Specifying integration limits

[NominHanggai]

Specifying integration limits

[scarlehoff]

Hi @Mulliken, thanks for opening the issue!

You cannot. But you can easily transform any 0-1 random variable to any x_min, x_max in your integrand, assuming r is the random variable between 0 and 1 and x_min, x_max your integration limits for this variable:

x = x_min + r*(x_max - x_min)
jac = (x_max - x_min)
[...]
result *= jac

Since you changed the integration limits the result needs to be multiply the result by the jacobian of the transformation.

tbh, this is something that has come up a few times already in the past so I think we will either add the option or document what I wrote above (which might be obvious but better explicit than implicit!)

[NominHanggai]

Thanks @scarlehoff! Adding this explicitly to the doc would help a lot!

Although now I understand the integration limits, I still have some questions about the code in /example/simgauss_tf.py. What does this line coef = tf.reduce_sum(tf.range(n100 + 1)) do? What is n100 defined for?

Thanks!

[scarlehoff]

That is just an example, in this case the 100 is used several times so I put it as a variable to give a bit more conplexity to the example.

[NominHanggai]

How n100 is related to the Gaussian integrand? For example, I can understand coef += tf.reduce_sum(tf.square((xarr - 1.0 / 2.0) / a), axis=1) is the exponent in the Gaussian integrand, but what does n100 do?

[scarlehoff]

It's just a way of adding complexity to the integrand. Actually, the first and third line cancel each other:

    coef = tf.reduce_sum(tf.range(n100 + 1))
    coef += tf.reduce_sum(tf.square((xarr - 1.0 / 2.0) / a), axis=1)
    coef -= (n100 + 1) * n100 / 2.0

so the result corresponds only to the line in the middle.

[NominHanggai]

Gotcha! Thanks @scarlehoff !