| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Numeric.AD.Rank1.Forward.Double
Synopsis
- data ForwardDouble
- grad :: Traversable f => (f ForwardDouble -> ForwardDouble) -> f Double -> f Double
- grad' :: Traversable f => (f ForwardDouble -> ForwardDouble) -> f Double -> (Double, f Double)
- gradWith :: Traversable f => (Double -> Double -> b) -> (f ForwardDouble -> ForwardDouble) -> f Double -> f b
- gradWith' :: Traversable f => (Double -> Double -> b) -> (f ForwardDouble -> ForwardDouble) -> f Double -> (Double, f b)
- jacobian :: (Traversable f, Traversable g) => (f ForwardDouble -> g ForwardDouble) -> f Double -> g (f Double)
- jacobian' :: (Traversable f, Traversable g) => (f ForwardDouble -> g ForwardDouble) -> f Double -> g (Double, f Double)
- jacobianWith :: (Traversable f, Traversable g) => (Double -> Double -> b) -> (f ForwardDouble -> g ForwardDouble) -> f Double -> g (f b)
- jacobianWith' :: (Traversable f, Traversable g) => (Double -> Double -> b) -> (f ForwardDouble -> g ForwardDouble) -> f Double -> g (Double, f b)
- jacobianT :: (Traversable f, Functor g) => (f ForwardDouble -> g ForwardDouble) -> f Double -> f (g Double)
- jacobianWithT :: (Traversable f, Functor g) => (Double -> Double -> b) -> (f ForwardDouble -> g ForwardDouble) -> f Double -> f (g b)
- diff :: (ForwardDouble -> ForwardDouble) -> Double -> Double
- diff' :: (ForwardDouble -> ForwardDouble) -> Double -> (Double, Double)
- diffF :: Functor f => (ForwardDouble -> f ForwardDouble) -> Double -> f Double
- diffF' :: Functor f => (ForwardDouble -> f ForwardDouble) -> Double -> f (Double, Double)
- du :: Functor f => (f ForwardDouble -> ForwardDouble) -> f (Double, Double) -> Double
- du' :: Functor f => (f ForwardDouble -> ForwardDouble) -> f (Double, Double) -> (Double, Double)
- duF :: (Functor f, Functor g) => (f ForwardDouble -> g ForwardDouble) -> f (Double, Double) -> g Double
- duF' :: (Functor f, Functor g) => (f ForwardDouble -> g ForwardDouble) -> f (Double, Double) -> g (Double, Double)
Documentation
data ForwardDouble Source #
Instances
Gradient
grad :: Traversable f => (f ForwardDouble -> ForwardDouble) -> f Double -> f Double Source #
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 => (f ForwardDouble -> ForwardDouble) -> 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) -> (f ForwardDouble -> ForwardDouble) -> f Double -> f b Source #
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) -> (f ForwardDouble -> ForwardDouble) -> 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) => (f ForwardDouble -> g ForwardDouble) -> 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) => (f ForwardDouble -> g ForwardDouble) -> 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) -> (f ForwardDouble -> g ForwardDouble) -> 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) -> (f ForwardDouble -> g ForwardDouble) -> 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) => (f ForwardDouble -> g ForwardDouble) -> f Double -> f (g Double) Source #
A fast, simple, transposed Jacobian computed with forward-mode AD.
jacobianWithT :: (Traversable f, Functor g) => (Double -> Double -> b) -> (f ForwardDouble -> g ForwardDouble) -> 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 :: (ForwardDouble -> ForwardDouble) -> Double -> Double Source #
The diff function calculates the first derivative of a scalar-to-scalar function by forward-mode AD
>>>diff sin 01.0
diff' :: (ForwardDouble -> ForwardDouble) -> Double -> (Double, Double) Source #
diffF :: Functor f => (ForwardDouble -> f ForwardDouble) -> Double -> f Double Source #
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 => (ForwardDouble -> f ForwardDouble) -> 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 => (f ForwardDouble -> ForwardDouble) -> f (Double, Double) -> Double Source #
Compute the directional derivative of a function given a zipped up Functor of the input values and their derivatives
du' :: Functor f => (f ForwardDouble -> ForwardDouble) -> 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