For completeness, cholesky factorization takes about 0.7 seconds.
On Tuesday, April 26, 2016 at 6:40:50 PM UTC+2, Kristoffer Carlsson wrote: > > 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> >> >> >>
