proposal to cut out romberg and quanc8 functions

I don't have any strong opinions about this. But romberg and quanc8
have the advantage that they can be nested:

(%i1) romberg(romberg(x^2+y^2, x, 0, y), y, 0, 1);
(%o1) 0.33333333333333
(%i2) integrate(integrate(x^2+y^2, x, 0, y), y, 0, 1);
(%o2) 1/3

Andrej

On 1/3/07, Robert Dodier <robert.dodier at gmail.com> wrote:
> Hello, I want to cut out the romberg and quanc8 functions.
> These are numerical quadrature functions which are superseded
> by QUADPACK. I believe that it will improve Maxima to remove
> these obsolete functions.
>
> Specifically I want (1) to move
>
> demo/rombrg.dem
> doc/share/rombrg.usg
> src/rombrg.lisp
>
> share/numeric/qq.dem
> share/numeric/qq.lisp
> share/numeric/qq.usg
>
> to the archive directory, and (2) to cut out the descriptions of the
> romberg and quanc8 stuff from the reference manual.
>
> (There is also a version of romberg which uses bigfloat computations.
> I am undecided about whether or not to also remove that.)
>
> romberg implements Romberg's extrapolation method.
> quanc8 implements an adaptive Newton-Cotes method.
> These methods are superseded by the Gauss-Kronrod methods
> implemented in QUADPACK. The QUADPACK functions are
> extrapolation methods, and the basic rules are Gaussian
> quadrature rules. Also, QUADPACK contains methods for
> specific problems (infinite interval, integrand with diferent
> weight functions, Cauchy principal value) and romberg and
> quanc8 do not.
>
> Empirically I have tested the romberg, quanc8, and quad_qags
> (from QUADPACK) on a set of 15 problems collected from the
> documentation for romberg, quanc8, and QUADPACK.
> Except for one problem in which numerical integration is expected
> to fail, I found that quad_qags always reports success and always
> meets the specified relative error tolerance (1e-6).
> romberg failed to converge or failed with a programming error
> in several cases, although it met the error tolerance otherwise.
> quanc8 failed to converge or failed with a programming error in
> some cases, and reported success without meeting the relative
> error tolerance in some others, and reported success and met
> the error tolerance in others.
>
> Thus I believe that it can established that QUADPACK is superior
> both from theoretical considerations and empirical observations.
>
> I would like to know if you are opposed to cutting romberg and quanc8.
>
> All the best, & hope this helps,
> Robert Dodier
>
> PS.
> input script: http://maxima.sourceforge.net/misc/compare_quadrature.mac
> raw output: http://maxima.sourceforge.net/misc/compare_quadrature.log
> summary: http://maxima.sourceforge.net/misc/compare_quadrature.txt
> (and also shown here)
>
>     legend:
>
>     (t/F, nnn) = (met relative error claim, #function evaluations)
>     F.C. = failed to converge
>     f.c.e. = failed to converge, but that was expected
>     X/0 = division by 0
>
>             quad_qags   romberg     quanc8
>
>     F1      (t, 609)    F.C.        (t, 289)
>
>     F2      (t, 441)    (t, 85)     (t, 1089)
>
>     F3      (t, 2037)   F.C.        (F, 481)
>
>     F4      (t, 105)    (t, 257)    (t, 65)
>
>     F5      (t, 21)     (t, 17)     (t, 33)
>
>     F6      (t, 21)     (t, 65)     (t, 33)
>
>     F7      (t, 399)    F.C.        (t, 305)
>
>     F8      (t, 357)    (t, 2049)   (F, 145)
>
>     F9      (t, 441)    (t, 277)    (t, 5937)
>
>     F10     f.c.e.      f.c.e.      f.c.e.
>
>     F11     (t, 525)    (t, 2049)   (F, 33)
>
>     F12     (t, 525)    (t, 1025)   (t, 353)
>
>     F13     (t, 231)    X/0         X/0
>
>     F14     (t, 693)    F.C.        F.C.
>
>     F15     (t, 819)    X/0         X/0
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