Feature/distribution speed up #261
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…ew pdf, cdf, icdf methods in Uniform and Normal
…nto feature/distribution_speed_up
…al.py and test_uniform.py
…nto feature/distribution_speed_up
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Distribution Improvements
Implement faster Uniform and Normal distribution methods and add string representations to all distributions.
Description
Added the closed form expressions for the probability density function (PDF), cumulative distribution function (CDF) and inverse cumulative distribution function (iCDF) for the normal and uniform distributions. Additionally, added string representations to all distributions using the
__repr__method. In accordance with the Python documentation the printable representation can be used to recreate the instance.Related Issue
N/A
Motivation and Context
No official issue, but this was implemented after extensive profiling of the uniform and normal distributions lead to the conclusion that the SciPy implementations can be a bottleneck during large computations. The new methods in this PR are noticeably faster than the SciPy implementations.
Adding the printable representation of the distributions allows for easier debugging and makes UQpy a better teaching tool.
How Has This Been Tested?
All string representations have been tested to confirm accurate implementation. New tests are added for the PDF, CDF, and iCDF methods to ensure consistency with SciPy methods when inputs are not-a-number and infinity, as well as numerical accuracy when the inputs take on values in the support of the relevant distribution.
Types of changes
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