Re: About diagonal matrices

[Jaroslav Hajek]

On Sun, Mar 1, 2009 at 9:16 PM, Daniel J Sebald <address@hidden> wrote:
> Jaroslav Hajek wrote:
>>
>> On Sun, Mar 1, 2009 at 8:23 PM, Daniel J Sebald <address@hidden>
>> wrote:
>>
>>> dbateman wrote:
>>>
>>>
>>>> Well I'm finally somewhere I can write an e-mail from easily, though I
>>>> haven't had the time to reread the thread. The issue I considered in the
>>>> past like this was operations like "speye(n) .^ 0" or "speye(n) ./ 0"
>>>> where
>>>> the 0.^0 and 0./0 terms of the matrix should create a NaN in the
>>>> resulting
>>>> matrix I hadn't considered the "speye(n) OP NaN" but didn't and don't
>>>> yet
>>>> see why it should be different if the NaN is pre-existing rather than
>>>> created by the binary operation, otherwise the NaN values won't
>>>> propagate
>>>> and in fact might very likely disappear. You seem to think, and have
>>>> convince John that disappearing NaN's are a good thing so I'll try to
>>>> reread
>>>> the thread and respond again later on.
>>>
>>> I think a "default sparse value" solves this, no matter what one thinks
>>> the
>>> defined behavior should be.  Call the indeces assigned the default value
>>> the
>>> "sparse set".  The sparse set could be NaN, while assigned values could
>>> also
>>> happen to be NaN.
>>
>>
>> No, it doesn't. At least not completely - just the simple cases. See
>> my previous examples about this. And it would make the sparse
>> operations more complicated and probably less efficient.
>> You are, obviously, free to propose a detailed implementation. But
>> please be more specific.
>
> Say I define a sparse matrix where indeces (i,j) in S are zero.  Call S the
> sparse set.  I.e.,
> M(i,j) = 0 for (i,j) in S
>        m_i,j otherwise
>
> Now, do an operation on M (something simple so we can avoid the issues of
> set operations across sparse matrices... I know, that's where all the work
> is), say M/0.  Then
>
> M(i,j)/0 = Nan for (i,j) in S
>          m_i,j / 0 otherwise
>
> We've kept track of the sparse set, so we still know what this.  Little has
> changed, assigned from assigning the sparse set a value.  Correct?
>

Yes. That's the simple case. Now please describe how to multiply two
sparse matrices.
Or, to get you something simple, how you multiply a full * sparse matrix.


> For the more general operations of two sparse sets, I proposed in a previous
> email to keep track of index sets.  It adds more complexity.

I'm still somewhat confused, probably. Octave indeed does keep track
of the sparsity pattern for sparse matrices. Otherwise, they could
hardly be sparse.

>
>
>>> The value of the sparse matrix is when it comes time to use it in
>>> operations
>>> where a full matrix would consume the CPU.  So it does make sense to keep
>>> track of the sparse set.
>>>
>>
>>
>> Huh? I don't understand.
>
> What is the purpose of sparse sets?  Represent large matrices that are
> mostly zero (or some default value, I argue).  Also, when solving matrix
> operations or systems of equations that are sparse, much of the computations
> can be discarded.
>

OK, that's the general idea of sparse matrices. How does it relate to
our specific problem?


> Dan
>



-- 
RNDr. Jaroslav Hajek
computing expert
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz