Re: [WWdevel] parser fun_cmp() error?

[P G. L. <gl...@um...>]

Hi Davide,

> This problem has got me thinking about whether it would be possible to 
> help the professor out with analyzing their functions and telling them 
> if they are nearly linear, for example, or if the values are very large 
> or very small, or if the value of the function varies greatly if the 
> constants are varied slightly, and other such things that could cause 
> numeric instability.

My first reaction is that having some sort of testing like this could be 
very useful.  My experience has been that most of the time I'm pretty good 
at anticipating problems, but that's taken me a while to develop, and it 
somehow doesn't translate well to when I'm proofreading problems that I 
get from someone else.  Something that caught "basic errors" like 
ill-behaved functions could be very useful to flag where things like the 
default limits should be changed.

Then I would just have to remember that I should use it.  :)

Gavin

On Fri, 23 Sep 2005 at 11:00 Davide P.Cervone wrote:

>> You can also adjust the tolerances.  The default relTol is .1 meaning 0.1%. 
>> This may not be suitable for this problem.
>
> Yes, but my point was (as you suggest above) that that isn't really going to 
> solve the problem because the two functions really ARE nearly identical on 
> the tested range.  Jacking up the tolerances in order to distinguish between 
> these two will cause it to fail to mark correct answers where the students 
> have replaced the fractions by decimal approximations, for example.  This is 
> why I said "yes and no" as the answer to "is this a tolerance issue".
>
> This problem has got me thinking about whether it would be possible to help 
> the professor out with analyzing their functions and telling them if they are 
> nearly linear, for example, or if the values are very large or very small, or 
> if the value of the function varies greatly if the constants are varied 
> slightly, and other such things that could cause numeric instability.  It 
> would be possible to set a flag that starts "testing mode" and have the 
> answer checker report these sorts of potential problems.  Even just producing 
> a graph of the function on the default range might be illuminating.  Do you 
> think this might be helpful?
>
> Davide

-- 
P. Gavin LaRose, Ph.D.  Program Manager (Instructional Tech.)
Math Dept., University of Michigan
gl...@um...                        "There's no use in trying," [Alice]
734.764.6454                             said. "One Can't believe impossible
http://www.math.lsa.umich.edu/~glarose/  things." "I daresay you haven't had
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                                                               - Lewis Carrol