ism3d.maths.stats.custom_ppf

ism3d.maths.stats.custom_ppf(func, q, sersic_n=1)

* we also wrap the random generator into rv_continous class * *** but this inline function may have better performance without the error checking overhead in rv_continous class

To build a fast persodu-random genenrator for an analytical function, the key is calculate the inverse cumlutative diftributon function or Percent Point Function (PPF) in high precisiom: This is the parameter reliazation values as a function of CDF (Percent point function):

https://docs.scipy.org/doc/scipy-0.16.1/reference/generated/scipy.stats.norm.html https://docs.scipy.org/doc/scipy/reference/tutorial/stats/continuous.html https://github.com/scipy/scipy/blob/master/scipy/stats/_continuous_distns.py https://docs.scipy.org/doc/scipy/reference/special.html

Sometimes this function will have an analytical form, which will be good in terms of performance and precision.

should support vector Although this is 1D, any fancy function can be further manupilated

https://reference.wolfram.com/language/ref/InverseCDF.html

calculate ppf from percent cutoff for common (regularized/normalized) PDF this can be used for inverse transform sampling

If “u” is an uniform random number from (0,1), then the output would be a sample following the desired distribution *

see also the appendix Xue+2020

see also: inverseCDF.nb in MM12

If “-ss” is in the function name, we will use scipy.stats build-in RV class

• typicall using scipy.special will be faster

to use this function as inverse survive function (ISF) try:

sp=1-q x=custom_ppf(func,sp)

sersic_n only works for func=”sersic2d”

The interpolation sample should stay in:

x <-> SF or x <->log(SF) space

As it’s difficult to keep the numerical accuracy and x <-> CDF for large x + close to one CDF table : when you set up a x grid, for large x, the corrspoding CDF will one due to numerical precision