On Oct. 6, 2011, Raymond Toy wrote:
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>So? I think it just means that quadpack was rather conservative in its
>estimate of what the relative error actually was >and the limit was too low
>for quadpack to refine the estimate any further.
>
>But what if you didn't know the analytical solution and therefore the
>"true" error? All you would have is the >estimated value. Then what?
The first step should be to roughly estimate the size of the
integral. I think quad_qag with key = 6, limit = 800, epsrel = 1.0E-2
just to get a rough value, even if an oscillatory integrand.
The next step is to use either quad_qag (default) or
quad_qags (if option 'singular' is added to the input line)
and just use reasonable values for the optional parameters,
hide the intermediate results from the users, (that also means
to surpress the slatec error messages)
and use the results returned to use better option values
if needed to get the default or requested precision. This
might require several passes.
If the integrand is too hard, we simply tell the user that.
Ted