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felixhekhorn wants to merge 3 commits into from
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Add minus to expanded #151

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beda6b0
Add minus to expanded
felixhekhorn Oct 10, 2022
bda69f3
Extend minus to NS
felixhekhorn Oct 11, 2022
fd85f32
Make test_scale_variation_a_vs_b slightly more verbose
felixhekhorn Nov 7, 2022
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20 changes: 10 additions & 10 deletions src/eko/scale_variations/expanded.py
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Original file line number Diff line number Diff line change
@@ -1,5 +1,5 @@
# -*- coding: utf-8 -*-
r"""This module contains the scale variation operator for the expanded scheme (``ModSV=expanded``).
r"""Contains the scale variation operator for the expanded scheme (``ModSV=expanded``).
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felixhekhorn marked this conversation as resolved.

The expressions can be obtained using Eqs. (3.33) and (3.38) of :cite:`AbdulKhalek:2019ihb`.
Be aware that corresponding the signs of the ingredients there are a number of differences.
Expand All @@ -15,7 +15,7 @@

@nb.njit(cache=True)
def variation_as1(gamma, L):
r"""Computes the |NLO| anomalous dimension variation.
r"""Compute the |NLO| anomalous dimension variation.

Parameters
----------
Expand All @@ -34,7 +34,7 @@ def variation_as1(gamma, L):

@nb.njit(cache=True)
def variation_as2(gamma, L, beta0, g0e2):
r"""Computes the |NNLO| anomalous dimension variation.
r"""Compute the |NNLO| anomalous dimension variation.

Parameters
----------
Expand All @@ -57,7 +57,7 @@ def variation_as2(gamma, L, beta0, g0e2):

@nb.njit(cache=True)
def variation_as3(gamma, L, beta0, beta1, g0e2, g0e3, g1g0, g0g1):
r"""Computes the |N3LO| anomalous dimension variation.
r"""Compute the |N3LO| anomalous dimension variation.

Parameters
----------
Expand Down Expand Up @@ -118,14 +118,14 @@ def non_singlet_variation(gamma, a_s, order, nf, L):
"""
sv_ker = 1.0
if order[0] >= 2:
sv_ker += a_s * variation_as1(gamma, L)
sv_ker -= a_s * variation_as1(gamma, L)
if order[0] >= 3:
beta0 = beta.beta_qcd_as2(nf)
sv_ker += a_s**2 * variation_as2(gamma, L, beta0, gamma[0] ** 2)
sv_ker -= a_s**2 * variation_as2(gamma, L, beta0, gamma[0] ** 2)
if order[0] >= 4:
beta1 = beta.beta_qcd((3, 0), nf)
g0g1 = gamma[0] * gamma[1]
sv_ker += a_s**3 * variation_as3(
sv_ker -= a_s**3 * variation_as3(
gamma, L, beta0, beta1, gamma[0] ** 2, gamma[0] ** 3, g0g1, g0g1
)
return sv_ker
Expand Down Expand Up @@ -156,18 +156,18 @@ def singlet_variation(gamma, a_s, order, nf, L):
sv_ker = np.eye(2, dtype=np.complex_)
gamma = np.ascontiguousarray(gamma)
if order[0] >= 2:
sv_ker += a_s * variation_as1(gamma, L)
sv_ker -= a_s * variation_as1(gamma, L)
if order[0] >= 3:
beta0 = beta.beta_qcd_as2(nf)
gamma0e2 = gamma[0] @ gamma[0]
sv_ker += a_s**2 * variation_as2(gamma, L, beta0, gamma0e2)
sv_ker -= a_s**2 * variation_as2(gamma, L, beta0, gamma0e2)
if order[0] >= 4:
beta1 = beta.beta_qcd((3, 0), nf)
gamma0e3 = gamma0e2 @ gamma[0]
# here the product is not commutative
g1g0 = gamma[1] @ gamma[0]
g0g1 = gamma[0] @ gamma[1]
sv_ker += a_s**3 * variation_as3(
sv_ker -= a_s**3 * variation_as3(
gamma, L, beta0, beta1, gamma0e2, gamma0e3, g1g0, g0g1
)
return sv_ker
12 changes: 10 additions & 2 deletions tests/eko/test_sv_expanded.py
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Expand Up @@ -91,7 +91,12 @@ def scheme_diff(g, k, pto, is_singlet):
)
ker_b = ker * expanded.non_singlet_variation(gns, a1, order, nf, L)
ns_diff = scheme_diff(gns, L, order, False)
np.testing.assert_allclose((ker_a - ker_b) / ker, ns_diff, atol=1e-3)
np.testing.assert_allclose(
(ker_a - ker_b) / ker,
ns_diff,
atol=1e-3,
err_msg=f"L={L},order={order},non-singlet",
)

# Singlet kernels
gs = gamma_singlet(order, n, nf)
Expand All @@ -105,5 +110,8 @@ def scheme_diff(g, k, pto, is_singlet):
ker_b = ker @ expanded.singlet_variation(gs, a1, order, nf, L)
s_diff = scheme_diff(gs, L, order, True)
np.testing.assert_allclose(
(ker_a - ker_b) @ np.linalg.inv(ker), s_diff, atol=5e-3
(ker_a - ker_b) @ np.linalg.inv(ker),
s_diff,
atol=5e-3,
err_msg=f"L={L},order={order},singlet",
)