Portability | GHC only |
---|---|
Stability | experimental |
Maintainer | ekmett@gmail.com |
Safe Haskell | None |
- findZero :: (Fractional a, Eq a) => (forall s. Forward a s -> Forward a s) -> a -> [a]
- inverse :: (Fractional a, Eq a) => (forall s. Forward a s -> Forward a s) -> a -> a -> [a]
- fixedPoint :: (Fractional a, Eq a) => (forall s. Forward a s -> Forward a s) -> a -> [a]
- extremum :: (Fractional a, Eq a) => (forall s s'. On (Forward (Forward a s') s) -> On (Forward (Forward a s') s)) -> a -> [a]
- gradientDescent :: (Traversable f, Fractional a, Ord a) => (forall s. Reifies s Tape => f (Reverse a s) -> Reverse a s) -> f a -> [f a]
- gradientAscent :: (Traversable f, Fractional a, Ord a) => (forall s. Reifies s Tape => f (Reverse a s) -> Reverse a s) -> f a -> [f a]
- conjugateGradientDescent :: (Traversable f, Ord a, Fractional a) => (forall s1 s2 s3 s4. Chosen s4 => f (Or (On (Forward (Forward a s1) s2)) (Kahn a s3) s4) -> Or (On (Forward (Forward a s1) s2)) (Kahn a s3) s4) -> f a -> [f a]
- conjugateGradientAscent :: (Traversable f, Ord a, Fractional a) => (forall s1 s2 s3 s4. Chosen s4 => f (Or (On (Forward (Forward a s1) s2)) (Kahn a s3) s4) -> Or (On (Forward (Forward a s1) s2)) (Kahn a s3) s4) -> f a -> [f a]
Newton's Method (Forward AD)
findZero :: (Fractional a, Eq a) => (forall s. Forward a s -> Forward a s) -> 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.) 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]
>>>
last $ take 10 $ findZero ((+1).(^2)) (1 :+ 1)
0.0 :+ 1.0
inverse :: (Fractional a, Eq a) => (forall s. Forward a s -> Forward a s) -> a -> a -> [a]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 :: (Fractional a, Eq a) => (forall s. Forward a s -> Forward a s) -> 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.)
If the stream becomes constant (it converges), no further elements are returned.
>>>
last $ take 10 $ fixedPoint cos 1
0.7390851332151607
extremum :: (Fractional a, Eq a) => (forall s s'. On (Forward (Forward a s') s) -> On (Forward (Forward a s') s)) -> 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.) If the stream
becomes constant (it converges), no further elements are returned.
>>>
last $ take 10 $ extremum cos 1
0.0
Gradient Ascent/Descent (Reverse AD)
gradientDescent :: (Traversable f, Fractional a, Ord a) => (forall s. Reifies s Tape => f (Reverse a s) -> Reverse a s) -> 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. Reifies s Tape => f (Reverse a s) -> Reverse a s) -> f a -> [f a]Source
Perform a gradient descent using reverse mode automatic differentiation to compute the gradient.
conjugateGradientDescent :: (Traversable f, Ord a, Fractional a) => (forall s1 s2 s3 s4. Chosen s4 => f (Or (On (Forward (Forward a s1) s2)) (Kahn a s3) s4) -> Or (On (Forward (Forward a s1) s2)) (Kahn a s3) s4) -> f a -> [f a]Source
Perform a conjugate gradient descent using reverse mode automatic differentiation to compute the gradient, and using forward-on-forward mode for computing extrema.
>>>
let sq x = x * x
>>>
let rosenbrock [x,y] = sq (1 - x) + 100 * sq (y - sq x)
>>>
rosenbrock [0,0]
1>>>
rosenbrock (conjugateGradientDescent rosenbrock [0, 0] !! 5) < 0.1
True
conjugateGradientAscent :: (Traversable f, Ord a, Fractional a) => (forall s1 s2 s3 s4. Chosen s4 => f (Or (On (Forward (Forward a s1) s2)) (Kahn a s3) s4) -> Or (On (Forward (Forward a s1) s2)) (Kahn a s3) s4) -> f a -> [f a]Source
Perform a conjugate gradient ascent using reverse mode automatic differentiation to compute the gradient.