tag:blogger.com,1999:blog-11295132.post1593552387558031235..comments2019-02-21T03:59:37.273-08:00Comments on A Neighborhood of Infinity: Dimensionful MatricesDan Piponihttps://plus.google.com/107913314994758123748noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-11295132.post-22139652586612737522017-03-30T13:42:01.347-07:002017-03-30T13:42:01.347-07:00R effort here: https://cran.r-project.org/web/pack...R effort here: https://cran.r-project.org/web/packages/units/index.htmlmdsumnerhttps://www.blogger.com/profile/03049597568852739302noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-80375646065937103412016-08-13T00:04:16.019-07:002016-08-13T00:04:16.019-07:00If you don't know already, you might want to s...If you don't know already, you might want to see what F# does: https://blogs.msdn.microsoft.com/andrewkennedy/2008/08/29/units-of-measure-in-f-part-one-introducing-units/<br /><br />Though, no matrices, AFAIK.Radu Grigorehttps://www.blogger.com/profile/02991214367108471744noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1976295009933504302016-08-10T20:10:33.842-07:002016-08-10T20:10:33.842-07:00if we were to represent the vectors as hlists in h...if we were to represent the vectors as hlists in haskell (or in scala via shapeless) we would be able to express these multidimensional arrays. we could then have interpreters which may "compile" them down to some target (for the ones where the types conformed).Suhailhttps://www.blogger.com/profile/15921470476730871931noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-43912039140545216032016-08-07T18:04:17.453-07:002016-08-07T18:04:17.453-07:00I once tried, and failed, to work out how to do di...I once tried, and failed, to work out how to do dimensioned clifford algebra in the particular case of momentum. I've left the incorrect blog post [with prepended mea culpa] at http://grampsgrumps.blogspot.com.au/2014/11/multivector-momentum.html in the hope of inspiring someone. I have a feeling that understanding how to do that correctly would be a useful step.Robert Smarthttps://www.blogger.com/profile/01183856757175002949noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-15076781814760480022016-08-07T07:52:01.293-07:002016-08-07T07:52:01.293-07:00We've tried a few times to implement this in H...We've tried a few times to implement this in Haskell on top of the dimensional library. It actually works really well in the "forward" direction (determining the dimensions of the results when all input dimensions are known), but can't check any complicated uses that are polymorphic in dimension. I am working on a type checker plugin for GHC to rectify that, but there are a few complications and so my attention got diverted to lower-hanging fruit.Douglas McCleanhttps://www.blogger.com/profile/06662331850663558712noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-19276946987775363942016-08-07T06:49:27.326-07:002016-08-07T06:49:27.326-07:00The outer product view also corresponds nicely to ...The outer product view also corresponds nicely to the view of matrices as linear transformations between two vector spaces.<br /><br />I love the analysis of Conjugate Gradient – when working on Fortress we loved to trot this one out (internally, too). If we'd realized that getting the dimensions right corresponded to preconditioning, it would have made discussing dimensioned matrices with the supercomputing crowd so much easier. It's still a challenge to turn this into a sparse matrix representation without doing horrifying things with dependent types, though.J. Maessenhttps://www.blogger.com/profile/01577860012705910561noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-10165069072007511712016-08-07T06:47:58.116-07:002016-08-07T06:47:58.116-07:00George Hart has written a book on this topic calle...George Hart has written a book on this topic called "Multidimensional Analysis".<br />You can find a summary and and an article on his website.<br /><br />http://www.georgehart.com/research/multanal.html<br />http://www.georgehart.com/research/tdm.ps<br />Jan Van lenthttps://www.blogger.com/profile/18101186713270599994noreply@blogger.com