lufact ill condition on sparse matrix

[colinfang]

Basically, I cannot use lufact on a simple sparse matrix, but the dense version works fine.

Forgive me if I missed something obvious. Is it a result of some linear algebra concept?

A = sparse(Int[],Int[],Float64[], 3,3)
A[1,1] = 1
A[3,1] = 1
A[3,3] = 1
A[1,3] = 1

full(A)
3x3 Array{Float64,2}:
 1.0  0.0  1.0
 0.0  0.0  0.0
 1.0  0.0  1.0

B = lufact(A)
LoadError: Base.SparseMatrix.UMFPACK.MatrixIllConditionedException("")

B = lufact(full(A))

Base.LinAlg.LU{Float64,Array{Float64,2}}(3x3 Array{Float64,2}:
 1.0  0.0  1.0
 0.0  0.0  0.0
 1.0  0.0  0.0,Int32[1,2,3],2)

[andreasnoack]

The matrix you are trying to factorize is singular and therefore the factorization fails. That is the case for both the sparse and the dense version. If you look at the result from the dense factorization, you'll see a 2 after the Int32[1,2,3] which is an error code. The factorization has failed when that value is larger that zero.

In the sparse case we throw an exception when the matrix is singular instead of returning the failed factorization. You could argue that we are inconsistent here and maybe we should not throw an exception in the sparse case. Note, however, that you cannot do much with a failed LU factorization. The reason why we don't throw in the dense case is because we want to use the information to compute det(A)=0, see #1499, and indeed

julia> det(A)
ERROR: Base.SparseMatrix.UMFPACK.MatrixIllConditionedException("")
 in umfpack_numeric! at sparse/umfpack.jl:173
 in lufact at sparse/umfpack.jl:114
 in det at linalg/generic.jl:508

[colinfang]

thank you for the explanation.