Added LU decomposition algorthim

Author: sourav-625

src/test/java/com/thealgorithms/matrix/LUDecompositionTest.java

@@ -8,33 +8,33 @@ public class LUDecompositionTest {
 
     @Test
     public void testLUDecomposition() {
-        double[][] A = {{4, 3}, {6, 3}};
+        double[][] a = {{4, 3}, {6, 3}};
 
         // Perform LU decomposition
-        LUDecomposition.LU lu = LUDecomposition.decompose(A);
-        double[][] L = lu.l;
-        double[][] U = lu.u;
+        LUDecomposition.LU lu = LUDecomposition.decompose(a);
+        double[][] l = lu.l;
+        double[][] u = lu.u;
 
-        // Reconstruct A from L and U
-        double[][] reconstructed = multiplyMatrices(L, U);
+        // Reconstruct a from l and u
+        double[][] reconstructed = multiplyMatrices(l, u);
 
-        // Assert that reconstructed matrix matches original A
-        for (int i = 0; i < A.length; i++) {
-            assertArrayEquals(A[i], reconstructed[i], 1e-9);
+        // Assert that reconstructed matrix matches original a
+        for (int i = 0; i < a.length; i++) {
+            assertArrayEquals(a[i], reconstructed[i], 1e-9);
         }
     }
 
     // Helper method to multiply two matrices
-    private double[][] multiplyMatrices(double[][] A, double[][] B) {
-        int n = A.length;
-        double[][] C = new double[n][n];
+    private double[][] multiplyMatrices(double[][] a, double[][] b) {
+        int n = a.length;
+        double[][] c = new double[n][n];
         for (int i = 0; i < n; i++) {
             for (int j = 0; j < n; j++) {
                 for (int k = 0; k < n; k++) {
-                    C[i][j] += A[i][k] * B[k][j];
+                    c[i][j] += a[i][k] * b[k][j];
                 }
             }
         }
-        return C;
+        return c;
     }
 }