Add full(F::Factorization) for various kinds of factorization #9290
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| @@ -108,6 +108,7 @@ convert{T}(::Type{Factorization{T}}, C::CholeskyPivoted) = convert(CholeskyPivot | |||
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| full{T,S}(C::Cholesky{T,S,:U}) = C[:U]'C[:U] | |||
| full{T,S}(C::Cholesky{T,S,:L}) = C[:L]*C[:L]' | |||
| full{T}(F::CholeskyPivoted{T}) = (ip=invperm(F[:p]); (F[:L] * F[:U])[ip,ip]) | |||
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Type parameter is not necessary here. The type parameters are only included in the definitions for the usual Cholesky in order to be able specify :U and :L.
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Thanks for that. Please see the comments in the code. |
Include changes suggested by Andreas Noack
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OK, adapted and squashed the PR. I am sorry that squashing outdates the diffs on github. |
| ## Can we determine the source/result is Real? This is not stored in the type Eigen | ||
| full(F::Eigen) = F.vectors * Diagonal(F.values) / F.vectors | ||
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| full(F::Hessenberg) = (fq = full(F[:Q]); fq * F[:H] * fq') |
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You shouldn't construct the full Q here. It is expensive. Use something like q = full(F[:Q]); (q * F[:H]) * q'. The parentheses will avoid the bug I try to fix in #9170.
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I get the parentheses, but I don't really understand your remark about not reconstructing the full Q. Do you mean LAPACK.orghr! is too expensive? Should I try to not extract the first row/column of Q?
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@davidavdav I'm going through old issues and can see that this one fell under the radar. If you rebase then I'll merge. |
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I have this almost rebased. |
This PR generalizes
full(::Cholesky)to various other factorizations:CholeskyPivoted,QR,QRCompactWY,QRPivoted,Eigen,Hessenberg,Schur,SVD,LDLt, andLU. The idea is thatA = full(F::Factorization)is the opposite ofF = factorize(A). I implemented the reconstruction for all factorizations, apart frombkfact---somehow the.ipivencoding is too hard to understand for me, see http://www.nag.com/numeric/FL/nagdoc_fl22/pdf/F07/f07mdf.pdf , section 5.5.The patch includes code, tests and a line of documention.