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Re: pseudo code for doing SVD on 2D sparse array [message #64419 is a reply to message #64321]

Sun, 21 December 2008 06:46

Brian Borchers
Messages: 1
Registered: December 2008

Junior Member

On Dec 21, 4:41 am, erano <eran.o...@gmail.com> wrote:
> Hi,
> I wish to solve Ax=B
> A is sparse array (size m*n), in format of [ x_index, y_index, value ]
> B is vector length m
> x is unknown vector length n
> n=1,000,000
> m=2*n
>

The title of your posting refers to the SVD, but the body of the
posting indicates that you want to solve a linear system of equations,
perhaps in the least squares sense.

Unfortunately, computing the SVD of your 2,000,000 by 1,000,000 sparse
matrix is utterly impractical- it would require the storage of a
1,000,000 by 1,000,000 fully dense matrix and a 2,000,000 by 2,000,000
fully dense matrix, which would take up about 2.4e13 bytes of
storage...

Finding a least squares solution to the system of equation should
probably be done using an iterative method such as lsqr. In order to
do this, you'll first want to convert your data into a MATLAB sparse
matrix with

As=sparse(A(:,1),A(:,2),A(:,3));

Then solve with

x=lsqr(As,b);

Since your matrix is extremely large, this could take a long time or
simply fail to converge. If so, you might want to loosen the default
tolerance, introduce a preconditioner, etc. The documentation on lsqr
explains how to do these things.

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[Message index]

		pseudo code for doing SVD on 2D sparse array By: erano on Sun, 21 December 2008 03:41
		Re: pseudo code for doing SVD on 2D sparse array By: Evgenii Rudnyi on Mon, 22 December 2008 07:17
		Re: pseudo code for doing SVD on 2D sparse array By: Jeremy Bailin on Mon, 22 December 2008 07:07
		Re: pseudo code for doing SVD on 2D sparse array By: erano on Tue, 23 December 2008 06:58
		Re: pseudo code for doing SVD on 2D sparse array By: spellucci on Sun, 21 December 2008 08:30
		Re: pseudo code for doing SVD on 2D sparse array By: Brian Borchers on Sun, 21 December 2008 06:46

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