A good uncertainty (interval) arithmetic library?

Question

edited

Given that the words "uncertain" and "uncertainty" are fairly ubiquitous, it's hard to Google "uncertainty arithmetic" and get anything immediately helpful. Thus, can anyone suggest a good library of routines, in almost any programming/scripting language, that implements handling of uncertain values, as per this description:

Use uncertainty arithmetic to record values that are approximations, for which there is a measured tolerance. This is when we are unsure about a value, but know the upper and lower bounds it can have, expressed as a ±value.

Answer 1

It's not a library, but your question reminded me of an example in "Expert F#" that describes probabilistic workflows:

instead of writing expressions to compute, say, integers, we instead write expressions that compute distributions of integers. This case study is based on a paper by Ramsey and Pfeffer from 2002.

You can read the excerpt on google books.

Answer 2

I'd probably go about this by declaring a class called UncertainValue, with methods and properties such as (psuedocode):

class UncertainValue
{
  private double upperbound;
  private double lowerbound;
  private double nominalvalue;
  private double certainty;
  ...
  UncertainValue add(UncertainValue value);
  UncertainValue multiply(UncertainValue factor);
}

I realise this doesn't answer your question in terms of finding a pre-made library, sorry.

Answer 3

Have a look at Thomas Flanagan's Error Propagation Java class. The approach it uses is most excellent for handling uncertainty without excess trouble.

Answer 4

I believe "Interval Arithmetic" is the more common name for what you're looking for. boost::interval would be my first choice for a supporting library.

Answer 5

If you are looking for an error propagation module (this is different from interval arithmetic, but error propagation is what is commonly used by scientists), I would suggest that you have a look at my uncertainties Python module. It handles error/uncertainty propagation in a transparent way, and, contrary to many implementations, properly handles correlations between variables.