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.
Abstractions are provided via 4 type classes:
ERUnitFnBase: generalises polynomials with floating point coefficients.
ERFnApprox: generalises functions enclosures on a certain unspecified domain.
ERUnitFnApprox (extends ERFnApprox): generalises function graph enclosures on the domain
[-1,1]^n
.ERFnDomApprox (extends ERFnApprox): generalises function enclosures over a specified and queriable domain box (an instance of class DomainBox).
At all levels, all field operations are supported as well as some elementary operations, namely exp, sin and cos. Log and sqrt are planned to be added soon. End users are expected to work only with implementations of ERFnDomApprox.
Implementations of ERUnitFnBase:
ERChebPoly
By using the Chebyshev basis on domain [-1,1]^n
,
we gain simple and optimally rounding degree reduction
as well as relatively simple handling of rounding
in other operations.
Implementations of ERUnitFnApprox:
ERFnInterval
Implementations of ERFnDomApprox:
ERFnDomTranslApprox: builds a basic implementation using an instance of ERUnitFnApprox.
ERFnTuple: extends another implementation of ERFnDomApprox to work with lists of functions simultaneously.
ERFnDomEdgesApprox: separately enclose a function on its domain box as well as on all the domain's hyper-edges (including the corners) using another implementation of ERFnDomApprox.
ERFnPiecewise: allows the domain box to be bisected to an arbitrary finite depth and uses another implementation of ERFnDomApprox to approximate the function on each segment.
Simple examples of usage can be found in tests: Demo.hs.
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
- 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.Elementary
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Eval
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Field
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Integration
- Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom
- Data.Number.ER.RnToRm
- ER
- Number
Flags
Automatic Flags
Name | Description | Default |
---|---|---|
containers-in-base | Disabled |
Use -f <flag> to enable a flag, or -f -<flag> to disable that flag. More info
Downloads
- AERN-RnToRm-0.3.0.2.tar.gz [browse] (Cabal source package)
- Package description (as included in the package)
Maintainer's Corner
For package maintainers and hackage trustees
Candidates
- No Candidates
Versions [RSS] | 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 (==0.9.6), base, binary (>=0.4), containers [details] |
License | BSD-3-Clause |
Copyright | (c) 2007-2008 Michal Konecny |
Author | Michal Konecny (Aston University) |
Maintainer | mik@konecny.aow.cz |
Category | Data, Math |
Uploaded | by MichalKonecny at 2008-08-07T11:12:23Z |
Distributions | |
Reverse Dependencies | 3 direct, 0 indirect [details] |
Downloads | 11235 total (40 in the last 30 days) |
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Status | Docs uploaded by user Build status unknown [no reports yet] |