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| Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Basic | | Portability | portable | | Stability | experimental | | Maintainer | mik@konecny.aow.cz |
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| Description |
Internal module for Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.
Definition of the polynomial datatype and simple related functions.
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| Synopsis |
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| data ERChebPoly box b = ERChebPoly {} | | | type TermKey box = box | | | chplConstTermKey :: DomainBox box varid d => box | | | chplIsConstTermKey :: DomainBox box varid d => box -> Bool | | | chplTermOrder :: (DomainBox box varid d, Num d) => box -> d | | | chplTermArity :: DomainBox box varid d => box -> Int | | | chplGetDegree :: (ERRealBase b, DomainBox box varid d, Num d, Ord d) => ERChebPoly box b -> d | | | chplConst :: (ERRealBase b, DomainBox box varid Int, Ord box) => b -> ERChebPoly box b | | | chplVar :: (ERRealBase b, DomainBox box varid Int, Ord box) => varid -> ERChebPoly box b | | | chplNormaliseUp :: (ERRealBase b, DomainBox box varid Int, Ord box) => ERChebPoly box b -> ERChebPoly box b | | | chplNormaliseDown :: (ERRealBase b, DomainBox box varid Int, Ord box) => ERChebPoly box b -> ERChebPoly box b | | | chplNormalise :: (ERRealBase b, DomainBox box varid Int, Ord box) => ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b) | | | chplShow :: (ERRealBase b, DomainBox box varid Int, Ord box) => Bool -> ERChebPoly box b -> String | | | chebToXBasis :: (ERRealBase b, DomainBox box varid Int, Ord box) => Map (TermKey box) b -> Map (TermKey box) b | | | termXterms :: (DomainBox box varid Int, Ord box) => TermKey box -> Map (TermKey box) Integer | | | chebyXCoeffsLists :: (Num d1, Enum d1, Num d2, Enum d2) => [[(d1, d2)]] | | | chebyXCoeffs :: (Num d, Enum d) => [[d]] |
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| Documentation |
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A polynomial represented by its coefficients it the Chebyshev basis.
The polynomials are never to be used outside the domain [-1,1]^n.
All operations are rounded in such a way that the resulting polynomial
is a point-wise upper or lower bound of the exact result.
| | Constructors | |  Instances | | Typeable2 ERChebPoly | | (ERRealBase rb, RealFrac rb, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid rb ([] ((,) rb rb)), DomainBoxMappable boxra boxras varid (ERInterval rb) ([] (ERInterval rb)), DomainIntBox boxra varid (ERInterval rb)) => ERUnitFnBase boxb boxra varid rb (ERInterval rb) (ERChebPoly box rb) | | (Eq box, Eq b) => Eq (ERChebPoly box b) | | (ERRealBase b, DomainBox box varid Int, Ord box) => Fractional (ERChebPoly box b) | | (Data box, Data b, Ord box) => Data (ERChebPoly box b) | | (ERRealBase b, DomainBox box varid Int, Ord box) => Num (ERChebPoly box b) | | (ERRealBase b, DomainBox box varid Int, Ord box) => Ord (ERChebPoly box b) | | (ERRealBase b, DomainBox box varid Int, Ord box) => Show (ERChebPoly box b) | | (Ord a, Binary a, Binary b) => Binary (ERChebPoly a b) |
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| Inspect all terms of the polynomial and return the
degree of the highest degree term.
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| make a basic x polynomial for a given variable number
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| :: (ERRealBase b, DomainBox box varid Int, Ord box) | | | => Map (TermKey box) b | polynomial in Chebyshev basis
| | -> Map (TermKey box) b | approxition of the equivalent polynomial in X^n basis
| conversion of polynomials from Chebyshev basis to the X^n basis
(not exact - suffering from rounding in the coefficient conversions)
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| :: (DomainBox box varid Int, Ord box) | | | => TermKey box | a Chebyshev term represented by the Chebyshev degrees
for each variable in the term
| | -> Map (TermKey box) Integer | the polynomial equivalent to the given Chebyshev term
(using integer coefficients)
| | conversion of one Chebyshev term to the X^n basis
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| Chebyshev polynomials expressed as associative lists power -> coeff
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| Chebyshev polynomials expressed as lists of integer coefficients for powers 0,1,2...
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| Produced by Haddock version 2.4.2 |
