Scalar det_of_minor(
const std::vector<Scalar>& a ,
size_t m ,
size_t n ,
std::vector<size_t>& r ,
std::vector<size_t>& c )
{
const size_t R0 = r[m]; // R(0)
size_t Cj = c[m]; // C(j) (case j = 0)
size_t Cj1 = m; // C(j-1) (case j = 0)
// check for 1 by 1 case
if( n == 1 ) return a[ R0 * m + Cj ];
// initialize determinant of the minor M
Scalar detM;
detM = 0;
// initialize sign of factor for next sub-minor
int s = 1;
// remove row with index 0 in M from all the sub-minors of M
r[m] = r[R0];
// for each column of M
for(size_t j = 0; j < n; j++)
{ // element with index (0,j) in the minor M
Scalar M0j = a[ R0 * m + Cj ];
// remove column wht index j in M to form next sub-minor S of M
c[Cj1] = c[Cj];
// compute determinant of the current sub-minor S
Scalar detS = det_of_minor(a, m, n - 1, r, c);
// restore column Cj to representaion of M as a minor of A
c[Cj1] = Cj;
// include this sub-minor term in the summation
if( s > 0 )
detM = detM + M0j * detS;
else detM = detM - M0j * detS;
// advance to next column of M
Cj1 = Cj;
Cj = c[Cj];
s = - s;
}
// restore row zero to the minor representation for M
r[m] = R0;
// return the determinant of the minor M
return detM;
}
inline Scalar operator()(const Vector &x) const
{ size_t i = m_ * m_;
while(i--)
a_[i] = x[i];
return det_of_minor(a_, m_, m_, r_, c_);
}
