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improve quadgk docs (fix #10649)
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stevengj committed Mar 28, 2015
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Expand Up @@ -1690,6 +1690,14 @@ some built-in integration support in Julia.
Alternatively, a different norm can be specified by passing a `norm`-like
function as the `norm` keyword argument (which defaults to `vecnorm`).

[Only one-dimensional integrals are provided by this function. For
multi-dimensional integration (cubature), there are many different
algorithms (often much better than simple nested 1d integrals)
and the optimal choice tends to be very problem-dependent. See
the Julia external-package listing for available algorithms for
multidimensional integration or other specialized tasks (such as
integrals of highly oscillatory or singular functions).]

The algorithm is an adaptive Gauss-Kronrod integration technique:
the integral in each interval is estimated using a Kronrod rule
(``2*order+1`` points) and the error is estimated using an embedded
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3 comments on commit b535042

@ViralBShah
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How about a link to Cubature and any others? The package listing is a bit daunting.

@stevengj
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Do we really want to single out particular external packages here?

There are also decent importance-sampled Monte-Carlo algorithms in GSL (which are often better than Cubature for ≳ 6 dimensions or for nonsmooth integrands), the fastgauss package, and presumably other packages will be added in the future. It just seems like this list could get out of hand...

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Yes, it could get out of hand. But if I was a newcomer, it would be impossible to figure this out. Also, if users are recommended such packages, they should also be high quality. I think such a list would actually be worthwhile to have. Maybe the right time to do it is after the 0.4 release.

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