mcovalt/iluzero.jl

A Julia implementation of incomplete LU factorization with zero level of fill in.

iluzero.jl's Issues

ilu0 returns wrong results for sparse matrix solve

Thanks for the great package, this is a very useful tool!

I am having issues using the factorization for some matrices. I tried using the ilu0 factorization on a small matrix 10x10 with good condition number. The result is very different from what I obtain with the base \ operator. I have attached an example below:

using Random
Random.seed!(0)

n = 10
B = sprand(n,n,1.0) # works
B = sprand(n,n,0.9) # doesn't work
cond(Matrix(B))
lu_factorization = ilu0(B)
x0 = zeros(n)
r = rand(n)
ldiv!(x0, lu_factorization, r)
norm(B * x0 - r, Inf)
x1 = B \ r
norm(B * x1 - r, Inf)
norm(x0 - x1, Inf)

Interestingly when all the entries in the matrix are filled the results is correct.
I am not sure if I am missing something here, can you help me sort this issue out?

Thanks for your help!
Simon

Using this package with CSR matrices?

How difficult would it be to accommodate CSR matrices? The advantage of
that storage format is that it is amenable to parallel processing with multiple threads,
which can be used to advantage in the preconditioned CG iteration.

Excellent package

Thank you kindly sir. It is very useful to me.

Register this package?

It would be nice to register this package. We can do an ILU factorization with zero fill-in of any matrix type (Float32, Float64, Float128, BigFloat..). It's not the case with ImcompleteLU package.
It's a good preconditioner for iterative methods. I would like to use it in our package Krylov.jl.

Extension for Incomplete Cholesky Decomposition

Any chance to extend this to incomplete Cholesky decomposition?

In my C implemetation I also implemented the 𝜏 approach.
Any chance to have that as well?

README too pessimistic?

I find this part of the README pessimistic to the point that it might turn users away:

Why use ILUZero.jl? You probably shouldn't. Julia's built in factorization methods are much better.

The point of this package isn't to compete with (complete) factorization packages such as SuiteSparse. I feel the importance of LU(0) for preconditioning could be stressed instead.