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defects.py
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import numpy as np
from convert import K
from getuv import getuv,getab,gettheta,getuvlist,getablist,getuvLlist,getabLlist,h1,getuverr,getuverrlist
import multiprocessing
import time
import os
from powerlaw import gpower
import numpy.random
def defects(g,N,T,numt):
start=time.time()
kset=K(N)[0]
kset=kset[(N/2):]
u=np.zeros([numt,(N/2)],complex)
v=np.zeros([numt,(N/2)],complex)
for kind in np.arange(len(kset)):
uv=getuv(kset[kind],g,T,numt)
u[:,kind]=uv[:,0]
v[:,kind]=uv[:,1]
term1=2*np.real(u[-1,:].conj()*v[-1,:])
term1=-term1*np.sin(kset)
term2=np.absolute(v[-1,:])**2
term2=-2*np.cos(kset)*term2
term1=np.sum(term1)
term2=np.sum(term2)
numdef=(N/2)+term1+term2
end=time.time()
print end-start
return numdef/N
def dPdg(g,k,T,numt):
dgds=np.zeros([numt],complex)
#kset=K(N)[0]
#kset=kset[(N/2):]
kset=np.array([k])
u=np.zeros([numt,len(kset)],complex)
v=np.zeros([numt,len(kset)],complex)
x=np.zeros([numt,len(kset)],complex)
y=np.zeros([numt,len(kset)],complex)
for kind in np.arange(len(kset)):
uv=getuv(kset[kind],g,T,numt)
u[:,kind]=uv[:,0]
v[:,kind]=uv[:,1]
ab=getab(kset[kind],g,T,numt)
x[:,kind]=ab[:,0]
y[:,kind]=ab[:,1]
term1=u[-1,:].conj()*x[-1,:] + v[-1,:].conj()*y[-1,:]
term2=u[-1,:].conj()*y[-1,:] + v[-1,:].conj()*x[-1,:]
term2=-term2*np.sin(kset)
term3=-2*np.cos(kset)*v[-1,:].conj()*y[-1,:]
fact1=term1+term2+term3
for q in np.arange(numt):
fact2=y[q,:].conj()*v[q,:]-x[q,:].conj()*u[q,:]
dgds[q]=np.sum(fact1*fact2)
return -8*np.imag(dgds)
def dDdg(g,N,T,numt):
dgds=np.zeros([numt],complex)
kset=K(N)[0]
kset=kset[(N/2):]
u=np.zeros([numt,len(kset)],complex)
v=np.zeros([numt,len(kset)],complex)
x=np.zeros([numt,len(kset)],complex)
y=np.zeros([numt,len(kset)],complex)
for kind in np.arange(len(kset)):
uv=getuv(kset[kind],g,T,numt)
u[:,kind]=uv[:,0]
v[:,kind]=uv[:,1]
ab=getab(kset[kind],g,T,numt)
x[:,kind]=ab[:,0]
y[:,kind]=ab[:,1]
term1=u[-1,:].conj()*x[-1,:] + v[-1,:].conj()*y[-1,:]
term2=u[-1,:].conj()*y[-1,:] + v[-1,:].conj()*x[-1,:]
term2=-term2*np.sin(kset)
term3=-2*np.cos(kset)*v[-1,:].conj()*y[-1,:]
fact1=term1+term2+term3
for q in np.arange(numt):
fact2=y[q,:].conj()*v[q,:]-x[q,:].conj()*u[q,:]
dgds[q]=np.sum(fact1*fact2)
return -8*np.imag(dgds)
def defectstime(g,N,T,numt):
kset=K(N)[0]
kset=kset[(N/2):]
u=np.zeros([numt,(N/2)],complex)
v=np.zeros([numt,(N/2)],complex)
for kind in np.arange(len(kset)): #this step parallelized
uv=getuv(kset[kind],g,T,numt)
u[:,kind]=uv[:,0]
v[:,kind]=uv[:,1]
D=np.zeros([numt])
kD=np.zeros([len(kset),numt],complex)
for q in np.arange(numt):
term1=u[q,:].conj()*v[q,:] + v[q,:].conj()*u[q,:]
term1=-term1*np.sin(kset)
term2=v[q,:].conj()*v[q,:]
term2=-2*np.cos(kset)*term2
kD[:,q]=((1+term1+term2)/N)
term1=np.sum(term1)
term2=np.sum(term2)
numdef=(N/2)+term1+term2
D[q]=np.real(numdef/N)
#also calculate fidelity
f=np.zeros([numt])
theta=np.zeros([len(kset)])
for q in np.arange(numt):
for kind in np.arange(len(kset)):
theta[kind]=gettheta(kset[kind],g[q])
fid=u[q,:]*np.cos(theta) + v[q,:]*np.sin(theta)
f[q]=np.abs(fid.prod())**2
return D,f,kD
def gaussmult(dg,T):
# beta=
# b=T/beta
t=np.linspace(-T,T,len(dg))
# dg=dg*np.exp(-(30./(T**2))*((t-(T/2))**2))
# a=T*((gi/(2.*(beta**2)))+1.-(2./gi))
# f=((t-T)**2)*np.exp(-((t-a)/b)**2)
# f=f/np.amax(abs(f))
# dg=dg*f
f=-(t**2)+(T**2)
f=f/np.amax(f)
dg=dg*f
return dg
#no gaussmult for now
def climb_dPdg(s,g,k,T,numt):
dp=dPdg(g,k,T,numt)
dp=-gaussmult(dp,T)
return dp
def climb_dDdg(s,g,N,T,numt):
dg=dDdg(g,N,T,numt)
dg=-gaussmult(dg,T)
return dg
def climb_dDdgpar(s,g,N,T,numt):
dg=dDdgpar(g,N,T,numt)
dg=-gaussmult(dg,T)
return dg
def climb_dDdh(s,h,N,T,numt):
g=1.-(h**2)
dh=dDdg(g,N,T,numt)
dh=-2*h*dh
dh=-gauss2mult(dh,T)
return dh
def climb_dDdhpar(s,h,N,T,numt):
g=1.-(h**2)
dh=dDdgpar(g,N,T,numt)
dh=-2*h*dh
dh=-gauss2mult(dh,T)
return dh
def gauss2mult(dh,T):
n=len(dh)
n=n/2
# dh1=dh[:n]
# dh2=dh[n:]
t1=np.linspace(-T,0,n)
t2=np.linspace(0,T,n)
# dh1=dh1*np.exp(-(30./((T/2.)**2))*((t1+(T/2.))**2))
# dh2=dh2*np.exp(-(30./((T/2.)**2))*((t2-(T/2.))**2))
f1=((-(t1+(T/2.))**2)+((T/2.)**2))
f2=((-(t2-(T/2.))**2)+((T/2.)**2))
f=np.concatenate((f1,f2))
f=f/np.amax(f)
dh=dh*f
return dh
def defectstimeh(h,N,T,numt):
g=1.-(h**2)
D,f=defectstime(g,N,T,numt)
return D,f
def defectstimehpar(h,N,T,numt):
g=1.-(h**2)
D,f=defectstimepar(g,N,T,numt)
return D,f
# def defectspar(g,N,T,numt):
# start=time.time()
# kset=K(N)[0]
# kset=kset[(N/2):]
# u=np.zeros([numt,(N/2)],complex)
# v=np.zeros([numt,(N/2)],complex)
# outq=multiprocessing.Queue()
# def getuvpar(k):
# return getuv(k,g,T,numt)
# def worker(kind,outq):
# uv=getuvpar(kset[kind])
# u=uv[:,0]
# v=uv[:,1]
# dict={'kind':kind,'u':u,'v':v}
# outq.put(dict)
# if hasattr(os,'getppid'):
# print 'parent process:',os.getppid()
# print 'process id:',os.getpid()
# procs=[]
# for kind in np.arange(len(kset)):
# p=multiprocessing.Process(target=worker,args=(kind,outq))
# procs.append(p)
# p.start()
# for z in np.arange(len(kset)):
# dict=outq.get()
# kindex=dict['kind']
# u[:,kindex]=dict['u']
# v[:,kindex]=dict['v']
# for p in procs:
# p.join()
# term1=2*np.real(u[-1,:].conj()*v[-1,:])
# term1=-term1*np.sin(kset)
# term2=np.absolute(v[-1,:])**2
# term2=-2*np.cos(kset)*term2
# term1=np.sum(term1)
# term2=np.sum(term2)
# numdef=(N/2)+term1+term2
# end=time.time()
# print end-start
# return numdef/N
def defectstimepar(g,N,T,numt):
kset=K(N)[0]
kset=kset[(N/2):]
u=np.zeros([numt,(N/2)],complex)
v=np.zeros([numt,(N/2)],complex)
poolsize=8
masterlist=[]
for k in kset:
list=[]
list.append(k)
list.append(g)
list.append(T)
list.append(numt)
masterlist.append(list)
pool=multiprocessing.Pool(processes=poolsize)
pool_output=pool.map(getuvlist,masterlist)
pool.close()
pool.join()
for z in xrange(len(kset)):
uv=pool_output[z]
u[:,z]=uv[:,0]
v[:,z]=uv[:,1]
D=np.zeros([numt])
kD=np.zeros([len(kset),numt],complex)
for q in np.arange(numt):
term1=u[q,:].conj()*v[q,:] + v[q,:].conj()*u[q,:]
term1=-term1*np.sin(kset)
term2=v[q,:].conj()*v[q,:]
term2=-2*np.cos(kset)*term2
kD[:,q]=((1+term1+term2)/N)
term1=np.sum(term1)
term2=np.sum(term2)
numdef=(N/2)+term1+term2
D[q]=np.real(numdef/N)
#also calculate fidelity
f=np.zeros([numt])
theta=np.zeros([len(kset)])
for q in np.arange(numt):
for kind in np.arange(len(kset)):
theta[kind]=gettheta(kset[kind],g[q])
fid=u[q,:]*np.cos(theta) + v[q,:]*np.sin(theta)
f[q]=np.abs(fid.prod())**2
return D,f,kD
def defectstimeparerr(g,N,T,numt,err):
kset=K(N)[0]
kset=kset[(N/2):]
u=np.zeros([numt,(N/2)],complex)
v=np.zeros([numt,(N/2)],complex)
poolsize=8
masterlist=[]
for k in kset:
list=[]
list.append(k)
list.append(g)
list.append(T)
list.append(numt)
list.append(err)
masterlist.append(list)
pool=multiprocessing.Pool(processes=poolsize)
pool_output=pool.map(getuverrlist,masterlist)
pool.close()
pool.join()
for z in xrange(len(kset)):
uv=pool_output[z]
u[:,z]=uv[:,0]
v[:,z]=uv[:,1]
D=np.zeros([numt])
kD=np.zeros([len(kset),numt],complex)
for q in np.arange(numt):
term1=u[q,:].conj()*v[q,:] + v[q,:].conj()*u[q,:]
term1=-term1*np.sin(kset)
term2=v[q,:].conj()*v[q,:]
term2=-2*np.cos(kset)*term2
kD[:,q]=((1+term1+term2)/N)
term1=np.sum(term1)
term2=np.sum(term2)
numdef=(N/2)+term1+term2
D[q]=np.real(numdef/N)
#also calculate fidelity
f=np.zeros([numt])
theta=np.zeros([len(kset)])
for q in np.arange(numt):
for kind in np.arange(len(kset)):
theta[kind]=gettheta(kset[kind],g[q])
fid=u[q,:]*np.cos(theta) + v[q,:]*np.sin(theta)
f[q]=np.abs(fid.prod())**2
return D,f,kD
def dDdgpar(g,N,T,numt):
dgds=np.zeros([numt],complex)
kset=K(N)[0]
kset=kset[(N/2):]
u=np.zeros([numt,len(kset)],complex)
v=np.zeros([numt,len(kset)],complex)
x=np.zeros([numt,len(kset)],complex)
y=np.zeros([numt,len(kset)],complex)
poolsize=1
masterlist=[]
for k in kset:
list=[]
list.append(k)
list.append(g)
list.append(T)
list.append(numt)
masterlist.append(list)
pooluv=multiprocessing.Pool(processes=poolsize)
pool_outputuv=pooluv.map(getuvlist,masterlist)
pooluv.close()
poolab=multiprocessing.Pool()
pool_outputab=poolab.map(getablist,masterlist)
poolab.close()
pooluv.join()
poolab.join()
for z in xrange(len(kset)):
uv=pool_outputuv[z]
xy=pool_outputab[z]
u[:,z]=uv[:,0]
v[:,z]=uv[:,1]
x[:,z]=xy[:,0]
y[:,z]=xy[:,1]
D=np.zeros([numt])
for q in np.arange(numt):
term1=u[q,:].conj()*v[q,:] + v[q,:].conj()*u[q,:]
term1=-term1*np.sin(kset)
term2=v[q,:].conj()*v[q,:]
term2=-2*np.cos(kset)*term2
term1=np.sum(term1)
term2=np.sum(term2)
numdef=(N/2)+term1+term2
D[q]=np.real(numdef/N)
term1=u[-1,:].conj()*x[-1,:] + v[-1,:].conj()*y[-1,:]
term2=u[-1,:].conj()*y[-1,:] + v[-1,:].conj()*x[-1,:]
term2=-term2*np.sin(kset)
term3=-2*np.cos(kset)*v[-1,:].conj()*y[-1,:]
fact1=term1+term2+term3
for q in np.arange(numt):
fact2=y[q,:].conj()*v[q,:]-x[q,:].conj()*u[q,:]
dgds[q]=np.sum(fact1*fact2)
return -8*np.imag(dgds),D
def climb_dDdrpar(s,r,N,T,numt):
t=np.linspace(-T,T,numt)
g=gpower(t,T,r)
dg,D=dDdgpar(g,N,T,numt)
dg=-dg
dr=-(np.abs(t/T)**r)*np.sign(t)*np.log(np.abs(t/T))
return np.dot(dg,dr),D[-1]
def climb_dDdlambpar(s,lamb,g,N,T,numt):
dg=dDdlambpar(g,lamb,N,T,numt)
dg=-gaussmult(dg,T)
return dg
def dDdlambpar(g,lamb,N,T,numt):
dgds=np.zeros([numt],complex)
kset=K(N)[0]
kset=kset[(N/2):]
u=np.zeros([numt,len(kset)],complex)
v=np.zeros([numt,len(kset)],complex)
x=np.zeros([numt,len(kset)],complex)
y=np.zeros([numt,len(kset)],complex)
poolsize=5
masterlist=[]
for k in kset:
list=[]
list.append(k)
list.append(g)
list.append(lamb)
list.append(N)
list.append(T)
list.append(numt)
masterlist.append(list)
pooluv=multiprocessing.Pool(processes=poolsize)
pool_outputuv=pooluv.map(getuvLlist,masterlist)
pooluv.close()
poolab=multiprocessing.Pool()
pool_outputab=poolab.map(getabLlist,masterlist)
poolab.close()
pooluv.join()
poolab.join()
for z in xrange(len(kset)):
uv=pool_outputuv[z]
xy=pool_outputab[z]
u[:,z]=uv[:,0]
v[:,z]=uv[:,1]
x[:,z]=xy[:,0]
y[:,z]=xy[:,1]
term1=u[-1,:].conj()*x[-1,:] + v[-1,:].conj()*y[-1,:]
term2=u[-1,:].conj()*y[-1,:] + v[-1,:].conj()*x[-1,:]
term2=-term2*np.sin(kset)
term3=-2*np.cos(kset)*v[-1,:].conj()*y[-1,:]
fact1=term1+term2+term3
for q in np.arange(numt):
fact2=y[q,:].conj()*u[q,:]-x[q,:].conj()*v[q,:]
fact2=-4*1j*h1(g[q],N)*np.sin(kset)*fact2
dgds[q]=np.sum(fact1*fact2)
return -8*np.imag(dgds)
def defectsLtimepar(g,lamb,N,T,numt):
kset=K(N)[0]
kset=kset[(N/2):]
u=np.zeros([numt,(N/2)],complex)
v=np.zeros([numt,(N/2)],complex)
poolsize=5
masterlist=[]
for k in kset:
list=[]
list.append(k)
list.append(g)
list.append(lamb)
list.append(T)
list.append(numt)
masterlist.append(list)
pool=multiprocessing.Pool(processes=poolsize)
pool_output=pool.map(getuvLlist,masterlist)
pool.close()
pool.join()
for z in xrange(len(kset)):
uv=pool_output[z]
u[:,z]=uv[:,0]
v[:,z]=uv[:,1]
D=np.zeros([numt])
for q in np.arange(numt):
term1=u[q,:].conj()*v[q,:] + v[q,:].conj()*u[q,:]
term1=-term1*np.sin(kset)
term2=v[q,:].conj()*v[q,:]
term2=-2*np.cos(kset)*term2
term1=np.sum(term1)
term2=np.sum(term2)
numdef=(N/2)+term1+term2
D[q]=np.real(numdef/N)
return D
def noisepulse(g,eta):
gerr=np.zeros(g.shape)
for k in xrange(len(g)):
gerr[k]=g[k] + numpy.random.uniform(-eta/2,eta/2)
return gerr