https://github.com/pprunty/hart_approximation
https://github.com/pprunty/hart_approximation
Last synced: 2 months ago
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- Host: GitHub
- URL: https://github.com/pprunty/hart_approximation
- Owner: pprunty
- Created: 2022-03-22T13:33:55.000Z (about 3 years ago)
- Default Branch: master
- Last Pushed: 2023-11-23T23:41:33.000Z (over 1 year ago)
- Last Synced: 2023-11-24T00:27:45.742Z (over 1 year ago)
- Language: C++
- Size: 934 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
Part of a college assignment...
# Hart Approximation to Normal Distribution
This is a simple program that implements Hart's polynomial approximation to the Normal or Gaussian
distribution. The method provides a high precision approximation of the cumulative distribution
function (C.D.F) whose implementation lends itself to C++ since we can use constexpressions to evaluate
many of the values needed for the polynomial approximation at run time. The results are comparable in
speed and precision to that of the Boost C++ Libraries.
## Contents
1. [Overview](#overview)
2. [Requirements](#requirements)
3. [Compilation and Usage](#compilation-and-usage)
4. [Known Issues](#known-issues)
## Overview
The Gaussian object allows calculations for the ERF, CDF and PDF of a Gaussian object with given mean
and stdev.
## Requirements
- gcc
- gnuplot (if you would like to produce graphics)
- gsl (for using Sobol qrng, otherwise comment out that part of the code (L.48-56 in coord.cc))
## Compilation and Usage
To compile the code simply run the following command inside a terminal in the project directory:
```shell
make
```
To run a test on the code, simply run the following command inside a terminal in the project directory:
```shell
./main
```
Note: I know I can add this to the Makefile as 'make plot' but I prefer to leave the commands here so I can return to them.
## Results
Using Hart Approximation we see that we get very similar results to that of the Gaussian object used in the
Boost library. Likewise, we get similar, if not better performance output using Hart Approximation.
```shell
Normal Distribution with mean = 0.000000 and stdev = 1.000000
-----------------------------------------------------------
x Phi(x) Method
-3.0 0.00134989803163 Hart approx.
-3.0 0.00134989803163 BOOST Library.
-2.0 0.02275013194818 Hart approx.
-2.0 0.02275013194818 BOOST Library.
-1.0 0.15865525393146 Hart approx.
-1.0 0.15865525393146 BOOST Library.
-0.5 0.30853753872599 Hart approx.
-0.5 0.30853753872599 BOOST Library.
0.0 0.50000000000000 Hart approx.
0.0 0.50000000000000 BOOST Library.
0.5 0.69146246127401 Hart approx.
0.5 0.69146246127401 BOOST Library.
1.0 0.84134474606854 Hart approx.
1.0 0.84134474606854 BOOST Library.
2.0 0.97724986805182 Hart approx.
2.0 0.97724986805182 BOOST Library.
3.0 0.99865010196837 Hart approx.
3.0 0.99865010196837 BOOST Library.
-----------------------------------------------------------
Normal Distribution with mean = 1.00000000000000 and stdev = 2.00000000000000
-----------------------------------------------------------
x Phi(x) Method
-3.0 0.02275013194818 Hart approx.
-3.0 0.02275013194818 BOOST Library.
-2.0 0.06680720126886 Hart approx.
-2.0 0.06680720126886 BOOST Library.
-1.0 0.15865525393146 Hart approx.
-1.0 0.15865525393146 BOOST Library.
-0.5 0.22662735237687 Hart approx.
-0.5 0.22662735237687 BOOST Library.
0.0 0.30853753872599 Hart approx.
0.0 0.30853753872599 BOOST Library.
0.5 0.40129367431708 Hart approx.
0.5 0.40129367431708 BOOST Library.
1.0 0.50000000000000 Hart approx.
1.0 0.50000000000000 BOOST Library.
2.0 0.69146246127401 Hart approx.
2.0 0.69146246127401 BOOST Library.
3.0 0.84134474606854 Hart approx.
3.0 0.84134474606854 BOOST Library.
-----------------------------------------------------------
CPU time used (per clock_gettime()): 0.016768 seconds.
```
## Known Issues
None at present.