Add matrix multiplication with double[][] and unit tests (#6417)

* MatrixMultiplication.java created and updated.

* Add necessary comment to MatrixMultiplication.java

* Create MatrixMultiplicationTest.java

* method for 2 by 2 matrix multiplication is created

* Use assertMatrixEquals(), otherwise there can be error due to floating point arithmetic errors

* assertMatrixEquals method created and updated

* method created for 3by2 matrix multiply with 2by1 matrix

* method created for null matrix multiplication

* method for test matrix dimension error

* method for test empty matrix input

* testMultiply3by2and2by1 test case updated

* Check for empty matrices part updated

* Updated Unit test coverage

* files updated

* clean the code

* clean the code

* Updated files with google-java-format

* Updated files

* Updated files

* Updated files

* Updated files

* Add reference links and complexities

* Add test cases for 1by1 matrix and non-rectangular matrix

* Add reference links and complexities

---------

Co-authored-by: Deniz Altunkapan <93663085+DenizAltunkapan@users.noreply.github.com>

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

@@ -0,0 +1,69 @@
+package com.thealgorithms.matrix;
+
+/**
+ * This class provides a method to perform matrix multiplication.
+ *
+ * <p>Matrix multiplication takes two 2D arrays (matrices) as input and
+ * produces their product, following the mathematical definition of
+ * matrix multiplication.
+ *
+ * <p>For more details:
+ * https://www.geeksforgeeks.org/java/java-program-to-multiply-two-matrices-of-any-size/
+ * https://en.wikipedia.org/wiki/Matrix_multiplication
+ *
+ * <p>Time Complexity: O(n^3) – where n is the dimension of the matrices
+ * (assuming square matrices for simplicity).
+ *
+ * <p>Space Complexity: O(n^2) – for storing the result matrix.
+ *
+ *
+ * @author Nishitha Wihala Pitigala
+ *
+ */
+
+public final class MatrixMultiplication {
+    private MatrixMultiplication() {
+    }
+
+    /**
+     * Multiplies two matrices.
+     *
+     * @param matrixA the first matrix rowsA x colsA
+     * @param matrixB the second matrix rowsB x colsB
+     * @return the product of the two matrices rowsA x colsB
+     * @throws IllegalArgumentException if the matrices cannot be multiplied
+     */
+    public static double[][] multiply(double[][] matrixA, double[][] matrixB) {
+        // Check the input matrices are not null
+        if (matrixA == null || matrixB == null) {
+            throw new IllegalArgumentException("Input matrices cannot be null");
+        }
+
+        // Check for empty matrices
+        if (matrixA.length == 0 || matrixB.length == 0 || matrixA[0].length == 0 || matrixB[0].length == 0) {
+            throw new IllegalArgumentException("Input matrices must not be empty");
+        }
+
+        // Validate the matrix dimensions
+        if (matrixA[0].length != matrixB.length) {
+            throw new IllegalArgumentException("Matrices cannot be multiplied: incompatible dimensions.");
+        }
+
+        int rowsA = matrixA.length;
+        int colsA = matrixA[0].length;
+        int colsB = matrixB[0].length;
+
+        // Initialize the result matrix with zeros
+        double[][] result = new double[rowsA][colsB];
+
+        // Perform matrix multiplication
+        for (int i = 0; i < rowsA; i++) {
+            for (int j = 0; j < colsB; j++) {
+                for (int k = 0; k < colsA; k++) {
+                    result[i][j] += matrixA[i][k] * matrixB[k][j];
+                }
+            }
+        }
+        return result;
+    }
+}

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

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+package com.thealgorithms.matrix;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import org.junit.jupiter.api.Test;
+
+public class MatrixMultiplicationTest {
+
+    private static final double EPSILON = 1e-9; // for floating point comparison
+
+    @Test
+    void testMultiply1by1() {
+        double[][] matrixA = {{1.0}};
+        double[][] matrixB = {{2.0}};
+        double[][] expected = {{2.0}};
+
+        double[][] result = MatrixMultiplication.multiply(matrixA, matrixB);
+        assertMatrixEquals(expected, result);
+    }
+
+    @Test
+    void testMultiply2by2() {
+        double[][] matrixA = {{1.0, 2.0}, {3.0, 4.0}};
+        double[][] matrixB = {{5.0, 6.0}, {7.0, 8.0}};
+        double[][] expected = {{19.0, 22.0}, {43.0, 50.0}};
+
+        double[][] result = MatrixMultiplication.multiply(matrixA, matrixB);
+        assertMatrixEquals(expected, result); // Use custom method due to floating point issues
+    }
+
+    @Test
+    void testMultiply3by2and2by1() {
+        double[][] matrixA = {{1.0, 2.0}, {3.0, 4.0}, {5.0, 6.0}};
+        double[][] matrixB = {{7.0}, {8.0}};
+        double[][] expected = {{23.0}, {53.0}, {83.0}};
+
+        double[][] result = MatrixMultiplication.multiply(matrixA, matrixB);
+        assertMatrixEquals(expected, result);
+    }
+
+    @Test
+    void testMultiplyNonRectangularMatrices() {
+        double[][] matrixA = {{1.0, 2.0, 3.0}, {4.0, 5.0, 6.0}};
+        double[][] matrixB = {{7.0, 8.0}, {9.0, 10.0}, {11.0, 12.0}};
+        double[][] expected = {{58.0, 64.0}, {139.0, 154.0}};
+
+        double[][] result = MatrixMultiplication.multiply(matrixA, matrixB);
+        assertMatrixEquals(expected, result);
+    }
+
+    @Test
+    void testNullMatrixA() {
+        double[][] b = {{1, 2}, {3, 4}};
+        assertThrows(IllegalArgumentException.class, () -> MatrixMultiplication.multiply(null, b));
+    }
+
+    @Test
+    void testNullMatrixB() {
+        double[][] a = {{1, 2}, {3, 4}};
+        assertThrows(IllegalArgumentException.class, () -> MatrixMultiplication.multiply(a, null));
+    }
+
+    @Test
+    void testMultiplyNull() {
+        double[][] matrixA = {{1.0, 2.0}, {3.0, 4.0}};
+        double[][] matrixB = null;
+
+        Exception exception = assertThrows(IllegalArgumentException.class, () -> MatrixMultiplication.multiply(matrixA, matrixB));
+
+        String expectedMessage = "Input matrices cannot be null";
+        String actualMessage = exception.getMessage();
+
+        assertTrue(actualMessage.contains(expectedMessage));
+    }
+
+    @Test
+    void testIncompatibleDimensions() {
+        double[][] a = {{1.0, 2.0}};
+        double[][] b = {{1.0, 2.0}};
+        assertThrows(IllegalArgumentException.class, () -> MatrixMultiplication.multiply(a, b));
+    }
+
+    @Test
+    void testEmptyMatrices() {
+        double[][] a = new double[0][0];
+        double[][] b = new double[0][0];
+        assertThrows(IllegalArgumentException.class, () -> MatrixMultiplication.multiply(a, b));
+    }
+
+    private void assertMatrixEquals(double[][] expected, double[][] actual) {
+        assertEquals(expected.length, actual.length, "Row count mismatch");
+        for (int i = 0; i < expected.length; i++) {
+            assertEquals(expected[i].length, actual[i].length, "Column count mismatch at row " + i);
+            for (int j = 0; j < expected[i].length; j++) {
+                assertEquals(expected[i][j], actual[i][j], EPSILON, "Mismatch at (" + i + "," + j + ")");
+            }
+        }
+    }
+}