customized wide-ball evaluation for integration

[Stephen Crowley]

Hi Fredrik and all,,

 I have a rather complicated function I'm trying to integrate (the Heston model characteristic function) and im running into problems with the initial wide-ball evaluation

 

φ is not finite at ([10.050 +/- 9.96] + -4.0000i)

I know the modulus of the function is a constant,

does the notes in the paper about integration in arb at the end mean that I should special-case the situation where a wide-ball is passed in, and instead of evaluating as normally which would give a nan, just set a ball at the center with bounds equal to the maximum modulus ? would that be enough to kick-start the integration?

Thanks in advance,

Stephen

[Fredrik Johansson]

Hi Stephen,

I'm not familiar with the Heston model characteristic function. If there is some form of removable singularity that prevents getting a finite enclosure, it is indeed necessary to rewrite the expression in some way.

A simple example would be something like sin(x)/x. If the input is [0 +/- r1] + [0 +/- r2]*i, say, you could return the magnitude bound exp(|r2|), for example.

Fredrik

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