Portability | GHC only |
---|---|

Stability | experimental |

Maintainer | ekmett@gmail.com |

Safe Haskell | Safe-Infered |

- 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]
- gradientDescent :: (Traversable f, Fractional a, Ord a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> [f a]
- gradientAscent :: (Traversable f, Fractional a, Ord a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> [f a]

# Newton's Method (Forward 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
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

# Gradient Ascent/Descent (Reverse AD)

gradientDescent :: (Traversable f, Fractional a, Ord a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> [f a]Source

The `gradientDescent`

function performs a multivariate
optimization, based on the naive-gradient-descent in the file
`stalingrad/examples/flow-tests/pre-saddle-1a.vlad`

from the
VLAD compiler Stalingrad sources. Its output is a stream of
increasingly accurate results. (Modulo the usual caveats.)

It uses reverse mode automatic differentiation to compute the gradient.

gradientAscent :: (Traversable f, Fractional a, Ord a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> [f a]Source