# basicfunctions: Basic functions In ipptoolbox: IPP Toolbox

## Description

Helpful functions for creating and handling BPAs

## Usage

 ```1 2 3``` ```dsstruct(x) dsnorm(y) dsred(y, thres = 0.001) ```

## Arguments

 `x` Matrix/BPA `y` BPA `thres` Minimal mass value of a focal element desired

## Details

dsstruct

Creates a new BPA from a matrix and normalizes it.

dsnorm

Normalizes a BPA (i. e. masses sum up to 1, no lower bound larger than higher bound).

dsred

Reduces the number of focal elements in a BPA by merging adjoint elements.

The IPP Toolbox represents BPAs in a discretized form. A BPA is stored as a matrix (3 columns) that lists the focal elements. The first and second columns contain lower and upper bounds, the third column the masses of the focal elements. The function dsstruct is a simple function to create a valid BPA. It takes a three-column matrix of the above type as an input. It performs some checks (upper bound >= lower bound, masses sum up to 1) and returns a valid BPA (possibly switching lower & upper bounds of focal elements, normalizing masses to 1) with the according warning messages.

## Author(s)

Philipp Limbourg <p.limbourg@uni-due.de>

## References

Ferson, S., V. Kreinovich, et al. (2003). Constructing Probability Boxes and Dempster-Shafer Structures. Sandia Report. Albuquerque, USA, Sandia National Laboratories.

## Examples

 ```1 2 3 4 5``` ```a=dsstruct(matrix(c(2,3,0.1,1.5,5,0.9),ncol=3,byrow=TRUE)) b=dsstruct(matrix(c(2,3,0.5,10,5,0.9),ncol=3,byrow=TRUE)) c=dsodf('qexp',10000,dsstruct(c(10,20,1))); d=dsred(c,0.02) dscdf(d); ```

ipptoolbox documentation built on May 2, 2019, 2:09 a.m.