* Initial commit

3 files changed, 74 insertions, 0 deletions

diff --git a/README.md b/README.md
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+++ b/README.md
diff --git a/solvers.py b/solvers.py
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+"""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
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+#!/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()