| Portability | GHC only |
|---|---|
| Stability | experimental |
| Maintainer | [email protected] |
| Safe Haskell | Safe-Infered |
Numeric.AD.Halley
Contents
Description
Root finding using Halley's rational method (the second in the class of Householder methods). Assumes the function is three times continuously differentiable and converges cubically when progress can be made.
- findZero :: (Fractional a, Eq a) => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]
- inverse :: (Fractional a, Eq a) => (forall s. Mode s => AD s a -> AD s a) -> a -> a -> [a]
- fixedPoint :: (Fractional a, Eq a) => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]
- extremum :: (Fractional a, Eq a) => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]
Halley's Method (Tower AD)
findZero :: (Fractional a, Eq a) => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]Source
The findZero function finds a zero of a scalar function using
Halley's method; its output is a stream of increasingly accurate
results. (Modulo the usual caveats.)
Examples:
take 10 $ findZero (\\x->x^2-4) 1 -- converge to 2.0
module Data.Complex take 10 $ findZero ((+1).(^2)) (1 :+ 1) -- converge to (0 :+ 1)@
inverse :: (Fractional a, Eq a) => (forall s. Mode s => AD s a -> AD s a) -> a -> a -> [a]Source
The inverse function inverts a scalar function using
Halley's method; its output is a stream of increasingly accurate
results. (Modulo the usual caveats.)
Note: the take 10 $ inverse sqrt 1 (sqrt 10) example that works for Newton's method
fails with Halley's method because the preconditions do not hold.
fixedPoint :: (Fractional a, Eq a) => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]Source
The fixedPoint function find a fixedpoint of a scalar
function using Halley's method; its output is a stream of
increasingly accurate results. (Modulo the usual caveats.)
take 10 $ fixedPoint cos 1 -- converges to 0.7390851332151607