from pytriqs.base.plot.mpl_interface import oplot
from pytriqs.base.gf_local import GfImFreq, Omega, inverse
g = GfImFreq(indices = [1], beta = 300, n_matsubara = 1000, name = "g")
g <<= inverse( Omega + 0.5 )
# the data we want to fit...
# The green function for omega \in [0,0.2]
X,Y = g.x_data_view (x_window = (0,0.2), flatten_y = True )
from pytriqs.base.fit.fit import Fit, linear, quadratic
fitl = Fit ( X,Y.imag, linear )
fitq = Fit ( X,Y.imag, quadratic )
oplot (g, '-o', x_window = (0,5) )
oplot (fitl , '-x', x_window = (0,0.5) )
oplot (fitq , '-x', x_window = (0,1) )
# a bit more complex, we want to fit with a one fermion level ....
# Cf the definition of linear and quadratic in the lib
one_fermion_level = lambda X, a,b : 1/(a * X *1j + b), r"${1}/(%f x + %f)$" , (1,1)
fit1 = Fit ( X,Y, one_fermion_level )
oplot (fit1 , '-x', x_window = (0,3) )
L = 101 # Number of Matsubara frequencies used in the Pade approximation
eta = 0.01 # Imaginary frequency shift
## Test Green's functions ##
# Two Lorentzians
def GLorentz(z):
return 0.7/(z-2.6+0.3*1j) + 0.3/(z+3.4+0.1*1j)
# Semicircle
def GSC(z):
return 2.0*(z + sqrt(1-z**2)*(log(1-z) - log(-1+z))/pi)
# A superposition of GLorentz(z) and GSC(z) with equal weights
def G(z):
return 0.5*GLorentz(z) + 0.5*GSC(z)
# Matsubara GF
gm = GfImFreq(indices = [0], beta = beta, name = "gm")
gm <<= Function(G)
gm._tail.zero()
gm._tail[1] = array([[1.0]])
# Analytic continuation of gm
g_pade = GfReFreq(indices = [0], beta = beta, mesh_array = arange(-6,6,0.01), name = "g_pade")
g_pade.set_from_pade(gm, N_Matsubara_Frequencies = L, Freq_Offset = eta)
from pytriqs.base.archive import HDFArchive
R = HDFArchive('pade.output.h5','w')
R['g_pade'] = g_pade
from pytriqs.base.lattice.tight_binding import *
from pytriqs.base.dos import HilbertTransform
from pytriqs.base.gf_local import GfImFreq
# Define a DOS (here on a square lattice)
BL = BravaisLattice(Units = [(1,0,0) , (0,1,0) ], orbital_positions= {"" : (0,0,0)} )
t = -1.00 # First neighbour Hopping
tp = 0.0*t # Second neighbour Hopping
hop= { (1,0) : [[ t]],
(-1,0) : [[ t]],
(0,1) : [[ t]],
(0,-1) : [[ t]],
(1,1) : [[ tp]],
(-1,-1): [[ tp]],
(1,-1) : [[ tp]],
(-1,1) : [[ tp]]}
TB = TightBinding (BL, hop)
d = dos(TB, n_kpts= 500, n_eps = 101, name = 'dos')[0]
#define a Hilbert transform
H = HilbertTransform(d)
#fill a Green function
G = GfImFreq(indices = ['up','down'], beta = 20)
Sigma0 = GfImFreq(indices = ['up','down'], beta = 20); Sigma0.zero()
G <<= H(Sigma = Sigma0,mu=0.)
