from getBoundary import getBoundary

import numpy as np

import pylab as pl

from fig import fig, saveFig, printText, fill_between

from printStatus import printRatio

from pickle import load, dump

from scipy.integrate import quad

from scipy.integrate import quadrature

hpsis=np.logspace(-6,1.5,300)

a2=0.1

from solveBC import sweep, findrho

try:

bbs,sols=load(open('cache/sols'+str(a2)))

except IOError:

print('Solve for sweep of different horizon BCs...')

bbs,sols=sweep(lambda x,y: getBoundary(x,y,[0,a2]), hpsis, oscN=1, status=True)

dump((bbs,sols),open('cache/sols'+str(a2),'w'))

rho=-np.array(bbs)[:,:,1,1].real

rhoc=min([min(r) for r in rho])#rho, in units used at Tc

fig(11)

Trs=list(np.linspace(0.15,1,100))+list(np.linspace(1,1.3,20))[1:]

zh=1

T=3./(zh*4.*np.pi)

wvs= [1e-5,1e-4]#+list(np.linspace(1e-3,1,150))[1:]+list(np.logspace(0,1.5,20))[1:]

#pl.xscale('log')

#pl.yscale('log')

first=True

y1s=[]

y2s=[]

for j in range(len(Trs)):

Tr=Trs[j]

rho=rhoc/Tr**2

Tc=T*np.sqrt(rho/rhoc)

if Tr<1:

rhoSol=findrho(lambda x,y: getBoundary(x,y,[0,a2]), sols, hpsis, bbs, rho)

else:

bb,osc=getBoundary(1,0,[0,a2])

guess=rho/(-bb[1][1])

from scipy.optimize import fsolve

hphi=fsolve(lambda hphi:rho+getBoundary(hphi,0,[0,a2])[0][1][1], guess)

rhoSol=[[hphi,0]]

assert(len(rhoSol)==1)

rhoSol=rhoSol[0]

sigmas=[]

bb,osc=getBoundary(rhoSol[0],rhoSol[1], [0,a2],plot=True)

mu=bb[1][0]

sigmas=[]

for wvi in range(len(wvs)):

printRatio(j*len(wvs)+wvi,len(Trs)*len(wvs))

bb,osc=getBoundary(rhoSol[0],rhoSol[1], [mu*wvs[wvi],a2])

assert(osc==0)

sigmas.append(-1j*bb[2][1]/( bb[2][0]*(mu*wvs[wvi]) ))

first=False

#tot=np.trapz([s.real-1 for s in sigmas],x=[w*mu for w in wvs])

qws=[]

qsigmas=[]

C=0.15

def sigmaf(lwv):

return (qsigmas[-1].real-1)*(wv+C)*mu

tot,_=quad(sigmaf,np.log(1e-3+C),np.log(30.+C),epsrel=0.003,epsabs=0.003)

#tot,_=quadrature(sigmaf,np.log(1e-3+C),np.log(30.+C),rtol=0.01,tol=0.01,vec_func=False)

print('tot/Tc: '+str(tot/Tc))

s=sorted(range(len(qws)),key=lambda i:qws[i])

qws=[qws[i] for i in s]

qsigmas=[qsigmas[i] for i in s]

pl.plot(qws,[s.real-1 for s in qsigmas],ls='-',c='k',label=r'$\mathrm{Im}(\sigma)$'if first else '',marker='.')

y1s.append(tot/Tc)

if Tr<1:

assert( abs(sigmas[0].imag*wvs[0]/(sigmas[1].imag*wvs[1]) -1 )<0.001 )

print( abs(sigmas[0].imag*wvs[0]/(sigmas[1].imag*wvs[1]) -1 ) )

y2s.append(sigmas[0].imag*mu*wvs[0]*np.pi/2/Tc)

else:

print sigmas[0].imag

#assert(sigmas[0].imag<0.1)

y2s.append(0)

#pl.plot([wvs[0],wvs[-1]],[1,1],ls=':',c='k')

#pl.plot([wvs[0],wvs[-1]],[0,0],ls=':',c='k')

#printText([wvs[0],wvs[-1]],[1,1],0,5.,r'$\sigma=1$')

fig(0)

#pl.plot(Trs,y1s,c='k',ls='-')

#pl.plot(Trs,[y1s[i]+y2s[i] for i in range(len(Trs))],c='k',ls='-')

ymin=min(y1s)*1.2

fill_between(Trs, [ymin for i in Trs], y1s,hatch='/',facecolor='white',label=r'$\int_0^\infty\mathrm{Re}(\sigma_n(\omega)-1)\mathrm{d}\omega$')#, facecolor='blue', alpha=0.5)

fill_between(Trs, y1s, [y1s[i]+y2s[i] for i in range(len(Trs))], hatch=r'\\', facecolor='white',label=r'$\Sigma_\delta$')#, facecolor='red', alpha=0.5)

pl.plot(Trs,[y1s[i]+y2s[i] for i in range(len(Trs))],c='r',ls='-',label=r'$\Sigma_\delta+\int_0^\infty\mathrm{Re}(\sigma_n(\omega)-1)\mathrm{d}\omega$',lw=1)

pl.ylim(ymin,-ymin*0.8)

pl.xlim(Trs[0],Trs[-1])

pl.xlabel(r'$\frac{T}{T_c}$')

pl.ylabel(r'$[T_c]$')

handles, labels = pl.gca().get_legend_handles_labels()

pl.legend(handles[::-1], labels[::-1])

saveFig('sum_rule_a2'+str(a2))

pl.show()