determinant algorithm of a 4x4 matrix

Question

I pick the first row and multiply each element by its cofactor, but in some cases the method is returning nan. For example,

in this case the method returns nan.

Does anyone know what I did wrong?

getDet3 returns determinant of a 3x3 matrix and it works fine.

-(double) getDet4:(double[4][4])mat {
    double det = 0;
    double small[3][3];

    int i, j, k;
    int i_ = 1, j_;

    for ( i=0; i<4; i++ ){

        if (mat[0][i] == 0) continue;

        // get the small matrix here
        for ( j=0; j<3; j++ ){
            j_ = 0;
            for ( k=0; k<3; k++ ){
                if ( i == j_ ) j_++;
                small[j][k] = mat[i_][j_];
                j_++;
            }
            i_++;
        }

        det += mat[0][i] * [self getDet3:small] * pow(-1, i+j);
    }

    return det;
}

Why you are using cycle variable j in pow(-1, i+j)? Why you don't reset row-variable i_ to 1? Have you debugged the code and checked that `small` contains right data? — MBo, Nov 10 '14 at 15:22

score 1 · Accepted Answer · answered Nov 10 '14 at 15:24

Well, there are a few mistakes in your code.

1) The initialization of i_ = 1 should be done just before the j loop, otherwise it will keep the old value.

2) The computation of pow(-1, i+j) should only depend on i, since j has the same value every time in that expression (namely, 3).

So, assuming that getDet3 is correct, the mistake is introduced by i_ going out of bounds. As a whole, the code should look like:

-(double) getDet4:(double[4][4])mat {
    double det = 0;
    double small[3][3];

    int i, j, k;
    int i_, j_;

    for ( i=0; i<4; i++ ){

        if (mat[0][i] == 0) continue;

        // get the small matrix here
        i_ = 1;
        for ( j=0; j<3; j++ ){
            j_ = 0;
            for ( k=0; k<3; k++ ){
                if ( i == j_ ) j_++;
                small[j][k] = mat[i_][j_];
                j_++;
            }
            i_++;
        }

        det += mat[0][i] * [self getDet3:small] * pow(-1, i);
    }

    return det;
}

score 0 · Answer 2 · answered Nov 10 '14 at 15:22

Personally, I find your variable names confusing. If I understand your idea correctly, you expect i_ to have the value j + 1 and j_ to be k < i ? k : k + 1. IMHO, it would have been less confusing to have named them j_p andk_`, or even to just use the equivalent expression.

In any event, you don't reinitialize i_ inside the outer for loop. So it actually just keeps on incrementing, resulting in array indices outside of the array bounds.

determinant algorithm of a 4x4 matrix

2 Answers2