LCPQ/dft_tools
3
0
Fork 0
mirror of https://github.com/triqs/dft_tools synced 2025-04-25 17:54:54 +02:00
Code Issues Releases Wiki Activity

removed preconditioned newton in favor of brent

Browse Source
This commit is contained in:
alberto-carta 2023-02-01 18:02:20 +01:00 committed by Alexander Hampel
parent 27bdb61136
commit d68d6d8974
1 changed files with 58 additions and 31 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

89
python/triqs_dft_tools/sumk_dft.py
View File

@ -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, newton
from scipy.optimize import minimize, newton, brenth, brentq
class SumkDFT(object):
@ -1965,7 +1965,7 @@ class SumkDFT(object):
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
* brent: finds bounds and proceeds with hyperbolic brent method, a compromise between speed and ensuring convergence
Returns
-------
@ -1974,9 +1974,45 @@ class SumkDFT(object):
within specified precision.
"""
def find_bounds(function, x_init, delta_x, max_loops=1000):
mpi.report("Finding bounds on chemical potential" )
x= x_init
# First find the bounds
y1 = function(x)
eps = np.sign(y1)
x1= x;
x2= x1;y2 = y1
nbre_loop=0
#abort the loop after maxiter is reached or when y1 and y2 have different sign
while (nbre_loop<= max_loops) and (y2*y1)>0:
nbre_loop +=1
x1=x2
y1=y2
x2 -= eps*delta_x
y2 = function(x2)
if nbre_loop > (max_loops):
raise ValueError("The bounds could not be found")
# Make sure that x2 > x1
if x1 > x2:
x1,x2 = x2,x1
y1,y2 = y2,y1
mpi.report(f"mu_interval: [ {x1:.4f} ; {x2:.4f} ]")
mpi.report(f"delta to target density interval: [ {y1:.4f} ; {y2:.4f} ]")
return x1, x2
# previous implementation
def F_bisection(mu): return self.total_density(mu=mu, broadening=broadening).real
density = self.density_required - self.charge_below
def F_newton(mu):
#using scipy.optimize
def F_optimize(mu):
mpi.report("Trying out mu = {}".format(str(mu)))
calc_dens = self.total_density(mu=mu, broadening=broadening).real - density
@ -1987,52 +2023,43 @@ class SumkDFT(object):
match method.lower():
case "dichotomy":
mpi.report("SUMK calc_mu: Using dichtomy adjustment to find chemical potential")
mpi.report("\nSUMK calc_mu: Using dichtomy adjustment to find chemical potential\n")
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,
mpi.report("\nSUMK calc_mu: Using Newton method to find chemical potential\n")
self.chemical_potential = newton(func=F_optimize,
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]
case 'brent':
mpi.report("\nSUMK calc_mu: Using Brent method to find chemical potential")
mpi.report("SUMK calc_mu: Finding bounds \n")
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,
mu_guess_0, mu_guess_1 = find_bounds(function=F_optimize,
x_init=self.chemical_potential,
delta_x=delta, max_loops=max_loops,
)
mu_guess_1 += 0.01 #scrambles higher lying interval to avoid getting stuck
mpi.report("\nSUMK calc_mu: Searching root with Brent method\n")
self.chemical_potential = brenth(f=F_optimize,
a=mu_guess_0,
b=mu_guess_1,
xtol=precision, maxiter=max_loops,
)
case _:
raise ValueError(
f"SUMK calc_mu: The method selected: {method}, is not implemented",
f"SUMK calc_mu: The method selected: {method}, is not implemented\n",
"""
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
* newton: newton method, fastest convergence but more unstable
* brent: finds bounds and proceeds with hyperbolic brent method, a compromise between speed and ensuring convergence
"""
)