[Developers] [Patches] Make ADMConstraints GF public

Erik Schnetter schnetter at cct.lsu.edu
Sun Sep 17 11:24:20 CDT 2006

On Sep 16, 2006, at 23:41:56, Jonathan Thornburg wrote:

> On Sat, 16 Sep 2006, Erik Schnetter wrote:
>> The "sum" reduction has the problem that it can easily lead to  
>> large absolute
>> differences that are small relative differences.  The "average"  
>> reduction
>> behaves better in that respect, and, apart from that, tests the  
>> same thing.  I
>> suggest to avoid using the sum reduction in test cases.
> I'm confused:  Since    average := sum / sum_of_weights   , why does
>   average   not also "lead to large absolute differences that are  
> small
> relative differences"?

Because of the division by "sum_of_weights".  If you assume 10^6 grid  
points, then the absolute difference in the sum is 10^6 times the  
absolution difference in the average.  If you allow an absolute  
difference of 10^-12, then there are often cases where the average is  
deemed accurate enough, while the sum is deemed inaccurate.

Let me give an example:

Assume there are 10^6 grid points, all having the value 1.0 plus a  
small error of the order of 10^-14.  Then we have

the exact values:

	average: 1.0
	sum: 10^6

the perturbed values:

	average: 1.0 + 10^-14
	sum: 10^6 + 10^-8

The relative error of the perturbed values with respect to the  
accurate values is 10^-14 for both the average and the sum.  The  
absolute errors differ; the absolute error for the average is 10^-14,  
while the absolute error of the sum is 10^-8.


Erik Schnetter <schnetter at cct.lsu.edu>

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