Rename variables

Author: 99991

maths/cholesky_decomposition.py

@@ -1,7 +1,7 @@
 import numpy as np
 
 
-def cholesky_decomposition(a: np.ndarray) -> np.ndarray:
+def cholesky_decomposition(matrix: np.ndarray) -> np.ndarray:
     """Return a Cholesky decomposition of the matrix A.
 
     The Cholesky decomposition decomposes the square, positive definite matrix A
@@ -42,11 +42,13 @@ def cholesky_decomposition(a: np.ndarray) -> np.ndarray:
     True
     """
 
-    assert a.shape[0] == a.shape[1], f"Matrix A is not square, {a.shape=}"
-    assert np.allclose(a, a.T), "Matrix A must be symmetric"
+    assert (
+        matrix.shape[0] == matrix.shape[1]
+    ), f"Input matrix is not square, {matrix.shape=}"
+    assert np.allclose(matrix, matrix.T), "Input matrix must be symmetric"
 
-    n = a.shape[0]
-    lower_triangle = np.tril(a)
+    n = matrix.shape[0]
+    lower_triangle = np.tril(matrix)
 
     for i in range(n):
         for j in range(i + 1):
@@ -65,9 +67,13 @@ def cholesky_decomposition(a: np.ndarray) -> np.ndarray:
     return lower_triangle
 
 
-def solve_cholesky(lower_triangle: np.ndarray, y: np.ndarray) -> np.ndarray:
+def solve_cholesky(
+    lower_triangle: np.ndarray,
+    right_hand_side: np.ndarray,
+) -> np.ndarray:
     """Given a Cholesky decomposition L L^T = A of a matrix A, solve the
-    system of equations A X = Y where Y is either a matrix or a vector.
+    system of equations A X = Y where the right-hand side Y is either
+    a matrix or a vector.
 
     >>> L = np.array([[2, 0], [3, 4]], dtype=float)
     >>> Y = np.array([[22, 54], [81, 193]], dtype=float)
@@ -84,13 +90,13 @@ def solve_cholesky(lower_triangle: np.ndarray, y: np.ndarray) -> np.ndarray:
     ), "Matrix L is not lower triangular"
 
     # Handle vector case by reshaping to matrix and then flattening again
-    if len(y.shape) == 1:
-        return solve_cholesky(lower_triangle, y.reshape(-1, 1)).ravel()
+    if len(right_hand_side.shape) == 1:
+        return solve_cholesky(lower_triangle, right_hand_side.reshape(-1, 1)).ravel()
 
-    n = y.shape[0]
+    n = right_hand_side.shape[0]
 
-    # Solve L W = B for W
-    w = y.copy()
+    # Solve L W = Y for W
+    w = right_hand_side.copy()
     for i in range(n):
         for j in range(i):
             w[i] -= lower_triangle[i, j] * w[j]