-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | piecewise linear and cubic Hermite interpolation
--   
--   Represent real functions by linear or cubic segments. The package
--   provides both data structures for efficient lookup of interpolation
--   intervals, and computation of basis functions.
--   
--   There are two examples that can be built with
--   
--   <pre>
--   cabal install -fbuildExamples
--   </pre>
--   
--   <ul>
--   <li><tt>example/Plot.hs</tt>: Interpolate a sinus curve using
--   piecewise linear interpolation and piecewise Hermite cubic
--   interpolation. For the latter one we provide the derivatives of the
--   sinus function at the interpolation nodes.</li>
--   <li><tt>example/Fit.hs</tt>: Demonstrates how to use the basis
--   functions for fitting an interpolation function to a given function
--   using a linear least squares solver like <tt><a>\</a></tt> from
--   <tt>hmatrix</tt>. We use a distorted sinus as target.</li>
--   </ul>
--   
--   The package needs only Haskell 98.
@package interpolation
@version 0.0

module Numeric.Interpolation.Piece
type T x y ny = (x, ny) -> (x, ny) -> x -> y
linear :: Fractional a => T a a a

-- | Hermite interpolation with one derivative per node. That is, the
--   interpolating polynomial is cubic.
hermite1 :: Fractional a => T a a (a, a)

module Numeric.Interpolation.NodeList
data T x y
Interval :: T x y
Node :: (x, y) -> (T x y) -> (T x y) -> T x y

-- | list must be sorted with respect to first element
fromList :: [(x, y)] -> T x y
toList :: T x y -> [(x, y)]
singleton :: x -> y -> T x y
lookup :: Ord x => T x y -> x -> (Maybe (x, y), Maybe (x, y))
instance (Eq x, Eq y) => Eq (T x y)
instance (Ord x, Ord y) => Ord (T x y)
instance (Show x, Show y) => Show (T x y)

module Numeric.Interpolation.Basis.Compact
linear :: Num b => [a] -> [T a b]
hermite1 :: Num b => [a] -> [T a (b, b)]

-- | Cubic interpolation where the derivative at a node is set to the slope
--   of the two adjacent nodes.
cubicLinear :: Fractional a => [a] -> [T a (a, a)]

-- | Cubic interpolation where the derivative at a node is set to the slope
--   of the parabola through the current and the two adjacent nodes.
cubicParabola :: Fractional a => [a] -> [T a (a, a)]

module Numeric.Interpolation.Basis
linear :: Num b => [a] -> [T a b]
hermite1 :: Num b => [a] -> [T a (b, b)]

-- | Cubic interpolation where the derivative at a node is set to the slope
--   of the two adjacent nodes.
cubicLinear :: Fractional a => [a] -> [T a (a, a)]

-- | Cubic interpolation where the derivative at a node is set to the slope
--   of the parabola through the current and the two adjacent nodes.
cubicParabola :: Fractional a => [a] -> [T a (a, a)]

-- | <tt>coefficientsToLinear nodes coefficients</tt> creates an
--   interpolation function for <tt>nodes</tt>, where the
--   <tt>coefficients</tt> correspond to the basis functions constructed
--   with <tt>Basis.linear nodes</tt>.
coefficientsToLinear :: [a] -> [b] -> T a b

-- | Cf. <a>coefficientsToLinear</a>
coefficientsToHermite1 :: [a] -> [b] -> T a (b, b)

-- | Cf. <a>coefficientsToLinear</a>
coefficientsToCubicLinear :: Fractional a => [a] -> [a] -> T a (a, a)

-- | Cf. <a>coefficientsToLinear</a>
coefficientsToCubicParabola :: Fractional a => [a] -> [a] -> T a (a, a)

module Numeric.Interpolation.Type
data T x y ny
Cons :: ([x] -> [y] -> String) -> T x y ny -> ([x] -> [T x ny]) -> ([x] -> [y] -> T x ny) -> (ny -> y) -> T x y ny
ssvFromNodes :: T x y ny -> [x] -> [y] -> String
interpolatePiece :: T x y ny -> T x y ny
basisFunctions :: T x y ny -> [x] -> [T x ny]
coefficientsToInterpolator :: T x y ny -> [x] -> [y] -> T x ny
valueFromNode :: T x y ny -> ny -> y
linear :: T Double Double Double
cubic :: T Double Double (Double, Double)
cubicLinear :: T Double Double (Double, Double)
cubicParabola :: T Double Double (Double, Double)

module Numeric.Interpolation.Piecewise

-- | It is a checked error to interpolate outside of the range of nodes.
interpolate :: Ord x => T x y ny -> T x ny -> x -> y

-- | Outside the range of nodes the interpolation function takes the value
--   of the respective border.
interpolateConstantExt :: Ord x => T x y ny -> T x ny -> x -> y

module Numeric.Interpolation.Basis.Full
linear :: Num b => [a] -> [T a b]
hermite1 :: Num b => [a] -> [T a (b, b)]