-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | Wrapper of numeric-optimization package for using with AD package -- -- Please see the README on GitHub at -- https://github.com/msakai/nonlinear-optimization-ad/tree/master/numeric-optimization-ad#readme @package numeric-optimization-ad @version 0.1.0.1 -- | This module is a wrapper of Numeric.Optimization that uses -- ad's automatic differentiation. module Numeric.Optimization.AD -- | Synonym of minimizeReverse minimize :: forall f. Traversable f => Method -> Params (f Double) -> (forall s. Reifies s Tape => f (Reverse s Double) -> Reverse s Double) -> Maybe (f (Double, Double)) -> [Constraint] -> f Double -> IO (Result (f Double)) -- | Minimization of scalar function of one or more variables. -- -- This is a wrapper of minimize and use -- Numeric.AD.Mode.Reverse to compute gradient. -- -- It cannot be used with methods that requires hessian (e.g. -- Newton). -- -- Example: -- -- 
--   {-# LANGUAGE FlexibleContexts #-}
--   import Numeric.Optimization.AD
--   
--   main :: IO ()
--   main = do
--     (x, result, stat) <- minimizeReverse LBFGS def rosenbrock Nothing [] [-3,-4]
--     print (resultSuccess result)  -- True
--     print (resultSolution result)  -- [0.999999999009131,0.9999999981094296]
--     print (resultValue result)  -- 1.8129771632403013e-18
--   
--   -- https://en.wikipedia.org/wiki/Rosenbrock_function
--   rosenbrock :: Floating a => [a] -> a
--   -- rosenbrock :: Reifies s Tape => [Reverse s Double] -> Reverse s Double
--   rosenbrock [x,y] = sq (1 - x) + 100 * sq (y - sq x)
--   
--   sq :: Floating a => a -> a
--   sq x = x ** 2
--
minimizeReverse :: forall f. Traversable f => Method -> Params (f Double) -> (forall s. Reifies s Tape => f (Reverse s Double) -> Reverse s Double) -> Maybe (f (Double, Double)) -> [Constraint] -> f Double -> IO (Result (f Double)) -- | Minimization of scalar function of one or more variables. -- -- This is a wrapper of minimize and use -- Numeric.AD.Mode.Sparse to compute gradient and hessian. -- -- Unlike minimizeReverse, it can be used with methods that -- requires hessian (e.g. Newton). -- -- Example: -- -- 
--   {-# LANGUAGE FlexibleContexts #-}
--   import Numeric.Optimization.AD
--   
--   main :: IO ()
--   main = do
--     (x, result, stat) <- minimizeSparse Newton def rosenbrock Nothing [] [-3,-4]
--     print (resultSuccess result)  -- True
--     print (resultSolution result)  -- [0.9999999999999999,0.9999999999999998]
--     print (resultValue result)  -- 1.232595164407831e-32
--   
--   -- https://en.wikipedia.org/wiki/Rosenbrock_function
--   rosenbrock :: Floating a => [a] -> a
--   -- rosenbrock :: [AD s (Sparse Double)] -> AD s (Sparse Double)
--   rosenbrock [x,y] = sq (1 - x) + 100 * sq (y - sq x)
--   
--   sq :: Floating a => a -> a
--   sq x = x ** 2
--
minimizeSparse :: forall f. Traversable f => Method -> Params (f Double) -> (forall s. f (AD s (Sparse Double)) -> AD s (Sparse Double)) -> Maybe (f (Double, Double)) -> [Constraint] -> f Double -> IO (Result (f Double)) -- | Type of constraint -- -- Currently, no constraints are supported. data Constraint -- | Selection of numerical optimization algorithms data Method -- | Conjugate gradient method based on Hager and Zhang [1]. -- -- The implementation is provided by nonlinear-optimization package [3] -- which is a binding library of [2]. -- -- This method requires gradient but does not require hessian. -- -- CGDescent :: Method -- | Limited memory BFGS (L-BFGS) algorithm [1] -- -- The implementtion is provided by lbfgs package [2] which is a binding -- of liblbfgs [3]. -- -- This method requires gradient but does not require hessian. -- -- LBFGS :: Method -- | Native implementation of Newton method -- -- This method requires both gradient and hessian. Newton :: Method -- | Whether a Method is supported under the current environment. isSupportedMethod :: Method -> Bool -- | Parameters for optimization algorithms -- -- TODO: -- -- data Params a Params :: Maybe (a -> IO Bool) -> Maybe Double -> Params a -- | If callback function returns True, the algorithm execution is -- terminated. [paramsCallback] :: Params a -> Maybe (a -> IO Bool) -- | Tolerance for termination. When tol is specified, the -- selected algorithm sets some relevant solver-specific tolerance(s) -- equal to tol. [paramsTol] :: Params a -> Maybe Double -- | Optimization result data Result a Result :: Bool -> String -> a -> Double -> Maybe a -> Maybe (Matrix Double) -> Maybe (Matrix Double) -> Statistics -> Result a -- | Whether or not the optimizer exited successfully. [resultSuccess] :: Result a -> Bool -- | Description of the cause of the termination. [resultMessage] :: Result a -> String -- | Solution [resultSolution] :: Result a -> a -- | Value of the function at the solution. [resultValue] :: Result a -> Double -- | Gradient at the solution [resultGrad] :: Result a -> Maybe a -- | Hessian at the solution; may be an approximation. [resultHessian] :: Result a -> Maybe (Matrix Double) -- | Inverse of Hessian at the solution; may be an approximation. [resultHessianInv] :: Result a -> Maybe (Matrix Double) -- | Statistics of optimizaion process [resultStatistics] :: Result a -> Statistics -- | Statistics of optimizaion process data Statistics Statistics :: Int -> Int -> Int -> Int -> Statistics -- | Total number of iterations. [totalIters] :: Statistics -> Int -- | Total number of function evaluations. [funcEvals] :: Statistics -> Int -- | Total number of gradient evaluations. [gradEvals] :: Statistics -> Int -- | Total number of hessian evaluations. [hessEvals] :: Statistics -> Int -- | The bad things that can happen when you use the library. data OptimizationException UnsupportedProblem :: String -> OptimizationException UnsupportedMethod :: Method -> OptimizationException GradUnavailable :: OptimizationException HessianUnavailable :: OptimizationException -- | A class for types with a default value. class Default a -- | The default value for this type. def :: Default a => a data AD s a -- | Embed a constant auto :: Mode t => Scalar t -> t data Reverse s a class Reifies (s :: k) a | s -> a data Tape -- | We only store partials in sorted order, so the map contained in a -- partial will only contain partials with equal or greater keys to that -- of the map in which it was found. This should be key for efficiently -- computing sparse hessians. there are only n + k - 1 choose -- k distinct nth partial derivatives of a function with k -- inputs. data Sparse a instance Data.Traversable.Traversable f => Numeric.Optimization.IsProblem (Numeric.Optimization.AD.ProblemSparse f) instance Data.Traversable.Traversable f => Numeric.Optimization.HasGrad (Numeric.Optimization.AD.ProblemSparse f) instance Data.Traversable.Traversable f => Numeric.Optimization.HasHessian (Numeric.Optimization.AD.ProblemSparse f) instance Data.Traversable.Traversable f => Numeric.Optimization.Optionally (Numeric.Optimization.HasGrad (Numeric.Optimization.AD.ProblemSparse f)) instance Data.Traversable.Traversable f => Numeric.Optimization.Optionally (Numeric.Optimization.HasHessian (Numeric.Optimization.AD.ProblemSparse f)) instance Data.Traversable.Traversable f => Numeric.Optimization.IsProblem (Numeric.Optimization.AD.ProblemReverse f) instance Data.Traversable.Traversable f => Numeric.Optimization.HasGrad (Numeric.Optimization.AD.ProblemReverse f) instance Data.Traversable.Traversable f => Numeric.Optimization.Optionally (Numeric.Optimization.HasGrad (Numeric.Optimization.AD.ProblemReverse f)) instance Numeric.Optimization.Optionally (Numeric.Optimization.HasHessian (Numeric.Optimization.AD.ProblemReverse f))