{"action":"created","issue":{"url":"https://api.github.com/repos/JuliaLinearAlgebra/Arpack.jl/issues/4","repository_url":"https://api.github.com/repos/JuliaLinearAlgebra/Arpack.jl","labels_url":"https://api.github.com/repos/JuliaLinearAlgebra/Arpack.jl/issues/4/labels{/name}","comments_url":"https://api.github.com/repos/JuliaLinearAlgebra/Arpack.jl/issues/4/comments","events_url":"https://api.github.com/repos/JuliaLinearAlgebra/Arpack.jl/issues/4/events","html_url":"https://github.com/JuliaLinearAlgebra/Arpack.jl/pull/4","id":333994683,"node_id":"MDExOlB1bGxSZXF1ZXN0MTk2MDc0NjE2","number":4,"title":"Explicit transform in eigs + fix for generalized eigproblems","user":{"login":"jarlebring","id":11163595,"node_id":"MDQ6VXNlcjExMTYzNTk1","avatar_url":"https://avatars3.githubusercontent.com/u/11163595?v=4","gravatar_id":"","url":"https://api.github.com/users/jarlebring","html_url":"https://github.com/jarlebring","followers_url":"https://api.github.com/users/jarlebring/followers","following_url":"https://api.github.com/users/jarlebring/following{/other_user}","gists_url":"https://api.github.com/users/jarlebring/gists{/gist_id}","starred_url":"https://api.github.com/users/jarlebring/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jarlebring/subscriptions","organizations_url":"https://api.github.com/users/jarlebring/orgs","repos_url":"https://api.github.com/users/jarlebring/repos","events_url":"https://api.github.com/users/jarlebring/events{/privacy}","received_events_url":"https://api.github.com/users/jarlebring/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":15,"created_at":"2018-06-20T09:26:49Z","updated_at":"2018-06-20T15:14:51Z","closed_at":null,"author_association":"NONE","pull_request":{"url":"https://api.github.com/repos/JuliaLinearAlgebra/Arpack.jl/pulls/4","html_url":"https://github.com/JuliaLinearAlgebra/Arpack.jl/pull/4","diff_url":"https://github.com/JuliaLinearAlgebra/Arpack.jl/pull/4.diff","patch_url":"https://github.com/JuliaLinearAlgebra/Arpack.jl/pull/4.patch"},"body":"This is the modifications in the PR https://github.com/JuliaLang/julia/pull/27428 adapted for the Arpack.jl repo.\r\n\r\n```\r\njulia> Pkg.clone(\"git@github.com:jarlebring/Arpack.jl.git\");\r\njulia> using Arpack\r\njulia> A=sprandn(100,100,0.1); e1=eye(100,1); A=A+100*e1*e1';\r\njulia> C=I+0.0001*sprandn(100,100,0.1);\r\njulia> B=C*C';  # symm. pos. definite\r\njulia> λ1=Arpack.eigs(A,B,explicittransform=false,sigma=1.0)[1]\r\n6-element Array{Complex{Float64},1}:\r\n 1.1368082363358505 + 0.0im                \r\n  1.196559880250286 - 0.3354973502149164im \r\n  1.196559880250286 + 0.3354973502149164im \r\n 1.3939829317687282 + 0.0im                \r\n 0.6344981630423718 - 0.33394638283076294im\r\n 0.6344981630423718 + 0.33394638283076294im\r\n\r\njulia> λ2=Arpack.eigs(A,B,explicittransform=true,sigma=1.0)[1]\r\n6-element Array{Complex{Float64},1}:\r\n 1.1368082363358496 + 0.0im                \r\n 1.1965598802502784 + 0.33549735021491733im\r\n 1.1965598802502784 - 0.33549735021491733im\r\n  1.393982931768731 + 0.0im                \r\n 0.6344981630423725 + 0.33394638283076955im\r\n 0.6344981630423725 - 0.33394638283076955im\r\n```"},"comment":{"url":"https://api.github.com/repos/JuliaLinearAlgebra/Arpack.jl/issues/comments/398788250","html_url":"https://github.com/JuliaLinearAlgebra/Arpack.jl/pull/4#issuecomment-398788250","issue_url":"https://api.github.com/repos/JuliaLinearAlgebra/Arpack.jl/issues/4","id":398788250,"node_id":"MDEyOklzc3VlQ29tbWVudDM5ODc4ODI1MA==","user":{"login":"jarlebring","id":11163595,"node_id":"MDQ6VXNlcjExMTYzNTk1","avatar_url":"https://avatars3.githubusercontent.com/u/11163595?v=4","gravatar_id":"","url":"https://api.github.com/users/jarlebring","html_url":"https://github.com/jarlebring","followers_url":"https://api.github.com/users/jarlebring/followers","following_url":"https://api.github.com/users/jarlebring/following{/other_user}","gists_url":"https://api.github.com/users/jarlebring/gists{/gist_id}","starred_url":"https://api.github.com/users/jarlebring/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jarlebring/subscriptions","organizations_url":"https://api.github.com/users/jarlebring/orgs","repos_url":"https://api.github.com/users/jarlebring/repos","events_url":"https://api.github.com/users/jarlebring/events{/privacy}","received_events_url":"https://api.github.com/users/jarlebring/received_events","type":"User","site_admin":false},"created_at":"2018-06-20T15:14:51Z","updated_at":"2018-06-20T15:14:51Z","author_association":"NONE","body":"I tried it and I didn't manage to make the extra factorization trick work reliably. \r\n\r\nThis is indeed shifting a bit beyond the original idea of the PR. The symmetric shift-and-invert with cholesky sounds like another feature, which maybe deserves separate thought. In order to accommodate that we later may want to add this, instead of letting  `explicittransform` take values  true,false,nothing, we could change it to take values `:shiftinvert`, `:none`, `:auto` such that we later allow `:symmshiftinvert` without breaking old code."}}
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