diff --git a/lowpass_oracle_ai.cpp b/lowpass_oracle_ai.cpp
index f683da7..92e1b54 100644
--- a/lowpass_oracle_ai.cpp
+++ b/lowpass_oracle_ai.cpp
@@ -160,4 +160,3 @@ int main() {
 
     return 0;
 }
-
diff --git a/src/ellalgo/cutting_plane.py b/src/ellalgo/cutting_plane.py
index 13caacf..21434d8 100644
--- a/src/ellalgo/cutting_plane.py
+++ b/src/ellalgo/cutting_plane.py
@@ -1,6 +1,5 @@
 import copy
-from typing import Any, MutableSequence, Optional, Tuple, Union
-from typing import Generic
+from typing import Any, Generic, MutableSequence, Optional, Tuple, Union
 
 from .ell_config import CutStatus, Options
 from .ell_typing import (
@@ -83,7 +82,10 @@ def cutting_plane_feas(
 
 
 def cutting_plane_optim(
-    omega: OracleOptim[ArrayType], space: SearchSpace[ArrayType], target, options=Options()
+    omega: OracleOptim[ArrayType],
+    space: SearchSpace[ArrayType],
+    target,
+    options=Options(),
 ) -> Tuple[Optional[ArrayType], float, int]:
     """Cutting-plane method for solving convex optimization problem
 
@@ -146,7 +148,10 @@ def cutting_plane_feas_q(
 
 
 def cutting_plane_optim_q(
-    omega: OracleOptimQ[ArrayType], space_q: SearchSpaceQ[ArrayType], target, options=Options()
+    omega: OracleOptimQ[ArrayType],
+    space_q: SearchSpaceQ[ArrayType],
+    target,
+    options=Options(),
 ) -> Tuple[Optional[ArrayType], float, int]:
     """Cutting-plane method for solving convex discrete optimization problem
 
diff --git a/src/ellalgo/ell_calc.py b/src/ellalgo/ell_calc.py
index b438e46..6258595 100644
--- a/src/ellalgo/ell_calc.py
+++ b/src/ellalgo/ell_calc.py
@@ -1,8 +1,8 @@
 from math import sqrt
-from typing import Tuple, Optional
+from typing import Optional, Tuple
 
-from .ell_config import CutStatus
 from .ell_calc_core import EllCalcCore
+from .ell_config import CutStatus
 
 
 class EllCalc:
diff --git a/src/ellalgo/ell_stable.py b/src/ellalgo/ell_stable.py
index 7d3601a..9da664a 100644
--- a/src/ellalgo/ell_stable.py
+++ b/src/ellalgo/ell_stable.py
@@ -4,7 +4,7 @@
 
 from .ell_calc import EllCalc
 from .ell_config import CutStatus
-from .ell_typing import SearchSpace, SearchSpaceQ, ArrayType
+from .ell_typing import ArrayType, SearchSpace, SearchSpaceQ
 
 Matrix = np.ndarray
 CutChoice = Union[float, ArrayType]  # single or parallel
diff --git a/src/ellalgo/ell_typing.py b/src/ellalgo/ell_typing.py
index e90896e..890bc83 100644
--- a/src/ellalgo/ell_typing.py
+++ b/src/ellalgo/ell_typing.py
@@ -1,7 +1,8 @@
 from abc import ABC, abstractmethod
-from typing import MutableSequence, Optional, Tuple, Union
-from typing import Generic, TypeVar
+from typing import Generic, MutableSequence, Optional, Tuple, TypeVar, Union
+
 import numpy as np
+
 from .ell_config import CutStatus
 
 ArrayType = TypeVar("ArrayType", bound=np.ndarray)
diff --git a/src/ellalgo/oracles/lowpass_oracle.py b/src/ellalgo/oracles/lowpass_oracle.py
index 85a0c98..e8e2cb7 100644
--- a/src/ellalgo/oracles/lowpass_oracle.py
+++ b/src/ellalgo/oracles/lowpass_oracle.py
@@ -1,7 +1,7 @@
+from math import floor
 from typing import Tuple
 
 import numpy as np
-from math import floor
 
 Arr = np.ndarray
 Cut = Tuple[Arr, float]
@@ -40,7 +40,9 @@
 class LowpassOracle:
     more_alt: bool = True
 
-    def __init__(self, ndim: int, wpass: float, wstop: float, lp_sq: float, up_sq: float):
+    def __init__(
+        self, ndim: int, wpass: float, wstop: float, lp_sq: float, up_sq: float
+    ):
         # *********************************************************************
         # optimization parameters
         # *********************************************************************
@@ -110,8 +112,8 @@ def assess_optim(self, x: Arr, sp_sq: float):
 
         # case 1 (unlikely)
         if x[0] < 0:
-            grade = np.zeros(ndim)
-            grade[0] = -1.0
+            grad = np.zeros(ndim)
+            grad[0] = -1.0
             return (grad, -x[0]), None
 
         # Begin objective function
diff --git a/tests/test_lowpass.py b/tests/test_lowpass.py
index c517df8..8d76944 100644
--- a/tests/test_lowpass.py
+++ b/tests/test_lowpass.py
@@ -1,6 +1,7 @@
 import time
 
 import numpy as np
+
 from ellalgo.cutting_plane import Options, cutting_plane_optim
 from ellalgo.ell import Ell
 from ellalgo.oracles.lowpass_oracle import create_lowpass_case
@@ -33,7 +34,7 @@ def run_lowpass(use_parallel_cut: bool, duration=0.000001):
 
 
 def test_lowpass():
-    """ Test the lowpass case with parallel cut """
+    """Test the lowpass case with parallel cut"""
     result, feasible = run_lowpass(True)
     assert feasible
     assert result >= 1083
@@ -41,7 +42,7 @@ def test_lowpass():
 
 
 def test_no_parallel_cut():
-    """ Test the lowpass case with no parallel cut """
+    """Test the lowpass case with no parallel cut"""
     result, feasible = run_lowpass(False)
     assert feasible
     assert result >= 16461