From 7b2c94a475a61a2a114baa095d0dae8e27f82383 Mon Sep 17 00:00:00 2001
From: tfotakis-signaloid
 <213429317+tfotakis-signaloid@users.noreply.github.com>
Date: Wed, 18 Feb 2026 11:31:38 +0200
Subject: [PATCH 1/2] Updated to version `1.7.1`

---
 .flake8                                       |   9 +-
 .github/workflows/signaloid-python.yaml       |   3 +
 poetry.lock                                   | 337 ++++++++++++-----
 pyproject.toml                                |   5 +-
 src/signaloid/circuitpython/plot_wrapper.py   |  55 ++-
 src/signaloid/distributional/__init__.py      |   2 +-
 src/signaloid/distributional/dirac_delta.py   |  17 +-
 .../distributional/dirac_delta_test.py        |   5 +-
 .../distributional/distributional.py          | 171 +++++----
 .../distributional/distributional_test.py     | 352 ++++++++++++------
 .../plot_histogram_dirac_deltas.py            | 151 ++++----
 .../plot_histogram_dirac_deltas_test.py       |  73 ++--
 .../plot_wrapper.py                           |  27 +-
 .../plot_wrapper_test.py                      |  21 +-
 src/signaloid/uxdata_toolkit.py               |  22 +-
 15 files changed, 759 insertions(+), 491 deletions(-)

diff --git a/.flake8 b/.flake8
index da459c2..d79ac3b 100644
--- a/.flake8
+++ b/.flake8
@@ -1,6 +1,6 @@
 [flake8]
-max-complexity = 20
-max-line-length = 79
+max-complexity = 10
+max-line-length = 88
 
 extend-ignore = 
     # Let formatting take care of line length (not flake8)
@@ -8,5 +8,8 @@ extend-ignore =
     E203
 
 per-file-ignores =
-    src/signaloid/distributional_information_plotting/*: F841
+    # Ignore complex mains in these scripts for now
+    # We should aim is to address all of these in the future
+    src/signaloid/distributional_information_plotting/*: C901
+    src/signaloid/distributional/*: C901
 
diff --git a/.github/workflows/signaloid-python.yaml b/.github/workflows/signaloid-python.yaml
index 618af16..b6438be 100644
--- a/.github/workflows/signaloid-python.yaml
+++ b/.github/workflows/signaloid-python.yaml
@@ -65,6 +65,9 @@ jobs:
     - name: Lint
       run: poetry run flake8 src/
 
+    - name: Check format
+      run: poetry run black --check src/
+
     - name: Typecheck
       run: poetry run mypy -p signaloid
 
diff --git a/poetry.lock b/poetry.lock
index ebf35ba..48016ff 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -1,5 +1,72 @@
 # This file is automatically @generated by Poetry 2.2.1 and should not be changed by hand.
 
+[[package]]
+name = "black"
+version = "25.11.0"
+description = "The uncompromising code formatter."
+optional = false
+python-versions = ">=3.9"
+groups = ["dev"]
+files = [
+    {file = "black-25.11.0-cp310-cp310-macosx_10_9_x86_64.whl", hash = "sha256:ec311e22458eec32a807f029b2646f661e6859c3f61bc6d9ffb67958779f392e"},
+    {file = "black-25.11.0-cp310-cp310-macosx_11_0_arm64.whl", hash = "sha256:1032639c90208c15711334d681de2e24821af0575573db2810b0763bcd62e0f0"},
+    {file = "black-25.11.0-cp310-cp310-manylinux2014_x86_64.manylinux_2_17_x86_64.manylinux_2_28_x86_64.whl", hash = "sha256:0c0f7c461df55cf32929b002335883946a4893d759f2df343389c4396f3b6b37"},
+    {file = "black-25.11.0-cp310-cp310-win_amd64.whl", hash = "sha256:f9786c24d8e9bd5f20dc7a7f0cdd742644656987f6ea6947629306f937726c03"},
+    {file = "black-25.11.0-cp311-cp311-macosx_10_9_x86_64.whl", hash = "sha256:895571922a35434a9d8ca67ef926da6bc9ad464522a5fe0db99b394ef1c0675a"},
+    {file = "black-25.11.0-cp311-cp311-macosx_11_0_arm64.whl", hash = "sha256:cb4f4b65d717062191bdec8e4a442539a8ea065e6af1c4f4d36f0cdb5f71e170"},
+    {file = "black-25.11.0-cp311-cp311-manylinux2014_x86_64.manylinux_2_17_x86_64.manylinux_2_28_x86_64.whl", hash = "sha256:d81a44cbc7e4f73a9d6ae449ec2317ad81512d1e7dce7d57f6333fd6259737bc"},
+    {file = "black-25.11.0-cp311-cp311-win_amd64.whl", hash = "sha256:7eebd4744dfe92ef1ee349dc532defbf012a88b087bb7ddd688ff59a447b080e"},
+    {file = "black-25.11.0-cp312-cp312-macosx_10_13_x86_64.whl", hash = "sha256:80e7486ad3535636657aa180ad32a7d67d7c273a80e12f1b4bfa0823d54e8fac"},
+    {file = "black-25.11.0-cp312-cp312-macosx_11_0_arm64.whl", hash = "sha256:6cced12b747c4c76bc09b4db057c319d8545307266f41aaee665540bc0e04e96"},
+    {file = "black-25.11.0-cp312-cp312-manylinux2014_x86_64.manylinux_2_17_x86_64.manylinux_2_28_x86_64.whl", hash = "sha256:6cb2d54a39e0ef021d6c5eef442e10fd71fcb491be6413d083a320ee768329dd"},
+    {file = "black-25.11.0-cp312-cp312-win_amd64.whl", hash = "sha256:ae263af2f496940438e5be1a0c1020e13b09154f3af4df0835ea7f9fe7bfa409"},
+    {file = "black-25.11.0-cp313-cp313-macosx_10_13_x86_64.whl", hash = "sha256:0a1d40348b6621cc20d3d7530a5b8d67e9714906dfd7346338249ad9c6cedf2b"},
+    {file = "black-25.11.0-cp313-cp313-macosx_11_0_arm64.whl", hash = "sha256:51c65d7d60bb25429ea2bf0731c32b2a2442eb4bd3b2afcb47830f0b13e58bfd"},
+    {file = "black-25.11.0-cp313-cp313-manylinux2014_x86_64.manylinux_2_17_x86_64.manylinux_2_28_x86_64.whl", hash = "sha256:936c4dd07669269f40b497440159a221ee435e3fddcf668e0c05244a9be71993"},
+    {file = "black-25.11.0-cp313-cp313-win_amd64.whl", hash = "sha256:f42c0ea7f59994490f4dccd64e6b2dd49ac57c7c84f38b8faab50f8759db245c"},
+    {file = "black-25.11.0-cp314-cp314-macosx_10_15_x86_64.whl", hash = "sha256:35690a383f22dd3e468c85dc4b915217f87667ad9cce781d7b42678ce63c4170"},
+    {file = "black-25.11.0-cp314-cp314-macosx_11_0_arm64.whl", hash = "sha256:dae49ef7369c6caa1a1833fd5efb7c3024bb7e4499bf64833f65ad27791b1545"},
+    {file = "black-25.11.0-cp314-cp314-manylinux2014_x86_64.manylinux_2_17_x86_64.manylinux_2_28_x86_64.whl", hash = "sha256:5bd4a22a0b37401c8e492e994bce79e614f91b14d9ea911f44f36e262195fdda"},
+    {file = "black-25.11.0-cp314-cp314-win_amd64.whl", hash = "sha256:aa211411e94fdf86519996b7f5f05e71ba34835d8f0c0f03c00a26271da02664"},
+    {file = "black-25.11.0-cp39-cp39-macosx_10_9_x86_64.whl", hash = "sha256:a3bb5ce32daa9ff0605d73b6f19da0b0e6c1f8f2d75594db539fdfed722f2b06"},
+    {file = "black-25.11.0-cp39-cp39-macosx_11_0_arm64.whl", hash = "sha256:9815ccee1e55717fe9a4b924cae1646ef7f54e0f990da39a34fc7b264fcf80a2"},
+    {file = "black-25.11.0-cp39-cp39-manylinux2014_x86_64.manylinux_2_17_x86_64.manylinux_2_28_x86_64.whl", hash = "sha256:92285c37b93a1698dcbc34581867b480f1ba3a7b92acf1fe0467b04d7a4da0dc"},
+    {file = "black-25.11.0-cp39-cp39-win_amd64.whl", hash = "sha256:43945853a31099c7c0ff8dface53b4de56c41294fa6783c0441a8b1d9bf668bc"},
+    {file = "black-25.11.0-py3-none-any.whl", hash = "sha256:e3f562da087791e96cefcd9dda058380a442ab322a02e222add53736451f604b"},
+    {file = "black-25.11.0.tar.gz", hash = "sha256:9a323ac32f5dc75ce7470501b887250be5005a01602e931a15e45593f70f6e08"},
+]
+
+[package.dependencies]
+click = ">=8.0.0"
+mypy-extensions = ">=0.4.3"
+packaging = ">=22.0"
+pathspec = ">=0.9.0"
+platformdirs = ">=2"
+pytokens = ">=0.3.0"
+tomli = {version = ">=1.1.0", markers = "python_version < \"3.11\""}
+typing-extensions = {version = ">=4.0.1", markers = "python_version < \"3.11\""}
+
+[package.extras]
+colorama = ["colorama (>=0.4.3)"]
+d = ["aiohttp (>=3.10)"]
+jupyter = ["ipython (>=7.8.0)", "tokenize-rt (>=3.2.0)"]
+uvloop = ["uvloop (>=0.15.2)"]
+
+[[package]]
+name = "click"
+version = "8.1.8"
+description = "Composable command line interface toolkit"
+optional = false
+python-versions = ">=3.7"
+groups = ["dev"]
+files = [
+    {file = "click-8.1.8-py3-none-any.whl", hash = "sha256:63c132bbbed01578a06712a2d1f497bb62d9c1c0d329b7903a866228027263b2"},
+    {file = "click-8.1.8.tar.gz", hash = "sha256:ed53c9d8990d83c2a27deae68e4ee337473f6330c040a31d4225c9574d16096a"},
+]
+
+[package.dependencies]
+colorama = {version = "*", markers = "platform_system == \"Windows\""}
+
 [[package]]
 name = "colorama"
 version = "0.4.6"
@@ -7,7 +74,7 @@ description = "Cross-platform colored terminal text."
 optional = false
 python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*,!=3.5.*,!=3.6.*,>=2.7"
 groups = ["dev"]
-markers = "sys_platform == \"win32\""
+markers = "platform_system == \"Windows\" or sys_platform == \"win32\""
 files = [
     {file = "colorama-0.4.6-py2.py3-none-any.whl", hash = "sha256:4f1d9991f5acc0ca119f9d443620b77f9d6b33703e51011c16baf57afb285fc6"},
     {file = "colorama-0.4.6.tar.gz", hash = "sha256:08695f5cb7ed6e0531a20572697297273c47b8cae5a63ffc6d6ed5c201be6e44"},
@@ -393,89 +460,103 @@ files = [
 
 [[package]]
 name = "librt"
-version = "0.7.8"
+version = "0.8.1"
 description = "Mypyc runtime library"
 optional = false
 python-versions = ">=3.9"
 groups = ["dev"]
 markers = "platform_python_implementation != \"PyPy\""
 files = [
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 typing = ["typing-extensions ; python_version < \"3.10\""]
 xmp = ["defusedxml"]
 
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+    {file = "pytokens-0.4.1-cp38-cp38-musllinux_1_2_x86_64.whl", hash = "sha256:dcafc12c30dbaf1e2af0490978352e0c4041a7cde31f4f81435c2a5e8b9cabb6"},
+    {file = "pytokens-0.4.1-cp38-cp38-win_amd64.whl", hash = "sha256:42f144f3aafa5d92bad964d471a581651e28b24434d184871bd02e3a0d956037"},
+    {file = "pytokens-0.4.1-cp39-cp39-macosx_11_0_arm64.whl", hash = "sha256:34bcc734bd2f2d5fe3b34e7b3c0116bfb2397f2d9666139988e7a3eb5f7400e3"},
+    {file = "pytokens-0.4.1-cp39-cp39-manylinux2014_aarch64.manylinux_2_17_aarch64.manylinux_2_28_aarch64.whl", hash = "sha256:941d4343bf27b605e9213b26bfa1c4bf197c9c599a9627eb7305b0defcfe40c1"},
+    {file = "pytokens-0.4.1-cp39-cp39-manylinux2014_x86_64.manylinux_2_17_x86_64.manylinux_2_28_x86_64.whl", hash = "sha256:3ad72b851e781478366288743198101e5eb34a414f1d5627cdd585ca3b25f1db"},
+    {file = "pytokens-0.4.1-cp39-cp39-musllinux_1_2_x86_64.whl", hash = "sha256:682fa37ff4d8e95f7df6fe6fe6a431e8ed8e788023c6bcc0f0880a12eab80ad1"},
+    {file = "pytokens-0.4.1-cp39-cp39-win_amd64.whl", hash = "sha256:30f51edd9bb7f85c748979384165601d028b84f7bd13fe14d3e065304093916a"},
+    {file = "pytokens-0.4.1-py3-none-any.whl", hash = "sha256:26cef14744a8385f35d0e095dc8b3a7583f6c953c2e3d269c7f82484bf5ad2de"},
+    {file = "pytokens-0.4.1.tar.gz", hash = "sha256:292052fe80923aae2260c073f822ceba21f3872ced9a68bb7953b348e561179a"},
+]
+
+[package.extras]
+dev = ["black", "build", "mypy", "pytest", "pytest-cov", "setuptools", "tox", "twine", "wheel"]
+
 [[package]]
 name = "six"
 version = "1.17.0"
@@ -1114,4 +1267,4 @@ type = ["pytest-mypy"]
 [metadata]
 lock-version = "2.1"
 python-versions = ">=3.9,<3.14"
-content-hash = "3b7cb6bb3bf6ce2f30a29ca175522aab3852b6c1cb15546fabb6bbd62b701439"
+content-hash = "63160cd2ba1b7a4bc3522f8e61c57b5850b9a7d65679156db664bfdfa8f0c1eb"
diff --git a/pyproject.toml b/pyproject.toml
index d666ed9..6bace64 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,6 +1,6 @@
 [tool.poetry]
 name = "signaloid"
-version = "1.7.0"
+version = "1.7.1"
 description = ""
 authors = [
 	"Signaloid <info@signaloid.com>"
@@ -18,6 +18,7 @@ pytest = "^8.4.2"
 mypy = "^1.19.1"
 flake8 = "^7.3.0"
 toml = "^0.10.2"
+black = {version = "^25.11.0", python = ">=3.9"}
 
 [build-system]
 requires = ["poetry_core>=1.0.0"]
@@ -34,6 +35,8 @@ signaloid-uxdata-toolkit = "signaloid.uxdata_toolkit:main"
 [tool.mypy]
 warn_unused_configs = true
 strict = true
+disallow_any_generics = false
+python_version = "3.9"
 
 [[tool.mypy.overrides]]
 module = [
diff --git a/src/signaloid/circuitpython/plot_wrapper.py b/src/signaloid/circuitpython/plot_wrapper.py
index 1d7cf96..8ccce65 100644
--- a/src/signaloid/circuitpython/plot_wrapper.py
+++ b/src/signaloid/circuitpython/plot_wrapper.py
@@ -34,9 +34,9 @@
 from circuitpython_uplot.scatter import Pointer, Scatter
 
 from signaloid.circuitpython.extended_ulab_numpy import np
-from signaloid.distributional_information_plotting.plot_histogram_dirac_deltas import \
-    PlotData
-
+from signaloid.distributional_information_plotting.plot_histogram_dirac_deltas import (
+    PlotData,
+)
 
 # The background color of the plot
 BG_COLOR = 0xFFFFFF
@@ -73,7 +73,7 @@
 
 
 def apply_array_multiplier(arr, multiplier):
-    arr = np.divide(arr, 10 ** multiplier)
+    arr = np.divide(arr, 10**multiplier)
 
     return arr
 
@@ -81,7 +81,7 @@ def apply_array_multiplier(arr, multiplier):
 def transform_array_with_multiplier(arr):
     max_value = max(np.abs(arr))
     multiplier = int(math.log(max_value, 10)) + (-1 if max_value < 1 else 0)
-    arr = np.divide(arr, 10 ** multiplier)
+    arr = np.divide(arr, 10**multiplier)
 
     return arr, multiplier
 
@@ -193,8 +193,8 @@ def render_histogram(plot, boundary_positions, bin_heights, width, align, edgeco
 
 
 def render_x_multiplier(g, c, multiplier):
-    anchored_x = c.points[1][0] + X_SHIFT - .5 * TICK_SIZE
-    anchored_y = c.points[1][1] - Y_SHIFT + .5 * TICK_SIZE
+    anchored_x = c.points[1][0] + X_SHIFT - 0.5 * TICK_SIZE
+    anchored_y = c.points[1][1] - Y_SHIFT + 0.5 * TICK_SIZE
     text_area = label.Label(
         font=terminalio.FONT,
         text=f"e{multiplier:+d}",
@@ -209,7 +209,7 @@ def render_x_multiplier(g, c, multiplier):
 
 def render_y_multiplier(g, c, multiplier):
     minh = min(c.points[:][1])
-    anchored_x = c.points[1][0] + X_SHIFT - .5 * TICK_SIZE
+    anchored_x = c.points[1][0] + X_SHIFT - 0.5 * TICK_SIZE
     anchored_y = minh - 2 * TICK_SIZE
     text_area = label.Label(
         font=terminalio.FONT,
@@ -230,7 +230,10 @@ def render_non_finite_values(g, nan, neg_inf, pos_inf):
         color=TEXT_COLOR,
         line_spacing=0.8,
         anchor_point=(0.5, 1.0),
-        anchored_position=(board.DISPLAY.width // 2, board.DISPLAY.height - 1.5 * TICK_SIZE),
+        anchored_position=(
+            board.DISPLAY.width // 2,
+            board.DISPLAY.height - 1.5 * TICK_SIZE,
+        ),
         label_direction="LTR",
     )
     g.append(text_area)
@@ -342,7 +345,9 @@ def render_particle_value_value_label(g, particle_value):
     g.append(text_area)
 
 
-def render_particle_value_line(plot, particle_value, bin_heights, width, rangex, rangey, facecolor):
+def render_particle_value_line(
+    plot, particle_value, bin_heights, width, rangex, rangey, facecolor
+):
     # To draw the particle value, we need to create a rectangle, the same
     # way we create the histogram bars
 
@@ -389,18 +394,14 @@ def render_particle_value_line_label(g, c):
 
 def render_logo(g):
     # Add the Signaloid logo to the top right corner of the screen
-    bitmap = displayio.OnDiskBitmap(
-        open("assets/signaloid_logo_24x24.bmp", "rb")
-    )
+    bitmap = displayio.OnDiskBitmap(open("assets/signaloid_logo_24x24.bmp", "rb"))
     sprite = displayio.TileGrid(
         bitmap,
         pixel_shader=bitmap.pixel_shader,
         width=1,
         height=1,
     )
-    sprite.x = (
-        board.DISPLAY.width - SIGNALOID_LOGO_SIZE - SIGNALOID_LOGO_MARGIN
-    )
+    sprite.x = board.DISPLAY.width - SIGNALOID_LOGO_SIZE - SIGNALOID_LOGO_MARGIN
     sprite.y = SIGNALOID_LOGO_MARGIN
     g.append(sprite)
 
@@ -442,17 +443,14 @@ def bar(
     render_bg_plot(g)
     plot = create_main_plot(g)
 
-    boundary_positions, boundary_multiplier = transform_array_with_multiplier(boundary_positions)
+    boundary_positions, boundary_multiplier = transform_array_with_multiplier(
+        boundary_positions
+    )
     bin_heights, bin_heights_multiplier = transform_array_with_multiplier(bin_heights)
     width = apply_array_multiplier(width, boundary_multiplier)
 
     c, rangex, rangey = render_histogram(
-        plot,
-        boundary_positions,
-        bin_heights,
-        width,
-        align,
-        edgecolor
+        plot, boundary_positions, bin_heights, width, align, edgecolor
     )
 
     render_x_multiplier(g, c, boundary_multiplier)
@@ -463,7 +461,7 @@ def bar(
             g,
             plot_data.dist.nan_dirac_delta.mass,
             plot_data.dist.neg_inf_dirac_delta.mass,
-            plot_data.dist.pos_inf_dirac_delta.mass
+            plot_data.dist.pos_inf_dirac_delta.mass,
         )
 
     render_title(g, title)
@@ -472,11 +470,8 @@ def bar(
     render_y_axis_label(g)
 
     # Show the particle value
-    if (
-        particle_value is not None
-        and np.isfinite(particle_value)
-    ):
-        particle_value_normalized = particle_value / (10 ** boundary_multiplier)
+    if particle_value is not None and np.isfinite(particle_value):
+        particle_value_normalized = particle_value / (10**boundary_multiplier)
         if (
             particle_value_normalized >= rangex[0]
             and particle_value_normalized <= rangex[1]
@@ -488,7 +483,7 @@ def bar(
                 width,
                 rangex,
                 rangey,
-                facecolor
+                facecolor,
             )
             render_particle_value_line_label(g, c)
 
diff --git a/src/signaloid/distributional/__init__.py b/src/signaloid/distributional/__init__.py
index c396678..5a50be9 100644
--- a/src/signaloid/distributional/__init__.py
+++ b/src/signaloid/distributional/__init__.py
@@ -1,4 +1,4 @@
 from signaloid.distributional.distributional import DistributionalValue
 from signaloid.distributional.dirac_delta import DiracDelta
 
-__all__ = ['DistributionalValue', 'DiracDelta']
+__all__ = ["DistributionalValue", "DiracDelta"]
diff --git a/src/signaloid/distributional/dirac_delta.py b/src/signaloid/distributional/dirac_delta.py
index d2fe185..00ea644 100644
--- a/src/signaloid/distributional/dirac_delta.py
+++ b/src/signaloid/distributional/dirac_delta.py
@@ -18,12 +18,11 @@
 #   FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 #   DEALINGS IN THE SOFTWARE.
 
+from __future__ import annotations
 import sys
 import math
 
-if sys.implementation.name != 'circuitpython':
-    from typing import Optional
-
+if sys.implementation.name != "circuitpython":
     # Use numpy for accelerated computing
     import numpy as np
 else:
@@ -36,10 +35,7 @@
 
 class DiracDelta:
     def __init__(
-        self,
-        position: float,
-        raw_mass: Optional[int] = None,
-        mass: Optional[float] = None
+        self, position: float, raw_mass: int | None = None, mass: float | None = None
     ) -> None:
         """Initializes the Dirac Delta, given a position, and a mass in either
         a fixed-point or a floating point representation. If both representations
@@ -50,10 +46,10 @@ def __init__(
         :type position: float
         :param raw_mass: The Dirac Delta mass in 64bit fixed-point representation,
         defaults to None.
-        :type raw_mass: Optional[int]
+        :type raw_mass: int | None
         :param mass: The Dirac Delta mass in floating-point representation,
         defaults to None.
-        :type mass: Optional[float]
+        :type mass: float | None
         """
         self.position: float = position
         self._raw_mass: int = 0
@@ -124,8 +120,7 @@ def __add__(self, other: "DiracDelta") -> "DiracDelta":
         """
         combined_mass: float = self.mass + other.mass
         combined_position: float = (
-            self.position * self.mass
-            + other.position * other.mass
+            self.position * self.mass + other.position * other.mass
         ) / combined_mass
 
         return DiracDelta(position=combined_position, mass=combined_mass)
diff --git a/src/signaloid/distributional/dirac_delta_test.py b/src/signaloid/distributional/dirac_delta_test.py
index 3e39cc5..6f46ba8 100644
--- a/src/signaloid/distributional/dirac_delta_test.py
+++ b/src/signaloid/distributional/dirac_delta_test.py
@@ -67,10 +67,7 @@ def test_dirac_delta_operations(self) -> None:
         d3 = d1 + d2
 
         combined_mass: float = 2.3 + 5.6
-        combined_position: float = (
-            1.2 * 2.3
-            + 4.5 * 5.6
-        ) / combined_mass
+        combined_position: float = (1.2 * 2.3 + 4.5 * 5.6) / combined_mass
         self.assertTrue(d3.position == combined_position)
         self.assertTrue(d3.mass == combined_mass)
 
diff --git a/src/signaloid/distributional/distributional.py b/src/signaloid/distributional/distributional.py
index 0cda2ca..546fff0 100644
--- a/src/signaloid/distributional/distributional.py
+++ b/src/signaloid/distributional/distributional.py
@@ -18,17 +18,15 @@
 #   FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 #   DEALINGS IN THE SOFTWARE.
 
+from __future__ import annotations
 import math
 import sys
 import re
 import struct
 
-if sys.implementation.name != 'circuitpython':
-    from typing import Optional, Union
-
+if sys.implementation.name != "circuitpython":
     # Use numpy for accelerated computing
     import numpy as np
-    from numpy.typing import NDArray
 else:
     # Use the extended version of ulab's numpy when running on CircuitPython
     from signaloid.circuitpython.extended_ulab_numpy import np  # type: ignore[no-redef]
@@ -57,37 +55,39 @@
         "position_single": "<f",
         "position_double": "<d",
         "mass": "<Q",
-    }
+    },
 }
 
 
 class DistributionalValue:
     def __init__(
         self,
-        particle_value: Optional[float] = None,
-        UR_type: Optional[int] = None,
-        dirac_deltas: Optional[list[DiracDelta]] = None,
-        double_precision: bool = True
+        particle_value: float | None = None,
+        UR_type: int | None = None,
+        dirac_deltas: list[DiracDelta] | None = None,
+        double_precision: bool = True,
     ) -> None:
-        self.particle_value: Optional[float] = particle_value
-        self.UR_type: Optional[int] = UR_type
-        self._dirac_deltas: list[DiracDelta] = dirac_deltas if dirac_deltas is not None else []
+        self.particle_value: float | None = particle_value
+        self.UR_type: int | None = UR_type
+        self._dirac_deltas: list[DiracDelta] = (
+            dirac_deltas if dirac_deltas is not None else []
+        )
         self.double_precision = double_precision
         """
         properties
         """
-        self._mean: Optional[float] = None
-        self._variance: Optional[float] = None
+        self._mean: float | None = None
+        self._variance: float | None = None
 
         self.nan_dirac_delta: DiracDelta = DiracDelta(position=np.nan, mass=np.nan)
         self.neg_inf_dirac_delta: DiracDelta = DiracDelta(position=-np.inf, mass=np.nan)
         self.pos_inf_dirac_delta: DiracDelta = DiracDelta(position=np.inf, mass=np.nan)
 
-        self._has_no_zero_mass: Optional[bool] = None
-        self._is_finite: Optional[bool] = None
-        self._is_sorted: Optional[bool] = None
-        self._is_cured: Optional[bool] = None
-        self._is_full_valid_TTR: Optional[bool] = None
+        self._has_no_zero_mass: bool | None = None
+        self._is_finite: bool | None = None
+        self._is_sorted: bool | None = None
+        self._is_cured: bool | None = None
+        self._is_full_valid_TTR: bool | None = None
 
     @property
     def dirac_deltas(self) -> list[DiracDelta]:
@@ -112,41 +112,47 @@ def finite_dirac_deltas(self) -> list[DiracDelta]:
         return self.dirac_deltas
 
     @property
-    def positions(self) -> NDArray[np.float64]:
+    def positions(self) -> np.ndarray:
         """The list af all the Dirac Delta positions.
 
         :return: The list of all the Dirac Delta positions.
-        :rtype: NDArray[np.float64]
+        :rtype: np.ndarray
         """
-        arr: NDArray[np.float64] = np.array([dd.position for dd in self.dirac_deltas], dtype=np.float64)
+        arr: np.ndarray = np.array(
+            [dd.position for dd in self.dirac_deltas], dtype=np.float64
+        )
         return arr
 
     @property
-    def masses(self) -> NDArray[np.float64]:
+    def masses(self) -> np.ndarray:
         """The list af all the Dirac Delta floating-point masses.
 
         :return: The list of all the Dirac Delta floating-point masses.
-        :rtype: NDArray[np.float64]
+        :rtype: np.ndarray
         """
-        arr: NDArray[np.float64] = np.array([dd.mass for dd in self.dirac_deltas], dtype=np.float64)
+        arr: np.ndarray = np.array(
+            [dd.mass for dd in self.dirac_deltas], dtype=np.float64
+        )
         return arr
 
     @property
-    def raw_masses(self) -> NDArray[np.uint64]:
+    def raw_masses(self) -> np.ndarray:
         """The list af all the Dirac Delta fixed-point masses.
 
         :return: The list of all the Dirac Delta fixed-point masses.
-        :rtype: NDArray[np.uint64]
+        :rtype: np.ndarray
         """
-        arr: NDArray[np.uint64] = np.array([dd.raw_mass for dd in self.dirac_deltas], dtype=np.uint64)
+        arr: np.ndarray = np.array(
+            [dd.raw_mass for dd in self.dirac_deltas], dtype=np.uint64
+        )
         return arr
 
     @property
-    def mean(self) -> Optional[float]:
+    def mean(self) -> float | None:
         """The mean position of all the Dirac Deltas.
 
         :return: The mean position of all the Dirac Deltas.
-        :rtype: Optional[float]
+        :rtype: float | None
         """
         if self._mean is None:
             self.calculate_mean()
@@ -154,16 +160,16 @@ def mean(self) -> Optional[float]:
         return self._mean
 
     @mean.setter
-    def mean(self, mean: Optional[float]):
+    def mean(self, mean: float | None):
         """Sets the mean position of all the Dirac Deltas explicitly (it does
         not interfere with the Dirac Deltas list).
 
         :param mean: The mean value to use.
-        :type mean: Optional[float]
+        :type mean: float | None
         """
         self._mean = mean
 
-    def calculate_mean(self) -> Optional[float]:
+    def calculate_mean(self) -> float | None:
         """Calculated the mean position of all the Dirac Deltas based on the
         Dirac Deltas list.
 
@@ -199,38 +205,33 @@ def UR_order(self) -> int:
         return len(self.dirac_deltas)
 
     @property
-    def variance(self) -> Optional[float]:
+    def variance(self) -> float | None:
         """The positional variance of all the Dirac Deltas.
 
         :return: The positional variance of all the Dirac Deltas.
-        :rtype: Optional[float]
+        :rtype: float | None
         """
         if self._variance is None:
             self.calculate_variance()
 
         return self._variance
 
-    def calculate_variance(self) -> Optional[float]:
+    def calculate_variance(self) -> float | None:
         """Calculates the positional variance of all the Dirac Deltas.
 
         :return: The calculated positional variance of all the Dirac Deltas.
-        :rtype: Optional[float]
+        :rtype: float | None
         """
         # Calculate weighted sample variance
-        if (
-            self.mean is None
-            or self.UR_order == 0
-            or not np.isfinite(self.mean)
-        ):
+        if self.mean is None or self.UR_order == 0 or not np.isfinite(self.mean):
             self._variance = None
         else:
             total_mass: float = 0
             total_weighted_squared_diffs: float = 0
             for dd in self.dirac_deltas:
                 total_weighted_squared_diffs += (
-                    ((dd.position - self.mean) ** 2)
-                    * dd.mass
-                )
+                    (dd.position - self.mean) ** 2
+                ) * dd.mass
                 total_mass += dd.mass
 
             self._variance = total_weighted_squared_diffs / total_mass
@@ -280,7 +281,7 @@ def __bytes__(self) -> bytes:
         result = self.export(to_str=False)
         return result if isinstance(result, bytes) else bytes()
 
-    def export(self, to_str: bool = True) -> Union[str, bytes]:
+    def export(self, to_str: bool = True) -> str | bytes:
         """
         Constructs the Ux string/Ux bytes with particle value for the `DistributionalValue`.
 
@@ -320,13 +321,17 @@ def export(self, to_str: bool = True) -> Union[str, bytes]:
 
         if to_str:
             # Particle value (double in string format)
-            UxString += str(self.particle_value) if self.particle_value is not None else ""
+            UxString += (
+                str(self.particle_value) if self.particle_value is not None else ""
+            )
             UxString += "Ux"
 
             fmt = STRUCT_FORMATS["str"]
         else:
             # Particle value (double)                           (8 bytes)
-            particle_value = self.particle_value if self.particle_value is not None else 0
+            particle_value = (
+                self.particle_value if self.particle_value is not None else 0
+            )
             fmt = STRUCT_FORMATS["bytes"]
             buffer += struct.pack(fmt["particle"], particle_value)
 
@@ -344,7 +349,9 @@ def export(self, to_str: bool = True) -> Union[str, bytes]:
         buffer += struct.pack(fmt["UR_order"], self.UR_order)
 
         # Choose the format based on double_precision flag
-        position_format = fmt["position_double" if self.double_precision else "position_single"]
+        position_format = fmt[
+            "position_double" if self.double_precision else "position_single"
+        ]
 
         # Pairs of:
         # - Support position (double or float)              (8 or 4 bytes)
@@ -363,9 +370,8 @@ def export(self, to_str: bool = True) -> Union[str, bytes]:
 
     @staticmethod
     def parse(
-        dist: Union[str, bytes],
-        double_precision: Optional[bool] = None
-    ) -> "Optional[DistributionalValue]":
+        dist: str | bytes, double_precision: bool | None = None
+    ) -> "DistributionalValue | None":
         """
         Constructs a `DistributionalValue` after parsing an input that can be
         a UxString or a byte array.
@@ -423,7 +429,7 @@ def parse(
 
             # Match an optional floating-point or integer number, followed by 'Ux',
             # and then hexadecimal characters
-            if sys.implementation.name == 'circuitpython':
+            if sys.implementation.name == "circuitpython":
                 parts = dist.split("Ux")
                 index = 0
                 if len(parts) == 2:
@@ -432,12 +438,16 @@ def parse(
 
                 buffer = bytes.fromhex(parts[index])
             else:
-                pattern = r"^([-+]?\d*\.?\d+(?:e[-+]\d+)?|nan|[-+]?inf)?Ux([0-9A-Fa-f]+)$"
+                pattern = (
+                    r"^([-+]?\d*\.?\d+(?:e[-+]\d+)?|nan|[-+]?inf)?Ux([0-9A-Fa-f]+)$"
+                )
                 match = re.match(pattern, dist)
                 if not match:
                     return None
 
-                dist_value.particle_value = float(match.group(1)) if match.group(1) else None
+                dist_value.particle_value = (
+                    float(match.group(1)) if match.group(1) else None
+                )
 
                 buffer = bytes.fromhex(match.group(2))
         elif isinstance(dist, (bytes, bytearray)):
@@ -445,7 +455,9 @@ def parse(
             fmt = STRUCT_FORMATS["bytes"]
 
             buffer = dist
-            dist_value.particle_value = struct.unpack(fmt["particle"], buffer[offset:offset + 8])[0]
+            dist_value.particle_value = struct.unpack(
+                fmt["particle"], buffer[offset : offset + 8]
+            )[0]
             offset += 8
         else:
             print("Error: ", type(dist))
@@ -457,26 +469,24 @@ def parse(
         if len(buffer) < min_length:
             return None
 
-        dist_value.UR_type = struct.unpack(fmt["UR_type"], buffer[offset:offset + 1])[0]
+        dist_value.UR_type = struct.unpack(fmt["UR_type"], buffer[offset : offset + 1])[
+            0
+        ]
         offset += 1
 
         # Not used, uncomment if needed
         # number_of_samples = struct.unpack(fmt["sample_count"], buffer[offset:offset + 8])[0]
         offset += 8
 
-        dist_value.mean = struct.unpack(fmt["mean"], buffer[offset:offset + 8])[0]
+        dist_value.mean = struct.unpack(fmt["mean"], buffer[offset : offset + 8])[0]
         offset += 8
 
-        UR_order = struct.unpack(fmt["UR_order"], buffer[offset:offset + 4])[0]
+        UR_order = struct.unpack(fmt["UR_order"], buffer[offset : offset + 4])[0]
         offset += 4
 
         # Validate UR_order - reasonable upper limit to prevent processing
         # extremely large inputs that might be malicious
-        if (
-            UR_order is None
-            or UR_order < 0
-            or UR_order > 10000
-        ):
+        if UR_order is None or UR_order < 0 or UR_order > 10000:
             return None
 
         # Calculate expected length based on UR_order
@@ -497,14 +507,16 @@ def parse(
             if len(buffer) < expected_length:
                 return None
 
-        position_format = fmt["position_double" if double_precision else "position_single"]
+        position_format = fmt[
+            "position_double" if double_precision else "position_single"
+        ]
 
         for _ in range(UR_order):
-            support_position_bytes = buffer[offset:offset + bytes_per_position]
+            support_position_bytes = buffer[offset : offset + bytes_per_position]
             offset += bytes_per_position
             position = struct.unpack(position_format, support_position_bytes)[0]
 
-            mass_bytes = buffer[offset:offset + 8]
+            mass_bytes = buffer[offset : offset + 8]
             offset += 8
             raw_mass = struct.unpack(fmt["mass"], mass_bytes)[0]
 
@@ -545,7 +557,7 @@ def mean_relative_diff(self, other: "DistributionalValue") -> float:
         return abs((self.mean - other.mean) / other.mean)
 
     @property
-    def has_no_zero_mass(self) -> Optional[bool]:
+    def has_no_zero_mass(self) -> bool | None:
         """
         The property that no Dirac delta of the `DistributionalValue` has a zero mass.
 
@@ -557,7 +569,7 @@ def has_no_zero_mass(self) -> Optional[bool]:
 
         return self._has_no_zero_mass
 
-    def check_has_no_zero_mass(self) -> Optional[bool]:
+    def check_has_no_zero_mass(self) -> bool | None:
         """
         Checks the property that no Dirac delta of the `DistributionalValue` has a zero
         mass.
@@ -589,7 +601,7 @@ def drop_zero_mass_positions(self) -> None:
         self._has_no_zero_mass = True
 
     @property
-    def is_finite(self) -> Optional[bool]:
+    def is_finite(self) -> bool | None:
         """
         The property that all Dirac deltas of the `DistributionalValue` have finite
         positions, i.e., no NaN, -Inf, or Inf values.
@@ -603,7 +615,7 @@ def is_finite(self) -> Optional[bool]:
 
         return self._is_finite
 
-    def check_is_finite(self) -> Optional[bool]:
+    def check_is_finite(self) -> bool | None:
         """
         Checks the property that all Dirac deltas of the `DistributionalValue` have
         finite positions, i.e., no NaN, -Inf, or Inf values.
@@ -622,7 +634,7 @@ def check_is_finite(self) -> Optional[bool]:
         return True
 
     @property
-    def is_sorted(self) -> Optional[bool]:
+    def is_sorted(self) -> bool | None:
         """
         The property that the Dirac deltas of the `DistributionalValue` are sorted
         according to their positions. The NaN, -Inf, and Inf positional values
@@ -637,7 +649,7 @@ def is_sorted(self) -> Optional[bool]:
 
         return self._is_sorted
 
-    def check_is_sorted(self) -> Optional[bool]:
+    def check_is_sorted(self) -> bool | None:
         """
         Checks The property that the Dirac deltas of the `DistributionalValue` are
         sorted according to their positions. The NaN, -Inf, and Inf positional values
@@ -697,7 +709,7 @@ def sort(self) -> None:
         self._is_sorted = True
 
     @property
-    def is_cured(self) -> Optional[bool]:
+    def is_cured(self) -> bool | None:
         """
         The property that no two Dirac deltas of the `DistributionalValue` have
         the same positional value, including NaN, -Inf, and Inf.
@@ -711,7 +723,7 @@ def is_cured(self) -> Optional[bool]:
 
         return self._is_cured
 
-    def check_is_cured(self) -> Optional[bool]:
+    def check_is_cured(self) -> bool | None:
         """
         Checks the property that no two Dirac deltas of the `DistributionalValue` have
         the same positional value, including NaN, -Inf, and Inf.
@@ -773,9 +785,8 @@ def combine_dirac_deltas(
             mean_threshold = finite_mean * relative_mean_threshold
 
             range_threshold = (
-                (self.finite_dirac_deltas[-1].position - self.dirac_deltas[0].position)
-                * relative_range_threshold
-            )
+                self.finite_dirac_deltas[-1].position - self.dirac_deltas[0].position
+            ) * relative_range_threshold
 
             threshold = max(mean_threshold, range_threshold)
 
@@ -797,7 +808,7 @@ def combine_dirac_deltas(
         self._is_cured = True
 
     @property
-    def is_full_valid_TTR(self) -> Optional[bool]:
+    def is_full_valid_TTR(self) -> bool | None:
         """
         The property that the Dirac deltas of the `DistributionalValue` form
         a full valid TTR. "Full" means that there are 2^n Dirac deltas (after
@@ -814,7 +825,7 @@ def is_full_valid_TTR(self) -> Optional[bool]:
 
         return self._is_full_valid_TTR
 
-    def check_is_full_valid_TTR(self) -> Optional[bool]:
+    def check_is_full_valid_TTR(self) -> bool | None:
         """
         Checks the property that the Dirac deltas of the `DistributionalValue`
         form a full and valid TTR. "Full" means that there are 2^n Dirac deltas
diff --git a/src/signaloid/distributional/distributional_test.py b/src/signaloid/distributional/distributional_test.py
index 7e154f7..a3e97b6 100644
--- a/src/signaloid/distributional/distributional_test.py
+++ b/src/signaloid/distributional/distributional_test.py
@@ -18,27 +18,26 @@
 #   FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 #   DEALINGS IN THE SOFTWARE.
 
+from __future__ import annotations
 import csv
-from typing import Optional
 import unittest
-
 from signaloid.distributional.dirac_delta import DiracDelta
 from signaloid.distributional.distributional import DistributionalValue
 
 
 def read_string_bytes_pairs_from_csv(
-    csv_filename: str
-) -> Optional[list[tuple[str, bytes]]]:
+    csv_filename: str,
+) -> list[tuple[str, bytes]] | None:
     """
     Reads pairs of Ux strings and Ux bytes(in hex format) from a csv file
 
     Args:
         csv_filename: The input csv file path
     Returns:
-        pairs: list of (string_value, bytearray_value) tuples
+        pairs: list of tuples of (string_value, bytearray_value)
     """
     pairs: list[tuple[str, bytes]] = []
-    with open(csv_filename, 'r') as csvfile:
+    with open(csv_filename, "r") as csvfile:
         reader = csv.reader(csvfile)
         for row in reader:
             if len(row) == 2:
@@ -51,7 +50,7 @@ def read_string_bytes_pairs_from_csv(
 class TestUxParsing(unittest.TestCase):
     def test_parse_ux_strings_values(
         self,
-        input_filename: str = "src/signaloid/distributional/test_ux_value_pairs.csv"
+        input_filename: str = "src/signaloid/distributional/test_ux_value_pairs.csv",
     ) -> None:
         """
         Test parsing Ux string values and converting them to Ux bytes
@@ -71,7 +70,7 @@ def test_parse_ux_strings_values(
 
     def test_parse_ux_bytes_values(
         self,
-        input_filename: str = "src/signaloid/distributional/test_ux_value_pairs.csv"
+        input_filename: str = "src/signaloid/distributional/test_ux_value_pairs.csv",
     ) -> None:
         """
         Test parsing Ux bytes and converting them to Ux strings
@@ -94,150 +93,269 @@ def test_check_is_full_valid_TTR(self):
         Test checking DistributionalValues for Full & Valid TTR
         """
         probabilitiesSlope = [
-            0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.8, 0.7, 0.6, 0.5, 0.4,
-            0.3, 0.2, 0.1
+            0.1,
+            0.2,
+            0.3,
+            0.4,
+            0.5,
+            0.6,
+            0.7,
+            0.8,
+            0.8,
+            0.7,
+            0.6,
+            0.5,
+            0.4,
+            0.3,
+            0.2,
+            0.1,
         ]
-        dist = DistributionalValue(dirac_deltas=[
-            DiracDelta(position=position, mass=mass)
-            for position, mass in enumerate(probabilitiesSlope)
-        ])
+        dist = DistributionalValue(
+            dirac_deltas=[
+                DiracDelta(position=position, mass=mass)
+                for position, mass in enumerate(probabilitiesSlope)
+            ]
+        )
         self.assertFalse(dist.check_is_full_valid_TTR())
 
-        dist = DistributionalValue(dirac_deltas=[
-            DiracDelta(position=i, mass=0.1 * (i + 1))
-            for i in range(16)
-        ])
+        dist = DistributionalValue(
+            dirac_deltas=[DiracDelta(position=i, mass=0.1 * (i + 1)) for i in range(16)]
+        )
         self.assertFalse(dist.check_is_full_valid_TTR())
 
-        dist = DistributionalValue(dirac_deltas=[
-            DiracDelta(position=i, mass=0.1)
-            for i in range(16)
-        ])
+        dist = DistributionalValue(
+            dirac_deltas=[DiracDelta(position=i, mass=0.1) for i in range(16)]
+        )
         self.assertTrue(dist.check_is_full_valid_TTR())
 
         gaussianMotherTTR16Positions = [
-            -2.2194097942437231, -1.5678879053053274, -1.1997100902860450,
-            -0.9205473016275229, -0.6859608829556935, -0.4772650338604341,
-            -0.2817093825097764, -0.0931705533484249, 0.0931705533484249,
-            0.2817093825097764, 0.4772650338604341, 0.6859608829556935,
-            0.9205473016275229, 1.1997100902860450, 1.5678879053053274,
-            2.2194097942437231
+            -2.2194097942437231,
+            -1.5678879053053274,
+            -1.1997100902860450,
+            -0.9205473016275229,
+            -0.6859608829556935,
+            -0.4772650338604341,
+            -0.2817093825097764,
+            -0.0931705533484249,
+            0.0931705533484249,
+            0.2817093825097764,
+            0.4772650338604341,
+            0.6859608829556935,
+            0.9205473016275229,
+            1.1997100902860450,
+            1.5678879053053274,
+            2.2194097942437231,
         ]
         gaussianMotherTTR16Probabilities = [
-            0.0339789420851602, 0.0520280112620429, 0.0601091352703015,
-            0.0663526532241763, 0.0686569819948156, 0.0714941307381180,
-            0.0732557829230397, 0.0741243625023456, 0.0741243625023456,
-            0.0732557829230397, 0.0714941307381180, 0.0686569819948156,
-            0.0663526532241763, 0.0601091352703015, 0.0520280112620429,
-            0.0339789420851602
+            0.0339789420851602,
+            0.0520280112620429,
+            0.0601091352703015,
+            0.0663526532241763,
+            0.0686569819948156,
+            0.0714941307381180,
+            0.0732557829230397,
+            0.0741243625023456,
+            0.0741243625023456,
+            0.0732557829230397,
+            0.0714941307381180,
+            0.0686569819948156,
+            0.0663526532241763,
+            0.0601091352703015,
+            0.0520280112620429,
+            0.0339789420851602,
         ]
-        dist = DistributionalValue(dirac_deltas=[
-            DiracDelta(position=position, mass=mass)
-            for position, mass in zip(
-                gaussianMotherTTR16Positions,
-                gaussianMotherTTR16Probabilities
-            )
-        ])
+        dist = DistributionalValue(
+            dirac_deltas=[
+                DiracDelta(position=position, mass=mass)
+                for position, mass in zip(
+                    gaussianMotherTTR16Positions, gaussianMotherTTR16Probabilities
+                )
+            ]
+        )
         self.assertTrue(dist.check_is_full_valid_TTR())
 
         exponentialMotherTTR16Positions = [
-            0.0463101200943282, 0.1434539976121732, 0.2473298485428934,
-            0.3589406008993048, 0.4795601941139194, 0.6107690295987392,
-            0.7545735507649249, 0.9136511262522184, 1.0940956889209921,
-            1.3020972163662070, 1.5437301020205228, 1.8320038271142292,
-            2.1944919248629803, 2.6809449590891815, 3.4180232931306736,
-            5.0000000000000000
+            0.0463101200943282,
+            0.1434539976121732,
+            0.2473298485428934,
+            0.3589406008993048,
+            0.4795601941139194,
+            0.6107690295987392,
+            0.7545735507649249,
+            0.9136511262522184,
+            1.0940956889209921,
+            1.3020972163662070,
+            1.5437301020205228,
+            1.8320038271142292,
+            2.1944919248629803,
+            2.6809449590891815,
+            3.4180232931306736,
+            5.0000000000000000,
         ]
         exponentialMotherTTR16Probabilities = [
-            0.0898043375672398, 0.0869428363237056, 0.0839866334859530,
-            0.0809192993370894, 0.0777683023008333, 0.0744401048312553,
-            0.0709620923605228, 0.0672969526219585, 0.0650216515596327,
-            0.0606655024127962, 0.0559943437573481, 0.0508626602050525,
-            0.0462377199658062, 0.0393104949029426, 0.0314714294791298,
-            0.0183156388887342
+            0.0898043375672398,
+            0.0869428363237056,
+            0.0839866334859530,
+            0.0809192993370894,
+            0.0777683023008333,
+            0.0744401048312553,
+            0.0709620923605228,
+            0.0672969526219585,
+            0.0650216515596327,
+            0.0606655024127962,
+            0.0559943437573481,
+            0.0508626602050525,
+            0.0462377199658062,
+            0.0393104949029426,
+            0.0314714294791298,
+            0.0183156388887342,
         ]
-        dist = DistributionalValue(dirac_deltas=[
-            DiracDelta(position=position, mass=mass)
-            for position, mass in zip(
-                exponentialMotherTTR16Positions,
-                exponentialMotherTTR16Probabilities
-            )
-        ])
+        dist = DistributionalValue(
+            dirac_deltas=[
+                DiracDelta(position=position, mass=mass)
+                for position, mass in zip(
+                    exponentialMotherTTR16Positions, exponentialMotherTTR16Probabilities
+                )
+            ]
+        )
         self.assertTrue(dist.check_is_full_valid_TTR())
 
         laplaceMotherTTR16Positions = [
-            -4.0000000000000000, -2.4180232931306736, -1.6809449590891815,
-            -1.1944919248629803, -0.8320038271142292, -0.5437301020205228,
-            -0.3020972163662070, -0.0940956889209921, 0.0940956889209921,
-            0.3020972163662070, 0.5437301020205228, 0.8320038271142292,
-            1.1944919248629803, 1.6809449590891815, 2.4180232931306736,
-            4.0000000000000000
+            -4.0000000000000000,
+            -2.4180232931306736,
+            -1.6809449590891815,
+            -1.1944919248629803,
+            -0.8320038271142292,
+            -0.5437301020205228,
+            -0.3020972163662070,
+            -0.0940956889209921,
+            0.0940956889209921,
+            0.3020972163662070,
+            0.5437301020205228,
+            0.8320038271142292,
+            1.1944919248629803,
+            1.6809449590891815,
+            2.4180232931306736,
+            4.0000000000000000,
         ]
         laplaceMotherTTR16Probabilities = [
-            0.0248935341839320, 0.0427741074343744, 0.0534285019812003,
-            0.0628435769862145, 0.0691295224912407, 0.0761042035660443,
-            0.0824529664115212, 0.0883735869454727, 0.0883735869454727,
-            0.0824529664115212, 0.0761042035660443, 0.0691295224912407,
-            0.0628435769862145, 0.0534285019812003, 0.0427741074343744,
-            0.0248935341839320
+            0.0248935341839320,
+            0.0427741074343744,
+            0.0534285019812003,
+            0.0628435769862145,
+            0.0691295224912407,
+            0.0761042035660443,
+            0.0824529664115212,
+            0.0883735869454727,
+            0.0883735869454727,
+            0.0824529664115212,
+            0.0761042035660443,
+            0.0691295224912407,
+            0.0628435769862145,
+            0.0534285019812003,
+            0.0427741074343744,
+            0.0248935341839320,
         ]
-        dist = DistributionalValue(dirac_deltas=[
-            DiracDelta(position=position, mass=mass)
-            for position, mass in zip(
-                laplaceMotherTTR16Positions,
-                laplaceMotherTTR16Probabilities
-            )
-        ])
+        dist = DistributionalValue(
+            dirac_deltas=[
+                DiracDelta(position=position, mass=mass)
+                for position, mass in zip(
+                    laplaceMotherTTR16Positions, laplaceMotherTTR16Probabilities
+                )
+            ]
+        )
         self.assertTrue(dist.check_is_full_valid_TTR())
 
         logisticMotherTTR16Positions = [
-            -4.5562387049543025, -2.9418421436602556, -2.1587856510880987,
-            -1.6144447065491812, -1.1828706566397532, -0.8138506279227880,
-            -0.4770709791304498, -0.1572607957522052, 0.1572607957522052,
-            0.4770709791304498, 0.8138506279227880, 1.1828706566397532,
-            1.6144447065491812, 2.1587856510880987, 2.9418421436602556,
-            4.5562387049543025
+            -4.5562387049543025,
+            -2.9418421436602556,
+            -2.1587856510880987,
+            -1.6144447065491812,
+            -1.1828706566397532,
+            -0.8138506279227880,
+            -0.4770709791304498,
+            -0.1572607957522052,
+            0.1572607957522052,
+            0.4770709791304498,
+            0.8138506279227880,
+            1.1828706566397532,
+            1.6144447065491812,
+            2.1587856510880987,
+            2.9418421436602556,
+            4.5562387049543025,
         ]
         logisticMotherTTR16Probabilities = [
-            0.0281433474818693, 0.0475738959372374, 0.0580005680032459,
-            0.0662821885776473, 0.0702935070589577, 0.0743920703246041,
-            0.0770073268795160, 0.0783070957369223, 0.0783070957369223,
-            0.0770073268795160, 0.0743920703246041, 0.0702935070589577,
-            0.0662821885776473, 0.0580005680032459, 0.0475738959372374,
-            0.0281433474818693
+            0.0281433474818693,
+            0.0475738959372374,
+            0.0580005680032459,
+            0.0662821885776473,
+            0.0702935070589577,
+            0.0743920703246041,
+            0.0770073268795160,
+            0.0783070957369223,
+            0.0783070957369223,
+            0.0770073268795160,
+            0.0743920703246041,
+            0.0702935070589577,
+            0.0662821885776473,
+            0.0580005680032459,
+            0.0475738959372374,
+            0.0281433474818693,
         ]
-        dist = DistributionalValue(dirac_deltas=[
-            DiracDelta(position=position, mass=mass)
-            for position, mass in zip(
-                logisticMotherTTR16Positions,
-                logisticMotherTTR16Probabilities
-            )
-        ])
+        dist = DistributionalValue(
+            dirac_deltas=[
+                DiracDelta(position=position, mass=mass)
+                for position, mass in zip(
+                    logisticMotherTTR16Positions, logisticMotherTTR16Probabilities
+                )
+            ]
+        )
         self.assertTrue(dist.check_is_full_valid_TTR())
 
         gumbel1MotherTTR16Positions = [
-            -1.3722373849766128, -0.9285915299813774, -0.6394795296057504,
-            -0.3977265029274728, -0.1773165596233781, 0.0336306411453416,
-            0.2453949715783402, 0.4637578398478052, 0.6941280516995109,
-            0.9432140395136739, 1.2205265612985903, 1.5396243403711020,
-            1.9288304844468449, 2.4378800713555984, 3.1930831163570588,
-            4.7879260278453658
+            -1.3722373849766128,
+            -0.9285915299813774,
+            -0.6394795296057504,
+            -0.3977265029274728,
+            -0.1773165596233781,
+            0.0336306411453416,
+            0.2453949715783402,
+            0.4637578398478052,
+            0.6941280516995109,
+            0.9432140395136739,
+            1.2205265612985903,
+            1.5396243403711020,
+            1.9288304844468449,
+            2.4378800713555984,
+            3.1930831163570588,
+            4.7879260278453658,
         ]
         gumbel1MotherTTR16Probabilities = [
-            0.0476295697963972, 0.0667881624671499, 0.0730630564420902,
-            0.0772153676471943, 0.0768815694664325, 0.0772987007741402,
-            0.0765686001679291, 0.0749309749136895, 0.0721865495667472,
-            0.0689189559863393, 0.0648623956919026, 0.0599040616210838,
-            0.0552629494040690, 0.0475407218497456, 0.0384337406899792,
-            0.0225146235151103
+            0.0476295697963972,
+            0.0667881624671499,
+            0.0730630564420902,
+            0.0772153676471943,
+            0.0768815694664325,
+            0.0772987007741402,
+            0.0765686001679291,
+            0.0749309749136895,
+            0.0721865495667472,
+            0.0689189559863393,
+            0.0648623956919026,
+            0.0599040616210838,
+            0.0552629494040690,
+            0.0475407218497456,
+            0.0384337406899792,
+            0.0225146235151103,
         ]
-        dist = DistributionalValue(dirac_deltas=[
-            DiracDelta(position=position, mass=mass)
-            for position, mass in zip(
-                gumbel1MotherTTR16Positions,
-                gumbel1MotherTTR16Probabilities
-            )
-        ])
+        dist = DistributionalValue(
+            dirac_deltas=[
+                DiracDelta(position=position, mass=mass)
+                for position, mass in zip(
+                    gumbel1MotherTTR16Positions, gumbel1MotherTTR16Probabilities
+                )
+            ]
+        )
         self.assertTrue(dist.check_is_full_valid_TTR())
 
 
diff --git a/src/signaloid/distributional_information_plotting/plot_histogram_dirac_deltas.py b/src/signaloid/distributional_information_plotting/plot_histogram_dirac_deltas.py
index 027b533..5110306 100644
--- a/src/signaloid/distributional_information_plotting/plot_histogram_dirac_deltas.py
+++ b/src/signaloid/distributional_information_plotting/plot_histogram_dirac_deltas.py
@@ -18,15 +18,13 @@
 #   FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 #   DEALINGS IN THE SOFTWARE.
 
+from __future__ import annotations
 import sys
 import math
 
-if sys.implementation.name != 'circuitpython':
-    from typing import Optional
-
+if sys.implementation.name != "circuitpython":
     # Use numpy for accelerated computing
     import numpy as np
-    from numpy.typing import NDArray
 else:
     # Use the extended version of ulab's numpy when running on CircuitPython
     from signaloid.circuitpython.extended_ulab_numpy import np  # type: ignore[no-redef]
@@ -37,62 +35,57 @@
 
 class PlotData:
     def __init__(
-        self,
-        dist: DistributionalValue,
-        plotting_resolution: Optional[int] = None
+        self, dist: DistributionalValue, plotting_resolution: int | None = None
     ) -> None:
-        if (
-            dist.mean is None
-            or dist.UR_order == 0
-        ):
+        if dist.mean is None or dist.UR_order == 0:
             raise ValueError("Failed to load data")
 
         self.dist = dist
-        self.plotting_resolution: Optional[int] = plotting_resolution
-        self.plotting_ttr_order: Optional[int] = None
+        self.plotting_resolution: int | None = plotting_resolution
+        self.plotting_ttr_order: int | None = None
 
-        self._positions: NDArray[np.float64] = np.array([], dtype=np.float64)
-        self._masses: NDArray[np.float64] = np.array([], dtype=np.float64)
-        self._widths: NDArray[np.float64] = np.array([], dtype=np.float64)
-        self._max_value: Optional[float] = None
+        self._positions: np.ndarray = np.array([], dtype=np.float64)
+        self._masses: np.ndarray = np.array([], dtype=np.float64)
+        self._widths: np.ndarray = np.array([], dtype=np.float64)
+        self._max_value: float | None = None
 
         self._construct_plot_data()
 
     @property
-    def positions(self) -> NDArray[np.float64]:
+    def positions(self) -> np.ndarray:
         """The boundary positions list.
 
         :return: The boundary positions list.
-        :rtype: NDArray[np.float64]
+        :rtype: np.ndarray
         """
         return self._positions
 
     @positions.setter
-    def positions(self, positions: NDArray[np.float64]) -> None:
+    def positions(self, positions: np.ndarray) -> None:
         """Sets the boundary positions list, resetting the widths to avoid faulty
         values.
 
         :param positions: The boundary positions list to use
-        :type positions: NDArray[np.float64]
+        :type positions: np.ndarray
         """
         self._positions = positions
         self._widths = np.array([], dtype=np.float64)
 
     @property
-    def masses(self) -> NDArray[np.float64]:
+    def masses(self) -> np.ndarray:
         """The bin heights list.
 
         :return: The bin heights list.
-        :rtype: NDArray[np.float64]
+        :rtype: np.ndarray
         """
         return self._masses
 
     @masses.setter
-    def masses(self, masses: NDArray[np.float64]) -> None:
+    def masses(self, masses: np.ndarray) -> None:
         """Sets the bin heights list, resetting the max value to avoid faulty value.
 
         :param masses: The bin heights list to use.
-        :type masses: NDArray[np.float64]
+        :type masses: np.ndarray
         """
         self._masses = masses
         self._max_value = None
@@ -144,11 +137,11 @@ def max_value(self) -> float:
         return self._max_value
 
     @property
-    def widths(self) -> NDArray[np.float64]:
+    def widths(self) -> np.ndarray:
         """The widths list between each pair of positions.
 
         :return: The widths list.
-        :rtype: NDArray[np.float64]
+        :rtype: np.ndarray
         """
         if not self._widths.size > 0:
             self._widths = self.positions[1:] - self.positions[:-1]
@@ -159,8 +152,8 @@ def widths(self) -> NDArray[np.float64]:
     def _determine_boundary_positions(
         finite_sorted_dirac_deltas: list[DiracDelta],
         exponent: int,
-        use_ttr_binning: bool
-    ) -> tuple[NDArray[np.float64], NDArray[np.float64]]:
+        use_ttr_binning: bool,
+    ) -> tuple[np.ndarray, np.ndarray]:
         """
         If `use_ttr_binning` is true:
         Determines the internal boundary positions (and probabilities) using the
@@ -204,8 +197,7 @@ def _determine_boundary_positions(
             step = 2**n
             for i in range(2 ** (n + 1), number_of_boundaries - 1, 2 ** (n + 2)):
                 boundary_probabilities[i] = (
-                    boundary_probabilities[i - step]
-                    + boundary_probabilities[i + step]
+                    boundary_probabilities[i - step] + boundary_probabilities[i + step]
                 )
                 boundary_positions[i] = (
                     boundary_probabilities[i - step] * boundary_positions[i - step]
@@ -232,12 +224,12 @@ def _determine_boundary_positions(
     @staticmethod
     def _handle_extremal_bins(
         finite_sorted_dirac_deltas: list[DiracDelta],
-        boundary_positions: NDArray[np.float64],
-        boundary_probabilities: NDArray[np.float64],
-        bin_widths: NDArray[np.float64],
-        bin_heights: NDArray[np.float64],
+        boundary_positions: np.ndarray,
+        boundary_probabilities: np.ndarray,
+        bin_widths: np.ndarray,
+        bin_heights: np.ndarray,
         left: bool = True,
-    ) -> tuple[NDArray[np.float64], NDArray[np.float64], NDArray[np.float64]]:
+    ) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
         """
         Checking if (d/dx)^2 = 0 boundary condition has a solution.
         If not, falling back to the boundary condition d/dx = 0.
@@ -282,40 +274,35 @@ def _handle_extremal_bins(
                 elif any(roots_positive):
                     w0 = max(root1, root2)
 
-        if (
-            w0 is None
-            or math.isinf(det)
-            or math.isnan(det)
-        ):
+        if w0 is None or math.isinf(det) or math.isnan(det):
             # The boundary condition d/dx = 0.
-            boundary_positions[0 if left else -1] = (
-                boundary_positions[1 if left else -2]
-                + (-1 if left else 1) * (
-                    boundary_positions[2 if left else -2]
-                    - boundary_positions[1 if left else -3]
-                )
+            boundary_positions[0 if left else -1] = boundary_positions[
+                1 if left else -2
+            ] + (-1 if left else 1) * (
+                boundary_positions[2 if left else -2]
+                - boundary_positions[1 if left else -3]
             )
         else:
             # The boundary condition (d/dx)^2 = 0.
             boundary_positions[0 if left else -1] = (
-                boundary_positions[1 if left else -2]
-                + (-1 if left else 1) * w0
+                boundary_positions[1 if left else -2] + (-1 if left else 1) * w0
             )
 
         bin_widths[0 if left else -1] = (
             boundary_positions[1 if left else -1]
             - boundary_positions[0 if left else -2]
         )
-        averageHeight = (
-            finite_sorted_dirac_deltas[0 if left else -1].mass
-            / (bin_widths[0 if left else -1] + bin_widths[1 if left else -2])
+        averageHeight = finite_sorted_dirac_deltas[0 if left else -1].mass / (
+            bin_widths[0 if left else -1] + bin_widths[1 if left else -2]
         )
         bin_heights[0 if left else -1] = (
-            averageHeight * bin_widths[1 if left else -2]
+            averageHeight
+            * bin_widths[1 if left else -2]
             / bin_widths[0 if left else -1]
         )
         bin_heights[1 if left else -2] = (
-            averageHeight * bin_widths[0 if left else -1]
+            averageHeight
+            * bin_widths[0 if left else -1]
             / bin_widths[1 if left else -2]
         )
 
@@ -324,9 +311,9 @@ def _handle_extremal_bins(
     @staticmethod
     def _get_binning(
         finite_sorted_dirac_deltas: list[DiracDelta],
-        boundary_positions: NDArray[np.float64],
-        boundary_probabilities: NDArray[np.float64]
-    ) -> tuple[NDArray[np.float64], NDArray[np.float64], NDArray[np.float64]]:
+        boundary_positions: np.ndarray,
+        boundary_probabilities: np.ndarray,
+    ) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
         """
         Finds the binning for the given finite and sorted Dirac deltas and the
         calculated internal boundary positions and probabilities.
@@ -383,10 +370,10 @@ def _get_binning(
 
     @staticmethod
     def _create_binning(
-            finite_sorted_dirac_deltas: list[DiracDelta],
-            exponent: int,
-            use_ttr_binning: bool
-    ) -> tuple[NDArray[np.float64], NDArray[np.float64], NDArray[np.float64]]:
+        finite_sorted_dirac_deltas: list[DiracDelta],
+        exponent: int,
+        use_ttr_binning: bool,
+    ) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
         """
         - If `use_ttr_binning` is true:
             Creates a binning using the TTR binning method. The TTR binning method
@@ -411,7 +398,10 @@ def _create_binning(
                 bin widths, and bin heights that describe the output binning.
         """
 
-        boundary_positions, boundary_probabilities = PlotData._determine_boundary_positions(
+        (
+            boundary_positions,
+            boundary_probabilities,
+        ) = PlotData._determine_boundary_positions(
             finite_sorted_dirac_deltas, exponent, use_ttr_binning
         )
 
@@ -423,9 +413,7 @@ def _create_binning(
 
     @staticmethod
     def _bin_pdf_expected_dirac_delta(
-            boundary_positions: NDArray[np.float64],
-            bin_widths: NDArray[np.float64],
-            bin_heights: NDArray[np.float64]
+        boundary_positions: np.ndarray, bin_widths: np.ndarray, bin_heights: np.ndarray
     ) -> DiracDelta:
         """
         Computes the expected Dirac delta of an input bin PDF.
@@ -448,16 +436,18 @@ def _bin_pdf_expected_dirac_delta(
                 probability * (boundary_positions[i + 1] + boundary_positions[i]) / 2
             )
 
-        expected_dirac_delta = DiracDelta(moment_sum / probability_sum, mass=probability_sum)
+        expected_dirac_delta = DiracDelta(
+            moment_sum / probability_sum, mass=probability_sum
+        )
 
         return expected_dirac_delta
 
     @staticmethod
     def _bin_pdf_to_ttr(
-            boundary_positions: NDArray[np.float64],
-            bin_widths: NDArray[np.float64],
-            bin_heights: NDArray[np.float64],
-            order: int
+        boundary_positions: np.ndarray,
+        bin_widths: np.ndarray,
+        bin_heights: np.ndarray,
+        order: int,
     ) -> list[DiracDelta]:
         """
         Computes TTR for an input bin PDF.
@@ -480,12 +470,12 @@ def _bin_pdf_to_ttr(
         if order == 0:
             return [expected_dirac_delta]
 
-        low_boundary_positions: NDArray[np.float64] = np.array([], dtype=np.float64)
-        low_bin_widths: NDArray[np.float64] = np.array([], dtype=np.float64)
-        low_bin_heights: NDArray[np.float64] = np.array([], dtype=np.float64)
-        high_boundary_positions: NDArray[np.float64] = np.array([], dtype=np.float64)
-        high_bin_widths: NDArray[np.float64] = np.array([], dtype=np.float64)
-        high_bin_heights: NDArray[np.float64] = np.array([], dtype=np.float64)
+        low_boundary_positions: np.ndarray = np.array([], dtype=np.float64)
+        low_bin_widths: np.ndarray = np.array([], dtype=np.float64)
+        low_bin_heights: np.ndarray = np.array([], dtype=np.float64)
+        high_boundary_positions: np.ndarray = np.array([], dtype=np.float64)
+        high_bin_widths: np.ndarray = np.array([], dtype=np.float64)
+        high_bin_heights: np.ndarray = np.array([], dtype=np.float64)
 
         for i, boundary_position in enumerate(boundary_positions):
             if boundary_position == expected_dirac_delta.position:
@@ -544,7 +534,9 @@ def _construct_plot_data(self) -> None:
             return
 
         if len(finite_dirac_deltas) == 1:
-            self.positions = np.array([finite_dirac_deltas[0].position], dtype=np.float64)
+            self.positions = np.array(
+                [finite_dirac_deltas[0].position], dtype=np.float64
+            )
             self.masses = np.array([finite_dirac_deltas[0].mass], dtype=np.float64)
             return
 
@@ -558,9 +550,8 @@ def _construct_plot_data(self) -> None:
         log2_of_plotting_resolution = self.plotting_resolution.bit_length() - 1
         self.plotting_ttr_order = log2_of_plotting_resolution - 1
 
-        if (
-            self.plotting_resolution > 2
-            and self.plotting_resolution > 2 ** (self.plotting_ttr_order + 1)
+        if self.plotting_resolution > 2 and self.plotting_resolution > 2 ** (
+            self.plotting_ttr_order + 1
         ):
             raise ValueError(
                 "plot_histogram_dirac_deltas: plotting_resolution must be a power of 2!"
diff --git a/src/signaloid/distributional_information_plotting/plot_histogram_dirac_deltas_test.py b/src/signaloid/distributional_information_plotting/plot_histogram_dirac_deltas_test.py
index 3e1e288..8010b8d 100644
--- a/src/signaloid/distributional_information_plotting/plot_histogram_dirac_deltas_test.py
+++ b/src/signaloid/distributional_information_plotting/plot_histogram_dirac_deltas_test.py
@@ -24,7 +24,9 @@
 import numpy as np
 
 from signaloid.distributional.dirac_delta import DiracDelta
-from signaloid.distributional_information_plotting.plot_histogram_dirac_deltas import PlotData
+from signaloid.distributional_information_plotting.plot_histogram_dirac_deltas import (
+    PlotData,
+)
 
 
 class TestCreateBinning(unittest.TestCase):
@@ -55,8 +57,7 @@ def test_create_binning_property_dirac_deltas_average_of_bins(self) -> None:
 
             dirac_deltas = [
                 DiracDelta(position, mass=mass)
-                for position, mass in
-                zip(dirac_delta_positions, dirac_delta_masses)
+                for position, mass in zip(dirac_delta_positions, dirac_delta_masses)
             ]
             dirac_deltas.sort()
 
@@ -69,21 +70,26 @@ def test_create_binning_property_dirac_deltas_average_of_bins(self) -> None:
 
             for j in range(number_of_dirac_deltas[i]):
                 probability_under_first_bin = bin_widths[2 * j] * bin_heights[2 * j]
-                probability_under_second_bin = bin_widths[2 * j + 1] * bin_heights[2 * j + 1]
-                probability_under_bins = probability_under_first_bin + probability_under_second_bin
+                probability_under_second_bin = (
+                    bin_widths[2 * j + 1] * bin_heights[2 * j + 1]
+                )
+                probability_under_bins = (
+                    probability_under_first_bin + probability_under_second_bin
+                )
                 mean_of_first_bin = boundary_positions[2 * j] + bin_widths[2 * j] / 2
-                mean_of_second_bin = boundary_positions[2 * j + 1] + bin_widths[2 * j + 1] / 2
+                mean_of_second_bin = (
+                    boundary_positions[2 * j + 1] + bin_widths[2 * j + 1] / 2
+                )
                 mean_of_bins = (
-                    mean_of_first_bin * probability_under_first_bin +
-                    mean_of_second_bin * probability_under_second_bin
+                    mean_of_first_bin * probability_under_first_bin
+                    + mean_of_second_bin * probability_under_second_bin
                 ) / probability_under_bins
                 self.assertLess(
                     abs(input_ensemble[j].mass - probability_under_bins),
-                    probability_threshold
+                    probability_threshold,
                 )
                 self.assertLess(
-                    abs(input_ensemble[j].position - mean_of_bins),
-                    position_threshold
+                    abs(input_ensemble[j].position - mean_of_bins), position_threshold
                 )
 
     def test_create_binning_property_preserve_ttr(self) -> None:
@@ -103,24 +109,23 @@ def test_create_binning_property_preserve_ttr(self) -> None:
 
         for i in range(number_of_testcases):
             gaussian_mean = np.random.uniform(*gaussian_mean_range)
-            gaussian_standard_deviation = np.random.uniform(*gaussian_standard_deviation_range)
+            gaussian_standard_deviation = np.random.uniform(
+                *gaussian_standard_deviation_range
+            )
             dirac_delta_positions = np.random.normal(
                 gaussian_mean, gaussian_standard_deviation, number_of_samples
             )
-            dirac_delta_masses = [1/number_of_samples] * number_of_samples
+            dirac_delta_masses = [1 / number_of_samples] * number_of_samples
             ttr_order = random.sample(range(4, 11), 1)[0]
 
             input_dirac_deltas = [
                 DiracDelta(position, mass=mass)
-                for position, mass in
-                zip(dirac_delta_positions, dirac_delta_masses)
+                for position, mass in zip(dirac_delta_positions, dirac_delta_masses)
             ]
 
-            input_ttr_dirac_deltas = dirac_deltas_to_ttr(
-                input_dirac_deltas, ttr_order
-            )
+            input_ttr_dirac_deltas = dirac_deltas_to_ttr(input_dirac_deltas, ttr_order)
 
-            if len(input_ttr_dirac_deltas) != 2 ** ttr_order:
+            if len(input_ttr_dirac_deltas) != 2**ttr_order:
                 continue
             ttr_orders.append(ttr_order)
             input_ttrs.append(input_ttr_dirac_deltas)
@@ -133,33 +138,29 @@ def test_create_binning_property_preserve_ttr(self) -> None:
             )
 
             binning_dirac_deltas: list[DiracDelta] = []
-            for position, width, height in zip(boundary_positions[:-1], bin_widths, bin_heights):
-                binning_dirac_deltas.append(DiracDelta(
-                    position=position + width / 2,
-                    mass=width * height
-                ))
-
-            binning_ttr = dirac_deltas_to_ttr(
-                binning_dirac_deltas, exponent
-            )
+            for position, width, height in zip(
+                boundary_positions[:-1], bin_widths, bin_heights
+            ):
+                binning_dirac_deltas.append(
+                    DiracDelta(position=position + width / 2, mass=width * height)
+                )
+
+            binning_ttr = dirac_deltas_to_ttr(binning_dirac_deltas, exponent)
 
             self.assertEqual(len(input_ttr), len(binning_ttr))
 
             for input_ttr_dd, binning_ttr_dd in zip(input_ttr, binning_ttr):
                 self.assertLess(
-                    abs(input_ttr_dd.mass - binning_ttr_dd.mass),
-                    probability_threshold
+                    abs(input_ttr_dd.mass - binning_ttr_dd.mass), probability_threshold
                 )
                 self.assertLess(
                     abs(input_ttr_dd.position - binning_ttr_dd.position),
-                    position_threshold
+                    position_threshold,
                 )
 
 
 def dirac_deltas_to_ttr(
-    dirac_deltas: list[DiracDelta],
-    order: int,
-    count: int = 0
+    dirac_deltas: list[DiracDelta], order: int, count: int = 0
 ) -> list[DiracDelta]:
     """
     Computes the TTR for an input ensemble of Dirac deltas.
@@ -198,7 +199,9 @@ def dirac_deltas_to_ttr(
 
         current_dirac_delta = [DiracDelta(average_position, mass=total_mass)]
         low_dirac_deltas = [dd for dd in dirac_deltas if dd.position < average_position]
-        high_dirac_deltas = [dd for dd in dirac_deltas if dd.position >= average_position]
+        high_dirac_deltas = [
+            dd for dd in dirac_deltas if dd.position >= average_position
+        ]
 
     ttr: list[DiracDelta] = []
     if order > 0:
diff --git a/src/signaloid/distributional_information_plotting/plot_wrapper.py b/src/signaloid/distributional_information_plotting/plot_wrapper.py
index 3809d83..8911208 100644
--- a/src/signaloid/distributional_information_plotting/plot_wrapper.py
+++ b/src/signaloid/distributional_information_plotting/plot_wrapper.py
@@ -24,13 +24,12 @@
 import matplotlib
 import matplotlib.pyplot as plt
 
-from signaloid.distributional_information_plotting.plot_histogram_dirac_deltas import PlotData
+from signaloid.distributional_information_plotting.plot_histogram_dirac_deltas import (
+    PlotData,
+)
 
 
-def printv(
-        verbose: bool,
-        formatString: str,
-        *args) -> None:
+def printv(verbose: bool, formatString: str, *args) -> None:
     """
     A wrapper for `print()` that allows for controlled verbosity.
 
@@ -94,7 +93,9 @@ def plot(
         ncols=2 if plot_data.dist.has_special_values else 1,
         sharey=False,
         figsize=(10 + (3 if plot_data.dist.has_special_values else 0), 6),
-        gridspec_kw={"width_ratios": [4.2, 1]} if plot_data.dist.has_special_values else None,
+        gridspec_kw=(
+            {"width_ratios": [4.2, 1]} if plot_data.dist.has_special_values else None
+        ),
     )
 
     if not plot_data.dist.has_special_values:
@@ -111,11 +112,7 @@ def plot(
             text="",
             xy=(plot_data.positions[0], plot_data.masses[0]),
             xytext=(plot_data.positions[0], 0),
-            arrowprops={
-                "arrowstyle": "->",
-                "facecolor": "black",
-                "lw": 3
-            },
+            arrowprops={"arrowstyle": "->", "facecolor": "black", "lw": 3},
         )
     else:
         # Plot the binning.
@@ -126,7 +123,7 @@ def plot(
             align="edge",
             edgecolor="#33A333",
             facecolor="#33A333" + "40",
-            hatch="\\"
+            hatch="\\",
         )
 
     # Default kwargs for plt.annotate
@@ -157,11 +154,7 @@ def plot(
     if plot_data.dist.has_special_values:
         fig.sca(axes[1])
         plt.bar(
-            x=[
-                "NaN",
-                "-Inf",
-                "Inf"
-            ],
+            x=["NaN", "-Inf", "Inf"],
             height=[
                 plot_data.dist.nan_dirac_delta.mass,
                 plot_data.dist.neg_inf_dirac_delta.mass,
diff --git a/src/signaloid/distributional_information_plotting/plot_wrapper_test.py b/src/signaloid/distributional_information_plotting/plot_wrapper_test.py
index e9b262f..87edcd0 100644
--- a/src/signaloid/distributional_information_plotting/plot_wrapper_test.py
+++ b/src/signaloid/distributional_information_plotting/plot_wrapper_test.py
@@ -18,22 +18,21 @@
 #   FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 #   DEALINGS IN THE SOFTWARE.
 
+from __future__ import annotations
 import csv
 import os
 import shutil
 import tempfile
-from typing import Optional
 import unittest
-
 from signaloid.distributional.distributional import DistributionalValue
-from signaloid.distributional_information_plotting.plot_histogram_dirac_deltas import PlotData
+from signaloid.distributional_information_plotting.plot_histogram_dirac_deltas import (
+    PlotData,
+)
 
 from .plot_wrapper import plot
 
 
-def read_ux_strings_from_csv(
-    csv_filename: str
-) -> Optional[list[str]]:
+def read_ux_strings_from_csv(csv_filename: str) -> list[str] | None:
     """
     Reads Ux strings from a csv file
 
@@ -43,7 +42,7 @@ def read_ux_strings_from_csv(
         ux_strings: list of Ux strings
     """
     ux_strings: list[str] = []
-    with open(csv_filename, 'r') as csvfile:
+    with open(csv_filename, "r") as csvfile:
         reader = csv.reader(csvfile)
         for row in reader:
             ux_strings.append(row[0])
@@ -62,7 +61,7 @@ def tearDown(self) -> None:
 
     def test_plot_wrapper(
         self,
-        input_filename: str = "src/signaloid/distributional/test_ux_value_pairs.csv"
+        input_filename: str = "src/signaloid/distributional/test_ux_value_pairs.csv",
     ) -> None:
         """
         Test parsing and plotting Ux Strings
@@ -85,9 +84,11 @@ def test_plot_wrapper(
             plot_data = PlotData(distValue)
             self.assertIsNotNone(plot_data, "Failed to parse data")
 
-            filepath = os.path.join(self.test_dir, f'file{i}.png')
+            filepath = os.path.join(self.test_dir, f"file{i}.png")
             plot(plot_data, path=filepath, save=True)
-            self.assertTrue(os.path.exists(filepath), f"File was not created: {filepath}")
+            self.assertTrue(
+                os.path.exists(filepath), f"File was not created: {filepath}"
+            )
 
 
 if __name__ == "__main__":
diff --git a/src/signaloid/uxdata_toolkit.py b/src/signaloid/uxdata_toolkit.py
index f811715..553756e 100644
--- a/src/signaloid/uxdata_toolkit.py
+++ b/src/signaloid/uxdata_toolkit.py
@@ -38,15 +38,16 @@
 import matplotlib.pyplot as plt
 
 from signaloid.distributional.distributional import DistributionalValue
-from signaloid.distributional_information_plotting.plot_histogram_dirac_deltas import \
-    PlotData
+from signaloid.distributional_information_plotting.plot_histogram_dirac_deltas import (
+    PlotData,
+)
 from signaloid.distributional_information_plotting.plot_wrapper import plot
 
 
 def parse_arguments() -> argparse.Namespace:
     # Create the parser
     parser = argparse.ArgumentParser(
-        description='Set of tools for working with Signaloid Ux data.'
+        description="Set of tools for working with Signaloid Ux data."
     )
 
     command_subparsers = parser.add_subparsers(
@@ -73,18 +74,19 @@ def command_plot_parser(command_subparsers: Any) -> None:
   %(prog)s 0.40007Ux0000000000000000013FD99AC12423C7C7000000013FD99AC12423C7C78000000000000000
   %(prog)s 09168733bf9ad93f000100000000000000c7c72324c19ad93f01000000c7c72324c19ad93f0000000000000080
   %(prog)s -o output.png 0.40007Ux0000000000000000013FD99AC12423C7C7000000013FD99AC12423C7C78000000000000000
-        """
+        """,
     )
 
     plot_parser.add_argument(
-        '-o', '--output',
+        "-o",
+        "--output",
         type=str,
-        default='plot.png',
-        help='Output PNG filename (default: plot.png)'
+        default="plot.png",
+        help="Output PNG filename (default: plot.png)",
     )
 
     plot_parser.add_argument(
-        'ux_data',
+        "ux_data",
         type=str,
         help='Ux-string or Ux-bytes to plot (e.g., "90.6Ux04000000...")',
     )
@@ -154,14 +156,14 @@ def command_plot(args: argparse.Namespace) -> None:
         plot_data = PlotData(dist_value)
 
         # Set matplotlib to non-interactive backend for saving
-        matplotlib.use('Agg')
+        matplotlib.use("Agg")
 
         # Plot the distribution using the plot wrapper function
         print("Generating plot...")
         plot(plot_data)
 
         # Save the figure to file
-        plt.savefig(args.output, dpi=300, bbox_inches='tight')
+        plt.savefig(args.output, dpi=300, bbox_inches="tight")
         print(f"✓ Plot saved to: {args.output}")
     except Exception as e:
         print(f"\nError parsing or plotting Ux-data: {e}")

From 9aae2bddc3981ac2d320cc7c1d06b49a6af21d20 Mon Sep 17 00:00:00 2001
From: tfotakis-signaloid
 <213429317+tfotakis-signaloid@users.noreply.github.com>
Date: Wed, 18 Feb 2026 18:14:17 +0200
Subject: [PATCH 2/2] Updated to version `1.7.2`

---
 poetry.lock                                      |  8 ++++----
 pyproject.toml                                   |  2 +-
 .../plot_wrapper.py                              | 16 ++++++++--------
 3 files changed, 13 insertions(+), 13 deletions(-)

diff --git a/poetry.lock b/poetry.lock
index 48016ff..261d7a3 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -798,15 +798,15 @@ tests = ["pytest (>=9)", "typing-extensions (>=4.15)"]
 
 [[package]]
 name = "pex"
-version = "2.90.0"
+version = "2.90.1"
 description = "The PEX packaging toolchain."
 optional = false
 python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*,<3.16,>=2.7"
 groups = ["dev"]
 files = [
-    {file = "pex-2.90.0-py2.py35.py36.py37.py38.py39.py310.py311-none-any.whl", hash = "sha256:212356e1feb4ffd0977dde04e872ecefe99d8fef99688f77e7fd43c5c9ca9545"},
-    {file = "pex-2.90.0-py3.py312-none-any.whl", hash = "sha256:99cc9603e3e56e9a166dd1d051ecedd6170cb1c377d5aa6dfddf7bde41ba7b18"},
-    {file = "pex-2.90.0.tar.gz", hash = "sha256:1411041eedf7d162be894ca9201d0115f012182906e93c5818ce669dc229bc9f"},
+    {file = "pex-2.90.1-py2.py35.py36.py37.py38.py39.py310.py311-none-any.whl", hash = "sha256:fb26165ae3e4260008e8058d2752b1a8d4e3a6085402682ec82246c439c1910a"},
+    {file = "pex-2.90.1-py3.py312-none-any.whl", hash = "sha256:c80aa4144bafd126f619d578673df98bd11f12fe707d587427f746660b7dac2b"},
+    {file = "pex-2.90.1.tar.gz", hash = "sha256:cbb9ebf6408bdc8112f4ad27914bd1cf90850ca960fe7af5f55f28c6807bae34"},
 ]
 
 [package.extras]
diff --git a/pyproject.toml b/pyproject.toml
index 6bace64..d081532 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,6 +1,6 @@
 [tool.poetry]
 name = "signaloid"
-version = "1.7.1"
+version = "1.7.2"
 description = ""
 authors = [
 	"Signaloid <info@signaloid.com>"
diff --git a/src/signaloid/distributional_information_plotting/plot_wrapper.py b/src/signaloid/distributional_information_plotting/plot_wrapper.py
index 8911208..ec6b68a 100644
--- a/src/signaloid/distributional_information_plotting/plot_wrapper.py
+++ b/src/signaloid/distributional_information_plotting/plot_wrapper.py
@@ -18,9 +18,9 @@
 #   FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 #   DEALINGS IN THE SOFTWARE.
 
+from __future__ import annotations
 import math
-from typing import Any, Optional, Union
-
+from typing import Any
 import matplotlib
 import matplotlib.pyplot as plt
 
@@ -49,12 +49,12 @@ def plot(
     no_special_y: bool = False,
     save: bool = False,
     verbose: bool = False,
-    x_lim: Optional[tuple[float, float]] = None,
-    y_lim: Optional[tuple[float, float]] = None,
-    x_label: Optional[str] = None,
-    x_tick_label_rotation: Optional[float] = None,
+    x_lim: tuple[float, float] | None = None,
+    y_lim: tuple[float, float] | None = None,
+    x_label: str | None = None,
+    x_tick_label_rotation: float | None = None,
     font_size: int = 20,
-    matplotlib_rc_params_override: Optional[dict[str, str]] = None,
+    matplotlib_rc_params_override: dict[str, str] | None = None,
 ) -> bool:
     """
     Args:
@@ -75,7 +75,7 @@ def plot(
         `True` if successful, `False` else.
     """
 
-    matplotlib_rcParams_update_defaults: dict[str, Union[int, str, bool]] = {
+    matplotlib_rcParams_update_defaults: dict[str, int | str | bool] = {
         "font.size": font_size,
         "figure.facecolor": "FFFFFF30",
         "axes.facecolor": "FFFFFF30",