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Added multiple zero finding methods to sumk.calc_mu

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alberto-carta 2023-01-31 20:46:08 +01:00 committed by Alexander Hampel
parent 03aa19b90d
commit 27bdb61136
2 changed files with 68 additions and 8 deletions
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1
.gitignore vendored
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@ -1,2 +1,3 @@
compile_commands.json
doc/cpp2rst_generated
build/

75
python/triqs_dft_tools/sumk_dft.py
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@ -36,7 +36,7 @@ from .block_structure import BlockStructure
from itertools import product
from warnings import warn
from scipy import compress
from scipy.optimize import minimize
from scipy.optimize import minimize, newton
class SumkDFT(object):
@ -1945,7 +1945,7 @@ class SumkDFT(object):
"""
self.chemical_potential = mu
def calc_mu(self, precision=0.01, broadening=None, delta=0.5, max_loops=100):
def calc_mu(self, precision=0.01, broadening=None, delta=0.5, max_loops=100, method="dichotomy"):
r"""
Searches for the chemical potential that gives the DFT total charge.
A simple bisection method is used.
@ -1961,6 +1961,12 @@ class SumkDFT(object):
max_loops : int, optional
Number of dichotomy loops maximally performed.
max_loops : string, optional
Type of optimization used:
* dichotomy: usual bisection algorithm from the TRIQS library
* newton: newton method, faster convergence but more unstable
* preconditioned_newton: uses a dichotomy adjustement with low tolerence to initialize the newton algorithm to improve stability
Returns
-------
mu : float
@ -1968,14 +1974,67 @@ class SumkDFT(object):
within specified precision.
"""
def F(mu): return self.total_density(mu=mu, broadening=broadening).real
def F_bisection(mu): return self.total_density(mu=mu, broadening=broadening).real
density = self.density_required - self.charge_below
def F_newton(mu):
self.chemical_potential = dichotomy.dichotomy(function=F,
x_init=self.chemical_potential, y_value=density,
precision_on_y=precision, delta_x=delta, max_loops=max_loops,
x_name="Chemical Potential", y_name="Total Density",
verbosity=3)[0]
mpi.report("Trying out mu = {}".format(str(mu)))
calc_dens = self.total_density(mu=mu, broadening=broadening).real - density
mpi.report("Delta to target density = {}".format(str(calc_dens)))
return calc_dens
#check for lowercase matching for the method variable
match method.lower():
case "dichotomy":
mpi.report("SUMK calc_mu: Using dichtomy adjustment to find chemical potential")
self.chemical_potential = dichotomy.dichotomy(function=F_bisection,
x_init=self.chemical_potential, y_value=density,
precision_on_y=precision, delta_x=delta, max_loops=max_loops,
x_name="Chemical Potential", y_name="Total Density",
verbosity=3)[0]
case 'newton':
mpi.report("SUMK calc_mu: Using newton method to find chemical potential")
self.chemical_potential = newton(func=F_newton,
x0=self.chemical_potential,
tol=precision, maxiter=max_loops,
)
case 'preconditioned-newton':
mpi.report("SUMK calc_mu: preconditioning newton with low tolerance dichtomy")
mu_guess_0 = dichotomy.dichotomy(function=F_bisection,
x_init=self.chemical_potential, y_value=density,
precision_on_y=0.2, delta_x=delta, max_loops=max_loops,
x_name="Chemical Potential", y_name="Total Density",
verbosity=3)[0]
mu_guess_1 = dichotomy.dichotomy(function=F_bisection,
x_init=mu_guess_0, y_value=density,
precision_on_y=0.05, delta_x=delta, max_loops=max_loops,
x_name="Chemical Potential", y_name="Total Density",
verbosity=3)[0]
mu_guess_1 = np.round(mu_guess_1, 4)+0.01 # rounding off second guess in case it is numerically too similar to guess 0
mpi.report(f"SUMK calc_mu: Chemical potential guesses are: {mu_guess_0} and {mu_guess_1}")
mpi.report("SUMK calc_mu: Refining guesses with newton method to find chemical potential")
self.chemical_potential = newton(func=F_newton,
x0=mu_guess_0,
x1=mu_guess_1,
tol=precision, maxiter=max_loops,
)
case _:
raise ValueError(
f"SUMK calc_mu: The method selected: {method}, is not implemented",
"""
Please check for typos or select one of the following:
* dichotomy: usual bisection algorithm from the TRIQS library
* newton: newton method, faster convergence but more unstable
* preconditioned_newton: uses a dichotomy adjustement with low tolerence to initialize the newton algorithm to improve stability
"""
)
return self.chemical_potential