For matrix operation, Why is "ikj" faster than "ijk"? [duplicate]

Question

For matrix operation...

ijk-algorithm

public static int[][] ijkAlgorithm(int[][] A, int[][] B) {
    int n = A.length;
    int[][] C = new int[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;
}

ikj-algorithm

public static int[][] ikjAlgorithm(int[][] A, int[][] B) {
    int n = A.length;
    int[][] C = new int[n][n];
    for (int i = 0; i < n; i++) {
        for (int k = 0; k < n; k++) {
            for (int j = 0; j < n; j++) {
                C[i][j] += A[i][k] * B[k][j];
            }
        }
    }
    return C;
}

I know ikj is faster than ijk, but don't know why. Have any simple explanation? Thank you.

Answer 1

In the second snippet, the compiler can optimise

    for (int k = 0; k < n; k++) {
        for (int j = 0; j < n; j++) {
            C[i][j] += A[i][k] * B[k][j];
        }
    }

into something equivalent to

    for (int k = 0; k < n; k++) {
        int temp = A[i][k];  
        for (int j = 0; j < n; j++) {
            C[i][j] += temp * B[k][j];
        }
    }

but no such optimisation can be made in the first snippet. So the second snippet requires fewer lookups into the arrays.