In [1]:
# This line configures matplotlib to show figures embedded in the notebook,
# instead of opening a new window for each figure. More about that later.
# If you are using an old version of IPython, try using '%pylab inline' instead.
%matplotlib inline
%load_ext snakeviz
import numpy as np
from scipy.optimize import minimize
from scipy.optimize import rosen, differential_evolution
from scipy.special import expit
import matplotlib.pyplot as plt
import scipy
from matplotlib.lines import Line2D
import timeit
import pandas as pd
import plotly.plotly as py
from plotly.graph_objs import *
import plotly.tools as tls
In [2]:
# Here are the initial values
# For test use
array12 = np.asarray(np.split(np.random.rand(1,60)[0],12))
In [3]:
# Here is the activation function
def act(x):
return expit(x)
In [4]:
# Density matrix in the forms that I wrote down on my Neutrino Physics notebook
# x is a real array of 12 arrays.
init = np.array([1.0,0.0,0.0,0.0])
def rho(x,ti,initialCondition):
elem = np.ones(4)
for i in np.linspace(0,3,4):
elem[i] = np.sum(ti*x[i*3]*act(ti*x[i*3+1] + x[i*3+2]) )
return init + elem
In [5]:
rho(array12,0,init)
Out[5]:
In [6]:
# Hamiltonian of the problem, in terms of four real components
hamil = np.array( [ np.cos(2.0),np.sin(2.0) , np.sin(2.0),np.cos(2.0) ] )
#hamil = 1.0/2*np.array( [ -np.cos(2.0),np.sin(2.0) , np.sin(2.0),np.cos(2.0) ] )
print hamil
In [35]:
# Cost function for each time step
def rhop(x,ti,initialCondition):
rhoprime = np.zeros(4)
for i in np.linspace(0,3,4):
rhoprime[i] = np.sum(x[i*3] * (act(ti*x[i*3+1] + x[i*3+2]) ) ) + np.sum( ti*x[i*3]* (act(ti*x[i*3+1] + x[i*3+2]) ) * (1 - (act(ti*x[i*3+1] + x[i*3+2]) ) )* x[i*3+1] )
return rhoprime
## This is the regularization
regularization = 0.0001
def costi(x,ti,initialCondition):
rhoi = rho(x,ti,initialCondition)
rhopi = rhop(x,ti,initialCondition)
costTemp = np.zeros(4)
costTemp[0] = ( rhopi[0] - 2.0*rhoi[2]*hamil[1] )**2
costTemp[1] = ( rhopi[1] - 2.0*rhoi[2]*hamil[0] )**2
costTemp[2] = ( rhopi[2] + 2.0*rhoi[1]*hamil[0] - hamil[1] * (rhoi[3] - rhoi[0] ) )**2
costTemp[3] = ( rhopi[3] + 2.0*rhoi[2]*hamil[1] )**2
return np.sum(costTemp)# + 2.0*np.sum(rhoi[0]+rhoi[3]-1.0)**2
# return np.sum(costTemp) + regularization*np.sum(x**2)
In [36]:
costi(array12,0,init)
Out[36]:
In [37]:
def cost(x,t,initialCondition):
costTotal = map(lambda t: costi(x,t,initialCondition),t)
return np.sum(costTotal)
In [38]:
cost(array12,np.array([0,1,2]),init)
#cost(xresult,np.array([0,4,11]),init)
Out[38]:
In [39]:
# with ramdom initial guess
initGuess = np.asarray(np.split(np.random.rand(1,60)[0],12))
#initGuess = np.split(np.zeros(60),12)
endpoint = 2
tlin = np.linspace(0,endpoint,11)
costF = lambda x: cost(x,tlin,init)
startSLSQP = timeit.default_timer()
costvFResultSLSQP = minimize(costF,initGuess,method="SLSQP",tol=1e-20)
stopSLSQP = timeit.default_timer()
print stopSLSQP - startSLSQP
print costvFResultSLSQP
In [40]:
xmid = costvFResultSLSQP.get("x")
startSLSQP = timeit.default_timer()
costvFResultSLSQP = minimize(costF,xmid,method="SLSQP",tol=1e-30,options={"ftol":1e-30,"maxiter":100000})
#costvFResultSLSQP = minimize(costF,xmid,method='Nelder-Mead',tol=1e-15,options={"ftol":1e-15, "maxfev": 1000000,"maxiter":1000000})
stopSLSQP = timeit.default_timer()
print stopSLSQP - startSLSQP
print costvFResultSLSQP
In [41]:
xresult = costvFResultSLSQP.get("x")
#xresult = np.array([-0.01486401, 2.25493868, -1.84543911, -0.07335087, 2.2548026 ,
# -1.84421662, 0.10454078, -1.64040244, 2.99923129, 0.01486399,
# 2.2549433 , -1.84544286, 0.61994826, 0.96756294, 0.60929092,
# 0.23839364, 0.45364599, 0.18426882, 0.30242425, 0.96719724,
# 0.13016584, 0.9192801 , 0.116001 , 0.46777053, 0.17497595,
# 0.96035958, 0.21763616, 0.73997804, 0.88071662, 0.1620245 ,
# 0.66904538, 0.66084959, 0.89772078, 0.49020208, 0.67802378,
# 0.53307714, 0.59867975, 0.16864478, 0.4257949 , 0.5364126 ,
# 0.78476644, 0.4910997 , 0.834945 , 0.45061367, 0.16736545,
# 0.42579168, 0.16877594, 0.98282177, 0.08852038, 0.12633737,
# 0.50922379, 0.93146299, 0.66505978, 0.33157336, 0.05408186,
# 0.04504323, 0.27311737, 0.27651656, 0.47313653, 0.12806564])
#xresult = np.array([-1.37886409, 2.81454922, -0.3571002 , 0.02582831, -1.05414931,
# -1.52308153, -2.24747468, 0.33947049, -0.32310112, -1.43887103,
# 0.81176258, 0.05139705, -1.02669705, -0.97236805, -0.27536667,
# 0.34860447, -1.06962772, 0.89978175, 2.39662887, -1.45165477,
# -1.54636469, -2.79921374, -1.30335793, -0.62844367, -3.04440811,
# -2.74566393, -2.16222918, -1.60535643, -0.77298204, 0.13848754,
# -0.36544212, 1.23901581, -0.80586367, -0.30212561, -1.02818302,
# -2.82928373, -0.80776632, -2.90056107, -2.42432246, -2.87572658,
# -0.8645904 , -0.59526987, -1.87029203, -1.60957508, -1.83106839,
# 1.07020356, -0.84892132, -0.97053555, -0.2005098 , -0.72422578,
# -3.32948549, -4.99349947, -3.46242765, -3.52481528, -3.36820222,
# -4.1848837 , -1.90748847, -2.09206645, -4.10831718, 2.76094325])
print xresult
In [42]:
rho(xresult,10,init)
Out[42]:
In [43]:
plttlin=np.linspace(0,endpoint,100)
pltdata11 = np.array([])
for i in plttlin:
pltdata11 = np.append(pltdata11 ,rho(xresult,i,init)[0] )
print pltdata11
In [44]:
MMA_optmize_Vac_pltdata = np.genfromtxt('./assets/homogen/MMA_optmize_Vac_pltdata.txt', delimiter = ',')
plt.figure(figsize=(16,9.36))
plt.ylabel('MMArho11')
plt.xlabel('Time')
plt.plot(np.linspace(0,15,4501),MMA_optmize_Vac_pltdata,"r-",label="MMAVacrho11")
plt.plot(plttlin,pltdata11,"b4-",label="vac_rho11")
plt.show()
#py.iplot_mpl(plt.gcf(),filename="MMA-rho11-Vac-80-60")
In [ ]:
In [45]:
print scipy.__version__
In [ ]:
# with ramdom initial guess
devoendpoint = 2
devotlin = np.linspace(0,endpoint,11)
devocostF = lambda x: cost(x,devotlin,init)
bounds=np.zeros([3*4*5,2])
for i in range(3*4*5):
bounds[i,0]=-5
bounds[i,1]=5
#print bounds
startdevo = timeit.default_timer()
devo = differential_evolution(devocostF,bounds,strategy='best1bin',tol=1e-10,maxiter=1000,polish=True)
stopdevo = timeit.default_timer()
print stopdevo - startdevo
print devo
In [ ]:
devoxresult=devo.get("x")
In [ ]:
devoplttlin=np.linspace(0,devoendpoint,100)
devopltdata11 = np.array([])
for i in devoplttlin:
devopltdata11 = np.append(devopltdata11 ,rho(devoxresult,i,init)[0] )
print devopltdata11
In [ ]:
plt.figure(figsize=(16,9.36))
plt.ylabel('MMArho11')
plt.xlabel('Time')
plt.plot(np.linspace(0,15,4501),MMA_optmize_Vac_pltdata,"r-",label="MMAVacrho11")
plt.plot(devoplttlin,devopltdata11,"b4-",label="devo_vac_rho11")
plt.show()
#py.iplot_mpl(plt.gcf(),filename="MMA-rho11-Vac-80-60")
In [ ]:
In [ ]:
print scipy.__version__
In [ ]: