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Add Bessel Functions and Pochhammer Symbols #96
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Adding the actual functions to our math lib won't be bad, but I'm not sure how we're going to do the fwd mode and reverse mode auto diff with the series. I've worked out what the fwd mode auto diff would be as a series for bessel functions of the first kind, but I'm not sure how to condense it:
Check out the identities in the descriptions in the Boost
doc:They work them out directly for Bessel functions of the first
and second kind.- Bob
On 5/29/13 2:42 PM, Peter Li wrote:
Adding the actual functions to our math lib won't be bad, but I'm not sure how we're going to do the fwd mode and
reverse mode auto diff with the series. I've worked out what the fwd mode auto diff would be as a series for bessel
functions of the first kind, but I'm not sure how to condense it:image https://f.cloud.github.com/assets/3487481/580693/457b0b90-c88d-11e2-8bd3-c7a3f2f2e8d0.png
—
Reply to this email directly or view it on GitHub #96 (comment).I worked it out and I think the derivatives they give are with respect
to z. That's helpful for rev mode, but we still have the problem with
forward mode. And now that I think about it, I think I have the same
problem with Owen's T, which I still need to implement in fwd mode.Peter
On 5/29/13 2:55 PM, Bob Carpenter wrote:
Check out the identities in the descriptions in the Boost
doc:They work them out directly for Bessel functions of the first
and second kind.- Bob
On 5/29/13 2:42 PM, Peter Li wrote:
Adding the actual functions to our math lib won't be bad, but I'm
not sure how we're going to do the fwd mode and
reverse mode auto diff with the series. I've worked out what the fwd
mode auto diff would be as a series for bessel
functions of the first kind, but I'm not sure how to condense it:image
https://f.cloud.github.com/assets/3487481/580693/457b0b90-c88d-11e2-8bd3-c7a3f2f2e8d0.png—
Reply to this email directly or view it on GitHub
#96 (comment).—
Reply to this email directly or view it on GitHub
#96 (comment).On 5/29/13 3:24 PM, Peter Li wrote:
I worked it out and I think the derivatives they give are with respect
to z.Right.
But the order's an int, so we shouldn't need to differentiate
with respect to that.That's helpful for rev mode, but we still have the problem with
forward mode. And now that I think about it, I think I have the same
problem with Owen's T, which I still need to implement in fwd mode.For either forward or reverse you need the same partial derivatives.
So if you can do one, you can do the other.- Bob
Alright. What category would the Bessel functions go under?
On 5/29/13 3:58 PM, Peter Li wrote:
Alright. What category would the Bessel functions go under?
Category as in special function? They should go wherever
the gamma functions go.It'll be great to get these in because they're required for
a bunch of fancy distributions that will then be relatively
easy to code up in Stan.- Bob
Bessel functions of first and second kind.
And the Pocchammer symbols: