From bb523b4cf7553bc393e7b58e7f064c138f075c41 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Fri, 21 Jul 2023 16:06:35 +0200
Subject: [PATCH 01/40] Add mypy

---
 .pre-commit-config.yaml       | 7 +++++++
 benchmarks/__init__.py        | 0
 benchmarks/ekobox/__init__.py | 0
 pyproject.toml                | 7 +++++++
 4 files changed, 14 insertions(+)
 create mode 100644 benchmarks/__init__.py
 create mode 100644 benchmarks/ekobox/__init__.py

diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 7ebbb534b..0a34b041f 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -42,6 +42,13 @@ repos:
         args: ["--add-ignore=D107,D105"]
         additional_dependencies:
           - toml
+  - repo: https://github.com/pre-commit/mirrors-mypy
+    rev: v1.4.1
+    hooks:
+      - id: mypy
+        additional_dependencies: [types-PyYAML]
+        pass_filenames: false
+        args: [".", "--ignore-missing-imports"]
   - repo: https://github.com/pre-commit/pre-commit
     rev: v3.3.3
     hooks:
diff --git a/benchmarks/__init__.py b/benchmarks/__init__.py
new file mode 100644
index 000000000..e69de29bb
diff --git a/benchmarks/ekobox/__init__.py b/benchmarks/ekobox/__init__.py
new file mode 100644
index 000000000..e69de29bb
diff --git a/pyproject.toml b/pyproject.toml
index 31be6cb0c..1f7d239c5 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -171,3 +171,10 @@ max-args = 10
 
 [tool.pydocstyle]
 convention = "numpy"
+
+[tool.mypy]
+exclude = [
+  'extras/',
+  'benchmarks/env',
+  'doc/',
+]

From 103567c5c3a508bb57a4a615e4cf5f794ada9c5d Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Fri, 21 Jul 2023 16:39:43 +0200
Subject: [PATCH 02/40] Restrict mypy and start fixing

---
 .pre-commit-config.yaml                | 2 +-
 pyproject.toml                         | 7 -------
 src/eko/couplings.py                   | 5 +++--
 src/eko/evolution_operator/__init__.py | 3 ++-
 src/eko/evolution_operator/grid.py     | 4 ++--
 src/eko/quantities/couplings.py        | 3 +--
 6 files changed, 9 insertions(+), 15 deletions(-)

diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 0a34b041f..a8dc75857 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -48,7 +48,7 @@ repos:
       - id: mypy
         additional_dependencies: [types-PyYAML]
         pass_filenames: false
-        args: [".", "--ignore-missing-imports"]
+        args: ["--ignore-missing-imports", "src/"]
   - repo: https://github.com/pre-commit/pre-commit
     rev: v3.3.3
     hooks:
diff --git a/pyproject.toml b/pyproject.toml
index 1f7d239c5..31be6cb0c 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -171,10 +171,3 @@ max-args = 10
 
 [tool.pydocstyle]
 convention = "numpy"
-
-[tool.mypy]
-exclude = [
-  'extras/',
-  'benchmarks/env',
-  'doc/',
-]
diff --git a/src/eko/couplings.py b/src/eko/couplings.py
index b0d39a070..1b3620032 100644
--- a/src/eko/couplings.py
+++ b/src/eko/couplings.py
@@ -8,10 +8,11 @@
 
 """
 import logging
-from typing import Iterable, List
+from typing import Dict, Iterable, List, Tuple
 
 import numba as nb
 import numpy as np
+import numpy.typing as npt
 import scipy
 
 from . import constants, matchings
@@ -474,7 +475,7 @@ def assert_positive(name, var):
                 self.decoupled_running,
             )
         # cache
-        self.cache = {}
+        self.cache: Dict[Tuple[float, float, int, float, float], npt.NDArray] = {}
 
     @property
     def mu2_ref(self):
diff --git a/src/eko/evolution_operator/__init__.py b/src/eko/evolution_operator/__init__.py
index eab3c64de..6a49551a5 100644
--- a/src/eko/evolution_operator/__init__.py
+++ b/src/eko/evolution_operator/__init__.py
@@ -8,6 +8,7 @@
 import os
 import time
 from multiprocessing import Pool
+from typing import Dict, Tuple
 
 import numba as nb
 import numpy as np
@@ -617,7 +618,7 @@ def __init__(
         # TODO make 'cut' external parameter?
         self._mellin_cut = mellin_cut
         self.is_threshold = is_threshold
-        self.op_members = {}
+        self.op_members: Dict[Tuple[int, int], OpMember] = {}
         self.order = tuple(config["order"])
         self.alphaem_running = self.managers["couplings"].alphaem_running
         if self.log_label == "Evolution":
diff --git a/src/eko/evolution_operator/grid.py b/src/eko/evolution_operator/grid.py
index ca8a46d51..ad97f6e42 100644
--- a/src/eko/evolution_operator/grid.py
+++ b/src/eko/evolution_operator/grid.py
@@ -6,7 +6,7 @@
 """
 import logging
 from dataclasses import astuple
-from typing import Dict, List, Optional
+from typing import Any, Dict, List, Optional
 
 import numpy as np
 import numpy.typing as npt
@@ -61,7 +61,7 @@ def __init__(
         interpol_dispatcher: InterpolatorDispatcher,
     ):
         # check
-        config = {}
+        config: Dict[str, Any] = {}
         config["order"] = order
         config["intrinsic_range"] = intrinsic_flavors
         config["xif2"] = xif**2
diff --git a/src/eko/quantities/couplings.py b/src/eko/quantities/couplings.py
index 449abab38..01b11d138 100644
--- a/src/eko/quantities/couplings.py
+++ b/src/eko/quantities/couplings.py
@@ -1,7 +1,6 @@
 """Types and quantities related to theory couplings."""
 import dataclasses
 import enum
-from typing import Optional
 
 from ..io.dictlike import DictLike
 from ..io.types import FlavorsNumber, LinearScale, ReferenceRunning, Scalar
@@ -22,7 +21,7 @@ class CouplingsInfo(DictLike):
     alphaem: Coupling
     scale: LinearScale
     max_num_flavs: FlavorsNumber
-    num_flavs_ref: Optional[FlavorsNumber]
+    num_flavs_ref: FlavorsNumber
     r"""Number of active flavors at strong coupling reference scale.
 
     I.e. :math:`n_{f,\text{ref}}(\mu^2_{\text{ref}})`, formerly called

From e7b6e9360390e0224664b2faf6e21f9327f15a12 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Fri, 21 Jul 2023 16:58:36 +0200
Subject: [PATCH 03/40] Start fixing tests for num_flavs_ref=None

---
 tests/eko/quantities/test_couplings.py |  2 +-
 tests/eko/test_couplings.py            | 28 ++++++++++++++------------
 2 files changed, 16 insertions(+), 14 deletions(-)

diff --git a/tests/eko/quantities/test_couplings.py b/tests/eko/quantities/test_couplings.py
index 0a3b97415..00ccae9d1 100644
--- a/tests/eko/quantities/test_couplings.py
+++ b/tests/eko/quantities/test_couplings.py
@@ -3,7 +3,7 @@
 
 def test_couplings_ref():
     scale = 90.0
-    d = dict(alphas=0.1, alphaem=0.01, scale=scale, max_num_flavs=6, num_flavs_ref=None)
+    d = dict(alphas=0.1, alphaem=0.01, scale=scale, max_num_flavs=6, num_flavs_ref=5)
     couplings = CouplingsInfo.from_dict(d)
     assert couplings.scale == scale
     assert not couplings.em_running
diff --git a/tests/eko/test_couplings.py b/tests/eko/test_couplings.py
index 62110da16..646a56448 100644
--- a/tests/eko/test_couplings.py
+++ b/tests/eko/test_couplings.py
@@ -54,7 +54,7 @@ def test_init(self):
                 alphas=alpharef[0],
                 alphaem=alpharef[1],
                 scale=muref,
-                num_flavs_ref=None,
+                num_flavs_ref=5,
                 max_num_flavs=6,
             )
         )
@@ -152,18 +152,19 @@ def test_ref(self):
             (0, np.inf, np.inf),
             (2, 4, 175),
         ]
+        nfrefs = (3, 4, 5)
         alpharef = (0.118, 0.00781)
         muref = 91.0
-        couplings = CouplingsInfo.from_dict(
-            dict(
-                alphas=alpharef[0],
-                alphaem=alpharef[1],
-                scale=muref,
-                num_flavs_ref=None,
-                max_num_flavs=6,
+        for thresh_setup, nfref in zip(thresh_setups, nfrefs):
+            couplings = CouplingsInfo.from_dict(
+                dict(
+                    alphas=alpharef[0],
+                    alphaem=alpharef[1],
+                    scale=muref,
+                    num_flavs_ref=nfref,
+                    max_num_flavs=6,
+                )
             )
-        )
-        for thresh_setup in thresh_setups:
             for order_s in [1, 2, 3, 4]:
                 for order_em in [0, 1, 2]:
                     for evmod in CouplingEvolutionMethod:
@@ -220,9 +221,10 @@ def test_exact(self):
             (0, np.inf, np.inf),
             (2, 4, 175),
         ]
+        nfrefs = (3, 4, 5)
         alpharef = np.array([0.118, 0.00781])
         muref = 91.0
-        for thresh_setup in thresh_setups:
+        for thresh_setup, nfref in zip(thresh_setups, nfrefs):
             for qcd in range(1, 4 + 1):
                 for qed in range(2 + 1):
                     for em_running in [
@@ -235,7 +237,7 @@ def test_exact(self):
                                 alphas=alpharef[0],
                                 alphaem=alpharef[1],
                                 scale=muref,
-                                num_flavs_ref=None,
+                                num_flavs_ref=nfref,
                                 max_num_flavs=6,
                                 em_running=em_running,
                             )
@@ -298,7 +300,7 @@ def benchmark_expanded_n3lo(self):
             alphas=alpharef[0],
             alphaem=alpharef[1],
             scale=muref,
-            num_flavs_ref=None,
+            num_flavs_ref=5,
             max_num_flavs=6,
         )
         m2c = 2

From bbfc166bd1e8a8fefaaf1e4c6c0e4907a5af3ca8 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Fri, 21 Jul 2023 17:28:05 +0200
Subject: [PATCH 04/40] Apply more mypy fixes

---
 src/eko/evolution_operator/__init__.py        |  4 ++--
 .../operator_matrix_element.py                |  3 ++-
 src/eko/io/inventory.py                       |  4 ++--
 src/eko/io/struct.py                          | 22 +++++++++----------
 src/eko/msbar_masses.py                       |  2 +-
 5 files changed, 18 insertions(+), 17 deletions(-)

diff --git a/src/eko/evolution_operator/__init__.py b/src/eko/evolution_operator/__init__.py
index 6a49551a5..4251c5a4e 100644
--- a/src/eko/evolution_operator/__init__.py
+++ b/src/eko/evolution_operator/__init__.py
@@ -604,8 +604,8 @@ class Operator(sv.ModeMixin):
 
     log_label = "Evolution"
     # complete list of possible evolution operators labels
-    full_labels = br.full_labels
-    full_labels_qed = br.full_unified_labels
+    full_labels = list(br.full_labels)
+    full_labels_qed = list(br.full_unified_labels)
 
     def __init__(
         self, config, managers, segment: Segment, mellin_cut=5e-2, is_threshold=False
diff --git a/src/eko/evolution_operator/operator_matrix_element.py b/src/eko/evolution_operator/operator_matrix_element.py
index 5696ead19..809279c77 100644
--- a/src/eko/evolution_operator/operator_matrix_element.py
+++ b/src/eko/evolution_operator/operator_matrix_element.py
@@ -3,6 +3,7 @@
 import copy
 import functools
 import logging
+from typing import List, Tuple
 
 import numba as nb
 import numpy as np
@@ -208,7 +209,7 @@ class OperatorMatrixElement(Operator):
         (br.matching_hminus_pid, br.matching_hminus_pid),
     ]
     # still valid in QED since Sdelta and Vdelta matchings are diagonal
-    full_labels_qed = copy.deepcopy(full_labels)
+    full_labels_qed: List[Tuple[int, int]] = copy.deepcopy(full_labels)
 
     def __init__(self, config, managers, nf, q2, is_backward, L, is_msbar):
         super().__init__(config, managers, Segment(q2, q2, nf))
diff --git a/src/eko/io/inventory.py b/src/eko/io/inventory.py
index efdd2e9b0..d22046c76 100644
--- a/src/eko/io/inventory.py
+++ b/src/eko/io/inventory.py
@@ -2,7 +2,7 @@
 import base64
 from dataclasses import asdict, dataclass, field
 from pathlib import Path
-from typing import Dict, Generic, Optional, Type, TypeVar
+from typing import Dict, Generic, Literal, Optional, Type, TypeVar
 
 import yaml
 
@@ -10,7 +10,7 @@
 from .items import Header, Operator
 
 NBYTES = 8
-ENDIANNESS = "little"
+ENDIANNESS: Literal["little", "big"] = "little"
 
 HEADER_EXT = ".yaml"
 ARRAY_EXT = [".npy", ".npz"]
diff --git a/src/eko/io/struct.py b/src/eko/io/struct.py
index fecba3c57..3185c71ef 100644
--- a/src/eko/io/struct.py
+++ b/src/eko/io/struct.py
@@ -373,17 +373,17 @@ def open(cls, path: os.PathLike, mode="r"):
             raise ValueError(f"Unknown file mode: {mode}")
 
         tmpdir = pathlib.Path(tempfile.mkdtemp(prefix=TEMP_PREFIX))
-        if load:
-            cls.load(path, tmpdir)
-            metadata = Metadata.load(tmpdir)
-            opened = cls(
-                **inventories(tmpdir, access),
-                metadata=metadata,
-                access=access,
-            )
-            opened.operators.sync()
-        else:
-            opened = Builder(path=tmpdir, access=access)
+        if not load:
+            return Builder(path=tmpdir, access=access)
+        # load existing instead
+        cls.load(path, tmpdir)
+        metadata = Metadata.load(tmpdir)
+        opened: EKO = cls(
+            **inventories(tmpdir, access),
+            metadata=metadata,
+            access=access,
+        )
+        opened.operators.sync()
 
         return opened
 
diff --git a/src/eko/msbar_masses.py b/src/eko/msbar_masses.py
index 356a81019..c72893fc3 100644
--- a/src/eko/msbar_masses.py
+++ b/src/eko/msbar_masses.py
@@ -395,7 +395,7 @@ def sc(thr_masses):
     heavy_quarks = quark_names[3:]
     hq_idxs = np.arange(0, 3)
     if nf_ref > 4:
-        heavy_quarks = reversed(heavy_quarks)
+        heavy_quarks = str(reversed(heavy_quarks))
         hq_idxs = reversed(hq_idxs)
 
     # loop on heavy quarks and compute the msbar masses

From 2d8d8bf55c6be567701a6db02dc66948d667595b Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Fri, 21 Jul 2023 17:55:27 +0200
Subject: [PATCH 05/40] Apply more mypy fixes 2

---
 src/eko/evolution_operator/__init__.py |  5 ++++-
 src/eko/evolution_operator/grid.py     | 11 +++++------
 src/eko/msbar_masses.py                |  2 +-
 3 files changed, 10 insertions(+), 8 deletions(-)

diff --git a/src/eko/evolution_operator/__init__.py b/src/eko/evolution_operator/__init__.py
index 4251c5a4e..0f9c52c4f 100644
--- a/src/eko/evolution_operator/__init__.py
+++ b/src/eko/evolution_operator/__init__.py
@@ -579,6 +579,9 @@ def quad_ker_qed(
     return ker
 
 
+OPMEMBERS = Dict[Tuple[int, int], OpMember]
+
+
 class Operator(sv.ModeMixin):
     """Internal representation of a single EKO.
 
@@ -618,7 +621,7 @@ def __init__(
         # TODO make 'cut' external parameter?
         self._mellin_cut = mellin_cut
         self.is_threshold = is_threshold
-        self.op_members: Dict[Tuple[int, int], OpMember] = {}
+        self.op_members: OPMEMBERS = {}
         self.order = tuple(config["order"])
         self.alphaem_running = self.managers["couplings"].alphaem_running
         if self.log_label == "Evolution":
diff --git a/src/eko/evolution_operator/grid.py b/src/eko/evolution_operator/grid.py
index ad97f6e42..af478be9e 100644
--- a/src/eko/evolution_operator/grid.py
+++ b/src/eko/evolution_operator/grid.py
@@ -5,7 +5,6 @@
 
 """
 import logging
-from dataclasses import astuple
 from typing import Any, Dict, List, Optional
 
 import numpy as np
@@ -17,9 +16,9 @@
 from ..interpolation import InterpolatorDispatcher
 from ..io.runcards import Configs, Debug
 from ..io.types import EvolutionPoint as EPoint
-from ..io.types import Order
+from ..io.types import Order, SquaredScale
 from ..matchings import Atlas, Segment, flavor_shift, is_downward_path
-from . import Operator, flavors, matching_condition, physical
+from . import OPMEMBERS, Operator, flavors, matching_condition, physical
 from .operator_matrix_element import OperatorMatrixElement
 
 logger = logging.getLogger(__name__)
@@ -95,8 +94,8 @@ def __init__(
             couplings=couplings,
             interpol_dispatcher=interpol_dispatcher,
         )
-        self._threshold_operators = {}
-        self._matching_operators = {}
+        self._threshold_operators: Dict[Segment, Operator] = {}
+        self._matching_operators: Dict[SquaredScale, OPMEMBERS] = {}
 
     def get_threshold_operators(self, path: List[Segment]) -> List[Operator]:
         """Generate the threshold operators.
@@ -118,7 +117,7 @@ def get_threshold_operators(self, path: List[Segment]) -> List[Operator]:
         is_downward = is_downward_path(path)
         shift = flavor_shift(is_downward)
         for seg in path[:-1]:
-            new_op_key = astuple(seg)
+            new_op_key = seg
             kthr = self.config["thresholds_ratios"][seg.nf - shift]
             ome = OperatorMatrixElement(
                 self.config,
diff --git a/src/eko/msbar_masses.py b/src/eko/msbar_masses.py
index c72893fc3..f13582110 100644
--- a/src/eko/msbar_masses.py
+++ b/src/eko/msbar_masses.py
@@ -395,7 +395,7 @@ def sc(thr_masses):
     heavy_quarks = quark_names[3:]
     hq_idxs = np.arange(0, 3)
     if nf_ref > 4:
-        heavy_quarks = str(reversed(heavy_quarks))
+        heavy_quarks = "".join([e for e in reversed(heavy_quarks)])
         hq_idxs = reversed(hq_idxs)
 
     # loop on heavy quarks and compute the msbar masses

From 494da3c0ccd3d081cc3e345f39e96457b0fd46a3 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Fri, 21 Jul 2023 18:02:56 +0200
Subject: [PATCH 06/40] Rename OpMembers

---
 src/eko/evolution_operator/__init__.py | 4 ++--
 src/eko/evolution_operator/grid.py     | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/eko/evolution_operator/__init__.py b/src/eko/evolution_operator/__init__.py
index 0f9c52c4f..d079bed3d 100644
--- a/src/eko/evolution_operator/__init__.py
+++ b/src/eko/evolution_operator/__init__.py
@@ -579,7 +579,7 @@ def quad_ker_qed(
     return ker
 
 
-OPMEMBERS = Dict[Tuple[int, int], OpMember]
+OpMembers = Dict[Tuple[int, int], OpMember]
 
 
 class Operator(sv.ModeMixin):
@@ -621,7 +621,7 @@ def __init__(
         # TODO make 'cut' external parameter?
         self._mellin_cut = mellin_cut
         self.is_threshold = is_threshold
-        self.op_members: OPMEMBERS = {}
+        self.op_members: OpMembers = {}
         self.order = tuple(config["order"])
         self.alphaem_running = self.managers["couplings"].alphaem_running
         if self.log_label == "Evolution":
diff --git a/src/eko/evolution_operator/grid.py b/src/eko/evolution_operator/grid.py
index af478be9e..5035b22b2 100644
--- a/src/eko/evolution_operator/grid.py
+++ b/src/eko/evolution_operator/grid.py
@@ -18,7 +18,7 @@
 from ..io.types import EvolutionPoint as EPoint
 from ..io.types import Order, SquaredScale
 from ..matchings import Atlas, Segment, flavor_shift, is_downward_path
-from . import OPMEMBERS, Operator, flavors, matching_condition, physical
+from . import Operator, OpMembers, flavors, matching_condition, physical
 from .operator_matrix_element import OperatorMatrixElement
 
 logger = logging.getLogger(__name__)
@@ -95,7 +95,7 @@ def __init__(
             interpol_dispatcher=interpol_dispatcher,
         )
         self._threshold_operators: Dict[Segment, Operator] = {}
-        self._matching_operators: Dict[SquaredScale, OPMEMBERS] = {}
+        self._matching_operators: Dict[SquaredScale, OpMembers] = {}
 
     def get_threshold_operators(self, path: List[Segment]) -> List[Operator]:
         """Generate the threshold operators.

From 48ac90e43ae60e37af173d5db15f36e2caf0f2fb Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Fri, 21 Jul 2023 18:22:05 +0200
Subject: [PATCH 07/40] Fix mypy in io/legacy

---
 src/eko/io/legacy.py | 32 +++++++++++++++++++++-----------
 1 file changed, 21 insertions(+), 11 deletions(-)

diff --git a/src/eko/io/legacy.py b/src/eko/io/legacy.py
index 1df9941b1..c7799d0fb 100644
--- a/src/eko/io/legacy.py
+++ b/src/eko/io/legacy.py
@@ -12,15 +12,19 @@
 import numpy as np
 import yaml
 
-from eko.interpolation import XGrid
-from eko.io.runcards import flavored_mugrid
-from eko.quantities.heavy_quarks import HeavyInfo, HeavyQuarkMasses, MatchingRatios
-
+from ..interpolation import XGrid
+from ..io.runcards import flavored_mugrid
+from ..quantities.heavy_quarks import (
+    HeavyInfo,
+    HeavyQuarkMasses,
+    MatchingRatios,
+    QuarkMassScheme,
+)
 from . import raw
 from .dictlike import DictLike
 from .struct import EKO, Operator
 from .types import EvolutionPoint as EPoint
-from .types import RawCard
+from .types import RawCard, ReferenceRunning
 
 
 def load_tar(source: os.PathLike, dest: os.PathLike, errors: bool = False):
@@ -38,8 +42,8 @@ def load_tar(source: os.PathLike, dest: os.PathLike, errors: bool = False):
         whether to load also errors (default ``False``)
 
     """
-    with tempfile.TemporaryDirectory() as tmpdir:
-        tmpdir = pathlib.Path(tmpdir)
+    with tempfile.TemporaryDirectory() as tmpdirr:
+        tmpdir = pathlib.Path(tmpdirr)
 
         with tarfile.open(source, "r") as tar:
             raw.safe_extractall(tar, tmpdir)
@@ -92,10 +96,16 @@ def from_old(cls, old: RawCard):
         """Load from old metadata."""
         heavy = HeavyInfo(
             num_flavs_init=4,
-            num_flavs_max_pdf=None,
-            intrinsic_flavors=None,
-            masses=HeavyQuarkMasses([1.51, 4.92, 172.5]),
-            masses_scheme=None,
+            num_flavs_max_pdf=5,
+            intrinsic_flavors=[],
+            masses=HeavyQuarkMasses(
+                [
+                    ReferenceRunning([1.51, np.inf]),
+                    ReferenceRunning([4.92, np.inf]),
+                    ReferenceRunning([172.5, np.inf]),
+                ]
+            ),
+            masses_scheme=QuarkMassScheme.POLE,
             matching_ratios=MatchingRatios([1.0, 1.0, 1.0]),
         )
         return cls(heavy=heavy)

From bab8cf2c44ab4ab79947b65b786f36a308424d03 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Fri, 21 Jul 2023 18:44:40 +0200
Subject: [PATCH 08/40] Fix mypy in box/{genpdf,apply}

---
 src/ekobox/apply.py           | 46 +++++++++++++++++++++--------------
 src/ekobox/genpdf/__init__.py |  6 ++---
 2 files changed, 31 insertions(+), 21 deletions(-)

diff --git a/src/ekobox/apply.py b/src/ekobox/apply.py
index c392ffe78..5e62b4a06 100644
--- a/src/ekobox/apply.py
+++ b/src/ekobox/apply.py
@@ -1,10 +1,14 @@
 """Apply operator evolution to PDF set."""
 
+from dataclasses import dataclass
+from typing import Dict, Optional, Union
+
 import numpy as np
 
 from eko import basis_rotation as br
 from eko import interpolation
 from eko.io import EKO
+from eko.io.types import EvolutionPoint
 
 
 def apply_pdf(
@@ -48,6 +52,14 @@ def apply_pdf(
 CONTRACTION = "ajbk,bk"
 
 
+@dataclass
+class PdfResult:
+    """Helper class to collect PDF results."""
+
+    pdfs: Dict[Union[int, str], float]
+    errors: Optional[Dict[Union[int, str], float]] = None
+
+
 def apply_pdf_flavor(
     eko: EKO, lhapdf_like, targetgrid=None, flavor_rotation=None, qed=False
 ):
@@ -83,36 +95,33 @@ def apply_pdf_flavor(
         )
 
     # build output
-    out_grid = {}
+    out_grid: Dict[EvolutionPoint, PdfResult] = {}
     for ep, elem in eko.items():
         pdf_final = np.einsum(CONTRACTION, elem.operator, pdfs, optimize="optimal")
         if elem.error is not None:
             error_final = np.einsum(CONTRACTION, elem.error, pdfs, optimize="optimal")
         else:
             error_final = None
-        out_grid[ep] = {
-            "pdfs": dict(zip(eko.bases.targetpids, pdf_final)),
-            "errors": None,
-        }
+        out_grid[ep] = PdfResult(dict(zip(eko.bases.targetpids, pdf_final)))
         if error_final is not None:
-            out_grid[ep]["errors"] = dict(zip(eko.bases.targetpids, error_final))
+            out_grid[ep].errors = dict(zip(eko.bases.targetpids, error_final))
 
     # rotate to evolution basis
     if flavor_rotation is not None:
         for q2, op in out_grid.items():
             pdf = flavor_rotation @ np.array(
-                [op["pdfs"][pid] for pid in br.flavor_basis_pids]
+                [op.pdfs[pid] for pid in br.flavor_basis_pids]
             )
             if not qed:
                 evol_basis = br.evol_basis
             else:
                 evol_basis = br.unified_evol_basis
-            op["pdfs"] = dict(zip(evol_basis, pdf))
-            if op["errors"] is not None:
+            op.pdfs = dict(zip(evol_basis, pdf))
+            if op.errors is not None:
                 errors = flavor_rotation @ np.array(
-                    [op["errors"][pid] for pid in br.flavor_basis_pids]
+                    [op.errors[pid] for pid in br.flavor_basis_pids]
                 )
-                op["errors"] = dict(zip(evol_basis, errors))
+                op.errors = dict(zip(evol_basis, errors))
 
     # rotate/interpolate to target grid
     if targetgrid is not None:
@@ -124,11 +133,12 @@ def apply_pdf_flavor(
 
         rot = b.get_interpolation(targetgrid)
         for evpdf in out_grid.values():
-            for pdf_label in evpdf["pdfs"]:
-                evpdf["pdfs"][pdf_label] = np.matmul(rot, evpdf["pdfs"][pdf_label])
-                if evpdf["errors"] is not None:
-                    evpdf["errors"][pdf_label] = np.matmul(
-                        rot, evpdf["errors"][pdf_label]
-                    )
-
+            for pdf_label in evpdf.pdfs:
+                evpdf.pdfs[pdf_label] = np.matmul(rot, evpdf.pdfs[pdf_label])
+                if evpdf.errors is not None:
+                    evpdf.errors[pdf_label] = np.matmul(rot, evpdf.errors[pdf_label])
+    # cast back to be backward compatible
+    real_out_grid = {}
+    for ep, res in out_grid.items():
+        real_out_grid[ep] = {"pdfs": res.pdfs, "errors": res.errors}
     return out_grid
diff --git a/src/ekobox/genpdf/__init__.py b/src/ekobox/genpdf/__init__.py
index af94a410e..5c88b9b7c 100644
--- a/src/ekobox/genpdf/__init__.py
+++ b/src/ekobox/genpdf/__init__.py
@@ -16,7 +16,7 @@
 
 
 def take_data(
-    parent_pdf_set: Optional[Union[str, dict]] = None,
+    parent_pdf_set=None,
     members: bool = False,
     xgrid: Optional[List[float]] = None,
     evolgrid: Optional[List[EPoint]] = None,
@@ -62,7 +62,7 @@ def take_data(
             all_blocks.append(
                 [
                     generate_block(
-                        toylh.xfxQ2, xgrid, sorted_q2grid, br.flavor_basis_pids
+                        toylh.xfxQ2, xgrid, sorted_q2grid, list(br.flavor_basis_pids)
                     )
                 ]
             )
@@ -86,7 +86,7 @@ def take_data(
                     else parent_pdf_set[pid](x, Q2),
                     xgrid,
                     sorted_q2grid,
-                    br.flavor_basis_pids,
+                    list(br.flavor_basis_pids),
                 )
             ]
         )

From e61c8e6bf73f5ed60982a915a2ac75ed2eb26f84 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Mon, 24 Jul 2023 13:11:04 +0200
Subject: [PATCH 09/40] Fix ekomark/plots

---
 src/ekomark/plots.py | 15 ++++++++-------
 1 file changed, 8 insertions(+), 7 deletions(-)

diff --git a/src/ekomark/plots.py b/src/ekomark/plots.py
index 92a155de3..90602a0c1 100644
--- a/src/ekomark/plots.py
+++ b/src/ekomark/plots.py
@@ -1,6 +1,7 @@
 """Plotting tools to show the evolved PDF and the computed operators."""
 import io
 import pprint
+from typing import Dict, List, Tuple
 
 import matplotlib.pyplot as plt
 import numpy as np
@@ -230,7 +231,7 @@ def save_operators_to_pdf(path, theory, ops, me: EKO, skip_pdfs, change_lab=Fals
     """
     ops_names = list(me.bases.targetpids)
     if np.allclose(ops_names, br.rotate_flavor_to_evolution):
-        ops_names = br.evol_basis_pids
+        ops_names = list(br.evol_basis_pids)
     else:
         raise ValueError("Can not reconstruct PDF names")
     ops_id = f"o{ops['hash'][:6]}_t{theory['hash'][:6]}"
@@ -244,16 +245,16 @@ def save_operators_to_pdf(path, theory, ops, me: EKO, skip_pdfs, change_lab=Fals
 
         # plot the operators
         # it's necessary to reshuffle the eko output
-        for mu2 in me.mu2grid:
-            results = me[mu2].operator
-            errors = me[mu2].error
+        for ep, op in me.items():
+            results = op.operator
+            errors = op.error
 
             # loop on pids
             for label_out, res, res_err in zip(ops_names, results, errors):
                 if label_out in skip_pdfs:
                     continue
-                new_op = {}
-                new_op_err = {}
+                new_op: Dict[Tuple[int, ...], List[float]] = {}
+                new_op_err: Dict[Tuple[int, ...], List[float]] = {}
                 # loop on xgrid point
                 for j in range(len(me.xgrid)):
                     # loop on pid in
@@ -279,7 +280,7 @@ def save_operators_to_pdf(path, theory, ops, me: EKO, skip_pdfs, change_lab=Fals
                     fig = None
                     try:
                         fig = plot_operator(
-                            f"Operator ({lab_in};{lab_out}) µ_F^2 = {mu2} GeV^2",
+                            f"Operator ({lab_in};{lab_out}) µ_F^2 = {ep[0]} GeV^2, nf = {ep[1]}",
                             new_op[label_in],
                             new_op_err[label_in],
                         )

From e40a71812bc954a5c6c90edc2b6d6e3378e8ac7e Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Mon, 24 Jul 2023 14:50:08 +0200
Subject: [PATCH 10/40] Fix ekobox/cli

---
 src/ekobox/cli/inspect.py  |  2 +-
 src/ekobox/cli/run.py      | 16 ++++++++--------
 src/ekobox/cli/runcards.py |  4 +++-
 3 files changed, 12 insertions(+), 10 deletions(-)

diff --git a/src/ekobox/cli/inspect.py b/src/ekobox/cli/inspect.py
index f37f09cce..06f6588ed 100644
--- a/src/ekobox/cli/inspect.py
+++ b/src/ekobox/cli/inspect.py
@@ -27,7 +27,7 @@ def subcommand(ctx, path: pathlib.Path):
 @click.pass_obj
 def sub_mu2(operator: EKO):
     """Check operator's mu2grid."""
-    rich.print_json(data=operator.mu2grid.tolist())
+    rich.print_json(data=operator.mu2grid)
 
 
 @subcommand.command("cards")
diff --git a/src/ekobox/cli/run.py b/src/ekobox/cli/run.py
index 16e11c5fd..db88167e4 100644
--- a/src/ekobox/cli/run.py
+++ b/src/ekobox/cli/run.py
@@ -52,11 +52,11 @@ def subcommand(paths: Sequence[pathlib.Path]):
     else:
         output = operator.parent / OUTPUT
 
-    theory = yaml.safe_load(theory.read_text(encoding="utf-8"))
-    if "order" in theory:
-        theory = TheoryCard.from_dict(theory)
-    operator = yaml.safe_load(operator.read_text(encoding="utf-8"))
-    if "configs" in operator:
-        operator = OperatorCard.from_dict(operator)
-
-    eko.solve(theory, operator, path=output)
+    tc = yaml.safe_load(theory.read_text(encoding="utf-8"))
+    if "order" in tc:
+        tc = TheoryCard.from_dict(tc)
+    oc = yaml.safe_load(operator.read_text(encoding="utf-8"))
+    if "configs" in oc:
+        oc = OperatorCard.from_dict(oc)
+
+    eko.solve(tc, oc, path=output)
diff --git a/src/ekobox/cli/runcards.py b/src/ekobox/cli/runcards.py
index 1ad7d91d4..7fc46f1ef 100644
--- a/src/ekobox/cli/runcards.py
+++ b/src/ekobox/cli/runcards.py
@@ -2,6 +2,8 @@
 import logging
 import pathlib
 
+import numpy as np
+
 from .. import cards
 from . import library as lib
 from .base import command
@@ -34,6 +36,6 @@ def sub_example(destination: pathlib.Path):
     cards.dump(theory.raw, path=destination / "theory.yaml")
     operator = cards.example.operator()
     operator.mu0 = 1.65
-    operator.mu2grid = [1e5]
+    operator.mugrid = [(np.sqrt(1e5), 5)]
     cards.dump(operator.raw, path=destination / "operator.yaml")
     _logger.info(f"Runcards generated to '{destination}'")

From 9271ebc5950b188376c16f8bc163baea93ba8a8a Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Mon, 24 Jul 2023 15:13:25 +0200
Subject: [PATCH 11/40] Make managers class

---
 src/eko/evolution_operator/__init__.py         | 10 +++++-----
 src/eko/evolution_operator/grid.py             | 18 ++++++++++++++----
 .../operator_matrix_element.py                 |  2 +-
 src/eko/runner/parts.py                        |  9 +++++----
 tests/eko/evolution_operator/test_init.py      |  8 +++++++-
 5 files changed, 32 insertions(+), 15 deletions(-)

diff --git a/src/eko/evolution_operator/__init__.py b/src/eko/evolution_operator/__init__.py
index d079bed3d..fea8d15fe 100644
--- a/src/eko/evolution_operator/__init__.py
+++ b/src/eko/evolution_operator/__init__.py
@@ -623,7 +623,7 @@ def __init__(
         self.is_threshold = is_threshold
         self.op_members: OpMembers = {}
         self.order = tuple(config["order"])
-        self.alphaem_running = self.managers["couplings"].alphaem_running
+        self.alphaem_running = self.managers.couplings.alphaem_running
         if self.log_label == "Evolution":
             self.a = self.compute_a()
             self.compute_aem_list()
@@ -645,7 +645,7 @@ def xif2(self):
     @property
     def int_disp(self):
         """Return the interpolation dispatcher."""
-        return self.managers["interpol_dispatcher"]
+        return self.managers.interpolator
 
     @property
     def grid_size(self):
@@ -668,7 +668,7 @@ def mu2(self):
 
     def compute_a(self):
         """Return the computed values for :math:`a_s` and :math:`a_{em}`."""
-        coupling = self.managers["couplings"]
+        coupling = self.managers.couplings
         a0 = coupling.a(
             self.mu2[0],
             nf_to=self.nf,
@@ -708,7 +708,7 @@ def compute_aem_list(self):
             as1 = self.a_s[1]
             aem0 = self.a_em[0]
             aem1 = self.a_em[1]
-            q2ref = self.managers["couplings"].mu2_ref
+            q2ref = self.managers.couplings.mu2_ref
             delta_from = abs(self.q2_from - q2ref)
             delta_to = abs(self.q2_to - q2ref)
             # I compute the values in aem_list starting from the mu2
@@ -719,7 +719,7 @@ def compute_aem_list(self):
             else:
                 a_start = np.array([as0, aem0])
                 mu2_start = self.q2_from
-            couplings = self.managers["couplings"]
+            couplings = self.managers.couplings
             mu2_steps = utils.geomspace(self.q2_from, self.q2_to, 1 + ev_op_iterations)
             mu2_l = mu2_steps[0]
             self.as_list = np.array(
diff --git a/src/eko/evolution_operator/grid.py b/src/eko/evolution_operator/grid.py
index 5035b22b2..1180697a6 100644
--- a/src/eko/evolution_operator/grid.py
+++ b/src/eko/evolution_operator/grid.py
@@ -5,6 +5,7 @@
 
 """
 import logging
+from dataclasses import dataclass
 from typing import Any, Dict, List, Optional
 
 import numpy as np
@@ -27,6 +28,15 @@
 """In particular, only the ``operator`` and ``error`` fields are expected."""
 
 
+@dataclass(frozen=True)
+class Managers:
+    """Set of steering objects."""
+
+    atlas: Atlas
+    couplings: Couplings
+    interpolator: InterpolatorDispatcher
+
+
 class OperatorGrid(sv.ModeMixin):
     """Collection of evolution operators for several scales.
 
@@ -89,10 +99,10 @@ def __init__(
 
         self.config = config
         self.q2_grid = mu2grid
-        self.managers = dict(
-            thresholds_config=atlas,
+        self.managers = Managers(
+            atlas=atlas,
             couplings=couplings,
-            interpol_dispatcher=interpol_dispatcher,
+            interpolator=interpol_dispatcher,
         )
         self._threshold_operators: Dict[Segment, Operator] = {}
         self._matching_operators: Dict[SquaredScale, OpMembers] = {}
@@ -153,7 +163,7 @@ def generate(self, q2: EPoint) -> OpDict:
 
         """
         # The lists of areas as produced by the thresholds
-        path = self.managers["thresholds_config"].path(q2)
+        path = self.managers.atlas.path(q2)
         # Prepare the path for the composition of the operator
         thr_ops = self.get_threshold_operators(path)
         # we start composing with the highest operator ...
diff --git a/src/eko/evolution_operator/operator_matrix_element.py b/src/eko/evolution_operator/operator_matrix_element.py
index 809279c77..8966a62b9 100644
--- a/src/eko/evolution_operator/operator_matrix_element.py
+++ b/src/eko/evolution_operator/operator_matrix_element.py
@@ -306,7 +306,7 @@ def a_s(self):
 
         Note that here you need to use :math:`a_s^{n_f+1}`
         """
-        sc = self.managers["couplings"]
+        sc = self.managers.couplings
         return sc.a_s(
             self.q2_from
             * (self.xif2 if self.sv_mode == sv.Modes.exponentiated else 1.0),
diff --git a/src/eko/runner/parts.py b/src/eko/runner/parts.py
index e385b8f49..9f97a6de5 100644
--- a/src/eko/runner/parts.py
+++ b/src/eko/runner/parts.py
@@ -16,13 +16,14 @@
 from ..evolution_operator import matching_condition
 from ..evolution_operator import operator_matrix_element as ome
 from ..evolution_operator import physical
+from ..evolution_operator.grid import Managers
 from ..io import EKO
 from ..io.items import Evolution, Matching, Operator
 from ..quantities.heavy_quarks import QuarkMassScheme
 from . import commons
 
 
-def managers(eko: EKO) -> dict:
+def managers(eko: EKO) -> Managers:
     """Collect managers for operator computation.
 
     .. todo::
@@ -32,10 +33,10 @@ def managers(eko: EKO) -> dict:
     """
     tcard = eko.theory_card
     ocard = eko.operator_card
-    return dict(
-        thresholds_config=commons.atlas(tcard, ocard),
+    return Managers(
+        atlas=commons.atlas(tcard, ocard),
         couplings=commons.couplings(tcard, ocard),
-        interpol_dispatcher=commons.interpolator(ocard),
+        interpolator=commons.interpolator(ocard),
     )
 
 
diff --git a/tests/eko/evolution_operator/test_init.py b/tests/eko/evolution_operator/test_init.py
index 642de5bb7..92a335f79 100644
--- a/tests/eko/evolution_operator/test_init.py
+++ b/tests/eko/evolution_operator/test_init.py
@@ -1,4 +1,5 @@
 import os
+from dataclasses import dataclass
 
 import numpy as np
 import pytest
@@ -201,7 +202,12 @@ def compute(self, a_ref, nf, scale_from, scale_to):
         return a_ref
 
 
-fake_managers = {"couplings": FakeCoupling()}
+@dataclass(frozen=True)
+class FakeManagers:
+    couplings: FakeCoupling
+
+
+fake_managers = FakeManagers(couplings=FakeCoupling())
 
 
 class TestOperator:

From 80b85f157476f258798ec5c2d4eab2b1aec99471 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Mon, 24 Jul 2023 15:16:27 +0200
Subject: [PATCH 12/40] Use backported return in apply

---
 src/ekobox/apply.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/ekobox/apply.py b/src/ekobox/apply.py
index 5e62b4a06..ace0ccca1 100644
--- a/src/ekobox/apply.py
+++ b/src/ekobox/apply.py
@@ -141,4 +141,4 @@ def apply_pdf_flavor(
     real_out_grid = {}
     for ep, res in out_grid.items():
         real_out_grid[ep] = {"pdfs": res.pdfs, "errors": res.errors}
-    return out_grid
+    return real_out_grid

From 34c68a57a9587829a7c593563f5feaf83ecbc5fe Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Mon, 24 Jul 2023 15:28:48 +0200
Subject: [PATCH 13/40] Fix eko/io/legacy masses usage

---
 src/eko/io/legacy.py | 14 +++++++++-----
 1 file changed, 9 insertions(+), 5 deletions(-)

diff --git a/src/eko/io/legacy.py b/src/eko/io/legacy.py
index c7799d0fb..d580f7373 100644
--- a/src/eko/io/legacy.py
+++ b/src/eko/io/legacy.py
@@ -26,6 +26,10 @@
 from .types import EvolutionPoint as EPoint
 from .types import RawCard, ReferenceRunning
 
+_MC = 1.51
+_MB = 4.92
+_MT = 172.5
+
 
 def load_tar(source: os.PathLike, dest: os.PathLike, errors: bool = False):
     """Load tar representation from file.
@@ -63,7 +67,7 @@ def load_tar(source: os.PathLike, dest: os.PathLike, errors: bool = False):
     if op5 is None:
         op5 = metaold["mu2grid"]
     grid = op5to4(
-        flavored_mugrid(op5, theory.heavy.masses, theory.heavy.matching_ratios), arrays
+        flavored_mugrid(op5, [_MC, _MB, _MT], theory.heavy.matching_ratios), arrays
     )
 
     with EKO.create(dest) as builder:
@@ -100,9 +104,9 @@ def from_old(cls, old: RawCard):
             intrinsic_flavors=[],
             masses=HeavyQuarkMasses(
                 [
-                    ReferenceRunning([1.51, np.inf]),
-                    ReferenceRunning([4.92, np.inf]),
-                    ReferenceRunning([172.5, np.inf]),
+                    ReferenceRunning([_MC, np.inf]),
+                    ReferenceRunning([_MB, np.inf]),
+                    ReferenceRunning([_MT, np.inf]),
                 ]
             ),
             masses_scheme=QuarkMassScheme.POLE,
@@ -134,7 +138,7 @@ def from_old(cls, old: RawCard):
             mu2list = old["mu2grid"]
         mu2grid = np.array(mu2list)
         evolgrid = flavored_mugrid(
-            np.sqrt(mu2grid).tolist(), [1.51, 4.92, 172.5], [1, 1, 1]
+            np.sqrt(mu2grid).tolist(), [_MC, _MB, _MT], [1, 1, 1]
         )
 
         xgrid = XGrid(old["interpolation_xgrid"])

From d6d17340b4c2592d8a5680bbf106f93f77476961 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Mon, 24 Jul 2023 15:55:08 +0200
Subject: [PATCH 14/40] Fix remaining mypy errors

---
 src/eko/io/struct.py        | 6 ++++--
 src/eko/runner/operators.py | 4 +++-
 2 files changed, 7 insertions(+), 3 deletions(-)

diff --git a/src/eko/io/struct.py b/src/eko/io/struct.py
index 3185c71ef..ce4679871 100644
--- a/src/eko/io/struct.py
+++ b/src/eko/io/struct.py
@@ -272,7 +272,7 @@ def approx(
         Raises
         ------
         ValueError
-            if multiple values are find in the neighbourhood
+            if multiple values are found in the neighbourhood
 
         """
         eps = np.array([ep_ for ep_ in self if ep_[1] == ep[1]])
@@ -280,7 +280,9 @@ def approx(
         close = eps[np.isclose(ep[0], mu2s, rtol=rtol, atol=atol)]
 
         if len(close) == 1:
-            return tuple(close[0])
+            found = close[0]
+            assert isinstance(found[0], float)
+            return (found[0], int(found[1]))
         if len(close) == 0:
             return None
         raise ValueError(f"Multiple values of Q2 have been found close to {ep}")
diff --git a/src/eko/runner/operators.py b/src/eko/runner/operators.py
index 5a0a219c7..bfc4ce407 100644
--- a/src/eko/runner/operators.py
+++ b/src/eko/runner/operators.py
@@ -16,7 +16,9 @@ def retrieve(
     elements = []
     for head in headers:
         inv = parts if isinstance(head, Evolution) else parts_matching
-        elements.append(inv[head])
+        op = inv[head]
+        assert isinstance(op, Operator)
+        elements.append(op)
 
     return elements
 

From 6e0f434b9c1792dad9c79bed9e013e2a5b5cdd1d Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Tue, 25 Jul 2023 16:11:22 +0200
Subject: [PATCH 15/40] Remove init from benchmarks

---
 benchmarks/__init__.py        | 0
 benchmarks/ekobox/__init__.py | 0
 2 files changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 benchmarks/__init__.py
 delete mode 100644 benchmarks/ekobox/__init__.py

diff --git a/benchmarks/__init__.py b/benchmarks/__init__.py
deleted file mode 100644
index e69de29bb..000000000
diff --git a/benchmarks/ekobox/__init__.py b/benchmarks/ekobox/__init__.py
deleted file mode 100644
index e69de29bb..000000000

From e8c218e0d5e7c7e90ecfd40d22f6f9d58bd2d142 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Thu, 17 Aug 2023 17:26:56 +0200
Subject: [PATCH 16/40] Drop new_op_key variable in grid

---
 src/eko/evolution_operator/grid.py | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/src/eko/evolution_operator/grid.py b/src/eko/evolution_operator/grid.py
index 1180697a6..9c0c6c1df 100644
--- a/src/eko/evolution_operator/grid.py
+++ b/src/eko/evolution_operator/grid.py
@@ -127,7 +127,6 @@ def get_threshold_operators(self, path: List[Segment]) -> List[Operator]:
         is_downward = is_downward_path(path)
         shift = flavor_shift(is_downward)
         for seg in path[:-1]:
-            new_op_key = seg
             kthr = self.config["thresholds_ratios"][seg.nf - shift]
             ome = OperatorMatrixElement(
                 self.config,
@@ -138,13 +137,13 @@ def get_threshold_operators(self, path: List[Segment]) -> List[Operator]:
                 np.log(kthr),
                 self.config["HQ"] == "MSBAR",
             )
-            if new_op_key not in self._threshold_operators:
+            if seg not in self._threshold_operators:
                 # Compute the operator and store it
                 logger.info("Prepare threshold operator")
                 op_th = Operator(self.config, self.managers, seg, is_threshold=True)
                 op_th.compute()
-                self._threshold_operators[new_op_key] = op_th
-            thr_ops.append(self._threshold_operators[new_op_key])
+                self._threshold_operators[seg] = op_th
+            thr_ops.append(self._threshold_operators[seg])
 
             # Compute the matching conditions and store it
             if seg.target not in self._matching_operators:

From 54d9e53401476339afc34bafc0b6718ca523a6b2 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Thu, 17 Aug 2023 17:32:28 +0200
Subject: [PATCH 17/40] Define couplings cache key type

---
 src/eko/couplings.py | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/src/eko/couplings.py b/src/eko/couplings.py
index 1b3620032..5cd35ef2b 100644
--- a/src/eko/couplings.py
+++ b/src/eko/couplings.py
@@ -381,6 +381,10 @@ def couplings_expanded_fixed_alphaem(order, couplings_ref, nf, scale_from, scale
     return np.array([res_as, aem])
 
 
+_CouplingsCacheKey = Tuple[float, float, int, float, float]
+"""Cache key containing (a0, a1, nf, scale_from, scale_to)."""
+
+
 class Couplings:
     r"""Compute the strong and electromagnetic coupling constants :math:`a_s, a_{em}`.
 
@@ -475,7 +479,7 @@ def assert_positive(name, var):
                 self.decoupled_running,
             )
         # cache
-        self.cache: Dict[Tuple[float, float, int, float, float], npt.NDArray] = {}
+        self.cache: Dict[_CouplingsCacheKey, npt.NDArray] = {}
 
     @property
     def mu2_ref(self):

From 9b0d8048b98a708a6616e482b2ac955f6475cd30 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Thu, 17 Aug 2023 17:38:56 +0200
Subject: [PATCH 18/40] Define label type in apply

---
 src/ekobox/apply.py | 7 +++++--
 1 file changed, 5 insertions(+), 2 deletions(-)

diff --git a/src/ekobox/apply.py b/src/ekobox/apply.py
index ace0ccca1..97d1a0168 100644
--- a/src/ekobox/apply.py
+++ b/src/ekobox/apply.py
@@ -51,13 +51,16 @@ def apply_pdf(
 
 CONTRACTION = "ajbk,bk"
 
+_PdfLabel = Union[int, str]
+"""PDF identifier: either PID or label."""
+
 
 @dataclass
 class PdfResult:
     """Helper class to collect PDF results."""
 
-    pdfs: Dict[Union[int, str], float]
-    errors: Optional[Dict[Union[int, str], float]] = None
+    pdfs: Dict[_PdfLabel, float]
+    errors: Optional[Dict[_PdfLabel, float]] = None
 
 
 def apply_pdf_flavor(

From 3b576005797436986452c2cab91c726d0d009328 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Thu, 17 Aug 2023 17:46:05 +0200
Subject: [PATCH 19/40] Cast labels in evop/Operator

---
 src/eko/evolution_operator/__init__.py                | 4 ++--
 src/eko/evolution_operator/operator_matrix_element.py | 8 ++++----
 2 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/src/eko/evolution_operator/__init__.py b/src/eko/evolution_operator/__init__.py
index fea8d15fe..6e008e322 100644
--- a/src/eko/evolution_operator/__init__.py
+++ b/src/eko/evolution_operator/__init__.py
@@ -607,8 +607,8 @@ class Operator(sv.ModeMixin):
 
     log_label = "Evolution"
     # complete list of possible evolution operators labels
-    full_labels = list(br.full_labels)
-    full_labels_qed = list(br.full_unified_labels)
+    full_labels: Tuple[Tuple[int, int], ...] = br.full_labels
+    full_labels_qed: Tuple[Tuple[int, int], ...] = br.full_unified_labels
 
     def __init__(
         self, config, managers, segment: Segment, mellin_cut=5e-2, is_threshold=False
diff --git a/src/eko/evolution_operator/operator_matrix_element.py b/src/eko/evolution_operator/operator_matrix_element.py
index 8966a62b9..deb763499 100644
--- a/src/eko/evolution_operator/operator_matrix_element.py
+++ b/src/eko/evolution_operator/operator_matrix_element.py
@@ -3,7 +3,7 @@
 import copy
 import functools
 import logging
-from typing import List, Tuple
+from typing import Tuple
 
 import numba as nb
 import numpy as np
@@ -196,7 +196,7 @@ class OperatorMatrixElement(Operator):
 
     log_label = "Matching"
     # complete list of possible matching operators labels
-    full_labels = [
+    full_labels = (
         *br.singlet_labels,
         (br.matching_hplus_pid, 21),
         (br.matching_hplus_pid, 100),
@@ -207,9 +207,9 @@ class OperatorMatrixElement(Operator):
         (200, br.matching_hminus_pid),
         (br.matching_hminus_pid, 200),
         (br.matching_hminus_pid, br.matching_hminus_pid),
-    ]
+    )
     # still valid in QED since Sdelta and Vdelta matchings are diagonal
-    full_labels_qed: List[Tuple[int, int]] = copy.deepcopy(full_labels)
+    full_labels_qed: Tuple[Tuple[int, int], ...] = copy.deepcopy(full_labels)
 
     def __init__(self, config, managers, nf, q2, is_backward, L, is_msbar):
         super().__init__(config, managers, Segment(q2, q2, nf))

From bbe955c54302f2ad3ee80cd65dec8bae2c4ccb78 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felixhekhorn@users.noreply.github.com>
Date: Thu, 17 Aug 2023 17:49:57 +0200
Subject: [PATCH 20/40] Update src/eko/runner/operators.py

Co-authored-by: Alessandro Candido <candido.ale@gmail.com>
---
 src/eko/runner/operators.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/eko/runner/operators.py b/src/eko/runner/operators.py
index bfc4ce407..19f53c243 100644
--- a/src/eko/runner/operators.py
+++ b/src/eko/runner/operators.py
@@ -17,7 +17,7 @@ def retrieve(
     for head in headers:
         inv = parts if isinstance(head, Evolution) else parts_matching
         op = inv[head]
-        assert isinstance(op, Operator)
+        assert op is not None
         elements.append(op)
 
     return elements

From 16e38092e5eeb42d43348bb07c1d3417e7747a14 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Thu, 17 Aug 2023 17:56:01 +0200
Subject: [PATCH 21/40] Introduce OperatorLabel type

---
 src/eko/evolution_operator/__init__.py                | 8 +++++---
 src/eko/evolution_operator/operator_matrix_element.py | 3 +--
 src/eko/io/types.py                                   | 8 ++++----
 3 files changed, 10 insertions(+), 9 deletions(-)

diff --git a/src/eko/evolution_operator/__init__.py b/src/eko/evolution_operator/__init__.py
index 6e008e322..3681f0663 100644
--- a/src/eko/evolution_operator/__init__.py
+++ b/src/eko/evolution_operator/__init__.py
@@ -21,6 +21,7 @@
 from .. import basis_rotation as br
 from .. import interpolation, mellin
 from .. import scale_variations as sv
+from ..io.types import OperatorLabel
 from ..kernels import non_singlet as ns
 from ..kernels import non_singlet_qed as qed_ns
 from ..kernels import singlet as s
@@ -579,7 +580,8 @@ def quad_ker_qed(
     return ker
 
 
-OpMembers = Dict[Tuple[int, int], OpMember]
+OpMembers = Dict[OperatorLabel, OpMember]
+"""Map of all operators."""
 
 
 class Operator(sv.ModeMixin):
@@ -607,8 +609,8 @@ class Operator(sv.ModeMixin):
 
     log_label = "Evolution"
     # complete list of possible evolution operators labels
-    full_labels: Tuple[Tuple[int, int], ...] = br.full_labels
-    full_labels_qed: Tuple[Tuple[int, int], ...] = br.full_unified_labels
+    full_labels: Tuple[OperatorLabel, ...] = br.full_labels
+    full_labels_qed: Tuple[OperatorLabel, ...] = br.full_unified_labels
 
     def __init__(
         self, config, managers, segment: Segment, mellin_cut=5e-2, is_threshold=False
diff --git a/src/eko/evolution_operator/operator_matrix_element.py b/src/eko/evolution_operator/operator_matrix_element.py
index deb763499..7a5a3ce6c 100644
--- a/src/eko/evolution_operator/operator_matrix_element.py
+++ b/src/eko/evolution_operator/operator_matrix_element.py
@@ -3,7 +3,6 @@
 import copy
 import functools
 import logging
-from typing import Tuple
 
 import numba as nb
 import numpy as np
@@ -209,7 +208,7 @@ class OperatorMatrixElement(Operator):
         (br.matching_hminus_pid, br.matching_hminus_pid),
     )
     # still valid in QED since Sdelta and Vdelta matchings are diagonal
-    full_labels_qed: Tuple[Tuple[int, int], ...] = copy.deepcopy(full_labels)
+    full_labels_qed = copy.deepcopy(full_labels)
 
     def __init__(self, config, managers, nf, q2, is_backward, L, is_msbar):
         super().__init__(config, managers, Segment(q2, q2, nf))
diff --git a/src/eko/io/types.py b/src/eko/io/types.py
index 5573bafbb..dc8c490c4 100644
--- a/src/eko/io/types.py
+++ b/src/eko/io/types.py
@@ -1,7 +1,6 @@
 """Common type definitions, only used for static analysis."""
 import enum
-import typing
-from typing import Any, Dict, Generic, Tuple, TypeVar
+from typing import Any, Dict, Generic, List, Tuple, TypeVar
 
 # Energy scales
 # -------------
@@ -22,8 +21,9 @@
 Order = Tuple[int, int]
 FlavorsNumber = int
 FlavorIndex = int
-IntrinsicFlavors = typing.List[FlavorIndex]
-N3LOAdVariation = typing.Tuple[int, int, int, int]
+IntrinsicFlavors = List[FlavorIndex]
+N3LOAdVariation = Tuple[int, int, int, int]
+OperatorLabel = Tuple[int, int]
 
 # Evolution coordinates
 # ---------------------

From c9cdc72dfc37932fda2ad91d8f17129cc2a4b3b1 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Thu, 17 Aug 2023 17:58:08 +0200
Subject: [PATCH 22/40] Remove list comprension in msbar

---
 src/eko/msbar_masses.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/eko/msbar_masses.py b/src/eko/msbar_masses.py
index f13582110..ca4fd6731 100644
--- a/src/eko/msbar_masses.py
+++ b/src/eko/msbar_masses.py
@@ -395,7 +395,7 @@ def sc(thr_masses):
     heavy_quarks = quark_names[3:]
     hq_idxs = np.arange(0, 3)
     if nf_ref > 4:
-        heavy_quarks = "".join([e for e in reversed(heavy_quarks)])
+        heavy_quarks = "".join(reversed(heavy_quarks))
         hq_idxs = reversed(hq_idxs)
 
     # loop on heavy quarks and compute the msbar masses

From c946b3f21745c060aa29109c101ad090daa3a5c8 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Thu, 17 Aug 2023 18:25:27 +0200
Subject: [PATCH 23/40] Upgrade banana

---
 poetry.lock    | 1525 ++++++++++++++++++++++++++----------------------
 pyproject.toml |    2 +-
 2 files changed, 813 insertions(+), 714 deletions(-)

diff --git a/poetry.lock b/poetry.lock
index 53d012a61..9d5f9c818 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -38,14 +38,14 @@ files = [
 
 [[package]]
 name = "astroid"
-version = "2.15.5"
+version = "2.15.6"
 description = "An abstract syntax tree for Python with inference support."
 category = "dev"
 optional = false
 python-versions = ">=3.7.2"
 files = [
-    {file = "astroid-2.15.5-py3-none-any.whl", hash = "sha256:078e5212f9885fa85fbb0cf0101978a336190aadea6e13305409d099f71b2324"},
-    {file = "astroid-2.15.5.tar.gz", hash = "sha256:1039262575027b441137ab4a62a793a9b43defb42c32d5670f38686207cd780f"},
+    {file = "astroid-2.15.6-py3-none-any.whl", hash = "sha256:389656ca57b6108f939cf5d2f9a2a825a3be50ba9d589670f393236e0a03b91c"},
+    {file = "astroid-2.15.6.tar.gz", hash = "sha256:903f024859b7c7687d7a7f3a3f73b17301f8e42dfd9cc9df9d4418172d3e2dbd"},
 ]
 
 [package.dependencies]
@@ -139,14 +139,14 @@ files = [
 
 [[package]]
 name = "banana-hep"
-version = "0.6.9"
+version = "0.6.10"
 description = "Benchmark QCD physics"
 category = "main"
 optional = true
 python-versions = ">=3.8.0,<3.12"
 files = [
-    {file = "banana_hep-0.6.9-py3-none-any.whl", hash = "sha256:e857b777eb0f64b0bf5e0a2b7cc6afcb5680a60dc3bdd7ce9c34c4bf3b94828b"},
-    {file = "banana_hep-0.6.9.tar.gz", hash = "sha256:0b9f5cd3e4e44d5c8117bab93c832784009feb6d87d5a874da0d47fc91ab0514"},
+    {file = "banana_hep-0.6.10-py3-none-any.whl", hash = "sha256:e50fcfad55220a9f14b3b3d056f5ba893e1ee2579f875a6786a0273e73f8b3f7"},
+    {file = "banana_hep-0.6.10.tar.gz", hash = "sha256:48c584bcb169de4769241ee34f5a067f9f719aaa64f512d3b9251bbe90e80002"},
 ]
 
 [package.dependencies]
@@ -201,14 +201,14 @@ css = ["tinycss2 (>=1.1.0,<1.2)"]
 
 [[package]]
 name = "certifi"
-version = "2023.5.7"
+version = "2023.7.22"
 description = "Python package for providing Mozilla's CA Bundle."
 category = "dev"
 optional = false
 python-versions = ">=3.6"
 files = [
-    {file = "certifi-2023.5.7-py3-none-any.whl", hash = "sha256:c6c2e98f5c7869efca1f8916fed228dd91539f9f1b444c314c06eef02980c716"},
-    {file = "certifi-2023.5.7.tar.gz", hash = "sha256:0f0d56dc5a6ad56fd4ba36484d6cc34451e1c6548c61daad8c320169f91eddc7"},
+    {file = "certifi-2023.7.22-py3-none-any.whl", hash = "sha256:92d6037539857d8206b8f6ae472e8b77db8058fec5937a1ef3f54304089edbb9"},
+    {file = "certifi-2023.7.22.tar.gz", hash = "sha256:539cc1d13202e33ca466e88b2807e29f4c13049d6d87031a3c110744495cb082"},
 ]
 
 [[package]]
@@ -290,99 +290,99 @@ pycparser = "*"
 
 [[package]]
 name = "charset-normalizer"
-version = "3.1.0"
+version = "3.2.0"
 description = "The Real First Universal Charset Detector. Open, modern and actively maintained alternative to Chardet."
 category = "dev"
 optional = false
 python-versions = ">=3.7.0"
 files = [
-    {file = "charset-normalizer-3.1.0.tar.gz", hash = "sha256:34e0a2f9c370eb95597aae63bf85eb5e96826d81e3dcf88b8886012906f509b5"},
-    {file = "charset_normalizer-3.1.0-cp310-cp310-macosx_10_9_universal2.whl", hash = "sha256:e0ac8959c929593fee38da1c2b64ee9778733cdf03c482c9ff1d508b6b593b2b"},
-    {file = "charset_normalizer-3.1.0-cp310-cp310-macosx_10_9_x86_64.whl", hash = "sha256:d7fc3fca01da18fbabe4625d64bb612b533533ed10045a2ac3dd194bfa656b60"},
-    {file = "charset_normalizer-3.1.0-cp310-cp310-macosx_11_0_arm64.whl", hash = "sha256:04eefcee095f58eaabe6dc3cc2262f3bcd776d2c67005880894f447b3f2cb9c1"},
-    {file = "charset_normalizer-3.1.0-cp310-cp310-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:20064ead0717cf9a73a6d1e779b23d149b53daf971169289ed2ed43a71e8d3b0"},
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 [[package]]
 name = "click"
-version = "8.1.3"
+version = "8.1.6"
 description = "Composable command line interface toolkit"
 category = "main"
 optional = true
 python-versions = ">=3.7"
 files = [
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 [package.dependencies]
@@ -402,18 +402,18 @@ files = [
 
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 name = "comm"
-version = "0.1.3"
+version = "0.1.4"
 description = "Jupyter Python Comm implementation, for usage in ipykernel, xeus-python etc."
 category = "dev"
 optional = false
 python-versions = ">=3.6"
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 ]
 
 [package.dependencies]
-traitlets = ">=5.3"
+traitlets = ">=4"
 
 [package.extras]
 lint = ["black (>=22.6.0)", "mdformat (>0.7)", "mdformat-gfm (>=0.3.5)", "ruff (>=0.0.156)"]
@@ -496,72 +496,64 @@ test-no-images = ["pytest", "pytest-cov", "wurlitzer"]
 
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+version = "7.3.0"
 description = "Code coverage measurement for Python"
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 optional = false
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+python-versions = ">=3.8"
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 [package.extras]
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+    {file = "fonttools-4.42.0-cp39-cp39-win_amd64.whl", hash = "sha256:ae7df0ae9ee2f3f7676b0ff6f4ebe48ad0acaeeeaa0b6839d15dbf0709f2c5ef"},
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+    {file = "fonttools-4.42.0.tar.gz", hash = "sha256:614b1283dca88effd20ee48160518e6de275ce9b5456a3134d5f235523fc5065"},
 ]
 
 [package.extras]
@@ -927,14 +919,14 @@ files = [
 
 [[package]]
 name = "importlib-metadata"
-version = "6.6.0"
+version = "6.8.0"
 description = "Read metadata from Python packages"
 category = "main"
 optional = false
-python-versions = ">=3.7"
+python-versions = ">=3.8"
 files = [
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 ]
 
 [package.dependencies]
@@ -943,26 +935,26 @@ zipp = ">=0.5"
 [package.extras]
 docs = ["furo", "jaraco.packaging (>=9)", "jaraco.tidelift (>=1.4)", "rst.linker (>=1.9)", "sphinx (>=3.5)", "sphinx-lint"]
 perf = ["ipython"]
-testing = ["flake8 (<5)", "flufl.flake8", "importlib-resources (>=1.3)", "packaging", "pyfakefs", "pytest (>=6)", "pytest-black (>=0.3.7)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=1.3)", "pytest-flake8", "pytest-mypy (>=0.9.1)", "pytest-perf (>=0.9.2)"]
+testing = ["flufl.flake8", "importlib-resources (>=1.3)", "packaging", "pyfakefs", "pytest (>=6)", "pytest-black (>=0.3.7)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=2.2)", "pytest-mypy (>=0.9.1)", "pytest-perf (>=0.9.2)", "pytest-ruff"]
 
 [[package]]
 name = "importlib-resources"
-version = "5.12.0"
+version = "6.0.1"
 description = "Read resources from Python packages"
 category = "main"
 optional = false
-python-versions = ">=3.7"
+python-versions = ">=3.8"
 files = [
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+    {file = "importlib_resources-6.0.1.tar.gz", hash = "sha256:4359457e42708462b9626a04657c6208ad799ceb41e5c58c57ffa0e6a098a5d4"},
 ]
 
 [package.dependencies]
 zipp = {version = ">=3.1.0", markers = "python_version < \"3.10\""}
 
 [package.extras]
-docs = ["furo", "jaraco.packaging (>=9)", "jaraco.tidelift (>=1.4)", "rst.linker (>=1.9)", "sphinx (>=3.5)", "sphinx-lint"]
-testing = ["flake8 (<5)", "pytest (>=6)", "pytest-black (>=0.3.7)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=1.3)", "pytest-flake8", "pytest-mypy (>=0.9.1)"]
+docs = ["furo", "jaraco.packaging (>=9.3)", "jaraco.tidelift (>=1.4)", "rst.linker (>=1.9)", "sphinx (>=3.5)", "sphinx-lint"]
+testing = ["pytest (>=6)", "pytest-black (>=0.3.7)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=2.2)", "pytest-mypy (>=0.9.1)", "pytest-ruff"]
 
 [[package]]
 name = "iniconfig"
@@ -978,14 +970,14 @@ files = [
 
 [[package]]
 name = "ipykernel"
-version = "6.23.2"
+version = "6.25.1"
 description = "IPython Kernel for Jupyter"
 category = "dev"
 optional = false
 python-versions = ">=3.8"
 files = [
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+    {file = "ipykernel-6.25.1.tar.gz", hash = "sha256:050391364c0977e768e354bdb60cbbfbee7cbb943b1af1618382021136ffd42f"},
 ]
 
 [package.dependencies]
@@ -1070,22 +1062,22 @@ requirements-deprecated-finder = ["pip-api", "pipreqs"]
 
 [[package]]
 name = "jedi"
-version = "0.18.2"
+version = "0.19.0"
 description = "An autocompletion tool for Python that can be used for text editors."
 category = "main"
 optional = false
 python-versions = ">=3.6"
 files = [
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 ]
 
 [package.dependencies]
-parso = ">=0.8.0,<0.9.0"
+parso = ">=0.8.3,<0.9.0"
 
 [package.extras]
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-qa = ["flake8 (==3.8.3)", "mypy (==0.782)"]
+qa = ["flake8 (==5.0.4)", "mypy (==0.971)", "types-setuptools (==67.2.0.1)"]
 testing = ["Django (<3.1)", "attrs", "colorama", "docopt", "pytest (<7.0.0)"]
 
 [[package]]
@@ -1108,36 +1100,54 @@ i18n = ["Babel (>=2.7)"]
 
 [[package]]
 name = "jsonschema"
-version = "4.17.3"
+version = "4.19.0"
 description = "An implementation of JSON Schema validation for Python"
 category = "dev"
 optional = false
-python-versions = ">=3.7"
+python-versions = ">=3.8"
 files = [
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 ]
 
 [package.dependencies]
-attrs = ">=17.4.0"
+attrs = ">=22.2.0"
 importlib-resources = {version = ">=1.4.0", markers = "python_version < \"3.9\""}
+jsonschema-specifications = ">=2023.03.6"
 pkgutil-resolve-name = {version = ">=1.3.10", markers = "python_version < \"3.9\""}
-pyrsistent = ">=0.14.0,<0.17.0 || >0.17.0,<0.17.1 || >0.17.1,<0.17.2 || >0.17.2"
+referencing = ">=0.28.4"
+rpds-py = ">=0.7.1"
 
 [package.extras]
 format = ["fqdn", "idna", "isoduration", "jsonpointer (>1.13)", "rfc3339-validator", "rfc3987", "uri-template", "webcolors (>=1.11)"]
 format-nongpl = ["fqdn", "idna", "isoduration", "jsonpointer (>1.13)", "rfc3339-validator", "rfc3986-validator (>0.1.0)", "uri-template", "webcolors (>=1.11)"]
 
+[[package]]
+name = "jsonschema-specifications"
+version = "2023.7.1"
+description = "The JSON Schema meta-schemas and vocabularies, exposed as a Registry"
+category = "dev"
+optional = false
+python-versions = ">=3.8"
+files = [
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+
+[package.dependencies]
+importlib-resources = {version = ">=1.4.0", markers = "python_version < \"3.9\""}
+referencing = ">=0.28.0"
+
 [[package]]
 name = "jupyter-client"
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+version = "8.3.0"
 description = "Jupyter protocol implementation and client libraries"
 category = "dev"
 optional = false
 python-versions = ">=3.8"
 files = [
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 ]
 
 [package.dependencies]
@@ -1326,36 +1336,36 @@ files = [
 
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 description = "lightweight wrapper around basic LLVM functionality"
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 python-versions = ">=3.8"
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 [package.dependencies]
@@ -1528,7 +1538,7 @@ kiwisolver = ">=1.0.1"
 numpy = ">=1.20"
 packaging = ">=20.0"
 pillow = ">=6.2.0"
-pyparsing = ">=2.3.1"
+pyparsing = ">=2.3.1,<3.1"
 python-dateutil = ">=2.7"
 
 [[package]]
@@ -1560,14 +1570,14 @@ files = [
 
 [[package]]
 name = "mistune"
-version = "2.0.5"
-description = "A sane Markdown parser with useful plugins and renderers"
+version = "3.0.1"
+description = "A sane and fast Markdown parser with useful plugins and renderers"
 category = "dev"
 optional = false
-python-versions = "*"
+python-versions = ">=3.7"
 files = [
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 [[package]]
@@ -1595,14 +1605,14 @@ test = ["flaky", "ipykernel (>=6.19.3)", "ipython", "ipywidgets", "nbconvert (>=
 
 [[package]]
 name = "nbconvert"
-version = "7.5.0"
+version = "7.7.4"
 description = "Converting Jupyter Notebooks"
 category = "dev"
 optional = false
-python-versions = ">=3.7"
+python-versions = ">=3.8"
 files = [
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 [package.dependencies]
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 jupyter-core = ">=4.7"
 jupyterlab-pygments = "*"
 markupsafe = ">=2.0"
-mistune = ">=2.0.3,<3"
+mistune = ">=2.0.3,<4"
 nbclient = ">=0.5.0"
 nbformat = ">=5.7"
 packaging = "*"
@@ -1629,19 +1639,19 @@ docs = ["ipykernel", "ipython", "myst-parser", "nbsphinx (>=0.2.12)", "pydata-sp
 qtpdf = ["nbconvert[qtpng]"]
 qtpng = ["pyqtwebengine (>=5.15)"]
 serve = ["tornado (>=6.1)"]
-test = ["ipykernel", "ipywidgets (>=7)", "pre-commit", "pytest", "pytest-dependency"]
-webpdf = ["pyppeteer (>=1,<1.1)"]
+test = ["flaky", "ipykernel", "ipywidgets (>=7)", "pre-commit", "pytest", "pytest-dependency"]
+webpdf = ["playwright"]
 
 [[package]]
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-version = "5.9.0"
+version = "5.9.2"
 description = "The Jupyter Notebook format"
 category = "dev"
 optional = false
 python-versions = ">=3.8"
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 [package.dependencies]
@@ -1676,48 +1686,48 @@ traitlets = ">=5"
 
 [[package]]
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 description = "Patch asyncio to allow nested event loops"
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 python-versions = ">=3.5"
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 python-versions = ">=3.8"
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 [package.dependencies]
@@ -1727,40 +1737,40 @@ numpy = ">=1.21,<1.25"
 
 [[package]]
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 python-versions = ">=3.8"
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 python-versions = ">=3.7"
 files = [
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@@ -2061,14 +2061,14 @@ testing = ["pytest", "pytest-benchmark"]
 
 [[package]]
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+version = "3.0.39"
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 category = "main"
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 python-versions = ">=3.7.0"
 files = [
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 [package.dependencies]
@@ -2178,14 +2178,14 @@ files = [
 
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+version = "2.16.1"
 description = "Pygments is a syntax highlighting package written in Python."
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 python-versions = ">=3.7"
 files = [
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@@ -2193,18 +2193,18 @@ plugins = ["importlib-metadata"]
 
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+version = "2.17.5"
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 category = "dev"
 optional = false
 python-versions = ">=3.7.2"
 files = [
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 [package.dependencies]
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 colorama = {version = ">=0.4.5", markers = "sys_platform == \"win32\""}
 dill = [
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 [package.dependencies]
 cffi = {version = "*", markers = "implementation_name == \"pypy\""}
 
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 version = "2.31.0"
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 [package.extras]
 jupyter = ["ipywidgets (>=7.5.1,<8.0.0)"]
 
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+    {file = "SQLAlchemy-1.4.49.tar.gz", hash = "sha256:06ff25cbae30c396c4b7737464f2a7fc37a67b7da409993b182b024cec80aed9"},
 ]
 
 [package.dependencies]
@@ -2984,35 +3083,35 @@ files = [
 
 [[package]]
 name = "tomlkit"
-version = "0.11.8"
+version = "0.12.1"
 description = "Style preserving TOML library"
 category = "dev"
 optional = false
 python-versions = ">=3.7"
 files = [
-    {file = "tomlkit-0.11.8-py3-none-any.whl", hash = "sha256:8c726c4c202bdb148667835f68d68780b9a003a9ec34167b6c673b38eff2a171"},
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 ]
 
 [[package]]
 name = "tornado"
-version = "6.3.2"
+version = "6.3.3"
 description = "Tornado is a Python web framework and asynchronous networking library, originally developed at FriendFeed."
 category = "dev"
 optional = false
 python-versions = ">= 3.8"
 files = [
-    {file = "tornado-6.3.2-cp38-abi3-macosx_10_9_universal2.whl", hash = "sha256:c367ab6c0393d71171123ca5515c61ff62fe09024fa6bf299cd1339dc9456829"},
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-    {file = "tornado-6.3.2-cp38-abi3-manylinux_2_5_x86_64.manylinux1_x86_64.manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:5b17b1cf5f8354efa3d37c6e28fdfd9c1c1e5122f2cb56dac121ac61baa47cbe"},
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-    {file = "tornado-6.3.2-cp38-abi3-win32.whl", hash = "sha256:7efcbcc30b7c654eb6a8c9c9da787a851c18f8ccd4a5a3a95b05c7accfa068d2"},
-    {file = "tornado-6.3.2-cp38-abi3-win_amd64.whl", hash = "sha256:0c325e66c8123c606eea33084976c832aa4e766b7dff8aedd7587ea44a604cdf"},
-    {file = "tornado-6.3.2.tar.gz", hash = "sha256:4b927c4f19b71e627b13f3db2324e4ae660527143f9e1f2e2fb404f3a187e2ba"},
+    {file = "tornado-6.3.3-cp38-abi3-macosx_10_9_universal2.whl", hash = "sha256:502fba735c84450974fec147340016ad928d29f1e91f49be168c0a4c18181e1d"},
+    {file = "tornado-6.3.3-cp38-abi3-macosx_10_9_x86_64.whl", hash = "sha256:805d507b1f588320c26f7f097108eb4023bbaa984d63176d1652e184ba24270a"},
+    {file = "tornado-6.3.3-cp38-abi3-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:1bd19ca6c16882e4d37368e0152f99c099bad93e0950ce55e71daed74045908f"},
+    {file = "tornado-6.3.3-cp38-abi3-manylinux_2_5_i686.manylinux1_i686.manylinux_2_17_i686.manylinux2014_i686.whl", hash = "sha256:7ac51f42808cca9b3613f51ffe2a965c8525cb1b00b7b2d56828b8045354f76a"},
+    {file = "tornado-6.3.3-cp38-abi3-manylinux_2_5_x86_64.manylinux1_x86_64.manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:71a8db65160a3c55d61839b7302a9a400074c9c753040455494e2af74e2501f2"},
+    {file = "tornado-6.3.3-cp38-abi3-musllinux_1_1_aarch64.whl", hash = "sha256:ceb917a50cd35882b57600709dd5421a418c29ddc852da8bcdab1f0db33406b0"},
+    {file = "tornado-6.3.3-cp38-abi3-musllinux_1_1_i686.whl", hash = "sha256:7d01abc57ea0dbb51ddfed477dfe22719d376119844e33c661d873bf9c0e4a16"},
+    {file = "tornado-6.3.3-cp38-abi3-musllinux_1_1_x86_64.whl", hash = "sha256:9dc4444c0defcd3929d5c1eb5706cbe1b116e762ff3e0deca8b715d14bf6ec17"},
+    {file = "tornado-6.3.3-cp38-abi3-win32.whl", hash = "sha256:65ceca9500383fbdf33a98c0087cb975b2ef3bfb874cb35b8de8740cf7f41bd3"},
+    {file = "tornado-6.3.3-cp38-abi3-win_amd64.whl", hash = "sha256:22d3c2fa10b5793da13c807e6fc38ff49a4f6e1e3868b0a6f4164768bb8e20f5"},
+    {file = "tornado-6.3.3.tar.gz", hash = "sha256:e7d8db41c0181c80d76c982aacc442c0783a2c54d6400fe028954201a2e032fe"},
 ]
 
 [[package]]
@@ -3033,26 +3132,26 @@ test = ["argcomplete (>=2.0)", "pre-commit", "pytest", "pytest-mock"]
 
 [[package]]
 name = "typing-extensions"
-version = "4.6.3"
+version = "4.7.1"
 description = "Backported and Experimental Type Hints for Python 3.7+"
 category = "main"
 optional = false
 python-versions = ">=3.7"
 files = [
-    {file = "typing_extensions-4.6.3-py3-none-any.whl", hash = "sha256:88a4153d8505aabbb4e13aacb7c486c2b4a33ca3b3f807914a9b4c844c471c26"},
-    {file = "typing_extensions-4.6.3.tar.gz", hash = "sha256:d91d5919357fe7f681a9f2b5b4cb2a5f1ef0a1e9f59c4d8ff0d3491e05c0ffd5"},
+    {file = "typing_extensions-4.7.1-py3-none-any.whl", hash = "sha256:440d5dd3af93b060174bf433bccd69b0babc3b15b1a8dca43789fd7f61514b36"},
+    {file = "typing_extensions-4.7.1.tar.gz", hash = "sha256:b75ddc264f0ba5615db7ba217daeb99701ad295353c45f9e95963337ceeeffb2"},
 ]
 
 [[package]]
 name = "urllib3"
-version = "2.0.3"
+version = "2.0.4"
 description = "HTTP library with thread-safe connection pooling, file post, and more."
 category = "dev"
 optional = false
 python-versions = ">=3.7"
 files = [
-    {file = "urllib3-2.0.3-py3-none-any.whl", hash = "sha256:48e7fafa40319d358848e1bc6809b208340fafe2096f1725d05d67443d0483d1"},
-    {file = "urllib3-2.0.3.tar.gz", hash = "sha256:bee28b5e56addb8226c96f7f13ac28cb4c301dd5ea8a6ca179c0b9835e032825"},
+    {file = "urllib3-2.0.4-py3-none-any.whl", hash = "sha256:de7df1803967d2c2a98e4b11bb7d6bd9210474c46e8a0401514e3a42a75ebde4"},
+    {file = "urllib3-2.0.4.tar.gz", hash = "sha256:8d22f86aae8ef5e410d4f539fde9ce6b2113a001bb4d189e0aed70642d602b11"},
 ]
 
 [package.extras]
@@ -3063,24 +3162,24 @@ zstd = ["zstandard (>=0.18.0)"]
 
 [[package]]
 name = "virtualenv"
-version = "20.23.0"
+version = "20.24.3"
 description = "Virtual Python Environment builder"
 category = "dev"
 optional = false
 python-versions = ">=3.7"
 files = [
-    {file = "virtualenv-20.23.0-py3-none-any.whl", hash = "sha256:6abec7670e5802a528357fdc75b26b9f57d5d92f29c5462ba0fbe45feacc685e"},
-    {file = "virtualenv-20.23.0.tar.gz", hash = "sha256:a85caa554ced0c0afbd0d638e7e2d7b5f92d23478d05d17a76daeac8f279f924"},
+    {file = "virtualenv-20.24.3-py3-none-any.whl", hash = "sha256:95a6e9398b4967fbcb5fef2acec5efaf9aa4972049d9ae41f95e0972a683fd02"},
+    {file = "virtualenv-20.24.3.tar.gz", hash = "sha256:e5c3b4ce817b0b328af041506a2a299418c98747c4b1e68cb7527e74ced23efc"},
 ]
 
 [package.dependencies]
-distlib = ">=0.3.6,<1"
-filelock = ">=3.11,<4"
-platformdirs = ">=3.2,<4"
+distlib = ">=0.3.7,<1"
+filelock = ">=3.12.2,<4"
+platformdirs = ">=3.9.1,<4"
 
 [package.extras]
-docs = ["furo (>=2023.3.27)", "proselint (>=0.13)", "sphinx (>=6.1.3)", "sphinx-argparse (>=0.4)", "sphinxcontrib-towncrier (>=0.2.1a0)", "towncrier (>=22.12)"]
-test = ["covdefaults (>=2.3)", "coverage (>=7.2.3)", "coverage-enable-subprocess (>=1)", "flaky (>=3.7)", "packaging (>=23.1)", "pytest (>=7.3.1)", "pytest-env (>=0.8.1)", "pytest-freezegun (>=0.4.2)", "pytest-mock (>=3.10)", "pytest-randomly (>=3.12)", "pytest-timeout (>=2.1)", "setuptools (>=67.7.1)", "time-machine (>=2.9)"]
+docs = ["furo (>=2023.5.20)", "proselint (>=0.13)", "sphinx (>=7.0.1)", "sphinx-argparse (>=0.4)", "sphinxcontrib-towncrier (>=0.2.1a0)", "towncrier (>=23.6)"]
+test = ["covdefaults (>=2.3)", "coverage (>=7.2.7)", "coverage-enable-subprocess (>=1)", "flaky (>=3.7)", "packaging (>=23.1)", "pytest (>=7.4)", "pytest-env (>=0.8.2)", "pytest-freezer (>=0.4.8)", "pytest-mock (>=3.11.1)", "pytest-randomly (>=3.12)", "pytest-timeout (>=2.1)", "setuptools (>=68)", "time-machine (>=2.10)"]
 
 [[package]]
 name = "wcwidth"
@@ -3204,19 +3303,19 @@ files = [
 
 [[package]]
 name = "zipp"
-version = "3.15.0"
+version = "3.16.2"
 description = "Backport of pathlib-compatible object wrapper for zip files"
 category = "main"
 optional = false
-python-versions = ">=3.7"
+python-versions = ">=3.8"
 files = [
-    {file = "zipp-3.15.0-py3-none-any.whl", hash = "sha256:48904fc76a60e542af151aded95726c1a5c34ed43ab4134b597665c86d7ad556"},
-    {file = "zipp-3.15.0.tar.gz", hash = "sha256:112929ad649da941c23de50f356a2b5570c954b65150642bccdd66bf194d224b"},
+    {file = "zipp-3.16.2-py3-none-any.whl", hash = "sha256:679e51dd4403591b2d6838a48de3d283f3d188412a9782faadf845f298736ba0"},
+    {file = "zipp-3.16.2.tar.gz", hash = "sha256:ebc15946aa78bd63458992fc81ec3b6f7b1e92d51c35e6de1c3804e73b799147"},
 ]
 
 [package.extras]
-docs = ["furo", "jaraco.packaging (>=9)", "jaraco.tidelift (>=1.4)", "rst.linker (>=1.9)", "sphinx (>=3.5)", "sphinx-lint"]
-testing = ["big-O", "flake8 (<5)", "jaraco.functools", "jaraco.itertools", "more-itertools", "pytest (>=6)", "pytest-black (>=0.3.7)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=1.3)", "pytest-flake8", "pytest-mypy (>=0.9.1)"]
+docs = ["furo", "jaraco.packaging (>=9.3)", "jaraco.tidelift (>=1.4)", "rst.linker (>=1.9)", "sphinx (>=3.5)", "sphinx-lint"]
+testing = ["big-O", "jaraco.functools", "jaraco.itertools", "more-itertools", "pytest (>=6)", "pytest-black (>=0.3.7)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=2.2)", "pytest-ignore-flaky", "pytest-mypy (>=0.9.1)", "pytest-ruff"]
 
 [extras]
 box = ["click", "rich"]
@@ -3225,4 +3324,4 @@ mark = ["banana-hep", "matplotlib", "pandas", "sqlalchemy"]
 [metadata]
 lock-version = "2.0"
 python-versions = "^3.8,<3.12"
-content-hash = "1b953c2ab9f1d4629f923a290a9db0b092ce2ff711b2e6009372cf1d602d5da3"
+content-hash = "223b56c91574c33cd1f4b6b74a6bde4002d72ab471ef8f90dc6d453b4936756e"
diff --git a/pyproject.toml b/pyproject.toml
index 31be6cb0c..ac9192de3 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -44,7 +44,7 @@ PyYAML = "^6.0"
 lz4 = "^4.0.2"
 numba = "^0.57.0"
 # ekomark
-banana-hep = { version = "^0.6.9", optional = true }
+banana-hep = { version = "^0.6.10", optional = true }
 sqlalchemy = { version = "^1.4.21", optional = true }
 pandas = { version = "^1.3.0", optional = true }
 matplotlib = { version = "^3.5.1", optional = true }

From a49fca63858f9e7101e8dc1a40a63e54606e9e20 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Fri, 12 Jan 2024 16:40:44 +0200
Subject: [PATCH 24/40] Fix evol_pdf

---
 src/ekobox/evol_pdf.py | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/src/ekobox/evol_pdf.py b/src/ekobox/evol_pdf.py
index 94c8e416c..4310a0eda 100644
--- a/src/ekobox/evol_pdf.py
+++ b/src/ekobox/evol_pdf.py
@@ -60,12 +60,16 @@ def evolve_pdfs(
 
     # apply PDF to eko
     evolved_PDF_list = []
+    q2block_per_nf = {}
     with EKO.read(eko_path) as eko_output:
         for initial_PDF in initial_PDF_list:
             evolved_PDF_list.append(
                 apply.apply_pdf(eko_output, initial_PDF, targetgrid)
             )
 
+        # separate by nf the evolgrid (and order per nf/q)
+        q2block_per_nf = regroup_evolgrid(eko_output.evolgrid)  # pylint: disable=E1101
+
     # update info file
     if targetgrid is None:
         targetgrid = operators_card.xgrid
@@ -80,9 +84,6 @@ def evolve_pdfs(
         info_update=info_update,
     )
 
-    # separate by nf the evolgrid (and order per nf/q)
-    q2block_per_nf = regroup_evolgrid(eko_output.evolgrid)
-
     # write all replicas
     all_member_blocks = []
     for evolved_PDF in evolved_PDF_list:

From 78e533cee78e30e441973fdc219d4be8f27ac4eb Mon Sep 17 00:00:00 2001
From: juacrumar <juacrumar@lairen.eu>
Date: Tue, 16 Jul 2024 09:41:34 +0200
Subject: [PATCH 25/40] use nf to generate alpha_s

---
 src/ekobox/info_file.py | 24 +++++++++---------------
 1 file changed, 9 insertions(+), 15 deletions(-)

diff --git a/src/ekobox/info_file.py b/src/ekobox/info_file.py
index 26e3cb170..fb744ce4b 100644
--- a/src/ekobox/info_file.py
+++ b/src/ekobox/info_file.py
@@ -68,19 +68,13 @@ def build(
         hqm_scheme=theory_card.heavy.masses_scheme,
         thresholds_ratios=np.power(list(iter(theory_card.heavy.matching_ratios)), 2.0),
     )
-    alphas_values = np.array(
-        [
-            4.0
-            * np.pi
-            * sc.a_s(
-                muf2,
-            )
-            for muf2 in operators_card.mu2grid
-        ],
-        dtype=float,
-    )
-    template_info["AlphaS_Vals"] = alphas_values.tolist()
-    template_info["AlphaS_Qs"] = np.array(
-        [mu for mu, _ in operators_card.mugrid]
-    ).tolist()
+
+    alphas_values = []
+    alphas_qs = []
+    for mu, nf in operators_card.mugrid:
+        alphas_values.append(float(4.0 * np.pi * sc.a_s(mu * mu, nf_to=nf)))
+        alphas_qs.append(mu)
+
+    template_info["AlphaS_Vals"] = alphas_values
+    template_info["AlphaS_Qs"] = alphas_qs
     return template_info

From cb6953df9adeef319c6f23f6aedcc21993ad601b Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Tue, 16 Jul 2024 14:15:58 +0300
Subject: [PATCH 26/40] Check sorting of alphas in LHAPDF info

---
 src/ekobox/evol_pdf.py         | 10 +-----
 src/ekobox/info_file.py        | 62 +++++++++++++++++++++++++++-------
 src/ekobox/utils.py            |  9 +++++
 tests/ekobox/test_info_file.py | 40 ++++++++++++++++++++++
 4 files changed, 100 insertions(+), 21 deletions(-)

diff --git a/src/ekobox/evol_pdf.py b/src/ekobox/evol_pdf.py
index ddd80f75a..0045cdd28 100644
--- a/src/ekobox/evol_pdf.py
+++ b/src/ekobox/evol_pdf.py
@@ -1,13 +1,13 @@
 """Tools to evolve actual PDFs."""
 
 import pathlib
-from collections import defaultdict
 
 from eko import basis_rotation as br
 from eko.io import EKO
 from eko.runner import managed
 
 from . import apply, genpdf, info_file
+from .utils import regroup_evolgrid
 
 DEFAULT_NAME = "eko.tar"
 
@@ -95,14 +95,6 @@ def evolve_pdfs(
         genpdf.install_pdf(name)
 
 
-def regroup_evolgrid(evolgrid: list):
-    """Split evolution points by nf and sort by scale."""
-    by_nf = defaultdict(list)
-    for q, nf in sorted(evolgrid, key=lambda ep: ep[1]):
-        by_nf[nf].append(q)
-    return {nf: sorted(qs) for nf, qs in by_nf.items()}
-
-
 def collect_blocks(evolved_PDF: dict, q2block_per_nf: dict, xgrid: list):
     """Collect all LHAPDF blocks for a given replica.
 
diff --git a/src/ekobox/info_file.py b/src/ekobox/info_file.py
index fb744ce4b..c9ac88b0c 100644
--- a/src/ekobox/info_file.py
+++ b/src/ekobox/info_file.py
@@ -9,6 +9,7 @@
 from eko.io.runcards import OperatorCard, TheoryCard
 
 from .genpdf import load
+from .utils import regroup_evolgrid
 
 
 def build(
@@ -16,19 +17,19 @@ def build(
     operators_card: OperatorCard,
     num_members: int,
     info_update: dict,
-):
-    """Generate a lhapdf info file from theory and operators card.
+) -> dict:
+    """Generate a lhapdf info file.
 
     Parameters
     ----------
-    theory_card : dict
+    theory_card :
         theory card
-    operators_card : dict
-        operators_card
-    num_members : int
+    operators_card :
+        operators card
+    num_members :
         number of pdf set members
-    info_update : dict
-        info to update
+    info_update :
+        additional info to update
 
     Returns
     -------
@@ -56,8 +57,45 @@ def build(
     template_info["MCharm"] = theory_card.heavy.masses.c.value
     template_info["MBottom"] = theory_card.heavy.masses.b.value
     template_info["MTop"] = theory_card.heavy.masses.t.value
+    # dump alphas
+    template_info.update(build_alphas(theory_card, operators_card))
+    return template_info
+
+
+def build_alphas(
+    theory_card: TheoryCard,
+    operators_card: OperatorCard,
+) -> dict:
+    """Generate a couplings section of lhapdf info file.
+
+    Parameters
+    ----------
+    theory_card : dict
+        theory card
+    operators_card : dict
+        operators card
+
+    Returns
+    -------
+    dict
+        info file section in lhapdf format
+    """
+    # start with meta stuff
+    template_info = {}
     template_info["AlphaS_MZ"] = theory_card.couplings.alphas
     template_info["AlphaS_OrderQCD"] = theory_card.order[0] - 1
+
+    # check we have disjoint scale ranges
+    evolgrid = regroup_evolgrid(operators_card.mugrid)
+    nfs = list(evolgrid.keys())
+    for j in range(len(nfs) - 1):
+        # equal points are allowed by LHAPDF
+        if evolgrid[nfs[j]][-1] > evolgrid[nfs[j + 1]][0]:
+            raise ValueError(
+                f"Last scale point for nf={nfs[j]} is bigger than first in nf={nfs[j+1]}"
+            )
+
+    # add actual values
     evmod = couplings.couplings_mod_ev(operators_card.configs.evolution_method)
     quark_masses = [(x.value) ** 2 for x in theory_card.heavy.masses]
     sc = couplings.Couplings(
@@ -68,12 +106,12 @@ def build(
         hqm_scheme=theory_card.heavy.masses_scheme,
         thresholds_ratios=np.power(list(iter(theory_card.heavy.matching_ratios)), 2.0),
     )
-
     alphas_values = []
     alphas_qs = []
-    for mu, nf in operators_card.mugrid:
-        alphas_values.append(float(4.0 * np.pi * sc.a_s(mu * mu, nf_to=nf)))
-        alphas_qs.append(mu)
+    for nf, mus in evolgrid.items():
+        for mu in mus:
+            alphas_values.append(float(4.0 * np.pi * sc.a_s(mu * mu, nf_to=nf)))
+            alphas_qs.append(mu)
 
     template_info["AlphaS_Vals"] = alphas_values
     template_info["AlphaS_Qs"] = alphas_qs
diff --git a/src/ekobox/utils.py b/src/ekobox/utils.py
index 0047d0872..091cde15e 100644
--- a/src/ekobox/utils.py
+++ b/src/ekobox/utils.py
@@ -1,6 +1,7 @@
 """Generic utilities to work with EKOs."""
 
 import os
+from collections import defaultdict
 from typing import Optional
 
 import numpy as np
@@ -78,3 +79,11 @@ def ekos_product(
 
     if path is not None:
         final_eko.close()
+
+
+def regroup_evolgrid(evolgrid: list):
+    """Split evolution points by nf and sort by scale."""
+    by_nf = defaultdict(list)
+    for q, nf in sorted(evolgrid, key=lambda ep: ep[1]):
+        by_nf[nf].append(q)
+    return {nf: sorted(qs) for nf, qs in by_nf.items()}
diff --git a/tests/ekobox/test_info_file.py b/tests/ekobox/test_info_file.py
index 64af8eb93..f7267fbd4 100644
--- a/tests/ekobox/test_info_file.py
+++ b/tests/ekobox/test_info_file.py
@@ -1,6 +1,7 @@
 import math
 
 import numpy as np
+import pytest
 
 from ekobox import cards, info_file
 
@@ -23,3 +24,42 @@ def test_build():
     np.testing.assert_allclose(info["QMin"], math.sqrt(op.mu2grid[0]), rtol=1e-5)
     assert info["XMin"] == op.xgrid.raw[0]
     assert info["XMax"] == op.xgrid.raw[-1] == 1.0
+
+
+def test_build_alphas_good():
+    """Good configurations."""
+    theory = cards.example.theory()
+    theory.order = (2, 0)
+    theory.couplings.alphas = 0.2
+    op = cards.example.operator()
+    op.mu0 = 1.0
+    # base case
+    op.mugrid = [(10.0, 5), (100.0, 5)]
+    info = info_file.build_alphas(theory, op)
+    assert len(info["AlphaS_Vals"]) == 2
+    np.testing.assert_allclose(info["AlphaS_Qs"], [10.0, 100.0])
+    # several nf
+    op.mugrid = [(1.0, 3), (5.0, 3), (5.0, 4), (10.0, 5), (10.0, 5), (100.0, 5)]
+    info = info_file.build_alphas(theory, op)
+    assert len(info["AlphaS_Vals"]) == 6
+    np.testing.assert_allclose(info["AlphaS_Qs"], [1.0, 5.0, 5.0, 10.0, 10.0, 100.0])
+    # several nf with gap
+    op.mugrid = [(1.0, 3), (10.0, 3), (10.0, 5), (100.0, 5)]
+    info = info_file.build_alphas(theory, op)
+    assert len(info["AlphaS_Vals"]) == 4
+    np.testing.assert_allclose(info["AlphaS_Qs"], [1.0, 10.0, 10.0, 100.0])
+
+
+def test_build_alphas_bad():
+    """Bad configurations."""
+    theory = cards.example.theory()
+    theory.order = (2, 0)
+    theory.couplings.alphas = 0.2
+    op = cards.example.operator()
+    op.mu0 = 1.0
+    op.mugrid = [(5.0, 3), (15.0, 4), (10.0, 5), (100.0, 5)]
+    with pytest.raises(ValueError, match="is bigger"):
+        info_file.build_alphas(theory, op)
+    op.mugrid = [(5.0, 3), (10.0, 3), (10.0, 4), (15.0, 4), (10.0, 5)]
+    with pytest.raises(ValueError, match="is bigger"):
+        info_file.build_alphas(theory, op)

From d5f63fe7ac995fd9d0d38dba48f2a7969de01c28 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Tue, 16 Jul 2024 14:53:40 +0300
Subject: [PATCH 27/40] Lift scale check for LHAPDF

---
 src/ekobox/evol_pdf.py         | 19 ++++++++++++++++---
 src/ekobox/info_file.py        | 13 ++-----------
 tests/ekobox/test_evol_pdf.py  | 16 ++++++++++++++++
 tests/ekobox/test_info_file.py | 20 ++------------------
 4 files changed, 36 insertions(+), 32 deletions(-)

diff --git a/src/ekobox/evol_pdf.py b/src/ekobox/evol_pdf.py
index 0045cdd28..abdb2ec6a 100644
--- a/src/ekobox/evol_pdf.py
+++ b/src/ekobox/evol_pdf.py
@@ -2,6 +2,8 @@
 
 import pathlib
 
+import numpy as np
+
 from eko import basis_rotation as br
 from eko.io import EKO
 from eko.runner import managed
@@ -46,6 +48,18 @@ def evolve_pdfs(
     info_update : dict
         dict of info to add or update to default info file
     """
+    # separate by nf the evolgrid (and order per nf/q)
+    q2block_per_nf = regroup_evolgrid(operators_card.mugrid)
+
+    # check we have disjoint scale ranges
+    nfs = list(q2block_per_nf.keys())
+    for j in range(len(nfs) - 1):
+        # equal points are allowed by LHAPDF
+        if q2block_per_nf[nfs[j]][-1] > q2block_per_nf[nfs[j + 1]][0]:
+            raise ValueError(
+                f"Last scale point for nf={nfs[j]} is bigger than first in nf={nfs[j+1]}"
+            )
+
     # update op and th cards
     if path is not None:
         eko_path = pathlib.Path(path)
@@ -79,9 +93,8 @@ def evolve_pdfs(
         info_update=info_update,
     )
 
-    # separate by nf the evolgrid (and order per nf/q)
-    q2block_per_nf = regroup_evolgrid(eko_output.evolgrid)
-
+    # in the eko scales are squared
+    q2block_per_nf = {nf: np.power(q2s, 2) for nf, q2s in q2block_per_nf.items()}
     # write all replicas
     all_member_blocks = []
     for evolved_PDF in evolved_PDF_list:
diff --git a/src/ekobox/info_file.py b/src/ekobox/info_file.py
index c9ac88b0c..fc5c17f1d 100644
--- a/src/ekobox/info_file.py
+++ b/src/ekobox/info_file.py
@@ -84,18 +84,8 @@ def build_alphas(
     template_info = {}
     template_info["AlphaS_MZ"] = theory_card.couplings.alphas
     template_info["AlphaS_OrderQCD"] = theory_card.order[0] - 1
-
-    # check we have disjoint scale ranges
+    # prepare
     evolgrid = regroup_evolgrid(operators_card.mugrid)
-    nfs = list(evolgrid.keys())
-    for j in range(len(nfs) - 1):
-        # equal points are allowed by LHAPDF
-        if evolgrid[nfs[j]][-1] > evolgrid[nfs[j + 1]][0]:
-            raise ValueError(
-                f"Last scale point for nf={nfs[j]} is bigger than first in nf={nfs[j+1]}"
-            )
-
-    # add actual values
     evmod = couplings.couplings_mod_ev(operators_card.configs.evolution_method)
     quark_masses = [(x.value) ** 2 for x in theory_card.heavy.masses]
     sc = couplings.Couplings(
@@ -106,6 +96,7 @@ def build_alphas(
         hqm_scheme=theory_card.heavy.masses_scheme,
         thresholds_ratios=np.power(list(iter(theory_card.heavy.matching_ratios)), 2.0),
     )
+    # add actual values
     alphas_values = []
     alphas_qs = []
     for nf, mus in evolgrid.items():
diff --git a/tests/ekobox/test_evol_pdf.py b/tests/ekobox/test_evol_pdf.py
index 54bce6623..141787b49 100644
--- a/tests/ekobox/test_evol_pdf.py
+++ b/tests/ekobox/test_evol_pdf.py
@@ -1,4 +1,5 @@
 import numpy as np
+import pytest
 from banana import toy
 
 import eko
@@ -50,6 +51,21 @@ def test_evolve_pdfs_dump_path(fake_lhapdf, cd):
     assert p.exists()
 
 
+def test_evolve_pdfs_bad_scales(fake_lhapdf, cd):
+    """Bad scale configurations."""
+    theory, op = init_cards()
+    n = "test_evolve_pdfs_bad_scales"
+    op = cards.example.operator()
+    op.mugrid = [(5.0, 3), (15.0, 4), (10.0, 5), (100.0, 5)]
+    with pytest.raises(ValueError, match="is bigger"):
+        with cd(fake_lhapdf):
+            ev_p.evolve_pdfs([toy.mkPDF("", 0)], theory, op, name=n, path=fake_lhapdf)
+    op.mugrid = [(5.0, 3), (10.0, 3), (10.0, 4), (15.0, 4), (10.0, 5)]
+    with pytest.raises(ValueError, match="is bigger"):
+        with cd(fake_lhapdf):
+            ev_p.evolve_pdfs([toy.mkPDF("", 0)], theory, op, name=n, path=fake_lhapdf)
+
+
 def test_evolve_pdfs_dump_file(fake_lhapdf, cd):
     theory, op = init_cards()
     n = "test_evolve_pdfs_dump_file"
diff --git a/tests/ekobox/test_info_file.py b/tests/ekobox/test_info_file.py
index f7267fbd4..acf3f7272 100644
--- a/tests/ekobox/test_info_file.py
+++ b/tests/ekobox/test_info_file.py
@@ -1,7 +1,6 @@
 import math
 
 import numpy as np
-import pytest
 
 from ekobox import cards, info_file
 
@@ -34,12 +33,12 @@ def test_build_alphas_good():
     op = cards.example.operator()
     op.mu0 = 1.0
     # base case
-    op.mugrid = [(10.0, 5), (100.0, 5)]
+    op.mugrid = [(100.0, 5), (10.0, 5)]
     info = info_file.build_alphas(theory, op)
     assert len(info["AlphaS_Vals"]) == 2
     np.testing.assert_allclose(info["AlphaS_Qs"], [10.0, 100.0])
     # several nf
-    op.mugrid = [(1.0, 3), (5.0, 3), (5.0, 4), (10.0, 5), (10.0, 5), (100.0, 5)]
+    op.mugrid = [(5.0, 4), (10.0, 5), (1.0, 3), (5.0, 3), (10.0, 5), (100.0, 5)]
     info = info_file.build_alphas(theory, op)
     assert len(info["AlphaS_Vals"]) == 6
     np.testing.assert_allclose(info["AlphaS_Qs"], [1.0, 5.0, 5.0, 10.0, 10.0, 100.0])
@@ -48,18 +47,3 @@ def test_build_alphas_good():
     info = info_file.build_alphas(theory, op)
     assert len(info["AlphaS_Vals"]) == 4
     np.testing.assert_allclose(info["AlphaS_Qs"], [1.0, 10.0, 10.0, 100.0])
-
-
-def test_build_alphas_bad():
-    """Bad configurations."""
-    theory = cards.example.theory()
-    theory.order = (2, 0)
-    theory.couplings.alphas = 0.2
-    op = cards.example.operator()
-    op.mu0 = 1.0
-    op.mugrid = [(5.0, 3), (15.0, 4), (10.0, 5), (100.0, 5)]
-    with pytest.raises(ValueError, match="is bigger"):
-        info_file.build_alphas(theory, op)
-    op.mugrid = [(5.0, 3), (10.0, 3), (10.0, 4), (15.0, 4), (10.0, 5)]
-    with pytest.raises(ValueError, match="is bigger"):
-        info_file.build_alphas(theory, op)

From ac8dbe859d97747b4c3c144f991822987a85d418 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Thu, 18 Jul 2024 17:15:17 +0300
Subject: [PATCH 28/40] rust: Allow abbrev

---
 crates/doc-header.html         | 65 ++++++++++++++++++++++++++++++++++
 crates/eko/Cargo.toml          |  2 +-
 crates/eko/doc-header.html     |  1 +
 crates/eko/katex-header.html   |  1 -
 crates/ekore/Cargo.toml        |  2 +-
 crates/ekore/doc-header.html   |  1 +
 crates/ekore/katex-header.html |  1 -
 crates/katex-header.html       | 19 ----------
 crates/parse-abbrev.py         | 20 +++++++++++
 9 files changed, 89 insertions(+), 23 deletions(-)
 create mode 100644 crates/doc-header.html
 create mode 120000 crates/eko/doc-header.html
 delete mode 120000 crates/eko/katex-header.html
 create mode 120000 crates/ekore/doc-header.html
 delete mode 120000 crates/ekore/katex-header.html
 delete mode 100644 crates/katex-header.html
 create mode 100644 crates/parse-abbrev.py

diff --git a/crates/doc-header.html b/crates/doc-header.html
new file mode 100644
index 000000000..3b2f9651b
--- /dev/null
+++ b/crates/doc-header.html
@@ -0,0 +1,65 @@
+<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.10/dist/katex.min.css" integrity="sha384-wcIxkf4k558AjM3Yz3BBFQUbk/zgIYC2R0QpeeYb+TwlBVMrlgLqwRjRtGZiK7ww" crossorigin="anonymous">
+<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.10/dist/katex.min.js" integrity="sha384-hIoBPJpTUs74ddyc4bFZSM1TVlQDA60VBbJS0oA934VSz82sBx1X7kSx2ATBDIyd" crossorigin="anonymous"></script>
+<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.10/dist/contrib/auto-render.min.js" integrity="sha384-43gviWU0YVjaDtb/GhzOouOXtZMP/7XUzwPTstBeZFe/+rCMvRwr4yROQP43s0Xk" crossorigin="anonymous"></script>
+<script>
+    document.addEventListener("DOMContentLoaded", function() {
+        // activate KaTeX
+        renderMathInElement(document.body, {
+          // customised options
+          // • auto-render specific keys, e.g.:
+          delimiters: [
+              {left: '$$', right: '$$', display: true},
+              {left: '$', right: '$', display: false},
+              {left: '\\(', right: '\\)', display: false},
+              {left: '\\[', right: '\\]', display: true}
+          ],
+          // • rendering keys, e.g.:
+          throwOnError : false
+        });
+
+        // Allow abbreviations
+        let abbrevs = {
+            "EKO": "Evolution Kernel Operator",
+            "PDF": "Parton Distribution Function(s)",
+            "FF": "Fragmentation Function(s)",
+            "FNS": "Flavor Number Scheme",
+            "FFNS": "Fixed Flavor Number Scheme",
+            "VFNS": "Variable Flavor Number Scheme",
+            "LO": "Leading Order",
+            "NLO": "Next-to-Leading Order",
+            "NNLO": "Next-to-Next-to-Leading Order",
+            "N3LO": "Next-to-Next-to-Next-to-Leading Order",
+            "LL": "Leading Log",
+            "NLL": "Next-to-Leading Log",
+            "NNLL": "Next-to-Next-to-Leading Log",
+            "DGLAP": "Dokshitzer-Gribov-Lipatov-Altarelli-Parisi",
+            "PID": "(Monte Carlo) parton identifier",
+            "OME": "Operator Matrix Element",
+            "RGE": "Renormalization Group Equation",
+            "MHOU": "Missing Higher Order Uncertainties",
+            "QCD": "Quantum Chromodynamics",
+            "QED": "Quantum Electrodynamics",
+            "DIS": "Deep Inelastic Scattering",
+            "BFKL": "Balitsky-Fadin-Kuraev-Lipatov",
+            "FHMRUVV": "Falcioni, Herzog, Moch, Ruijl, Ueda, Vermaseren and Vogt",
+            "API": "Application Program Interface",
+        };
+        // parse abbreviations
+        let parsedAbbrevs = {};
+        for (el in abbrevs) {
+            parsedAbbrevs["|" + el + "|"] = "<abbr title='"+abbrevs[el]+"' >"+el+"</abbr>";
+        }
+        // do the actual replace
+        function replaceAbbrev(el) {
+            let txt = el.textContent;
+            for (k in parsedAbbrevs)
+                txt = txt.replace(k, parsedAbbrevs[k]);
+            el.innerHTML = txt;
+        }
+        // search texts
+        let longs = document.getElementsByClassName("docblock");
+        for (let el of longs) replaceAbbrev(el);
+        let shorts = document.getElementsByClassName("docblock-short");
+        for (let el of shorts) replaceAbbrev(el);
+    });
+</script>
diff --git a/crates/eko/Cargo.toml b/crates/eko/Cargo.toml
index 0fc9b2ee7..0fffdea1a 100644
--- a/crates/eko/Cargo.toml
+++ b/crates/eko/Cargo.toml
@@ -13,7 +13,7 @@ rust-version.workspace = true
 version.workspace = true
 
 [package.metadata.docs.rs]
-rustdoc-args = ["--html-in-header", "katex-header.html"]
+rustdoc-args = ["--html-in-header", "doc-header.html"]
 
 [lib]
 name = "ekors"
diff --git a/crates/eko/doc-header.html b/crates/eko/doc-header.html
new file mode 120000
index 000000000..22282661d
--- /dev/null
+++ b/crates/eko/doc-header.html
@@ -0,0 +1 @@
+../doc-header.html
\ No newline at end of file
diff --git a/crates/eko/katex-header.html b/crates/eko/katex-header.html
deleted file mode 120000
index 810e68dcb..000000000
--- a/crates/eko/katex-header.html
+++ /dev/null
@@ -1 +0,0 @@
-../katex-header.html
\ No newline at end of file
diff --git a/crates/ekore/Cargo.toml b/crates/ekore/Cargo.toml
index 86e9784eb..419bc126a 100644
--- a/crates/ekore/Cargo.toml
+++ b/crates/ekore/Cargo.toml
@@ -13,7 +13,7 @@ rust-version.workspace = true
 version.workspace = true
 
 [package.metadata.docs.rs]
-rustdoc-args = ["--html-in-header", "katex-header.html"]
+rustdoc-args = ["--html-in-header", "doc-header.html"]
 
 # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
 
diff --git a/crates/ekore/doc-header.html b/crates/ekore/doc-header.html
new file mode 120000
index 000000000..22282661d
--- /dev/null
+++ b/crates/ekore/doc-header.html
@@ -0,0 +1 @@
+../doc-header.html
\ No newline at end of file
diff --git a/crates/ekore/katex-header.html b/crates/ekore/katex-header.html
deleted file mode 120000
index 810e68dcb..000000000
--- a/crates/ekore/katex-header.html
+++ /dev/null
@@ -1 +0,0 @@
-../katex-header.html
\ No newline at end of file
diff --git a/crates/katex-header.html b/crates/katex-header.html
deleted file mode 100644
index ff018b9c3..000000000
--- a/crates/katex-header.html
+++ /dev/null
@@ -1,19 +0,0 @@
-<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.10/dist/katex.min.css" integrity="sha384-wcIxkf4k558AjM3Yz3BBFQUbk/zgIYC2R0QpeeYb+TwlBVMrlgLqwRjRtGZiK7ww" crossorigin="anonymous">
-<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.10/dist/katex.min.js" integrity="sha384-hIoBPJpTUs74ddyc4bFZSM1TVlQDA60VBbJS0oA934VSz82sBx1X7kSx2ATBDIyd" crossorigin="anonymous"></script>
-<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.10/dist/contrib/auto-render.min.js" integrity="sha384-43gviWU0YVjaDtb/GhzOouOXtZMP/7XUzwPTstBeZFe/+rCMvRwr4yROQP43s0Xk" crossorigin="anonymous"></script>
-<script>
-    document.addEventListener("DOMContentLoaded", function() {
-        renderMathInElement(document.body, {
-          // customised options
-          // • auto-render specific keys, e.g.:
-          delimiters: [
-              {left: '$$', right: '$$', display: true},
-              {left: '$', right: '$', display: false},
-              {left: '\\(', right: '\\)', display: false},
-              {left: '\\[', right: '\\]', display: true}
-          ],
-          // • rendering keys, e.g.:
-          throwOnError : false
-        });
-    });
-</script>
diff --git a/crates/parse-abbrev.py b/crates/parse-abbrev.py
new file mode 100644
index 000000000..b928ed03c
--- /dev/null
+++ b/crates/parse-abbrev.py
@@ -0,0 +1,20 @@
+"""Parse abbreviations from sphinx to Rust."""
+
+import pathlib
+import re
+
+SRC = (
+    pathlib.Path(__file__).parents[1]
+    / "doc"
+    / "source"
+    / "shared"
+    / "abbreviations.rst"
+)
+
+cnt = SRC.read_text("utf-8")
+for el in cnt.split(".."):
+    test = re.match(r"\s*(.+)\s+replace::\n\s+:abbr:`(.+?)\((.+)\)`", el.strip())
+    if test is None:
+        continue
+    # Print to terminal - the user can dump to the relevant file
+    print(f'"{test[2].strip()}": "{test[3].strip()}",')

From 6b004dba87d494415a71a78535c65fbe32b7c142 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Fri, 19 Jul 2024 14:37:54 +0300
Subject: [PATCH 29/40] Make add SV to ModeMixin name

---
 src/eko/evolution_operator/__init__.py       | 2 +-
 src/eko/evolution_operator/__init__.py.patch | 8 ++++----
 src/eko/evolution_operator/grid.py           | 2 +-
 src/eko/scale_variations/__init__.py         | 2 +-
 4 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/src/eko/evolution_operator/__init__.py b/src/eko/evolution_operator/__init__.py
index 1c759c5c5..16aa4bb5b 100644
--- a/src/eko/evolution_operator/__init__.py
+++ b/src/eko/evolution_operator/__init__.py
@@ -600,7 +600,7 @@ def quad_ker_qed(
     return ker
 
 
-class Operator(sv.ModeMixin):
+class Operator(sv.ScaleVariationModeMixin):
     """Internal representation of a single EKO.
 
     The actual matrices are computed upon calling :meth:`compute`.
diff --git a/src/eko/evolution_operator/__init__.py.patch b/src/eko/evolution_operator/__init__.py.patch
index a3bc24ec1..58c3f74fd 100644
--- a/src/eko/evolution_operator/__init__.py.patch
+++ b/src/eko/evolution_operator/__init__.py.patch
@@ -534,10 +534,10 @@ index 1c759c5c..5eb394d0 100644
 -    return ker
 -
 -
- class Operator(sv.ModeMixin):
+ class Operator(sv.ScaleVariationModeMixin):
      """Internal representation of a single EKO.
 
-@@ -780,50 +282,6 @@ class Operator(sv.ModeMixin):
+@@ -780,50 +282,6 @@ class Operator(sv.ScaleVariationModeMixin):
                  labels.extend(br.singlet_unified_labels)
          return labels
 
@@ -588,7 +588,7 @@ index 1c759c5c..5eb394d0 100644
      def initialize_op_members(self):
          """Init all operators with the identity or zeros."""
          eye = OpMember(
-@@ -846,10 +304,7 @@ class Operator(sv.ModeMixin):
+@@ -846,10 +304,7 @@ class Operator(sv.ScaleVariationModeMixin):
              else:
                  self.op_members[n] = zero.copy()
 
@@ -600,7 +600,7 @@ index 1c759c5c..5eb394d0 100644
          """Run the integration for each grid point.
 
          Parameters
-@@ -864,18 +319,56 @@ class Operator(sv.ModeMixin):
+@@ -864,18 +319,56 @@ class Operator(sv.ScaleVariationModeMixin):
          """
          column = []
          k, logx = log_grid
diff --git a/src/eko/evolution_operator/grid.py b/src/eko/evolution_operator/grid.py
index e64885418..2539c3fc7 100644
--- a/src/eko/evolution_operator/grid.py
+++ b/src/eko/evolution_operator/grid.py
@@ -29,7 +29,7 @@
 """In particular, only the ``operator`` and ``error`` fields are expected."""
 
 
-class OperatorGrid(sv.ModeMixin):
+class OperatorGrid(sv.ScaleVariationModeMixin):
     """Collection of evolution operators for several scales.
 
     The operator grid is the driver class of the evolution.
diff --git a/src/eko/scale_variations/__init__.py b/src/eko/scale_variations/__init__.py
index 4af80592b..9c43f1f9c 100644
--- a/src/eko/scale_variations/__init__.py
+++ b/src/eko/scale_variations/__init__.py
@@ -36,7 +36,7 @@ def sv_mode(s):
     return Modes.unvaried
 
 
-class ModeMixin:
+class ScaleVariationModeMixin:
     """Mixin to cast scale variation mode."""
 
     @property

From 7a6c1cc2c42bd63a42ad2e4bae4d362cd4daafb7 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Fri, 19 Jul 2024 15:15:12 +0300
Subject: [PATCH 30/40] Introduce EvoMethods

---
 src/eko/evolution_operator/__init__.py |  6 +++++
 src/eko/kernels/__init__.py            | 32 ++++++++++++++++++++++++++
 src/eko/scale_variations/__init__.py   | 13 ++++++-----
 tests/eko/kernels/test_init.py         | 21 +++++++++++++++++
 4 files changed, 66 insertions(+), 6 deletions(-)
 create mode 100644 tests/eko/kernels/test_init.py

diff --git a/src/eko/evolution_operator/__init__.py b/src/eko/evolution_operator/__init__.py
index 16aa4bb5b..8cd5829bd 100644
--- a/src/eko/evolution_operator/__init__.py
+++ b/src/eko/evolution_operator/__init__.py
@@ -20,6 +20,7 @@
 from .. import basis_rotation as br
 from .. import interpolation, mellin
 from .. import scale_variations as sv
+from ..kernels import ev_method
 from ..kernels import non_singlet as ns
 from ..kernels import non_singlet_qed as qed_ns
 from ..kernels import singlet as s
@@ -780,6 +781,11 @@ def labels(self):
                 labels.extend(br.singlet_unified_labels)
         return labels
 
+    @property
+    def ev_method(self):
+        """Return the evolution method."""
+        return ev_method(self.config["method"])
+
     def quad_ker(self, label, logx, areas):
         """Return partially initialized integrand function.
 
diff --git a/src/eko/kernels/__init__.py b/src/eko/kernels/__init__.py
index 7640727b5..a10998b23 100644
--- a/src/eko/kernels/__init__.py
+++ b/src/eko/kernels/__init__.py
@@ -1 +1,33 @@
 """The solutions to the |DGLAP| equations."""
+
+import enum
+
+
+class EvoMethods(enum.IntEnum):
+    """Enumerate evolution methods."""
+
+    ITERATE_EXACT = enum.auto()
+    ITERATE_EXPANDED = enum.auto()
+    PERTURBATIVE_EXACT = enum.auto()
+    PERTURBATIVE_EXPANDED = enum.auto()
+    TRUNCATED = enum.auto()
+    ORDERED_TRUNCATED = enum.auto()
+    DECOMPOSE_EXACT = enum.auto()
+    DECOMPOSE_EXPANDED = enum.auto()
+
+
+def ev_method(s: EvoMethods) -> EvoMethods:
+    """Return the evolution methods.
+
+    Parameters
+    ----------
+    s :
+        string representation
+
+    Returns
+    -------
+    i :
+        int representation
+
+    """
+    return EvoMethods[s.value.upper().replace("-", "_")]
diff --git a/src/eko/scale_variations/__init__.py b/src/eko/scale_variations/__init__.py
index 9c43f1f9c..21d56a503 100644
--- a/src/eko/scale_variations/__init__.py
+++ b/src/eko/scale_variations/__init__.py
@@ -6,29 +6,30 @@
 
 import enum
 
+from ..io.types import ScaleVariationsMethod
 from . import expanded, exponentiated
 
 
 class Modes(enum.IntEnum):
-    """Enumerate scale Variation modes."""
+    """Enumerate scale variation modes."""
 
     unvaried = enum.auto()
     exponentiated = enum.auto()
     expanded = enum.auto()
 
 
-def sv_mode(s):
+def sv_mode(s: ScaleVariationsMethod) -> Modes:
     """Return the scale variation mode.
 
     Parameters
     ----------
-    s : str
+    s :
         string representation
 
     Returns
     -------
-    enum.IntEnum
-        enum representation
+    i :
+        int representation
 
     """
     if s is not None:
@@ -40,6 +41,6 @@ class ScaleVariationModeMixin:
     """Mixin to cast scale variation mode."""
 
     @property
-    def sv_mode(self):
+    def sv_mode(self) -> Modes:
         """Return the scale variation mode."""
         return sv_mode(self.config["ModSV"])
diff --git a/tests/eko/kernels/test_init.py b/tests/eko/kernels/test_init.py
new file mode 100644
index 000000000..3717de275
--- /dev/null
+++ b/tests/eko/kernels/test_init.py
@@ -0,0 +1,21 @@
+from eko.io.types import EvolutionMethod
+from eko.kernels import EvoMethods, ev_method
+
+
+def test_ev_method():
+    methods = {
+        "iterate-expanded": EvoMethods.ITERATE_EXPANDED,
+        "decompose-expanded": EvoMethods.DECOMPOSE_EXPANDED,
+        "perturbative-expanded": EvoMethods.PERTURBATIVE_EXPANDED,
+        "truncated": EvoMethods.TRUNCATED,
+        "ordered-truncated": EvoMethods.ORDERED_TRUNCATED,
+        "iterate-exact": EvoMethods.ITERATE_EXACT,
+        "decompose-exact": EvoMethods.DECOMPOSE_EXACT,
+        "perturbative-exact": EvoMethods.PERTURBATIVE_EXACT,
+    }
+    assert len(methods.keys()) == len(EvolutionMethod)
+    assert len(methods.keys()) == len(EvoMethods)
+    for s, i in methods.items():
+        j = ev_method(EvolutionMethod(s))
+        assert j == i
+        assert isinstance(j, int)

From 5636b4a7e2e14f83ca0f5e34a24f71b53042e026 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Fri, 19 Jul 2024 15:45:25 +0300
Subject: [PATCH 31/40] Use EvoMethods in kernels

---
 src/eko/kernels/non_singlet.py               | 27 ++++++------
 src/eko/kernels/non_singlet_qed.py           |  4 +-
 src/eko/kernels/singlet.py                   | 19 +++++----
 src/eko/kernels/singlet_qed.py               |  7 ++--
 src/eko/kernels/valence_qed.py               |  5 ++-
 tests/eko/kernels/test_kernels_QEDns.py      |  3 +-
 tests/eko/kernels/test_kernels_QEDsinglet.py | 12 +++++-
 tests/eko/kernels/test_kernels_QEDvalence.py | 16 +++++--
 tests/eko/kernels/test_ns.py                 | 32 ++++++--------
 tests/eko/kernels/test_s.py                  | 44 ++++++++------------
 10 files changed, 87 insertions(+), 82 deletions(-)

diff --git a/src/eko/kernels/non_singlet.py b/src/eko/kernels/non_singlet.py
index bd5bd10f0..15b913438 100644
--- a/src/eko/kernels/non_singlet.py
+++ b/src/eko/kernels/non_singlet.py
@@ -4,6 +4,7 @@
 import numpy as np
 
 from .. import beta
+from . import EvoMethods
 from . import as4_evolution_integrals as as4_ei
 from . import evolution_integrals as ei
 
@@ -355,7 +356,7 @@ def dispatcher(
     ----------
     order : tuple(int,int)
         perturbation order
-    method : str
+    method : int
         method
     gamma_ns : numpy.ndarray
         non-singlet anomalous dimensions
@@ -378,38 +379,38 @@ def dispatcher(
     # use always exact in LO
     if order[0] == 1:
         return lo_exact(gamma_ns, a1, a0, betalist)
-    if method == "ordered-truncated":
+    if method is EvoMethods.ORDERED_TRUNCATED:
         return eko_ordered_truncated(
             gamma_ns, a1, a0, betalist, order, ev_op_iterations
         )
-    if method == "truncated":
+    if method is EvoMethods.TRUNCATED:
         return eko_truncated(gamma_ns, a1, a0, betalist, order, ev_op_iterations)
 
     # NLO
     if order[0] == 2:
         if method in [
-            "iterate-expanded",
-            "decompose-expanded",
-            "perturbative-expanded",
+            EvoMethods.ITERATE_EXPANDED,
+            EvoMethods.DECOMPOSE_EXPANDED,
+            EvoMethods.PERTURBATIVE_EXPANDED,
         ]:
             return nlo_expanded(gamma_ns, a1, a0, betalist)
-        # if method in ["iterate-exact", "decompose-exact", "perturbative-exact"]:
+        # exact is left
         return nlo_exact(gamma_ns, a1, a0, betalist)
     # NNLO
     if order[0] == 3:
         if method in [
-            "iterate-expanded",
-            "decompose-expanded",
-            "perturbative-expanded",
+            EvoMethods.ITERATE_EXPANDED,
+            EvoMethods.DECOMPOSE_EXPANDED,
+            EvoMethods.PERTURBATIVE_EXPANDED,
         ]:
             return nnlo_expanded(gamma_ns, a1, a0, betalist)
         return nnlo_exact(gamma_ns, a1, a0, betalist)
     # N3LO
     if order[0] == 4:
         if method in [
-            "iterate-expanded",
-            "decompose-expanded",
-            "perturbative-expanded",
+            EvoMethods.ITERATE_EXPANDED,
+            EvoMethods.DECOMPOSE_EXPANDED,
+            EvoMethods.PERTURBATIVE_EXPANDED,
         ]:
             return n3lo_expanded(gamma_ns, a1, a0, betalist)
         return n3lo_exact(gamma_ns, a1, a0, betalist)
diff --git a/src/eko/kernels/non_singlet_qed.py b/src/eko/kernels/non_singlet_qed.py
index 7a2de816a..d81d5076b 100644
--- a/src/eko/kernels/non_singlet_qed.py
+++ b/src/eko/kernels/non_singlet_qed.py
@@ -146,7 +146,7 @@ def as4_exact(gamma_ns, a1, a0, beta):
 @nb.njit(cache=True)
 def dispatcher(
     order,
-    method,
+    _method,
     gamma_ns,
     as_list,
     aem_half,
@@ -164,7 +164,7 @@ def dispatcher(
     ----------
     order : tuple(int,int)
         perturbation order
-    method : str
+    method : int
         method
     gamma_ns : numpy.ndarray
         non-singlet anomalous dimensions
diff --git a/src/eko/kernels/singlet.py b/src/eko/kernels/singlet.py
index 5983c0c67..e637af046 100644
--- a/src/eko/kernels/singlet.py
+++ b/src/eko/kernels/singlet.py
@@ -6,6 +6,7 @@
 from ekore import anomalous_dimensions as ad
 
 from .. import beta
+from . import EvoMethods
 from . import as4_evolution_integrals as as4_ei
 from . import evolution_integrals as ei
 
@@ -579,7 +580,7 @@ def dispatcher(  # pylint: disable=too-many-return-statements
     ----------
     order :  tuple(int,int)
         perturbative order
-    method : str
+    method : int
         method
     gamma_singlet : numpy.ndarray
         singlet anomalous dimensions matrices
@@ -609,9 +610,9 @@ def dispatcher(  # pylint: disable=too-many-return-statements
         return lo_exact(gamma_singlet, a1, a0, betalist)
 
     # Common method for NLO and NNLO
-    if method in ["iterate-exact", "iterate-expanded"]:
+    if method in [EvoMethods.ITERATE_EXACT, EvoMethods.ITERATE_EXPANDED]:
         return eko_iterate(gamma_singlet, a1, a0, betalist, order, ev_op_iterations)
-    if method == "perturbative-exact":
+    if method is EvoMethods.PERTURBATIVE_EXACT:
         return eko_perturbative(
             gamma_singlet,
             a1,
@@ -622,7 +623,7 @@ def dispatcher(  # pylint: disable=too-many-return-statements
             ev_op_max_order,
             True,
         )
-    if method == "perturbative-expanded":
+    if method is EvoMethods.PERTURBATIVE_EXPANDED:
         return eko_perturbative(
             gamma_singlet,
             a1,
@@ -633,19 +634,19 @@ def dispatcher(  # pylint: disable=too-many-return-statements
             ev_op_max_order,
             False,
         )
-    if method in ["truncated", "ordered-truncated"]:
+    if method in [EvoMethods.TRUNCATED, EvoMethods.ORDERED_TRUNCATED]:
         return eko_truncated(gamma_singlet, a1, a0, betalist, order, ev_op_iterations)
     # These methods are scattered for nlo and nnlo
-    if method == "decompose-exact":
+    if method is EvoMethods.DECOMPOSE_EXACT:
         if order[0] == 2:
             return nlo_decompose_exact(gamma_singlet, a1, a0, betalist)
-        elif order[0] == 3:
+        if order[0] == 3:
             return nnlo_decompose_exact(gamma_singlet, a1, a0, betalist)
         return n3lo_decompose_exact(gamma_singlet, a1, a0, nf)
-    if method == "decompose-expanded":
+    if method is EvoMethods.DECOMPOSE_EXPANDED:
         if order[0] == 2:
             return nlo_decompose_expanded(gamma_singlet, a1, a0, betalist)
-        elif order[0] == 3:
+        if order[0] == 3:
             return nnlo_decompose_expanded(gamma_singlet, a1, a0, betalist)
         return n3lo_decompose_expanded(gamma_singlet, a1, a0, nf)
     raise NotImplementedError("Selected method is not implemented")
diff --git a/src/eko/kernels/singlet_qed.py b/src/eko/kernels/singlet_qed.py
index c13dee95c..2f2ba8eee 100644
--- a/src/eko/kernels/singlet_qed.py
+++ b/src/eko/kernels/singlet_qed.py
@@ -6,6 +6,7 @@
 from ekore import anomalous_dimensions as ad
 
 from .. import beta
+from . import EvoMethods
 
 
 @nb.njit(cache=True)
@@ -66,7 +67,7 @@ def dispatcher(
     a_half,
     nf,
     ev_op_iterations,
-    ev_op_max_order,
+    _ev_op_max_order,
 ):
     """Determine used kernel and call it.
 
@@ -74,7 +75,7 @@ def dispatcher(
     ----------
     order : tuple(int,int)
         perturbative order
-    method : str
+    method : int
         method
     gamma_singlet : numpy.ndarray
         singlet anomalous dimensions matrices
@@ -96,7 +97,7 @@ def dispatcher(
     e_s : numpy.ndarray
         singlet EKO
     """
-    if method in ["iterate-exact", "iterate-expanded"]:
+    if method in [EvoMethods.ITERATE_EXACT, EvoMethods.ITERATE_EXPANDED]:
         return eko_iterate(
             gamma_singlet, as_list, a_half, nf, order, ev_op_iterations, 4
         )
diff --git a/src/eko/kernels/valence_qed.py b/src/eko/kernels/valence_qed.py
index 0d5b747c3..074dd95ed 100644
--- a/src/eko/kernels/valence_qed.py
+++ b/src/eko/kernels/valence_qed.py
@@ -2,6 +2,7 @@
 
 import numba as nb
 
+from . import EvoMethods
 from .singlet_qed import eko_iterate
 
 
@@ -14,7 +15,7 @@ def dispatcher(
     a_half,
     nf,
     ev_op_iterations,
-    ev_op_max_order,
+    _ev_op_max_order,
 ):
     """
     Determine used kernel and call it.
@@ -45,7 +46,7 @@ def dispatcher(
         e_v : numpy.ndarray
             singlet EKO
     """
-    if method in ["iterate-exact", "iterate-expanded"]:
+    if method in [EvoMethods.ITERATE_EXACT, EvoMethods.ITERATE_EXPANDED]:
         return eko_iterate(
             gamma_valence, as_list, a_half, nf, order, ev_op_iterations, 2
         )
diff --git a/tests/eko/kernels/test_kernels_QEDns.py b/tests/eko/kernels/test_kernels_QEDns.py
index bb18c3e17..9fce3097b 100644
--- a/tests/eko/kernels/test_kernels_QEDns.py
+++ b/tests/eko/kernels/test_kernels_QEDns.py
@@ -3,6 +3,7 @@
 
 from eko import basis_rotation as br
 from eko.couplings import Couplings
+from eko.kernels import EvoMethods
 from eko.kernels import non_singlet_qed as ns
 from eko.quantities.couplings import CouplingEvolutionMethod, CouplingsInfo
 from eko.quantities.heavy_quarks import QuarkMassScheme
@@ -14,7 +15,7 @@
     # "perturbative-expanded",
     # "truncated",
     # "ordered-truncated",
-    "iterate-exact",
+    EvoMethods.ITERATE_EXACT,
     # "decompose-exact",
     # "perturbative-exact",
 ]
diff --git a/tests/eko/kernels/test_kernels_QEDsinglet.py b/tests/eko/kernels/test_kernels_QEDsinglet.py
index b953c053c..2fee4e17f 100644
--- a/tests/eko/kernels/test_kernels_QEDsinglet.py
+++ b/tests/eko/kernels/test_kernels_QEDsinglet.py
@@ -1,6 +1,7 @@
 import numpy as np
 import pytest
 
+from eko.kernels import EvoMethods
 from eko.kernels import singlet_qed as s
 from ekore.anomalous_dimensions.unpolarized import space_like as ad
 
@@ -10,7 +11,7 @@
     # "perturbative-expanded",
     # "truncated",
     # "ordered-truncated",
-    "iterate-exact",
+    EvoMethods.ITERATE_EXACT,
     # "decompose-exact",
     # "perturbative-exact",
 ]
@@ -125,5 +126,12 @@ def test_zero_true_gamma(monkeypatch):
 def test_error():
     with pytest.raises(NotImplementedError):
         s.dispatcher(
-            (3, 2), "AAA", np.random.rand(4, 3, 2, 2), [0.2, 0.1], [0.01], 3, 10, 10
+            (3, 2),
+            "iterate-exact",
+            np.random.rand(4, 3, 2, 2),
+            [0.2, 0.1],
+            [0.01],
+            3,
+            10,
+            10,
         )
diff --git a/tests/eko/kernels/test_kernels_QEDvalence.py b/tests/eko/kernels/test_kernels_QEDvalence.py
index 29f0f3d7a..4b12a492b 100644
--- a/tests/eko/kernels/test_kernels_QEDvalence.py
+++ b/tests/eko/kernels/test_kernels_QEDvalence.py
@@ -1,6 +1,7 @@
 import numpy as np
 import pytest
 
+from eko.kernels import EvoMethods
 from eko.kernels import valence_qed as val
 from ekore import anomalous_dimensions
 
@@ -10,13 +11,13 @@
     # "perturbative-expanded",
     # "truncated",
     # "ordered-truncated",
-    "iterate-exact",
+    EvoMethods.ITERATE_EXACT,
     # "decompose-exact",
     # "perturbative-exact",
 ]
 
 
-def test_zero(monkeypatch):
+def test_zero():
     """No evolution results in exp(0)"""
     nf = 3
     ev_op_iterations = 2
@@ -57,7 +58,7 @@ def test_zero(monkeypatch):
                 )
 
 
-def test_zero_true_gamma(monkeypatch):
+def test_zero_true_gamma():
     """No evolution results in exp(0)"""
     nf = 3
     ev_op_iterations = 2
@@ -101,5 +102,12 @@ def test_zero_true_gamma(monkeypatch):
 def test_error():
     with pytest.raises(NotImplementedError):
         val.dispatcher(
-            (3, 2), "AAA", np.random.rand(4, 3, 2, 2), [0.2, 0.1], [0.01], 3, 10, 10
+            (3, 2),
+            "iterate-exact",
+            np.random.rand(4, 3, 2, 2),
+            [0.2, 0.1],
+            [0.01],
+            3,
+            10,
+            10,
         )
diff --git a/tests/eko/kernels/test_ns.py b/tests/eko/kernels/test_ns.py
index f78282142..70e7faf8d 100644
--- a/tests/eko/kernels/test_ns.py
+++ b/tests/eko/kernels/test_ns.py
@@ -5,19 +5,9 @@
 
 import ekore.anomalous_dimensions.unpolarized.space_like as ad
 from eko import beta
+from eko.kernels import EvoMethods
 from eko.kernels import non_singlet as ns
 
-methods = [
-    "iterate-expanded",
-    "decompose-expanded",
-    "perturbative-expanded",
-    "truncated",
-    "ordered-truncated",
-    "iterate-exact",
-    "decompose-exact",
-    "perturbative-exact",
-]
-
 
 def test_zero():
     """No evolution results in exp(0)"""
@@ -25,7 +15,7 @@ def test_zero():
     ev_op_iterations = 2
     gamma_ns = np.array([1 + 0.0j, 1 + 0j, 1 + 0j, 1 + 0j])
     for order in [1, 2, 3, 4]:
-        for method in methods:
+        for method in EvoMethods:
             np.testing.assert_allclose(
                 ns.dispatcher(
                     (order, 0), method, gamma_ns, 1.0, 1.0, nf, ev_op_iterations
@@ -54,7 +44,7 @@ def test_ode_lo():
     a0 = 0.3
     for a1 in [0.1, 0.2]:
         r = a1 * gamma_ns / (beta.beta_qcd((2, 0), nf) * a1**2)
-        for method in methods:
+        for method in EvoMethods:
             rhs = r * ns.dispatcher(
                 (1, 0), method, gamma_ns, a1, a0, nf, ev_op_iterations
             )
@@ -91,7 +81,7 @@ def test_ode_nlo():
         r = (a1 * gamma_ns[0] + a1**2 * gamma_ns[1]) / (
             beta.beta_qcd((2, 0), nf) * a1**2 + beta.beta_qcd((3, 0), nf) * a1**3
         )
-        for method in ["iterate-exact"]:
+        for method in [EvoMethods.ITERATE_EXACT]:
             rhs = r * ns.dispatcher(
                 (2, 0), method, gamma_ns, a1, a0, nf, ev_op_iterations
             )
@@ -130,7 +120,7 @@ def test_ode_nnlo():
             + beta.beta_qcd((3, 0), nf) * a1**2
             + beta.beta_qcd((4, 0), nf) * a1**3
         )
-        for method in ["iterate-exact"]:
+        for method in [EvoMethods.ITERATE_EXACT]:
             rhs = r * ns.dispatcher(
                 (3, 0), method, gamma_ns, a1, a0, nf, ev_op_iterations
             )
@@ -172,7 +162,7 @@ def test_ode_n3lo():
             + beta.beta_qcd((4, 0), nf) * a1**3
             + beta.beta_qcd((5, 0), nf) * a1**4
         )
-        for method in ["iterate-exact"]:
+        for method in [EvoMethods.ITERATE_EXACT]:
             rhs = r * ns.dispatcher(
                 (4, 0), method, gamma_ns, a1, a0, nf, ev_op_iterations
             )
@@ -202,7 +192,9 @@ def test_ode_n3lo():
 def test_error(monkeypatch):
     monkeypatch.setattr("eko.beta.beta_qcd", lambda *_args: 1.0)
     with pytest.raises(NotImplementedError, match="order is not implemented"):
-        ns.dispatcher((5, 0), "iterate-exact", np.random.rand(3) + 0j, 0.2, 0.1, 3, 10)
+        ns.dispatcher(
+            (5, 0), EvoMethods.ITERATE_EXACT, np.random.rand(3) + 0j, 0.2, 0.1, 3, 10
+        )
     with pytest.raises(NotImplementedError):
         ad.gamma_ns((2, 0), 10202, 1, (0, 0, 0, 0, 0, 0, 0), 3)
 
@@ -216,7 +208,7 @@ def test_gamma_usage():
     gamma_ns = np.full(4, np.nan)
     for order in range(1, 5):
         gamma_ns[order - 1] = np.random.rand()
-        for method in methods:
+        for method in EvoMethods:
             r = ns.dispatcher(
                 (order, 0), method, gamma_ns, a1, a0, nf, ev_op_iterations
             )
@@ -225,8 +217,8 @@ def test_gamma_usage():
     for order in range(1, 5):
         gamma_ns = np.random.rand(order)
         gamma_ns[order - 1] = np.nan
-        for method in methods:
-            if method == "ordered-truncated":
+        for method in EvoMethods:
+            if method is EvoMethods.ORDERED_TRUNCATED:
                 # we are actually dividing by a np.nan,
                 # since the sum of U vec is nan
                 warnings.simplefilter("ignore", RuntimeWarning)
diff --git a/tests/eko/kernels/test_s.py b/tests/eko/kernels/test_s.py
index 5380ba319..ff4fdfc0d 100644
--- a/tests/eko/kernels/test_s.py
+++ b/tests/eko/kernels/test_s.py
@@ -3,20 +3,10 @@
 import numpy as np
 import pytest
 
+from eko.kernels import EvoMethods
 from eko.kernels import singlet as s
 from ekore import anomalous_dimensions as ad
 
-methods = [
-    "iterate-expanded",
-    "decompose-expanded",
-    "perturbative-expanded",
-    "truncated",
-    "ordered-truncated",
-    "iterate-exact",
-    "decompose-exact",
-    "perturbative-exact",
-]
-
 
 def test_zero_lo(monkeypatch):
     """No evolution results in exp(0)"""
@@ -35,7 +25,7 @@ def test_zero_lo(monkeypatch):
             np.array([[0, 0], [0, 1]]),
         ),
     )
-    for method in methods:
+    for method in EvoMethods:
         np.testing.assert_allclose(
             s.dispatcher(
                 (1, 0), method, gamma_s, 1, 1, nf, ev_op_iterations, ev_op_max_order
@@ -75,8 +65,8 @@ def test_zero_nlo_decompose(monkeypatch):
         ),
     )
     for method in [
-        "decompose-expanded",
-        "decompose-exact",
+        EvoMethods.DECOMPOSE_EXPANDED,
+        EvoMethods.DECOMPOSE_EXACT,
     ]:
         np.testing.assert_allclose(
             s.dispatcher(
@@ -117,8 +107,8 @@ def test_zero_nnlo_decompose(monkeypatch):
         ),
     )
     for method in [
-        "decompose-expanded",
-        "decompose-exact",
+        EvoMethods.DECOMPOSE_EXPANDED,
+        EvoMethods.DECOMPOSE_EXACT,
     ]:
         np.testing.assert_allclose(
             s.dispatcher(
@@ -159,8 +149,8 @@ def test_zero_n3lo_decompose(monkeypatch):
         ),
     )
     for method in [
-        "decompose-expanded",
-        "decompose-exact",
+        EvoMethods.DECOMPOSE_EXPANDED,
+        EvoMethods.DECOMPOSE_EXACT,
     ]:
         np.testing.assert_allclose(
             s.dispatcher(
@@ -200,7 +190,7 @@ def test_similarity():
     ]:
         ref = s.dispatcher(
             order,
-            "decompose-exact",
+            EvoMethods.DECOMPOSE_EXACT,
             gamma_s,
             a1,
             a0,
@@ -208,7 +198,7 @@ def test_similarity():
             ev_op_iterations,
             ev_op_max_order,
         )
-        for method in methods:
+        for method in EvoMethods:
             np.testing.assert_allclose(
                 s.dispatcher(
                     order,
@@ -227,7 +217,9 @@ def test_similarity():
 
 def test_error():
     with pytest.raises(NotImplementedError):
-        s.dispatcher((4, 0), "AAA", np.random.rand(3, 2, 2), 0.2, 0.1, 3, 10, 10)
+        s.dispatcher(
+            (4, 0), "iterate-exact", np.random.rand(3, 2, 2), 0.2, 0.1, 3, 10, 10
+        )
 
 
 def mk_almost_diag_matrix(n, max_ang=np.pi / 8.0):
@@ -247,7 +239,7 @@ def test_gamma_usage():
     gamma_s = np.full((4, 2, 2), np.nan)
     for order in range(1, 5):
         gamma_s[order - 1] = mk_almost_diag_matrix(1)
-        for method in methods:
+        for method in EvoMethods:
             r = s.dispatcher(
                 (order, 0),
                 method,
@@ -263,8 +255,8 @@ def test_gamma_usage():
     for order in range(1, 5):
         gamma_s = mk_almost_diag_matrix(4)
         gamma_s[order - 1] = np.full((2, 2), np.nan)
-        for method in methods:
-            if "iterate" in method:
+        for method in EvoMethods:
+            if method in [EvoMethods.ITERATE_EXACT, EvoMethods.ITERATE_EXPANDED]:
                 # we are actually dividing by the determinant of
                 # matrix full of np.nan
                 warnings.simplefilter("ignore", RuntimeWarning)
@@ -287,8 +279,8 @@ def test_singlet_back():
     nf = 4
     a1 = 3.0
     a0 = 4.0
-    s10 = s.dispatcher(order, "iterate-exact", gamma_s, a1, a0, nf, 15, 1)
+    s10 = s.dispatcher(order, EvoMethods.ITERATE_EXACT, gamma_s, a1, a0, nf, 15, 1)
     np.testing.assert_allclose(
         np.linalg.inv(s10),
-        s.dispatcher(order, "iterate-exact", gamma_s, a0, a1, nf, 15, 1),
+        s.dispatcher(order, EvoMethods.ITERATE_EXACT, gamma_s, a0, a1, nf, 15, 1),
     )

From db2ef3ed63894e806b78e4c0ff41281179a3ac64 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Fri, 19 Jul 2024 16:03:51 +0300
Subject: [PATCH 32/40] Use EvoMethods in ev_op

---
 src/eko/evolution_operator/__init__.py      |  5 ++-
 tests/eko/evolution_operator/test_init.py   | 43 ++++++++++++++-------
 tests/eko/scale_variations/test_diff.py     |  4 +-
 tests/eko/scale_variations/test_expanded.py |  4 +-
 4 files changed, 36 insertions(+), 20 deletions(-)

diff --git a/src/eko/evolution_operator/__init__.py b/src/eko/evolution_operator/__init__.py
index 8cd5829bd..ec56b6db6 100644
--- a/src/eko/evolution_operator/__init__.py
+++ b/src/eko/evolution_operator/__init__.py
@@ -20,6 +20,7 @@
 from .. import basis_rotation as br
 from .. import interpolation, mellin
 from .. import scale_variations as sv
+from ..io.types import EvolutionMethod
 from ..kernels import ev_method
 from ..kernels import non_singlet as ns
 from ..kernels import non_singlet_qed as qed_ns
@@ -784,7 +785,7 @@ def labels(self):
     @property
     def ev_method(self):
         """Return the evolution method."""
-        return ev_method(self.config["method"])
+        return ev_method(EvolutionMethod(self.config["method"]))
 
     def quad_ker(self, label, logx, areas):
         """Return partially initialized integrand function.
@@ -809,7 +810,7 @@ def quad_ker(self, label, logx, areas):
             order=self.order,
             mode0=label[0],
             mode1=label[1],
-            method=self.config["method"],
+            method=self.ev_method,
             is_log=self.int_disp.log,
             logx=logx,
             areas=areas,
diff --git a/tests/eko/evolution_operator/test_init.py b/tests/eko/evolution_operator/test_init.py
index 597f645f8..23395f66b 100644
--- a/tests/eko/evolution_operator/test_init.py
+++ b/tests/eko/evolution_operator/test_init.py
@@ -11,6 +11,7 @@
 from eko.evolution_operator import Operator, quad_ker
 from eko.interpolation import InterpolatorDispatcher
 from eko.io.runcards import OperatorCard, ScaleVariationsMethod, TheoryCard
+from eko.kernels import EvoMethods
 from eko.kernels import non_singlet as ns
 from eko.kernels import non_singlet_qed as qed_ns
 from eko.kernels import singlet as s
@@ -25,7 +26,7 @@ def test_quad_ker_errors():
                 order=(1, 0),
                 mode0=mode0,
                 mode1=0,
-                method="",
+                method="iterate-exact",
                 is_log=True,
                 logx=np.log(0.1),
                 areas=[[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]],
@@ -60,15 +61,29 @@ def test_quad_ker(monkeypatch):
     monkeypatch.setattr(qed_ns, "dispatcher", lambda *args: 1.0)
     monkeypatch.setattr(s, "dispatcher", lambda *args: np.identity(2))
     params = [
-        ((1, 0), br.non_singlet_pids_map["ns+"], 0, "", 0.0, 0.0),
-        ((1, 0), br.non_singlet_pids_map["ns+"], 0, "", 0.123, 1.0),
-        ((3, 1), br.non_singlet_pids_map["ns+u"], 0, "", 0.0, 0.0),
-        ((1, 0), 100, 100, "", 0.123, 1.0),
-        ((1, 0), 100, 21, "", 0.0, 0.0),
-        ((1, 1), 100, 100, "iterate-exact", 0.123, 1.0),
-        ((1, 1), 100, 21, "iterate-exact", 0.123, 0.0),
-        ((1, 1), 10200, 10200, "iterate-exact", 0.123, 1.0),
-        ((1, 1), 10200, 10204, "iterate-exact", 0.123, 0.0),
+        ((1, 0), br.non_singlet_pids_map["ns+"], 0, EvoMethods.ITERATE_EXACT, 0.0, 0.0),
+        (
+            (1, 0),
+            br.non_singlet_pids_map["ns+"],
+            0,
+            EvoMethods.ITERATE_EXACT,
+            0.123,
+            1.0,
+        ),
+        (
+            (3, 1),
+            br.non_singlet_pids_map["ns+u"],
+            0,
+            EvoMethods.ITERATE_EXACT,
+            0.0,
+            0.0,
+        ),
+        ((1, 0), 100, 100, EvoMethods.ITERATE_EXACT, 0.123, 1.0),
+        ((1, 0), 100, 21, EvoMethods.ITERATE_EXACT, 0.0, 0.0),
+        ((1, 1), 100, 100, EvoMethods.ITERATE_EXACT, 0.123, 1.0),
+        ((1, 1), 100, 21, EvoMethods.ITERATE_EXACT, 0.123, 0.0),
+        ((1, 1), 10200, 10200, EvoMethods.ITERATE_EXACT, 0.123, 1.0),
+        ((1, 1), 10200, 10204, EvoMethods.ITERATE_EXACT, 0.123, 0.0),
     ]
     for order, mode0, mode1, method, logx, res in params:
         for is_log in [True, False]:
@@ -107,7 +122,7 @@ def test_quad_ker(monkeypatch):
                     order=(1, 0),
                     mode0=label[0],
                     mode1=label[1],
-                    method="",
+                    method=EvoMethods.ITERATE_EXACT,
                     is_log=True,
                     logx=0.123,
                     areas=np.zeros(3),
@@ -143,7 +158,7 @@ def test_quad_ker(monkeypatch):
                 order=(1, 1),
                 mode0=label[0],
                 mode1=label[1],
-                method="iterate-exact",
+                method=EvoMethods.ITERATE_EXACT,
                 is_log=True,
                 logx=0.123,
                 areas=np.zeros(3),
@@ -171,7 +186,7 @@ def test_quad_ker(monkeypatch):
         order=(1, 0),
         mode0=br.non_singlet_pids_map["ns+"],
         mode1=0,
-        method="",
+        method=EvoMethods.ITERATE_EXACT,
         is_log=True,
         logx=0.0,
         areas=np.zeros(3),
@@ -436,7 +451,7 @@ def quad_ker_pegasus(
     order = (2, 0)
     mode0 = br.non_singlet_pids_map["ns+"]
     mode1 = 0
-    method = ""
+    method = EvoMethods.ITERATE_EXACT
     logxs = np.log(int_disp.xgrid.raw)
     a1 = 1
     a0 = 2
diff --git a/tests/eko/scale_variations/test_diff.py b/tests/eko/scale_variations/test_diff.py
index c0dd67236..8ade8bcac 100644
--- a/tests/eko/scale_variations/test_diff.py
+++ b/tests/eko/scale_variations/test_diff.py
@@ -11,7 +11,7 @@
 from eko import basis_rotation as br
 from eko.beta import beta_qcd_as2, beta_qcd_as3
 from eko.couplings import CouplingEvolutionMethod, Couplings, CouplingsInfo
-from eko.kernels import non_singlet, singlet
+from eko.kernels import EvoMethods, non_singlet, singlet
 from eko.quantities.heavy_quarks import QuarkMassScheme
 from eko.scale_variations import expanded, exponentiated
 from ekore.anomalous_dimensions.unpolarized.space_like import gamma_ns, gamma_singlet
@@ -19,7 +19,7 @@
 NF = 4
 Q02 = 1.65**2
 Q12 = 100**2
-EV_METHOD = "truncated"
+EV_METHOD = EvoMethods.TRUNCATED
 
 
 def compute_a_s(q2, order):
diff --git a/tests/eko/scale_variations/test_expanded.py b/tests/eko/scale_variations/test_expanded.py
index 6af22dd51..bfacc1c96 100644
--- a/tests/eko/scale_variations/test_expanded.py
+++ b/tests/eko/scale_variations/test_expanded.py
@@ -2,7 +2,7 @@
 
 from eko import basis_rotation as br
 from eko.couplings import CouplingEvolutionMethod, Couplings, CouplingsInfo
-from eko.kernels import non_singlet, singlet
+from eko.kernels import EvoMethods, non_singlet, singlet
 from eko.quantities.heavy_quarks import QuarkMassScheme
 from eko.scale_variations import Modes, expanded
 from ekore.anomalous_dimensions.unpolarized.space_like import gamma_ns, gamma_singlet
@@ -10,7 +10,7 @@
 NF = 4
 Q02 = 1.65**2
 Q12 = 100**2
-EV_METHOD = "truncated"
+EV_METHOD = EvoMethods.TRUNCATED
 
 
 def compute_a_s(q2, order):

From 1b1e4ce4b651033fc1c23c89cb79f42a03019c66 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Fri, 19 Jul 2024 16:41:12 +0300
Subject: [PATCH 33/40] Introduce BackwardsMethods

---
 .../operator_matrix_element.py                | 50 ++++++++++++++++---
 src/eko/kernels/__init__.py                   |  6 ++-
 tests/eko/evolution_operator/test_ome.py      | 19 +++----
 3 files changed, 57 insertions(+), 18 deletions(-)

diff --git a/src/eko/evolution_operator/operator_matrix_element.py b/src/eko/evolution_operator/operator_matrix_element.py
index 202fd18d9..b4b6731b4 100644
--- a/src/eko/evolution_operator/operator_matrix_element.py
+++ b/src/eko/evolution_operator/operator_matrix_element.py
@@ -1,6 +1,7 @@
 """The |OME| for the non-trivial matching conditions in the |VFNS| evolution."""
 
 import copy
+import enum
 import functools
 import logging
 
@@ -20,6 +21,33 @@
 logger = logging.getLogger(__name__)
 
 
+class BackwardsMethods(enum.IntEnum):
+    """Enumerate backward methods."""
+
+    FORWARD = enum.auto()
+    EXACT = enum.auto()
+    EXPANDED = enum.auto()
+
+
+def bw_method(s: InversionMethod) -> BackwardsMethods:
+    """Return the backward method.
+
+    Parameters
+    ----------
+    s :
+        string representation
+
+    Returns
+    -------
+    i :
+        int representation
+
+    """
+    if s is not None:
+        return BackwardsMethods[s.value.upper()]
+    return BackwardsMethods.FORWARD
+
+
 @nb.njit(cache=True)
 def build_ome(A, matching_order, a_s, backward_method):
     r"""Construct the matching expansion in :math:`a_s` with the appropriate method.
@@ -32,7 +60,7 @@ def build_ome(A, matching_order, a_s, backward_method):
         perturbation matching order
     a_s : float
         strong coupling, needed only for the exact inverse
-    backward_method : InversionMethod or None
+    backward_method : BackwardsMethods
         empty or method for inverting the matching condition (exact or expanded)
 
     Returns
@@ -51,7 +79,7 @@ def build_ome(A, matching_order, a_s, backward_method):
     ome = np.eye(len(A[0]), dtype=np.complex_)
     A = A[:, :, :]
     A = np.ascontiguousarray(A)
-    if backward_method is InversionMethod.EXPANDED:
+    if backward_method is BackwardsMethods.EXPANDED:
         # expended inverse
         if matching_order[0] >= 1:
             ome -= a_s * A[0]
@@ -68,7 +96,7 @@ def build_ome(A, matching_order, a_s, backward_method):
         if matching_order[0] >= 3:
             ome += a_s**3 * A[2]
         # need inverse exact ?  so add the missing pieces
-        if backward_method is InversionMethod.EXACT:
+        if backward_method is BackwardsMethods.EXACT:
             ome = np.linalg.inv(ome)
     return ome
 
@@ -216,7 +244,9 @@ class OperatorMatrixElement(Operator):
 
     def __init__(self, config, managers, nf, q2, is_backward, L, is_msbar):
         super().__init__(config, managers, Segment(q2, q2, nf))
-        self.backward_method = config["backward_inversion"] if is_backward else None
+        self.backward_method = bw_method(
+            config["backward_inversion"] if is_backward else None
+        )
         if is_backward:
             self.is_intrinsic = True
         else:
@@ -241,7 +271,10 @@ def labels(self):
             logger.warning("%s: skipping non-singlet sector", self.log_label)
         else:
             labels.append((200, 200))
-            if self.is_intrinsic or self.backward_method is not None:
+            if (
+                self.is_intrinsic
+                or self.backward_method is not BackwardsMethods.FORWARD
+            ):
                 # intrinsic labels, which are not zero at NLO
                 labels.append((br.matching_hminus_pid, br.matching_hminus_pid))
                 # These contributions are always 0 for the moment
@@ -257,7 +290,10 @@ def labels(self):
                     (br.matching_hplus_pid, 100),
                 ]
             )
-            if self.is_intrinsic or self.backward_method is not None:
+            if (
+                self.is_intrinsic
+                or self.backward_method is not BackwardsMethods.FORWARD
+            ):
                 labels.extend(
                     [
                         (21, br.matching_hplus_pid),
@@ -329,7 +365,7 @@ def compute(self):
             self.log_label,
             self.order[0],
             self.order[1],
-            self.backward_method,
+            BackwardsMethods(self.backward_method).name,
         )
 
         self.integrate()
diff --git a/src/eko/kernels/__init__.py b/src/eko/kernels/__init__.py
index a10998b23..594fbf1fa 100644
--- a/src/eko/kernels/__init__.py
+++ b/src/eko/kernels/__init__.py
@@ -2,6 +2,8 @@
 
 import enum
 
+from ..io.types import EvolutionMethod
+
 
 class EvoMethods(enum.IntEnum):
     """Enumerate evolution methods."""
@@ -16,8 +18,8 @@ class EvoMethods(enum.IntEnum):
     DECOMPOSE_EXPANDED = enum.auto()
 
 
-def ev_method(s: EvoMethods) -> EvoMethods:
-    """Return the evolution methods.
+def ev_method(s: EvolutionMethod) -> EvoMethods:
+    """Return the evolution method.
 
     Parameters
     ----------
diff --git a/tests/eko/evolution_operator/test_ome.py b/tests/eko/evolution_operator/test_ome.py
index b844290c9..584635967 100644
--- a/tests/eko/evolution_operator/test_ome.py
+++ b/tests/eko/evolution_operator/test_ome.py
@@ -8,6 +8,7 @@
 from eko import interpolation, mellin
 from eko import scale_variations as sv
 from eko.evolution_operator.operator_matrix_element import (
+    BackwardsMethods,
     OperatorMatrixElement,
     build_ome,
     quad_ker,
@@ -33,7 +34,7 @@ def test_build_ome_as():
         aS = A_singlet((o, 0), N, nf, L, is_msbar)
 
         for a in [aNS, aS]:
-            for method in [None, InversionMethod.EXPANDED, InversionMethod.EXACT]:
+            for method in BackwardsMethods:
                 dim = len(a[0])
                 if o != 1:
                     assert len(a) == o
@@ -53,7 +54,7 @@ def test_build_ome_nlo():
     aNSi = A_non_singlet((1, 0), N, nf, L)
     aSi = A_singlet((1, 0), N, nf, L, is_msbar)
     for a in [aNSi, aSi]:
-        for method in [None, InversionMethod.EXPANDED, InversionMethod.EXACT]:
+        for method in BackwardsMethods:
             dim = len(a[0])
             # hh
             assert a[0, -1, -1] != 0.0
@@ -86,7 +87,7 @@ def test_quad_ker_errors():
                     is_log=True,
                     logx=0.123,
                     areas=[[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]],
-                    backward_method=None,
+                    backward_method=BackwardsMethods.FORWARD,
                     a_s=0.0,
                     nf=3,
                     L=0.0,
@@ -119,7 +120,7 @@ def test_quad_ker(monkeypatch):
                     is_log=is_log,
                     logx=0.123,
                     areas=np.zeros(3),
-                    backward_method=None,
+                    backward_method=BackwardsMethods.FORWARD,
                     a_s=0.0,
                     nf=3,
                     L=0.0,
@@ -138,7 +139,7 @@ def test_quad_ker(monkeypatch):
                     is_log=is_log,
                     logx=0.123,
                     areas=np.zeros(3),
-                    backward_method=None,
+                    backward_method=BackwardsMethods.FORWARD,
                     a_s=0.0,
                     nf=3,
                     L=0.0,
@@ -157,7 +158,7 @@ def test_quad_ker(monkeypatch):
                     is_log=is_log,
                     logx=0.0,
                     areas=np.zeros(3),
-                    backward_method=None,
+                    backward_method=BackwardsMethods.FORWARD,
                     a_s=0.0,
                     nf=3,
                     L=0.0,
@@ -191,7 +192,7 @@ def test_quad_ker(monkeypatch):
                 is_log=True,
                 logx=0.123,
                 areas=np.zeros(3),
-                backward_method=InversionMethod.EXPANDED,
+                backward_method=BackwardsMethods.EXPANDED,
                 a_s=0.0,
                 nf=3,
                 L=0.0,
@@ -228,7 +229,7 @@ def test_quad_ker(monkeypatch):
             is_log=True,
             logx=0.123,
             areas=np.zeros(3),
-            backward_method=InversionMethod.EXACT,
+            backward_method=BackwardsMethods.EXACT,
             a_s=0.0,
             nf=3,
             L=0.0,
@@ -252,7 +253,7 @@ def test_quad_ker(monkeypatch):
         is_log=True,
         logx=0.0,
         areas=np.array([0.01, 0.1, 1.0]),
-        backward_method=None,
+        backward_method=BackwardsMethods.FORWARD,
         a_s=0.0,
         nf=3,
         L=0.0,

From c88627f71da3df6780692cbcc1bd04c37d0776ae Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Mon, 22 Jul 2024 13:23:45 +0300
Subject: [PATCH 34/40] Rename matching method

---
 .../operator_matrix_element.py                | 34 ++++++++-----------
 src/ekomark/data/operators.py                 |  2 +-
 tests/eko/evolution_operator/test_ome.py      | 20 +++++------
 3 files changed, 25 insertions(+), 31 deletions(-)

diff --git a/src/eko/evolution_operator/operator_matrix_element.py b/src/eko/evolution_operator/operator_matrix_element.py
index b4b6731b4..cf6cbcb97 100644
--- a/src/eko/evolution_operator/operator_matrix_element.py
+++ b/src/eko/evolution_operator/operator_matrix_element.py
@@ -21,16 +21,16 @@
 logger = logging.getLogger(__name__)
 
 
-class BackwardsMethods(enum.IntEnum):
+class MatchingMethods(enum.IntEnum):
     """Enumerate backward methods."""
 
     FORWARD = enum.auto()
-    EXACT = enum.auto()
-    EXPANDED = enum.auto()
+    BACKWARD_EXACT = enum.auto()
+    BACKWARD_EXPANDED = enum.auto()
 
 
-def bw_method(s: InversionMethod) -> BackwardsMethods:
-    """Return the backward method.
+def matching_method(s: InversionMethod) -> MatchingMethods:
+    """Return the matching method.
 
     Parameters
     ----------
@@ -44,8 +44,8 @@ def bw_method(s: InversionMethod) -> BackwardsMethods:
 
     """
     if s is not None:
-        return BackwardsMethods[s.value.upper()]
-    return BackwardsMethods.FORWARD
+        return MatchingMethods[s.value.upper()]
+    return MatchingMethods.FORWARD
 
 
 @nb.njit(cache=True)
@@ -60,7 +60,7 @@ def build_ome(A, matching_order, a_s, backward_method):
         perturbation matching order
     a_s : float
         strong coupling, needed only for the exact inverse
-    backward_method : BackwardsMethods
+    backward_method : MatchingMethods
         empty or method for inverting the matching condition (exact or expanded)
 
     Returns
@@ -79,7 +79,7 @@ def build_ome(A, matching_order, a_s, backward_method):
     ome = np.eye(len(A[0]), dtype=np.complex_)
     A = A[:, :, :]
     A = np.ascontiguousarray(A)
-    if backward_method is BackwardsMethods.EXPANDED:
+    if backward_method is MatchingMethods.BACKWARD_EXPANDED:
         # expended inverse
         if matching_order[0] >= 1:
             ome -= a_s * A[0]
@@ -96,7 +96,7 @@ def build_ome(A, matching_order, a_s, backward_method):
         if matching_order[0] >= 3:
             ome += a_s**3 * A[2]
         # need inverse exact ?  so add the missing pieces
-        if backward_method is BackwardsMethods.EXACT:
+        if backward_method is MatchingMethods.BACKWARD_EXACT:
             ome = np.linalg.inv(ome)
     return ome
 
@@ -244,7 +244,7 @@ class OperatorMatrixElement(Operator):
 
     def __init__(self, config, managers, nf, q2, is_backward, L, is_msbar):
         super().__init__(config, managers, Segment(q2, q2, nf))
-        self.backward_method = bw_method(
+        self.backward_method = matching_method(
             config["backward_inversion"] if is_backward else None
         )
         if is_backward:
@@ -271,10 +271,7 @@ def labels(self):
             logger.warning("%s: skipping non-singlet sector", self.log_label)
         else:
             labels.append((200, 200))
-            if (
-                self.is_intrinsic
-                or self.backward_method is not BackwardsMethods.FORWARD
-            ):
+            if self.is_intrinsic or self.backward_method is not MatchingMethods.FORWARD:
                 # intrinsic labels, which are not zero at NLO
                 labels.append((br.matching_hminus_pid, br.matching_hminus_pid))
                 # These contributions are always 0 for the moment
@@ -290,10 +287,7 @@ def labels(self):
                     (br.matching_hplus_pid, 100),
                 ]
             )
-            if (
-                self.is_intrinsic
-                or self.backward_method is not BackwardsMethods.FORWARD
-            ):
+            if self.is_intrinsic or self.backward_method is not MatchingMethods.FORWARD:
                 labels.extend(
                     [
                         (21, br.matching_hplus_pid),
@@ -365,7 +359,7 @@ def compute(self):
             self.log_label,
             self.order[0],
             self.order[1],
-            BackwardsMethods(self.backward_method).name,
+            MatchingMethods(self.backward_method).name,
         )
 
         self.integrate()
diff --git a/src/ekomark/data/operators.py b/src/ekomark/data/operators.py
index ad928574d..03ad4d349 100644
--- a/src/ekomark/data/operators.py
+++ b/src/ekomark/data/operators.py
@@ -15,7 +15,7 @@
             ev_op_max_order=10,
             ev_op_iterations=10,
             backward_inversion="expanded",
-            n_integration_cores=0,
+            n_integration_cores=1,
             debug_skip_non_singlet=False,
             debug_skip_singlet=False,
             mugrid=[10],
diff --git a/tests/eko/evolution_operator/test_ome.py b/tests/eko/evolution_operator/test_ome.py
index 584635967..553e5823c 100644
--- a/tests/eko/evolution_operator/test_ome.py
+++ b/tests/eko/evolution_operator/test_ome.py
@@ -8,7 +8,7 @@
 from eko import interpolation, mellin
 from eko import scale_variations as sv
 from eko.evolution_operator.operator_matrix_element import (
-    BackwardsMethods,
+    MatchingMethods,
     OperatorMatrixElement,
     build_ome,
     quad_ker,
@@ -34,7 +34,7 @@ def test_build_ome_as():
         aS = A_singlet((o, 0), N, nf, L, is_msbar)
 
         for a in [aNS, aS]:
-            for method in BackwardsMethods:
+            for method in MatchingMethods:
                 dim = len(a[0])
                 if o != 1:
                     assert len(a) == o
@@ -54,7 +54,7 @@ def test_build_ome_nlo():
     aNSi = A_non_singlet((1, 0), N, nf, L)
     aSi = A_singlet((1, 0), N, nf, L, is_msbar)
     for a in [aNSi, aSi]:
-        for method in BackwardsMethods:
+        for method in MatchingMethods:
             dim = len(a[0])
             # hh
             assert a[0, -1, -1] != 0.0
@@ -87,7 +87,7 @@ def test_quad_ker_errors():
                     is_log=True,
                     logx=0.123,
                     areas=[[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]],
-                    backward_method=BackwardsMethods.FORWARD,
+                    backward_method=MatchingMethods.FORWARD,
                     a_s=0.0,
                     nf=3,
                     L=0.0,
@@ -120,7 +120,7 @@ def test_quad_ker(monkeypatch):
                     is_log=is_log,
                     logx=0.123,
                     areas=np.zeros(3),
-                    backward_method=BackwardsMethods.FORWARD,
+                    backward_method=MatchingMethods.FORWARD,
                     a_s=0.0,
                     nf=3,
                     L=0.0,
@@ -139,7 +139,7 @@ def test_quad_ker(monkeypatch):
                     is_log=is_log,
                     logx=0.123,
                     areas=np.zeros(3),
-                    backward_method=BackwardsMethods.FORWARD,
+                    backward_method=MatchingMethods.FORWARD,
                     a_s=0.0,
                     nf=3,
                     L=0.0,
@@ -158,7 +158,7 @@ def test_quad_ker(monkeypatch):
                     is_log=is_log,
                     logx=0.0,
                     areas=np.zeros(3),
-                    backward_method=BackwardsMethods.FORWARD,
+                    backward_method=MatchingMethods.FORWARD,
                     a_s=0.0,
                     nf=3,
                     L=0.0,
@@ -192,7 +192,7 @@ def test_quad_ker(monkeypatch):
                 is_log=True,
                 logx=0.123,
                 areas=np.zeros(3),
-                backward_method=BackwardsMethods.EXPANDED,
+                backward_method=MatchingMethods.BACKWARD_EXPANDED,
                 a_s=0.0,
                 nf=3,
                 L=0.0,
@@ -229,7 +229,7 @@ def test_quad_ker(monkeypatch):
             is_log=True,
             logx=0.123,
             areas=np.zeros(3),
-            backward_method=BackwardsMethods.EXACT,
+            backward_method=MatchingMethods.BACKWARD_EXACT,
             a_s=0.0,
             nf=3,
             L=0.0,
@@ -253,7 +253,7 @@ def test_quad_ker(monkeypatch):
         is_log=True,
         logx=0.0,
         areas=np.array([0.01, 0.1, 1.0]),
-        backward_method=BackwardsMethods.FORWARD,
+        backward_method=MatchingMethods.FORWARD,
         a_s=0.0,
         nf=3,
         L=0.0,

From d4a3f71889822f0311f342ec2d3ca97c049acf8f Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Mon, 22 Jul 2024 13:29:41 +0300
Subject: [PATCH 35/40] Fix MatchingMethods doc string

---
 src/eko/evolution_operator/operator_matrix_element.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/eko/evolution_operator/operator_matrix_element.py b/src/eko/evolution_operator/operator_matrix_element.py
index cf6cbcb97..87c76183a 100644
--- a/src/eko/evolution_operator/operator_matrix_element.py
+++ b/src/eko/evolution_operator/operator_matrix_element.py
@@ -22,7 +22,7 @@
 
 
 class MatchingMethods(enum.IntEnum):
-    """Enumerate backward methods."""
+    """Enumerate matching methods."""
 
     FORWARD = enum.auto()
     BACKWARD_EXACT = enum.auto()

From 7f079bc6001ac3f38d0d55ebd0a3cd271da7e976 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Mon, 22 Jul 2024 15:12:05 +0300
Subject: [PATCH 36/40] Fix matching renaming

---
 src/eko/evolution_operator/operator_matrix_element.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/eko/evolution_operator/operator_matrix_element.py b/src/eko/evolution_operator/operator_matrix_element.py
index 87c76183a..25e5df2dd 100644
--- a/src/eko/evolution_operator/operator_matrix_element.py
+++ b/src/eko/evolution_operator/operator_matrix_element.py
@@ -44,7 +44,7 @@ def matching_method(s: InversionMethod) -> MatchingMethods:
 
     """
     if s is not None:
-        return MatchingMethods[s.value.upper()]
+        return MatchingMethods["BACKWARD_" + s.value.upper()]
     return MatchingMethods.FORWARD
 
 

From e40acaec28c4212d5a3ffb809ece959d415c2016 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Wed, 24 Jul 2024 15:10:40 +0300
Subject: [PATCH 37/40] Allow only iterate-exact for QED

---
 src/eko/kernels/singlet_qed.py | 2 +-
 src/eko/kernels/valence_qed.py | 4 ++--
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/eko/kernels/singlet_qed.py b/src/eko/kernels/singlet_qed.py
index 2f2ba8eee..d63a2f1ac 100644
--- a/src/eko/kernels/singlet_qed.py
+++ b/src/eko/kernels/singlet_qed.py
@@ -97,7 +97,7 @@ def dispatcher(
     e_s : numpy.ndarray
         singlet EKO
     """
-    if method in [EvoMethods.ITERATE_EXACT, EvoMethods.ITERATE_EXPANDED]:
+    if method is EvoMethods.ITERATE_EXACT:
         return eko_iterate(
             gamma_singlet, as_list, a_half, nf, order, ev_op_iterations, 4
         )
diff --git a/src/eko/kernels/valence_qed.py b/src/eko/kernels/valence_qed.py
index 074dd95ed..186c70219 100644
--- a/src/eko/kernels/valence_qed.py
+++ b/src/eko/kernels/valence_qed.py
@@ -24,7 +24,7 @@ def dispatcher(
     ----------
     order : tuple(int,int)
         perturbative order
-    method : str
+    method : int
         method
     gamma_singlet : numpy.ndarray
         singlet anomalous dimensions matrices
@@ -46,7 +46,7 @@ def dispatcher(
         e_v : numpy.ndarray
             singlet EKO
     """
-    if method in [EvoMethods.ITERATE_EXACT, EvoMethods.ITERATE_EXPANDED]:
+    if method is EvoMethods.ITERATE_EXACT:
         return eko_iterate(
             gamma_valence, as_list, a_half, nf, order, ev_op_iterations, 2
         )

From c92c3a24a0cd2cc440048f1028af9b98ab63b49a Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Mon, 29 Jul 2024 18:11:07 +0000
Subject: [PATCH 38/40] [pre-commit.ci] pre-commit autoupdate
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

updates:
- [github.com/asottile/pyupgrade: v3.16.0 → v3.17.0](https://github.com/asottile/pyupgrade/compare/v3.16.0...v3.17.0)
- [github.com/pre-commit/pre-commit: v3.7.1 → v3.8.0](https://github.com/pre-commit/pre-commit/compare/v3.7.1...v3.8.0)
---
 .pre-commit-config.yaml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 67e901972..d579fb856 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -32,7 +32,7 @@ repos:
       - id: isort
         args: ["--profile", "black"]
   - repo: https://github.com/asottile/pyupgrade
-    rev: v3.16.0
+    rev: v3.17.0
     hooks:
       - id: pyupgrade
   - repo: https://github.com/pycqa/pydocstyle
@@ -53,6 +53,6 @@ repos:
       files: ^crates/.*\.rs$
       args: []
   - repo: https://github.com/pre-commit/pre-commit
-    rev: v3.7.1
+    rev: v3.8.0
     hooks:
       - id: validate_manifest

From 48476f9f2a3ab8121ff694db7c413fbb3bdddf1c Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Thu, 8 Aug 2024 14:49:28 +0300
Subject: [PATCH 39/40] Fix Rust ev_op patch

---
 src/eko/evolution_operator/__init__.py.patch | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/src/eko/evolution_operator/__init__.py.patch b/src/eko/evolution_operator/__init__.py.patch
index 58c3f74fd..d8258ee14 100644
--- a/src/eko/evolution_operator/__init__.py.patch
+++ b/src/eko/evolution_operator/__init__.py.patch
@@ -1,5 +1,5 @@
 diff --git a/src/eko/evolution_operator/__init__.py b/src/eko/evolution_operator/__init__.py
-index 1c759c5c..5eb394d0 100644
+index ec56b6db..374d0d0b 100644
 --- a/src/eko/evolution_operator/__init__.py
 +++ b/src/eko/evolution_operator/__init__.py
 @@ -3,15 +3,15 @@ r"""Contains the central operator classes.
@@ -20,7 +20,7 @@ index 1c759c5c..5eb394d0 100644
 
  import ekore.anomalous_dimensions.polarized.space_like as ad_ps
  import ekore.anomalous_dimensions.unpolarized.space_like as ad_us
-@@ -27,92 +27,10 @@ from ..kernels import singlet_qed as qed_s
+@@ -29,92 +29,10 @@ from ..kernels import singlet_qed as qed_s
  from ..kernels import valence_qed as qed_v
  from ..matchings import Segment, lepton_number
  from ..member import OpMember
@@ -114,7 +114,7 @@ index 1c759c5c..5eb394d0 100644
  spec = [
      ("is_singlet", nb.boolean),
      ("is_QEDsinglet", nb.boolean),
-@@ -184,422 +102,6 @@ class QuadKerBase:
+@@ -186,422 +104,6 @@ class QuadKerBase:
          return self.path.prefactor * pj * self.path.jac
 
 
@@ -537,9 +537,9 @@ index 1c759c5c..5eb394d0 100644
  class Operator(sv.ScaleVariationModeMixin):
      """Internal representation of a single EKO.
 
-@@ -780,50 +282,6 @@ class Operator(sv.ScaleVariationModeMixin):
-                 labels.extend(br.singlet_unified_labels)
-         return labels
+@@ -787,50 +289,6 @@ class Operator(sv.ScaleVariationModeMixin):
+         """Return the evolution method."""
+         return ev_method(EvolutionMethod(self.config["method"]))
 
 -    def quad_ker(self, label, logx, areas):
 -        """Return partially initialized integrand function.
@@ -564,7 +564,7 @@ index 1c759c5c..5eb394d0 100644
 -            order=self.order,
 -            mode0=label[0],
 -            mode1=label[1],
--            method=self.config["method"],
+-            method=self.ev_method,
 -            is_log=self.int_disp.log,
 -            logx=logx,
 -            areas=areas,
@@ -588,7 +588,7 @@ index 1c759c5c..5eb394d0 100644
      def initialize_op_members(self):
          """Init all operators with the identity or zeros."""
          eye = OpMember(
-@@ -846,10 +304,7 @@ class Operator(sv.ScaleVariationModeMixin):
+@@ -853,10 +311,7 @@ class Operator(sv.ScaleVariationModeMixin):
              else:
                  self.op_members[n] = zero.copy()
 
@@ -600,7 +600,7 @@ index 1c759c5c..5eb394d0 100644
          """Run the integration for each grid point.
 
          Parameters
-@@ -864,18 +319,56 @@ class Operator(sv.ScaleVariationModeMixin):
+@@ -871,18 +326,56 @@ class Operator(sv.ScaleVariationModeMixin):
          """
          column = []
          k, logx = log_grid

From b651ebe9699dc2ffcacd561e05bb52026e4d1944 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Thu, 8 Aug 2024 15:02:47 +0300
Subject: [PATCH 40/40] Fix Rust ev_op patch

---
 src/eko/evolution_operator/__init__.py.patch | 26 ++++++++++----------
 1 file changed, 13 insertions(+), 13 deletions(-)

diff --git a/src/eko/evolution_operator/__init__.py.patch b/src/eko/evolution_operator/__init__.py.patch
index 58c3f74fd..995d77b6b 100644
--- a/src/eko/evolution_operator/__init__.py.patch
+++ b/src/eko/evolution_operator/__init__.py.patch
@@ -1,8 +1,8 @@
 diff --git a/src/eko/evolution_operator/__init__.py b/src/eko/evolution_operator/__init__.py
-index 1c759c5c..5eb394d0 100644
+index fe07ade9..0f58c9e5 100644
 --- a/src/eko/evolution_operator/__init__.py
 +++ b/src/eko/evolution_operator/__init__.py
-@@ -3,15 +3,15 @@ r"""Contains the central operator classes.
+@@ -3,16 +3,16 @@ r"""Contains the central operator classes.
  See :doc:`Operator overview </code/Operators>`.
  """
 
@@ -11,6 +11,7 @@ index 1c759c5c..5eb394d0 100644
  import os
  import time
  from multiprocessing import Pool
+ from typing import Dict, Tuple
 
 +import ekors
  import numba as nb
@@ -20,7 +21,7 @@ index 1c759c5c..5eb394d0 100644
 
  import ekore.anomalous_dimensions.polarized.space_like as ad_ps
  import ekore.anomalous_dimensions.unpolarized.space_like as ad_us
-@@ -27,92 +27,10 @@ from ..kernels import singlet_qed as qed_s
+@@ -30,92 +30,10 @@ from ..kernels import singlet_qed as qed_s
  from ..kernels import valence_qed as qed_v
  from ..matchings import Segment, lepton_number
  from ..member import OpMember
@@ -114,7 +115,7 @@ index 1c759c5c..5eb394d0 100644
  spec = [
      ("is_singlet", nb.boolean),
      ("is_QEDsinglet", nb.boolean),
-@@ -184,422 +102,6 @@ class QuadKerBase:
+@@ -187,421 +105,6 @@ class QuadKerBase:
          return self.path.prefactor * pj * self.path.jac
 
 
@@ -533,13 +534,12 @@ index 1c759c5c..5eb394d0 100644
 -            )
 -    return ker
 -
--
- class Operator(sv.ScaleVariationModeMixin):
-     """Internal representation of a single EKO.
 
-@@ -780,50 +282,6 @@ class Operator(sv.ScaleVariationModeMixin):
-                 labels.extend(br.singlet_unified_labels)
-         return labels
+ OpMembers = Dict[OperatorLabel, OpMember]
+ """Map of all operators."""
+@@ -792,50 +295,6 @@ class Operator(sv.ScaleVariationModeMixin):
+         """Return the evolution method."""
+         return ev_method(EvolutionMethod(self.config["method"]))
 
 -    def quad_ker(self, label, logx, areas):
 -        """Return partially initialized integrand function.
@@ -564,7 +564,7 @@ index 1c759c5c..5eb394d0 100644
 -            order=self.order,
 -            mode0=label[0],
 -            mode1=label[1],
--            method=self.config["method"],
+-            method=self.ev_method,
 -            is_log=self.int_disp.log,
 -            logx=logx,
 -            areas=areas,
@@ -588,7 +588,7 @@ index 1c759c5c..5eb394d0 100644
      def initialize_op_members(self):
          """Init all operators with the identity or zeros."""
          eye = OpMember(
-@@ -846,10 +304,7 @@ class Operator(sv.ScaleVariationModeMixin):
+@@ -858,10 +317,7 @@ class Operator(sv.ScaleVariationModeMixin):
              else:
                  self.op_members[n] = zero.copy()
 
@@ -600,7 +600,7 @@ index 1c759c5c..5eb394d0 100644
          """Run the integration for each grid point.
 
          Parameters
-@@ -864,18 +319,56 @@ class Operator(sv.ScaleVariationModeMixin):
+@@ -876,18 +332,56 @@ class Operator(sv.ScaleVariationModeMixin):
          """
          column = []
          k, logx = log_grid