$\mathbf{UDU}^\top$ decomposition routines in LAPACK/Eigen?

Question

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?

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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.

Answer 1

Eigen's LDLT class actually performs a U^T.D.U factorization if the input matrix is column-major with the symmetric entries stored in the upper triangular part:

MatrixXd A;
// fill at least the upper triangular part of A
LDLT<MatrixXd,Upper> udu(A); // Only the upper part of A is read to form U
udu.matrixU(); // returns an expression of the triangular matrix U (column major)
udu.matrixL(); // returns an expression of the triangular matrix U^T (row major)
udu.vectorD(); // expression of the diagonal coefficients of the matrix D as a vector
udu.vectorD().asDiagonal(); // an expression of the diagonal matrix D