[pre-commit.ci] pre-commit autoupdate (#11322)

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

updates:
- [github.com/astral-sh/ruff-pre-commit: v0.2.2 → v0.3.2](https://github.com/astral-sh/ruff-pre-commit/compare/v0.2.2...v0.3.2)
- [github.com/pre-commit/mirrors-mypy: v1.8.0 → v1.9.0](https://github.com/pre-commit/mirrors-mypy/compare/v1.8.0...v1.9.0)

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

machine_learning/linear_discriminant_analysis.py

@@ -1,47 +1,48 @@
 """
-    Linear Discriminant Analysis
+Linear Discriminant Analysis
 
 
 
-    Assumptions About Data :
-        1. The input variables has a gaussian distribution.
-        2. The variance calculated for each input variables by class grouping is the
-           same.
-        3. The mix of classes in your training set is representative of the problem.
+Assumptions About Data :
+    1. The input variables has a gaussian distribution.
+    2. The variance calculated for each input variables by class grouping is the
+       same.
+    3. The mix of classes in your training set is representative of the problem.
 
 
-    Learning The Model :
-        The LDA model requires the estimation of statistics from the training data :
-            1. Mean of each input value for each class.
-            2. Probability of an instance belong to each class.
-            3. Covariance for the input data for each class
+Learning The Model :
+    The LDA model requires the estimation of statistics from the training data :
+        1. Mean of each input value for each class.
+        2. Probability of an instance belong to each class.
+        3. Covariance for the input data for each class
 
-        Calculate the class means :
-            mean(x) = 1/n ( for i = 1 to i = n --> sum(xi))
+    Calculate the class means :
+        mean(x) = 1/n ( for i = 1 to i = n --> sum(xi))
 
-        Calculate the class probabilities :
-            P(y = 0) = count(y = 0) / (count(y = 0) + count(y = 1))
-            P(y = 1) = count(y = 1) / (count(y = 0) + count(y = 1))
+    Calculate the class probabilities :
+        P(y = 0) = count(y = 0) / (count(y = 0) + count(y = 1))
+        P(y = 1) = count(y = 1) / (count(y = 0) + count(y = 1))
 
-        Calculate the variance :
-            We can calculate the variance for dataset in two steps :
-                1. Calculate the squared difference for each input variable from the
-                   group mean.
-                2. Calculate the mean of the squared difference.
-                ------------------------------------------------
-                Squared_Difference = (x - mean(k)) ** 2
-                Variance = (1 / (count(x) - count(classes))) *
-                    (for i = 1 to i = n --> sum(Squared_Difference(xi)))
+    Calculate the variance :
+        We can calculate the variance for dataset in two steps :
+            1. Calculate the squared difference for each input variable from the
+               group mean.
+            2. Calculate the mean of the squared difference.
+            ------------------------------------------------
+            Squared_Difference = (x - mean(k)) ** 2
+            Variance = (1 / (count(x) - count(classes))) *
+                (for i = 1 to i = n --> sum(Squared_Difference(xi)))
 
-    Making Predictions :
-        discriminant(x) = x * (mean / variance) -
-            ((mean ** 2) / (2 * variance)) + Ln(probability)
-        ---------------------------------------------------------------------------
-        After calculating the discriminant value for each class, the class with the
-        largest discriminant value is taken as the prediction.
+Making Predictions :
+    discriminant(x) = x * (mean / variance) -
+        ((mean ** 2) / (2 * variance)) + Ln(probability)
+    ---------------------------------------------------------------------------
+    After calculating the discriminant value for each class, the class with the
+    largest discriminant value is taken as the prediction.
 
-    Author: @EverLookNeverSee
+Author: @EverLookNeverSee
 """
+
 from collections.abc import Callable
 from math import log
 from os import name, system