Remove separate directory for gaussian_elimination_pivoting.py (#11445)

* updating DIRECTORY.md

* Remove separate directory for gaussian_elimination_pivoting.py

Delete the directory linear_algebra/src/gaussian_elimination_pivoting/
and move its algorithm file, gaussian_elimination_pivoting.py, into the
parent src/ directory. The gaussian_elimination_pivoting/ directory only
exists because gaussian_elimination_pivoting.py reads an example numpy
array from matrix.txt, but this input file and IO operation is entirely
unnecessary because gaussian_elimination_pivoting.py already has the
exact same array hard-coded into a variable.

* updating DIRECTORY.md

---------

Co-authored-by: tianyizheng02 <tianyizheng02@users.noreply.github.com>

DIRECTORY.md

@@ -540,8 +540,7 @@
   * [Lu Decomposition](linear_algebra/lu_decomposition.py)
   * Src
     * [Conjugate Gradient](linear_algebra/src/conjugate_gradient.py)
-    * Gaussian Elimination Pivoting
-      * [Gaussian Elimination Pivoting](linear_algebra/src/gaussian_elimination_pivoting/gaussian_elimination_pivoting.py)
+    * [Gaussian Elimination Pivoting](linear_algebra/src/gaussian_elimination_pivoting.py)
     * [Lib](linear_algebra/src/lib.py)
     * [Polynom For Points](linear_algebra/src/polynom_for_points.py)
     * [Power Iteration](linear_algebra/src/power_iteration.py)

linear_algebra/src/gaussian_elimination_pivoting.py

@@ -1,15 +1,5 @@
 import numpy as np
 
-matrix = np.array(
-    [
-        [5.0, -5.0, -3.0, 4.0, -11.0],
-        [1.0, -4.0, 6.0, -4.0, -10.0],
-        [-2.0, -5.0, 4.0, -5.0, -12.0],
-        [-3.0, -3.0, 5.0, -5.0, 8.0],
-    ],
-    dtype=float,
-)
-
 
 def solve_linear_system(matrix: np.ndarray) -> np.ndarray:
     """
@@ -87,15 +77,18 @@ def solve_linear_system(matrix: np.ndarray) -> np.ndarray:
 
 if __name__ == "__main__":
     from doctest import testmod
-    from pathlib import Path
 
     testmod()
-    file_path = Path(__file__).parent / "matrix.txt"
-    try:
-        matrix = np.loadtxt(file_path)
-    except FileNotFoundError:
-        print(f"Error: {file_path} not found.  Using default matrix instead.")
 
-    # Example usage:
-    print(f"Matrix:\n{matrix}")
-    print(f"{solve_linear_system(matrix) = }")
+    example_matrix = np.array(
+        [
+            [5.0, -5.0, -3.0, 4.0, -11.0],
+            [1.0, -4.0, 6.0, -4.0, -10.0],
+            [-2.0, -5.0, 4.0, -5.0, -12.0],
+            [-3.0, -3.0, 5.0, -5.0, 8.0],
+        ],
+        dtype=float,
+    )
+
+    print(f"Matrix:\n{example_matrix}")
+    print(f"{solve_linear_system(example_matrix) = }")

linear_algebra/src/gaussian_elimination_pivoting/matrix.txt

@@ -1,4 +0,0 @@
-5.0 -5.0 -3.0 4.0 -11.0
-1.0 -4.0 6.0 -4.0 -10.0
--2.0 -5.0 4.0 -5.0 -12.0
--3.0 -3.0 5.0 -5.0 8.0