From 45aaf49cb3fe07b006316bacac1318f07a08cc19 Mon Sep 17 00:00:00 2001
From: Thomas Albers Raviola <thomas@thomaslabs.org>
Date: Tue, 14 May 2024 11:13:31 +0200
Subject: * Initial commit

---
 README.md       |  0
 solvers.py      | 20 ++++++++++++++++++++
 test_solvers.py | 54 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 74 insertions(+)
 create mode 100644 README.md
 create mode 100644 solvers.py
 create mode 100644 test_solvers.py

diff --git a/README.md b/README.md
new file mode 100644
index 0000000..e69de29
diff --git a/solvers.py b/solvers.py
new file mode 100644
index 0000000..7aa9568
--- /dev/null
+++ b/solvers.py
@@ -0,0 +1,20 @@
+"""Routines for solving a linear system of equations."""
+
+import numpy as np
+from numpy.typing import NDArray
+
+
+def gaussian_eliminate(aa: NDArray[np.float_], bb: NDArray[np.float_]) -> NDArray[np.float_] | None:
+    """Solves a linear system of equations (Ax = b) by Gauss-elimination
+
+    Args:
+        aa: Matrix with the coefficients. Shape: (n, n).
+        bb: Right hand side of the equation. Shape: (n,)
+
+    Returns:
+        Vector xx with the solution of the linear equation or None
+        if the equations are linearly dependent.
+    """
+    nn = aa.shape[0]
+    xx = np.zeros((nn,), dtype=np.float_)
+    return xx
diff --git a/test_solvers.py b/test_solvers.py
new file mode 100644
index 0000000..ad37c8c
--- /dev/null
+++ b/test_solvers.py
@@ -0,0 +1,54 @@
+#!/usr/bin/env python3
+"""Contains routines to test the solvers module"""
+
+import numpy as np
+from numpy.typing import NDArray
+import solvers
+
+
+def main() -> None:
+    """Main testing function."""
+
+    print("\nTest elimination")
+    test_elimination_3()
+    print("\nTest pivot")
+    test_pivot_3()
+    print("\nTest linear dependency")
+    test_lindep_3()
+
+
+def test_elimination_3() -> None:
+    """Tests elimination with 3 variables."""
+    aa = np.array([[2.0, 4.0, 4.0], [5.0, 4.0, 2.0], [1.0, 2.0, -1.0]], dtype=np.float_)
+    bb = np.array([1.0, 4.0, 2.0], dtype=np.float_)
+    xx_expected = np.array([0.666666666666667, 0.416666666666667, -0.5], dtype=np.float_)
+    xx_gauss = solvers.gaussian_eliminate(aa, bb)
+    _check_result(xx_expected, xx_gauss)
+
+
+def test_pivot_3() -> None:
+    """Tests a solution with 3 variables, where pivot is necessary."""
+    aa = np.array([[2.0, 4.0, 4.0], [1.0, 2.0, -1.0], [5.0, 4.0, 2.0]])
+    bb = np.array([1.0, 2.0, 4.0])
+    xx_expected = np.array([0.666666666666667, 0.416666666666667, -0.5])
+    xx_gauss = solvers.gaussian_eliminate(aa, bb)
+    _check_result(xx_expected, xx_gauss)
+
+
+def test_lindep_3() -> None:
+    """Tests a linearly dependent system wit three variables."""
+    aa = np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0], [7.0, 8.0, 9.0]])
+    bb = np.array([1.0, 2.0, 3.0])
+    xx_expected = None
+    xx_gauss = solvers.gaussian_eliminate(aa, bb)
+    _check_result(xx_expected, xx_gauss)
+
+
+def _check_result(expected: NDArray[np.float_] | None, obtained: NDArray[np.float_] | None) -> None:
+    """Checks results by printing expected and obtained one."""
+    print("Expected:", expected)
+    print("Obtained:", obtained)
+
+
+if __name__ == "__main__":
+    main()
-- 
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