IntervalMonoFuncs.jl

A collection of monotonic maps. Only 1D endomorphisms on finite intervals are considered for now.

Consider 1D monotonic functions on an interval, i.e.

$$ f: \left[ a,b \right] \rightarrow \left[ a,b \right] \subset\mathbb{R}, a < b.$$

This package create piecewise-linear functions and logistic-probit functions of this type; see nomenclature section of the documentation. They can be used to create transport maps that transform the uniform distribution on an interval to some piecewise-uniform distribution that has mass concentrated in the user-specified regions.

See the documentation page for details.

Install:

From the Julia REPL, type ] then add https://github.com/RoyCCWang/IntervalMonoFuncs.jl.

Examples

All example Julia scripts are in the /examples folder. There are also full example guides based on the example Julia scripts on the documentation website.

Notes

There are known numerical instabilities for certain parameter combinations with evalcompositelogisticprobit() and evalinversecompositelogisticprobit(). We advise the user to test for numerical stability when using a particular combination of parameters (a and b) for those functions in the application at hand. See /examples/logistic-probit.jl for an example of stability test.