def f(a):
print "Evaluating a =", a
print "Mesh parameters:"
print "r_min =", r_min
print "r_max =", r_max
print "a =", a
print "N =", N
r = mesh_log(r_min, r_max, a, N)
print r
# Potential:
vr = -Z/r
# Speed of light taken from:
# http://arxiv.org/abs/1012.3627
#c = 137.035999037
# Elk value:
c = 137.035999679
# Polynomial degree for predictor-corrector:
np = 4
tot_error = -1
# (n, l):
# either k == l, or k == l + 1:
for n in range(1, 7):
for l in range(0, n):
k_list = []
if l > 0:
k_list.append(l)
k_list.append(l+1)
for k in k_list:
# Initial guess:
E = -1.0
E, g, f = rdirac(c, n, l, k, np, r, vr, E)
E_exact = E_nl_dirac(n, l, spin_up=(k == l+1), Z=Z, c=c)
delta = abs(E-E_exact)
if delta > tot_error:
tot_error = delta
print ("(n=%d, l=%d, k=%d): E_calc=%12.6f E_xact=%12.6f " + \
"delta=%9.2e") % (n, l, k, E, E_exact, delta)
print "tot_error = ", tot_error
return tot_error
def f(a):
assert len(a) == 1
a = a[0]
print "Evaluating a =", a
# Mesh:
#r = create_hyperbolic_grid(rmin=5e-8, rmax=20, k0=30000)
#r = create_log_mesh(a=1e-5, b=100, par=10000, n_elem=10000)
r = mesh_log(r_min=1e-8, r_max=50, a=a, N=1000)
# Potential:
vr = -Z/r
# Speed of light taken from:
# http://arxiv.org/abs/1012.3627
c = 137.035999037
# Polynomial degree for predictor-corrector:
np = 2
tot_error = -1
# (n, l):
# either k == l, or k == l + 1:
for n in range(1, 5):
for l in range(0, n):
k_list = []
if l > 0:
k_list.append(l)
k_list.append(l+1)
for k in k_list:
# Initial guess:
E = -1.0
E, g, f = rdirac(c, n, l, k, np, r, vr, E)
E_exact = E_nl_dirac(n, l, spin_up=(k == l+1), Z=Z, c=c)
delta = abs(E-E_exact)
if delta > tot_error:
tot_error = delta
#print ("(n=%d, l=%d, k=%d): E_calc=%12.6f E_xact=%12.6f " + \
# "delta=%9.2e") % (n, l, k, E, E_exact, delta)
return tot_error
def f(a):
# Mesh:
#r = create_hyperbolic_grid(rmin=5e-8, rmax=20, k0=30000)
#r = create_log_mesh(a=1e-5, b=100, par=10000, n_elem=10000)
r = mesh_exp(r_min=1e-8, r_max=50, a=a, N=1000)
Z = 82
# Potential:
vr = -Z/r
# Speed of light taken from:
# http://arxiv.org/abs/1012.3627
c = 137.035999037
# Polynomial degree for predictor-corrector:
np = 2
tot_error = -1
# (n, l):
# either k == l, or k == l + 1:
for n in range(1, 5):
for l in range(0, n):
k_list = []
if l > 0:
k_list.append(l)
k_list.append(l+1)
for k in k_list:
# Initial guess:
E = -1.0
E, R = rdirac(c, n, l, k, np, r, vr, E)
E_exact = E_nl_dirac(n, l, spin_up=(k == l+1), Z=Z, c=c)
delta = abs(E-E_exact)
if delta > tot_error:
tot_error = delta
return tot_error
except dftatom_ConvergeError, e:
raise ConvergeError(str(e))
return E, R
elif solver == "elk":
from elk.pyelk import rdirac
if relat == 2:
k = l + 1
elif relat == 3:
k = l
else:
raise ValueError("relat must be 2 or 3")
#E_init = params.get("E_init", -3000)
E_init = params.get("E_init", -1)
# Polynomial degree for predictor-corrector:
np = params.get("np", 4)
E, R = rdirac(c, n, l, k, np, r, u, E_init)
if abs(E) > 1e6:
raise ConvergeError("Elk solver didn't converge")
return E, R
else:
raise Exception("Uknown solver")
def solve_hydrogen_like_atom(Z, mesh_params, solver_params, verbose=False):
from sympy.physics.hydrogen import E_nl_dirac, E_nl
from sympy import TableForm
r_min = mesh_params["r_min"]
r_max = mesh_params["r_max"]
a = mesh_params["a"]
N = mesh_params["N"]
r = mesh_exp(r_min, r_max, a, N)
if verbose: