def test_RF_free_energy():
import cDFT.minimisation as minimisation
test_data = minimisation.DFT(0.2, 'Hard Wall', 0.5, 1.0, 1024, 0.005,
'Rosenfeld')
print(test_data.n0.shape)
test_wdens = np.genfromtxt(
'../Tests/Test_data/Wilding_Weighted_densities_RF_free_energy')
test_data.n0[:] = test_wdens[:, 1]
test_data.n1[:] = test_wdens[:, 2]
test_data.n2[:] = test_wdens[:, 3]
test_data.n3[:] = test_wdens[:, 4]
test_data.n1v[:] = test_wdens[:, 5]
test_data.n2v[:] = test_wdens[:, 6]
test_data.n3neg[:] = 1.0 - test_wdens[:, 4]
test_data.rho[:] = test_wdens[:, 7]
free_energy = np.zeros(1024)
free_energy = Rosenfeld_free_energy(test_data)
free_energy_excess = np.sum(free_energy[:test_data.N - 3 * test_data.NiR] *
0.005)
free_energy_ideal = np.sum(
test_data.Temp *
test_data.rho[test_data.NiR:test_data.N - 2 * test_data.NiR] *
(np.log(test_data.rho[test_data.NiR:test_data.N - 2 * test_data.NiR]) -
1.0)) * 0.005
free_energy_ideal -= np.sum(
test_data.rho[test_data.NiR:test_data.N - 2 * test_data.NiR] *
(test_data.mu + np.log(0.38197))) * 0.005
print(
f'Excess = {free_energy_excess:.6f}\t Ideal = {free_energy_ideal:.6f}\t total = {free_energy_excess+free_energy_ideal:.6f}\n'
)
def test_RF_derivatives():
"""
Run this to check the output of the derivatives for the RF function match those
of the test data provided by the 'spherical_working.c' Wilding program.
"""
import cDFT.minimisation as minimisation
test_data = minimisation.DFT(0.2, 'Hard Wall', 0.5, 1.0, 256, 0.05,
'Rosenfeld')
test_wdens = np.genfromtxt(
'../Tests/Test_data/Wilding_Weighted_Densities_RF')
print(test_wdens.shape)
test_data.n0[:] = test_wdens[:, 1]
test_data.n1[:] = test_wdens[:, 2]
test_data.n2[:] = test_wdens[:, 3]
test_data.n3[:] = test_wdens[:, 4]
test_data.n1v[:] = test_wdens[:, 5]
test_data.n2v[:] = test_wdens[:, 6]
test_data.n3neg[:] = 1.0 - test_wdens[:, 4]
del test_wdens
calculate_Rosenfeld_derivatives(test_data)
with open('../test_RF_derivatives', 'w') as divs:
divs.write(
f'i rho d2 d3 d2v \n')
for i in range(1, test_data.N):
divs.write(
f'{i:{3}} {test_data.rho[i]:{7}.{5}} {test_data.d2[i]:{12}.{10}} {test_data.d3[i]:{12}.{10}} {test_data.d2v[i]:{12}.{10}}\n'
)
def test_WB_derivatives():
"""
Run this to check the ouput of the derivatives for the WB functional match those
of the test data provided by Roth.
"""
import cDFT.minimisation as minimisation
test_data = minimisation.DFT(0.2, 'Hard Wall', 1.0, 1.0, 256, 0.05,
'Whitebear')
test_wdens = np.genfromtxt('../Tests/Test_data/Roth_Weighted_Densities_WB')
print(test_wdens.shape)
test_data.n0[1:216] = test_wdens[:, 3]
test_data.n1[1:216] = test_wdens[:, 4]
test_data.n2[1:216] = test_wdens[:, 5]
test_data.n3[1:216] = test_wdens[:, 6]
test_data.n1v[1:216] = test_wdens[:, 7]
test_data.n2v[1:216] = test_wdens[:, 8]
test_data.n3neg[1:216] = 1.0 - test_wdens[:, 6]
del test_wdens
calculate_Whitebear_derivatives(test_data)
with open('../test_WB_derivatives', 'w') as divs:
divs.write(
f'i rho d2 d3 d2v \n')
for i in range(1, test_data.N):
divs.write(
f'{i:{3}} {test_data.rho[i]:{7}.{5}} {test_data.d2[i]:{12}.{10}} {test_data.d3[i]:{12}.{10}} {test_data.d2v[i]:{12}.{10}}\n'
)
def adsorption_sum_rule(DFT, alpha, file_path, geometry, Rs=None):
if geometry == 'planar':
minimise = minimisation.planar(DFT, alpha, file_path)
elif geometry == 'spherical':
minimise = minimisation.spherical(DFT, Rs, alpha, file_path)
minimise.minimise()
mu_old = minimise.DFT.mu + minimise.DFT.Temp * np.log(
minimise.DFT.rho_bulk)
if geometry == 'planar':
adsorp = adsorption('planar', minimise)
gamma_old = surface_tension('planar', minimise)
elif geometry == 'spherical':
adsorp = adsorption('spherical', minimise)
gamma_old = surface_tension('spherical', minimise)
del minimise
new_DFT = minimisation.DFT(DFT.eta * (1.00001), DFT.Vext_type, DFT.R,
DFT.Temp, DFT.N, DFT.dr, DFT.functional)
if geometry == 'planar':
minimise = minimisation.planar(new_DFT, alpha, file_path)
elif geometry == 'spherical':
minimise = minimisation.spherical(new_DFT, Rs, alpha, file_path)
mu_new = minimise.DFT.mu + minimise.DFT.Temp * np.log(
minimise.DFT.rho_bulk)
minimise.minimise()
if geometry == 'planar':
gamma_new = surface_tension('planar', minimise)
elif geometry == 'spherical':
gamma_new = surface_tension('spherical', minimise)
del minimise
dmu = mu_new - mu_old
deriv = -1.0 * (gamma_new - gamma_old) / dmu
print(f'\n----------------------------------------------------')
print(f'Adsorption = {adsorp:.10f} -dgamma/dmu = {deriv:.10f}')
print(f'Relative Error = {abs(deriv-adsorp)/adsorp:.10f}')
print(f'----------------------------------------------------\n')
return adsorp, deriv
In the mean time, enjoy playing around with cDFT! """ # To use the package, we import the various files import cDFT.minimisation as minimisation import cDFT.output as output import cDFT.standard_routines as standard_routines import numpy as np import matplotlib.pyplot as plt # The DFT object is specified as packing fraction, interaction, radius of spheres, # temperature, number of grid points (recommended to be a power of 2), grid discretisation \ # and functional. RF = minimisation.DFT(0.2,'Hard Wall',1.0,1.0,2**14,0.005,'Rosenfeld') # To initiate a planar minimisation, you must give a DFT, a mixing parameter (recommended # to be between 0.01 and 0.1) and an output filepath. To minimise, then just call the # minimise routine. planar = minimisation.planar(RF, 0.1, './RF_planar_example/') planar.minimise() # To see the density profile, send the minimisation object to output. This is # saved to a pdf in the output directory './RF_planar_example/'. output.plot_single_density(planar) # For the planar geometry, the surface tension, grand potential and adsorption can be found. # We can also explore the accuracy of the minimisation using some sum rules relating to these. # To find the surface tension, or the excess grand potential, use the standard_routines package, # specifying first the geometry as a string, and then sending the minimisation object.