polynomial function enclosures (PFEs) approximating exact real functions

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BSD3 licensed by Michal Konecny (Aston University)
Maintained by

AERN-RnToRm provides datatypes and abstractions for approximating functions of type D -> R^m where D is a bounded interval in R^n with non-empty interior.

The main datatype are function enclosures whose boundaries are piece-wise polynomial with a bounded degree. (This degree can be set arbitrarily high or as low as 0.) This datatype is supported by safely rounding operations whose precision can be increased arbitrarily, so that they all converge to the exact operations. Field operations, integration, maximisation and some elementary operations (namely exp, sin, cos) are among those already implemented.

For an architectural overview, see module Data.Number.ER.RnToRm.

A mathematical description of the very basics as well as a brief comparison with Taylor Models is included in the paper

Simple examples of usage can be found in folder examples and a test suite can be run via the module in the folder tests.

Changes 29 July 2009: renamed "demos" fodler to "examples"
0.5.0: 28 July 2009
* Made the testing harness more generic so that it can be used
for any base. Also a readable report is produced for each
tested property with statistics for timing and precision.
* New support for anti-consistent function enclosures and twin arithmetic
(analogous to directed/improper intervals such as [2,0] and
outer+inner rounded Kaucher arithmetic over them).
* Fixed many bugs.
* Improved precision of enclosure comparison. 24 February 2009: fixed errors in haddoc comments
0.4.9: 23 February 2009
* Added a quickcheck testing harness for the polynomial arithmetic core.
* Rewritten polynomial arithmetic core.
* Fixed many rounding errors affecting almost all operations.
* New operation: substitution into an enclosure of a *monotone* function.
* In enclosure arithmetic, now can set a limit on the size of each enclosure representation.
This is important for many-variate polynomials that tend to have very many terms.
0.4.2: 1 December 2008
* substantially improved division by a constant PFE (polynomial function enclosure)
* added proper handling of overflown coefficients
0.4.1: 30 September 2008
* updated to work with AERN-Real 0.9.7
0.4: 20 August 2008
* fixed several serious bugs in sin and cos
* added arctan 7 August 2008
* revamped package description to make it much shorter and linked it
to the main module 7 August 2008
* deleted irrelevant/confusing text from package description 7 August 2008
* fixed markup in package description
0.3.0: 7 August 2008
* initial release of AERN-RnToRm after one year of work and two successful
internal applications

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