def get_sigma_eig(self,wlist=None,interp='spline',kk_method='mac'):
'''
kk-relation to get (index1,index2) component of Sigma, we ignored pi factor here, for we will get U*FG^{-1}.
For reference:
* Initial version: J. Phys.: Condens. Matter 10.8365.
* The matrix version: PRB 79.214518
wlist:
the frequency space.
interp:
interpolation method.
* `spline`
* `pchip`
kk_method:
method to calculate kk-relation(Appl. Spectrosc. 42.952).
* `mac` -> using Maclaurin-method.
* `fft` -> using Successive Double Fourier Transformation method.
'''
nband=self.nband
print 'Interpolating A(w),B(w) to get self-energy Sigma(w).'
t0=time.time()
wl,Alist,Blist=self.data
if not wlist is None:
if interp=='pchip':
interpolator=pchip_interpolate
elif interp=='spline':
interpolator=matrix_spline
else:
raise Exception('Undefined interpolation method @get_sigma.')
Alist=interpolator(wl,Alist,wlist)
Blist=interpolator(wl,Blist,wlist)
else:
wlist=wl
Gilist=-pi*Alist
Filist=-pi*Blist
Gievals,Gievecs=eigh_sorted(Gilist)
#Fievals,Fievecs=eig_sorted(Filist)
if kk_method=='fft':
Grevals=kk_fft(Gievals,'i2r',expand=1.5)
Frlist=kk_fft(Filist,'i2r',expand=1.5)
elif kk_method=='mac':
Grevals=kk(Gievals,'i2r',wlist=wlist)
Frlist=kk(Filist,'i2r',wlist=wlist)
else:
raise Exception('Undefined calculation method for kk-relation!')
#Slist=self.U*array([(Br+1j*Bi).dot(inv(Ar+1j*Ai)) for Ar,Ai,Br,Bi in zip(Arlist,Alist,Brlist,Blist)])
#Srlist=(swapaxes(Slist.conj(),1,2)+Slist)/2.
#Silist=(swapaxes(Slist.conj(),1,2)-Slist)*(-1j/2.)
Gevals=Grevals+1j*Gievals
#Fevals=Frevals+1j*Fievals
invG=eigen_combine(1./Gevals,Gievecs)
F=Frlist+1j*Filist
#why here is a minus sign?!
S=-self.U*bcast_dot(F,invG)
t1=time.time()
print 'Elapse -> %s'%(t1-t0)
return S,invG,F
def measure(self,scale,dmmanagers,threadz=False,**kwargs):
'''
measure an operator(overload).
scale:
the EScale instance.
tdmanager:
the timeline manager, and instance TDManager.
threadz:
multi-threading over z.
**kwargs:
* FDM: wmin(-1),wmax(1),smearing_method(gaussian), b(0.5), tol(0 if zero temperature else 1e-12), nw(50)
* RDM: smearing_method(log_gaussian), b(0.4)
'''
AL=[];BL=[]
ntask=(scale.nz-1)/SIZE+1
for i in xrange(scale.nz):
if threadz:
if i/ntask==RANK:
print 'Measuring Sigma on core %s with Hamiltonian size %s.'%(RANK,dmmanagers[i].H.N)
w,A,B=self.get_expect(scale,dmmanagers[i],**kwargs)
AL.append(A)
BL.append(B)
else:
w,A,B=self.get_expect(scale,dmmanagers[i],**kwargs)
AL.append(A)
BL.append(B)
if threadz:
AL=COMM.gather(AL,root=0)
BL=COMM.gather(BL,root=0)
if RANK==0:
AL=concatenate(AL,axis=0)
BL=concatenate(BL,axis=0)
w,A,B=w,mean(AL,axis=0),mean(BL,axis=0)
A,B=COMM.bcast(A,root=0),COMM.bcast(B,root=0)
else:
A,B=mean(AL,axis=0),mean(BL,axis=0)
print 'Fixing Occational Negative Eigenvalues of A.'
aevals,aevecs=eigh(A)
amin=aevals.min()
if amin<0:
print 'Fixing Negative spectrum up to %s'%amin
aevals[aevals<0]=0
Alist=eigen_combine(aevals,aevecs)
self.data=w,A,B
def load_data(self,filename,fix_neg=False):
'''
load data.
filename:
the filename.
fix_neg:
fix negative eigenvalues of A of True.
'''
f=open(filename,'r')
self.data=pickle.load(f)
if fix_neg:
print 'Fixing Occational Negative Eigenvalues of A.'
Alist=self.data[1]
aevals,aevecs=eigh(Alist)
amin=aevals.min()
if amin<0:
print 'Fixing Negative spectrum up to %s'%amin
aevals[aevals<0]=0
self.data=self.data[0],eigen_combine(aevals,aevecs),self.data[2]
f.close()