mirror of https://github.com/triqs/dft_tools
Add more integrators for the transport integral
It is now possible to use trapz, simps and quadl (with cubic
spline) to perform the omega integration needed in the transport code.
This commit is contained in:
Manuel Zingl
parent
6ecbf6720d
commit
b6e33ecc23
|
|
@ -18,13 +18,15 @@
|
|||
# TRIQS. If not, see <http://www.gnu.org/licenses/>.
|
||||
#
|
||||
################################################################################
|
||||
|
||||
import sys
|
||||
from types import *
|
||||
import numpy
|
||||
from pytriqs.gf.local import *
|
||||
import pytriqs.utility.mpi as mpi
|
||||
from symmetry import *
|
||||
from sumk_dft import SumkDFT
|
||||
from scipy.integrate import *
|
||||
from scipy.interpolate import *
|
||||
|
||||
class SumkDFTTools(SumkDFT):
|
||||
"""
|
||||
|
|
@ -613,8 +615,8 @@ class SumkDFTTools(SumkDFT):
|
|||
if (energy_window[0] >= energy_window[1] or energy_window[0] >= 0 or energy_window[1] <= 0):
|
||||
assert 0, "transport_distribution: energy_window wrong!"
|
||||
|
||||
if (abs(self.fermi_dis(energy_window[0]*beta)*self.fermi_dis(-energy_window[0]*beta)) > 1e-5
|
||||
or abs(self.fermi_dis(energy_window[1]*beta)*self.fermi_dis(-energy_window[1]*beta)) > 1e-5):
|
||||
if (abs(self.fermi_dis(energy_window[0],beta)*self.fermi_dis(-energy_window[0],beta)) > 1e-5
|
||||
or abs(self.fermi_dis(energy_window[1],beta)*self.fermi_dis(-energy_window[1],beta)) > 1e-5):
|
||||
mpi.report("\n####################################################################")
|
||||
mpi.report("transport_distribution: WARNING - energy window might be too narrow!")
|
||||
mpi.report("####################################################################\n")
|
||||
|
|
@ -718,8 +720,8 @@ class SumkDFTTools(SumkDFT):
|
|||
self.Gamma_w[direction] = (mpi.all_reduce(mpi.world, self.Gamma_w[direction], lambda x, y : x + y)
|
||||
/ self.cellvolume(self.lattice_type, self.lattice_constants, self.lattice_angles)[1] / self.n_symmetries)
|
||||
|
||||
|
||||
def transport_coefficient(self, direction, iq, n, beta):
|
||||
|
||||
def transport_coefficient(self, direction, iq, n, beta, method=None):
|
||||
r"""
|
||||
Calculates the transport coefficient A_n in a given direction for a given :math:`\Omega`. The required members (Gamma_w, directions, Om_mesh) have to be obtained first
|
||||
by calling the function :meth:`transport_distribution <pytriqs.applications.dft.sumk_dft_tools.SumkDFTTools.transport_distribution>`. For n>0 A is set to NaN if :math:`\Omega` is not 0.0.
|
||||
|
|
@ -734,6 +736,9 @@ class SumkDFTTools(SumkDFT):
|
|||
Number of the desired moment of the transport distribution.
|
||||
beta : double
|
||||
Inverse temperature :math:`\beta`.
|
||||
method : string
|
||||
Integration method: cubic spline and scipy.integrate.quad ('quad'), simpson rule ('simps'), trapezoidal rule ('trapz'), rectangular integration (otherwise)
|
||||
Note that the sampling points of the the self-energy are used!
|
||||
|
||||
Returns
|
||||
-------
|
||||
|
|
@ -744,24 +749,39 @@ class SumkDFTTools(SumkDFT):
|
|||
if not (mpi.is_master_node()): return
|
||||
|
||||
assert hasattr(self,'Gamma_w'), "transport_coefficient: Run transport_distribution first or load data from h5!"
|
||||
A = 0.0
|
||||
omegaT = self.omega * beta
|
||||
d_omega = self.omega[1] - self.omega[0]
|
||||
if (self.Om_mesh[iq] == 0.0):
|
||||
for iw in xrange(self.Gamma_w[direction].shape[1]):
|
||||
A += self.Gamma_w[direction][iq, iw] * self.fermi_dis(omegaT[iw]) * self.fermi_dis(-omegaT[iw]) * numpy.float(omegaT[iw])**n * d_omega
|
||||
elif (n == 0.0):
|
||||
for iw in xrange(self.Gamma_w[direction].shape[1]):
|
||||
A += (self.Gamma_w[direction][iq, iw] * (self.fermi_dis(omegaT[iw]) - self.fermi_dis(omegaT[iw] + self.Om_mesh[iq] * beta))
|
||||
/ (self.Om_mesh[iq] * beta) * d_omega)
|
||||
else:
|
||||
A = numpy.nan
|
||||
A = A * numpy.pi * (2.0-self.SP)
|
||||
|
||||
if (self.Om_mesh[iq] == 0.0 or n == 0.0):
|
||||
A = 0.0
|
||||
# setup the integrand
|
||||
if (self.Om_mesh[iq] == 0.0):
|
||||
A_int = self.Gamma_w[direction][iq] * (self.fermi_dis(self.omega,beta) * self.fermi_dis(-self.omega,beta)) * (self.omega*beta)**n
|
||||
elif (n == 0.0):
|
||||
A_int = self.Gamma_w[direction][iq] * (self.fermi_dis(self.omega,beta) - self.fermi_dis(self.omega+self.Om_mesh[iq],beta))/(self.Om_mesh[iq]*beta)
|
||||
|
||||
# w-integration
|
||||
if method == 'quad':
|
||||
# quad on interpolated w-points with cubic spline
|
||||
A_int_interp = interp1d(self.omega,A_int,kind='cubic')
|
||||
A = quad(A_int_interp, min(self.omega), max(self.omega), epsabs=1.0e-12,epsrel=1.0e-12,limit = 500)
|
||||
A = A[0]
|
||||
elif method == 'simps':
|
||||
# simpson rule for w-grid
|
||||
A = simps(A_int,self.omega)
|
||||
elif method == 'trapz':
|
||||
# trapezoidal rule for w-grid
|
||||
A = numpy.trapz(A_int,self.omega)
|
||||
else:
|
||||
# rectangular integration for w-grid (orignal implementation)
|
||||
d_w = self.omega[1] - self.omega[0]
|
||||
for iw in xrange(self.Gamma_w[direction].shape[1]):
|
||||
A += A_int[iw]*d_w
|
||||
A = A * numpy.pi * (2.0-self.SP)
|
||||
else:
|
||||
A = numpy.nan
|
||||
return A
|
||||
|
||||
|
||||
def conductivity_and_seebeck(self, beta):
|
||||
|
||||
def conductivity_and_seebeck(self, beta, method=None):
|
||||
r"""
|
||||
Calculates the Seebeck coefficient and the optical conductivity by calling
|
||||
:meth:`transport_coefficient <pytriqs.applications.dft.sumk_dft_tools.SumkDFTTools.transport_coefficient>`.
|
||||
|
|
@ -794,8 +814,8 @@ class SumkDFTTools(SumkDFT):
|
|||
|
||||
for direction in self.directions:
|
||||
for iq in xrange(n_q):
|
||||
A0[direction][iq] = self.transport_coefficient(direction, iq=iq, n=0, beta=beta)
|
||||
A1[direction][iq] = self.transport_coefficient(direction, iq=iq, n=1, beta=beta)
|
||||
A0[direction][iq] = self.transport_coefficient(direction, iq=iq, n=0, beta=beta, method=method)
|
||||
A1[direction][iq] = self.transport_coefficient(direction, iq=iq, n=1, beta=beta, method=method)
|
||||
print "A_0 in direction %s for Omega = %.2f %e a.u." % (direction, self.Om_mesh[iq], A0[direction][iq])
|
||||
print "A_1 in direction %s for Omega = %.2f %e a.u." % (direction, self.Om_mesh[iq], A1[direction][iq])
|
||||
if ~numpy.isnan(A1[direction][iq]):
|
||||
|
|
@ -810,7 +830,7 @@ class SumkDFTTools(SumkDFT):
|
|||
return self.optic_cond, self.seebeck
|
||||
|
||||
|
||||
def fermi_dis(self, x):
|
||||
def fermi_dis(self,w,beta):
|
||||
r"""
|
||||
Fermi distribution.
|
||||
|
||||
|
|
@ -819,11 +839,13 @@ class SumkDFTTools(SumkDFT):
|
|||
|
||||
Parameters
|
||||
----------
|
||||
x : double
|
||||
Inverse temperature times frequency :math:`\beta\omega`.
|
||||
|
||||
w : double
|
||||
frequency
|
||||
beta : double
|
||||
inverse temperature
|
||||
|
||||
Returns
|
||||
-------
|
||||
f : double
|
||||
"""
|
||||
return 1.0/(numpy.exp(x)+1)
|
||||
return 1.0/(numpy.exp(w*beta)+1)
|
||||
|
|
|
|||
Loading…
Reference in New Issue