################################################################################
#
# TRIQS: a Toolbox for Research in Interacting Quantum Systems
#
# Copyright (C) 2011 by M. Ferrero, O. Parcollet
#
# TRIQS is free software: you can redistribute it and/or modify it under the
# terms of the GNU General Public License as published by the Free Software
# Foundation, either version 3 of the License, or (at your option) any later
# version.
#
# TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
# details.
#
# You should have received a copy of the GNU General Public License along with
# TRIQS. If not, see <http://www.gnu.org/licenses/>.
#
################################################################################
from sumk_discrete import SumkDiscrete
from pytriqs.lattice.tight_binding import TBLattice
class SumkDiscreteFromLattice (SumkDiscrete) :
r"""
* Computes
.. math::
G \leftarrow \sum_k (\omega + \mu - \epsilon_k - \Sigma(k,\omega))^{-1}
for GF functions with blocks of the size of the matrix eps_k with a discrete sum.
* The object contains the discretized hoppings and points in the arrays
Hopping, BZ_Points,BZ_weights,Mu_Pattern,Overlap (IF non orthogonal)
It can also generate a grid (ReComputeGrid) for a regular grid or a Gauss-Legendre sum
for the whole Brillouin Zone or a patch of the BZ.
"""
def __init__(self, lattice, patch = None, n_points = 8, method = "Riemann") :
"""
:param lattice: The underlying pytriqs.lattice or pytriqs.super_lattice provinding t(k)
:param n_points: Number of points in the BZ in EACH direction
:param method: Riemann (default) or 'Gauss' (not checked)
"""
assert isinstance(lattice,TBLattice), "lattice must be a TBLattice instance"
self.SL = lattice
self.patch,self.method = patch,method
# init the array
SumkDiscrete.__init__ (self, dim = self.SL.dim, gf_struct = lattice.OrbitalNames)
self.Recompute_Grid(n_points, method)
#-------------------------------------------------------------
def __reduce__(self) :
return self.__class__, (self.SL, self.patch, self.BZ_weights.shape[0],self.method)
#-------------------------------------------------------------
def Recompute_Grid (self, n_points, method="Riemann", Q=None) :
"""(Re)Computes the grid on the patch given at construction :
* n_points : Number of points in the BZ in EACH direction
* method : Riemann (default) or 'Gauss' (not checked)
* Q : anything from which a 1d-array can be computed.
computes t(k+Q) instead of t(k) (useful for bare chi_0)
"""
assert method in ["Riemann","Gauss"], "method %s is not recognized"%method
self.method = method
self.resize_arrays(n_points)
if self.patch :
self.__Compute_Grid_One_patch(self.patch, n_points , method, Q)
else :
self.__Compute_Grid(n_points, method, Q)
#-------------------------------------------------------------
def __Compute_Grid (self, n_bz, method="Riemann", Q=None) :
"""
Internal
"""
n_bz_A,n_bz_B, n_bz_C = n_bz, (n_bz if self.dim > 1 else 1), (n_bz if self.dim > 2 else 1)
nk = n_bz_A* n_bz_B* n_bz_C
self.resize_arrays(nk)
# compute the points where to evaluate the function in the BZ and with the weights
def pts1d(N):
for n in range(N) :
yield (n - N/2 +1.0) / N
if method=="Riemann" :
BZ_weights=1.0/nk
k_index =0
for nz in pts1d(n_bz_C) :
for ny in pts1d(n_bz_B) :
for nx in pts1d(n_bz_A) :
self.BZ_Points[k_index,:] = (nx,ny,nz)[0:self.dim]
k_index +=1
elif method=="Gauss" :
assert 0, "Gauss : NR gauleg not checked"
k_index =0
for wa,ptsa in NR.Gauleg(-pi,pi,n_bz_A) :
for wb,ptsb in NR.Gauleg(-pi,pi,n_bz_B) :
for wc,ptsc in NR.Gauleg(-pi,pi,n_bz_C) :
self.BZ_Points[k_index,:] = (ptsa,ptsb,ptsc)[0:self.dim] /(2*pi)
self.BZ_weights[k_index] = wa * wb * wc
k_index +=1
else :
raise IndexError, "Summation method unknown"
# A shift
if Q :
try :
Q = numpy.array(Q)
assert len(Q.shape) ==1
except :
raise RuntimeError, "Q is not of correct type"
for k_index in range(self.N_kpts()) :
self.BZ_Points[k_index,:] +=Q
# Compute the discretized hoppings from the Superlattice
self.Hopping[:,:,:] = self.SL.hopping(self.BZ_Points.transpose()).transpose(2,0,1)
if self.orthogonal_basis:
self.Mu_Pattern[:,:] = self.SL.MuPattern[:,:]
else :
assert 0 , "not checked"
self.Overlap[:,:,:] = self.SL.Overlap(BZ_Points.transpose())
mupat = self.SL.Mu_Pattern()
for k_index in range(self.N_kpts()) :
self.Mu_Pattern[:,:,k_index] = Num.dot( mupat ,self.Overlap[:,:,k_index])
#-------------------------------------------------------------
def __Compute_Grid_One_patch(self, patch, n_bz, method = "Riemann", Q=None) :
"""
Internal
"""
tritemp = numpy.array(patch._triangles)
ntri = len(tritemp)/3
nk = n_bz*n_bz*ntri
self.resize_arrays(nk)
# Reshape the list to group 3 points together
triangles = tritemp.reshape((ntri,3,2))
total_weight = 0
# Loop over all k-points in the triangles
k_index = 0
for (a,b,c),w in zip(triangles,patch._weights):
g = ((a+b+c)/3.0-a)/n_bz;
for i in range(n_bz):
s = i/float(n_bz)
for j in range(n_bz-i):
t = j/float(n_bz)
for k in range(2):
rv = a+s*(b-a)+t*(c-a)+(k+1)*g
if k == 0 or j < n_bz-i-1:
self.BZ_Points[k_index] = rv
self.BZ_weights[k_index] = w/(n_bz*n_bz)
total_weight += self.BZ_weights[k_index]
k_index = k_index+1
# Normalize weights so that they sum up to 1
self.BZ_weights /= total_weight
# Compute the discretized hoppings from the Superlattice
self.Hopping[:,:,:] = self.SL.hopping(self.BZ_Points.transpose()).transpose(2,0,1)
if self.orthogonal_basis:
self.Mu_Pattern[:,:] = self.SL.MuPattern[:,:]
else :
assert 0 , "not checked"