def test_beta():
"""beta-wrapper"""
nf = 3
np.testing.assert_allclose(beta.beta(0, nf), beta.beta_0(nf))
np.testing.assert_allclose(beta.beta(1, nf), beta.beta_1(nf))
np.testing.assert_allclose(beta.beta(2, nf), beta.beta_2(nf))
with pytest.raises(ValueError):
beta.beta(3, 3)
def test_der_nnlo_exa():
"""exact NNLO derivative"""
nf = 3
a0 = 0.3
a1 = 0.1
delta_a = -1e-6
# 02
rhs = 1.0 / (
beta.beta(0, nf) * a1 + beta.beta(1, nf) * a1 ** 2 + beta.beta(2, nf) * a1 ** 3
)
lhs = (
ei.j02_exact(a1 + 0.5 * delta_a, a0, nf)
- ei.j02_exact(a1 - 0.5 * delta_a, a0, nf)
) / delta_a
np.testing.assert_allclose(rhs, lhs, atol=np.abs(delta_a)) # in fact O(delta_a^2)
# 12
rhs = 1.0 / (beta.beta(0, nf) + beta.beta(1, nf) * a1 + beta.beta(2, nf) * a1 ** 2)
lhs = (
ei.j12_exact(a1 + 0.5 * delta_a, a0, nf)
- ei.j12_exact(a1 - 0.5 * delta_a, a0, nf)
) / delta_a
np.testing.assert_allclose(rhs, lhs, atol=np.abs(delta_a)) # in fact O(delta_a^2)
# 12
rhs = a1 / (beta.beta(0, nf) + beta.beta(1, nf) * a1 + beta.beta(2, nf) * a1 ** 2)
lhs = (
ei.j22_exact(a1 + 0.5 * delta_a, a0, nf)
- ei.j22_exact(a1 - 0.5 * delta_a, a0, nf)
) / delta_a
np.testing.assert_allclose(rhs, lhs, atol=np.abs(delta_a)) # in fact O(delta_a^2)
def test_ode_nlo():
nf = 3
ev_op_iterations = 10
gamma_ns = np.random.rand(2) + 0j
delta_a = -1e-6
a0 = 0.3
for a1 in [0.1, 0.2]:
r = (a1 * gamma_ns[0] + a1**2 * gamma_ns[1]) / (
beta.beta(0, nf) * a1**2 + beta.beta(1, nf) * a1**3)
for method in ["iterate-exact"]:
rhs = r * ns.dispatcher(1, method, gamma_ns, a1, a0, nf,
ev_op_iterations)
lhs = (ns.dispatcher(1, method, gamma_ns, a1 + 0.5 * delta_a, a0,
nf, ev_op_iterations) -
ns.dispatcher(1, method, gamma_ns, a1 - 0.5 * delta_a, a0,
nf, ev_op_iterations)) / delta_a
np.testing.assert_allclose(lhs, rhs, atol=np.abs(delta_a))
def test_der_nlo_exp():
"""expanded NLO derivative"""
nf = 3
a0 = 0.3
a1 = 0.1
delta_a = -1e-6
# 01
rhs = 1.0 / (beta.beta(0, nf) * a1 + beta.beta(1, nf) * a1 ** 2)
lhs = (
ei.j01_expanded(a1 + 0.5 * delta_a, a0, nf)
- ei.j01_expanded(a1 - 0.5 * delta_a, a0, nf)
) / delta_a
np.testing.assert_allclose(rhs, lhs, atol=np.abs((beta.b(1, nf) * a1) ** 2))
# 11
rhs = 1.0 / (beta.beta(0, nf) + beta.beta(1, nf) * a1)
lhs = (
ei.j11_expanded(a1 + 0.5 * delta_a, a0, nf)
- ei.j11_expanded(a1 - 0.5 * delta_a, a0, nf)
) / delta_a
np.testing.assert_allclose(rhs, lhs, atol=np.abs(beta.b(1, nf) * a1))
def test_der_lo():
"""LO derivative"""
nf = 3
a0 = 5
a1 = 3
delta_a = -1e-6
rhs = 1.0 / (beta.beta(0, nf) * a1)
lhs = (
ei.j00(a1 + 0.5 * delta_a, a0, nf) - ei.j00(a1 - 0.5 * delta_a, a0, nf)
) / delta_a
np.testing.assert_allclose(rhs, lhs)
def test_ode_lo():
nf = 3
ev_op_iterations = 10
gamma_ns = np.random.rand(1) + 0j
delta_a = -1e-6
a0 = 0.3
for a1 in [0.1, 0.2]:
r = a1 * gamma_ns / (beta.beta(0, nf) * a1**2)
for method in methods:
rhs = r * ns.dispatcher(0, method, gamma_ns, a1, a0, nf,
ev_op_iterations)
lhs = (ns.dispatcher(0, method, gamma_ns, a1 + 0.5 * delta_a, a0,
nf, ev_op_iterations) -
ns.dispatcher(0, method, gamma_ns, a1 - 0.5 * delta_a, a0,
nf, ev_op_iterations)) / delta_a
np.testing.assert_allclose(lhs, rhs, atol=np.abs(delta_a))
def _get_Lambda2_LO(self, as_ref, scale_ref, nf):
"""Transformation to Lambda_QCD"""
beta0 = beta(0, nf)
return scale_ref * np.exp(-1.0 / (as_ref * beta0))
def test_der_nnlo_exp():
"""expanded NNLO derivative"""
nf = 3
a0 = 0.3
a1 = 0.1
delta_a = -1e-6
# Integrals are expanded to the order 0( a_s^3 ) so they can match the derivative to a_s^2
# The corresponding prefactor prorpotional to a_s^2 are included in the tollerance.
# 02
rhs = 1.0 / (
beta.beta(0, nf) * a1 + beta.beta(1, nf) * a1 ** 2 + beta.beta(2, nf) * a1 ** 3
)
lhs = (
ei.j02_expanded(a1 + 0.5 * delta_a, a0, nf)
- ei.j02_expanded(a1 - 0.5 * delta_a, a0, nf)
) / delta_a
toll = (
(-beta.b(1, nf) ** 3 + 2 * beta.b(2, nf) * beta.b(1, nf))
/ beta.beta(0, nf)
* a1 ** 2
)
np.testing.assert_allclose(rhs, lhs, atol=np.abs(toll))
# 12
rhs = 1.0 / (beta.beta(0, nf) + beta.beta(1, nf) * a1 + beta.beta(2, nf) * a1 ** 2)
lhs = (
ei.j12_expanded(a1 + 0.5 * delta_a, a0, nf)
- ei.j12_expanded(a1 - 0.5 * delta_a, a0, nf)
) / delta_a
toll = (beta.b(1, nf) ** 2 - beta.b(2, nf)) / beta.beta(0, nf) * a1 ** 2
np.testing.assert_allclose(rhs, lhs, atol=np.abs(toll))
# 22
rhs = a1 / (beta.beta(0, nf) + beta.beta(1, nf) * a1 + beta.beta(2, nf) * a1 ** 2)
lhs = (
ei.j22_expanded(a1 + 0.5 * delta_a, a0, nf)
- ei.j22_expanded(a1 - 0.5 * delta_a, a0, nf)
) / delta_a
np.testing.assert_allclose(
rhs, lhs, atol=np.abs(beta.b(1, nf) / beta.beta(0, nf) * a1 ** 2)
)