Re: About diagonal matrices

[Jaroslav Hajek]

On Sun, Feb 22, 2009 at 5:07 PM, John W. Eaton <address@hidden> wrote:
> On 22-Feb-2009, Jaroslav Hajek wrote:
>
> | 1. Leave the assumed zeros treatment. Document it (I'm working on this)
>
> OK, after seeing your arguments and thinking about it a bit more, I
> agree that we should do this if
>
>  * There is no way for an operation involving a diagonal matrix to
>    wipe out an existing NaN value.  This is different from what we
>    have been talking about (generating NaN values with full matrix
>    operations vs. not generating them at all with a diagonal matrix
>    becuase the operations are skipped).  If you already have a NaN
>    value, I think you want to have it propagated through other
>    calculations.  I can't come up with any examples, and given that
>    you have apparently already taken care of cases like
>
>      diag ([1, 2]) ./ [1, 0; 3, 4]
>
>    I assume you thought about this problem.
>

Well, that's not really true. Consider:
a = sparse([1,2],[1,1],[1,2],3,3); a * [1; 1; NaN]
ans =

   1
   2
   0

I.e., in a situation where an element of a vector is always ignored
(due to the sparsity pattern), NaN is also ignored. Was this what you
were referring to? It's just the assumed zeros problem all again.
This cannot happen for square diagonal matrices, but can happen for
rectangular diagonal matrices:
diag(1:3,3,4) * [1:3,NaN]'
ans =

   1
   4
   9

The situation is really analogous. To say it differently, it's as if
you did a part of the calculation symbolically; therefore, the invalid
numerical value (which a NaN is) does not demonstrate itself.
If you only think about the diagonal and permutation matrices as
optimizations to full matrix operations, that should otherwise
preserve their properties, then they're probably not a good idea at
all.
I never thought Octave's operations should be regarded as defined
sequences of floating-point operations, but rather that they should
deliver approximations to mathematical results in any suitable way.
If we disagree on this basic point, then that's a fundamental problem
and in that case, the diagonal & permutation matrices were probably
not a good idea in the first place.
If not, then I actually do not understand where the problem is. Again,
I remind that the situation has been around for ages and is not
specific to Octave.


>  * There is a function to coerce a full matrix to a diagonal matrix.
>    It should require that all off-diagonal elements are numerically
>    zero.  This is not the same as the current diag function.

I don't understand this point? Why is such a function needed?

>  * We do not implement automatic conversion from full to diagonal or
>    full to sparse.
>

I don't think we do any such conversions, only the other way.

> Does that seem reasonable?
>
> jwe
>



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