def __init__(self, r, Ef, **kwargs):
params = {
'Temp': 0.01,
'Ecut': -1.5,
'B': 0.0,
'Mmax': 16,
'grid_intra': 'lin',
'grid_inter': 'exp'
}
params.update(**kwargs)
self.Emin = min(Ef, params['Ecut']) # Ecut could be both positive
self.Emax = max(Ef, params['Ecut']) # and negative
self.Temp = params['Temp']
self.r = r
self.rexp = util.make_exp_grid(r.min(), r.max(), len(r))
self.B = params['B']
self.mlist = np.array(range(0, params['Mmax']))
grid_dict = {'lin': self.r, 'exp': self.rexp}
r_inter = Grid(grid_dict[params['grid_inter']], params['grid_inter'])
r_intra = Grid(grid_dict[params['grid_intra']], params['grid_intra'])
if False: # Use this to skip kernel calculation; helpful in debugging
self.Q_Emin = np.zeros(
(len(self.rexp),
len(self.rexp))) #RPA_kernel(self.rexp, abs(self.Emin))
self.Q_Emax = np.zeros(np.shape(
self.Q_Emin)) #RPA_kernel(self.rexp, abs(self.Emax))
else:
# Full RPA kernel
self.Q_Emin = RPA_tot(r_inter, r_intra, abs(self.Emin))
self.Q_Emax = RPA_tot(r_inter, r_intra, abs(self.Emax))
#Kernel(self.rexp, RPA_kernel(self.rexp, abs(self.Emin)))
#self.Q_Emax = Kernel(self.rexp, RPA_kernel(self.rexp, abs(self.Emax)))
# m-resolved RPA kernel
if False:
self.Qm_Emax = self.Q_Emax
#np.zeros(np.shape(self.Q_Emin))#rpakernel.kernel_m(self.rexp, self.mlist, abs(self.Emax))
self.Qm_Emin = self.Q_Emin
#np.zeros(np.shape(self.Q_Emax))#rpakernel.kernel_m(self.rexp, self.mlist, abs(self.Emin))
else:
self.Qm_Emin = RPA_m(r_inter, r_intra, abs(self.Emin), self.mlist)
self.Qm_Emax = RPA_m(r_inter, r_intra, abs(self.Emax), self.mlist)
#rpakernel.kernel_m(self.rexp, self.mlist, abs(self.Emax))
#self.Qm_Emin =
#rpakernel.kernel_m(self.rexp, self.mlist, abs(self.Emin))
self.rho_0 = self.diracDensity(np.zeros(np.shape(r)))
self.Q_corr = RPA_corr(r_inter, r_intra, abs(self.Emax), self.mlist)
N = len(self.r)
def __init__ (self, r, Ef, **kwargs):
params = {
'Temp' : 0.01,
'Ecut' : -1.5,
'B' : 0.0,
'Mmax' : 16,
'grid_intra' : 'lin',
'grid_inter' : 'exp'
}
params.update(**kwargs)
self.Emin = min(Ef, params['Ecut']) # Ecut could be both positive
self.Emax = max(Ef, params['Ecut']) # and negative
self.Temp = params['Temp']
self.r = r
self.rexp = util.make_exp_grid(r.min(), r.max(), len(r))
self.B = params['B']
self.mlist = np.array(range(0, params['Mmax']))
grid_dict = {
'lin' : self.r,
'exp' : self.rexp
}
r_inter = Grid(grid_dict[params['grid_inter']], params['grid_inter'])
r_intra = Grid(grid_dict[params['grid_intra']], params['grid_intra'])
if False: # Use this to skip kernel calculation; helpful in debugging
self.Q_Emin = np.zeros((len (self.rexp), len(self.rexp)))#RPA_kernel(self.rexp, abs(self.Emin))
self.Q_Emax = np.zeros(np.shape(self.Q_Emin)) #RPA_kernel(self.rexp, abs(self.Emax))
else:
# Full RPA kernel
self.Q_Emin = RPA_tot(r_inter, r_intra, abs(self.Emin))
self.Q_Emax = RPA_tot(r_inter, r_intra, abs(self.Emax))
#Kernel(self.rexp, RPA_kernel(self.rexp, abs(self.Emin)))
#self.Q_Emax = Kernel(self.rexp, RPA_kernel(self.rexp, abs(self.Emax)))
# m-resolved RPA kernel
if False:
self.Qm_Emax = self.Q_Emax; #np.zeros(np.shape(self.Q_Emin))#rpakernel.kernel_m(self.rexp, self.mlist, abs(self.Emax))
self.Qm_Emin = self.Q_Emin; #np.zeros(np.shape(self.Q_Emax))#rpakernel.kernel_m(self.rexp, self.mlist, abs(self.Emin))
else:
self.Qm_Emin = RPA_m(r_inter, r_intra, abs(self.Emin), self.mlist)
self.Qm_Emax = RPA_m(r_inter, r_intra, abs(self.Emax), self.mlist)
#rpakernel.kernel_m(self.rexp, self.mlist, abs(self.Emax))
#self.Qm_Emin =
#rpakernel.kernel_m(self.rexp, self.mlist, abs(self.Emin))
self.rho_0 = self.diracDensity(np.zeros(np.shape(r)))
self.Q_corr = RPA_corr(r_inter, r_intra, abs(self.Emax), self.mlist)
N = len(self.r)
#U = Z / np.sqrt(r**2 + r_0**2)
#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
#
import rpakernel
import util
#import pylab as pl
import numpy as np
import mkrpa2
import rpam
import rpacorr
#kF = 3.0
rmin = 0.01
rmax = 50.0
N = 500
Mmax = 31
mlist = np.array(range(0, Mmax))
rexp = util.make_exp_grid(rmin, rmax, N)
rlin = util.make_lin_grid(rmin, rmax, N)
#Q0 = rpakernel.kernel_m_inter(rexp, mlist, 'exp')
#Q1 = mkrpa2.RPA_inter(rexp, 'exp')
Q2 = rpacorr.RPA_corr_inter(rexp, 'exp')
#for kF in [3.0, 2.0, 1.0, 0.5, 0.3, 0.2, 0.1, 2.5, 1.5, 0.5, 0.4, 0.35, 0.25, 0.15, 0.05]:
#for kF in [3.0, 1.0, 0.5, 0.4, 0.3, 0.2, 0.1]:
#for kF in np.arange(0.01, 0.5, 0.01):
grid_intra = 'exp'
r_dict = {'lin': rlin, 'exp': rexp}
intra_r = r_dict[grid_intra]
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
break
return U, rho
if __name__ == '__main__':
Nf = 4.0 ###
alpha = 2.5
rmin = 0.01
rmax = 100.0
N = 1000
Z = 1.0
r_0 = 1.0
import util
r = util.make_exp_grid(rmin, rmax, N)
#r = np.array(rexp)
#print rexp
print r
#import sys
#sys.exit(1)
tau_u_set = make_tau_set(8, 0.1, 0.01)
tau_rho_set = list(tau_u_set)
def rho_minus12(U, r):
return -U / r / 2.0 / np.pi**2 * Nf * alpha
Uext = Z / np.sqrt (r**2 + r_0**2)
U, rho = solve_coulomb(rho_minus12, Uext, r, tau_u_set, tau_rho_set)
#U = Z / np.sqrt(r**2 + r_0**2)
#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
