Underlying Implementation of LDL in Matlab

The general question is: how is the ldl implemented in Matlab?

Motivation: I want to confirm the ldl implementation is not using the same algorithm as the lu() function (which I'm aware uses umfpack). The reason I am asking is that when I compare the speed of the ldl and lu on the same sparse laplacian matrix, the ldl comes out a lot slower than doing [L,U,P,Q] = lu(A), even though we expect the ldl to be, at best, up to 50% faster. My hunch here is that the ldl is not using the same multifrontal solver as umfpack is:

Code snippet for reference:

A = (delsq(numgrid('L', 400)));
%A2 = full(delsq(numgrid('L', 40)));

bA = sum(A,2);
tic
[LA, DA, PA, SA] = ldl(A);
toc
x = SA*(PA'\(LA'\(DA\(LA\(PA\(SA*bA))))));

tic
[L,U,P,Q] = lu(A);
toc
xl = P\(U\(L\(Q\bA)));

figure(); plot(x);
hold on;
plot(xl)

[Torsten]

Does this help ?

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwisiNeFnpv1AhUiQvEDHQ6VAQIQFnoECBAQAQ&url=https%3A%2F%2Ffossies.org%2Flinux%2FSuiteSparse%2FLDL%2FDoc%2Fldl_userguide.pdf&usg=AOvVaw3MjZjEuRRNQz8zRFRCHLet

[Nathan Zhao]

yes, many thanks!