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From Gilles <>
Subject Re: [math] new feature to allow infinite limits in numerical integration.
Date Thu, 25 Jul 2013 12:33:26 GMT
On Wed, 24 Jul 2013 07:50:25 -0700, Ajo Fod wrote:
> It would be nice to know whether the Gauss-Hermite implementation 
> recently
>> added proves useful for that purpose; and if so, whether it could be 
>> added
>> as a non-trivial example in the user guide.
> I'll check it out when I get back to it.
>> How do you propose to do the test without a change of variables?
>> The test would consist in assessing how different adaptive 
>> strategies
>> perform
>> when integrating the transformed Gaussian over [-1, 1].
> How do you propose that I make the transformation to [-1,1] available 
> for
> the tests?

For the time being (i.e. until we gather ideas on how to represent a
change of variable in CM that would not necessarily be tied to the
computation of improper integrals), the test function can be stored in
the "test" part of the repository (see how functions are defined there
for e.g. testing root solvers), within the package that will provide
unit tests for adaptive strategies.

f(x) = N(mu, sigma; x)
tsq(x) = x * x
tcp(x) = (1 - tsq(x))
g(x) = x / tcp(x)
h(x) = (1 + tsq(x)) / (tcp(x) * tcp(x))
fc(x) = f(g(x)) * h(x)

So, for the caller (unit test), there is just the univariate function
"fc(x)" (probably parameterized with "mu" and "sigma") without any
reference to a change of variable.


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