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RE: RowReduce for SparseArray

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90989] RE: [mg90948] RowReduce for SparseArray
  • From: "Jose Luis Gomez" <jose.luis.gomez at itesm.mx>
  • Date: Sat, 2 Aug 2008 03:25:53 -0400 (EDT)
  • References: <200807310656.CAA07710@smc.vnet.net>

Dear Brey

I am Not sure if my response is going to be useful, or even interesting for
you, but I will give it a try anyway.

The Bra-Ket Dirac Notation, as used in Quantum Mechanics, could be regarded
as a special notation for sparse arrays (or sparse tensors), with the
difference that a given Dirac Notation expression usually does Not carry
information about the actual dimension of the tensor, it only carries
information about the non-zero elements of the matrix (tensor)

My point is that Dirac Notation can ALSO be used for NON-Quantum Mechanics
applications. Here you have some simple examples, where some calculations
are performed using Dirac Notation, and the same calculations are repeated
with "normal" matrices, and there is also conversion between matrices and
Dirac Notation (please notice that long-urls are usually broken in e-mails
and posts to this group, so you might have to "manually" reconstruct the
links below if they get broken in several lines):

http://homepage.cem.itesm.mx/lgomez/quantum/matrices/matrices.html 

http://homepage.cem.itesm.mx/lgomez/quantum/powerseries/powerseries.html 


So, if it seems interesting to use Dirac Notation for operators as an
alternative to Sparse Arrays, you could download and use our package for
Dirac Notation in Mathematica:

http://homepage.cem.itesm.mx/lgomez/quantum/index.htm 

If you do so, please let me know. It would be great for us to have examples
of our Quantum package applied to Non-Quantum-Mechanical applications.

Best regards
Jose 
Mexico



-----Mensaje original-----
De: brey_maastricht at hotmail.com [mailto:brey_maastricht at hotmail.com] 
Enviado el: Jueves, 31 de Julio de 2008 01:57
Para: mathgroup at smc.vnet.net
Asunto: [mg90948] RowReduce for SparseArray

Dear reader,

Unfortunately, the Mathematica function RowReduce does not work with
sparse datatypes.
To be precise: it accepts matrices of type SparseArray as input but
the output, the reduced matrix, is always a non sparse datatype.
Because of this my computations crash because storing the matrix as a
Normal[] type just uses too much memory, whereas it could be stored
when it was a SparseArray type.

Now I was wondering; does someone have an efficient RowReduce method
in Mathematica which is capable of returning SparseArrays, and also is
able to use arithmetic modulo p ( RowReduce[M, Modulo->p] ) ??

Kind regards,
Brey
The Netherlands




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