/// Fast 3x3 eigenvalue decomposition
bool eig3(Matrix3x3 &m, Float lambda[3]) {
Float subd[3];
/* Reduce to Hessenberg form */
tred3(m, lambda, subd);
/* Iteratively find the eigenvalues and eigenvectors
using implicitly shifted QL iterations */
if (!ql3(m, lambda, subd))
return false;
/* Sort the eigenvalues in decreasing order */
for (int i=0; i<2; ++i) {
/* Locate the maximum eigenvalue. */
int largest = i;
Float maxValue = lambda[largest];
for (int j = i+1; j<3; ++j) {
if (lambda[j] > maxValue) {
largest = j;
maxValue = lambda[largest];
}
}
if (largest != i) {
// Swap the eigenvalues.
std::swap(lambda[i], lambda[largest]);
// Swap the eigenvectors
for (int j=0; j<3; ++j)
std::swap(m(j, i), m(j, largest));
}
}
return true;
}
void EigenValues(const SymmetricMatrix& X, DiagonalMatrix& D,
SymmetricMatrix& A)
{ DiagonalMatrix E; tred3(X,D,E,A); tql1(D,E); }
