determinant algorithm of a 4x4 matrix - objective-c

Question

I pick the first row and multiply each element by its cofactor,
but in some cases the method is returning nan.
For example,
1 0 0 1
0 2 0 0
0 0 3 0
0 0 0 4
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;
}

Answer 1

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;
}

Answer 2

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.