def test_mesh_exp5():
eps = 1e-8
r = mesh_exp(0, 100, a=20, N=4)
correct = array([0. , 3.21724644, 11.95019684, 35.65507127, 100.])
assert (abs(r-correct) < eps).all()
r = mesh_exp(0, 100, a=40, N=4)
correct = array([0. , 1.78202223, 7.87645252, 28.71911092, 100.])
assert (abs(r-correct) < eps).all()
r = mesh_exp(0, 100, a=100, N=4)
correct = array([0. , 0.78625046, 4.43570179, 21.37495437, 100.])
assert (abs(r-correct) < eps).all()
def test_mesh_exp6():
eps = 1e-10
r = mesh_exp(1e-7, 50, 21.37, 700)
r_min, r_max, a, N = get_mesh_exp_params(r)
assert abs(r_min - 1e-7) < eps
assert abs(r_max - 50) < eps
assert abs(a - 21.37) < eps
assert N == 700
r = mesh_exp(1, 50, 21.37, 700)
r_min, r_max, a, N = get_mesh_exp_params(r)
assert abs(r_min - 1) < eps
assert abs(r_max - 50) < eps
assert abs(a - 21.37) < eps
assert N == 700
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
def test_mesh_exp4():
eps = 1e-10
r = mesh_exp(0, 10, 2, 50)
a = (r[-1] - r[-2]) / (r[1] - r[0])
assert abs(a - 2) < eps
r_min, r_max, a, N = get_mesh_exp_params(r)
assert abs(r_min - 0) < eps
assert abs(r_max - 10) < eps
assert abs(a - 2) < eps
assert N == 50
r = mesh_exp(0, 10, 3, 50)
a = (r[-1] - r[-2]) / (r[1] - r[0])
assert abs(a - 3) < eps
r = mesh_exp(0, 10, 4, 50)
a = (r[-1] - r[-2]) / (r[1] - r[0])
assert abs(a - 4) < eps
r = mesh_exp(0, 10, 10.5, 50)
a = (r[-1] - r[-2]) / (r[1] - r[0])
assert abs(a - 10.5) < eps
r = mesh_exp(0, 10, 1, 50)
a = (r[-1] - r[-2]) / (r[1] - r[0])
assert abs(a - 1) < eps
r = mesh_exp(0, 10, 0.5, 50)
a = (r[-1] - r[-2]) / (r[1] - r[0])
assert abs(a - 0.5) < eps
r = mesh_exp(0, 10, 0.1, 50)
a = (r[-1] - r[-2]) / (r[1] - r[0])
assert abs(a - 0.1) < eps
r_min, r_max, a, N = get_mesh_exp_params(r)
assert abs(r_min - 0) < eps
assert abs(r_max - 10) < eps
assert abs(a - 0.1) < eps
assert N == 50
def mesh_nist3_direct(r_min, r_max, N):
# Uniform mesh in rho:
rho = mesh_exp(log(r_min), log(r_max), a=1, N=N)
r = exp(rho)
return r
def mesh_nist3_direct(r_min, r_max, N):
# Uniform mesh in rho:
rho = mesh_exp(log(r_min), log(r_max), a=1, N=N)
r = exp(rho)
return r
Z = 92
eps = 1e-10
data = []
# 1
r = mesh_nist1_direct(1./(160*Z), 50, 15788)
r_min, r_max, a, N = get_mesh_exp_params(r)
assert (abs(mesh_exp(r_min, r_max, a, N) - r) < eps).all()
data.append((r_min, r_max, "%e" % a, N))
# 2
r = mesh_nist1_direct(1e-6/Z, 800/sqrt(Z), 8000)
r_min, r_max, a, N = get_mesh_exp_params(r)
assert (abs(mesh_exp(r_min, r_max, a, N) - r) < eps).all()
data.append((r_min, r_max, "%e" % a, N))
# 3
# H
#r = mesh_nist2_direct(4.34e-6/1, 0.002304, 50)
# U
r = mesh_nist2_direct(4.34e-6/Z, 0.002304, 50)
r_min, r_max, a, N = get_mesh_exp_params(r)
assert (abs(mesh_exp(r_min, r_max, a, N) - r) < eps).all()
def test_mesh_exp1():
eps = 1e-10
r = mesh_exp(0, 10, 2, 1)
correct = array([0., 10.])
assert (abs(r-correct) < eps).all()
def test_mesh_exp3():
eps = 1e-10
r = mesh_exp(0, 10, 2, 3)
correct = array([0, 2.2654091966098644, 5.4691816067802712, 10])
assert (abs(r-correct) < eps).all()
def test_mesh_exp2():
eps = 1e-10
r = mesh_exp(0, 10, 2, 2)
correct = array([0, 3 + 1./3, 10])
assert (abs(r-correct) < eps).all()