def Solve(self):
""" Solve the impurity problem """
# Find if an operator is in oplist
def mysearch(op):
l = [ k for (k,v) in OPdict.items() if (v-op).is_zero()]
assert len(l) <=1
return l[0] if l else None
# Same but raises an error if pb
def myfind(op):
r = mysearch(op)
if r==None : raise "Operator %s can not be found by myfind !"%r
return r
# For backward compatibility
self.update_params(self.__dict__)
# Test all a parameters before solutions
mpi.report(parameters.check(self.__dict__,self.Required,self.Optional))
# We have to add the Hamiltonian the epsilon part of G0
if type(self.H_Local) != type(Operator()) : raise "H_Local is not an operator"
H = self.H_Local
for a,alpha_list in self.GFStruct :
for mu in alpha_list :
for nu in alpha_list :
H += real(self.G0[a]._tail[2][mu,nu]) * Cdag(a,mu)*C(a,nu)
OPdict = {"Hamiltonian": H}
mpi.report("Hamiltonian with Eps0 term : ",H)
# First separate the quantum Numbers that are operators and those which are symmetries.
QuantumNumberOperators = dict( (n,op) for (n,op) in self.Quantum_Numbers.items() if type(op) == type(Operator()))
QuantumNumberSymmetries = dict( (n,op) for (n,op) in self.Quantum_Numbers.items() if type(op) != type(Operator()))
# Check that the quantum numbers commutes with the Hamiltonian
for name,op in QuantumNumberOperators.items():
assert commutator(self.H_Local ,op).is_zero(), "One quantum number is not commuting with Hamiltonian"
OPdict[name]=op
# Complete the OPdict with the fundamental operators
OPdict, nf, nb, SymChar, NameOpFundamentalList = operators.complete_op_list_with_fundamentals(OPdict)
# Add the operators to be averaged in OPdict and prepare the list for the C-code
self.Measured_Operators_Results = {}
self.twice_defined_Ops = {}
self.Operators_To_Average_List = []
for name, op in self.Measured_Operators.items():
opn = mysearch(op)
if opn == None :
OPdict[name] = op
self.Measured_Operators_Results[name] = 0.0
self.Operators_To_Average_List.append(name)
else:
mpi.report("Operator %s already defined as %s, using this instead for measuring"%(name,opn))
self.twice_defined_Ops[name] = opn
self.Measured_Operators_Results[opn] = 0.0
if opn not in self.Operators_To_Average_List: self.Operators_To_Average_List.append(opn)
# Time correlation functions are added
self.OpCorr_To_Average_List = []
for name, op in self.Measured_Time_Correlators.items():
opn = mysearch(op[0])
if opn == None :
OPdict[name] = op[0]
self.OpCorr_To_Average_List.append(name)
else:
mpi.report("Operator %s already defined as %s, using this instead for measuring"%(name,opn))
if opn not in self.OpCorr_To_Average_List: self.OpCorr_To_Average_List.append(opn)
# Create storage for data:
Nops = len(self.OpCorr_To_Average_List)
f = lambda L : GfImTime(indices = [0], beta = self.beta, n_time_points =L )
if (Nops>0):
self.Measured_Time_Correlators_Results = BlockGf(name_block_generator = [ ( n,f(self.Measured_Time_Correlators[n][1]) ) for n in self.Measured_Time_Correlators], make_copies=False)
else:
self.Measured_Time_Correlators_Results = BlockGf(name_block_generator = [ ( 'OpCorr',f(2) ) ], make_copies=False)
# Take care of the global moves
# First, given a function (a,alpha,dagger) -> (a', alpha', dagger')
# I construct a function on fundamental operators
def Map_GM_to_Fund_Ops( GM ) :
def f(fop) :
a,alpha, dagger = fop.name + (fop.dag,)
ap,alphap,daggerp = GM((a,alpha,dagger))
return Cdag(ap,alphap) if daggerp else C(ap,alphap)
return f
# Complete the OpList so that it is closed under the global moves
while 1:
added_something = False
for n,(proba,GM) in enumerate(self.Global_Moves):
# F is a function that map all operators according to the global move
F = extend_function_on_fundamentals(Map_GM_to_Fund_Ops(GM))
# Make sure that OPdict is complete, i.e. all images of OPdict operators are in OPdict
for name,op in OPdict.items() :
op_im = F(op)
if mysearch(op_im)==None :
# find the key and put in in the dictionnary
i=0
while 1:
new_name = name + 'GM' + i*'_' + "%s"%n
if new_name not in OPdict : break
added_something = True
OPdict[new_name] = op_im
# break the while loop
if not added_something: break
# Now I have all operators, I make the transcription of the global moves
self.Global_Moves_Mapping_List = []
for n,(proba,GM) in enumerate(self.Global_Moves):
F = extend_function_on_fundamentals(Map_GM_to_Fund_Ops(GM))
m = {}
for name,op in OPdict.items() :
op_im = F(op)
n1,n2 = myfind(op),myfind(op_im)
m[n1] = n2
name = "%s"%n
self.Global_Moves_Mapping_List.append((proba,m,name))
#mpi.report ("Global_Moves_Mapping_List", self.Global_Moves_Mapping_List)
# Now add the operator for F calculation if needed
if self.Use_F :
Hloc_WithoutQuadratic = self.H_Local.remove_quadratic()
for n,op in OPdict.items() :
if op.is_Fundamental():
op2 = commutator(Hloc_WithoutQuadratic,op)
if not mysearch(op2) : OPdict["%s_Comm_Hloc"%n] = op2
# All operators have real coefficients. Check this and remove the 0j term
# since the C++ expects operators with real numbers
for n,op in OPdict.items(): op.make_coef_real_and_check()
# Transcription of operators for C++
Oplist2 = operators.transcribe_op_list_for_C(OPdict)
SymList = [sym for (n,sym) in SymChar.items() if n in QuantumNumberSymmetries]
self.H_diag = C_Module.Hloc(nf,nb,Oplist2,QuantumNumberOperators,SymList,self.Quantum_Numbers_Selection,0)
# Create the C_Cag_Ops array which describes the grouping of (C,Cdagger) operator
# for the MonteCarlo moves : (a, alpha) block structure [ [ (C_name, Cdag_name)]]
self.C_Cdag_Ops = [ [ (myfind(C(a,alpha)), myfind(Cdag(a,alpha))) for alpha in al ] for a,al in self.GFStruct]
# Define G0_inv and correct it to have G0 to have perfect 1/omega behavior
self.G0_inv = inverse(self.G0)
Delta = self.G0_inv.delta()
for n,g in self.G0_inv:
assert(g.N1==g.N2)
identity=numpy.identity(g.N1)
self.G0[n] <<= gf_init.A_Omega_Plus_B(identity, g._tail[0])
self.G0[n] -= Delta[n]
#self.G0[n] <<= iOmega_n + g._tail[0] - Delta[n]
self.G0_inv <<= self.G0
self.G0.invert()
# Construct the function in tau
f = lambda g,L : GfImTime(indices = g.indices, beta = g.beta, n_time_points =L )
self.Delta_tau = BlockGf(name_block_generator = [ (n,f(g,self.N_Time_Slices_Delta) ) for n,g in self.G], make_copies=False, name='D')
self.G_tau = BlockGf(name_block_generator = [ (n,f(g,self.N_Time_Slices_Gtau) ) for n,g in self.G], make_copies=False, name='G')
self.F_tau = BlockGf(name_block_generator = self.G_tau, make_copies=True, name='F')
for (i,gt) in self.Delta_tau : gt.set_from_inverse_fourier(Delta[i])
mpi.report("Inv Fourier done")
if (self.Legendre_Accumulation):
self.G_Legendre = BlockGf(name_block_generator = [ (n,GfLegendre(indices =g.indices, beta =g.beta, n_legendre_coeffs =self.N_Legendre_Coeffs) ) for n,g in self.G], make_copies=False, name='Gl')
else:
self.G_Legendre = BlockGf(name_block_generator = [ (n,GfLegendre(indices =[1], beta =g.beta, n_legendre_coeffs =1) ) for n,g in self.G], make_copies=False, name='Gl') # G_Legendre must not be empty but is not needed in this case. So I make it as small as possible.
# Starting the C++ code
self.Sigma_Old <<= self.Sigma
C_Module.MC_solve(self.__dict__ ) # C++ solver
# Compute G on Matsubara axis possibly fitting the tail
if self.Legendre_Accumulation:
for s,g in self.G:
identity=numpy.zeros([g.N1,g.N2],numpy.float)
for i,m in enumerate (g._IndicesL):
for j,n in enumerate (g._IndicesR):
if m==n: identity[i,j]=1
self.G_Legendre[s].enforce_discontinuity(identity) # set the known tail
g <<= LegendreToMatsubara(self.G_Legendre[s])
else:
if (self.Time_Accumulation):
for name, g in self.G_tau:
identity=numpy.zeros([g.N1,g.N2],numpy.float)
for i,m in enumerate (g._IndicesL):
for j,n in enumerate (g._IndicesR):
if m==n: identity[i,j]=1
g._tail.zero()
g._tail[1] = identity
self.G[name].set_from_fourier(g)
# This is very sick... but what can we do???
self.Sigma <<= self.G0_inv - inverse(self.G)
self.fitTails()
self.G <<= inverse(self.G0_inv - self.Sigma)
# Now find the self-energy
self.Sigma <<= self.G0_inv - inverse(self.G)
mpi.report("Solver %(name)s has ended."%self.__dict__)
# for operator averages: if twice defined operator, rename output:
for op1,op2 in self.twice_defined_Ops.items():
self.Measured_Operators_Results[op1] = self.Measured_Operators_Results[op2]
for op1,op2 in self.twice_defined_Ops.items():
if op2 in self.Measured_Operators_Results.keys(): del self.Measured_Operators_Results[op2]
if self.Use_F :
for (n,f) in self.F: f.set_from_fourier(self.F_tau[n])
self.G2 = self.G0 + self.G0 * self.F
self.Sigma2 = self.F * inverse(self.G2)
def Solve(self,Iteration_Number=1,Test_Convergence=0.0001):
"""Calculation of the impurity Greens function using Hubbard-I"""
# Test all a parameters before solutions
print parameters.check(self.__dict__,self.Required,self.Optional)
#SolverBase.Solve(self,is_last_iteration,Iteration_Number,Test_Convergence)
if self.Converged :
mpi.report("Solver %(name)s has already converted: SKIPPING"%self.__dict__)
return
self.__save_eal('eal.dat',Iteration_Number)
mpi.report( "Starting Fortran solver %(name)s"%self.__dict__)
self.Sigma_Old <<= self.Sigma
self.G_Old <<= self.G
# call the fortran solver:
temp = 1.0/self.beta
gf,tail,self.atocc,self.atmag = gf_hi_fullu(e0f=self.ealmat, ur=self.ur, umn=self.umn, ujmn=self.ujmn,
zmsb=self.zmsb, nmom=self.Nmoments, ns=self.Nspin, temp=temp, verbosity = self.Verbosity)
#self.sig = sigma_atomic_fullu(gf=self.gf,e0f=self.eal,zmsb=self.zmsb,ns=self.Nspin,nlm=self.Nlm)
if (self.Verbosity==0):
# No fortran output, so give basic results here
mpi.report("Atomic occupancy in Hubbard I Solver : %s"%self.atocc)
mpi.report("Atomic magn. mom. in Hubbard I Solver : %s"%self.atmag)
# transfer the data to the GF class:
if (self.UseSpinOrbit):
nlmtot = self.Nlm*2 # only one block in this case!
else:
nlmtot = self.Nlm
M={}
isp=-1
for a,al in self.GFStruct:
isp+=1
#M[a] = gf[isp*self.Nlm:(isp+1)*self.Nlm,isp*self.Nlm:(isp+1)*self.Nlm,:]
M[a] = gf[isp*nlmtot:(isp+1)*nlmtot,isp*nlmtot:(isp+1)*nlmtot,:]
for i in range(min(self.Nmoments,10)):
self.tailtempl[a][i+1].array[:] = tail[i][isp*nlmtot:(isp+1)*nlmtot,isp*nlmtot:(isp+1)*nlmtot]
glist = lambda : [ GfImFreq(indices = al, beta = self.beta, n_matsubara = self.Nmsb, data =M[a], tail =self.tailtempl[a])
for a,al in self.GFStruct]
self.G = BlockGf(name_list = self.a_list, block_list = glist(),make_copies=False)
# Self energy:
self.G0 <<= gf_init.A_Omega_Plus_B(A=1,B=0.0)
M = [ self.ealmat[isp*nlmtot:(isp+1)*nlmtot,isp*nlmtot:(isp+1)*nlmtot] for isp in range((2*self.Nlm)/nlmtot) ]
self.G0 -= M
self.Sigma <<= self.G0 - inverse(self.G)
# invert G0
self.G0.invert()
def test_distance(G1,G2, dist) :
def f(G1,G2) :
print abs(G1._data.array - G2._data.array)
dS = max(abs(G1._data.array - G2._data.array).flatten())
aS = max(abs(G1._data.array).flatten())
return dS <= aS*dist
return reduce(lambda x,y : x and y, [f(g1,g2) for (i1,g1),(i2,g2) in izip(G1,G2)])
mpi.report("\nChecking Sigma for convergence...\nUsing tolerance %s"%Test_Convergence)
self.Converged = test_distance(self.Sigma,self.Sigma_Old,Test_Convergence)
if self.Converged :
mpi.report("Solver HAS CONVERGED")
else :
mpi.report("Solver has not yet converged")