Portability GHC only experimental ekmett@gmail.com Safe-Infered

Description

Synopsis

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 Newton'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 inverseNewton function inverts a scalar function using Newton's method; its output is a stream of increasingly accurate results. (Modulo the usual caveats.)

Example:

take 10 \$ inverseNewton sqrt 1 (sqrt 10)  -- converges to 10

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 Newton's method; its output is a stream of increasingly accurate results. (Modulo the usual caveats.)

take 10 \$ fixedPoint cos 1 -- converges to 0.7390851332151607

extremum :: (Fractional a, Eq a) => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]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.)

take 10 \$ extremum cos 1 -- convert to 0