Just want to let whoever may be interested to know that the adapt
function (package adapt) for multivariate integration may "cheat".
A student here made a function f(x,y)=g(x)g(y) on the unit square and
sent it to adapt, and adapt happily returned a value between 2 and 3
with an error estimate of the order E-11. He then used a 128-point
Legendre quadrature produced by the gaussq.f function from netlib to
calculate the univariate integral then squared it, and the result
differ from the adapt number in the 4th or 5th digit. Forcing adapt
to use more points doesn't seem to have any effect.
We were led to this experiment when we were testing the smolyak
cubature in SMOLPACK by Knut Petras, which gave the same number as the
squared Legendre.
Chong Gu
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