Performance of chol() on sparse matrices

[Andreas Stahel]

Dear Octave users

when testing code for a class a timing result on Octave 3.0.3 puzzled me.
generate a very sparse, symmetric, positive definite matrix Anxny (size 
62500x62500) and time a few commands

x=Anxny\b  -> 0.8 sec
R=chol(Anxny) -> 7.3 sec
x=R\(R'\b)  -> 2.3 sec
[L,U,P]=splu(Anxny) -> 12 sec

I would expect the Cholesky back-substitution to be fastest and 
cho(Anxny) to be comparable to Anxny\b !!

Would you happen to have hints on why this occurs

With best regards

Andreas

=============code =============
nx=250; ny=250;
hx=1/(nx+1); hy=1/(ny+1);
Dxx=spdiags([-ones(nx,1) 2*ones(nx,1) -ones(nx,1)],[-1 0 1],nx,nx)/(hx^2);
Dyy=spdiags([-ones(ny,1) 2*ones(ny,1) -ones(ny,1)],[-1 0 1],ny,ny)/(hy^2);
Anxny=kron(speye(ny),Dxx) + kron(Dyy,speye(nx));

b=ones(nx*ny,1);
t0=cputime;
x2=Anxny\b;
SolveTime=cputime()-t0
t0=cputime;
R=chol(Anxny);
CholTime=cputime()-t0
t0=cputime;
x3=R\(R'\b);
CholSolveTime=cputime()-t0
t0=cputime;
[L,U,P]=splu(Anxny);
LUTime=cputime()-t0

--
Andreas Stahel       E-Mail: address@hidden
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