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