Cholesky Decomposition of a Sparse Symmetric Positive Semidefinite (SPSD) Singular Matrix

The context I encountered it is in Solve Large Scale Underdetermined Linear Equation with per Element Equality Constraint.

The matrix to decompose, \boldsymbol{B}_{\mathcal{U}}, is SPSD. When I set check = false I get the correct result. Yet I wonder if the missing pivot is crucial in this context.

I thought it would be better in the original thread as it is the first that show up when you do a Google search. So it is better to have high Information / Thread ratio (The same problem for the 2 cases: Dense / Sparse).