Does $\log(\det(A))$ equals sum of log of diagonal elements of D in LDLT decomposition?

Question

For a large matrix $A$, I need to evaluate the $\log(\det(A))$. I already have it's LDLT decomposition.

Is it possible to evaluate the $\log\det$ with the elements of the diagonal $D$ of the LDLT decomposition?

Thanks!

Answer 1

Note

$$\det (A) = \det (LDL^T) = \det (L) \det (D) \det(L^T) = \det D$$

as $L$ is lower triangular with diagonal entries all one.