ufuncs, iterators

[Matthew Knepley]

Simon Burton <simon at arrowtheory.com> writes:

> Oh, that should probably read:
>
> exp( -1/2\sigma^{2} ||x1_{i} - x2_{j}||_{2}^{2}) 
>
> And when we vectorize this operation:
>
> ||x1_i - x2_j||^2 = ||x1_i||^2 + ||x2_i||^2 + 2*(x1_i,x2_j)
>
> and the last term is the ip matrix.
>
> It seems that this expression satisfies the linear operator
> requirement (it's invarient under linear isometries).

  I am looking again, and it appears to be the normalized graph laplacian.
This is indeed a linear operator which we need to support.

     Matt

> Simon.
>
>
> On Thu, 18 Aug 2005 23:12:21 -0500 (CDT)
> Barry Smith <bsmith at mcs.anl.gov> wrote:
>
>> 
>>   In terms of exp( -1/2\sigma^{2} ||x_{i} - x_{j}||_{2}^{2})  
>> what are they?
>> 
>>    Thanks
>> 
>>    Barry
>> 
>> 
>> On Fri, 19 Aug 2005, Simon Burton wrote:
>> 
>> > On Thu, 18 Aug 2005 22:49:29 -0500 (CDT)
>> > Barry Smith <bsmith at mcs.anl.gov> wrote:
>> > 
>> > > 
>> > >   What is x1, x2 and ip?
>> > > 
>> > >    Barry
>> > 
>> > x1 and x2 are 2-arrays; their rows are the 'sample' vectors.
>> > ip is the matrix of all inner products from x1 and x2.
>> > 
>> > Simon.
>> > 
>> > 
>> > 
>> 
>
>
> -- 
> Simon Burton, B.Sc.
> Licensed PO Box 8066
> ANU Canberra 2601
> Australia
> Ph. 61 02 6249 6940
> http://arrowtheory.com 
>
>
>

-- 
"Failure has a thousand explanations. Success doesn't need one" -- Sir Alec Guiness