[pre-commit.ci] pre-commit autoupdate -- ruff 2025 stable format (#12521)

* [pre-commit.ci] pre-commit autoupdate

updates:
- [github.com/astral-sh/ruff-pre-commit: v0.8.6 → v0.9.1](https://github.com/astral-sh/ruff-pre-commit/compare/v0.8.6...v0.9.1)

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update maths/dual_number_automatic_differentiation.py

* Update maths/dual_number_automatic_differentiation.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update dual_number_automatic_differentiation.py

* Update dual_number_automatic_differentiation.py

* No <fin-streamer> tag with the specified data-test attribute found.

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

machine_learning/linear_discriminant_analysis.py

@@ -322,7 +322,7 @@ def main():
             user_count = valid_input(
                 input_type=int,
                 condition=lambda x: x > 0,
-                input_msg=(f"Enter The number of instances for class_{i+1}: "),
+                input_msg=(f"Enter The number of instances for class_{i + 1}: "),
                 err_msg="Number of instances should be positive!",
             )
             counts.append(user_count)
@@ -333,7 +333,7 @@ def main():
         for a in range(n_classes):
             user_mean = valid_input(
                 input_type=float,
-                input_msg=(f"Enter the value of mean for class_{a+1}: "),
+                input_msg=(f"Enter the value of mean for class_{a + 1}: "),
                 err_msg="This is an invalid value.",
             )
             user_means.append(user_mean)