[SciPy-user] Sparse with fast element-wise multiply?

[David Warde-Farley]

On 17-Dec-07, at 11:41 PM, Nathan Bell wrote:

> Currently elementwise multiplication is exposed through A**B where A  
> and B are
> csr_matrix or csc_matrix objects.  You can expect similar  
> performance to A+B.

Whoa, you're not kidding:

In [19]: time multiply_coo(k1,k2)
CPU times: user 0.77 s, sys: 0.08 s, total: 0.85 s
Wall time: 0.86
Out[19]:
<7083x7083 sparse matrix of type '<type 'numpy.float64'>'
	with 24226 stored elements in COOrdinate format>

In [20]: time k1csr ** k2csr
CPU times: user 0.02 s, sys: 0.00 s, total: 0.02 s
Wall time: 0.02
Out[20]:
<7083x7083 sparse matrix of type '<type 'numpy.float64'>'
	with 24226 stored elements in Compressed Sparse Row format>


Actually it's about 5 times FASTER than adding the two of them.  
Probably because in the latter it's the union of the elements that is  
the result, rather than the (typically sparser) intersection.

> I don't know why ** was chosen, it was that way before I started  
> working on
> scipy.sparse.

It seems sensible enough to me; I don't know how often I've had to  
exponentiate a matrix (much less a sparse one) and if you want to do  
any serious exponentiation it's usually cheaper (and I'd expect more  
numerically stable) to diagonalize it once & exponentiate the  
eigenvalues.
Is this ** behaviour documented anywhere?

>  I've added a .multiply() method to the sparse matrix base class
> that goes through csr_matrix:
> http://projects.scipy.org/scipy/scipy/changeset/3682


Muchos gracias.

DWF