[Maxima] nintegrate function

Raymond Toy raymond.toy at ericsson.com
Wed May 23 13:16:46 CDT 2007

>>>>> "Andrej" == Andrej Vodopivec <andrej.vodopivec at gmail.com> writes:

    Andrej> I would like to see a nice wrapper function for quadpack integration
    Andrej> methods. I have written a nintegrate function:

    Andrej> (%i1) load(nintegrate)$
    Andrej> (%i2) nintegrate(x, x, 0, 1);
    Andrej> (%o2) 0.5
    Andrej> (%i3) nintegrate(exp(-x^2), x, 0, inf);
    Andrej> (%o3) .8862269254527579
    Andrej> (%i4) nintegrate(x, x, 0, inf);
    Andrej> Numerical integration failed with error code 5
    Andrej> -- an error.  To debug this try debugmode(true);
    Andrej> (%i5) nintegrate(x, x, 0, a);
    Andrej> (%o5) nintegrate(x,x,0,a)
    Andrej> (%i6) subst(a=1, %);
    Andrej> (%o6) 0.5
    Andrej> (%i7) nintegrate(nintegrate(x+y, x, 0, y), y, 0, 1);
    Andrej> (%o7) .5000000000000001
    Andrej> (%i8) plot2d(nintegrate(sin(t)/t, t, 0, x), [x,-10,10])$

I think this is a nice convenience function.  I like how it uses
quad_qags for bounded intervals, and quad_qagi for unbounded.  I
rarely ever use any other integration routine.

Some comments:

o What desired precision is used?
o Should the user be allowed to choose that?
o What about the max number of intervals allowed for the integrator?
o Should that be user selectable?
o A Lisp style comment:

     (if test result)

  is usually written

    (when test result)

I don't think you have to fix any of the comments above, but you
should at least consider them if you haven't already.  :-)


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