RFC: Lyapunov / Sylvester solver via LAPack xTRSYL #7435
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| # AX + XB + C = 0 | ||
| function sylvester{T<:BlasFloat}(A::StridedMatrix{T},B::StridedMatrix{T},C::StridedMatrix{T}) | ||
| RA, QA = schur(A) | ||
| RB, QB = schur(B') |
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would be nicer to avoid explicit transpositions (and the resultant matrix copies). Can't you use schur(B) and then compensate with the corresponding opB argument of trysyl?
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Ah, if QRQ' = B then (QRQ')' = QR'Q' = B' ...
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It seems like it is even easier than that, because trysyl allows you to implicitly treat one of the matrices as transposed.
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Needs documentation too. |
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Thank you for going through this with me. I did not push the documentation commit, comes in a minute. |
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Your tests seem to have changed the indentation on the entire test file. That makes it difficult to see what has changed. Could you fix that? |
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Cc: @andreasnoackjensen |
and taking some tests out of the inner loop in linalg1.jl
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I followed @stevengj's Tips and restored the skew indentation. One can fix the indentation later. |
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The test failed in |
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Looking good, except for the mysterious test failure. |
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Seems safe to include in 0.3. Any reservations? |
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Apparently this was an intermittent failure which went away with the last commit. |
RFC: Lyapunov / Sylvester solver via LAPack xTRSYL
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Could use a mention in NEWS.md |
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@jiahao Good idea. Done. |
As discussed in JuliaLang/LinearAlgebra.jl#76, solver for the Lyapunov equation
AX + XA' +C = 0and the Sylvester equation
AX + XB + C = 0Function name and arguments is oriented at the Matlab neighbors.
lyapchol(A,B) for the cholesky factor of
A*X + X*A' + B*B' = 0is still missing.