Added LU decomposition algorthim

Author: sourav-625

src/main/java/com/thealgorithms/matrix/LUDecomposition.java

@@ -85,19 +85,4 @@ public static void printMatrix(double[][] m) {
             System.out.println("]");
         }
     }
-
-    /**
-     * Demonstration (doctest)
-     */
-    public static void main(String[] args) {
-        double[][] a = {{2, -1, -2}, {-4, 6, 3}, {-4, -2, 8}};
-
-        LU result = decompose(a);
-
-        System.out.println("l matrix:");
-        printMatrix(result.l);
-
-        System.out.println("\nu matrix:");
-        printMatrix(result.u);
-    }
 }

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

@@ -0,0 +1,43 @@
+package com.thealgorithms.matrix;
+
+import static org.junit.jupiter.api.Assertions.assertArrayEquals;
+
+import org.junit.jupiter.api.Test;
+
+public class LUDecompositionTest {
+
+    @Test
+    public void testLUDecomposition() {
+        double[][] A = {
+            {4, 3},
+            {6, 3}
+        };
+
+        // Perform LU decomposition
+        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);
+
+        // 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];
+        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];
+                }
+            }
+        }
+        return C;
+    }
+}