MATLAB has a rsf2csf function that converts real Schur to complex Schur. Maybe an analogue in Julia is what I'm thinking about (and should alleviate the performance hit inside Lapack with the complex conversion, at least).
On Thursday, April 17, 2014 2:18:28 AM UTC-4, Joey Huchette wrote: > > A note in the docs seems like a reasonable solution, although I'm not sure > I agree that it's a completely transparent design decision. I've always > seen the real Schur form presented as an (important) computational trick to > avoid complex arithmetic, while the complex form is the mental model. I > have a feeling that many users may have never seen the real form before (as > a dumb little metric, neither Wikipedia nor Mathworld seem to mention it). > To bikeshed for a minute, calling an explicit conversion seems a little > bolted on for getting a complex Schur decomposition from a real matrix, > which seems like a common use case (at least for the MATLAB-style homework > questions like the one I was working on a few hours ago...). Just my two > cents. > > On Thursday, April 17, 2014 1:15:10 AM UTC-4, Andreas Noack Jensen wrote: >> >> I prefer the present solution where we use dispatch instead of keywords. >> I think it is transparent what is happening: real matrix -> real schur >> form, complex matrix -> complex schur form. However, we could add a line in >> the documentation explaining it. If you are okay with that idea, please >> open a pr. >> >> >> 2014-04-17 6:58 GMT+02:00 Joey Huchette <joehu...@gmail.com>: >> >>> Ahh simple enough, thanks. It might be nice to have a keyword argument >>> that just dispatches on this---it's not completely obvious that's the right >>> thing to do unless you dig around lapack.jl (or get a hint). I can PR. >>> >>> >>> On Thursday, April 17, 2014 12:18:00 AM UTC-4, Andreas Noack Jensen >>> wrote: >>> >>>> The trick is to convert your matrix to complex before the calculation. >>>> >>>> schurfact(complex(A))[:T] >>>> >>>> gives the triangular part. >>>> >>>> >>>> 2014-04-17 1:18 GMT+02:00 Joey Huchette <joehu...@gmail.com>: >>>> >>>> Is there an implementation in Base (or elsewhere) of a Schur >>>>> decomposition that returns a complex matrix matrix T that is triangular? >>>>> For reference, MATLAB has a optional switch between the two forms. I >>>>> didn't >>>>> do enough digging to see if this option is exposed by Lapack, so maybe >>>>> the >>>>> conversion could be done at the Julia level? Apologies if I overlooked it >>>>> in the docs/source. >>>>> >>>> >>>> >>>> >>>> -- >>>> Med venlig hilsen >>>> >>>> Andreas Noack Jensen >>>> >>> >> >> >> -- >> Med venlig hilsen >> >> Andreas Noack Jensen >> >
