ad 4.2.3 → 4.2.4

raw patch · 31 files changed

+341/−87 lines, 31 filesdep ~doctestPVP ok

version bump matches the API change (PVP)

Dependency ranges changed: doctest

API changes (from Hackage documentation)

Files

• .travis.yml +29/−29
• CHANGELOG.markdown +4/−0
• README.markdown +1/−1
• TODO +0/−43
• ad.cabal +4/−4
• src/Numeric/AD.hs +3/−0
• src/Numeric/AD/Internal/Combinators.hs +6/−0
• src/Numeric/AD/Internal/Dense.hs +8/−1
• src/Numeric/AD/Internal/Forward.hs +8/−2
• src/Numeric/AD/Internal/Forward/Double.hs +8/−2
• src/Numeric/AD/Internal/Identity.hs +3/−0
• src/Numeric/AD/Internal/Kahn.hs +3/−1
• src/Numeric/AD/Internal/Or.hs +2/−0
• src/Numeric/AD/Internal/Reverse.hs +4/−0
• src/Numeric/AD/Internal/Sparse.hs +2/−0
• src/Numeric/AD/Internal/Tower.hs +2/−0
• src/Numeric/AD/Jet.hs +3/−0
• src/Numeric/AD/Mode/Forward.hs +2/−0
• src/Numeric/AD/Mode/Forward/Double.hs +3/−0
• src/Numeric/AD/Mode/Kahn.hs +3/−0
• src/Numeric/AD/Mode/Reverse.hs +5/−2
• src/Numeric/AD/Mode/Sparse.hs +3/−0
• src/Numeric/AD/Newton/Double.hs +130/−0
• src/Numeric/AD/Rank1/Forward.hs +2/−0
• src/Numeric/AD/Rank1/Forward/Double.hs +3/−0
• src/Numeric/AD/Rank1/Kahn.hs +4/−1
• src/Numeric/AD/Rank1/Newton.hs +3/−0
• src/Numeric/AD/Rank1/Newton/Double.hs +83/−0
• src/Numeric/AD/Rank1/Sparse.hs +3/−0
• src/Numeric/AD/Rank1/Tower.hs +4/−1
• tests/doctests.hs +3/−0

@@ -1,44 +1,44 @@-env:- - GHCVER=7.0.1 CABALVER=1.16- - GHCVER=7.0.4 CABALVER=1.16- - GHCVER=7.2.2 CABALVER=1.16- - GHCVER=7.4.2 CABALVER=1.16- - GHCVER=7.6.3 CABALVER=1.16- - GHCVER=7.8.4 CABALVER=1.18- - GHCVER=7.10.1 CABALVER=1.22- - GHCVER=head CABALVER=1.22+language: c+sudo: false  matrix:+  include:+    - env: CABALVER=1.16 GHCVER=7.4.2 GHCOPTS="-Werror" JOPTS=""+      addons: {apt: {packages: [cabal-install-1.16, ghc-7.4.2], sources: [hvr-ghc]}}+    - env: CABALVER=1.18 GHCVER=7.6.3 GHCOPTS="-Werror" JOPTS="-j2"+      addons: {apt: {packages: [cabal-install-1.18, ghc-7.6.3], sources: [hvr-ghc]}}+    - env: CABALVER=1.18 GHCVER=7.8.4 GHCOPTS="-Werror" JOPTS="-j2"+      addons: {apt: {packages: [cabal-install-1.18, ghc-7.8.4], sources: [hvr-ghc]}}+    - env: CABALVER=1.22 GHCVER=7.10.1 GHCOPTS="" JOPTS="-j2"+      addons: {apt: {packages: [cabal-install-1.22, ghc-7.10.1],sources: [hvr-ghc]}}+    - env: CABALVER=head GHCVER=head GHCOPTS="" JOPTS="-j2"+      addons: {apt: {packages: [cabal-install-head,ghc-head],  sources: [hvr-ghc]}}+   allow_failures:-   - env: GHCVER=7.0.1 CABALVER=1.16-   - env: GHCVER=7.0.4 CABALVER=1.16-   - env: GHCVER=7.2.2 CABALVER=1.16-   - env: GHCVER=head CABALVER=1.22+   - env: CABALVER=head GHCVER=head GHCOPTS="" JOPTS="-j2"  before_install:- - travis_retry sudo add-apt-repository -y ppa:hvr/ghc- - travis_retry sudo apt-get update- - travis_retry sudo apt-get install cabal-install-$CABALVER ghc-$GHCVER- - export PATH=/opt/ghc/$GHCVER/bin:/opt/cabal/$CABALVER/bin:$PATH+ - export PATH=~/.cabal/bin:/opt/ghc/$GHCVER/bin:/opt/cabal/$CABALVER/bin:$PATH  - export CABAL=cabal-$CABALVER+ - travis_retry $CABAL update+ - if [ "$CABALVER" = "1.22" ]; then cabal install Cabal-1.22.4.0; fi  - $CABAL --version+ - echo "$(ghc --version) [$(ghc --print-project-git-commit-id 2> /dev/null || echo '?')]"  install:- - travis_retry $CABAL update- - $CABAL install "Cabal == $CABALVER.*"- - $CABAL install --enable-tests --only-dependencies+ - |    +   if [ $GHCVER = "head" ] || [ $GHCVER = "7.8.4" ] || [ $GHCVER = "7.10.1" ]; then+     $CABAL install --constraint=transformers\ installed happy alex+     export PATH=$HOME/.cabal/bin:$PATH+   fi+ - $CABAL install $JOPTS --enable-tests --only-dependencies --force  script:  - $CABAL configure -v2 --enable-tests- - $CABAL build- - $CABAL sdist- - export SRC_TGZ=$($CABAL info . | awk '{print $2 ".tar.gz";exit}') ;-   cd dist/;-   if [ -f "$SRC_TGZ" ]; then-      $CABAL install "$SRC_TGZ";-   else-      echo "expected '$SRC_TGZ' not found";-      exit 1;+ - $CABAL build $JOPTS --ghc-options=$GHCOPTS+ - |+   if [ $GHCVER != "head" ]; then+     $CABAL test    fi  notifications:

@@ -1,3 +1,7 @@+4.2.4+-----+* Added `Newton.Double` modules for performance.+ 4.2.3 ----- * `reflection` 2 support

@@ -1,7 +1,7 @@ ad == -[![Build Status](https://secure.travis-ci.org/ekmett/ad.png?branch=master)](http://travis-ci.org/ekmett/ad)+[![Hackage](https://img.shields.io/hackage/v/ad.svg)](https://hackage.haskell.org/package/ad) [![Build Status](https://secure.travis-ci.org/ekmett/ad.png?branch=master)](http://travis-ci.org/ekmett/ad)  A package that provides an intuitive API for [Automatic Differentiation](http://en.wikipedia.org/wiki/Automatic_differentiation) (AD) in Haskell. Automatic differentiation provides a means to calculate the derivatives of a function while evaluating it. Unlike numerical methods based on running the program with multiple inputs or symbolic approaches, automatic differentiation typically only decreases performance by a small multiplier. 

@@ -1,43 +0,0 @@-* Use the f-branching stream and tensors to generate:--    gradients :: Traversable f => FU f a -> f a -> Stream f a--* Allow the type to vary within our AD data type container, in the same fashion as Numeric.FAD.--    Although, while Pearlmutter and Siskind provided the functionality to permit-    it in the derivative combinators, they provided no combinators to convert,-    say, @Dual tag Float@ to a @Dual tag Double@, so that extra functionality cannot-    currently be leveraged.--  One approach: GADT'd Tape.-    Lets us use local matrix-valued jacobians as blackboxes.-    However, this requires a custom higher-order data-reify.--* Do we need some kind of Array implementation? These'd be easy:--    (new)?type ADArray s i e = Array i (AD s e)-    (new)?type ADIOArray s i e = IOArray i (AD s e)-    (new)?type ADSTArray s i e = STArray i (AD s e)--  But how to handle possibly unboxed arrays where possible?--    Mode s => ADUArray s i Float-    Mode s => ADIOUArray s i Float-    Mode s => ADSTUArray s i Float--  Forward admits fast unboxed array access, but how to avoid violating quantification over s?--  This seems to require baking the array type for Float and Double directly into the Mode.--  class ( IArray (ADArray s) e-        , MArray (ADSTArray s s') e (ST s')-        , MArray (ADIOArray s) e IO-        , Lifted s) => LiftedArray s e where--     type ADArr s e  :: * -> * -> *-     type ADSTArr s e :: * -> * -> *-     type ADIOArr s e :: * -> * -> *--  newtype ADArray s i e = ADArray (ADArr s e i e)--  class ( LiftedArray s Float, LiftedArray s Double, ...) => Mode s

@@ -1,5 +1,5 @@ name:          ad-version:       4.2.3+version:       4.2.4 license:       BSD3 license-File:  LICENSE copyright:     (c) Edward Kmett 2010-2015,@@ -19,7 +19,6 @@   .gitignore   .travis.yml   .vim.custom-  TODO   CHANGELOG.markdown   README.markdown   travis/cabal-apt-install@@ -77,7 +76,6 @@   location: git://github.com/ekmett/ad.git  library-  default-extensions: CPP   hs-source-dirs: src   include-dirs: include   default-language: Haskell2010@@ -137,11 +135,13 @@     Numeric.AD.Mode.Sparse     Numeric.AD.Mode.Tower     Numeric.AD.Newton+    Numeric.AD.Newton.Double     Numeric.AD.Rank1.Forward     Numeric.AD.Rank1.Forward.Double     Numeric.AD.Rank1.Halley     Numeric.AD.Rank1.Kahn     Numeric.AD.Rank1.Newton+    Numeric.AD.Rank1.Newton.Double     Numeric.AD.Rank1.Sparse     Numeric.AD.Rank1.Tower @@ -160,7 +160,7 @@   build-depends:     base,     directory,-    doctest >= 0.9.0.1 && <= 0.10,+    doctest >= 0.9.0.1 && <= 0.11,     filepath   ghc-options: -Wall -threaded   hs-source-dirs: tests

@@ -1,3 +1,4 @@+{-# LANGUAGE CPP #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE Rank2Types #-} {-# LANGUAGE TypeFamilies #-}@@ -131,7 +132,9 @@   ) where  import Data.Functor.Compose+#if __GLASGOW_HASKELL__ < 710 import Data.Traversable (Traversable)+#endif import Data.Reflection (Reifies) import Numeric.AD.Internal.Forward (Forward) import Numeric.AD.Internal.Kahn (Grad, vgrad, vgrad')

@@ -1,3 +1,4 @@+{-# LANGUAGE CPP #-} {-# OPTIONS_GHC -fno-warn-incomplete-patterns #-} {-# OPTIONS_HADDOCK not-home #-} -----------------------------------------------------------------------------@@ -17,8 +18,13 @@   , fromBy   ) where +#if __GLASGOW_HASKELL__ < 710 import Data.Traversable (Traversable, mapAccumL) import Data.Foldable (Foldable, toList)+#else+import Data.Traversable (mapAccumL)+import Data.Foldable (toList)+#endif import Numeric.AD.Mode import Numeric.AD.Jacobian 

@@ -41,9 +41,16 @@   ) where  import Control.Monad (join)+#if __GLASGOW_HASKELL__ < 710 import Data.Functor+#endif import Data.Typeable ()-import Data.Traversable (Traversable, mapAccumL)+import Data.Traversable+  ( mapAccumL+#if __GLASGOW_HASKELL__ < 710+  , Traversable+#endif+  ) import Data.Data () import Data.Number.Erf import Numeric.AD.Internal.Combinators

@@ -36,12 +36,18 @@   , transposeWith   ) where + import Control.Monad (join)+#if __GLASGOW_HASKELL__ < 710 import Control.Applicative hiding ((<**>))-import Data.Data import Data.Foldable (Foldable, toList)-import Data.Number.Erf import Data.Traversable (Traversable, mapAccumL)+#else+import Data.Foldable (toList)+import Data.Traversable (mapAccumL)+#endif+import Data.Data+import Data.Number.Erf import Numeric.AD.Internal.Combinators import Numeric.AD.Internal.Identity import Numeric.AD.Jacobian

@@ -1,3 +1,4 @@+{-# LANGUAGE CPP #-} {-# LANGUAGE BangPatterns #-} {-# LANGUAGE ConstraintKinds #-} {-# LANGUAGE FlexibleContexts #-}@@ -33,12 +34,17 @@   , transposeWith   ) where +#if __GLASGOW_HASKELL__ < 710 import Control.Applicative hiding ((<**>))-import Control.Monad (join) import Data.Foldable (Foldable, toList)+import Data.Traversable (Traversable, mapAccumL)+#else+import Data.Foldable (toList)+import Data.Traversable (mapAccumL)+#endif+import Control.Monad (join) import Data.Function (on) import Data.Number.Erf-import Data.Traversable (Traversable, mapAccumL) import Numeric.AD.Internal.Combinators import Numeric.AD.Internal.Identity import Numeric.AD.Jacobian

@@ -1,3 +1,4 @@+{-# LANGUAGE CPP #-} {-# LANGUAGE DeriveDataTypeable #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE FlexibleInstances #-}@@ -24,7 +25,9 @@   ) where  import Data.Data (Data)+#if __GLASGOW_HASKELL__ < 710 import Data.Monoid+#endif import Data.Number.Erf import Data.Typeable (Typeable) import Numeric.AD.Mode

@@ -48,8 +48,11 @@   , varId   ) where +#if __GLASGOW_HASKELL__ < 710 import Prelude hiding (mapM) import Control.Applicative (Applicative(..),(<$>))+import Data.Traversable (Traversable, mapM)+#endif import Control.Monad.ST import Control.Monad hiding (mapM) import Control.Monad.Trans.State@@ -63,7 +66,6 @@ import qualified Data.Reify.Graph as Reified import System.IO.Unsafe (unsafePerformIO) import Data.Data (Data)-import Data.Traversable (Traversable, mapM) import Data.Typeable (Typeable) import Numeric.AD.Internal.Combinators import Numeric.AD.Internal.Identity

@@ -28,7 +28,9 @@   , binary   ) where +#if __GLASGOW_HASKELL__ < 710 import Control.Applicative+#endif import Data.Number.Erf #if __GLASGOW_HASKELL__ >= 707 import Data.Typeable

@@ -64,7 +64,11 @@ import Data.Number.Erf import Data.Proxy import Data.Reflection+#if __GLASGOW_HASKELL__ < 710 import Data.Traversable (Traversable, mapM)+#else+import Data.Traversable (mapM)+#endif import Data.Typeable import Numeric.AD.Internal.Combinators import Numeric.AD.Internal.Identity

@@ -42,7 +42,9 @@   ) where  import Prelude hiding (lookup)+#if __GLASGOW_HASKELL__ < 710 import Control.Applicative hiding ((<**>))+#endif import Control.Comonad.Cofree import Control.Monad (join) import Data.Data

@@ -35,7 +35,9 @@   ) where  import Prelude hiding (all)+#if __GLASGOW_HASKELL__ < 710 import Control.Applicative hiding ((<**>))+#endif import Control.Monad (join) import Data.Foldable import Data.Data (Data)

@@ -26,10 +26,13 @@ #define MIN_VERSION_base(x,y,z) 1 #endif +#if __GLASGOW_HASKELL__ < 710 import Control.Applicative import Data.Foldable import Data.Traversable import Data.Monoid+#endif+ import Data.Typeable import Control.Comonad.Cofree 

@@ -44,7 +44,9 @@   , duF'   ) where +#if __GLASGOW_HASKELL__ < 710 import Data.Traversable (Traversable)+#endif import Numeric.AD.Internal.Forward import Numeric.AD.Internal.On import Numeric.AD.Internal.Type

@@ -1,3 +1,4 @@+{-# LANGUAGE CPP #-} {-# LANGUAGE Rank2Types #-} ----------------------------------------------------------------------------- -- |@@ -40,7 +41,9 @@   , duF'   ) where +#if __GLASGOW_HASKELL__ < 710 import Data.Traversable (Traversable)+#endif import Numeric.AD.Internal.Type (AD(AD), runAD) import Numeric.AD.Internal.Forward.Double (ForwardDouble) import qualified Numeric.AD.Rank1.Forward.Double as Rank1

@@ -1,3 +1,4 @@+{-# LANGUAGE CPP #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE FunctionalDependencies #-} {-# LANGUAGE MultiParamTypeClasses #-}@@ -45,7 +46,9 @@   , diffF'   ) where +#if __GLASGOW_HASKELL__ < 710 import Data.Traversable (Traversable)+#endif import Numeric.AD.Internal.Kahn (Kahn) import Numeric.AD.Internal.On import Numeric.AD.Internal.Type (AD(..))

@@ -1,3 +1,4 @@+{-# LANGUAGE CPP #-} {-# LANGUAGE Rank2Types #-} {-# LANGUAGE TemplateHaskell #-} {-# LANGUAGE BangPatterns #-}@@ -44,10 +45,12 @@   , diffF'   ) where -import Control.Applicative ((<$>))+#if __GLASGOW_HASKELL__ < 710+import Data.Functor ((<$>))+import Data.Traversable (Traversable)+#endif import Data.Functor.Compose import Data.Reflection (Reifies)-import Data.Traversable (Traversable) import Numeric.AD.Internal.On import Numeric.AD.Internal.Reverse import Numeric.AD.Mode

@@ -1,3 +1,4 @@+{-# LANGUAGE CPP #-} {-# LANGUAGE Rank2Types #-} ----------------------------------------------------------------------------- -- |@@ -36,7 +37,9 @@   ) where  import Control.Comonad.Cofree (Cofree)+#if __GLASGOW_HASKELL__ < 710 import Data.Traversable (Traversable)+#endif import Numeric.AD.Internal.Sparse (Sparse) import qualified Numeric.AD.Rank1.Sparse as Rank1 import Numeric.AD.Internal.Type

@@ -0,0 +1,130 @@+{-# LANGUAGE Rank2Types #-}+{-# LANGUAGE BangPatterns #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE TypeFamilies #-}+-----------------------------------------------------------------------------+-- |+-- Copyright   :  (c) Edward Kmett 2015+-- License     :  BSD3+-- Maintainer  :  ekmett@gmail.com+-- Stability   :  experimental+-- Portability :  GHC only+--+-----------------------------------------------------------------------------++module Numeric.AD.Newton.Double+  (+  -- * Newton's Method (Forward AD)+    findZero+  , inverse+  , fixedPoint+  , extremum+  -- * Gradient Ascent/Descent (Reverse AD)+  , conjugateGradientDescent+  , conjugateGradientAscent+  ) where++import Data.Foldable (all, sum)+import Data.Traversable+import Numeric.AD.Internal.Combinators+import Numeric.AD.Internal.Forward (Forward)+import Numeric.AD.Internal.Forward.Double (ForwardDouble)+import Numeric.AD.Internal.On+import Numeric.AD.Internal.Or+import Numeric.AD.Internal.Type (AD(..))+import Numeric.AD.Mode+import Numeric.AD.Rank1.Kahn as Kahn (Kahn, grad)+import qualified Numeric.AD.Rank1.Newton.Double as Rank1+import Prelude hiding (all, mapM, sum)++-- | 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]+findZero :: (forall s. AD s ForwardDouble -> AD s ForwardDouble) -> Double -> [Double]+findZero f = Rank1.findZero (runAD.f.AD)+{-# INLINE findZero #-}++-- | 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+inverse :: (forall s. AD s ForwardDouble -> AD s ForwardDouble) -> Double -> Double -> [Double]+inverse f = Rank1.inverse (runAD.f.AD)+{-# INLINE inverse  #-}++-- | 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+fixedPoint :: (forall s. AD s ForwardDouble -> AD s ForwardDouble) -> Double -> [Double]+fixedPoint f = Rank1.fixedPoint (runAD.f.AD)+{-# INLINE fixedPoint #-}++-- | 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+extremum :: (forall s. AD s (On (Forward ForwardDouble)) -> AD s (On (Forward ForwardDouble))) -> Double -> [Double]+extremum f = Rank1.extremum (runAD.f.AD)+{-# INLINE extremum #-}++-- | 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+conjugateGradientDescent+  :: Traversable f+  => (forall s. Chosen s => f (Or s (On (Forward ForwardDouble)) (Kahn Double)) -> Or s (On (Forward ForwardDouble)) (Kahn Double))+  -> f Double -> [f Double]+conjugateGradientDescent f = conjugateGradientAscent (negate . f)+{-# INLINE conjugateGradientDescent #-}++lfu :: Functor f => (f (Or F a b) -> Or F a b) -> f a -> a+lfu f = runL . f . fmap L++rfu :: Functor f => (f (Or T a b) -> Or T a b) -> f b -> b+rfu f = runR . f . fmap R++-- | Perform a conjugate gradient ascent using reverse mode automatic differentiation to compute the gradient.+conjugateGradientAscent+  :: Traversable f+  => (forall s. Chosen s => f (Or s (On (Forward ForwardDouble)) (Kahn Double)) -> Or s (On (Forward ForwardDouble)) (Kahn Double))+  -> f Double -> [f Double]+conjugateGradientAscent f x0 = takeWhile (all (\a -> a == a)) (go x0 d0 d0 delta0)+  where+    dot x y = sum $ zipWithT (*) x y+    d0 = Kahn.grad (rfu f) x0+    delta0 = dot d0 d0+    go xi _ri di deltai = xi : go xi1 ri1 di1 deltai1+      where+        ai = last $ take 20 $ Rank1.extremum (\a -> lfu f $ zipWithT (\x d -> auto x + a * auto d) xi di) 0+        xi1 = zipWithT (\x d -> x + ai*d) xi di+        ri1 = Kahn.grad (rfu f) xi1+        deltai1 = dot ri1 ri1+        bi1 = deltai1 / deltai+        di1 = zipWithT (\r d -> r + bi1 * d) ri1 di+{-# INLINE conjugateGradientAscent #-}

@@ -42,8 +42,10 @@   , duF'   ) where +#if __GLASGOW_HASKELL__ < 710 import Data.Traversable (Traversable) import Control.Applicative+#endif import Numeric.AD.Internal.Forward import Numeric.AD.Internal.On import Numeric.AD.Mode

@@ -1,3 +1,4 @@+{-# LANGUAGE CPP #-} module Numeric.AD.Rank1.Forward.Double   ( ForwardDouble   -- * Gradient@@ -25,8 +26,10 @@   , duF'   ) where +#if __GLASGOW_HASKELL__ < 710 import Control.Applicative import Data.Traversable (Traversable)+#endif import Numeric.AD.Mode import Numeric.AD.Internal.Forward.Double 

@@ -1,3 +1,4 @@+{-# LANGUAGE CPP #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE FunctionalDependencies #-} {-# LANGUAGE MultiParamTypeClasses #-}@@ -50,9 +51,11 @@   , Grad   ) where +#if __GLASGOW_HASKELL__ < 710 import Control.Applicative ((<$>))-import Data.Functor.Compose import Data.Traversable (Traversable)+#endif+import Data.Functor.Compose import Numeric.AD.Internal.On import Numeric.AD.Internal.Kahn import Numeric.AD.Mode

@@ -1,3 +1,4 @@+{-# LANGUAGE CPP #-} {-# LANGUAGE BangPatterns #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE ScopedTypeVariables #-}@@ -26,7 +27,9 @@  import Prelude hiding (all, mapM) import Data.Foldable (all)+#if __GLASGOW_HASKELL__ < 710 import Data.Traversable+#endif import Numeric.AD.Mode import Numeric.AD.Rank1.Forward (Forward, diff, diff') import Numeric.AD.Rank1.Kahn as Kahn (Kahn, gradWith')

@@ -0,0 +1,83 @@+{-# LANGUAGE CPP #-}+{-# LANGUAGE BangPatterns #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE TypeFamilies #-}+-----------------------------------------------------------------------------+-- |+-- Copyright   :  (c) Edward Kmett 2015+-- License     :  BSD3+-- Maintainer  :  ekmett@gmail.com+-- Stability   :  experimental+-- Portability :  GHC only+--+-----------------------------------------------------------------------------++module Numeric.AD.Rank1.Newton.Double+  (+  -- * Newton's Method (Forward)+    findZero+  , inverse+  , fixedPoint+  , extremum+  ) where++import Prelude hiding (all, mapM)+import Numeric.AD.Mode+import Numeric.AD.Rank1.Forward (Forward)+import qualified Numeric.AD.Rank1.Forward as Forward+import Numeric.AD.Rank1.Forward.Double (ForwardDouble, diff')+import Numeric.AD.Internal.On++-- | 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]+findZero :: (ForwardDouble -> ForwardDouble) -> Double -> [Double]+findZero f = go where+  go x = x : if x == xn then [] else go xn where+    (y,y') = diff' f x+    xn = x - y/y'+{-# INLINE findZero #-}++-- | 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+inverse :: (ForwardDouble -> ForwardDouble) -> Double -> Double -> [Double]+inverse f x0 y = findZero (\x -> f x - auto y) x0+{-# INLINE inverse  #-}++-- | 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+fixedPoint :: (ForwardDouble -> ForwardDouble) -> Double -> [Double]+fixedPoint f = findZero (\x -> f x - x)+{-# INLINE fixedPoint #-}++-- | 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+extremum :: (On (Forward ForwardDouble) -> On (Forward ForwardDouble)) -> Double -> [Double]+extremum f = findZero (Forward.diff (off . f . On))+{-# INLINE extremum #-}

@@ -1,3 +1,4 @@+{-# LANGUAGE CPP #-} ----------------------------------------------------------------------------- -- | -- Copyright   : (c) Edward Kmett 2010-2015@@ -45,7 +46,9 @@   ) where  import Control.Comonad+#if __GLASGOW_HASKELL__ < 710 import Data.Traversable+#endif import Control.Comonad.Cofree import Numeric.AD.Jet import Numeric.AD.Internal.Sparse

@@ -1,3 +1,4 @@+{-# LANGUAGE CPP #-} {-# LANGUAGE Rank2Types #-} {-# LANGUAGE BangPatterns #-} -----------------------------------------------------------------------------@@ -39,7 +40,9 @@   , dus0F   -- answer and all zero padded directional derivatives of (f a -> g a)   ) where -import Control.Applicative ((<$>))+#if __GLASGOW_HASKELL__ < 710+import Data.Functor ((<$>))+#endif import Numeric.AD.Internal.Tower import Numeric.AD.Mode 

@@ -1,7 +1,10 @@+{-# LANGUAGE CPP #-} module Main where  import Build_doctests (deps)+#if __GLASGOW_HASKELL__ < 710 import Control.Applicative+#endif import Control.Monad import Data.List import System.Directory