Computes the Sturm count, the number of negative pivots encountered while factoring tridiagonal
T - σ I = LDLT. This implementation works directly on the factors without
forming the tridiagonal matrix T. The Sturm count is also the number of eigenvalues of
T less than σ.
"Marques, Osni A., Riedy E. Jason, and Vomel Christof, "LAPACK working note 172: Benefits of
IEEE-754 features in modern symmetric tridiagonal eigensolvers", Technical Report UCB//
"Dhillon, Inderjit S. and Parlett, Beresford N., "Orthogonal eigenvectors and relative
gaps", SIAM Journal on Matrix Analysis and Applications, 2004, Vol. 25, pp. 858-899."