def test5b(filename, Norder, L=6.):
data = loadtxt(filename).transpose()
tau = data[0]
Gt = data[1]
beta = tau[-1]
x = linspace(-L,L,801)
gamma = 0.005
fGt = interpolate.UnivariateSpline(tau, Gt, s=0)
tau2 = linspace(0,beta,len(tau)*10)
fGt2 = fGt(tau2)
savetxt('Gt_interpolated', vstack((tau2,fGt2)).transpose())
Gm=[]
om=[]
for im in range(Norder):
omi = 2*im*pi/beta
om.append(omi)
Gm.append( integrate.trapz( fGt2*cos(tau2*omi), x=tau2 ) + 0j )
Gm = array(Gm)
om = array(om)
savetxt('Gm', vstack((om,real(Gm))).transpose())
Gx = PadeTest(om, Gm, x, gamma, Norder)
savetxt('dos.pade', vstack((x,real(Gx),imag(Gx))).transpose())
Ax = zeros(len(x),dtype=float)
for ix,xx in enumerate(x):
if (abs(xx)>1e-12):
Ax[ix] = imag(Gx[ix])/(pi*xx)
else:
Ax[ix] = 0.5*imag(Gx[ix-1])/(pi*x[ix-1]) + 0.5*imag(Gx[ix+1])/(pi*x[ix+1])
savetxt('Ax', vstack((x,Ax)).transpose())
Ker = me.initker_boson(x,beta,tau)
savetxt('gtn', vstack((tau, dot(Ax,Ker))).transpose())
def MaximumEntropy(p, tau, Gt):
beta = tau[-1]
random.seed(1) # seed for random numbers
omega = linspace(-p['L'], p['L'], 2 * p['Nw'] + 1)
f0, f1, f2 = me.initf0(omega)
fsg = 1
if p['statistics'] == 'fermi':
Gt = -Gt
fsg = -1
normalization = Gt[0] + Gt[-1]
Ker = me.initker_fermion(omega, beta, tau)
elif p['statistics'] == 'bose':
normalization = integrate.trapz(Gt, x=tau)
Ker = me.initker_boson(omega, beta, tau)
print 'beta=', beta
print 'normalization=', normalization
# Set error
if p['idg']:
sxt = ones(len(tau)) / (p['deltag']**2)
else:
sxt = Gt * p['deltag']
for i in range(len(sxt)):
if sxt[i] < 1e-5: sxt[i] = 1e-5
sxt = 1. / sxt**2
# Set model
if p['iflat'] == 0:
model = normalization * ones(len(omega)) / sum(f0)
elif p['iflat'] == 1:
model = exp(-omega**2 / p['gwidth'])
model *= normalization / dot(model, f0)
else:
dat = loadtxt('model.dat').transpose()
fm = interpolate.interp1d(dat[0], dat[1])
model = fm(omega)
model *= normalization / dot(model, f0)
#savetxt('brisi_test', vstack((tau, fsg*dot(model,Ker))).transpose())
print 'Model normalization=', dot(model, f0)
# Set starting Aw(omega)
Aw = random.rand(len(omega))
Aw = Aw * (normalization / dot(Aw, f0))
print 'Aw normalization=', dot(Aw, f0)
dlda = me.initdlda(omega, Ker, sxt)
temp = 10.
rfac = 1.
alpha = p['alpha0']
for itt in range(p['Nitt']):
print itt, 'Restarting maxent with rfac=', rfac, 'alpha=', alpha
iseed = random.randint(0, maxint)
me.maxent(Aw, rfac, alpha, temp, Ker, sxt, Gt, model, f0, p['Asteps'],
iseed)
S = me.entropy(Aw, model, f0)
Trc = me.lambdac(alpha, Aw, omega, dlda)
ratio = -2 * S * alpha / Trc
print 'Finished maxent with alpha=', alpha, '-2*alpha*S=', -2 * alpha * S, 'Trace=', Trc
print ' ratio=', ratio
savetxt('dos_' + str(itt), vstack((omega, Aw)).transpose())
temp = 0.001
rfac = 0.05
if abs(ratio - 1) < p['min_ratio']: break
if (abs(ratio) < 0.05):
alpha *= 0.5
else:
alpha *= (1. + 0.001 * (random.rand() - 0.5)) / ratio
for itt in range(p['Nr']):
print 'Smoothing itt ', itt
Aw = Broad(p['bwdth'], omega, Aw)
Aw *= (normalization / dot(Aw, f0)) # Normalizing Aw
savetxt('dos_' + str(p['Nitt']), vstack((omega, Aw)).transpose())
temp = 0.005
rfac = 0.005
iseed = random.randint(0, maxint)
me.maxent(Aw, rfac, alpha, temp, Ker, sxt, Gt, model, f0, p['Asteps'],
iseed)
S = me.entropy(Aw, model, f0)
Trc = me.lambdac(alpha, Aw, omega, dlda)
ratio = -2 * S * alpha / Trc
print 'Finished smoothing run with alpha=', alpha, '-2*alpha*S=', -2 * alpha * S, 'Trace=', Trc
print ' ratio=', ratio
savetxt('gtn', vstack((tau, fsg * dot(Aw, Ker))).transpose())
Aw = Broad(p['bwdth'], omega, Aw)
savetxt('dos.out', vstack((omega, Aw)).transpose())
return (Aw, omega)
