AERN-RnToRm: polynomial function enclosures (PFEs) approximating exact real functions
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 http://www-users.aston.ac.uk/~konecnym/papers/cfv08.html.
Simple examples of usage can be found in folder demos
and a test suite can be run via the module in the folder tests.
| Versions [faq] | 0.3.0, 0.3.0.1, 0.3.0.2, 0.3.0.3, 0.4, 0.4.1, 0.4.2, 0.4.9, 0.4.9.1, 0.5, 0.5.0.1 |
|---|---|
| Change log | ChangeLog |
| Dependencies | AERN-Real (>=0.10 && <0.10.1), base (==3.*), binary (>=0.4), containers, directory, filepath, html (>=1.0), QuickCheck (>=1.2 && <2), time [details] |
| License | BSD-3-Clause |
| Copyright | (c) 2007-2009 Michal Konecny, Jan Duracz |
| Author | Michal Konecny (Aston University) |
| Maintainer | mikkonecny@gmail.com |
| Category | Data, Math |
| Home page | http://www-users.aston.ac.uk/~konecnym/DISCERN |
| Uploaded | by MichalKonecny at Tue Jul 28 23:04:26 UTC 2009 |
| Distributions | NixOS:0.5.0.1 |
| Downloads | 6528 total (119 in the last 30 days) |
| Rating | (no votes yet) [estimated by rule of succession] |
| Your Rating | |
| Status | Docs uploaded by user Build status unknown [no reports yet] |
Modules
[Index]
- Data
- Number
- ER
- Data.Number.ER.RnToRm
- Data.Number.ER.RnToRm.Approx
- Data.Number.ER.RnToRm.BisectionTree
- Data.Number.ER.RnToRm.DefaultRepr
- Data.Number.ER.RnToRm.TestingDefs
- UnitDom
- Data.Number.ER.RnToRm.UnitDom.Approx
- Data.Number.ER.RnToRm.UnitDom.Base
- Tests
- Data.Number.ER.RnToRm.UnitDom.Base.Tests.Generate
- Properties
- Data.Number.ER.RnToRm.UnitDom.Base.Tests.Properties.Bounds
- Data.Number.ER.RnToRm.UnitDom.Base.Tests.Properties.Common
- Data.Number.ER.RnToRm.UnitDom.Base.Tests.Properties.Compose
- Data.Number.ER.RnToRm.UnitDom.Base.Tests.Properties.Division
- Data.Number.ER.RnToRm.UnitDom.Base.Tests.Properties.Elementary
- Data.Number.ER.RnToRm.UnitDom.Base.Tests.Properties.Enclosure
- Data.Number.ER.RnToRm.UnitDom.Base.Tests.Properties.Integration
- Data.Number.ER.RnToRm.UnitDom.Base.Tests.Properties.Reduce
- Data.Number.ER.RnToRm.UnitDom.Base.Tests.Properties.Ring
- Data.Number.ER.RnToRm.UnitDom.Base.Tests.Run
- Tests
- ChebyshevBase
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Basic
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Bounds
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Compose
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Derivative
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Division
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.DivisionInner
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Elementary
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.ElementaryInner
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Enclosure
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.EnclosureInner
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Eval
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Integration
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Reduce
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Ring
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom
- Data.Number.ER.RnToRm
- ER
- Number
Downloads
- AERN-RnToRm-0.5.tar.gz [browse] (Cabal source package)
- Package description (as included in the package)