Safe Haskell | None |
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- data ForwardDouble a
- grad :: Traversable f => (forall s. f (ForwardDouble s) -> ForwardDouble s) -> f Double -> f Double
- grad' :: Traversable f => (forall s. f (ForwardDouble s) -> ForwardDouble s) -> f Double -> (Double, f Double)
- gradWith :: Traversable f => (Double -> Double -> b) -> (forall s. f (ForwardDouble s) -> ForwardDouble s) -> f Double -> f b
- gradWith' :: Traversable f => (Double -> Double -> b) -> (forall s. f (ForwardDouble s) -> ForwardDouble s) -> f Double -> (Double, f b)
- jacobian :: (Traversable f, Traversable g) => (forall s. f (ForwardDouble s) -> g (ForwardDouble s)) -> f Double -> g (f Double)
- jacobian' :: (Traversable f, Traversable g) => (forall s. f (ForwardDouble s) -> g (ForwardDouble s)) -> f Double -> g (Double, f Double)
- jacobianWith :: (Traversable f, Traversable g) => (Double -> Double -> b) -> (forall s. f (ForwardDouble s) -> g (ForwardDouble s)) -> f Double -> g (f b)
- jacobianWith' :: (Traversable f, Traversable g) => (Double -> Double -> b) -> (forall s. f (ForwardDouble s) -> g (ForwardDouble s)) -> f Double -> g (Double, f b)
- jacobianT :: (Traversable f, Functor g) => (forall s. f (ForwardDouble s) -> g (ForwardDouble s)) -> f Double -> f (g Double)
- jacobianWithT :: (Traversable f, Functor g) => (Double -> Double -> b) -> (forall s. f (ForwardDouble s) -> g (ForwardDouble s)) -> f Double -> f (g b)
- diff :: (forall s. ForwardDouble s -> ForwardDouble s) -> Double -> Double
- diff' :: (forall s. ForwardDouble s -> ForwardDouble s) -> Double -> (Double, Double)
- diffF :: Functor f => (forall s. ForwardDouble s -> f (ForwardDouble s)) -> Double -> f Double
- diffF' :: Functor f => (forall s. ForwardDouble s -> f (ForwardDouble s)) -> Double -> f (Double, Double)
- du :: Functor f => (forall s. f (ForwardDouble s) -> ForwardDouble s) -> f (Double, Double) -> Double
- du' :: Functor f => (forall s. f (ForwardDouble s) -> ForwardDouble s) -> f (Double, Double) -> (Double, Double)
- duF :: (Functor f, Functor g) => (forall s. f (ForwardDouble s) -> g (ForwardDouble s)) -> f (Double, Double) -> g Double
- duF' :: (Functor f, Functor g) => (forall s. f (ForwardDouble s) -> g (ForwardDouble s)) -> f (Double, Double) -> g (Double, Double)
Documentation
data ForwardDouble a Source
Enum (ForwardDouble s) | |
Eq (ForwardDouble s) | |
Floating (ForwardDouble s) | |
Fractional (ForwardDouble s) | |
Num (ForwardDouble s) | |
Ord (ForwardDouble s) | |
Read (ForwardDouble a) | |
Real (ForwardDouble s) | |
RealFloat (ForwardDouble s) | |
RealFrac (ForwardDouble s) | |
Show (ForwardDouble a) | |
Erf (ForwardDouble s) | |
InvErf (ForwardDouble s) | |
Mode (ForwardDouble s) | |
Jacobian (ForwardDouble s) |
Gradient
grad :: Traversable f => (forall s. f (ForwardDouble s) -> ForwardDouble s) -> f Double -> f DoubleSource
Compute the gradient of a function using forward mode AD.
Note, this performs O(n) worse than grad
for n
inputs, in exchange for better space utilization.
grad' :: Traversable f => (forall s. f (ForwardDouble s) -> ForwardDouble s) -> f Double -> (Double, f Double)Source
Compute the gradient and answer to a function using forward mode AD.
Note, this performs O(n) worse than grad'
for n
inputs, in exchange for better space utilization.
gradWith :: Traversable f => (Double -> Double -> b) -> (forall s. f (ForwardDouble s) -> ForwardDouble s) -> f Double -> f bSource
Compute the gradient of a function using forward mode AD and combine the result with the input using a user-specified function.
Note, this performs O(n) worse than gradWith
for n
inputs, in exchange for better space utilization.
gradWith' :: Traversable f => (Double -> Double -> b) -> (forall s. f (ForwardDouble s) -> ForwardDouble s) -> f Double -> (Double, f b)Source
Compute the gradient of a function using forward mode AD and the answer, and combine the result with the input using a user-specified function.
Note, this performs O(n) worse than gradWith'
for n
inputs, in exchange for better space utilization.
>>>
gradWith' (,) sum [0..4]
(10.0,[(0.0,1.0),(1.0,1.0),(2.0,1.0),(3.0,1.0),(4.0,1.0)])
Jacobian
jacobian :: (Traversable f, Traversable g) => (forall s. f (ForwardDouble s) -> g (ForwardDouble s)) -> f Double -> g (f Double)Source
Compute the Jacobian using Forward
mode AD
. This must transpose the result, so jacobianT
is faster and allows more result types.
>>>
jacobian (\[x,y] -> [y,x,x+y,x*y,exp x * sin y]) [pi,1]
[[0.0,1.0],[1.0,0.0],[1.0,1.0],[1.0,3.141592653589793],[19.472221418841606,12.502969588876512]]
jacobian' :: (Traversable f, Traversable g) => (forall s. f (ForwardDouble s) -> g (ForwardDouble s)) -> f Double -> g (Double, f Double)Source
Compute the Jacobian using Forward
mode AD
along with the actual answer.
jacobianWith :: (Traversable f, Traversable g) => (Double -> Double -> b) -> (forall s. f (ForwardDouble s) -> g (ForwardDouble s)) -> f Double -> g (f b)Source
Compute the Jacobian using Forward
mode AD
and combine the output with the input. This must transpose the result, so jacobianWithT
is faster, and allows more result types.
jacobianWith' :: (Traversable f, Traversable g) => (Double -> Double -> b) -> (forall s. f (ForwardDouble s) -> g (ForwardDouble s)) -> f Double -> g (Double, f b)Source
Compute the Jacobian using Forward
mode AD
combined with the input using a user specified function, along with the actual answer.
Transposed Jacobian
jacobianT :: (Traversable f, Functor g) => (forall s. f (ForwardDouble s) -> g (ForwardDouble s)) -> f Double -> f (g Double)Source
A fast, simple, transposed Jacobian computed with forward-mode AD.
jacobianWithT :: (Traversable f, Functor g) => (Double -> Double -> b) -> (forall s. f (ForwardDouble s) -> g (ForwardDouble s)) -> f Double -> f (g b)Source
A fast, simple, transposed Jacobian computed with Forward
mode AD
that combines the output with the input.
Derivatives
diff :: (forall s. ForwardDouble s -> ForwardDouble s) -> Double -> DoubleSource
The diff
function calculates the first derivative of a scalar-to-scalar function by forward-mode AD
>>>
diff sin 0
1.0
diff' :: (forall s. ForwardDouble s -> ForwardDouble s) -> Double -> (Double, Double)Source
diffF :: Functor f => (forall s. ForwardDouble s -> f (ForwardDouble s)) -> Double -> f DoubleSource
The diffF
function calculates the first derivatives of scalar-to-nonscalar function by Forward
mode AD
>>>
diffF (\a -> [sin a, cos a]) 0
[1.0,-0.0]
diffF' :: Functor f => (forall s. ForwardDouble s -> f (ForwardDouble s)) -> Double -> f (Double, Double)Source
The diffF'
function calculates the result and first derivatives of a scalar-to-non-scalar function by Forward
mode AD
>>>
diffF' (\a -> [sin a, cos a]) 0
[(0.0,1.0),(1.0,-0.0)]
Directional Derivatives
du :: Functor f => (forall s. f (ForwardDouble s) -> ForwardDouble s) -> f (Double, Double) -> DoubleSource
Compute the directional derivative of a function given a zipped up Functor
of the input values and their derivatives
du' :: Functor f => (forall s. f (ForwardDouble s) -> ForwardDouble s) -> f (Double, Double) -> (Double, Double)Source
Compute the answer and directional derivative of a function given a zipped up Functor
of the input values and their derivatives
duF :: (Functor f, Functor g) => (forall s. f (ForwardDouble s) -> g (ForwardDouble s)) -> f (Double, Double) -> g DoubleSource
Compute a vector of directional derivatives for a function given a zipped up Functor
of the input values and their derivatives.