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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~
>
>


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