[daip] SDGRID convolution function

[Eric Greisen]

Bob Garwood wrote:
> I think what I've been slow to wrap my head around is the difference 
> between weighting by a function that goes negative vs one that is always 
> positive.   i.e. thinking of it as something like <x> = 
> sum(x*wt)/sum(wt) we think of it as a weighted average of x.  But when 
> both x and wt can be negative then surprising things can happen.  In 
> this case it must be that an essentially unsampled point in the grid is 
> getting a small (in terms of abs(wt)) contribution from a couple of data 
> points such that the sum(x*wt) value is increasing (either positively or 
> negatively) while the sum(wt) value is decreasing.   That can't happen 
> for the exponential function, even at poorly sampled cells.
> 
> FYI: I've verified at least qualitatively that it will work for us to 
> process the data from each beam in a separate process (for 
> parallelization purposes) and then combine the resulting images with 
> weights to get the final image (as opposed to dbcon'ing all of the data 
> and then making one image).  For that I think it's best to use 
> reweight(2) = some very small number and capture the convolved image 
> (reweight(1)=2) and the weight image (reweight(1)=3).  Assuming all of 
> the beam images are made with the same center, cellsize, etc, then 
> combining the images is just summing the convolved images, summing the 
> weight images and dividing the two.  At that point you can apply a 
> cut-off in weights and blank the final image appropriately.  It's also 
> necessary when summing the images to watch out for the NaNs in the 
> things being summed.  In IDL I had to replace those with zeros before 
> summing.  I would expect that to be the same as doing it via dbcon and 
> one call to sdgrd and qualitatively it looks the same - I haven't yet 
> done a quantitative comparison.

Your first paragraph is an excellent explanation of the issue.  I may 
steal some to put in the help file.

Thinks closely and read the details about paragraph 2.  See also section 
10.4.3 which is about combining independent observations of the same 
field with proper weighting (task WTSUM).  What you propose I think will 
work but check the details closely.

I notices that Glen's data set did not actually appear to contain a 
spectral line.  Instead the images at all channels were noisy but about 
the same.  Is this correct?

Eric Greisen