Re: Re: Inverse of a Matrix

[aa...@buffalo.edu]

Hi Edward,
          I was searching online for an algorithm which calculates the inverse of
a matrix and is suitable for parallel computation and I came across this
algorithm called Gausian - Jordan elimination. The algorithm is as follows:

Loop from i=1 to n 
     In parallel for j =1 to n
            scale = a[j,i]/ a[i,j]
            if i!=j
                 for k=1 to n+1
                      a[j,k]= a[j,k]- scale* a[i,k]

What do you think of this algorithm ? Is it possible to implement it in Map
Reduce Paradigm ? 

Thank You

Abhishek Agrawal

SUNY- Buffalo
(716-435-7122)

On Sun 11/29/09  8:06 PM , "Edward J. Yoon" edwardyoon@apache.org sent:
> Sounds great. (I couldn't start yet.)
> 
> If you have any problem, question, and comments during the
> implementation, Pls feel free to let me know. I'll help you.
> 
> Thanks.
> 
> On Mon, Nov 30, 2009 at 7:30 AM,  <aa225@buffa
> lo.edu> wrote:> Hello,
> >      I am
> working on a project which requires me to compute the inverse of
> a> matrix. I saw on a forum in which you wrote that
> you were going to implement it> soon. I wanted to know is the source code of it
> available yet ? In the mean time> I will also start working on it, I will let you
> know if I have made any progress> in towards this end.
> >
> > Thank You
> >
> > Abhishek Agrawal
> >
> > SUNY- Buffalo
> > (716-435-7122)
> >
> >
> >
> >
> 
> 
> 
> -- 
> Best Regards, Edward J. Yoon @ NHN, corp.
> edwardy
> oon@apache.orghttp://blog.udanax.org
> 
> 
> 

Re: Re: Inverse of a Matrix

["Edward J. Yoon" <ed...@apache.org>]

> Loop from i=1 to n
>     In parallel for j =1 to n
>            scale = a[j,i]/ a[i,j]
>            if i!=j
>                 for k=1 to n+1
>                      a[j,k]= a[j,k]- scale* a[i,k]

Hi,

Above mentioned G.J.E algorithm is loop over rows... like a Map/Reduce
computation. However, The last line (a[j,k]= a[j,k]- scale* a[i,k])
means that replace all other rows. It's a big operation so won't work
on map function since mapper has a time limit.

> What do you think of this algorithm ? Is it possible to implement it in Map
> Reduce Paradigm ?

I think it's good method and possible, if you implement it using
iterative MapReduce computations.

On Thu, Dec 3, 2009 at 3:45 PM,  <aa...@buffalo.edu> wrote:
> Hi Edward,
>          I was searching online for an algorithm which calculates the inverse of
> a matrix and is suitable for parallel computation and I came across this
> algorithm called Gausian - Jordan elimination. The algorithm is as follows:
>
> Loop from i=1 to n
>     In parallel for j =1 to n
>            scale = a[j,i]/ a[i,j]
>            if i!=j
>                 for k=1 to n+1
>                      a[j,k]= a[j,k]- scale* a[i,k]
>
> What do you think of this algorithm ? Is it possible to implement it in Map
> Reduce Paradigm ?
>
> Thank You
>
> Abhishek Agrawal
>
> SUNY- Buffalo
> (716-435-7122)
>
> On Sun 11/29/09  8:06 PM , "Edward J. Yoon" edwardyoon@apache.org sent:
>> Sounds great. (I couldn't start yet.)
>>
>> If you have any problem, question, and comments during the
>> implementation, Pls feel free to let me know. I'll help you.
>>
>> Thanks.
>>
>> On Mon, Nov 30, 2009 at 7:30 AM,  <aa225@buffa
>> lo.edu> wrote:> Hello,
>> >      I am
>> working on a project which requires me to compute the inverse of
>> a> matrix. I saw on a forum in which you wrote that
>> you were going to implement it> soon. I wanted to know is the source code of it
>> available yet ? In the mean time> I will also start working on it, I will let you
>> know if I have made any progress> in towards this end.
>> >
>> > Thank You
>> >
>> > Abhishek Agrawal
>> >
>> > SUNY- Buffalo
>> > (716-435-7122)
>> >
>> >
>> >
>> >
>>
>>
>>
>> --
>> Best Regards, Edward J. Yoon @ NHN, corp.
>> edwardy
>> oon@apache.orghttp://blog.udanax.org
>>
>>
>>
>
>



-- 
Best Regards, Edward J. Yoon @ NHN, corp.
edwardyoon@apache.org
http://blog.udanax.org