Copyright | (c) Edward Kmett 2015-2021 |
---|---|
License | BSD3 |
Maintainer | ekmett@gmail.com |
Stability | experimental |
Portability | GHC only |
Safe Haskell | Safe-Inferred |
Language | Haskell2010 |
Synopsis
- findZero :: (ForwardDouble -> ForwardDouble) -> Double -> [Double]
- inverse :: (ForwardDouble -> ForwardDouble) -> Double -> Double -> [Double]
- fixedPoint :: (ForwardDouble -> ForwardDouble) -> Double -> [Double]
- extremum :: (On (Forward ForwardDouble) -> On (Forward ForwardDouble)) -> Double -> [Double]
Newton's Method (Forward)
findZero :: (ForwardDouble -> ForwardDouble) -> Double -> [Double] Source #
The findZero
function finds a zero of a scalar function using
Newton's method; its output is a stream of increasingly accurate
results. (Modulo the usual caveats.) If the stream becomes constant
("it converges"), no further elements are returned.
Examples:
>>>
take 10 $ findZero (\x->x^2-4) 1
[1.0,2.5,2.05,2.000609756097561,2.0000000929222947,2.000000000000002,2.0]
inverse :: (ForwardDouble -> ForwardDouble) -> Double -> Double -> [Double] Source #
The inverse
function inverts a scalar function using
Newton's method; its output is a stream of increasingly accurate
results. (Modulo the usual caveats.) If the stream becomes
constant ("it converges"), no further elements are returned.
Example:
>>>
last $ take 10 $ inverse sqrt 1 (sqrt 10)
10.0
fixedPoint :: (ForwardDouble -> ForwardDouble) -> Double -> [Double] Source #
The fixedPoint
function find a fixedpoint of a scalar
function using Newton's method; its output is a stream of
increasingly accurate results. (Modulo the usual caveats.)
If the stream becomes constant ("it converges"), no further elements are returned.
>>>
last $ take 10 $ fixedPoint cos 1
0.7390851332151607
extremum :: (On (Forward ForwardDouble) -> On (Forward ForwardDouble)) -> Double -> [Double] Source #
The extremum
function finds an extremum of a scalar
function using Newton's method; produces a stream of increasingly
accurate results. (Modulo the usual caveats.) If the stream
becomes constant ("it converges"), no further elements are returned.
>>>
last $ take 10 $ extremum cos 1
0.0