Re: Re: Orthogonazlie with Method->"Householder"
- To: mathgroup at smc.vnet.net
- Subject: [mg97873] Re: [mg97791] Re: Orthogonazlie with Method->"Householder"
- From: Maris Ozols <marozols at gmail.com>
- Date: Tue, 24 Mar 2009 05:32:32 -0500 (EST)
- References: <gpvh97$grj$1@smc.vnet.net> <200903221044.FAA08003@smc.vnet.net>
> What do you think about starting the famous "bugs and caveats" site > with this post? Well, we have to decide were are we going to host it. I have not properly investigated these possibilities yet, but I am thinking about one of the following two: http://code.google.com/ http://www.mathematica-users.org/ ~Maris Ozols~ p.s. After my post "Maintaining a Mathematica bug list" I got an e-mail from WRI (regarding the bugs I mentioned). I sent a replay with the following questions: > Thus, I would be very happy if you could comment on the WRI plans on > > (1) making Mathematica bug information more publicly available and > (2) improving the communication between Mathematica users and WRI, and > also among the users themselves. > > I promise that I won't disclose your answers if you intend so. I would really like to know their plans (but I promised that I will not disclose them) before we decide to set up our own bug list -- who knows, maybe next day they start an official one. I'm still waiting for the reply... p.p.s. If anybody is still interested, the singular values of M are: {44.4484, 44.4484, 27.0427, 17.7007, 8.90436, 8.90436} On Sun, Mar 22, 2009 at 6:44 AM, ADL <alberto.dilullo at tiscali.it> wrote: > Maris, I did the following computations also using the Rationalize > version of your matrix: > > In[1]:= ClearAll[M, oM, MR, oMR]; > > In[2]:= M = {...}; (* deleted from the post *) > > In[3]:= MR = Rationalize[M, 10^(-16)]; > oMR = Orthogonalize[MR]; > > In[5]:= methods = {"GramSchmidt", "ModifiedGramSchmidt", > "Householder", "Reorthogonalization"}; > > In[6]:= (oM[#] = Orthogonalize[M, Method -> #]) & /@ methods; > > In[7]:= MatrixRank[oMR] > > Out[7]= 6 > > In[8]:= MatrixRank[oM[#]] & /@ methods > > Out[8]= {6,6,12,6} > > In[9]:= Chop@Max@Abs@(oM[#] - oMR) & /@ methods > > Out[9]= {0,0,1.23961912632296,0} > > In[10]:= $Version > > Out[10]= 7.0 for Microsoft Windows (32-bit) (February 18, 2009) > > > >From this, I would say that the issue is not accuracy but the fact > that "Householder" is not working properly. If it is a feature, it is > a discount feature: you get 12 at the price of 6. > > What do you think about starting the famous "bugs and caveats" site > with this post? > > ADL > > > > > Maris Ozols ha scritto: > >> I have a large numeric matrix M (see below), whose rank is 6. Clearly, >> the rank of Orthogonalize[M] must be the same (in particular, it >> should not increase). However, if I execute the following code on my >> matrix M: >> >> MatrixRank@M >> MatrixRank@Orthogonalize[M] >> MatrixRank@Orthogonalize[M,Method->"Householder"] >> >> I get 6, 6, and 12. So it appears to me that Householder's method has >> doubled the rank of M. I am using Mathematica 7.0 in Linux. >> >> Is this a bug or a feature? >> >> ~Maris Ozols~ > >
- References:
- Re: Orthogonazlie with Method->"Householder"
- From: ADL <alberto.dilullo@tiscali.it>
- Re: Orthogonazlie with Method->"Householder"