| Copyright | (c) 2016 Alexey Khudyakov |
|---|---|
| License | BSD3 |
| Maintainer | alexey.skladnoy@gmail.com, bos@serpentine.com |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | Safe-Inferred |
| Language | Haskell2010 |
Numeric.Series
Description
Functions for working with infinite sequences. In particular summation of series and evaluation of continued fractions.
Synopsis
- data Sequence a = forall s. Sequence s (s -> (a, s))
- enumSequenceFrom :: Num a => a -> Sequence a
- enumSequenceFromStep :: Num a => a -> a -> Sequence a
- scanSequence :: (b -> a -> b) -> b -> Sequence a -> Sequence b
- sumSeries :: Sequence Double -> Double
- sumPowerSeries :: Double -> Sequence Double -> Double
- sequenceToList :: Sequence a -> [a]
- evalContFractionB :: Sequence ( Double , Double ) -> Double
Data type for infinite sequences.
Infinite series. It's represented as opaque state and step function.
Constructors
| forall s. Sequence s (s -> (a, s)) |
Instances
| Functor Sequence Source # | |
| Applicative Sequence Source # | |
|
Defined in Numeric.Series |
|
| Fractional a => Fractional ( Sequence a) Source # |
Elementwise operations with sequences |
| Num a => Num ( Sequence a) Source # |
Elementwise operations with sequences |
|
Defined in Numeric.Series Methods (+) :: Sequence a -> Sequence a -> Sequence a Source # (-) :: Sequence a -> Sequence a -> Sequence a Source # (*) :: Sequence a -> Sequence a -> Sequence a Source # negate :: Sequence a -> Sequence a Source # abs :: Sequence a -> Sequence a Source # signum :: Sequence a -> Sequence a Source # fromInteger :: Integer -> Sequence a Source # |
|
Constructors
enumSequenceFrom :: Num a => a -> Sequence a Source #
enumSequenceFrom x
generate sequence:
\[ a_n = x + n \]
enumSequenceFromStep :: Num a => a -> a -> Sequence a Source #
enumSequenceFromStep x d
generate sequence:
\[ a_n = x + nd \]
scanSequence :: (b -> a -> b) -> b -> Sequence a -> Sequence b Source #
Analog of
scanl
for sequence.
Summation of series
sumSeries :: Sequence Double -> Double Source #
Calculate sum of series
\[ \sum_{i=0}^\infty a_i \]
Summation is stopped when
\[ a_{n+1} < \varepsilon\sum_{i=0}^n a_i \]
where ε is machine precision (
m_epsilon
)
sumPowerSeries :: Double -> Sequence Double -> Double Source #
Calculate sum of series
\[ \sum_{i=0}^\infty x^ia_i \]
Calculation is stopped when next value in series is less than ε·sum.
sequenceToList :: Sequence a -> [a] Source #
Convert series to infinite list
Evaluation of continued fractions
evalContFractionB :: Sequence ( Double , Double ) -> Double Source #
Evaluate continued fraction using modified Lentz algorithm. Sequence contain pairs (a[i],b[i]) which form following expression:
\[ b_0 + \frac{a_1}{b_1+\frac{a_2}{b_2+\frac{a_3}{b_3 + \cdots}}} \]
Modified Lentz algorithm is described in Numerical recipes 5.2 "Evaluation of Continued Fractions"