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.
$\mathbf{UDU}^\top$ decomposition routines in LAPACK/Eigen?
linear algebra;matrices;lapack;eigen
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 ALDLT<MatrixXd,Upper> udu(A); // Only the upper part of A is read to form Uudu.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 vectorudu.vectorD().asDiagonal(); // an expression of the diagonal matrix D