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From: Peter.V<anroose@es...>  20020327 16:25:22

> whereas for 30 equations it goes banana (wrong solution): > > vnl_lsqr.cxx : x = 0 is the exact solution. No iterations were performed. > vnl_lsqr.cxx : The iteration limit ITNLIM was reached. > vnl_lsqr.cxx : residual norm estimate = 3.24731 > vnl_lsqr.cxx : result norm estimate = 14.2702 > vnl_lsqr.cxx : condition no. estimate = 106.047 > vnl_lsqr.cxx : iterations = 30 Whenever you see the message "The iteration limit ITNLIM was reached" you can expect that the result is incorrect or at least imprecise. Could you try changing the # iterations to 120 in this case? P.S. I've changed the default in vnl_lsqr.h to 4*n. Peter. 
From: Andrew Fitzgibbon <awf@ro...>  20020327 16:04:47

Also, Domi, can you run the profiler to see where the 10 mins is spent? MATLAB has pretty highly optimized code paths  we may be able to gain a factor of 25 just by microoptimizing the sparse matrix stuff. A. 
From: Peter.V<anroose@es...>  20020327 15:51:34

> vnl_lsqr.cxx : The iteration limit ITNLIM was reached. From v3p/netlib/lsqr.c : /* ITNLIM input An upper limit on the number of iterations. */ /* Suggested value: */ /* ITNLIM = n/2 for wellconditioned systems */ /* with clustered singular values, */ /* ITNLIM = 4*n otherwise. */ ITNLIM is the 17th parameter to lsqr_() It can be set in vnl_lsqr by the method set_max_iterations(int). The default is "n", which should probably be changed to "4*n". Peter. 
From: Ian Scott <ian.scott@st...>  20020327 14:56:06

Sorry, http://www.isbe.man.ac.uk/public_vxl_doc/books/vxl/book.html#SEC60 > Original Message > From: Andrew Fitzgibbon [mailto:awf@...] > Sent: Wednesday, March 27, 2002 2:54 PM > To: Ian Scott > Subject: RE: [Vxlusers] vnl_sqrt does solve Ax=b but toooo sloooow > > > > 4bidden > > >http://www.isbe.man.ac.uk/internal/software/c++/isbe_vxl_doc/ > books/vxl/ > book.html#SEC60 > > 
From: Ian Scott <ian.scott@st...>  20020327 14:31:21

> This solves my (naive) test linear system but: > > 1) I have to set no. of interations to 2x size of A, otherwise I get > wrong solution, If the default value isn't big enough, it could indicate a bug in vnl_lsqr. Have a look at the documentation in the underlying netlib function, it may tell you something useful. > > 2) It takes 10 minutes for 10,000 x 10,000 while matlab takes only 1 > minute to give the same. > > 3) I have to solve ~ 10,000 x 10,000 maaaaaaany times in my > calculations > > Any ideas how to improve things? Find a better algorithm in the literature and add it to vnl. http://www.isbe.man.ac.uk/internal/software/c++/isbe_vxl_doc/books/vxl/book. html#SEC60 Ian. 
From: <domi@vi...>  20020327 14:22:01

> perhaps increase the interation limit Great. Thank you Ian. This solves my (naive) test linear system but: 1) I have to set no. of interations to 2x size of A, otherwise I get wrong solution, 2) It takes 10 minutes for 10,000 x 10,000 while matlab takes only 1 minute to give the same. 3) I have to solve ~ 10,000 x 10,000 maaaaaaany times in my calculations Any ideas how to improve things? dominique 
From: <domi@vi...>  20020327 13:26:31

vnl_sqrt doesnt solve Ax=b for systems aleardy around 30. For 20 it gives good results (for a naive linear problem) and: vnl_lsqr.cxx : x = 0 is the exact solution. No iterations were performed. vnl_lsqr.cxx : The iteration limit ITNLIM was reached. vnl_lsqr.cxx : residual norm estimate = 8.40484e06 vnl_lsqr.cxx : result norm estimate = 14.6304 vnl_lsqr.cxx : condition no. estimate = 67.683 vnl_lsqr.cxx : iterations = 20 whereas for 30 equations it goes banana (wrong solution): vnl_lsqr.cxx : x = 0 is the exact solution. No iterations were performed. vnl_lsqr.cxx : The iteration limit ITNLIM was reached. vnl_lsqr.cxx : residual norm estimate = 3.24731 vnl_lsqr.cxx : result norm estimate = 14.2702 vnl_lsqr.cxx : condition no. estimate = 106.047 vnl_lsqr.cxx : iterations = 30 I guess residual norm estimate holds the key. Any ideas? thanks Dominique 
From: <domi@vi...>  20020327 12:50:43

> I think vnl_lsqr is the class you are looking for. From the documentation Ian, yes, you are right. I was there before, but I didnt know I can use it (well, matix inverse and least squares are kind of two different jobs, arent they?). I checked  it works for small systems, but if it works good enough for huge sparse systems I will know in a day or two. > I readily acknowledge that VXL's documentation is far from perfect. If you > can think of some better documentation (either for the vnl chapter in the > book, or the doxygen output,) we would be grateful. Improvements to the VXL > code or documentation are always welcome. I dont need a perfect documentation (although a little bit less messy would be great). Instead I prefer the idea of getting in touch with someone who had similar problem (and asking him for solution). I can offer the same. thank you Dominique 
From: Ian Scott <ian.scott@st...>  20020327 09:35:38

> I see a lot of classes, but none is giving me either an > inverse of a big > *sparse* matrix or a corresponding solution  not to mention other > expectations/doubts I wrote about :( I think vnl_lsqr is the class you are looking for. From the documentation http://www.isbe.man.ac.uk/public_vxl_doc/vxl/vnl/html/class_vnl_lsqr.html "vnl_lsqr implements an algorithm for large, sparse linear systems and sparse, linear least squares" As I undestand it, linear least squares applied to the equation Ax=b will give you a least squares solution for x, which is as good as you are likely to get for a massive sparse matrix A. > I'm sorry, but there is no clear answer there to "questions > like this". The place for an overview of numerical algorithms is a book like "Numerical Recipes." There is no point in us replicating this sort of information in VXL's documentation. However, the search engine and documentation do provide a means of finding algorithms. vnl_lsqr comes 4th on a search for "vnl sparse". Ok, the vnl_lsqr documentation doesn't mention the word "inverse" (because it doesn't actually do an inverse,) but this is exactly the process I used to answer your question. I readily acknowledge that VXL's documentation is far from perfect. If you can think of some better documentation (either for the vnl chapter in the book, or the doxygen output,) we would be grateful. Improvements to the VXL code or documentation are always welcome. Ian. 