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https://github.com/triqs/dft_tools
synced 2024-06-25 06:32:22 +02:00
removed preconditioned newton in favor of brent
This commit is contained in:
alberto-carta
Alexander Hampel
parent
27bdb61136
commit
d68d6d8974
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@ -36,7 +36,7 @@ from .block_structure import BlockStructure
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from itertools import product
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from warnings import warn
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from scipy import compress
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from scipy.optimize import minimize, newton
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from scipy.optimize import minimize, newton, brenth, brentq
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class SumkDFT(object):
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@ -1965,7 +1965,7 @@ class SumkDFT(object):
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Type of optimization used:
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* dichotomy: usual bisection algorithm from the TRIQS library
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* newton: newton method, faster convergence but more unstable
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* preconditioned_newton: uses a dichotomy adjustement with low tolerence to initialize the newton algorithm to improve stability
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* brent: finds bounds and proceeds with hyperbolic brent method, a compromise between speed and ensuring convergence
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Returns
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-------
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@ -1974,9 +1974,45 @@ class SumkDFT(object):
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within specified precision.
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"""
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def find_bounds(function, x_init, delta_x, max_loops=1000):
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mpi.report("Finding bounds on chemical potential" )
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x= x_init
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# First find the bounds
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y1 = function(x)
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eps = np.sign(y1)
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x1= x;
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x2= x1;y2 = y1
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nbre_loop=0
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#abort the loop after maxiter is reached or when y1 and y2 have different sign
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while (nbre_loop<= max_loops) and (y2*y1)>0:
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nbre_loop +=1
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x1=x2
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y1=y2
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x2 -= eps*delta_x
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y2 = function(x2)
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if nbre_loop > (max_loops):
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raise ValueError("The bounds could not be found")
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# Make sure that x2 > x1
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if x1 > x2:
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x1,x2 = x2,x1
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y1,y2 = y2,y1
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mpi.report(f"mu_interval: [ {x1:.4f} ; {x2:.4f} ]")
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mpi.report(f"delta to target density interval: [ {y1:.4f} ; {y2:.4f} ]")
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return x1, x2
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# previous implementation
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def F_bisection(mu): return self.total_density(mu=mu, broadening=broadening).real
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density = self.density_required - self.charge_below
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def F_newton(mu):
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#using scipy.optimize
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def F_optimize(mu):
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mpi.report("Trying out mu = {}".format(str(mu)))
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calc_dens = self.total_density(mu=mu, broadening=broadening).real - density
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@ -1987,52 +2023,43 @@ class SumkDFT(object):
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match method.lower():
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case "dichotomy":
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mpi.report("SUMK calc_mu: Using dichtomy adjustment to find chemical potential")
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mpi.report("\nSUMK calc_mu: Using dichtomy adjustment to find chemical potential\n")
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self.chemical_potential = dichotomy.dichotomy(function=F_bisection,
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x_init=self.chemical_potential, y_value=density,
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precision_on_y=precision, delta_x=delta, max_loops=max_loops,
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x_name="Chemical Potential", y_name="Total Density",
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verbosity=3)[0]
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case 'newton':
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mpi.report("SUMK calc_mu: Using newton method to find chemical potential")
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self.chemical_potential = newton(func=F_newton,
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mpi.report("\nSUMK calc_mu: Using Newton method to find chemical potential\n")
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self.chemical_potential = newton(func=F_optimize,
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x0=self.chemical_potential,
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tol=precision, maxiter=max_loops,
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)
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case 'preconditioned-newton':
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mpi.report("SUMK calc_mu: preconditioning newton with low tolerance dichtomy")
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mu_guess_0 = dichotomy.dichotomy(function=F_bisection,
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x_init=self.chemical_potential, y_value=density,
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precision_on_y=0.2, delta_x=delta, max_loops=max_loops,
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x_name="Chemical Potential", y_name="Total Density",
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verbosity=3)[0]
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case 'brent':
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mpi.report("\nSUMK calc_mu: Using Brent method to find chemical potential")
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mpi.report("SUMK calc_mu: Finding bounds \n")
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mu_guess_1 = dichotomy.dichotomy(function=F_bisection,
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x_init=mu_guess_0, y_value=density,
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precision_on_y=0.05, delta_x=delta, max_loops=max_loops,
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x_name="Chemical Potential", y_name="Total Density",
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verbosity=3)[0]
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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
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mpi.report(f"SUMK calc_mu: Chemical potential guesses are: {mu_guess_0} and {mu_guess_1}")
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mpi.report("SUMK calc_mu: Refining guesses with newton method to find chemical potential")
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self.chemical_potential = newton(func=F_newton,
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x0=mu_guess_0,
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x1=mu_guess_1,
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tol=precision, maxiter=max_loops,
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mu_guess_0, mu_guess_1 = find_bounds(function=F_optimize,
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x_init=self.chemical_potential,
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delta_x=delta, max_loops=max_loops,
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)
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mu_guess_1 += 0.01 #scrambles higher lying interval to avoid getting stuck
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mpi.report("\nSUMK calc_mu: Searching root with Brent method\n")
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self.chemical_potential = brenth(f=F_optimize,
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a=mu_guess_0,
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b=mu_guess_1,
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xtol=precision, maxiter=max_loops,
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)
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case _:
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raise ValueError(
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f"SUMK calc_mu: The method selected: {method}, is not implemented",
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f"SUMK calc_mu: The method selected: {method}, is not implemented\n",
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"""
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Please check for typos or select one of the following:
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* dichotomy: usual bisection algorithm from the TRIQS library
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* newton: newton method, faster convergence but more unstable
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* preconditioned_newton: uses a dichotomy adjustement with low tolerence to initialize the newton algorithm to improve stability
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* newton: newton method, fastest convergence but more unstable
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* brent: finds bounds and proceeds with hyperbolic brent method, a compromise between speed and ensuring convergence
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"""
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)
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