[Octave-bug-tracker] [bug #62412] integral gives consistent inaccurate result for improper integral to inf

[Nicholas Jankowski]

Update of bug #62412 (project octave):

                Severity:              3 - Normal => 2 - Minor              
                  Status:                    None => Confirmed              
                 Release:                   6.2.0 => dev                    
        Operating System:       Microsoft Windows => Any                    

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Follow-up Comment #1:

as a comparison, in matlab 2022a:


>> integral(f,1,inf)
Warning: Reached the limit on the maximum number of intervals in use.
Approximate bound on error is   2.2e-03. The integral may not exist, or it
may be difficult to approximate numerically to the requested accuracy. 
> In integralCalc/iterateScalarValued (line 372)
In integralCalc/vadapt (line 132)
In integralCalc (line 83)
In integral (line 87) 

ans =

  -9.993656849721580


So even matlab recognizes some issues with this one.

As the help describes, Octave's integral is a wrapper to quadcc, quadgk, or
quadv,selected based on the type of inputs/options chosen, and better accuracy
may be obtained by running them directly. quadv breaks on that one, but if I
run the other two manually in octave, it appears integral is choosing quadcc:


>> quadcc(f,1,inf)
ans = -9.784172499874394

>> quadgk(f,1,inf)
warning: quadgk: maximum interval count (650) exceeded
warning: called from
    quadgk at line 393 column 7

warning: quadgk: Error tolerance not met.  Estimated error 0.00605827
warning: called from
    quadgk at line 404 column 5

ans = -9.990824621478369

>> quadgk(f,1,inf, "maxintervalcount", 100000)
warning: quadgk: non-finite integrand encountered
warning: called from
    quadgk at line 348 column 7

warning: quadgk: Error tolerance not met.  Estimated error 0.00178496
warning: called from
    quadgk at line 404 column 5

ans = -9.994594924648961


funny enough, the best answer in Octave comes from just calling the 'old'
routine 'quad:

Octave:
>> quad(f,1,inf)
ans = -9.999999999999767

matlab:
>> quad(f,1,inf)
Warning: Infinite or Not-a-Number function value encountered. 
> In quad (line 100) 
ans =
   NaN


it may be that there's some improvement that can be done in function
selection, but the goal when implementing integral was to get a compatible
function in place. it hasn't really been revisited for improvement since.


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