def load(self, method):
"""Make sure all necessary attributes have been initialized"""
assert method in ('real', 'recip_gauss', 'recip_ewald'),\
str(method) + ' is an invalid method name,\n' +\
'use either real, recip_gauss, or recip_ewald'
if method.startswith('recip'):
if self.gd.comm.size > 1:
raise RuntimeError("Cannot do parallel FFT, use method='real'")
if not hasattr(self, 'k2'):
self.k2, self.N3 = construct_reciprocal(self.gd)
if method.endswith('ewald') and not hasattr(self, 'ewald'):
# cutoff radius
assert self.gd.orthogonal
rc = 0.5 * np.average(self.gd.cell_cv.diagonal())
# ewald potential: 1 - cos(k rc)
self.ewald = (np.ones(self.gd.n_c) -
np.cos(np.sqrt(self.k2) * rc))
# lim k -> 0 ewald / k2
self.ewald[0, 0, 0] = 0.5 * rc**2
elif method.endswith('gauss') and not hasattr(self, 'ng'):
gauss = Gaussian(self.gd)
self.ng = gauss.get_gauss(0) / sqrt(4 * pi)
self.vg = gauss.get_gauss_pot(0) / sqrt(4 * pi)
else: # method == 'real'
if not hasattr(self, 'solve'):
if self.poisson is not None:
self.solve = self.poisson.solve
else:
solver = PoissonSolver(nn=2)
solver.set_grid_descriptor(self.gd)
solver.initialize(load_gauss=True)
self.solve = solver.solve
def initialize(self, gd, load_gauss=False):
# XXX this won't work now, but supposedly this class will be deprecated
# in favour of FFTPoissonSolver, no?
self.gd = gd
if self.gd.comm.size > 1:
raise RuntimeError('Cannot do parallel FFT.')
self.k2, self.N3 = construct_reciprocal(self.gd)
if load_gauss:
gauss = Gaussian(self.gd)
self.rho_gauss = gauss.get_gauss(0)
self.phi_gauss = gauss.get_gauss_pot(0)
def initialize(self, gd, load_gauss=False):
# XXX this won't work now, but supposedly this class will be deprecated
# in favour of FFTPoissonSolver, no?
self.gd = gd
if self.gd.comm.size > 1:
raise RuntimeError('Cannot do parallel FFT.')
self.k2, self.N3 = construct_reciprocal(self.gd)
if load_gauss:
gauss = Gaussian(self.gd)
self.rho_gauss = gauss.get_gauss(0)
self.phi_gauss = gauss.get_gauss_pot(0)
def load_gauss(self, center=None):
"""Load compensating charge distribution for charged systems.
See Appendix B of
A. Held and M. Walter, J. Chem. Phys. 141, 174108 (2014).
"""
# XXX Check if update is needed (dielectric changed)?
epsr, dx_epsr, dy_epsr, dz_epsr = self.dielectric.eps_gradeps
gauss = Gaussian(self.gd, center=center)
rho_g = gauss.get_gauss(0)
phi_g = gauss.get_gauss_pot(0)
x, y, z = gauss.xyz
fac = 2. * np.sqrt(gauss.a) * np.exp(-gauss.a * gauss.r2)
fac /= np.sqrt(np.pi) * gauss.r2
fac -= erf(np.sqrt(gauss.a) * gauss.r) / (gauss.r2 * gauss.r)
fac *= 2.0 * 1.7724538509055159
dx_phi_g = fac * x
dy_phi_g = fac * y
dz_phi_g = fac * z
sp = dx_phi_g * dx_epsr + dy_phi_g * dy_epsr + dz_phi_g * dz_epsr
rho = epsr * rho_g - 1. / (4. * np.pi) * sp
invnorm = np.sqrt(4. * np.pi) / self.gd.integrate(rho)
self.phi_gauss = phi_g * invnorm
self.rho_gauss = rho * invnorm
Nc = (N, N, N) # Number of grid points along each axis
gd = GridDescriptor(Nc, (a, a, a), 0) # Grid-descriptor object
solver = PoissonSolver(nn=3) # Numerical poisson solver
solver.set_grid_descriptor(gd)
solve = solver.solve
xyz, r2 = coordinates(gd) # Matrix with the square of the radial coordinate
print(r2.shape)
r = np.sqrt(r2) # Matrix with the values of the radial coordinate
nH = np.exp(-2 * r) / pi # Density of the hydrogen atom
gauss = Gaussian(gd) # An instance of Gaussian
# /------------------------------------------------\
# | Check if Gaussian densities are made correctly |
# \------------------------------------------------/
for gL in range(2, 9):
g = gauss.get_gauss(gL) # a gaussian of gL'th order
print('\nGaussian of order', gL)
for mL in range(9):
m = gauss.get_moment(g, mL) # the mL'th moment of g
print(' %s\'th moment = %2.6f' % (mL, m))
equal(m, gL == mL, 1e-4)
# Check the moments of the constructed 1s density
print('\nDensity of Hydrogen atom')
for L in range(4):
m = gauss.get_moment(nH, L)
print(' %s\'th moment = %2.6f' % (L, m))
equal(m, (L == 0) / sqrt(4 * pi), 1.5e-3)
# Check that it is removed correctly
v = gauss.remove_moment(nH, 0)
def load_gauss(self):
if not hasattr(self, 'rho_gauss'):
gauss = Gaussian(self.gd)
self.rho_gauss = gauss.get_gauss(0)
self.phi_gauss = gauss.get_gauss_pot(0)
gd = GridDescriptor(Nc, (a, a, a), 0) # Grid-descriptor object
solver = PoissonSolver(nn=3) # Numerical poisson solver
solver.set_grid_descriptor(gd)
solver.initialize()
solve = solver.solve
xyz, r2 = coordinates(gd) # Matrix with the square of the radial coordinate
print(r2.shape)
r = np.sqrt(r2) # Matrix with the values of the radial coordinate
nH = np.exp(-2 * r) / pi # Density of the hydrogen atom
gauss = Gaussian(gd) # An instance of Gaussian
# /------------------------------------------------\
# | Check if Gaussian densities are made correctly |
# \------------------------------------------------/
for gL in range(2, 9):
g = gauss.get_gauss(gL) # a gaussian of gL'th order
print("\nGaussian of order", gL)
for mL in range(9):
m = gauss.get_moment(g, mL) # the mL'th moment of g
print(" %s'th moment = %2.6f" % (mL, m))
equal(m, gL == mL, 1e-4)
# Check the moments of the constructed 1s density
print("\nDensity of Hydrogen atom")
for L in range(4):
m = gauss.get_moment(nH, L)
print(" %s'th moment = %2.6f" % (L, m))
equal(m, (L == 0) / sqrt(4 * pi), 1.5e-3)
# Check that it is removed correctly
v = gauss.remove_moment(nH, 0)
def load_gauss(self, center=None):
if not hasattr(self, 'rho_gauss') or center is not None:
gauss = Gaussian(self.gd, center=center)
self.rho_gauss = gauss.get_gauss(0)
self.phi_gauss = gauss.get_gauss_pot(0)
# solver = HelmholtzSolver(0.16) # Numerical poisson solver
solver.set_grid_descriptor(gd)
solver.initialize()
xyz, r2 = coordinates(gd) # Matrix with the square of the radial coordinate
gauss = Gaussian(gd, a=inv_width) # An instance of Gaussian
test_screened_poisson = ScreenedPoissonGaussian(gd, a=inv_width)
# /-------------------------------------------------\
# | Check if Gaussian potentials are made correctly |
# \-------------------------------------------------/
# Array for storing the potential
pot = gd.zeros(dtype=float, global_array=False)
solver.load_gauss()
vg = test_screened_poisson.get_phi(-coupling) # esp. for dampening
# Get analytic functions
ng = gauss.get_gauss(0)
# vg = solver.phi_gauss
# Solve potential numerically
niter = solver.solve(pot, ng, charge=None, zero_initial_phi=True)
# Determine residual
# residual = norm(pot - vg)
residual = gd.integrate((pot - vg)**2)**0.5
# print result
print 'residual %s'%(
residual)
assert residual < 0.003
# mpirun -np 2 python gauss_func.py --gpaw-parallel --gpaw-debug
def load_gauss(self):
if not hasattr(self, 'rho_gauss'):
gauss = Gaussian(self.gd)
self.rho_gauss = gauss.get_gauss(0)
self.phi_gauss = gauss.get_gauss_pot(0)
psolvers = (WeightedFDPoissonSolver, ADM12PoissonSolver,
PolarizationPoissonSolver)
# test neutral system with constant permittivity
parprint('neutral, constant permittivity')
epsinf = 80.
eps = gd.zeros()
eps.fill(epsinf)
qs = (-1., 1.)
shifts = (-1., 1.)
rho = gd.zeros()
phi_expected = gd.zeros()
for q, shift in zip(qs, shifts):
gauss_norm = q / np.sqrt(4 * np.pi)
gauss = Gaussian(gd, center=(box / 2. + shift) * np.ones(3) / Bohr)
rho += gauss_norm * gauss.get_gauss(0)
phi_expected += gauss_norm * gauss.get_gauss_pot(0) / epsinf
for ps in psolvers:
phi = solve(ps, eps, rho)
parprint(ps, np.abs(phi - phi_expected).max())
equal(phi, phi_expected, 1e-3)
# test charged system with constant permittivity
parprint('charged, constant permittivity')
epsinf = 80.
eps = gd.zeros()
eps.fill(epsinf)
q = -2.
gauss_norm = q / np.sqrt(4 * np.pi)
gauss = Gaussian(gd, center=(box / 2. + 1.) * np.ones(3) / Bohr)
Nc = (N, N, N) # Number of grid points along each axis
gd = GridDescriptor(Nc, (a, a, a), 0) # Grid-descriptor object
solver = PoissonSolver(nn=3, use_charge_center=True)
solver.set_grid_descriptor(gd)
solver.initialize()
gauss = Gaussian(gd, a=inv_width, center=center_of_charge)
test_poisson = Gaussian(gd, a=inv_width, center=center_of_charge)
# /-------------------------------------------------\
# | Check if Gaussian potentials are made correctly |
# \-------------------------------------------------/
# Array for storing the potential
pot = gd.zeros(dtype=float, global_array=False)
solver.load_gauss()
vg = test_poisson.get_gauss_pot(0)
# Get analytic functions
ng = gauss.get_gauss(0)
# vg = solver.phi_gauss
# Solve potential numerically
niter = solver.solve(pot, ng, charge=1.0, zero_initial_phi=False)
# Determine residual
# residual = norm(pot - vg)
residual = gd.integrate((pot - vg)**2)**0.5
print('residual %s' % (
residual))
assert residual < 1e-5 # Better than 5.x
# mpirun -np 2 python gauss_func.py --gpaw-parallel --gpaw-debug
