def solve_coulomb(rho_U, Uext, r, tau_u_set, tau_rho_set, **kwarg):
params = {
'it' : 0,
'zero_endpoint' : False,
'display_callback' : empty_callback,
'fname_template' : "data/coulombsim-it=%d.npz"
}
params.update(kwarg)
print params
zero_endpoint = params['zero_endpoint']
it = params['it']
display_callback = params['display_callback']
fname_template = params['fname_template']
rexp = util.make_exp_grid(r.min(), r.max(), len(r))
C = coulomb.kernel( rexp )
U = np.array( Uext )
rho = np.zeros( (len(r)) )
j = 0
zero_U = True
def mkFilename(it):
fname = fname_template % (it)
print "fname: ", fname
return fname
if it > 0: # Load previous solution, if possible
data = np.load( mkFilename( it ) )
rho = data['rho']
U = data['U']
while True:
tau_U = tau_u_set [it % len(tau_u_set)]
tau_rho = tau_rho_set[it % len(tau_rho_set)]
it += 1
U1 = np.dot( C, util.gridswap(r, rexp, rho ) )
U1 = util.gridswap(rexp, r, U1)
#rho = util.gridswap(rexp, r, rho)
U1 += Uext
if zero_endpoint: U1 -= U1[-1];
err_U = linalg.norm(U - U1)
U += tau_U * (U1 - U)
if zero_endpoint: U -= U[-1];
rho1 = rho_U(U, r)
err_rho = linalg.norm(rho1 - rho)
rho += tau_rho * (rho1 - rho)
print "U error", err_U, "rho error", err_rho, "it", it
np.savez(mkFilename( it ), rho=rho, U=U, rho1=rho1, U1=U1, r=r)
display_callback(it, r, U, rho, U1, rho1)
if (err_U < (1e-4)) and (err_rho < (1e-5)):
break
if (err_U > 1e+6) or (err_rho > 1e+6):
print "A clear divergence"
break
return U, rho
#def Ur(rx):
# if rx > r_0:
# return -Z/rx
# return -Z / r_0
#U = np.vectorize(Ur)(r)
#def rho_b(rx):
# #if rx > r_0: return 0.0;
# #return Z / math.pi / r_0**2
# return r_0**2 / math.pi / (rx**2 + r_0**2)**2 * Z
delta_func = deltafunc.DeltaGauss(r_0)
#delta_func = deltafunc.DeltaCubic(r_0)
rho_bare = Z * delta_func.rho(r)
U = Z * delta_func.U(r)
rexp = util.make_exp_grid(0.001, 50.0, 1000)
Qcoul = Kernel(rexp, coulomb.kernel(rexp))
#rho_bare = np.vectorize(rho_b)(r)
#U = Qcoul(r, rho_bare)
#U[0:3] = U[3]
if True:
import pylab as pl
pl.plot (r, U)
pl.plot (r, Z / np.sqrt(r**2 + r_0**2))
pl.figure()
pl.loglog(r, np.abs(U))
pl.loglog(r, Z / np.sqrt(r**2 + r_0**2))
pl.show ()
rho_th = - math.pi / 8.0 * rho_bare
#rho_th = -Z * r_0 / 16.0 / np.sqrt(r**2 + r_0**2)**3
rho_RPA = graphene.rho_RPA(U)
#def Ur(rx):
# if rx > r_0:
# return -Z/rx
# return -Z / r_0
#U = np.vectorize(Ur)(r)
#def rho_b(rx):
# #if rx > r_0: return 0.0;
# #return Z / math.pi / r_0**2
# return r_0**2 / math.pi / (rx**2 + r_0**2)**2 * Z
delta_func = deltafunc.DeltaGauss(r_0)
#delta_func = deltafunc.DeltaCubic(r_0)
rho_bare = Z * delta_func.rho(r)
U = Z * delta_func.U(r)
rexp = util.make_exp_grid(0.001, 50.0, 1000)
Qcoul = Kernel(rexp, coulomb.kernel(rexp))
#rho_bare = np.vectorize(rho_b)(r)
#U = Qcoul(r, rho_bare)
#U[0:3] = U[3]
if True:
import pylab as pl
pl.plot(r, U)
pl.plot(r, Z / np.sqrt(r**2 + r_0**2))
pl.figure()
pl.loglog(r, np.abs(U))
pl.loglog(r, Z / np.sqrt(r**2 + r_0**2))
pl.show()
rho_th = -math.pi / 8.0 * rho_bare
#rho_th = -Z * r_0 / 16.0 / np.sqrt(r**2 + r_0**2)**3
rho_RPA = graphene.rho_RPA(U)