Matrix multiplication in Java using 2D ArrayLists

Question

I am trying to implement a simple matrix multiplication in Java, where I am storing the matrices in two-dimensional ArrayLists. It would seem the error is caused by the setting of matrix Result , inside the nested for loop, but I do not understand why.

import java.util.ArrayList;
import java.util.Collections;
import java.util.Arrays;

public class Test {
    public static void main(String args[]) {
        int n = 2;

        ArrayList<ArrayList<Integer>> Result =
                new ArrayList<ArrayList<Integer>>(
                        Collections.nCopies(n, new ArrayList<Integer>(
                                Collections.nCopies(n, 0))));
        ArrayList<ArrayList<Integer>> A = new ArrayList<ArrayList<Integer>>();
        ArrayList<ArrayList<Integer>> B = new ArrayList<ArrayList<Integer>>();

        A.add(new ArrayList<Integer>(Arrays.asList(1, 6)));
        A.add(new ArrayList<Integer>(Arrays.asList(2, 2)));
        B.add(new ArrayList<Integer>(Arrays.asList(0, 9)));
        B.add(new ArrayList<Integer>(Arrays.asList(5, 6)));

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                for (int k = 0; k < n; k++) {
                    int val = A.get(i).get(k) * B.get(k).get(j);
                    Result.get(i).set(j, Result.get(i).get(j) + val);
                }
            }
        }
    }
}

The code produces the result:

A * B = [[40, 75], [40, 75]]

when in fact it should be:

A * B = [[30, 45], [10, 30]]

Answer 1

The Result is incorrectly initialized.

ArrayList<ArrayList<Integer>> Result = new ArrayList<ArrayList<Integer>>(
    Collections.nCopies(n,
        new ArrayList<Integer>(Collections.nCopies(n, 0))));

This creates a matrix where two rows (or columns, depending how you look at that) are in fact same row (column), referenced twice.

You can init Result like that:

List<List<Integer>> result = new ArrayList<>();
for (int i = 0; i < n; i++) {
    result.add(new ArrayList<>(Collections.nCopies(n, 0)));
}

Answer 2

Multiplication of square matrices using 2D lists:

int n = 2;
// three square matrices n×n
List<List<Integer>>
        a = Arrays.asList(Arrays.asList(1, 6), Arrays.asList(2, 2)),
        b = Arrays.asList(Arrays.asList(0, 9), Arrays.asList(5, 6)),
        // resulting matrix
        c = Arrays.asList(Arrays.asList(0, 0), Arrays.asList(0, 0));

// rows of the 'a' matrix
for (int i = 0; i < n; i++) {
    // columns of the 'b' matrix
    for (int j = 0; j < n; j++) {
        // columns of the 'a' matrix,
        // aka rows of the 'b' matrix
        for (int k = 0; k < n; k++) {
            // previous value
            int val = c.get(i).get(j);
            // sum of the products of the i-th row
            // of 'a' and the j-th column of 'b'
            val += a.get(i).get(k) * b.get(k).get(j);
            // set new value
            c.get(i).set(j, val);
        }
    }
}

// output
System.out.println(a); // [[1, 6], [2, 2]]
System.out.println(b); // [[0, 9], [5, 6]]
System.out.println(c); // [[30, 45], [10, 30]]

---

^{See also: Algorithm of the matrix multiplication}

Answer 3

You can use arrays instead of lists , because all three matrices before and after multiplication usually have constant sizes. But with lists, you can use a mutable AtomicInteger instead of an immutable Integer . Your code might look like this:

int n = 2;
// matrices
List<List<AtomicInteger>> a = List.of(
        List.of(new AtomicInteger(1), new AtomicInteger(6)),
        List.of(new AtomicInteger(2), new AtomicInteger(2)));
List<List<AtomicInteger>> b = List.of(
        List.of(new AtomicInteger(0), new AtomicInteger(9)),
        List.of(new AtomicInteger(5), new AtomicInteger(6)));
// resulting matrix
List<List<AtomicInteger>> c = List.of(
        List.of(new AtomicInteger(0), new AtomicInteger(0)),
        List.of(new AtomicInteger(0), new AtomicInteger(0)));

// matrix multiplication
for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
        for (int k = 0; k < n; k++) {
            int val = a.get(i).get(k).get() * b.get(k).get(j).get();
            c.get(i).get(j).getAndAdd(val);
        }
    }
}

// output
System.out.println(a); // [[1, 6], [2, 2]]
System.out.println(b); // [[0, 9], [5, 6]]
System.out.println(c); // [[30, 45], [10, 30]]

---

^{See also: Floating point matrix multiplication}