## vxl-users

 [Vxl-users] fastest linear solver From: - 2011-09-22 16:35:10 ```Hi all, I changed an existing implementation for solving a linear system using LAPACK to VNL. The LAPACK implementation used LU decomposition for solving the system. The fastest equivalent for dense matrices I could find for VNL was vnl_qr, however this is too slow for my application. So my question is: is vnl_qr the fastest way to solve the linear system AX=B where A,X,B are dense matrices, (and A is symmetric and pos. def.) or is there a better way? Thanks a lot for your help! ```
 Re: [Vxl-users] fastest linear solver From: Ian Scott - 2011-09-22 18:03:03 ```Chris, Pretty much all of vnl's interesting algorithms are wrappers around bits of netlib (LAPACK, LINPACK, MINPACK, etc.) Where LAPACK provides a good algorithm for something, vnl will not have anything better. The main advantage of VNL over BLAS and LAPACK is a better API. That was just a general comment, there may be some specific algorithm in VNL that solves your problem optimally fast. Although if I understand linear algebra well enough, only Gauss elimination is faster than LU decomposition in the dense, non-singular, but otherwise unconstrained case. Anyway, I can't find an implementation of Gauss elimination or LU decomposition in VNL. As to faster options, feel free to add a wrapper for LAPACKs LU decomposition function. Sorry I can't be more help. Ian. On 22/09/2011 17:34, baumgach@... wrote: > Hi all, > > I changed an existing implementation for solving a linear system using > LAPACK to VNL. The LAPACK implementation used LU decomposition for > solving the system. The fastest equivalent for dense matrices I could > find for VNL was vnl_qr, however this is too slow for my application. > So my question is: is vnl_qr the fastest way to solve the linear > system AX=B where A,X,B are dense matrices, (and A is symmetric and > pos. def.) or is there a better way? > > Thanks a lot for your help! > > > > ------------------------------------------------------------------------------ > All the data continuously generated in your IT infrastructure contains a > definitive record of customers, application performance, security > threats, fraudulent activity and more. Splunk takes this data and makes > sense of it. Business sense. IT sense. Common sense. > http://p.sf.net/sfu/splunk-d2dcopy1 > _______________________________________________ > Vxl-users mailing list > Vxl-users@... > https://lists.sourceforge.net/lists/listinfo/vxl-users > ```
 Re: [Vxl-users] fastest linear solver From: - 2011-09-22 19:45:04 ```Thanks Ian, I might consider doing that. The goal for now is to get rid of the LAPACK wrapper so the application is only dependant on ITK. If I start adding new lapack functions I won't be able to use ITK out of the box. (the lapack function dgesv for LU decomposition, unfortunately, isn't in the netlib directory of ITK.) But maybe it will be my only solution. - Chris Quoting "Ian Scott" : > Chris, > > Pretty much all of vnl's interesting algorithms are wrappers around > bits of netlib (LAPACK, LINPACK, MINPACK, etc.) Where LAPACK > provides a good algorithm for something, vnl will not have anything > better. > > The main advantage of VNL over BLAS and LAPACK is a better API. > > That was just a general comment, there may be some specific > algorithm in VNL that solves your problem optimally fast. Although > if I understand linear algebra well enough, only Gauss elimination > is faster than LU decomposition in the dense, non-singular, but > otherwise unconstrained case. Anyway, I can't find an implementation > of Gauss elimination or LU decomposition in VNL. > > As to faster options, feel free to add a wrapper for LAPACKs LU > decomposition function. > > Sorry I can't be more help. > > Ian. > > > On 22/09/2011 17:34, baumgach@... wrote: >> Hi all, >> >> I changed an existing implementation for solving a linear system using >> LAPACK to VNL. The LAPACK implementation used LU decomposition for >> solving the system. The fastest equivalent for dense matrices I could >> find for VNL was vnl_qr, however this is too slow for my application. >> So my question is: is vnl_qr the fastest way to solve the linear >> system AX=B where A,X,B are dense matrices, (and A is symmetric and >> pos. def.) or is there a better way? >> >> Thanks a lot for your help! >> >> >> >> ------------------------------------------------------------------------------ >> All the data continuously generated in your IT infrastructure contains a >> definitive record of customers, application performance, security >> threats, fraudulent activity and more. Splunk takes this data and makes >> sense of it. Business sense. IT sense. Common sense. >> http://p.sf.net/sfu/splunk-d2dcopy1 >> _______________________________________________ >> Vxl-users mailing list >> Vxl-users@... >> https://lists.sourceforge.net/lists/listinfo/vxl-users >> > ```