Modulemath-functions-0.3.4.4Haskell2010

Numeric.Series

Functions for working with infinite sequences. In particular summation of series and evaluation of continued fractions.

Data type for infinite sequences.

1 declaration

datadata Sequence a

Infinite series. It's represented as opaque state and step function.

Instances4Functor, Applicative, Fractional, Num

Functor SequenceDefined in math-functions-0.3.4.4 · Numeric.Series
Applicative SequenceDefined in math-functions-0.3.4.4 · Numeric.Series
Fractional a => Fractional (Sequence a)Defined in math-functions-0.3.4.4 · Numeric.Series
Elementwise operations with sequences
Num a => Num (Sequence a)Defined in math-functions-0.3.4.4 · Numeric.Series
Elementwise operations with sequences

3 declarations

valueenumSequenceFrom :: Num a => a -> Sequence a

enumSequenceFrom x generate sequence:

a_n = x + n

valueenumSequenceFromStep :: Num a => a -> a -> Sequence a

enumSequenceFromStep x d generate sequence:

a_n = x + nd

valuescanSequence :: (b -> a -> b) -> b -> Sequence a -> Sequence b

Analog of scanl for sequence.

3 declarations

valuesumSeries :: Sequence Double -> Double

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)

valuesumPowerSeries :: Double -> Sequence Double -> Double

Calculate sum of series

\sum_{i=0}^\infty x^ia_i

Calculation is stopped when next value in series is less than ε·sum.

valuesequenceToList :: Sequence a -> [a]

Convert series to infinite list

1 declaration

valueevalContFractionB :: Sequence (Double, Double) -> Double

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"