def iterate( vec_vhxc, pb, conf, eig_solver, n_eigs, mtx_b, log,
n_electron = 5 ):
global itercount
itercount += 1
from sfepy.physics import dft
pb.update_materials( extra_mat_args = {'mat_v' : {'vhxc' : vec_vhxc}} )
dummy = pb.create_state_vector()
output( 'assembling lhs...' )
tt = time.clock()
mtx_a = eval_term_op( dummy, conf.equations['lhs'], pb,
dw_mode = 'matrix', tangent_matrix = pb.mtx_a )
output( '...done in %.2f s' % (time.clock() - tt) )
print 'computing the Ax=Blx Kohn-Sham problem...'
eigs, mtx_s_phi = eig_solver( mtx_a, mtx_b, conf.options.n_eigs )
if len(eigs) < n_electron:
print len(eigs)
print eigs
raise Exception("Not enough eigenvalues have converged. Exiting.")
print "saving solutions, iter=%d" % itercount
out = {}
var_name = pb.variables.get_names( kind = 'state' )[0]
for ii in xrange( len(eigs) ):
vec_phi = pb.variables.make_full_vec( mtx_s_phi[:,ii] )
update_state_to_output( out, pb, vec_phi, var_name+'%03d' % ii )
pb.save_state( "tmp/iter%d.vtk" % itercount, out = out )
print "solutions saved"
vec_phi = nm.zeros_like( vec_vhxc )
vec_n = nm.zeros_like( vec_vhxc )
for ii in xrange( n_electron ):
vec_phi = pb.variables.make_full_vec( mtx_s_phi[:,ii] )
vec_n += vec_phi ** 2
vec_vxc = nm.zeros_like( vec_vhxc )
for ii, val in enumerate( vec_n ):
vec_vxc[ii] = dft.getvxc( val/(4*pi), 0 )
pb.set_equations( conf.equations_vh )
pb.time_update()
pb.variables['n'].data_from_data( vec_n )
print "Solving Ax=b Poisson equation"
vec_vh = pb.solve()
#sphere = eval_term_op( dummy, conf.equations['sphere'], pb)
#print sphere
norm = nla.norm( vec_vh + vec_vxc )
log( norm, norm )
return eigs, mtx_s_phi, vec_n, vec_vh, vec_vxc
def iterate(self, v_hxc_qp, eig_solver,
mtx_a_equations, mtx_a_variables, mtx_b, log, file_output,
n_electron=None):
from sfepy.physics import dft
self.itercount += 1
pb = self.problem
opts = self.app_options
n_electron = get_default( n_electron, opts.n_electron )
sh = self.qp_shape
v_hxc_qp = nm.array(v_hxc_qp, dtype=nm.float64)
v_hxc_qp.shape = (sh[0] * sh[1],) + sh[2:]
mat_v = Materials(mtx_a_equations.collect_materials())['mat_v']
mat_v.set_extra_args(vhxc=v_hxc_qp)
mat_v.time_update(None, pb.domain, mtx_a_equations)
v_hxc_qp.shape = sh
v_ion_qp = mat_v.get_data(('Omega', 'i1'), 0, 'V_ion')
output( 'assembling lhs...' )
tt = time.clock()
mtx_a = eval_equations(mtx_a_equations, mtx_a_variables,
mode='weak', dw_mode='matrix')
output( '...done in %.2f s' % (time.clock() - tt) )
assert_( nm.alltrue( nm.isfinite( mtx_a.data ) ) )
output( 'computing the Ax=Blx Kohn-Sham problem...' )
tt = time.clock()
eigs, mtx_s_phi = eig_solver( mtx_a, mtx_b,
opts.n_eigs, eigenvectors = True )
output( '...done in %.2f s' % (time.clock() - tt) )
n_eigs_ok = len(eigs)
output( 'setting-up smearing...' )
e_f, smear_tuned = setup_smearing( eigs, n_electron )
output( 'Fermi energy:', e_f )
if e_f is None:
raise Exception("cannot find Fermi energy - exiting.")
weights = smear_tuned(eigs)
output( '...done' )
if (weights[-1] > 1e-12):
output("last smearing weight is nonzero (%s eigs ok)!" % n_eigs_ok)
output( "saving solutions, iter=%d..." % self.itercount )
out = {}
var_name = mtx_a_variables.get_names(kind='state')[0]
for ii in xrange( n_eigs_ok ):
vec_phi = mtx_a_variables.make_full_vec(mtx_s_phi[:,ii])
update_state_to_output( out, pb, vec_phi, var_name+'%03d' % ii )
name = op.join( opts.output_dir, "iter%d" % self.itercount )
pb.save_state('.'.join((name, opts.output_format)), out=out)
output( "...solutions saved" )
output('computing total charge...')
tt = time.clock()
aux = pb.create_evaluable('dq_state_in_volume_qp.i1.Omega(Psi)')
psi_equations, psi_variables = aux
var = psi_variables['Psi']
n_qp = nm.zeros_like(v_hxc_qp)
for ii in xrange( n_eigs_ok ):
vec_phi = mtx_a_variables.make_full_vec(mtx_s_phi[:,ii])
var.data_from_any(vec_phi)
phi_qp = eval_equations(psi_equations, psi_variables)
n_qp += weights[ii] * (phi_qp ** 2)
output('...done in %.2f s' % (time.clock() - tt))
ap, vg = var.get_approximation(('i1', 'Omega', 0), 'Volume')
det = vg.variable(1)
charge = (det * n_qp).sum()
## Same as above.
## out = nm.zeros((n_qp.shape[0], 1, 1, 1), dtype=nm.float64)
## vg.integrate(out, n_qp)
## charge = out.sum()
vec_n = self._interp_to_nodes(n_qp)
var.data_from_any(vec_n)
charge_n = pb.evaluate('di_volume_integrate.i1.Omega(Psi)', Psi=var)
##
# V_xc in quadrature points.
v_xc_qp = nm.zeros((nm.prod(self.qp_shape),), dtype=nm.float64)
for ii, val in enumerate(n_qp.flat):
## print ii, val
v_xc_qp[ii] = dft.getvxc(val, 0)
assert_(nm.isfinite(v_xc_qp).all())
v_xc_qp.shape = self.qp_shape
mat_key = mat_v.datas.keys()[0]
pb.set_equations( pb.conf.equations_vh )
pb.select_bcs( ebc_names = ['VHSurface'] )
pb.update_materials()
output( "solving Ax=b Poisson equation" )
pb.materials['mat_n'].reset()
pb.materials['mat_n'].set_all_data({mat_key : {0: {'N' : n_qp}}})
vec_v_h = pb.solve()
var.data_from_any(vec_v_h)
v_h_qp = pb.evaluate('dq_state_in_volume_qp.i1.Omega(Psi)', Psi=var)
v_hxc_qp = v_h_qp + v_xc_qp
norm = nla.norm(v_hxc_qp.ravel())
dnorm = abs(norm - self.norm_v_hxc0)
log(norm, max(dnorm,1e-20)) # logplot of pure 0 fails.
file_output( '%d: F(x) = |VH + VXC|: %f, abs(F(x) - F(x_prev)): %e'\
% (self.itercount, norm, dnorm) )
file_output("-"*70)
file_output('Fermi energy:', e_f)
file_output("----------------------------------------")
file_output(" # | eigs | smearing")
file_output("----|-----------------|-----------------")
for ii in xrange( n_eigs_ok ):
file_output("% 3d | %-15s | %-15s" % (ii+1, eigs[ii], weights[ii]))
file_output("----------------------------------------")
file_output("charge_qp: ", charge)
file_output("charge_n: ", charge_n)
file_output("----------------------------------------")
file_output("|N|: ", nla.norm(n_qp.ravel()))
file_output("|V_H|: ", nla.norm(v_h_qp.ravel()))
file_output("|V_XC|: ", nla.norm(v_xc_qp.ravel()))
file_output("|V_HXC|: ", norm)
if self.iter_hook is not None: # User postprocessing.
pb.select_bcs(ebc_names=['ZeroSurface'])
mtx_phi = self.make_full(mtx_s_phi)
data = Struct(iteration = self.itercount,
eigs = eigs, weights = weights,
mtx_s_phi = mtx_s_phi, mtx_phi = mtx_phi,
vec_n = vec_n, vec_v_h = vec_v_h,
n_qp = n_qp, v_ion_qp = v_ion_qp, v_h_qp = v_h_qp,
v_xc_qp = v_xc_qp, file_output = file_output)
self.iter_hook(self.problem, data = data)
file_output("-"*70)
self.norm_v_hxc0 = norm
return eigs, mtx_s_phi, vec_n, vec_v_h, v_ion_qp, v_xc_qp, v_hxc_qp
