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 __canonical_move__(self,right,tol):
'''
Move l-index by one with specific direction.
Parameters
--------------
right:
Move l to right if True.
tol:
The tolerence for compression.
'''
nsite=self.nsite
l=self.l
hndim=self.hndim
if (l>=nsite and right) or (l<=0 and not right):
raise ValueError('Can not move to %s for l = %s with %s sites in total.'%('right' if right else 'left',l,nsite))
if right:
B0=self.BL.pop(0)
B0=swapaxes(self.S[:,newaxis]*B0,0,1)
M=reshape(B0,(-1,B0.shape[-1]))
U,S,V=svd(M,full_matrices=False)
kpmask=abs(S)>tol
U,S,V=U[:,kpmask],S[kpmask],V[kpmask]
self.AL.append(swapaxes(reshape(U,(-1,hndim,U.shape[1])),0,1))
self.S=S
if len(self.BL)>0:
self.BL[0]=bcast_dot(V,self.BL[0])
else:
self.S*=V[0,0]
else:
A0=self.AL.pop(-1)
A0=swapaxes(A0*self.S,0,1)
M=reshape(A0,(A0.shape[0],-1))
U,S,V=svd(M,full_matrices=False)
kpmask=abs(S)>tol
U,S,V=U[:,kpmask],S[kpmask],V[kpmask]
self.BL.insert(0,swapaxes(reshape(V,(V.shape[0],hndim,-1)),0,1))
self.S=S
if len(self.AL)>0:
self.AL[-1]=bcast_dot(self.AL[-1],U)
else:
self.S*=U[0,0]