
'a':params.a,
'm1':params.m1,
'm2':params.m2,
'k_s1':params.k_s1,
'k_s2':params.k_s2,
'k_I':params.k_I,
'D':params.D,
'tau1':params.tau1,
'tau2':params.tau2}
# Initialize the solver
self.dde = dde23(eqns=self.eqns, params=eqns_params, supportcode=self.support_c_code)
# Initialize history of the state variables
self.initHist(tMainSim)
# Set the simulation parameters
tFinalSecSim = self.solverParams.mainSimStep
self.dde.set_sim_params(tfinal=tFinalSecSim, AbsTol=self.solverParams.absTol, RelTol=self.solverParams.relTol, dtmax=None)
# Run the secondary simulation
self.dde.run()
def enso_dde_model(kappa, tau, b, nyears = 120, subsample_to_monthly = False):
from pydelay import dde23
eqn = {'h' : '-tanh(kappa * h(t-tau)) + b*cos(2*pi*t)'}
params = {
'kappa' : kappa,
'tau' : tau,
'b' : b,
'pi' : np.pi
}
histfunc = {'h' : lambda t: 1.}
dde = dde23(eqns = eqn, params = params)
dde.set_sim_params(tfinal = 10000, dtmax = 0.01)
dde.hist_from_funcs(histfunc, 100)
dde.run()
dt = 0.001
sol = dde.sample(1000, 10000, dt) # 1 is year, int step is month
t = sol['t']
h = sol['h']
t = t[:nyears/dt]
h = h[:nyears/dt]
if subsample_to_monthly:
step = int((1/12.)/dt)
t = t[::step]
h = h[::step]
return t, h
def calcmsf(self, alpha, beta, transients=5, final=4000):
"""MSF ausrechnen.
"""
le = 0
self.params['alpha'] = alpha
self.params['beta'] = beta
system = neteqns(self.groups, self.H, self.T, self.eqns, params=self.params, coupling=self.coupling)
system.update(neteqns(self.groups, self.H, self.T, self.vareqns, params=self.params, coupling=self.coupling, var=True))
# print system # debug
for i in range(final):
sdde = dde23(eqns=system, params=self.params, debug=False)
sdde.set_sim_params(tfinal=self.params['tau'])
if i==0:
sdde.hist_from_arrays(self.__fillinitdict(self.transient, sdde.hist))
else:
norm = self.__calcnorm(linsol)
if i > transients:
le += log(norm)
sdde.hist_from_arrays(self.__renormalized(linsol, norm))
sdde.run()
sol = sdde.sol
linsol = sdde.sol_spl(self.resarray)
exponent = le/((i-transients)*self.params['tau'])
return exponent.real
def transient(self, initial_conditions, tmax):
"""Zunaechst die History mit der Zeitserie eines Systems fuellen.
Aber nur, wenn noch nichts gepickled und nichts an sys.argv[0]
(das File mit den Gleichungen) geändert wurde.
"""
import cPickle as pickle
import hashlib
file1 = hashlib.md5(open(sys.argv[0]).read()).hexdigest()+'.pickle'
try:
sol1 = pickle.load(open(file1,'r'))
print >> sys.stderr, 'Transiente wird aus {0} genommen'.format(file1)
except:
eqns1 = neteqns([[rowsum(self.G,0)]], self.H, self.T, self.eqns, params=self.params, coupling=self.coupling)
print >> sys.stderr, 'rechne Transiente für 1 System mit Gleichungen:'
print >> sys.stderr, eqns1 #Debug
dde1 = dde23(eqns=eqns1, params=self.params)
dde1.set_sim_params(tfinal=tmax)
for v in initial_conditions:
for w in dde1.hist:
if re.match(v,w):
dde1.hist[w] += initial_conditions[v]
dde1.run()
sol1 = dde1.sol
del(dde1)
pickle.dump(sol1,open(file1,'w'))
return sol1
def dde_solver(t_i,Ac_i,Am_i,Bc_i,Bm_i,Rm_i,AB_i,AR_i,tf):
# the model equations
eqns = {
'Ac' : '-k1*Rm*Ac',
'Am' : 'k1*Rm(t-tau1)*Ac(t-tau1)*Heavi(t-tau1) - k2*Am*Rm + k2*AR - k2*Am*Bm + k3*AB',
'Bc' : '-k4*Am*Bc',
'Bm' : 'k4*Am(t-tau2)*Bc(t-tau2)*Heavi(t-tau2) - k2*Am*Bm + k3*AB',
'Rm' : 'qR - k2*Am*Rm + k2*AR',
'AB' : 'k2*Am*Bm - k3*AB',
'AR' : 'k2*Am*Rm - k2*AR',
}
# define parameters
params = {
'k1' : const.k1,
'k2' : const.k2,
'k3' : const.k3,
'k4' : const.k4,
'qR' : const.qR,
'tau1' : const.tau1,
'tau2' : const.tau2,
}
# initial conditions
histdict = {
't' : t_i,
'Ac' : Ac_i,
'Am' : Am_i,
'Bc' : Bc_i,
'Bm' : Bm_i,
'Rm' : Rm_i,
'AB' : AB_i,
'AR' : AR_i,
}
# intialize the solver
dde = dde23(eqns=eqns, params=params)
dde.hist_from_arrays(histdict,useend=False)
# set the simulation parameters
# (solve from t=0 to t=tf and limit the maximum step size to 1.0)
dde.set_sim_params(tfinal=tf, dtmax=1)
# run the simulator
dde.run()
# get the solutions from the history dict
t = dde.sol['t']
Ac= dde.sol['Ac']
Am= dde.sol['Am']
Bc = dde.sol['Bc']
Bm = dde.sol['Bm']
Rm = dde.sol['Rm']
AB = dde.sol['AB']
AR = dde.sol['AR']
return(t,Ac,Am,Bc,Bm,Rm,AB,AR)
def simulateInPieces(eqns, params, histfuncs, tfinal, num_pieces, sample_dt):
"""
Simulate until `tfinal` in `num_pieces` steps to avoid memory
overflow. Return the final solution sampled with a resolution of
`sample_dt`.
"""
piece_length = tfinal * 1.0 / num_pieces
n = 0
# simulatie first piece with the given `histfuncs`
dde = dde23(eqns=eqns, params=params)
dde.set_sim_params(tfinal=piece_length)
dde.hist_from_funcs(histfuncs)
dde.run()
maxinterval = 4
resolution = 1E-4
# set the history array for the next runs
hist = HistoryCache(dde, maxinterval, resolution)
# Sample the final result.
# You may choose to write something to disc isntead
result = dde.sample(0, piece_length, sample_dt)
n += 1
while n < num_pieces:
dde = dde23(eqns=eqns, params=params)
dde.set_sim_params(tfinal=piece_length)
hist.initializeHistory(dde)
dde.run()
# extend the previous result with the new piece
tmp = dde.sample(0, piece_length, sample_dt)
for key, value in tmp.iteritems():
# By definition the simulation always starts at t=0.
# So we have to shift the time array for the new piece
if key == 't':
result[key] = np.append(result[key], value + n * piece_length)
else:
result[key] = np.append(result[key], value)
n += 1
hist = HistoryCache(dde, maxinterval, resolution)
return result
def run_transient(self, inits, ttransients=20):
ttime = ttransients * self.params['tau']
tsystem = neteqns(self.groups, self.H, self.T, self.eqns, params=self.params, coupling=self.coupling)
tdde = dde23(eqns=tsystem, params=self.params)
tdde.set_sim_params(tfinal=ttime)
for v in inits:
for w in tdde.hist:
if re.match(v,w):
tdde.hist[w][-1] = inits[v]
tdde.run()
self.transient = tdde.sol_spl(self.resarray)
def __init__(self, eqns, G, H, T, params, coupling, noise):
self.G = G
self.H = H
self.T = T
self.params = params
self.coupling = coupling
self.eqns = eqns
self.noise = noise
self.sol = dict()
self.eqnsN = neteqns(self.G, self.H, self.T, self.eqns, params=self.params, coupling=self.coupling)
self.noiseN = netnoise(self.eqnsN, self.noise)
print >> sys.stderr, 'Gleichungen fuers ganze Netz:'
print >> sys.stderr, self.eqnsN #Debug
print >> sys.stderr, 'Noise fuers ganze Netz:'
print >> sys.stderr, self.noiseN #Debug
self.ddeN = dde23(eqns=self.eqnsN, params=self.params, noise=self.noiseN)
# import the solver
from pydelay import dde23
eqns = {'x': '-x + k*x(t-10) + A* f(w,t)'}
params = {'k': 0.1, 'w': 2.0, 'A': 0.5}
# We can define a c function to be used in the equations
mycode = """
double f(double w, double t) {
return sin(w*t);
}
"""
# initalise the solver
dde = dde23(eqns=eqns, params=params, supportcode=mycode)
# set the simulation parameters
dde.set_sim_params(tfinal=40)
# we can define the history as a python function
def myhist(t):
return 0.01 * t**2
dde.hist_from_funcs({'x': myhist})
# run the simulation
dde.run()
'n': '(p - n - (1.0 +n) * pow(abs(E),2))/T'
}
params = {
'a': 4.0,
'p': 1.0,
'T': 200.0,
'K': 0.1,
'tau': tau,
'nu': 10**-5,
'n0': 10.0
}
noise = {'E': 'sqrt(0.5*nu*(n+n0)) * (gwn() + ii*gwn())'}
dde = dde23(eqns=laser_equations, params=params, noise=noise)
dde.set_sim_params(tfinal=tfinal)
# use a dictionary to set the history
thist = np.linspace(0, tau, tfinal)
Ehist = np.zeros(len(thist)) + 1.0
nhist = np.zeros(len(thist)) - 0.2
dic = {'t': thist, 'E': Ehist, 'n': nhist}
# 'useend' is True by default in hist_from_dict and thus the
# time array is shifted correctly
dde.hist_from_arrays(dic)
dde.run()
t = dde.sol['t']
params = {
'k': 0.1,
'w': 2.0,
'A': 0.5
}
# We can define a c function to be used in the equations
mycode = """
double f(double w, double t) {
return sin(w*t);
}
"""
# initalise the solver
dde = dde23(eqns=eqns, params=params, supportcode=mycode)
# set the simulation parameters
dde.set_sim_params(tfinal=40)
# we can define the history as a python function
def myhist(t):
return 0.01*t**2
dde.hist_from_funcs({'x': myhist})
# run the simulation
dde.run()
sol = dde.sample(0.01)
t = sol['t']
def __init__(self, params = None, **kwargs):
if params == None:
params = AttributeDict(kwargs)
self.params = params
#Calculate the equilibrium point
def mu1(s, m, k):
return (m*s)/(k + s)
def mu2(s, m, k, k_I):
return (m*s)/(k + s + (s/k_I)*(s/k_I))
def eq_s1(s1, *args):
(_k1, _k2, _k3, _s1_in, _s2_in, a, m1, _m2, k_s1, _k_s2, _k_I, D, _tau1, _tau2) = args
return a*D - mu1(s1, m1, k_s1)
def eq_s2(s2, *args):
(_k1, _k2, _k3, _s1_in, _s2_in, a, _m1, m2, _k_s1, k_s2, k_I, D, _tau1, _tau2) = args
return a*D - mu2(s2, m2, k_s2, k_I)
eqs_args = (
params.k1, params.k2, params.k3,
params.s1_in, params.s2_in, params.a,
params.m1, params.m2,
params.k_s1, params.k_s2, params.k_I,
params.D, params.tau1, params.tau2)
s1_eqpnt = fsolve(eq_s1, 1.0, args = eqs_args)[0]
x1_eqpnt = (params.s1_in - s1_eqpnt)/(params.a*params.k1)
if x1_eqpnt < 0:
s1_eqpnt = params.s1_in
x1_eqpnt = 0.0
s2_eqpnt_sol, _info, ier, _msg = fsolve(eq_s2, 1.0, args = eqs_args, full_output = True)
if ier != 1 or s2_eqpnt_sol[0] < 0:
x2_eqpnt = 0.0
s2_eqpnt = params.s2_in + params.k2*mu1(s1_eqpnt, params.m1, params.k_s1) * x1_eqpnt / params.D
else:
s2_eqpnt = s2_eqpnt_sol[0]
x2_eqpnt = ((params.s2_in - s2_eqpnt)*params.D + params.k2*mu1(s1_eqpnt, params.m1, params.k_s1)*x1_eqpnt) \
/ (params.k3 * mu2(s2_eqpnt, params.m2, params.k_s2, params.k_I))
self.equilibriumPoint = [s1_eqpnt, x1_eqpnt, s2_eqpnt, x2_eqpnt]
if plotEqulibriumValuesAtTheEnd:
print "equilibrium point (s1, x1, s2, x2) = ", self.equilibriumPoint
# Define the specific growth rates (in 'C' source code)
support_c_code = """
double mu1(double s, double m, double k) {
return (m*s)/(k + s);
}
double mu2(double s, double m, double k, double k_I) {
return (m*s)/(k + s + (s/k_I)*(s/k_I));
}
"""
# Define the equations
eqns = {
's1': 'D*(s1_in - s1) - k1*mu1(s1, m1, k_s1)*x1',
'x1': 'mu1(s1(t-tau1), m1, k_s1)*x1(t-tau1) - a*D*x1',
's2': 'D*(s2_in - s2) + k2*mu1(s1, m1, k_s1)*x1 - k3*mu2(s2, m2, k_s2, k_I)*x2',
'x2': 'mu2(s2(t-tau2), m2, k_s2, k_I)*x2(t-tau2) - a*D*x2'
}
# Define the parameters
eqns_params = {
'k1' : params.k1,
'k2' : params.k2,
'k3' : params.k3,
's1_in' : params.s1_in,
's2_in' : params.s2_in,
'a' : params.a,
'm1' : params.m1,
'm2' : params.m2,
'k_s1' : params.k_s1,
'k_s2' : params.k_s2,
'k_I' : params.k_I,
'D' : params.D,
'tau1' : params.tau1,
'tau2' : params.tau2,
}
# Initialize the solver
self.dde = dde23(eqns=eqns, params=eqns_params, supportcode=support_c_code)
# Set the initial conditions (i.e. set the history of the state variables)
histfunc = {
's1': lambda t: params.s1_hist_vals,
'x1': lambda t: params.x1_hist_vals,
's2': lambda t: params.s2_hist_vals,
'x2': lambda t: params.x2_hist_vals
}
self.dde.hist_from_funcs(histfunc, 10.) #:TRICKY: 10. is 'nn' - sample in the interval
import numpy as np
import pylab as pl
from pydelay import dde23
eqns = { 'x' : '0.25 * x(t-tau) / (1.0 + pow(x(t-tau),10.0)) -0.1*x' }
dde = dde23(eqns=eqns, params={'tau': 15})
dde.set_sim_params(tfinal=1000, dtmax=1.0, AbsTol=10**-6, RelTol=10**-3)
histfunc = {'x': lambda t: 0.5 }
dde.hist_from_funcs(histfunc, 51)
dde.run()
sol1 = dde.sample(515, 1000, 0.1)
x1 = sol1['x']
sol2 = dde.sample(500, 1000-15, 0.1)
x2 = sol2['x']
pl.plot(x1, x2)
pl.xlabel('$x(t)$')
pl.ylabel('$x(t-15)$')
pl.show()
I1_hist = np.random.uniform(0.0, 1., n_t)
I2_hist = np.random.uniform(0.0, 1., n_t)
histdic = {
't': t_hist,
'Exc1': E1_hist,
'Exc2': E2_hist,
'Inh1': I1_hist,
'Inh2': I2_hist
}
eqns = {
'Exc1': func(0, 'E'),
'Inh1': func(0, 'I'),
'Exc2': func(1, 'E'),
'Inh2': func(1, 'I')
}
dde = dde23(eqns, pardict)
dde.set_sim_params(dtmin=1.e-3,
AbsTol=9.e-5,
RelTol=0.001,
tfinal=t_final,
dtmax=0.1,
MaxIter=1000000,
dt0=0.001)
dde.hist_from_arrays(histdic)
dde.run()
sol = dde.sample(tstart=tc, tfinal=None, dt=dt1)
t = sol['t']
E1[i, :] = sol['Exc1']
E2[i, :] = sol['Exc2']
corEE[i] = find_corr(E1[i, :], E2[i, :])
# Programs 12c: The Mackey-Glass DDE.
# See Figure 12.5(a).
# pydelay must be on your computer.
import pylab as pl
from pydelay import dde23
# define the equations
eqns = {'x': '2 * x(t-tau) / (1.0 + pow(x(t-tau),p)) - x'}
#define the parameters
params = {'tau': 2, 'p': 10}
# Initialise the solver
dde = dde23(eqns=eqns, params=params)
# set the simulation parameters
# (solve from t=0 to t=1000 and limit the maximum step size to 1.0)
dde.set_sim_params(tfinal=1000, dtmax=1.0)
# set the history of to the constant function 0.5 (using a python lambda function)
histfunc = {'x': lambda t: 0.5}
dde.hist_from_funcs(histfunc, 51)
# run the simulator
dde.run()
# Make a plot of x(t) vs x(t-tau):
# Sample the solution twice with a stepsize of dt=0.1:
# once in the interval [515, 1000]
import pylab as pl
from pydelay import dde23
# define the equations
eqns = {
'x' : '0.25 * x(t-tau) / (1.0 + pow(x(t-tau),p)) -0.1*x'
}
#define the parameters
params = {
'tau': 15,
'p' : 10
}
# Initialise the solver
dde = dde23(eqns=eqns, params=params)
# set the simulation parameters
# (solve from t=0 to t=1000 and limit the maximum step size to 1.0)
dde.set_sim_params(tfinal=1000, dtmax=1.0)
# set the history of to the constant function 0.5 (using a python lambda function)
histfunc = {
'x': lambda t: 0.5
}
dde.hist_from_funcs(histfunc, 51)
# run the simulator
dde.run()
# Make a plot of x(t) vs x(t-tau):
if( c==n ){
work = false;
}else{ c++; }
}
fclose(fr);
return narma;
}
"""
print(params)
tau_real = 7.958e-6 # tau(s)
theta_real = 1.59e-3 # theta(s)
# Initialise the solver
dde = dde23(eqns=eqns, params=params, supportcode=inputcode)
#set the simulation parameters
# (solve from t=0 to t=tfinal and limit the maximum step size to dtmax)
T = params['T']
tfinal = 55 * T
tcut = 10 * T
dde.set_sim_params(tfinal=tfinal, dtmax=0.05, AbsTol=10**-3, RelTol=10**-2)
# set the history using a python lambda function
histfunc = {
'x': lambda t: -0.01 * np.sin(185.0 * t),
'y': lambda t: -0.01 * np.cos(223.0 * t)
}
dde.hist_from_funcs(histfunc, 1000)
def do_pydelay(
self,
**_KwargVariablesDict
):
#debug
'''
self.debug(('self.',self,[]))
'''
#network first
self.network(
**{
'RecruitingConcludeConditionTuplesList':[
(
'MroClassesList',
operator.contains,
Equationer.EquationerClass
)
]
}
)
#link
self.PydelayedDeriveEquationersList=self.NetworkedDeriveConnectersList
#map populate and neurongroup
self.PydelayedEquationDictsList=map(
lambda __PydelayedDeriveEquationer:
__PydelayedDeriveEquationer.populate(
).equation(
).EquationingDifferentialDict,
self.PydelayedDeriveEquationersList
)
#Check
if 'eqns' not in self.PydelayingKwargVariablesDict:
self.PydelayingKwargVariablesDict['eqns']={}
#update
map(
lambda __PydelayedEquationDict:
self.PydelayingKwargVariablesDict['eqns'].update(__PydelayedEquationDict),
self.PydelayedEquationDictsList
)
#map populate and neurongroup
self.PydelayedParamDictsList=map(
lambda __PydelayedDeriveEquationer:
__PydelayedDeriveEquationer.EquationingParamDict,
self.PydelayedDeriveEquationersList
)
#Check
if 'params' not in self.PydelayingKwargVariablesDict:
self.PydelayingKwargVariablesDict['params']={}
#update
map(
lambda __PydelayedParamDict:
self.PydelayingKwargVariablesDict['params'].update(__PydelayedParamDict),
self.PydelayedParamDictsList
)
#map populate and neurongroup
self.PydelayedCodeStrsList=map(
lambda __PydelayedDeriveEquationer:
__PydelayedDeriveEquationer.EquationingCodeStr,
self.PydelayedDeriveEquationersList
)
#Check
if 'supportcode' not in self.PydelayingKwargVariablesDict:
self.PydelayingKwargVariablesDict['supportcode']=""
#update
map(
lambda __PydelayedCodeStr:
self.PydelayingKwargVariablesDict.__setitem__(
'supportcode',
self.PydelayingKwargVariablesDict['supportcode']+'\n'+__PydelayedCodeStr
),
self.PydelayedCodeStrsList
)
#debug
'''
self.debug(('self.',self,['PydelayingKwargVariablesDict']))
'''
#bind
self.PydelayedUnitsInt=len(self.PydelayingKwargVariablesDict['eqns'])
#set
self.PydelayedVariableStrsList=self.PydelayingKwargVariablesDict['eqns'].keys()
#Initialise the solver
self.PydelayedDde23Variable = dde23(
**self.PydelayingKwargVariablesDict
)
#Set params inside the solver
self.PydelayedDde23Variable.set_sim_params(
dtmax=self.PydelayingSampleStepTimeFloat
)
#Check if the init conditions was not yet define else give them equal to 0
if type(self.SimulatingInitFloatsArray)==None.__class__:
self.SimulatingInitFloatsArray=np.zeros(1,dtype=float)
if len(self.SimulatingInitFloatsArray)!=self.PydelayedUnitsInt:
self.SimulatingInitFloatsArray=np.array([0.]*self.PydelayedUnitsInt)
#Check if there is an history setted, else give the history as just the constant value of initial conditions
if len(self.PydelayingHistoryFunctionsDict)!=self.PydelayedUnitsInt:
#dict
self.PydelayingHistoryFunctionsDict=dict(
map(
lambda __Int,__KeyStr:
(__KeyStr,lambda _Time:self.SimulatingInitFloatsArray[__Int]),
xrange(self.PydelayedUnitsInt),
self.PydelayingKwargVariablesDict['eqns'].keys()
)
)
#hist_from_funcs
self.PydelayedDde23Variable.hist_from_funcs(self.PydelayingHistoryFunctionsDict)
#Set the size of the Buffer
if self.PydelayingStopTimeFloat<self.PydelayingBufferStepTimeFloat:
self.PydelayedBufferStepsInt=(int)(
self.PydelayingStopTimeFloat/self.PydelayingSampleStepTimeFloat
)
else:
self.PydelayedBufferStepsInt=(int)(
self.PydelayingBufferStepTimeFloat/self.PydelayingSampleStepTimeFloat
)
#debug
'''
self.debug(('self.',self,[
'PydelayedBufferStepsInt',
'SimulatingStopTimeFloat',
'PydelayingBufferStepTimeFloat'
]))
'''
#init the buffer array
self.PydelayedBufferFloatsArray=np.array(
(
self.PydelayedUnitsInt,
self.PydelayedBufferStepsInt
),
dtype=float
)
#set
self.PydelayedMoniterSampleTimeIndexIntsArray=np.array(
xrange(self.PydelayedBufferStepsInt)
)
#Check
if self.PydelayingMoniterVariableIndexIntsArray==None:
self.PydelayingMoniterVariableIndexIntsArray=np.array(xrange(self.PydelayedUnitsInt))
#collect the global monitor
self.collect(
"StateMoniters",
"Variable",
SYS.MoniterClass().update(
{
'MoniteringVariableStr':'PydelayedBufferFloatsArray',
'MoniteringSampleTimeIndexIntsArray':self.PydelayedMoniterSampleTimeIndexIntsArray,
'MoniteringVariableIndexIntsArray':self.PydelayingMoniterVariableIndexIntsArray,
'MoniteredTotalVariablesArray':np.zeros(
(
self.PydelayedUnitsInt,
(int)(
self.PydelayingStopTimeFloat-self.SimulatingStartTimeFloat
)/self.PydelayingSampleStepTimeFloat
)
,dtype=float
)
}
)
)
#Debug
'''
# calculate the intersection of nullclines
def intersection(X):
return nullcl_01(X) - nullcl_02(X)
X0 = 0
X_int = fsolve(intersection,X0)
Y_int = nullcl_01(X_int)
print "intersection of nullclines x_0 , y_0 : ", X_int, Y_int
## initalise the solver, without noise!
#dde = dde23(eqns=eqns, params=params)
# with noise :
dde = dde23(eqns=eqns,params=params, noise=noise)
tfinal = 250
dde.set_sim_params(tfinal)
dde.hist_from_funcs({'x1': lambda t : -0.05 , 'y1': lambda t: -0.75,
'x2': lambda t : 0 , 'y2': lambda t: 0 })
dde.run()
# sampling the numerical solution with sample size dt
sol = dde.sample(0,tfinal,dt=0.01)
# save the solution
x1 = sol['x1']
y1 = sol['y1']
import numpy as np
import pylab as pl
from pydelay import dde23
eqns = {'x': '0.25 * x(t-tau) / (1.0 + pow(x(t-tau),10.0)) -0.1*x'}
dde = dde23(eqns=eqns, params={'tau': 15})
dde.set_sim_params(tfinal=1000, dtmax=1.0, AbsTol=10**-6, RelTol=10**-3)
histfunc = {'x': lambda t: 0.5}
dde.hist_from_funcs(histfunc, 51)
dde.run()
sol1 = dde.sample(515, 1000, 0.1)
x1 = sol1['x']
sol2 = dde.sample(500, 1000 - 15, 0.1)
x2 = sol2['x']
pl.plot(x1, x2)
pl.xlabel('$x(t)$')
pl.ylabel('$x(t-15)$')
pl.show()
eqns = { 'E:C': '0.5*(1.0+ii*a)*E*n + K*E(t-tau)',
'n' : '(p - n - (1.0 +n) * pow(abs(E),2))/T'}
params = { 'a' : 4.0,
'p' : 1.0,
'T' : 1000.0,
'K' : 0.1,
'tau': 1000,
'nu' : 10**-5,
'n0' : 10.0
}
noise = { 'E': 'sqrt(0.5*nu*(n+n0)) * (gwn() + ii*gwn())' }
dde = dde23(eqns=eqns, params=params, noise=noise)
tfinal = 20000
dde.set_sim_params(tfinal=tfinal)
# use a dictionary to set the history
thist = np.linspace(0, 1000, 10000)
Ehist = np.sin(0.01*thist)*np.exp(1.0j*0.001*thist)
nhist = np.sin(0.01*thist)-1
dic = {'t' : thist, 'E': Ehist, 'n': nhist}
dde.hist_from_arrays(dic)
dde.run()
t = dde.sol['t']
def dde_initializer(Ac_i,Am_i,Bc_i,Bm_i,Rm_i,AB_i,AR_i,tf,dt):
# the model equations
eqns = {
'Ac' : '-k1*Rm*Ac',
'Am' : 'k1*Rm(t-tau1)*Ac(t-tau1)*Heavi(t-tau1) - k2*Am*Rm + k2*AR - k2*Am*Bm + k3*AB',
'Bc' : '-k4*Am*Bc',
'Bm' : 'k4*Am(t-tau2)*Bc(t-tau2)*Heavi(t-tau2) - k2*Am*Bm + k3*AB',
'Rm' : 'qR - k2*Am*Rm + k2*AR',
'AB' : 'k2*Am*Bm - k3*AB',
'AR' : 'k2*Am*Rm - k2*AR',
}
# define parameters
params = {
'k1' : const.k1,
'k2' : const.k2,
'k3' : const.k3,
'k4' : const.k4,
'qR' : const.qR,
'tau1' : const.tau1,
'tau2' : const.tau2,
}
# initial conditions
init_cond = {
'Ac' : Ac_i,
'Am' : Am_i,
'Bc' : Bc_i,
'Bm' : Bm_i,
'Rm' : Rm_i,
'AB' : AB_i,
'AR' : AR_i,
}
# intialize the solver
dde = dde23(eqns=eqns, params=params)
# set the simulation parameters
# (solve from t=0 to t=tf and limit the maximum step size to 1.0)
dde.set_sim_params(tfinal=tf, dtmax=1.0)
# set the history of the proteins
histfunc = {
'Ac' : lambda t: init_cond['Ac'],
'Am' : lambda t: init_cond['Am'],
'Bc' : lambda t: init_cond['Bc'],
'Bm' : lambda t: init_cond['Bm'],
'Rm' : lambda t: init_cond['Rm'],
'AB' : lambda t: init_cond['AB'],
'AR' : lambda t: init_cond['AR'],
}
dde.hist_from_funcs(histfunc,500)
# run the simulator
dde.run()
# Get solution at every t=0.1
sol1 = dde.sample(0,tf,0.1)
# get the solutions from the history dict
# t = dde.sol['t']
# Ac= dde.sol['Ac']
# Am= dde.sol['Am']
# Bc = dde.sol['Bc']
# Bm = dde.sol['Bm']
# Rm = dde.sol['Rm']
# AB = dde.sol['AB']
# AR = dde.sol['AR']
t = sol1['t']
Ac= sol1['Ac']
Am= sol1['Am']
Bc = sol1['Bc']
Bm = sol1['Bm']
Rm = sol1['Rm']
AB = sol1['AB']
AR = sol1['AR']
return(t,Ac,Am,Bc,Bm,Rm,AB,AR)
def __init__(self, params = None, **kwargs):
if params == None:
params = AttributeDict(kwargs)
self.params = params
#Calculate the equilibrium point
def mu1(s, m, k):
return (m*s)/(k + s)
def mu2(s, m, k, k_I):
return (m*s)/(k + s + (s/k_I)*(s/k_I))
def eq_s1(s1, *args):
(_k1, _k2, _k3, _s1_in, _s2_in, a, m1, _m2, k_s1, _k_s2, _k_I, D, tau1, _tau2) = args
return a*D - np.exp(-a*D*tau1) * mu1(s1, m1, k_s1)
def eq_s2(s2, *args):
(_k1, _k2, _k3, _s1_in, _s2_in, a, _m1, m2, _k_s1, k_s2, k_I, D, _tau1, tau2) = args
return a*D - np.exp(-a*D*tau2) * mu2(s2, m2, k_s2, k_I)
eqs_args = (
params.k1, params.k2, params.k3,
params.s1_in, params.s2_in, params.a,
params.m1, params.m2,
params.k_s1, params.k_s2, params.k_I,
params.D, params.tau1, params.tau2)
s1_eqpnt = fsolve(eq_s1, 1.0, args = eqs_args)[0]
x1_eqpnt = np.exp(-params.a*params.D*params.tau1) * (params.s1_in - s1_eqpnt)/(params.a*params.k1)
if x1_eqpnt < 0:
s1_eqpnt = params.s1_in
x1_eqpnt = 0.0
s2_eqpnt_sol, _info, ier, _msg = fsolve(eq_s2, 1.0, args = eqs_args, full_output = True)
if ier != 1 or s2_eqpnt_sol[0] < 0:
x2_eqpnt = 0.0
s2_eqpnt = params.s2_in + params.k2*mu1(s1_eqpnt, params.m1, params.k_s1) * x1_eqpnt / params.D
else:
s2_eqpnt = s2_eqpnt_sol[0]
x2_eqpnt = ((params.s2_in - s2_eqpnt)*params.D + params.k2*mu1(s1_eqpnt, params.m1, params.k_s1)*x1_eqpnt) \
/ (params.k3 * mu2(s2_eqpnt, params.m2, params.k_s2, params.k_I))
self.equilibriumPoint = [s1_eqpnt, x1_eqpnt, s2_eqpnt, x2_eqpnt]
if plotEqulibriumValuesAtTheEnd:
print "equilibrium point (s1, x1, s2, x2) = ", self.equilibriumPoint
# Define the specific growth rates (in 'C' source code)
support_c_code = """
double mu1(double s, double m, double k) {
return (m*s)/(k + s);
}
double mu2(double s, double m, double k, double k_I) {
return (m*s)/(k + s + (s/k_I)*(s/k_I));
}
"""
# Define the equations
eqns = {
's1': 'D*(s1_in - s1) - k1*mu1(s1, m1, k_s1)*x1',
'x1': 'exp(-a*D*tau1)*mu1(s1(t-tau1), m1, k_s1)*x1(t-tau1) - a*D*x1',
's2': 'D*(s2_in - s2) + k2*mu1(s1, m1, k_s1)*x1 - k3*mu2(s2, m2, k_s2, k_I)*x2',
'x2': 'exp(-a*D*tau2)*mu2(s2(t-tau2), m2, k_s2, k_I)*x2(t-tau2) - a*D*x2'
}
# Define the parameters
eqns_params = {
'k1' : params.k1,
'k2' : params.k2,
'k3' : params.k3,
's1_in' : params.s1_in,
's2_in' : params.s2_in,
'a' : params.a,
'm1' : params.m1,
'm2' : params.m2,
'k_s1' : params.k_s1,
'k_s2' : params.k_s2,
'k_I' : params.k_I,
'D' : params.D,
'tau1' : params.tau1,
'tau2' : params.tau2,
}
# Initialize the solver
self.dde = dde23(eqns=eqns, params=eqns_params, supportcode=support_c_code)
# Set the initial conditions (i.e. set the history of the state variables)
histfunc = {
's1': lambda t: params.s1_hist_vals,
'x1': lambda t: params.x1_hist_vals,
's2': lambda t: params.s2_hist_vals,
'x2': lambda t: params.x2_hist_vals
}
self.dde.hist_from_funcs(histfunc, 10.) #:TRICKY: 10. is 'nn' - sample in the interval
d1 = {E_keys[i]: E_values}
d2 = {I_keys[i]: I_values}
histdic.update(d1)
histdic.update(d2)
#build dictionaty of equations
d3 = dict(zip(E_keys, funcE(N, Cij, dij)))
d4 = dict(zip(I_keys, funcI(N)))
eqns = {}
eqns.update(d3)
eqns.update(d4)
print 'Computing ...'
start = timer()
dde = dde23(eqns)
dde.set_sim_params(dtmin=1.e-3,
AbsTol=9.e-5,
RelTol=0.001,
tfinal=t_final,
dtmax=0.1,
MaxIter=1000000,
dt0=0.001)
dde.hist_from_arrays(histdic)
dde.run()
sol = dde.sample(tstart=tc, tfinal=None, dt=dt1)
t = sol['t']
columns = int((t_final - tc) / dt1)
EE = np.zeros((N, columns))
for i in range(N):
EE[i, :] = sol[E_keys[i]]