For a 200 x 200 grid with a 2D elasticity PDE problem I get 2.4 seconds for lufact and 8.2 seconds from qr. The resulting stiffness matrix has a density of ~ 0.00022.
On Monday, April 25, 2016 at 10:49:40 PM UTC+2, Jonas Kersulis wrote: > > Can someone explain why qrfact is faster and requires less memory than > lufact for square, sparse matrices? LU is less computationally complex than > QR, and with decent pivoting LU should be able to preserve sparsity better > than QR, so I'm confused by what I'm seeing in practice. > > The plots below compare computation time, memory allocation, and garbage > collection time for the two factorization methods. I generated them by > factorizing sprand sparse matrices. The top plot shows results for matrices > with 10% nonzeros; the bottom plot shows results for matrices with 50% > nonzeros. The methods seem to converge in memory performance as density > increases, but LU loses to QR in both cases. > > I have looked through the paper describing the multifrontal QR algorithm > Julia calls, but I don't understand it fully. Before I spend more time > studying it, I figured I would see if someone here knows the secret sauce > that helps it beat LU. > > <https://lh3.googleusercontent.com/-EIfk6ZvRVY8/Vx6AN44Se4I/AAAAAAACOgI/hIKvJGOuRGc45IGlAJ_zobqoMUquBFeCwCLcB/s1600/2016-04-25-lu-vs-qr-01.png> > > <https://lh3.googleusercontent.com/-agWjcrtP4iE/Vx6ASu0AnBI/AAAAAAACOgM/sOyXToRy2BEuW1gjaIcHNsbEDLYtp-LtACLcB/s1600/2016-04-25-lu-vs-qr-05.png> > > >
