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optimization.py
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import numpy as np
from scipy.optimize import minimize
from scipy.integrate import odeint
import matplotlib.pyplot as plt
init = [-5,-1]
initH = 15
tlist = np.linspace(0,100,101)
mu = .5
rhw=6.64*(10**-5)
rsw=1/2.14
uh=0.9896/24
sleepstatus = 1
hac=0.098
uc=.1503
a=6.2*10**-6
omega=(2*np.pi)/24
t0=18.24
kappa=5
def objective(init,t,mu): #vanderpal
x,y=init
dxdt = mu*(x*omega**2-(1/3)*x**3-y)
dydt = (1/mu)*x*omega**2
dadt = [dxdt,dydt]
return dadt
def homSleep(initH,t,uh,rsw):
h=initH
tindex=0
dif = 100000000000
ttest = 0
for i in range(len(tlist)):
ttest = abs(tlist[i]-t)
if (ttest<dif):
dif=ttest
tindex=i
dhdt = rsw*(1-.1*solObj[:,0][tindex])*(uh-h)
return dhdt
def homWake(initH,t,t0,uh,rhw):
h=initH
#dhdt = -2*tw*((rhw)**2)*(uh-h)
dhdt=((t**2)/(t+t0))*rhw*(h-uc)
return dhdt
def testfunc(initB,t,kappa):
alphata=initB
didi = kappa*alphata
return didi
def circadian(initC,t,uc,a,hac):
#ifasleep, use sleep version of h, if awake use awake version
tindex=0
dif = 100000000000
ttest = 0
for i in range(len(tlist)):
ttest = abs(tlist[i]-t)
if (ttest<dif):
dif=ttest
tindex=i
if(sleepstatus == 0):
h = solhomSleep[:,0][tindex]
else:
h = solhomWake[:,0][tindex]
Ac = uc-a*((np.e)**(h/hac))
c = Ac*(.91*solObj[:,0][tindex]-.29*solObj[:,0][tindex])
return c
def cogt(t):
dif = 100000000000
ttest = 0
for i in range(len(tlist)):
ttest = abs(tlist[i]-t)
if (ttest<dif):
dif=ttest
tindex=i
if(sleepstatus == 0):
return solhomSleep[:,0][tindex] + solCircadian[:,0][tindex]
else:
return solhomWake[:,0][tindex] + solCircadian[:,0][tindex]
solObj = odeint(objective,init,tlist,args=(mu,))
solTestFunc=odeint(testfunc,initH,tlist,args=(kappa,))
#solObjDriven = odeint(objectiveDriven,init,tlist,args=(mu,))
solhomSleep = odeint(homSleep,initH,tlist,args=(uh,rsw,))
solhomWake = odeint(homWake,initH,tlist,args=(uh,t0,rhw,))
circarray=[]
for i in range(len(tlist)):
circarray.append(circadian(initH,tlist[i],uc,a,hac))
#solCircadian = odeint(circadian,init2,tlist,args=(uc,a,hac,))
#plt.plot(tlist, solObj[:, 0], '#008080', label='undriven')
#plt.plot(tlist, solhomSleep[:,0], 'r',label='solhomsleep')
#plt.plot(tlist, solObjDriven[:,0], 'r',label='driven')
#plt.plot(tlist, solhomWake[:,0], 'g',label='solhomWake')
#plt.plot(tlist, solTestFunc[:,0])
#plt.plot(tlist, circarray,'b', label='solcircadian')
plt.plot(tlist, solhomWake[:,0]+circarray, label='prod')
#plt.plot(tlist,circarray)
plt.xlim(0,54)
plt.ylim(-5,15)
plt.legend(loc='best')
plt.xlabel('t')
plt.grid()
plt.savefig("test.svg")
#def constraint1(x):
# return x[0]*x[1]*x[2]*x[3]-25.0
#
#def constraint2(x):
# sum_sq = 40
# for i in range(4):
# sum_sq = sum_sq - x[i]**2
# return sum_sq
#bnds = (b,b,b,b)
#con1 = {'type':'ineq','fun': constraint1}
#con2 = {'type':'eq','fun':constraint2}
#cons = [con1,con2]
#sol = minimize(objective,x0,method='SLSQP',\
#bounds=bnds)
#print(sol.x)