I want to compute a complicated integral with Vegas. The integral is
6-dimensional, and have
a sinusoidal factor in a linear combination of the integration
variables. The integration variables vary
from negative to positive infinity. I can't solve this integral by
simply using a coordinate substitution
that will turn each integration range to a finite range, because then
the sinusoidal factor will become pathologial.
Instead, I use a generalized spherical coordinate transformation,
which will turn the integration interval into a
finite interval, for 5 of the integration variables, where the
function called by vegas is computed as a Fourier integral
with respect to the radial parameter.
My problem is choosing good heuristics, for estimating to what
relative and absolute accuracy to use as parameters
to the Fourier integral.
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