[SciPy-user] Easy way to make a block diagonal matrix?

Bruce Southey bsouthey@gmail....
Thu May 21 08:38:01 CDT 2009


josef.pktd@gmail.com wrote:
> On Wed, May 20, 2009 at 9:32 PM, Bruce Southey <bsouthey@gmail.com> wrote:
>   
>> On Wed, May 20, 2009 at 7:23 PM,  <josef.pktd@gmail.com> wrote:
>>     
>>> 2009/5/20 Stéfan van der Walt <stefan@sun.ac.za>:
>>>       
>>>> 2009/5/21  <josef.pktd@gmail.com>:
>>>>         
>>>>> scipy.linalg has some matrix creation functions, some look like
>>>>>           
>>>> Thanks, that looks like a good spot.
>>>>
>>>> Please review the attached patch (if anybody does not want it to go
>>>> in, now is a good time to voice your concerns).
>>>>
>>>>         
>>> It might be better to preserve the dtype of the input arrays, e.g. I
>>> could think of a use for integer variables, e.g. dummy variables in
>>> regression or anova, or to allow an option for the dtype when you
>>> create the zeros array.
>>>
>>> I don't know if anybody would want complex or character matrices.
>>>
>>> I just checked, np.kron and np.diag preserves integer type, and
>>> np.kron converts to float for mixed types, diag preserves character
>>> type.
>>>
>>> otherwise it looks good and useful to me.
>>>
>>> Josef
>>> _______________________________________________
>>> SciPy-user mailing list
>>> SciPy-user@scipy.org
>>> http://mail.scipy.org/mailman/listinfo/scipy-user
>>>
>>>       
>> Hi,
>> What is the definition that you are using for a block diagonal matrix?
>>
>> Some definitions use square matrices:
>> http://en.wikipedia.org/wiki/Block_matrix#Block_diagonal_matrices
>> http://mathworld.wolfram.com/BlockDiagonalMatrix.html
>>
>> But Matlab's blkdiag function does not and, thus, it may not result in
>> a diagonal matrix:
>> http://www.mathworks.com/access/helpdesk/help/techdoc/index.html?/access/helpdesk/help/techdoc/ref/blkdiag.html
>>     
>
> Since it's just a useful function and not a mathematical concept, I
> think the meaning is clear from the construction and example, although
> the matlab explanation is more informative.
>   
I disagree because block diagonal does have a special meaning and the 
result is not a diagonal matrix!

> If all individual component matrices are square, then you get the
> wikipedia definition.
>   
My understanding is that only if the inputs are diagonal matrices will 
you get a block diagonal matrix from this function.

> But for regression with panel data or with dummy variables, the
> analogy to kronecker product is better, component matrices have many
> rows (observations) and only a few columns (regressors). I would have
> to look it up again, but I think the design matrix for a seemingly
> unrelated regression (SUR) would be just block_diag(x1,x2,...xn) and
> endogenous variable is vstack(y1,y2,...yn), I'm not sure what matrix
> operation (kronecker product) would yield the covariance matrix in one
> step.
> (there is only a stub at
> http://en.wikipedia.org/wiki/Seemingly_unrelated_regression and it
> doesn't look completely correct to me)
>
> The wikipedia page has more types of block matrices, and maybe some of
> them also have general use cases.
>
> I haven't gotten around yet to program anything for panel data or SUR,
> so I don't know what else might be needed.
>
> Josef
>
>   
I am not discounting the function because I am well aware of the 
potential uses of this (but not SUR models as I prefer the more general 
multivariate and mixed models). Rather I am objecting to the name 
because it does not return a block diagonal matrix.

Bruce


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