I would like to compute the decomposition of a real symmetric positive definite matrix $\mathbf{A} = \mathbf{UDU}^\top$.
LINPACK seems to have it as DSIFA
, but I cannot find an equivalent routine in LAPACK. It also doesn't appear to implemented in Eigen.
What other packages and routines support this decomposition?
Background:
In my field, the most common of Kalman Filter implemented in the "real world" is via UDU as evidenced in multiple books on the subject. I understand that there is an equivalent $\mathbf{LDL}^\top$ form, but I am trying to stick with the convention in my field.
DSIFA
doesn't do a genuine diagonal factorization, as the $\mathbf D$ factor it returns is in fact block-diagonal, at least if the input matrix is symmetric-indefinite (Bunch-Parlett). $\endgroup$