[SciPy-User] Large banded matrix least squares solution

[J. David Lee]

On 03/16/2011 03:02 PM, Charles R Harris wrote:
>
>
> On Wed, Mar 16, 2011 at 1:53 PM, J. David Lee <johnl at cs.wisc.edu 
> <mailto:johnl at cs.wisc.edu>> wrote:
>
>     Hello.
>
>     I'm trying to find a least squares solution to a system Ax=b,
>     where A is
>     a lower diagonal, banded matrix. The entries of A on a given diagonal
>     are all identical, with about 300 unique values, and A can be quite
>     large, on the order of 1e6 rows and columns.
>
>
> So this is sort of a convolution? Do you need exact, or will somewhat 
> approximate do? I think you can probably do something useful with an fft.
What I have is data from a detector that is passed through a shaping 
amplifier that turns voltage steps into pulses. I've measured the 
characteristic pulse shape, but now I'm interested to see if I can move 
backwards from the shaped data to the detector data. The idea is that we 
assume that there is a pulse at every time point and find the amplitude 
at each point in time to match our raw data.

Here is an image of the detector's data (green), and the shaped data (blue):

http://mywebspace.wisc.edu/jdlee1/web/detector_and_shaped_data.png

David

>     scipy.sparse.linalg.lsqr works on smaller examples, up to a few
>     thousand
>     rows and columns, but not much larger. It is also very time
>     consuming to
>     construct A, though I'm sure there must be a fast way to do that.
>
>     Given the amount of symmetry in the problem, I suspect there is a fast
>     way to calculate the result, or perhaps another way to solve the
>     problem
>     entirely.
>
>
> Chuck
>
>
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