Missing matrix/factorization functions

[kshyatt]

Re: JuliaLang/julia#5840, #136, JuliaLang/julia#8240

We have a lot of easy targets to fill out the linear algebra functionality. These methods don't work at all. They don't have fallbacks to the dense method, even. Feel free to add more:

• BunchKaufman
  • Matrix
  • det
  • logdet
• Symmetric{SparseMatrixCSC}
  • Matrix
  • det
  • logdet
  • eigvals
  • eigvecs
  • eigen
  • svdvals
  • svd
  • issparse
  • cond - broken because of eigvals
  • (-)A
  • isposdef
  • mul!
  • norm(A)
• LDLt{SymTridiagonal}
  • det
  • logdet
  • norm
  • tr
  • eigvals
  • eigvecs
  • svdvals
  • svd
  • cond
• Hessenberg, UpperHessenberg
  • eigen, eigvals: eigensolvers for Hessenberg matrices #858
  • qr (mentioned in more methods for Hessenberg factorizations #625)

[jeanm]

I would like to work on some of these. Is it still a good idea, in light of JuliaLang/julia#8240 ?

[kshyatt]

I don't see why it wouldn't be. Some things, like det and logdet, we should have anyway. If we do go through with that issue, we can cross that bridge when we get there anyway.

[sarvghotra]

@kshyatt Is isposdef() still missing ?

[kshyatt]

julia> a = sprand(5,5,0.3)
5x5 sparse matrix with 5 Float64 entries:
    [1, 2]  =  0.39171
    [2, 2]  =  0.689867
    [4, 2]  =  0.648607
    [3, 3]  =  0.403935
    [2, 5]  =  0.101027

julia> a = a + a.'
5x5 sparse matrix with 8 Float64 entries:
    [2, 1]  =  0.39171
    [1, 2]  =  0.39171
    [2, 2]  =  1.37973
    [4, 2]  =  0.648607
    [5, 2]  =  0.101027
    [3, 3]  =  0.80787
    [2, 4]  =  0.648607
    [2, 5]  =  0.101027

julia> a = Symmetric(a)
5x5 Symmetric{Float64,SparseMatrixCSC{Float64,Int64}}:
 0.0      0.39171   0.0      0.0       0.0
 0.39171  1.37973   0.0      0.648607  0.101027
 0.0      0.0       0.80787  0.0       0.0
 0.0      0.648607  0.0      0.0       0.0
 0.0      0.101027  0.0      0.0       0.0

julia> isposdef(a)
ERROR: MethodError: `isposdef!` has no method matching isposdef!(::Symmetric{Float64,SparseMatrixCSC{Float64,Int64}})
 [inlined code] from linalg/symmetric.jl:5
 in isposdef at linalg/dense.jl:33
 in eval at ./boot.jl:264

Seems to be!

[sarvghotra]

In order to write tests for logdet of BunchKaufman I referred tests of logdet of generic. In this just @test_approx_eq logdet(A) log(det(A)) is used. This doesn't deal with the case when determinant is negative, i.e. it would throw error.

[andreasnoack]

Notice that the test matrix A is constructed such that the determinant is positive. Further down, we test that it also throws for negative determinants.

[bencardoen]

Is this still open/relevant? If so, I'd like to help with a few (need them for my own work as well)

[oscardssmith]

I'm not sure. Test them out and see if they error.