linear 1.10.1.2 → 1.23.3
raw patch · 43 files changed
Files
- .ghci +0/−1
- .gitignore +19/−0
- .hlint.yaml +7/−0
- .travis.yml +0/−26
- CHANGELOG.markdown +317/−0
- LICENSE +1/−1
- README.markdown +2/−0
- Setup.lhs +4/−41
- linear.cabal +92/−46
- src/Linear.hs +3/−3
- src/Linear/Affine.hs +164/−26
- src/Linear/Algebra.hs +9/−0
- src/Linear/Binary.hs +2/−4
- src/Linear/Conjugate.hs +6/−1
- src/Linear/Covector.hs +12/−1
- src/Linear/Epsilon.hs +5/−1
- src/Linear/Instances.hs +4/−78
- src/Linear/Matrix.hs +502/−60
- src/Linear/Metric.hs +30/−4
- src/Linear/Plucker.hs +232/−67
- src/Linear/Plucker/Coincides.hs +38/−0
- src/Linear/Projection.hs +260/−0
- src/Linear/Quaternion.hs +188/−37
- src/Linear/Trace.hs +13/−11
- src/Linear/V.hs +351/−52
- src/Linear/V0.hs +161/−28
- src/Linear/V1.hs +170/−35
- src/Linear/V2.hs +201/−32
- src/Linear/V3.hs +231/−34
- src/Linear/V4.hs +351/−36
- src/Linear/Vector.hs +66/−117
- tests/Binary.hs +0/−19
- tests/Plucker.hs +0/−34
- tests/Prop/Quaternion.hs +28/−0
- tests/Prop/V3.hs +8/−0
- tests/Test.hs +24/−0
- tests/Unit/Binary.hs +20/−0
- tests/Unit/Plucker.hs +36/−0
- tests/Unit/V.hs +14/−0
- tests/UnitTests.hs +0/−12
- tests/doctests.hs +16/−27
- travis/cabal-apt-install +0/−27
- travis/config +0/−16
− .ghci
@@ -1,1 +0,0 @@-:set -isrc -idist/build/autogen -optP-include -optPdist/build/autogen/cabal_macros.h
.gitignore view
@@ -1,4 +1,5 @@ dist+dist-newstyle docs wiki TAGS@@ -11,3 +12,21 @@ *.hi *~ *#+.stack-work/+cabal-dev+*.chi+*.chs.h+*.dyn_o+*.dyn_hi+.hpc+.hsenv+.cabal-sandbox/+cabal.sandbox.config+*.prof+*.aux+*.hp+*.eventlog+cabal.project.local+cabal.project.local~+.HTF/+.ghc.environment.*
+ .hlint.yaml view
@@ -0,0 +1,7 @@+- arguments: [-XCPP]++- ignore: {name: Use fmap}+- ignore: {name: Avoid lambda}+- ignore: {name: Redundant lambda}+- ignore: {name: Unused LANGUAGE pragma}+- ignore: {name: Eta reduce, within: [Linear.Plucker, Linear.Quaternion, Linear.V, Linear.V0, Linear.V1, Linear.V2, Linear.V3, Linear.V4]}
− .travis.yml
@@ -1,26 +0,0 @@-language: haskell-before_install:- # Uncomment whenever hackage is down.- # - mkdir -p ~/.cabal && cp travis/config ~/.cabal/config && cabal update-- # Try installing some of the build-deps with apt-get for speed.- - travis/cabal-apt-install $mode--install:- - cabal configure $mode- - cabal build--script:- - $script- - hlint src --cpp-define HLINT--notifications:- irc:- channels:- - "irc.freenode.org#haskell-lens"- skip_join: true- template:- - "\x0313linear\x03/\x0306%{branch}\x03 \x0314%{commit}\x03 %{build_url} %{message}"--env:- - mode="--enable-tests" script="cabal test"
CHANGELOG.markdown view
@@ -1,3 +1,320 @@+1.23.3 [2026.01.10]+-------------------+* Remove unused `ghc-prim`, `tagged, `transformers-compat`, and `void`+ dependencies.++1.23.2 [2025.06.17]+-------------------+* Replace `test-framework` with `tasty` in the test suite.++1.23.1 [2025.03.03]+-------------------+* Add `Uniform` and `UniformRange` instances for `Plucker`, `Quaternion`, `V`,+ and `V{0,1,2,3,4}`.++1.23 [2024.04.15]+-----------------+* The direction of interpolation of `lerp` has been reversed;+ now `lerp 0 a b == a` and `lerp 1 a b == b`.+ This brings `lerp` in line not only with its implementation+ in other languages and frameworks, but also with `slerp` in this package.++1.22 [2022.11.30]+-----------------+* The types of `_Point` and `lensP` have been generalized:++ ```diff+ -_Point :: Iso' (Point f a) (f a)+ +_Point :: Iso (Point f a) (Point g b) (f a) (g b)++ -lensP :: Lens' (Point g a) (g a)+ +lensP :: Lens (Point f a) (Point g b) (f a) (g b)+ ```++ There is a chance that existing uses of `_Point` or `lensP` will fail to+ typecheck due to their more general types. You can use `_Point.simple` or+ `lensP.simple` to restore their old, more restricted types (where `simple`+ comes from `Control.Lens` in the `lens` library).++1.21.10 [2022.06.21]+--------------------+* Allow building with `vector-0.13.*`.++1.21.9 [2022.05.18]+-------------------+* Allow building with `transformers-0.6.*`.++1.21.8 [2021.11.15]+-------------------+* Allow building with `hashable-1.4.*`.+* Drop support for pre-8.0 versions of GHC.++1.21.7 [2021.09.20]+-------------------+* Fix a build error when using `random-1.2.1` or later.++1.21.6 [2021.07.05]+-------------------+* Fix a build error when configured with `-template-haskell`.++1.21.5 [2021.02.18]+-------------------+* Allow building with `lens-5.*`.++1.21.4 [2021.01.29]+-------------------+* Allow building with `vector-0.12.2` or later.+* The build-type has been changed from `Custom` to `Simple`.+ To achieve this, the `doctests` test suite has been removed in favor of using+ [`cabal-docspec`](https://github.com/phadej/cabal-extras/tree/master/cabal-docspec)+ to run the doctests.++1.21.3 [2020.10.03]+-------------------+* Allow building with GHC 9.0.++1.21.2 [2020.09.30]+-------------------+* Use `base-orphans-0.8.3` or later. This means that the `Linear.Instances`+ module no longer defines any orphan instances of its own, and the module is+ now a simple shim on top of `Data.Orphans` from `base-orphans`.++1.21.1 [2020.06.25]+-------------------+* Allow building with `random-1.2.*`.++1.21 [2020.02.03]+-----------------+* Add instances for direct sums (`Product`) and tensor products (`Compose`) of+ other vector spaces. This makes is much more convenient to do things like treat+ a matrix temporarily as a vector through Compose, or to consider things like+ Gauss-Jordan elimination, which wants augmented structures.+* Add `frobenius` for computing the Frobenius norm of a matrix.+* Added `Random` instances for `System.Random`. We had an indirect dependency+ through `vector` anyways.+* Add "obvious" zipping `Semigroup` and `Monoid` instances to all the+ representable vector spaces.+* Add `R1`..`R4` instances to `Quaternion`. `_w` is the scalar component so that+ `_x`,`_y`,`_z` can be directional.+* Add more solvers to `Linear.Matrix`, available with `base-4.8` or later.+* Add `unangle` function to `Linear.V2`.++1.20.9 [2019.05.02]+-------------------+* Derive `Lift` instances for `Plucker`, `Quaternion`, and `V{0,1,2,3,4}`.++1.20.8 [2018.07.03]+-------------------+* Add instances of the `Field` classes from `lens`.+* Add `Epsilon` instance for `Complex`.+* Use specialized implementations of the `null` and `length` methods in+ `Foldable` instances.+* Add `Hashable1` instances for data types in `linear`. Also add a+ `Hashable` instance for `V`.+* Fix a bug in which `Quaternion`s were incorrectly exponentiated.++1.20.7+------+* Support `semigroupoids-5.2.1` and `doctest-0.12`++1.20.6+------+* Revamp `Setup.hs` to use `cabal-doctest`. This makes it build+ with `Cabal-2.0`, and makes the `doctest`s work with `cabal new-build` and+ sandboxes.+* Make `(1 / x)` and `recip x` agree in the `Fractional` instance for `Quaternion`+* Use newtype instances for `Point` vectors in `Linear.Affine`+* Enable `PolyKinds` in `Linear.Trace`. Also enable `PolyKinds` when GHC 7.6 or+ later is used (previously, it was GHC 7.8 or later).+* Fix a segfault arising from the `MVector` instance for `V`+* Add `Finite` class for conversion between `V` and fixed-size vector types++1.20.5+------+* GHC 8 compatibility+* Fixed the `perspective` calculation.++1.20.4+------+* Compatibility with `base-orphans` 0.5++1.20.3+------+* Support `vector` 0.11.0.0.+* Support `cereal` 0.5+* You can now unboxed vectors of `V n` vectors.++1.20.2+------+* Modified the `doctest` machinery to work with `stack` and builds to non-standard locations.+* Removed the local `.ghci` file.+* Various numerical stability improvements were made to the quaternion and projection functions.++1.20.1+------+* Fixed doctests broken by the previous change.+* Unboxed vector instances for various linear data types now use unpacked integers even on older GHCs.++1.20+----+* `inv22`, `inv33` and `inv44` no longer attempt an epsilon check. They no longer return a `Maybe` result as a consequence.+ You should filter for the 0 determinant case yourself.++1.19.1.3+--------+* `vector` 0.11.0.0 support++1.19.1.2+--------+* Fix GHC 7.4.++1.19.1.1+--------+* Proper `reflection` 2 support++1.19.1+------+* `reflection` 2 support++1.19+----+* Change the Ixed instance for `Linear.V` to use `Int` as the index type. This makes `V n` a _lot_ easier to use.++1.18.3+------+* Compile warning-free on GHC 7.10.+++1.18.2+------+* Added `NFData` instance for `Point`++1.18.1+------+* Added an `-f-template-haskell` option to allow disabling `template-haskell` support. This is an unsupported configuration but may be useful for expert users in sandbox configurations.+* Added lenses for extracting corner various sub-matrices e.g. `_m22`, `_m33`++1.18.0.2+--------+* Fixed builds on even older GHCs.++1.18.0.1+--------+* Fixed the test suite.+* Fixed builds on older GHCs.++1.18+----+* Consolidated `eye2` .. `eye4` into a single `identity` combinator.+* Fixed the `Data` instance `V n a` for GHC 7.10-RC3.++1.17.1.1+--------+* `filepath` 1.4 support++1.17.1+------+* Added support for `Data.Functor.Classes` from `transformers` 0.5 via `transformers-compat`.+* Added missing support for `binary`, `bytes` and `cereal` for `Point`++1.17+----+* Better support for `binary`. Added support for `bytes` and `cereal`++1.16.4+------+* `ortho` and `inverseOrtho` now only require a `Fractional` constraint.+* Added missing `Floating` instances.++1.16.3+----+* Improve the performance of `fromQuaternion`, `mkTransformation`,+ `mkTransformationMat`, `basisFor`, `scaled` by using implementations+ that inline well for functions that were previously reference+ implementations.++1.16.2+----+* Added `NFData` instances for the various vector types.+* Added `!!/` operator for matrix division by scalar.++1.16.1+----+* Added `Trace` instance for `V1`.++1.16+----+* Renamed `kronecker` to `scaled`.++1.15.5+------+* Added `Metric` instances for `[]`, `ZipList`, `Maybe`+* Added `det44` and `inv44` to `Linear.Matrix`+* Added `Data` instance for `Point`++1.15.4+------+* Added Typeable and Data instances for V++1.15.3+------+* Added missing `FunctorWithIndex`, `FoldableWithIndex` and `TraversableWithIndex Int (V n)` instances for `V`++1.15.2+------+* Added `frustum`, analogous to the old `glFrustum` call.+* Added `inverseInfinitePerspective`, `inverseOrtho`, `inverseFrustum`.++1.15.1+------+* Added `inversePerspective`. It is much more accurate to compute it directly than to compute an inverse.++1.15.0.1+--------+* Fixed build failures caused by `Linear` re-exporting the old name.++1.15+----+* Renamed `Linear.Perspective` to `Linear.Projection`.+* Fixed a build issue with GHC HEAD.++1.14.0.1+--------+* Fixed test failures caused by 1.14++1.14+----+* Moved `Coincides` to `Linear.Plucker.Coincides`. The constructors `Line` and `Ray` oft collided with user code.++1.13+----+* Switched 'ortho' to follow the OpenGL handedness.++1.12.1+------+* Added "swizzle" lenses **e.g.** `_yzx`, which are useful for working with libraries like `gl`.++1.12+------+* Added 'transpose'+* Added missing 'Mxy' matrices up to 4 dimensions -- they were commonly reimplemented by users.++1.11.3+------+* Fixed an issue with `UndecidableInstances` on GHC 7.6.3++1.11.2+------+* Added `Linear.Perspective`.++1.11.1+------+* Added `_Point`, `relative` and a few instances for `Point`.++1.11+----+* Changed the 'representation' of `V n` from `E (V n)`, which was hard to use, to `Int`, which is a bit too permissive, but is easy to use.+ 1.10.1 ------ * Added `Linear.V2.angle`.
LICENSE view
@@ -1,4 +1,4 @@-Copyright 2011-14 Edward Kmett+Copyright 2011-2015 Edward Kmett All rights reserved.
README.markdown view
@@ -1,6 +1,8 @@ linear ====== +[](https://hackage.haskell.org/package/linear) [](https://github.com/ekmett/linear/actions?query=workflow%3AHaskell-CI)+ Highly polymorphic vector space operations on sparse and free vector spaces. Contact Information
Setup.lhs view
@@ -1,44 +1,7 @@ #!/usr/bin/runhaskell-\begin{code}-{-# OPTIONS_GHC -Wall #-}-module Main (main) where--import Data.List ( nub )-import Data.Version ( showVersion )-import Distribution.Package ( PackageName(PackageName), PackageId, InstalledPackageId, packageVersion, packageName )-import Distribution.PackageDescription ( PackageDescription(), TestSuite(..) )-import Distribution.Simple ( defaultMainWithHooks, UserHooks(..), simpleUserHooks )-import Distribution.Simple.Utils ( rewriteFile, createDirectoryIfMissingVerbose )-import Distribution.Simple.BuildPaths ( autogenModulesDir )-import Distribution.Simple.Setup ( BuildFlags(buildVerbosity), fromFlag )-import Distribution.Simple.LocalBuildInfo ( withLibLBI, withTestLBI, LocalBuildInfo(), ComponentLocalBuildInfo(componentPackageDeps) )-import Distribution.Verbosity ( Verbosity )-import System.FilePath ( (</>) )--main :: IO ()-main = defaultMainWithHooks simpleUserHooks- { buildHook = \pkg lbi hooks flags -> do- generateBuildModule (fromFlag (buildVerbosity flags)) pkg lbi- buildHook simpleUserHooks pkg lbi hooks flags- }--generateBuildModule :: Verbosity -> PackageDescription -> LocalBuildInfo -> IO ()-generateBuildModule verbosity pkg lbi = do- let dir = autogenModulesDir lbi- createDirectoryIfMissingVerbose verbosity True dir- withLibLBI pkg lbi $ \_ libcfg -> do- withTestLBI pkg lbi $ \suite suitecfg -> do- rewriteFile (dir </> "Build_" ++ testName suite ++ ".hs") $ unlines- [ "module Build_" ++ testName suite ++ " where"- , "deps :: [String]"- , "deps = " ++ (show $ formatdeps (testDeps libcfg suitecfg))- ]- where- formatdeps = map (formatone . snd)- formatone p = case packageName p of- PackageName n -> n ++ "-" ++ showVersion (packageVersion p)+> module Main (main) where -testDeps :: ComponentLocalBuildInfo -> ComponentLocalBuildInfo -> [(InstalledPackageId, PackageId)]-testDeps xs ys = nub $ componentPackageDeps xs ++ componentPackageDeps ys+> import Distribution.Simple -\end{code}+> main :: IO ()+> main = defaultMain
linear.cabal view
@@ -1,53 +1,85 @@ name: linear category: Math, Algebra-version: 1.10.1.2+version: 1.23.3 license: BSD3-cabal-version: >= 1.8+cabal-version: >= 1.10 license-file: LICENSE author: Edward A. Kmett maintainer: Edward A. Kmett <ekmett@gmail.com> stability: provisional homepage: http://github.com/ekmett/linear/ bug-reports: http://github.com/ekmett/linear/issues-copyright: Copyright (C) 2012-2014 Edward A. Kmett+copyright: Copyright (C) 2012-2015 Edward A. Kmett synopsis: Linear Algebra description: Types and combinators for linear algebra on free vector spaces-build-type: Custom-tested-with: GHC == 7.4.1, GHC == 7.4.2, GHC == 7.6.1+build-type: Simple+tested-with: GHC == 8.0.2+ , GHC == 8.2.2+ , GHC == 8.4.4+ , GHC == 8.6.5+ , GHC == 8.8.4+ , GHC == 8.10.7+ , GHC == 9.0.2+ , GHC == 9.2.8+ , GHC == 9.4.8+ , GHC == 9.6.7+ , GHC == 9.8.4+ , GHC == 9.10.3+ , GHC == 9.12.2+ , GHC == 9.14.1 extra-source-files:- .ghci .gitignore- .travis.yml+ .hlint.yaml .vim.custom- travis/cabal-apt-install- travis/config CHANGELOG.markdown README.markdown +flag template-haskell+ description:+ You can disable the use of the `template-haskell` package using `-f-template-haskell`.+ .+ Disabling this is an unsupported configuration, but it may be useful for accelerating builds in sandboxes for expert users.+ default: True+ manual: True++flag herbie+ description: Enable `herbie`.+ default: False+ manual: True+ source-repository head type: git- location: git://github.com/ekmett/linear.git+ location: https://github.com/ekmett/linear library build-depends: adjunctions >= 4 && < 5,- base >= 4.5 && < 5,- binary >= 0.5 && < 0.8,- containers >= 0.4 && < 0.6,- distributive >= 0.2.2 && < 1,- ghc-prim,- hashable >= 1.1 && < 1.3,- lens >= 4 && < 5,- reflection >= 1.3.2 && < 2,- semigroups >= 0.9 && < 1,- semigroupoids >= 3 && < 5,- tagged >= 0.4.4 && < 1,- template-haskell >= 2.7 && < 3.0,- transformers >= 0.2 && < 0.5,+ base >= 4.9 && < 5,+ base-orphans >= 0.8.3 && < 1,+ binary >= 0.5 && < 0.9,+ bytes >= 0.15 && < 1,+ cereal >= 0.4.1.1 && < 0.6,+ containers >= 0.4 && < 0.9,+ deepseq >= 1.1 && < 1.6,+ distributive >= 0.5.1 && < 1,+ hashable >= 1.2.7.0 && < 1.6,+ indexed-traversable >= 0.1.1 && < 0.2,+ lens >= 4.15.2 && < 6,+ random >= 1.2 && < 1.4,+ reflection >= 2 && < 3,+ semigroupoids >= 5.2.1 && < 7,+ transformers >= 0.5 && < 0.7, unordered-containers >= 0.2.3 && < 0.3,- vector >= 0.10 && < 0.11,- void >= 0.6 && < 1+ vector >= 0.12.1.2 && < 0.14 + if flag(template-haskell) && impl(ghc)+ build-depends: template-haskell >= 2.11.1.0 && < 3.0++ if flag(herbie)+ build-depends: HerbiePlugin >= 0.1 && < 0.2+ ghc-options: -fplugin=Herbie+ cpp-options: -DHERBIE+ exposed-modules: Linear Linear.Affine@@ -60,6 +92,8 @@ Linear.Matrix Linear.Metric Linear.Plucker+ Linear.Plucker.Coincides+ Linear.Projection Linear.Quaternion Linear.Trace Linear.V@@ -70,34 +104,46 @@ Linear.V4 Linear.Vector - ghc-options: -Wall -fwarn-tabs -O2 -fdicts-cheap -funbox-strict-fields+ ghc-options: -Wall -Wtabs -O2 -fdicts-cheap -funbox-strict-fields -Wno-trustworthy-safe hs-source-dirs: src --- Verify the results of the examples+ default-language: Haskell2010++ x-docspec-extra-packages: simple-reflect++-- We need this dummy test-suite to add simple-reflect to the install plan+--+-- When cabal-install's extra-packages support becomes widely available+-- (i.e. after 3.4 release), we can remove this test-suite. test-suite doctests- type: exitcode-stdio-1.0- main-is: doctests.hs- ghc-options: -Wall -Werror -threaded- hs-source-dirs: tests- build-depends:- base,- directory >= 1.0 && < 1.3,- doctest >= 0.8 && < 0.10,- filepath >= 1.3 && < 1.4,- lens,- simple-reflect >= 0.3.1+ type: exitcode-stdio-1.0+ main-is: doctests.hs+ hs-source-dirs: tests+ default-language: Haskell2010 -test-suite UnitTests+ build-depends: base < 5, simple-reflect >= 0.3.1++test-suite test type: exitcode-stdio-1.0- main-is: UnitTests.hs- other-modules: Plucker, Binary- ghc-options: -Wall -Werror -threaded+ main-is: Test.hs+ other-modules: Prop.Quaternion+ Prop.V3+ Unit.Binary+ Unit.Plucker+ Unit.V+ ghc-options: -Wall -threaded hs-source-dirs: tests build-depends: base, binary, bytestring,- test-framework >= 0.8,- test-framework-hunit >= 0.3,- HUnit >= 1.2.5,- linear+ deepseq,+ tasty >= 1.4 && < 1.6,+ tasty-hunit >= 0.10 && < 0.11,+ tasty-quickcheck >= 0.10 && < 0.12,+ linear,+ QuickCheck >= 2.5,+ reflection,+ vector+ default-language: Haskell2010+
src/Linear.hs view
@@ -1,6 +1,6 @@ ----------------------------------------------------------------------------- -- |--- Copyright : (C) 2012-2013 Edward Kmett,+-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett <ekmett@gmail.com>@@ -18,6 +18,7 @@ , module Linear.Epsilon , module Linear.Matrix , module Linear.Metric+ , module Linear.Projection , module Linear.Quaternion , module Linear.Trace , module Linear.V0@@ -36,6 +37,7 @@ import Linear.Instances () import Linear.Matrix import Linear.Metric+import Linear.Projection import Linear.Quaternion import Linear.Trace import Linear.V0@@ -44,5 +46,3 @@ import Linear.V3 import Linear.V4 import Linear.Vector--{-# ANN module "Hlint: ignore Use import/export shortcut" #-}
src/Linear/Affine.hs view
@@ -1,12 +1,19 @@ {-# LANGUAGE CPP #-} {-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE GeneralizedNewtypeDeriving #-} {-# LANGUAGE DeriveTraversable #-}+{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE TypeFamilies #-}-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702+{-# LANGUAGE TypeOperators #-}+{-# LANGUAGE RankNTypes #-} {-# LANGUAGE Trustworthy #-} {-# LANGUAGE DeriveGeneric #-}-#endif+{-# LANGUAGE DeriveDataTypeable #-}+{-# LANGUAGE StandaloneDeriving #-}+{-# LANGUAGE ScopedTypeVariables #-}+ ----------------------------------------------------------------------------- -- | -- License : BSD-style (see the file LICENSE)@@ -19,25 +26,37 @@ module Linear.Affine where import Control.Applicative+import Control.DeepSeq+import Control.Monad (liftM) import Control.Lens+import Data.Binary as Binary+import Data.Bytes.Serial+import Data.Coerce import Data.Complex (Complex)+import Data.Data import Data.Distributive import Data.Foldable as Foldable import Data.Functor.Bind+import Data.Functor.Classes+import Data.Functor.Product import Data.Functor.Rep as Rep import Data.HashMap.Lazy (HashMap) import Data.Hashable+import Data.Hashable.Lifted import Data.IntMap (IntMap) import Data.Ix+import Data.Kind import Data.Map (Map)+#if !(MIN_VERSION_base(4,11,0))+import Data.Semigroup (Semigroup)+#endif+import Data.Serialize as Cereal import Data.Vector (Vector)+import qualified Data.Vector.Generic.Mutable as M+import qualified Data.Vector.Generic as G+import qualified Data.Vector.Unboxed.Base as U import Foreign.Storable-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702-import GHC.Generics (Generic)-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706-import GHC.Generics (Generic1)-#endif+import GHC.Generics (Generic, Generic1) import Linear.Epsilon import Linear.Metric import Linear.Plucker@@ -49,10 +68,7 @@ import Linear.V3 import Linear.V4 import Linear.Vector--#ifdef HLINT-{-# ANN module "HLint: ignore Unused LANGUAGE pragma" #-}-#endif+import System.Random (Random(..)) -- | An affine space is roughly a vector space in which we have -- forgotten or at least pretend to have forgotten the origin.@@ -61,7 +77,7 @@ -- > (a .+^ u) .+^ v = a .+^ (u ^+^ v)@ -- > (a .-. b) ^+^ v = (a .+^ v) .-. q@ class Additive (Diff p) => Affine p where- type Diff p :: * -> *+ type Diff p :: Type -> Type infixl 6 .-. -- | Get the difference between two points as a vector offset.@@ -77,13 +93,21 @@ p .-^ v = p .+^ negated v {-# INLINE (.-^) #-} +instance (Affine f, Affine g) => Affine (Product f g) where+ type Diff (Product f g) = Product (Diff f) (Diff g)+ Pair a b .-. Pair c d = Pair (a .-. c) (b .-. d)+ Pair a b .+^ Pair c d = Pair (a .+^ c) (b .+^ d)+ Pair a b .-^ Pair c d = Pair (a .+^ c) (b .+^ d)+ -- | Compute the quadrance of the difference (the square of the distance) qdA :: (Affine p, Foldable (Diff p), Num a) => p a -> p a -> a qdA a b = Foldable.sum (fmap (join (*)) (a .-. b))+{-# INLINE qdA #-} -- | Distance between two points in an affine space distanceA :: (Floating a, Foldable (Diff p), Affine p) => p a -> p a -> a distanceA a b = sqrt (qdA a b)+{-# INLINE distanceA #-} #define ADDITIVEC(CTX,T) instance CTX => Affine T where type Diff T = T ; \ (.-.) = (^-^) ; {-# INLINE (.-.) #-} ; (.+^) = (^+^) ; {-# INLINE (.+^) #-} ; \@@ -113,53 +137,167 @@ -- type level newtype Point f a = P (f a) deriving ( Eq, Ord, Show, Read, Monad, Functor, Applicative, Foldable+ , Eq1, Ord1, Show1, Read1 , Traversable, Apply, Additive, Metric , Fractional , Num, Ix, Storable, Epsilon-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702- , Generic-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706- , Generic1-#endif+ , Semigroup, Monoid+ , Random, Hashable+ , Generic, Generic1, Data ) -lensP :: Lens' (Point g a) (g a)+instance Finite f => Finite (Point f) where+ type Size (Point f) = Size f+ toV (P v) = toV v+ fromV v = P (fromV v)++instance NFData (f a) => NFData (Point f a) where+ rnf (P x) = rnf x++instance Serial1 f => Serial1 (Point f) where+ serializeWith f (P p) = serializeWith f p+ deserializeWith m = P `liftM` deserializeWith m++instance Serial (f a) => Serial (Point f a) where+ serialize (P p) = serialize p+ deserialize = P `liftM` deserialize++instance Binary (f a) => Binary (Point f a) where+ put (P p) = Binary.put p+ get = P `liftM` Binary.get++instance Serialize (f a) => Serialize (Point f a) where+ put (P p) = Cereal.put p+ get = P `liftM` Cereal.get++instance Hashable1 f => Hashable1 (Point f) where+ liftHashWithSalt h s (P f) = liftHashWithSalt h s f+ {-# INLINE liftHashWithSalt #-}++lensP :: Lens (Point f a) (Point g b) (f a) (g b) lensP afb (P a) = P <$> afb a+{-# INLINE lensP #-} +_Point :: Iso (Point f a) (Point g b) (f a) (g b)+_Point = iso (\(P a) -> a) P+{-# INLINE _Point #-}++instance (t ~ Point g b) => Rewrapped (Point f a) t+instance Wrapped (Point f a) where+ type Unwrapped (Point f a) = f a+ _Wrapped' = _Point+ {-# INLINE _Wrapped' #-}++-- These are stolen from Data.Profunctor.Unsafe+(.#) :: Coercible b a => (b -> c) -> (a -> b) -> a -> c+f .# _ = coerce f+{-# INLINE (.#) #-}++(#.) :: Coercible c b => (b -> c) -> (a -> b) -> a -> c+(#.) _ = coerce (\x -> x :: b) :: forall a b. Coercible b a => a -> b+{-# INLINE (#.) #-}++unP :: Point f a -> f a+unP (P x) = x+{-# INLINE unP #-}++-- We can't use GND to derive 'Bind' because 'join' causes+-- role troubles. However, GHC 7.8 and above let us use+-- explicit coercions for (>>-). instance Bind f => Bind (Point f) where- join (P m) = P $ join $ fmap (\(P m')->m') m+ (>>-) = ((P .) . (. (unP .))) #. (>>-) .# unP+ join (P m) = P $ m >>- \(P m') -> m' instance Distributive f => Distributive (Point f) where distribute = P . collect (\(P p) -> p)+ collect = (P .) #. collect .# (unP .) instance Representable f => Representable (Point f) where type Rep (Point f) = Rep f- tabulate f = P (tabulate f)+ tabulate = P #. tabulate {-# INLINE tabulate #-}- index (P xs) = Rep.index xs+ index = Rep.index .# unP {-# INLINE index #-} +type instance Index (Point f a) = Index (f a)+type instance IxValue (Point f a) = IxValue (f a)++instance Ixed (f a) => Ixed (Point f a) where+ ix l = lensP . ix l+ {-# INLINE ix #-}++instance Traversable f => Each (Point f a) (Point f b) a b where+ each = traverse+ {-# INLINE each #-}+ instance R1 f => R1 (Point f) where _x = lensP . _x+ {-# INLINE _x #-} instance R2 f => R2 (Point f) where _y = lensP . _y+ {-# INLINE _y #-} _xy = lensP . _xy+ {-# INLINE _xy #-} instance R3 f => R3 (Point f) where _z = lensP . _z+ {-# INLINE _z #-} _xyz = lensP . _xyz+ {-# INLINE _xyz #-} instance R4 f => R4 (Point f) where _w = lensP . _w+ {-# INLINE _w #-} _xyzw = lensP . _xyzw+ {-# INLINE _xyzw #-} instance Additive f => Affine (Point f) where type Diff (Point f) = f- P x .-. P y = x ^-^ y- P x .+^ v = P (x ^+^ v)- P x .-^ v = P (x ^-^ v)+ (.-.) = (. unP) #. (^-^) .# unP+ {-# INLINE (.-.) #-}+ (.+^) = (P .) #. (^+^) .# unP+ {-# INLINE (.+^) #-}+ (.-^) = (P .) #. (^-^) .# unP+ {-# INLINE (.-^) #-} -- | Vector spaces have origins. origin :: (Additive f, Num a) => Point f a origin = P zero++-- | An isomorphism between points and vectors, given a reference+-- point.+relative :: (Additive f, Num a) => Point f a -> Iso' (Point f a) (f a)+relative p0 = iso (.-. p0) (p0 .+^)+{-# INLINE relative #-}++newtype instance U.Vector (Point f a) = V_P (U.Vector (f a))+newtype instance U.MVector s (Point f a) = MV_P (U.MVector s (f a))+instance U.Unbox (f a) => U.Unbox (Point f a)++instance U.Unbox (f a) => M.MVector U.MVector (Point f a) where+ {-# INLINE basicLength #-}+ {-# INLINE basicUnsafeSlice #-}+ {-# INLINE basicOverlaps #-}+ {-# INLINE basicUnsafeNew #-}+ {-# INLINE basicUnsafeRead #-}+ {-# INLINE basicUnsafeWrite #-}+ basicLength (MV_P v) = M.basicLength v+ basicUnsafeSlice m n (MV_P v) = MV_P (M.basicUnsafeSlice m n v)+ basicOverlaps (MV_P v) (MV_P u) = M.basicOverlaps v u+ basicUnsafeNew n = MV_P `liftM` M.basicUnsafeNew n+ basicUnsafeRead (MV_P v) i = P `liftM` M.basicUnsafeRead v i+ basicUnsafeWrite (MV_P v) i (P x) = M.basicUnsafeWrite v i x+ basicInitialize (MV_P v) = M.basicInitialize v+ {-# INLINE basicInitialize #-}++instance U.Unbox (f a) => G.Vector U.Vector (Point f a) where+ {-# INLINE basicUnsafeFreeze #-}+ {-# INLINE basicUnsafeThaw #-}+ {-# INLINE basicLength #-}+ {-# INLINE basicUnsafeSlice #-}+ {-# INLINE basicUnsafeIndexM #-}+ basicUnsafeFreeze (MV_P v) = V_P `liftM` G.basicUnsafeFreeze v+ basicUnsafeThaw ( V_P v) = MV_P `liftM` G.basicUnsafeThaw v+ basicLength ( V_P v) = G.basicLength v+ basicUnsafeSlice m n (V_P v) = V_P (G.basicUnsafeSlice m n v)+ basicUnsafeIndexM (V_P v) i = P `liftM` G.basicUnsafeIndexM v i
src/Linear/Algebra.hs view
@@ -1,6 +1,15 @@+{-# LANGUAGE CPP #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE FlexibleInstances #-}+-----------------------------------------------------------------------------+-- |+-- License : BSD-style (see the file LICENSE)+-- Maintainer : Edward Kmett <ekmett@gmail.com>+-- Stability : provisional+-- Portability : portable+--+----------------------------------------------------------------------------- module Linear.Algebra ( Algebra(..) , Coalgebra(..)
src/Linear/Binary.hs view
@@ -1,6 +1,6 @@ ----------------------------------------------------------------------------- -- |--- Copyright : (C) 2013-2014 Edward Kmett and Anthony Cowley+-- Copyright : (C) 2013-2015 Edward Kmett and Anthony Cowley -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett <ekmett@gmail.com>@@ -15,10 +15,8 @@ , getLinear ) where -import Control.Applicative import Data.Binary-import Data.Foldable (Foldable, traverse_)-import Data.Traversable (Traversable, sequenceA)+import Data.Foldable (traverse_) -- | Serialize a linear type. putLinear :: (Binary a, Foldable t) => t a -> Put
src/Linear/Conjugate.hs view
@@ -1,8 +1,9 @@ {-# LANGUAGE CPP #-} {-# LANGUAGE DefaultSignatures #-}+ ----------------------------------------------------------------------------- -- |--- Copyright : (C) 2012-2013 Edward Kmett,+-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett <ekmett@gmail.com>@@ -20,6 +21,10 @@ import Data.Int import Data.Word import Foreign.C.Types (CFloat, CDouble)++-- $setup+-- >>> import Data.Complex (Complex (..))+ -- | An involutive ring class Num a => Conjugate a where
src/Linear/Covector.hs view
@@ -1,4 +1,13 @@-{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, FlexibleContexts #-}+{-# LANGUAGE CPP, MultiParamTypeClasses, FlexibleInstances, FlexibleContexts #-}+-----------------------------------------------------------------------------+-- |+-- License : BSD-style (see the file LICENSE)+-- Maintainer : Edward Kmett <ekmett@gmail.com>+-- Stability : provisional+-- Portability : portable+--+-- Operations on affine spaces.+----------------------------------------------------------------------------- module Linear.Covector ( Covector(..) , ($*)@@ -35,7 +44,9 @@ Covector m >>- f = Covector $ \k -> m $ \a -> runCovector (f a) k instance Monad (Covector r) where+#if !(MIN_VERSION_base(4,11,0)) return a = Covector $ \k -> k a+#endif Covector m >>= f = Covector $ \k -> m $ \a -> runCovector (f a) k instance Num r => Alt (Covector r) where
src/Linear/Epsilon.hs view
@@ -1,6 +1,6 @@ ----------------------------------------------------------------------------- -- |--- Copyright : (C) 2012 Edward Kmett+-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- Maintainer : Edward Kmett <ekmett@gmail.com> -- Stability : provisional@@ -11,6 +11,7 @@ module Linear.Epsilon ( Epsilon(..) ) where+import Data.Complex (Complex, magnitude) import Foreign.C.Types (CFloat, CDouble) -- | Provides a fairly subjective test to see if a quantity is near zero.@@ -45,3 +46,6 @@ -- | @'abs' a '<=' 1e-12@ instance Epsilon CDouble where nearZero a = abs a <= 1e-12++instance (Epsilon a, RealFloat a) => Epsilon (Complex a) where+ nearZero = nearZero . magnitude
src/Linear/Instances.hs view
@@ -1,88 +1,14 @@-{-# OPTIONS_GHC -fno-warn-orphans #-}-{-# LANGUAGE CPP #-}-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702-{-# LANGUAGE Trustworthy #-}-#endif+{-# LANGUAGE Safe #-} ----------------------------------------------------------------------------- -- |--- Copyright : (C) 2012 Edward Kmett+-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- Maintainer : Edward Kmett <ekmett@gmail.com> -- Stability : provisional -- Portability : portable ----- Orphans+-- Re-exports orphan instances for @Complex@ from the @base-orphans@ package. ----------------------------------------------------------------------------- module Linear.Instances () where -import Control.Applicative-import Control.Monad.Fix-import Control.Monad.Zip-import Data.Complex-import Data.Foldable-import Data.Functor.Bind-import Data.HashMap.Lazy as HashMap-import Data.Hashable-import Data.Semigroup-import Data.Semigroup.Foldable-import Data.Semigroup.Traversable-import Data.Traversable--instance (Hashable k, Eq k) => Apply (HashMap k) where- (<.>) = HashMap.intersectionWith id--instance (Hashable k, Eq k) => Bind (HashMap k) where- -- this is needlessly painful- m >>- f = HashMap.fromList $ do- (k, a) <- HashMap.toList m- case HashMap.lookup k (f a) of- Just b -> [(k,b)]- Nothing -> []--instance Functor Complex where- fmap f (a :+ b) = f a :+ f b- {-# INLINE fmap #-}--instance Apply Complex where- (a :+ b) <.> (c :+ d) = a c :+ b d--instance Applicative Complex where- pure a = a :+ a- (a :+ b) <*> (c :+ d) = a c :+ b d--instance Bind Complex where- (a :+ b) >>- f = a' :+ b' where- a' :+ _ = f a- _ :+ b' = f b- {-# INLINE (>>-) #-}--instance Monad Complex where- return a = a :+ a- {-# INLINE return #-}-- (a :+ b) >>= f = a' :+ b' where- a' :+ _ = f a- _ :+ b' = f b- {-# INLINE (>>=) #-}--instance MonadZip Complex where- mzipWith = liftA2--instance MonadFix Complex where- mfix f = (let a :+ _ = f a in a) :+ (let _ :+ a = f a in a)--instance Foldable Complex where- foldMap f (a :+ b) = f a `mappend` f b- {-# INLINE foldMap #-}--instance Traversable Complex where- traverse f (a :+ b) = (:+) <$> f a <*> f b- {-# INLINE traverse #-}--instance Foldable1 Complex where- foldMap1 f (a :+ b) = f a <> f b- {-# INLINE foldMap1 #-}--instance Traversable1 Complex where- traverse1 f (a :+ b) = (:+) <$> f a <.> f b- {-# INLINE traverse1 #-}+import Data.Orphans ()
src/Linear/Matrix.hs view
@@ -1,11 +1,14 @@+{-# LANGUAGE BangPatterns #-} {-# LANGUAGE CPP #-} {-# LANGUAGE RankNTypes #-}-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702+{-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE Trustworthy #-}-#endif+{-# LANGUAGE TypeFamilies #-}+{-# LANGUAGE TypeOperators #-}+ --------------------------------------------------------------------------- -- |--- Copyright : (C) 2012-2013 Edward Kmett,+-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett <ekmett@gmail.com>@@ -15,27 +18,44 @@ -- Simple matrix operation for low-dimensional primitives. --------------------------------------------------------------------------- module Linear.Matrix- ( (!*!), (!+!), (!-!), (!*) , (*!), (!!*), (*!!)+ ( (!*!), (!+!), (!-!), (!*), (*!), (!!*), (*!!), (!!/) , column , adjoint- , M22, M33, M44, M43, m33_to_m44, m43_to_m44- , det22, det33, inv22, inv33- , eye2, eye3, eye4+ , M22, M23, M24, M32, M33, M34, M42, M43, M44+ , m33_to_m44, m43_to_m44+ , det22, det33, det44, inv22, inv33, inv44+ , identity , Trace(..) , translation+ , transpose , fromQuaternion , mkTransformation , mkTransformationMat+ , _m22, _m23, _m24+ , _m32, _m33, _m34+ , _m42, _m43, _m44+ , lu+ , luFinite+ , forwardSub+ , forwardSubFinite+ , backwardSub+ , backwardSubFinite+ , luSolve+ , luSolveFinite+ , luInv+ , luInvFinite+ , luDet+ , luDetFinite ) where -import Control.Applicative import Control.Lens hiding (index) import Control.Lens.Internal.Context import Data.Distributive import Data.Foldable as Foldable import Data.Functor.Rep-import Linear.Epsilon+import GHC.TypeLits import Linear.Quaternion+import Linear.V import Linear.V2 import Linear.V3 import Linear.V4@@ -43,6 +63,15 @@ import Linear.Conjugate import Linear.Trace +-- $setup+-- >>> import Control.Lens hiding (index)+-- >>> import Data.Complex (Complex (..))+-- >>> import Linear.V2+-- >>> import Linear.V3+-- >>> import Linear.V+-- >>> import qualified Data.IntMap as IntMap+-- >>> import Debug.SimpleReflect.Vars+ -- | This is a generalization of 'Control.Lens.inside' to work over any corepresentable 'Functor'. -- -- @@@ -62,18 +91,13 @@ i = tabulate $ \ e -> ipos $ go (index es e) o eb = tabulate $ \ e -> ipeek (index eb e) (go (index es e)) --- $setup--- >>> import Data.Complex--- >>> import Data.IntMap--- >>> import Debug.SimpleReflect.Vars- infixl 7 !*! -- | Matrix product. This can compute any combination of sparse and dense multiplication. -- -- >>> V2 (V3 1 2 3) (V3 4 5 6) !*! V3 (V2 1 2) (V2 3 4) (V2 4 5) -- V2 (V2 19 25) (V2 43 58) ----- >>> V2 (fromList [(1,2)]) (fromList [(2,3)]) !*! fromList [(1,V3 0 0 1), (2, V3 0 0 5)]+-- >>> V2 (IntMap.fromList [(1,2)]) (IntMap.fromList [(2,3)]) !*! IntMap.fromList [(1,V3 0 0 1), (2, V3 0 0 5)] -- V2 (V3 0 0 2) (V3 0 0 15) (!*!) :: (Functor m, Foldable t, Additive t, Additive n, Num a) => m (t a) -> t (n a) -> m (n a) f !*! g = fmap (\ f' -> Foldable.foldl' (^+^) zero $ liftI2 (*^) f' g) f@@ -132,6 +156,12 @@ (!!*) = flip (*!!) {-# INLINE (!!*) #-} +infixl 7 !!/+-- | Matrix-scalar division+(!!/) :: (Functor m, Functor r, Fractional a) => m (r a) -> a -> m (r a)+m !!/ s = fmap (^/ s) m+{-# INLINE (!!/) #-}+ -- | Hermitian conjugate or conjugate transpose -- -- >>> adjoint (V2 (V2 (1 :+ 2) (3 :+ 4)) (V2 (5 :+ 6) (7 :+ 8)))@@ -146,22 +176,39 @@ -- | A 2x2 matrix with row-major representation type M22 a = V2 (V2 a)+-- | A 2x3 matrix with row-major representation+type M23 a = V2 (V3 a)+-- | A 2x4 matrix with row-major representation+type M24 a = V2 (V4 a)+-- | A 3x2 matrix with row-major representation+type M32 a = V3 (V2 a) -- | A 3x3 matrix with row-major representation type M33 a = V3 (V3 a)--- | A 4x4 matrix with row-major representation-type M44 a = V4 (V4 a)+-- | A 3x4 matrix with row-major representation+type M34 a = V3 (V4 a)+-- | A 4x2 matrix with row-major representation+type M42 a = V4 (V2 a) -- | A 4x3 matrix with row-major representation type M43 a = V4 (V3 a)+-- | A 4x4 matrix with row-major representation+type M44 a = V4 (V4 a) -- | Build a rotation matrix from a unit 'Quaternion'. fromQuaternion :: Num a => Quaternion a -> M33 a fromQuaternion (Quaternion w (V3 x y z)) =- V3 (V3 (1-2*(y2+z2)) (2*(x*y-z*w)) (2*(x*z+y*w)))- (V3 (2*(x*y+z*w)) (1-2*(x2+z2)) (2*(y*z-x*w)))- (V3 (2*(x*z-y*w)) (2*(y*z+x*w)) (1-2*(x2+y2)))- where x2 = x * x- y2 = y * y- z2 = z * z+ V3 (V3 (1-2*(y2+z2)) (2*(xy-zw)) (2*(xz+yw)))+ (V3 (2*(xy+zw)) (1-2*(x2+z2)) (2*(yz-xw)))+ (V3 (2*(xz-yw)) (2*(yz+xw)) (1-2*(x2+y2)))+ where x2 = x*x+ y2 = y*y+ z2 = z*z+ xy = x*y+ xz = x*z+ xw = x*w+ yz = y*z+ yw = y*w+ zw = z*w+{-# INLINE fromQuaternion #-} -- | Build a transformation matrix from a rotation matrix and a -- translation vector.@@ -169,11 +216,13 @@ mkTransformationMat (V3 r1 r2 r3) (V3 tx ty tz) = V4 (snoc3 r1 tx) (snoc3 r2 ty) (snoc3 r3 tz) (V4 0 0 0 1) where snoc3 (V3 x y z) = V4 x y z+{-# INLINE mkTransformationMat #-} -- |Build a transformation matrix from a rotation expressed as a -- 'Quaternion' and a translation vector. mkTransformation :: Num a => Quaternion a -> V3 a -> M44 a mkTransformation = mkTransformationMat . fromQuaternion+{-# INLINE mkTransformation #-} -- | Convert from a 4x3 matrix to a 4x4 matrix, extending it with the @[ 0 0 0 1 ]@ column vector m43_to_m44 :: Num a => M43 a -> M44 a@@ -186,39 +235,19 @@ (V4 d e f 0) (V4 g h i 0) (V4 j k l 1)-{-# ANN m43_to_m44 "HLint: ignore Use camelCase" #-} -- | Convert a 3x3 matrix to a 4x4 matrix extending it with 0's in the new row and column. m33_to_m44 :: Num a => M33 a -> M44 a m33_to_m44 (V3 r1 r2 r3) = V4 (vector r1) (vector r2) (vector r3) (point 0)-{-# ANN m33_to_m44 "HLint: ignore Use camelCase" #-} --- |2x2 identity matrix.------ >>> eye2--- V2 (V2 1 0) (V2 0 1)-eye2 :: Num a => M22 a-eye2 = V2 (V2 1 0)- (V2 0 1)---- |3x3 identity matrix.------ >>> eye3--- V3 (V3 1 0 0) (V3 0 1 0) (V3 0 0 1)-eye3 :: Num a => M33 a-eye3 = V3 (V3 1 0 0)- (V3 0 1 0)- (V3 0 0 1)---- |4x4 identity matrix.+-- |The identity matrix for any dimension vector. ----- >>> eye4+-- >>> identity :: M44 Int -- V4 (V4 1 0 0 0) (V4 0 1 0 0) (V4 0 0 1 0) (V4 0 0 0 1)-eye4 :: Num a => M44 a-eye4 = V4 (V4 1 0 0 0)- (V4 0 1 0 0)- (V4 0 0 1 0)- (V4 0 0 0 1)+-- >>> identity :: V3 (V3 Int)+-- V3 (V3 1 0 0) (V3 0 1 0) (V3 0 0 1)+identity :: (Num a, Traversable t, Applicative t) => t (t a)+identity = scaled (pure 1) -- |Extract the translation vector (first three entries of the last -- column) from a 3x4 or 4x4 matrix.@@ -233,6 +262,51 @@ -- x ^. l = getConst (l Const x) -} +-- |Extract a 2x2 matrix from a matrix of higher dimensions by dropping excess+-- rows and columns.+_m22 :: (Representable t, R2 t, R2 v) => Lens' (t (v a)) (M22 a)+_m22 = column _xy._xy++-- |Extract a 2x3 matrix from a matrix of higher dimensions by dropping excess+-- rows and columns.+_m23 :: (Representable t, R2 t, R3 v) => Lens' (t (v a)) (M23 a)+_m23 = column _xyz._xy++-- |Extract a 2x4 matrix from a matrix of higher dimensions by dropping excess+-- rows and columns.+_m24 :: (Representable t, R2 t, R4 v) => Lens' (t (v a)) (M24 a)+_m24 = column _xyzw._xy++-- |Extract a 3x2 matrix from a matrix of higher dimensions by dropping excess+-- rows and columns.+_m32 :: (Representable t, R3 t, R2 v) => Lens' (t (v a)) (M32 a)+_m32 = column _xy._xyz++-- |Extract a 3x3 matrix from a matrix of higher dimensions by dropping excess+-- rows and columns.+_m33 :: (Representable t, R3 t, R3 v) => Lens' (t (v a)) (M33 a)+_m33 = column _xyz._xyz++-- |Extract a 3x4 matrix from a matrix of higher dimensions by dropping excess+-- rows and columns.+_m34 :: (Representable t, R3 t, R4 v) => Lens' (t (v a)) (M34 a)+_m34 = column _xyzw._xyz++-- |Extract a 4x2 matrix from a matrix of higher dimensions by dropping excess+-- rows and columns.+_m42 :: (Representable t, R4 t, R2 v) => Lens' (t (v a)) (M42 a)+_m42 = column _xy._xyzw++-- |Extract a 4x3 matrix from a matrix of higher dimensions by dropping excess+-- rows and columns.+_m43 :: (Representable t, R4 t, R3 v) => Lens' (t (v a)) (M43 a)+_m43 = column _xyz._xyzw++-- |Extract a 4x4 matrix from a matrix of higher dimensions by dropping excess+-- rows and columns.+_m44 :: (Representable t, R4 t, R4 v) => Lens' (t (v a)) (M44 a)+_m44 = column _xyzw._xyzw+ -- |2x2 matrix determinant. -- -- >>> det22 (V2 (V2 a b) (V2 c d))@@ -251,29 +325,49 @@ (V3 g h i)) = a * (e*i-f*h) - d * (b*i-c*h) + g * (b*f-c*e) {-# INLINE det33 #-} +-- |4x4 matrix determinant.+det44 :: Num a => M44 a -> a+det44 (V4 (V4 i00 i01 i02 i03)+ (V4 i10 i11 i12 i13)+ (V4 i20 i21 i22 i23)+ (V4 i30 i31 i32 i33)) =+ let+ s0 = i00 * i11 - i10 * i01+ s1 = i00 * i12 - i10 * i02+ s2 = i00 * i13 - i10 * i03+ s3 = i01 * i12 - i11 * i02+ s4 = i01 * i13 - i11 * i03+ s5 = i02 * i13 - i12 * i03++ c5 = i22 * i33 - i32 * i23+ c4 = i21 * i33 - i31 * i23+ c3 = i21 * i32 - i31 * i22+ c2 = i20 * i33 - i30 * i23+ c1 = i20 * i32 - i30 * i22+ c0 = i20 * i31 - i30 * i21+ in s0 * c5 - s1 * c4 + s2 * c3 + s3 * c2 - s4 * c1 + s5 * c0+{-# INLINE det44 #-}+ -- |2x2 matrix inverse. -- -- >>> inv22 $ V2 (V2 1 2) (V2 3 4)--- Just (V2 (V2 (-2.0) 1.0) (V2 1.5 (-0.5)))-inv22 :: (Epsilon a, Floating a) => M22 a -> Maybe (M22 a)-inv22 m@(V2 (V2 a b) (V2 c d))- | nearZero det = Nothing- | otherwise = Just $ (1 / det) *!! V2 (V2 d (-b)) (V2 (-c) a)+-- V2 (V2 (-2.0) 1.0) (V2 1.5 (-0.5))+inv22 :: Fractional a => M22 a -> M22 a+inv22 m@(V2 (V2 a b) (V2 c d)) = (1 / det) *!! V2 (V2 d (-b)) (V2 (-c) a) where det = det22 m {-# INLINE inv22 #-} -- |3x3 matrix inverse. -- -- >>> inv33 $ V3 (V3 1 2 4) (V3 4 2 2) (V3 1 1 1)--- Just (V3 (V3 0.0 0.5 (-1.0)) (V3 (-0.5) (-0.75) 3.5) (V3 0.5 0.25 (-1.5)))-inv33 :: (Epsilon a, Floating a) => M33 a -> Maybe (M33 a)+-- V3 (V3 0.0 0.5 (-1.0)) (V3 (-0.5) (-0.75) 3.5) (V3 0.5 0.25 (-1.5))+inv33 :: Fractional a => M33 a -> M33 a inv33 m@(V3 (V3 a b c) (V3 d e f) (V3 g h i))- | nearZero det = Nothing- | otherwise = Just $ (1 / det) *!! V3 (V3 a' b' c')- (V3 d' e' f')- (V3 g' h' i')+ = (1 / det) *!! V3 (V3 a' b' c')+ (V3 d' e' f')+ (V3 g' h' i') where a' = cofactor (e,f,h,i) b' = cofactor (c,b,i,h) c' = cofactor (b,c,e,f)@@ -287,3 +381,351 @@ det = det33 m {-# INLINE inv33 #-} ++-- | 'transpose' is just an alias for 'distribute'+--+-- > transpose (V3 (V2 1 2) (V2 3 4) (V2 5 6))+-- V2 (V3 1 3 5) (V3 2 4 6)+transpose :: (Distributive g, Functor f) => f (g a) -> g (f a)+transpose = distribute+{-# INLINE transpose #-}++-- |4x4 matrix inverse.+inv44 :: Fractional a => M44 a -> M44 a+inv44 (V4 (V4 i00 i01 i02 i03)+ (V4 i10 i11 i12 i13)+ (V4 i20 i21 i22 i23)+ (V4 i30 i31 i32 i33)) =+ let s0 = i00 * i11 - i10 * i01+ s1 = i00 * i12 - i10 * i02+ s2 = i00 * i13 - i10 * i03+ s3 = i01 * i12 - i11 * i02+ s4 = i01 * i13 - i11 * i03+ s5 = i02 * i13 - i12 * i03+ c5 = i22 * i33 - i32 * i23+ c4 = i21 * i33 - i31 * i23+ c3 = i21 * i32 - i31 * i22+ c2 = i20 * i33 - i30 * i23+ c1 = i20 * i32 - i30 * i22+ c0 = i20 * i31 - i30 * i21+ det = s0 * c5 - s1 * c4 + s2 * c3 + s3 * c2 - s4 * c1 + s5 * c0+ invDet = recip det+ in invDet *!! V4 (V4 (i11 * c5 - i12 * c4 + i13 * c3)+ (-i01 * c5 + i02 * c4 - i03 * c3)+ (i31 * s5 - i32 * s4 + i33 * s3)+ (-i21 * s5 + i22 * s4 - i23 * s3))+ (V4 (-i10 * c5 + i12 * c2 - i13 * c1)+ (i00 * c5 - i02 * c2 + i03 * c1)+ (-i30 * s5 + i32 * s2 - i33 * s1)+ (i20 * s5 - i22 * s2 + i23 * s1))+ (V4 (i10 * c4 - i11 * c2 + i13 * c0)+ (-i00 * c4 + i01 * c2 - i03 * c0)+ (i30 * s4 - i31 * s2 + i33 * s0)+ (-i20 * s4 + i21 * s2 - i23 * s0))+ (V4 (-i10 * c3 + i11 * c1 - i12 * c0)+ (i00 * c3 - i01 * c1 + i02 * c0)+ (-i30 * s3 + i31 * s1 - i32 * s0)+ (i20 * s3 - i21 * s1 + i22 * s0))+{-# INLINE inv44 #-}++-- | Compute the (L, U) decomposition of a square matrix using Crout's+-- algorithm. The 'Index' of the vectors must be 'Integral'.+lu :: ( Num a+ , Fractional a+ , Foldable m+ , Traversable m+ , Applicative m+ , Additive m+ , Ixed (m a)+ , Ixed (m (m a))+ , i ~ Index (m a)+ , i ~ Index (m (m a))+ , Eq i+ , Integral i+ , a ~ IxValue (m a)+ , m a ~ IxValue (m (m a))+ , Num (m a)+ )+ => m (m a)+ -> (m (m a), m (m a))+lu a =+ let n = fromIntegral (length a)+ initU = identity+ initL = zero+ buildLVal !i !j !l !u =+ let go !k !s+ | k == j = s+ | otherwise = go (k+1)+ ( s+ + ( (l ^?! ix i ^?! ix k)+ * (u ^?! ix k ^?! ix j)+ )+ )+ s' = go 0 0+ in l & (ix i . ix j) .~ ((a ^?! ix i ^?! ix j) - s')+ buildL !i !j !l !u+ | i == n = l+ | otherwise = buildL (i+1) j (buildLVal i j l u) u+ buildUVal !i !j !l !u =+ let go !k !s+ | k == j = s+ | otherwise = go (k+1)+ ( s+ + ( (l ^?! ix j ^?! ix k)+ * (u ^?! ix k ^?! ix i)+ )+ )+ s' = go 0 0+ in u & (ix j . ix i) .~ ( ((a ^?! ix j ^?! ix i) - s')+ / (l ^?! ix j ^?! ix j)+ )+ buildU !i !j !l !u+ | i == n = u+ | otherwise = buildU (i+1) j l (buildUVal i j l u)+ buildLU !j !l !u+ | j == n = (l, u)+ | otherwise =+ let l' = buildL j j l u+ u' = buildU j j l' u+ in buildLU (j+1) l' u'+ in buildLU 0 initL initU++-- | Compute the (L, U) decomposition of a square matrix using Crout's+-- algorithm, using the vector's 'Finite' instance to provide an index.+luFinite :: ( Num a+ , Fractional a+ , Functor m+ , Finite m+ , n ~ Size m+ , KnownNat n+ , Num (m a)+ )+ => m (m a)+ -> (m (m a), m (m a))+luFinite a =+ bimap (fmap fromV . fromV)+ (fmap fromV . fromV)+ (lu (fmap toV (toV a)))++-- | Solve a linear system with a lower-triangular matrix of coefficients with+-- forwards substitution.+forwardSub :: ( Num a+ , Fractional a+ , Foldable m+ , Additive m+ , Ixed (m a)+ , Ixed (m (m a))+ , i ~ Index (m a)+ , i ~ Index (m (m a))+ , Eq i+ , Ord i+ , Integral i+ , a ~ IxValue (m a)+ , m a ~ IxValue (m (m a))+ )+ => m (m a)+ -> m a+ -> m a+forwardSub a b =+ let n = fromIntegral (length b)+ initX = zero+ coeff !i !j !s !x+ | j == i = s+ | otherwise = coeff i (j+1) (s + ((a ^?! ix i ^?! ix j) * (x ^?! ix j))) x+ go !i !x+ | i == n = x+ | otherwise = go (i + 1) (x & ix i .~ ( ((b ^?! ix i) - coeff i 0 0 x)+ / (a ^?! ix i ^?! ix i)+ ))+ in go 0 initX++-- | Solve a linear system with a lower-triangular matrix of coefficients with+-- forwards substitution, using the vector's 'Finite' instance to provide an+-- index.+forwardSubFinite :: ( Num a+ , Fractional a+ , Foldable m+ , n ~ Size m+ , KnownNat n+ , Additive m+ , Finite m+ )+ => m (m a)+ -> m a+ -> m a+forwardSubFinite a b = fromV (forwardSub (fmap toV (toV a)) (toV b))++-- | Solve a linear system with an upper-triangular matrix of coefficients with+-- backwards substitution.+backwardSub :: ( Num a+ , Fractional a+ , Foldable m+ , Additive m+ , Ixed (m a)+ , Ixed (m (m a))+ , i ~ Index (m a)+ , i ~ Index (m (m a))+ , Eq i+ , Ord i+ , Integral i+ , a ~ IxValue (m a)+ , m a ~ IxValue (m (m a))+ )+ => m (m a)+ -> m a+ -> m a+backwardSub a b =+ let n = fromIntegral (length b)+ initX = zero+ coeff !i !j !s !x+ | j == n = s+ | otherwise = coeff i+ (j+1)+ (s + ((a ^?! ix i ^?! ix j) * (x ^?! ix j)))+ x+ go !i !x+ | i < 0 = x+ | otherwise = go (i-1)+ (x & ix i .~ ( ((b ^?! ix i) - coeff i (i+1) 0 x)+ / (a ^?! ix i ^?! ix i)+ ))+ in go (n-1) initX++-- | Solve a linear system with an upper-triangular matrix of coefficients with+-- backwards substitution, using the vector's 'Finite' instance to provide an+-- index.+backwardSubFinite :: ( Num a+ , Fractional a+ , Foldable m+ , n ~ Size m+ , KnownNat n+ , Additive m+ , Finite m+ )+ => m (m a)+ -> m a+ -> m a+backwardSubFinite a b = fromV (backwardSub (fmap toV (toV a)) (toV b))++-- | Solve a linear system with LU decomposition.+luSolve :: ( Num a+ , Fractional a+ , Foldable m+ , Traversable m+ , Applicative m+ , Additive m+ , Ixed (m a)+ , Ixed (m (m a))+ , i ~ Index (m a)+ , i ~ Index (m (m a))+ , Eq i+ , Integral i+ , a ~ IxValue (m a)+ , m a ~ IxValue (m (m a))+ , Num (m a)+ )+ => m (m a)+ -> m a+ -> m a+luSolve a b =+ let (l, u) = lu a+ in backwardSub u (forwardSub l b)++-- | Solve a linear system with LU decomposition, using the vector's 'Finite'+-- instance to provide an index.+luSolveFinite :: ( Num a+ , Fractional a+ , Functor m+ , Finite m+ , n ~ Size m+ , KnownNat n+ , Num (m a)+ )+ => m (m a)+ -> m a+ -> m a+luSolveFinite a b = fromV (luSolve (fmap toV (toV a)) (toV b))++-- | Invert a matrix with LU decomposition.+luInv :: ( Num a+ , Fractional a+ , Foldable m+ , Traversable m+ , Applicative m+ , Additive m+ , Distributive m+ , Ixed (m a)+ , Ixed (m (m a))+ , i ~ Index (m a)+ , i ~ Index (m (m a))+ , Eq i+ , Integral i+ , a ~ IxValue (m a)+ , m a ~ IxValue (m (m a))+ , Num (m a)+ )+ => m (m a)+ -> m (m a)+luInv a =+ let n = fromIntegral (length a)+ initA' = zero+ (l, u) = lu a+ go !i !a'+ | i == n = a'+ | otherwise = let e = zero & ix i .~ 1+ a'r = backwardSub u (forwardSub l e)+ in go (i+1) (a' & ix i .~ a'r)+ in transpose (go 0 initA')++-- | Invert a matrix with LU decomposition, using the vector's 'Finite' instance+-- to provide an index.+luInvFinite :: ( Num a+ , Fractional a+ , Functor m+ , Finite m+ , n ~ Size m+ , KnownNat n+ , Num (m a)+ )+ => m (m a)+ -> m (m a)+luInvFinite a = fmap fromV (fromV (luInv (fmap toV (toV a))))++-- | Compute the determinant of a matrix using LU decomposition.+luDet :: ( Num a+ , Fractional a+ , Foldable m+ , Traversable m+ , Applicative m+ , Additive m+ , Trace m+ , Ixed (m a)+ , Ixed (m (m a))+ , i ~ Index (m a)+ , i ~ Index (m (m a))+ , Eq i+ , Integral i+ , a ~ IxValue (m a)+ , m a ~ IxValue (m (m a))+ , Num (m a)+ )+ => m (m a)+ -> a+luDet a =+ let (l, u) = lu a+ p = Foldable.foldl (*) 1+ in p (diagonal l) * p (diagonal u)++-- | Compute the determinant of a matrix using LU decomposition, using the+-- vector's 'Finite' instance to provide an index.+luDetFinite :: ( Num a+ , Fractional a+ , Functor m+ , Finite m+ , n ~ Size m+ , KnownNat n+ , Num (m a)+ )+ => m (m a)+ -> a+luDetFinite = luDet . fmap toV . toV
src/Linear/Metric.hs view
@@ -1,11 +1,9 @@ {-# LANGUAGE CPP #-} {-# LANGUAGE DefaultSignatures #-}-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702 {-# LANGUAGE Trustworthy #-}-#endif ----------------------------------------------------------------------------- -- |--- Copyright : (C) 2012-2013 Edward Kmett,+-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett <ekmett@gmail.com>@@ -15,11 +13,14 @@ -- Free metric spaces ---------------------------------------------------------------------------- module Linear.Metric- ( Metric(..), normalize+ ( Metric(..), normalize, project ) where +import Control.Applicative import Data.Foldable as Foldable+import Data.Functor.Compose import Data.Functor.Identity+import Data.Functor.Product import Data.Vector (Vector) import Data.IntMap (IntMap) import Data.Map (Map)@@ -30,6 +31,7 @@ -- $setup -- >>> import Linear+-- -- | Free and sparse inner product/metric spaces. class Additive f => Metric f where@@ -66,9 +68,29 @@ signorm v = fmap (/m) v where m = norm v +instance (Metric f, Metric g) => Metric (Product f g) where+ dot (Pair a b) (Pair c d) = dot a c + dot b d+ quadrance (Pair a b) = quadrance a + quadrance b+ qd (Pair a b) (Pair c d) = qd a c + qd b d+ distance p q = sqrt (qd p q)++instance (Metric f, Metric g) => Metric (Compose f g) where+ dot (Compose a) (Compose b) = quadrance (liftI2 dot a b)+ quadrance = quadrance . fmap quadrance . getCompose+ qd (Compose a) (Compose b) = quadrance (liftI2 qd a b)+ distance (Compose a) (Compose b) = norm (liftI2 qd a b)+ instance Metric Identity where dot (Identity x) (Identity y) = x * y +instance Metric []++instance Metric Maybe++instance Metric ZipList where+ -- ZipList is missing its Foldable instance+ dot (ZipList x) (ZipList y) = dot x y+ instance Metric IntMap instance Ord k => Metric (Map k)@@ -82,3 +104,7 @@ normalize :: (Floating a, Metric f, Epsilon a) => f a -> f a normalize v = if nearZero l || nearZero (1-l) then v else fmap (/sqrt l) v where l = quadrance v++-- | @project u v@ computes the projection of @v@ onto @u@.+project :: (Metric v, Fractional a) => v a -> v a -> v a+project u v = ((v `dot` u) / quadrance u) *^ u
src/Linear/Plucker.hs view
@@ -4,13 +4,14 @@ {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE GADTs #-}-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702 {-# LANGUAGE Trustworthy #-} {-# LANGUAGE DeriveGeneric #-}-#endif+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE DeriveLift #-}+ ----------------------------------------------------------------------------- -- |--- Copyright : (C) 2012-2013 Edward Kmett,+-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett <ekmett@gmail.com>@@ -34,7 +35,8 @@ , quadranceToOrigin , closestToOrigin , isLine- , Coincides(..)+ , coincides+ , coincides' -- * Basis elements , p01, p02, p03 , p10, p12, p13@@ -44,50 +46,89 @@ , e01, e02, e03, e12, e31, e23 ) where +#if !MIN_VERSION_base(4,18,0) import Control.Applicative+#endif+import Control.DeepSeq (NFData(rnf)) import Control.Monad (liftM) import Control.Monad.Fix import Control.Monad.Zip-import Control.Lens hiding (index, (<.>))+import Control.Lens as Lens hiding (index, (<.>))+import Data.Binary as Binary+import Data.Bytes.Serial import Data.Distributive import Data.Foldable as Foldable+import qualified Data.Foldable.WithIndex as WithIndex import Data.Functor.Bind+import Data.Functor.Classes import Data.Functor.Rep+import qualified Data.Functor.WithIndex as WithIndex import Data.Hashable import Data.Semigroup import Data.Semigroup.Foldable+import Data.Serialize as Cereal+import qualified Data.Traversable.WithIndex as WithIndex+import qualified Data.Vector as V+import qualified Data.Vector.Generic.Mutable as M+import qualified Data.Vector.Generic as G+import qualified Data.Vector.Unboxed.Base as U import Foreign.Ptr (castPtr) import Foreign.Storable (Storable(..)) import GHC.Arr (Ix(..))-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702-import GHC.Generics (Generic)-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706-import GHC.Generics (Generic1)+import GHC.Generics (Generic, Generic1)+#if defined(MIN_VERSION_template_haskell)+import Language.Haskell.TH.Syntax (Lift) #endif-import qualified Data.Vector.Generic.Mutable as M-import qualified Data.Vector.Generic as G-import qualified Data.Vector.Unboxed.Base as U- import Linear.Epsilon import Linear.Metric+import Linear.V import Linear.V2 import Linear.V3 import Linear.V4 import Linear.Vector--{-# ANN module "HLint: ignore Reduce duplication" #-}+import System.Random (Random(..), Uniform)+import System.Random.Stateful (UniformRange(..)) -- | Plücker coordinates for lines in a 3-dimensional space. data Plucker a = Plucker !a !a !a !a !a !a deriving (Eq,Ord,Show,Read-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702- ,Generic-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706- ,Generic1+ ,Generic,Generic1+#if defined(MIN_VERSION_template_haskell)+ ,Lift #endif ) +instance Finite Plucker where+ type Size Plucker = 6+ toV (Plucker a b c d e f) = V (V.fromListN 6 [a,b,c,d,e,f])+ fromV (V v) = Plucker (v V.! 0) (v V.! 1) (v V.! 2) (v V.! 3) (v V.! 4) (v V.! 5)++instance Random a => Random (Plucker a) where+ random g = case random g of+ (a, g1) -> case random g1 of+ (b, g2) -> case random g2 of+ (c, g3) -> case random g3 of+ (d, g4) -> case random g4 of+ (e, g5) -> case random g5 of+ (f, g6) -> (Plucker a b c d e f, g6)+ randomR (Plucker a b c d e f, Plucker a' b' c' d' e' f') g = case randomR (a,a') g of+ (a'', g1) -> case randomR (b,b') g1 of+ (b'', g2) -> case randomR (c,c') g2 of+ (c'', g3) -> case randomR (d,d') g3 of+ (d'', g4) -> case randomR (e,e') g4 of+ (e'', g5) -> case randomR (f,f') g5 of+ (f'', g6) -> (Plucker a'' b'' c'' d'' e'' f'', g6)++instance Uniform a => Uniform (Plucker a) where++instance UniformRange a => UniformRange (Plucker a) where+ uniformRM (Plucker a b c d e f, Plucker a' b' c' d' e' f') g = Plucker+ <$> uniformRM (a, a') g+ <*> uniformRM (b, b') g+ <*> uniformRM (c, c') g+ <*> uniformRM (d, d') g+ <*> uniformRM (e, e') g+ <*> uniformRM (f, f') g+ instance Functor Plucker where fmap g (Plucker a b c d e f) = Plucker (g a) (g b) (g c) (g d) (g e) (g f) {-# INLINE fmap #-}@@ -123,8 +164,10 @@ {-# INLINE (>>-) #-} instance Monad Plucker where+#if !(MIN_VERSION_base(4,11,0)) return a = Plucker a a a a a a {-# INLINE return #-}+#endif Plucker a b c d e f >>= g = Plucker a' b' c' d' e' f' where Plucker a' _ _ _ _ _ = g a Plucker _ b' _ _ _ _ = g b@@ -154,6 +197,8 @@ foldMap g (Plucker a b c d e f) = g a `mappend` g b `mappend` g c `mappend` g d `mappend` g e `mappend` g f {-# INLINE foldMap #-}+ null _ = False+ length _ = 6 instance Traversable Plucker where traverse g (Plucker a b c d e f) =@@ -220,6 +265,44 @@ fromRational = pure . fromRational {-# INLINE fromRational #-} +instance Floating a => Floating (Plucker a) where+ pi = pure pi+ {-# INLINE pi #-}+ exp = fmap exp+ {-# INLINE exp #-}+ sqrt = fmap sqrt+ {-# INLINE sqrt #-}+ log = fmap log+ {-# INLINE log #-}+ (**) = liftA2 (**)+ {-# INLINE (**) #-}+ logBase = liftA2 logBase+ {-# INLINE logBase #-}+ sin = fmap sin+ {-# INLINE sin #-}+ tan = fmap tan+ {-# INLINE tan #-}+ cos = fmap cos+ {-# INLINE cos #-}+ asin = fmap asin+ {-# INLINE asin #-}+ atan = fmap atan+ {-# INLINE atan #-}+ acos = fmap acos+ {-# INLINE acos #-}+ sinh = fmap sinh+ {-# INLINE sinh #-}+ tanh = fmap tanh+ {-# INLINE tanh #-}+ cosh = fmap cosh+ {-# INLINE cosh #-}+ asinh = fmap asinh+ {-# INLINE asinh #-}+ atanh = fmap atanh+ {-# INLINE atanh #-}+ acosh = fmap acosh+ {-# INLINE acosh #-}+ instance Hashable a => Hashable (Plucker a) where hashWithSalt s (Plucker a b c d e f) = s `hashWithSalt` a `hashWithSalt` b `hashWithSalt` c `hashWithSalt` d `hashWithSalt` e `hashWithSalt` f {-# INLINE hashWithSalt #-}@@ -279,12 +362,12 @@ -- | These elements form a basis for the Plücker space, or the Grassmanian manifold @Gr(2,V4)@. -- -- @--- 'p01' :: Lens' ('Plucker' a) a--- 'p02' :: Lens' ('Plucker' a) a--- 'p03' :: Lens' ('Plucker' a) a--- 'p23' :: Lens' ('Plucker' a) a--- 'p31' :: Lens' ('Plucker' a) a--- 'p12' :: Lens' ('Plucker' a) a+-- 'p01' :: 'Lens'' ('Plucker' a) a+-- 'p02' :: 'Lens'' ('Plucker' a) a+-- 'p03' :: 'Lens'' ('Plucker' a) a+-- 'p23' :: 'Lens'' ('Plucker' a) a+-- 'p31' :: 'Lens'' ('Plucker' a) a+-- 'p12' :: 'Lens'' ('Plucker' a) a -- @ p01, p02, p03, p23, p31, p12 :: Lens' (Plucker a) a p01 g (Plucker a b c d e f) = (\a' -> Plucker a' b c d e f) <$> g a@@ -303,12 +386,12 @@ -- | These elements form an alternate basis for the Plücker space, or the Grassmanian manifold @Gr(2,V4)@. -- -- @--- 'p10' :: 'Num' a => Lens' ('Plucker' a) a--- 'p20' :: 'Num' a => Lens' ('Plucker' a) a--- 'p30' :: 'Num' a => Lens' ('Plucker' a) a--- 'p32' :: 'Num' a => Lens' ('Plucker' a) a--- 'p13' :: 'Num' a => Lens' ('Plucker' a) a--- 'p21' :: 'Num' a => Lens' ('Plucker' a) a+-- 'p10' :: 'Num' a => 'Lens'' ('Plucker' a) a+-- 'p20' :: 'Num' a => 'Lens'' ('Plucker' a) a+-- 'p30' :: 'Num' a => 'Lens'' ('Plucker' a) a+-- 'p32' :: 'Num' a => 'Lens'' ('Plucker' a) a+-- 'p13' :: 'Num' a => 'Lens'' ('Plucker' a) a+-- 'p21' :: 'Num' a => 'Lens'' ('Plucker' a) a -- @ p10, p20, p30, p32, p13, p21 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a) p10 = anti p01@@ -335,25 +418,31 @@ e31 = E p31 e12 = E p12 -instance FunctorWithIndex (E Plucker) Plucker where+instance WithIndex.FunctorWithIndex (E Plucker) Plucker where imap f (Plucker a b c d e g) = Plucker (f e01 a) (f e02 b) (f e03 c) (f e23 d) (f e31 e) (f e12 g) {-# INLINE imap #-} -instance FoldableWithIndex (E Plucker) Plucker where+instance WithIndex.FoldableWithIndex (E Plucker) Plucker where ifoldMap f (Plucker a b c d e g) = f e01 a `mappend` f e02 b `mappend` f e03 c `mappend` f e23 d `mappend` f e31 e `mappend` f e12 g {-# INLINE ifoldMap #-} -instance TraversableWithIndex (E Plucker) Plucker where+instance WithIndex.TraversableWithIndex (E Plucker) Plucker where itraverse f (Plucker a b c d e g) = Plucker <$> f e01 a <*> f e02 b <*> f e03 c <*> f e23 d <*> f e31 e <*> f e12 g {-# INLINE itraverse #-} +#if !MIN_VERSION_lens(5,0,0)+instance Lens.FunctorWithIndex (E Plucker) Plucker where imap = WithIndex.imap+instance Lens.FoldableWithIndex (E Plucker) Plucker where ifoldMap = WithIndex.ifoldMap+instance Lens.TraversableWithIndex (E Plucker) Plucker where itraverse = WithIndex.itraverse+#endif+ type instance Index (Plucker a) = E Plucker type instance IxValue (Plucker a) = a instance Ixed (Plucker a) where- ix = el+ ix i = el i {-# INLINE ix #-} instance Each (Plucker a) (Plucker b) a b where@@ -364,7 +453,7 @@ -- | Valid Plücker coordinates @p@ will have @'squaredError' p '==' 0@ -- -- That said, floating point makes a mockery of this claim, so you may want to use 'nearZero'.-squaredError :: (Eq a, Num a) => Plucker a -> a+squaredError :: Num a => Plucker a -> a squaredError v = v >< v {-# INLINE squaredError #-} @@ -396,15 +485,11 @@ | Counterclockwise -- ^ The lines pass each other counterclockwise -- (left-handed screw).- deriving (Eq, Show-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702- ,Generic-#endif- )+ deriving (Eq, Show,Generic) -- | Check how two lines pass each other. @passes l1 l2@ describes -- @l2@ when looking down @l1@.-passes :: (Epsilon a, Num a, Ord a) => Plucker a -> Plucker a -> LinePass+passes :: (Epsilon a, Ord a) => Plucker a -> Plucker a -> LinePass passes a b | nearZero s = Coplanar | s > 0 = Counterclockwise@@ -429,40 +514,49 @@ -- | Checks if two lines coincide in space. In other words, undirected equality. coincides :: (Epsilon a, Fractional a) => Plucker a -> Plucker a -> Bool coincides p1 p2 = Foldable.all nearZero $ (s *^ p2) - p1- where s = maybe 1 getFirst . getOption . fold $ saveDiv <$> p1 <*> p2- saveDiv x y | nearZero y = Option Nothing- | otherwise = Option . Just $ First (x / y)+ where s = maybe 1 getFirst . getOptionCompat . fold $ saveDiv <$> p1 <*> p2+ saveDiv x y | nearZero y = optionCompat Nothing+ | otherwise = optionCompat . Just $ First (x / y) {-# INLINABLE coincides #-} -- | Checks if two lines coincide in space, and have the same -- orientation. coincides' :: (Epsilon a, Fractional a, Ord a) => Plucker a -> Plucker a -> Bool coincides' p1 p2 = Foldable.all nearZero ((s *^ p2) - p1) && s > 0- where s = maybe 1 getFirst . getOption . fold $ saveDiv <$> p1 <*> p2- saveDiv x y | nearZero y = Option Nothing- | otherwise = Option . Just $ First (x / y)+ where s = maybe 1 getFirst . getOptionCompat . fold $ saveDiv <$> p1 <*> p2+ saveDiv x y | nearZero y = optionCompat Nothing+ | otherwise = optionCompat . Just $ First (x / y) {-# INLINABLE coincides' #-} --- | When lines are represented as Plücker coordinates, we have the--- ability to check for both directed and undirected--- equality. Undirected equality between 'Line's (or a 'Line' and a--- 'Ray') checks that the two lines coincide in 3D space. Directed--- equality, between two 'Ray's, checks that two lines coincide in 3D,--- and have the same direction. To accomodate these two notions of--- equality, we use an 'Eq' instance on the 'Coincides' data type.+-- The coincides and coincides' functions above require the use of a Maybe type+-- with the following Monoid instance: ----- For example, to check the /directed/ equality between two lines,--- @p1@ and @p2@, we write, @Ray p1 == Ray p2@.-data Coincides a where- Line :: (Epsilon a, Fractional a) => Plucker a -> Coincides a- Ray :: (Epsilon a, Fractional a, Ord a) => Plucker a -> Coincides a+-- instance Semigroup a => Monoid (Maybe a) where ...+--+-- Unfortunately, Maybe has only had such an instance since base-4.11. Prior+-- to that, its Monoid instance had an instance context of Monoid a, which is+-- too strong. To compensate, we use CPP to define an OptionCompat type+-- synonym, which is an alias for Maybe on recent versions of base and an alias+-- for Data.Semigroup.Option on older versions of base. We don't want to use+-- Option on recent versions of base, as it is deprecated.+#if MIN_VERSION_base(4,11,0)+type OptionCompat = Maybe -instance Eq (Coincides a) where- Line a == Line b = coincides a b- Line a == Ray b = coincides a b- Ray a == Line b = coincides a b- Ray a == Ray b = coincides' a b+optionCompat :: Maybe a -> OptionCompat a+optionCompat = id +getOptionCompat :: OptionCompat a -> Maybe a+getOptionCompat = id+#else+type OptionCompat = Option++optionCompat :: Maybe a -> OptionCompat a+optionCompat = Option++getOptionCompat :: OptionCompat a -> Maybe a+getOptionCompat = getOption+#endif+ -- | The minimum squared distance of a line from the origin. quadranceToOrigin :: Fractional a => Plucker a -> a quadranceToOrigin p = (v `dot` v) / (u `dot` u)@@ -512,6 +606,7 @@ M.basicUnsafeWrite a (o+3) w M.basicUnsafeWrite a (o+4) v M.basicUnsafeWrite a (o+5) u+ basicInitialize (MV_Plucker _ v) = M.basicInitialize v instance U.Unbox a => G.Vector U.Vector (Plucker a) where basicUnsafeFreeze (MV_Plucker n v) = liftM ( V_Plucker n) (G.basicUnsafeFreeze v)@@ -538,3 +633,73 @@ (let Plucker _ _ _ a _ _ = f a in a) (let Plucker _ _ _ _ a _ = f a in a) (let Plucker _ _ _ _ _ a = f a in a)++instance NFData a => NFData (Plucker a) where+ rnf (Plucker a b c d e f) = rnf a `seq` rnf b `seq` rnf c+ `seq` rnf d `seq` rnf e `seq` rnf f++instance Serial1 Plucker where+ serializeWith = traverse_+ deserializeWith k = Plucker <$> k <*> k <*> k <*> k <*> k <*> k++instance Serial a => Serial (Plucker a) where+ serialize = serializeWith serialize+ deserialize = deserializeWith deserialize++instance Binary a => Binary (Plucker a) where+ put = serializeWith Binary.put+ get = deserializeWith Binary.get++instance Serialize a => Serialize (Plucker a) where+ put = serializeWith Cereal.put+ get = deserializeWith Cereal.get++instance Eq1 Plucker where+ liftEq k (Plucker a1 b1 c1 d1 e1 f1)+ (Plucker a2 b2 c2 d2 e2 f2)+ = k a1 a2 && k b1 b2 && k c1 c2 && k d1 d2 && k e1 e2 && k f1 f2+instance Ord1 Plucker where+ liftCompare k (Plucker a1 b1 c1 d1 e1 f1)+ (Plucker a2 b2 c2 d2 e2 f2)+ = k a1 a2 `mappend` k b1 b2 `mappend` k c1 c2 `mappend` k d1 d2 `mappend` k e1 e2 `mappend` k f1 f2+instance Read1 Plucker where+ liftReadsPrec k _ z = readParen (z > 10) $ \r ->+ [ (Plucker a b c d e f, r7)+ | ("Plucker",r1) <- lex r+ , (a,r2) <- k 11 r1+ , (b,r3) <- k 11 r2+ , (c,r4) <- k 11 r3+ , (d,r5) <- k 11 r4+ , (e,r6) <- k 11 r5+ , (f,r7) <- k 11 r6+ ]+instance Show1 Plucker where+ liftShowsPrec k _ z (Plucker a b c d e f) = showParen (z > 10) $+ showString "Plucker " . k 11 a . showChar ' ' . k 11 b . showChar ' ' . k 11 c . showChar ' ' . k 11 d . showChar ' ' . k 11 e . showChar ' ' . k 11 f++instance Field1 (Plucker a) (Plucker a) a a where+ _1 f (Plucker x y z u v w) = f x <&> \x' -> Plucker x' y z u v w++instance Field2 (Plucker a) (Plucker a) a a where+ _2 f (Plucker x y z u v w) = f y <&> \y' -> Plucker x y' z u v w++instance Field3 (Plucker a) (Plucker a) a a where+ _3 f (Plucker x y z u v w) = f z <&> \z' -> Plucker x y z' u v w++instance Field4 (Plucker a) (Plucker a) a a where+ _4 f (Plucker x y z u v w) = f u <&> \u' -> Plucker x y z u' v w++instance Field5 (Plucker a) (Plucker a) a a where+ _5 f (Plucker x y z u v w) = f v <&> \v' -> Plucker x y z u v' w++instance Field6 (Plucker a) (Plucker a) a a where+ _6 f (Plucker x y z u v w) = f w <&> \w' -> Plucker x y z u v w'++instance Semigroup a => Semigroup (Plucker a) where+ (<>) = liftA2 (<>)++instance Monoid a => Monoid (Plucker a) where+ mempty = pure mempty+#if !(MIN_VERSION_base(4,11,0))+ mappend = liftA2 mappend+#endif
+ src/Linear/Plucker/Coincides.hs view
@@ -0,0 +1,38 @@+{-# LANGUAGE GADTs #-}+---------------------------------------------------------------------------------+-- |+-- Copyright : (C) 2012-2015 Edward Kmett+-- License : BSD-style (see the file LICENSE)+--+-- Maintainer : Edward Kmett <ekmett@gmail.com>+-- Stability : experimental+-- Portability : non-portable+--+-- Utility for working with Plücker coordinates for lines in 3d homogeneous space.+----------------------------------------------------------------------------------+module Linear.Plucker.Coincides+ ( Coincides(..)+ ) where++import Linear.Epsilon+import Linear.Plucker++-- | When lines are represented as Plücker coordinates, we have the+-- ability to check for both directed and undirected+-- equality. Undirected equality between 'Line's (or a 'Line' and a+-- 'Ray') checks that the two lines coincide in 3D space. Directed+-- equality, between two 'Ray's, checks that two lines coincide in 3D,+-- and have the same direction. To accomodate these two notions of+-- equality, we use an 'Eq' instance on the 'Coincides' data type.+--+-- For example, to check the /directed/ equality between two lines,+-- @p1@ and @p2@, we write, @Ray p1 == Ray p2@.+data Coincides a where+ Line :: (Epsilon a, Fractional a) => Plucker a -> Coincides a+ Ray :: (Epsilon a, Fractional a, Ord a) => Plucker a -> Coincides a++instance Eq (Coincides a) where+ Line a == Line b = coincides a b+ Line a == Ray b = coincides a b+ Ray a == Line b = coincides a b+ Ray a == Ray b = coincides' a b
+ src/Linear/Projection.hs view
@@ -0,0 +1,260 @@+{-# LANGUAGE CPP #-}+---------------------------------------------------------------------------+-- |+-- Copyright : (C) 2015 Edward Kmett+-- License : BSD-style (see the file LICENSE)+--+-- Maintainer : Edward Kmett <ekmett@gmail.com>+-- Stability : experimental+-- Portability : non-portable+--+-- Common projection matrices: e.g. perspective/orthographic transformation+-- matrices.+--+-- Analytically derived inverses are also supplied, because they can be+-- much more accurate in practice than computing them through general+-- purpose means+---------------------------------------------------------------------------+module Linear.Projection+ ( lookAt+ , perspective, inversePerspective+ , infinitePerspective, inverseInfinitePerspective+ , frustum, inverseFrustum+ , ortho, inverseOrtho+ ) where++import Control.Lens hiding (index)+import Linear.V3+import Linear.V4+import Linear.Matrix+import Linear.Epsilon+import Linear.Metric++-- $setup+-- >>> import Linear.Matrix+-- >>> import Linear.V2+-- >>> import Linear.V4++-- | Build a look at view matrix+lookAt+ :: (Epsilon a, Floating a)+ => V3 a -- ^ Eye+ -> V3 a -- ^ Center+ -> V3 a -- ^ Up+ -> M44 a+lookAt eye center up =+ V4 (V4 (xa^._x) (xa^._y) (xa^._z) xd)+ (V4 (ya^._x) (ya^._y) (ya^._z) yd)+ (V4 (-za^._x) (-za^._y) (-za^._z) zd)+ (V4 0 0 0 1)+ where za = normalize $ center - eye+ xa = normalize $ cross za up+ ya = cross xa za+ xd = -dot xa eye+ yd = -dot ya eye+ zd = dot za eye++-- | Build a matrix for a symmetric perspective-view frustum+perspective+ :: Floating a+ => a -- ^ FOV (y direction, in radians)+ -> a -- ^ Aspect ratio+ -> a -- ^ Near plane+ -> a -- ^ Far plane+ -> M44 a+perspective fovy aspect near far =+ V4 (V4 x 0 0 0)+ (V4 0 y 0 0)+ (V4 0 0 z w)+ (V4 0 0 (-1) 0)+ where tanHalfFovy = tan $ fovy / 2+ x = 1 / (aspect * tanHalfFovy)+ y = 1 / tanHalfFovy+ fpn = far + near+ fmn = far - near+ oon = 0.5/near+ oof = 0.5/far+ -- z = 1 / (near/fpn - far/fpn) -- would be better by .5 bits+ z = -fpn/fmn+ w = 1/(oof-oon) -- 13 bits error reduced to 0.17+ -- w = -(2 * far * near) / fmn++#ifdef HERBIE+{-# ANN perspective "NoHerbie" #-}+#endif++-- | Build an inverse perspective matrix+inversePerspective+ :: Floating a+ => a -- ^ FOV (y direction, in radians)+ -> a -- ^ Aspect ratio+ -> a -- ^ Near plane+ -> a -- ^ Far plane+ -> M44 a+inversePerspective fovy aspect near far =+ V4 (V4 a 0 0 0 )+ (V4 0 b 0 0 )+ (V4 0 0 0 (-1))+ (V4 0 0 c d )+ where tanHalfFovy = tan $ fovy / 2+ a = aspect * tanHalfFovy+ b = tanHalfFovy+ c = oon - oof+ d = oon + oof+ oon = 0.5/near+ oof = 0.5/far+++-- | Build a perspective matrix per the classic @glFrustum@ arguments.+frustum+ :: Floating a+ => a -- ^ Left+ -> a -- ^ Right+ -> a -- ^ Bottom+ -> a -- ^ Top+ -> a -- ^ Near+ -> a -- ^ Far+ -> M44 a+frustum l r b t n f =+ V4 (V4 x 0 a 0)+ (V4 0 y e 0)+ (V4 0 0 c d)+ (V4 0 0 (-1) 0)+ where+ rml = r-l+ tmb = t-b+ fmn = f-n+ x = 2*n/rml+ y = 2*n/tmb+ a = (r+l)/rml+ e = (t+b)/tmb+ c = negate (f+n)/fmn+ d = (-2*f*n)/fmn++inverseFrustum+ :: Floating a+ => a -- ^ Left+ -> a -- ^ Right+ -> a -- ^ Bottom+ -> a -- ^ Top+ -> a -- ^ Near+ -> a -- ^ Far+ -> M44 a+inverseFrustum l r b t n f =+ V4 (V4 rx 0 0 ax)+ (V4 0 ry 0 by)+ (V4 0 0 0 (-1))+ (V4 0 0 rd cd)+ where+ hrn = 0.5/n+ hrnf = 0.5/(n*f)+ rx = (r-l)*hrn+ ry = (t-b)*hrn+ ax = (r+l)*hrn+ by = (t+b)*hrn+ cd = (f+n)*hrnf+ rd = (n-f)*hrnf++-- | Build a matrix for a symmetric perspective-view frustum with a far plane at infinite+infinitePerspective+ :: Floating a+ => a -- ^ FOV (y direction, in radians)+ -> a -- ^ Aspect Ratio+ -> a -- ^ Near plane+ -> M44 a+infinitePerspective fovy a n =+ V4 (V4 x 0 0 0)+ (V4 0 y 0 0)+ (V4 0 0 (-1) w)+ (V4 0 0 (-1) 0)+ where+ t = n*tan(fovy/2)+ b = -t+ l = b*a+ r = t*a+ x = (2*n)/(r-l)+ y = (2*n)/(t-b)+ w = -2*n++inverseInfinitePerspective+ :: Floating a+ => a -- ^ FOV (y direction, in radians)+ -> a -- ^ Aspect Ratio+ -> a -- ^ Near plane+ -> M44 a+inverseInfinitePerspective fovy a n =+ V4 (V4 rx 0 0 0)+ (V4 0 ry 0 0)+ (V4 0 0 0 (-1))+ (V4 0 0 rw (-rw))+ where+ t = n*tan(fovy/2)+ b = -t+ l = b*a+ r = t*a+ hrn = 0.5/n+ rx = (r-l)*hrn+ ry = (t-b)*hrn+ rw = -hrn++-- | Build an orthographic perspective matrix from 6 clipping planes.+-- This matrix takes the region delimited by these planes and maps it+-- to normalized device coordinates between [-1,1]+--+-- This call is designed to mimic the parameters to the OpenGL @glOrtho@+-- call, so it has a slightly strange convention: Notably: the near and+-- far planes are negated.+--+-- Consequently:+--+-- @+-- 'ortho' l r b t n f !* 'V4' l b (-n) 1 = 'V4' (-1) (-1) (-1) 1+-- 'ortho' l r b t n f !* 'V4' r t (-f) 1 = 'V4' 1 1 1 1+-- @+--+-- Examples:+--+-- >>> ortho 1 2 3 4 5 6 !* V4 1 3 (-5) 1+-- V4 (-1.0) (-1.0) (-1.0) 1.0+--+-- >>> ortho 1 2 3 4 5 6 !* V4 2 4 (-6) 1+-- V4 1.0 1.0 1.0 1.0+ortho+ :: Fractional a+ => a -- ^ Left+ -> a -- ^ Right+ -> a -- ^ Bottom+ -> a -- ^ Top+ -> a -- ^ Near+ -> a -- ^ Far+ -> M44 a+ortho l r b t n f =+ V4 (V4 (-2*x) 0 0 ((r+l)*x))+ (V4 0 (-2*y) 0 ((t+b)*y))+ (V4 0 0 (2*z) ((f+n)*z))+ (V4 0 0 0 1)+ where x = recip(l-r)+ y = recip(b-t)+ z = recip(n-f)++-- | Build an inverse orthographic perspective matrix from 6 clipping planes+inverseOrtho+ :: Fractional a+ => a -- ^ Left+ -> a -- ^ Right+ -> a -- ^ Bottom+ -> a -- ^ Top+ -> a -- ^ Near+ -> a -- ^ Far+ -> M44 a+inverseOrtho l r b t n f =+ V4 (V4 x 0 0 c)+ (V4 0 y 0 d)+ (V4 0 0 z e)+ (V4 0 0 0 1)+ where x = 0.5*(r-l)+ y = 0.5*(t-b)+ z = 0.5*(n-f)+ c = 0.5*(l+r)+ d = 0.5*(b+t)+ e = -0.5*(n+f)
src/Linear/Quaternion.hs view
@@ -5,13 +5,14 @@ {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE CPP #-} {-# LANGUAGE TypeFamilies #-}-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702 {-# LANGUAGE Trustworthy #-} {-# LANGUAGE DeriveGeneric #-}-#endif+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE DeriveLift #-}+ ----------------------------------------------------------------------------- -- |--- Copyright : (C) 2012-2013 Edward Kmett,+-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett <ekmett@gmail.com>@@ -39,51 +40,82 @@ ) where import Control.Applicative+import Control.DeepSeq (NFData(rnf)) import Control.Monad (liftM) import Control.Monad.Fix import Control.Monad.Zip-import Control.Lens hiding ((<.>))+import Control.Lens as Lens hiding ((<.>))+import Data.Binary as Binary+import Data.Bytes.Serial import Data.Complex (Complex((:+))) import Data.Data import Data.Distributive import Data.Foldable+import qualified Data.Foldable.WithIndex as WithIndex import Data.Functor.Bind+import Data.Functor.Classes import Data.Functor.Rep+import qualified Data.Functor.WithIndex as WithIndex import Data.Hashable+import Data.Hashable.Lifted+#if !(MIN_VERSION_base(4,11,0))+import Data.Semigroup (Semigroup(..))+#endif+import Data.Serialize as Cereal import GHC.Arr (Ix(..)) import qualified Data.Foldable as F-import Data.Monoid-import Foreign.Ptr (castPtr, plusPtr)-import Foreign.Storable (Storable(..))-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702-import GHC.Generics (Generic)-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706-import GHC.Generics (Generic1)-#endif+import qualified Data.Traversable.WithIndex as WithIndex+import qualified Data.Vector as V import qualified Data.Vector.Generic.Mutable as M import qualified Data.Vector.Generic as G import qualified Data.Vector.Unboxed.Base as U+import Foreign.Ptr (castPtr, plusPtr)+import Foreign.Storable (Storable(..))+import GHC.Generics (Generic, Generic1)+#if defined(MIN_VERSION_template_haskell)+import Language.Haskell.TH.Syntax (Lift)+#endif import Linear.Epsilon import Linear.Conjugate import Linear.Metric+import Linear.V+import Linear.V2 import Linear.V3+import Linear.V4 import Linear.Vector import Prelude hiding (any)--{-# ANN module "HLint: ignore Reduce duplication" #-}+import System.Random (Random(..), Uniform)+import System.Random.Stateful (UniformRange(..)) -- | Quaternions data Quaternion a = Quaternion !a {-# UNPACK #-}!(V3 a)- deriving (Eq,Ord,Read,Show,Data,Typeable-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702- ,Generic-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706- ,Generic1+ deriving (Eq,Ord,Read,Show,Data+ ,Generic,Generic1+#if defined(MIN_VERSION_template_haskell)+ ,Lift #endif ) +instance Finite Quaternion where+ type Size Quaternion = 4+ toV (Quaternion a (V3 b c d)) = V (V.fromListN 4 [a, b, c, d])+ fromV (V v) = Quaternion (v V.! 0) (V3 (v V.! 1) (v V.! 2) (v V.! 3))++instance Random a => Random (Quaternion a) where+ random g = case random g of+ (a, g') -> case random g' of+ (b, g'') -> (Quaternion a b, g'')+ randomR (Quaternion a b, Quaternion c d) g = case randomR (a,c) g of+ (e, g') -> case randomR (b,d) g' of+ (f, g'') -> (Quaternion e f, g'')++instance Uniform a => Uniform (Quaternion a) where++instance UniformRange a => UniformRange (Quaternion a) where+ uniformRM (Quaternion a b, Quaternion c d) g = Quaternion+ <$> uniformRM (a, c) g+ <*> uniformRM (b, d) g+ instance Functor Quaternion where fmap f (Quaternion e v) = Quaternion (f e) (fmap f v) {-# INLINE fmap #-}@@ -149,23 +181,29 @@ index xs (E l) = view l xs {-# INLINE index #-} -instance FunctorWithIndex (E Quaternion) Quaternion where+instance WithIndex.FunctorWithIndex (E Quaternion) Quaternion where imap f (Quaternion a (V3 b c d)) = Quaternion (f ee a) $ V3 (f ei b) (f ej c) (f ek d) {-# INLINE imap #-} -instance FoldableWithIndex (E Quaternion) Quaternion where+instance WithIndex.FoldableWithIndex (E Quaternion) Quaternion where ifoldMap f (Quaternion a (V3 b c d)) = f ee a `mappend` f ei b `mappend` f ej c `mappend` f ek d {-# INLINE ifoldMap #-} -instance TraversableWithIndex (E Quaternion) Quaternion where+instance WithIndex.TraversableWithIndex (E Quaternion) Quaternion where itraverse f (Quaternion a (V3 b c d)) = Quaternion <$> f ee a <*> (V3 <$> f ei b <*> f ej c <*> f ek d) {-# INLINE itraverse #-} +#if !MIN_VERSION_lens(5,0,0)+instance Lens.FunctorWithIndex (E Quaternion) Quaternion where imap = WithIndex.imap+instance Lens.FoldableWithIndex (E Quaternion) Quaternion where ifoldMap = WithIndex.ifoldMap+instance Lens.TraversableWithIndex (E Quaternion) Quaternion where itraverse = WithIndex.itraverse+#endif+ type instance Index (Quaternion a) = E Quaternion type instance IxValue (Quaternion a) = a instance Ixed (Quaternion a) where- ix = el+ ix i = el i {-# INLINE ix #-} instance Each (Quaternion a) (Quaternion b) a b where@@ -177,6 +215,8 @@ {-# INLINE foldMap #-} foldr f z (Quaternion e v) = f e (F.foldr f z v) {-# INLINE foldr #-}+ null _ = False+ length _ = 4 instance Traversable Quaternion where traverse f (Quaternion e v) = Quaternion <$> f e <*> traverse f v@@ -233,6 +273,10 @@ hashWithSalt s (Quaternion a b) = s `hashWithSalt` a `hashWithSalt` b {-# INLINE hashWithSalt #-} +instance Hashable1 Quaternion where+ liftHashWithSalt h s (Quaternion a b) = liftHashWithSalt h (h s a) b+ {-# INLINE liftHashWithSalt #-}+ qNaN :: RealFloat a => Quaternion a qNaN = Quaternion fNaN (V3 fNaN fNaN fNaN) where fNaN = 0/0 {-# INLINE qNaN #-}@@ -252,7 +296,7 @@ (r0*q3-r1*q2+r2*q1-r3*q0)) ^/ (r0*r0 + r1*r1 + r2*r2 + r3*r3) {-# INLINE (/) #-}- recip q = q ^/ quadrance q+ recip q@(Quaternion e v) = Quaternion e (negate v) ^/ quadrance q {-# INLINE recip #-} fromRational x = Quaternion (fromRational x) 0 {-# INLINE fromRational #-}@@ -332,6 +376,29 @@ pow q t = exp (t *^ log q) {-# INLINE pow #-} +sqrte2pqiq :: (Floating a, Ord a) => a -> a -> a+sqrte2pqiq e qiq -- = sqrt (e*e + qiq)+ | e < - 1.5097698010472593e153 = -(qiq/e) - e+ | e < 5.582399551122541e57 = sqrt (e*e + qiq) -- direct definition+ | otherwise = (qiq/e) + e+-- {-# SPECIALIZE sqrte2pqiq :: Double -> Double -> Double #-}+-- {-# SPECIALIZE sqrte2pqiq :: Float -> Float -> Float #-}+#ifdef HERBIE+{-# ANN sqrte2pqiq "NoHerbie" #-}+#endif++tanrhs :: (Floating a, Ord a) => a -> a -> a -> a+tanrhs sai ai d -- = cosh ai * (sai / ai) / d -- improved from 6.04 bits of error to 0.19 bits+ | sai < -4.618902267687042e-52 = (sai / d / ai) * cosh ai+ | sai < 1.038530535935153e-39 = (cosh ai * sai) / ai / d+ | otherwise = (sai / d / ai) * cosh ai+-- {-# SPECIALIZE tanrhs :: Double -> Double -> Double -> Double #-}+-- {-# SPECIALIZE tanrhs :: Float -> Float -> Float -> Float #-}+#ifdef HERBIE+{-# ANN tanrhs "NoHerbie" #-}+#endif++ -- ehh.. instance RealFloat a => Floating (Quaternion a) where {-# SPECIALIZE instance Floating (Quaternion Float) #-}@@ -343,15 +410,18 @@ | ai <- sqrt qiq, exe <- exp e = reimagine (exe * cos ai) (exe * (sin ai / ai)) q where qiq = qi q {-# INLINE exp #-}- log q@(Quaternion e v@(V3 _i j k))+ log q@(Quaternion e v) | qiq == 0 = if e >= 0- then Quaternion (log e) v- else Quaternion (log (negate e)) (V3 pi j k) -- mmm, pi- | ai <- sqrt qiq, m <- sqrt (e*e + qiq) = reimagine (log m) (atan2 m e / ai) q+ then Quaternion (log e) v -- Using v rather than 0 preserves negative zeros+ else Quaternion (negate (log (negate e))) v -- negative scalar: negate quaternion, take log, negate again, preserves negative zeros+ | ai <- sqrt qiq = reimagine (log m) (acos (e / m) / ai) q where qiq = qi q+ m = sqrte2pqiq e qiq {-# INLINE log #-}+ x ** y = exp (y * log x) {-# INLINE (**) #-}+ sqrt q@(Quaternion e v) | m == 0 = q | qiq == 0 = if e > 0@@ -359,38 +429,44 @@ else Quaternion 0 (V3 (sqrt (negate e)) 0 0) | im <- sqrt (0.5*(m-e)) / sqrt qiq = Quaternion (0.5*(m+e)) (v^*im) where qiq = qi q- m = sqrt (e*e + qiq)+ m = sqrte2pqiq e qiq {-# INLINE sqrt #-}+ cos q@(Quaternion e v) | qiq == 0 = Quaternion (cos e) v- | ai <- sqrt qiq = reimagine (cos e * cosh ai) (- sin e * (sinh ai / ai)) q+ | ai <- sqrt qiq = reimagine (cos e * cosh ai) (- sin e / ai / sinh ai) q -- 0.15 bits error where qiq = qi q {-# INLINE cos #-}+ sin q@(Quaternion e v) | qiq == 0 = Quaternion (sin e) v- | ai <- sqrt qiq = reimagine (sin e * cosh ai) (cos e * (sinh ai / ai)) q+ | ai <- sqrt qiq = reimagine (sin e * cosh ai) (cos e * sinh ai / ai) q where qiq = qi q {-# INLINE sin #-}+ tan q@(Quaternion e v) | qiq == 0 = Quaternion (tan e) v | ai <- sqrt qiq, ce <- cos e, sai <- sinh ai, d <- ce*ce + sai*sai =- reimagine (ce * sin e / d) (cosh ai * (sai / ai) / d) q+ reimagine (ce * sin e / d) (tanrhs sai ai d) q where qiq = qi q {-# INLINE tan #-}+ sinh q@(Quaternion e v) | qiq == 0 = Quaternion (sinh e) v- | ai <- sqrt qiq = reimagine (sinh e * cos ai) (cosh e * (sin ai / ai)) q+ | ai <- sqrt qiq = reimagine (sinh e * cos ai) (cosh e * sin ai / ai) q where qiq = qi q {-# INLINE sinh #-}+ cosh q@(Quaternion e v) | qiq == 0 = Quaternion (cosh e) v- | ai <- sqrt qiq = reimagine (cosh e * cos ai) ((sinh e * sin ai) / ai) q+ | ai <- sqrt qiq = reimagine (cosh e * cos ai) (sin ai * (sinh e / ai)) q where qiq = qi q {-# INLINE cosh #-}+ tanh q@(Quaternion e v) | qiq == 0 = Quaternion (tanh e) v | ai <- sqrt qiq, se <- sinh e, cai <- cos ai, d <- se*se + cai*cai =- reimagine ((cosh e * se) / d) ((cai * (sin ai / ai)) / d) q+ reimagine (cosh e * se / d) (tanhrhs cai ai d) q where qiq = qi q {-# INLINE tanh #-} @@ -408,6 +484,15 @@ atanh = cut atanh {-# INLINE atanh #-} +tanhrhs :: (Floating a, Ord a) => a -> a -> a -> a+tanhrhs cai ai d -- = cai * (sin ai / ai) / d+ | d >= -4.2173720203427147e-29 && d < 4.446702369113811e64 = cai / (d * (ai / sin ai))+ | otherwise = cai * (1 / ai / sin ai) / d+-- {-# SPECIALIZE tanhrhs :: Double -> Double -> Double -> Double #-}+-- {-# SPECIALIZE tanhrhs :: Float -> Float -> Float -> Float #-}+#ifdef HERBIE+{-# ANN tanhrhs "NoHerbie" #-}+#endif -- | Helper for calculating with specific branch cuts cut :: RealFloat a => (Complex a -> Complex a) -> Quaternion a -> Quaternion a@@ -528,6 +613,7 @@ M.basicUnsafeWrite v (o+1) y M.basicUnsafeWrite v (o+2) z M.basicUnsafeWrite v (o+3) w+ basicInitialize (MV_Quaternion _ v) = M.basicInitialize v instance U.Unbox a => G.Vector U.Vector (Quaternion a) where basicUnsafeFreeze (MV_Quaternion n v) = liftM ( V_Quaternion n) (G.basicUnsafeFreeze v)@@ -550,3 +636,68 @@ (V3 (let Quaternion _ (V3 a _ _) = f a in a) (let Quaternion _ (V3 _ a _) = f a in a) (let Quaternion _ (V3 _ _ a) = f a in a))++instance NFData a => NFData (Quaternion a) where+ rnf (Quaternion a b) = rnf a `seq` rnf b++instance Serial1 Quaternion where+ serializeWith f (Quaternion a b) = f a >> serializeWith f b+ deserializeWith f = Quaternion <$> f <*> deserializeWith f++instance Serial a => Serial (Quaternion a) where+ serialize = serializeWith serialize+ deserialize = deserializeWith deserialize++instance Binary a => Binary (Quaternion a) where+ put = serializeWith Binary.put+ get = deserializeWith Binary.get++instance Serialize a => Serialize (Quaternion a) where+ put = serializeWith Cereal.put+ get = deserializeWith Cereal.get++instance Eq1 Quaternion where+ liftEq f (Quaternion a b) (Quaternion c d) = f a c && liftEq f b d+instance Ord1 Quaternion where+ liftCompare f (Quaternion a b) (Quaternion c d) = f a c `mappend` liftCompare f b d+instance Show1 Quaternion where+ liftShowsPrec f g d (Quaternion a b) = showsBinaryWith f (liftShowsPrec f g) "Quaternion" d a b+instance Read1 Quaternion where+ liftReadsPrec f g = readsData $ readsBinaryWith f (liftReadsPrec f g) "Quaternion" Quaternion++instance Field1 (Quaternion a) (Quaternion a) a a where+ _1 f (Quaternion w xyz) = f w <&> \w' -> Quaternion w' xyz++instance Field2 (Quaternion a) (Quaternion a) a a where+ _2 f (Quaternion w (V3 x y z)) = f x <&> \x' -> Quaternion w (V3 x' y z)++instance Field3 (Quaternion a) (Quaternion a) a a where+ _3 f (Quaternion w (V3 x y z)) = f y <&> \y' -> Quaternion w (V3 x y' z)++instance Field4 (Quaternion a) (Quaternion a) a a where+ _4 f (Quaternion w (V3 x y z)) = f z <&> \z' -> Quaternion w (V3 x y z')++instance Semigroup a => Semigroup (Quaternion a) where+ (<>) = liftA2 (<>)++instance Monoid a => Monoid (Quaternion a) where+ mempty = pure mempty+#if !(MIN_VERSION_base(4,11,0))+ mappend = liftA2 mappend+#endif++instance R1 Quaternion where+ _x f (Quaternion w (V3 x y z)) = f x <&> \x' -> Quaternion w (V3 x' y z)++instance R2 Quaternion where+ _y f (Quaternion w (V3 x y z)) = f y <&> \y' -> Quaternion w (V3 x y' z)+ _xy f (Quaternion w (V3 x y z)) = f (V2 x y) <&> \(V2 x' y') -> Quaternion w (V3 x' y' z)++instance R3 Quaternion where+ _z f (Quaternion w (V3 x y z)) = f z <&> \z' -> Quaternion w (V3 x y z')+ _xyz f (Quaternion w xyz) = Quaternion w <$> f xyz++instance R4 Quaternion where+ _w f (Quaternion w xyz) = f w <&> \w' -> Quaternion w' xyz+ _xyzw f (Quaternion w (V3 x y z)) = f (V4 x y z w) <&> \(V4 x' y' z' w') -> Quaternion w' (V3 x' y' z')+
src/Linear/Trace.hs view
@@ -1,12 +1,11 @@ {-# LANGUAGE CPP #-} {-# LANGUAGE TypeOperators #-} {-# LANGUAGE DefaultSignatures #-}-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702+{-# LANGUAGE PolyKinds #-} {-# LANGUAGE Trustworthy #-}-#endif --------------------------------------------------------------------------- -- |--- Copyright : (C) 2012-2013 Edward Kmett,+-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett <ekmett@gmail.com>@@ -17,20 +16,20 @@ --------------------------------------------------------------------------- module Linear.Trace ( Trace(..)+ , frobenius ) where import Control.Monad as Monad--- import Linear.V1 import Linear.V0+import Linear.V1 import Linear.V2 import Linear.V3 import Linear.V4 import Linear.Plucker import Linear.Quaternion import Linear.V-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ > 704+import Linear.Vector import Data.Complex-#endif import Data.Distributive import Data.Foldable as Foldable import Data.Functor.Bind as Bind@@ -38,13 +37,13 @@ import Data.Functor.Product import Data.Hashable import Data.HashMap.Lazy-import Data.IntMap-import Data.Map+import Data.IntMap (IntMap)+import Data.Map (Map) -- $setup -- >>> import Data.Complex--- >>> import Data.IntMap -- >>> import Debug.SimpleReflect.Vars+-- >>> import Linear.V2 class Functor m => Trace m where -- | Compute the trace of a matrix@@ -83,19 +82,18 @@ instance Dim n => Trace (V n) instance Trace V0+instance Trace V1 instance Trace V2 instance Trace V3 instance Trace V4 instance Trace Plucker instance Trace Quaternion -#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ > 704 instance Trace Complex where trace ((a :+ _) :+ (_ :+ b)) = a + b {-# INLINE trace #-} diagonal ((a :+ _) :+ (_ :+ b)) = a :+ b {-# INLINE diagonal #-}-#endif instance (Trace f, Trace g) => Trace (Product f g) where trace (Pair xx yy) = trace (pfst <$> xx) + trace (psnd <$> yy) where@@ -112,3 +110,7 @@ {-# INLINE trace #-} diagonal = Compose . fmap diagonal . diagonal . fmap distribute . getCompose . fmap getCompose {-# INLINE diagonal #-}++-- | Compute the <http://mathworld.wolfram.com/FrobeniusNorm.html Frobenius norm> of a matrix.+frobenius :: (Num a, Foldable f, Additive f, Additive g, Distributive g, Trace g) => f (g a) -> a+frobenius m = trace $ fmap (\ f' -> Foldable.foldl' (^+^) zero $ liftI2 (*^) f' m) (distribute m)
src/Linear/V.hs view
@@ -1,29 +1,23 @@ {-# LANGUAGE CPP #-}+{-# LANGUAGE TypeOperators #-} {-# LANGUAGE KindSignatures #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE GeneralizedNewtypeDeriving #-}+{-# LANGUAGE DefaultSignatures #-} {-# LANGUAGE Rank2Types #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE EmptyDataDecls #-} {-# LANGUAGE MultiParamTypeClasses, FlexibleContexts, FlexibleInstances, UndecidableInstances #-}-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 707+{-# LANGUAGE DeriveDataTypeable #-} {-# LANGUAGE DataKinds #-} {-# LANGUAGE PolyKinds #-} {-# LANGUAGE RoleAnnotations #-}-#define USE_TYPE_LITS 1-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702 {-# LANGUAGE Trustworthy #-} {-# LANGUAGE DeriveGeneric #-}-#endif -#ifndef MIN_VERSION_reflection-#define MIN_VERSION_reflection(x,y,z) 1-#endif- ----------------------------------------------------------------------------- -- |--- Copyright : (C) 2012-2013 Edward Kmett,+-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett <ekmett@gmail.com>@@ -34,71 +28,122 @@ ---------------------------------------------------------------------------- module Linear.V- ( V(toVector)+ ( V(V,toVector)+#ifdef MIN_VERSION_template_haskell , int+#endif , dim , Dim(..) , reifyDim , reifyVector+ , reifyDimNat+ , reifyVectorNat , fromVector+ , Finite(..)+ , _V, _V' ) where import Control.Applicative+import Control.DeepSeq (NFData)+import Control.Monad import Control.Monad.Fix+import Control.Monad.Trans.State import Control.Monad.Zip import Control.Lens as Lens+import Data.Binary as Binary+import Data.Bytes.Serial+import Data.Complex+import Data.Data import Data.Distributive import Data.Foldable as Foldable+import qualified Data.Foldable.WithIndex as WithIndex import Data.Functor.Bind+import Data.Functor.Classes import Data.Functor.Rep as Rep-import Data.Proxy+import qualified Data.Functor.WithIndex as WithIndex+import Data.Hashable+import Data.Hashable.Lifted+import Data.Kind import Data.Reflection as R-import Data.Vector as V+import Data.Serialize as Cereal+import qualified Data.Traversable.WithIndex as WithIndex+import qualified Data.Vector as V+import Data.Vector (Vector)+import Data.Vector.Fusion.Util (Box(..))+import qualified Data.Vector.Generic as G+import qualified Data.Vector.Unboxed as U+import qualified Data.Vector.Generic.Mutable as M import Foreign.Ptr import Foreign.Storable-#ifdef USE_TYPE_LITS import GHC.TypeLits-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702-import GHC.Generics (Generic)-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 707-import GHC.Generics (Generic1)-#endif-#if !(MIN_VERSION_reflection(1,3,0))+import GHC.Generics (Generic, Generic1)+#if !(MIN_VERSION_reflection(1,3,0)) && defined(MIN_VERSION_template_haskell) import Language.Haskell.TH #endif import Linear.Epsilon import Linear.Metric import Linear.Vector+import Prelude as P+#if !(MIN_VERSION_base(4,11,0))+import Data.Semigroup+#endif+import System.Random (Random(..))+import System.Random.Stateful (Uniform(..), UniformRange(..)) class Dim n where reflectDim :: p n -> Int -#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 707 type role V nominal representational-#endif -newtype V n a = V { toVector :: V.Vector a } deriving (Eq,Ord,Show,Read-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702- ,Generic-#endif--- GHC bug: https://ghc.haskell.org/trac/ghc/ticket/8468-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 707- ,Generic1-#endif+class Finite v where+ type Size (v :: Type -> Type) :: Nat -- this should allow kind k, for Reifies k Int+ toV :: v a -> V (Size v) a+ default toV :: Foldable v => v a -> V (Size v) a+ toV = V . V.fromList . Foldable.toList+ fromV :: V (Size v) a -> v a++instance Finite Complex where+ type Size Complex = 2+ toV (a :+ b) = V (V.fromListN 2 [a, b])+ fromV (V v) = (v V.! 0) :+ (v V.! 1)++_V :: (Finite u, Finite v) => Iso (V (Size u) a) (V (Size v) b) (u a) (v b)+_V = iso fromV toV++_V' :: Finite v => Iso (V (Size v) a) (V (Size v) b) (v a) (v b)+_V' = iso fromV toV++instance Finite (V (n :: Nat)) where+ type Size (V n) = n+ toV = id+ fromV = id++newtype V n a = V { toVector :: V.Vector a } deriving (Eq,Ord,Show,Read,NFData+ ,Generic,Generic1 )+ dim :: forall n a. Dim n => V n a -> Int dim _ = reflectDim (Proxy :: Proxy n) {-# INLINE dim #-} -#ifdef USE_TYPE_LITS instance KnownNat n => Dim (n :: Nat) where reflectDim = fromInteger . natVal {-# INLINE reflectDim #-}++instance (Dim n, Random a) => Random (V n a) where+ random = runState (V <$> V.replicateM (reflectDim (Proxy :: Proxy n)) (state random))+ randomR (V ls,V hs) = runState (V <$> V.zipWithM (\l h -> state $ randomR (l,h)) ls hs)++instance (Dim n, Uniform a) => Uniform (V n a) where+ uniformM g = V <$> V.replicateM (reflectDim (Proxy :: Proxy n)) (uniformM g)++instance (Dim n, UniformRange a) => UniformRange (V n a) where+ uniformRM (V ls, V hs) g = V <$> V.zipWithM (\l h -> uniformRM (l, h) g) ls hs+#if (MIN_VERSION_random(1,3,0))+ isInRange (V ls, V hs) (V xs) = V.and $ V.zipWith3 (\l h x -> isInRange (l, h) x) ls hs xs #endif -data ReifiedDim (s :: *)+data ReifiedDim (s :: Type) retagDim :: (Proxy s -> a) -> proxy (ReifiedDim s) -> a retagDim f _ = f Proxy@@ -108,13 +153,21 @@ reflectDim = retagDim reflect {-# INLINE reflectDim #-} -reifyDim :: Int -> (forall (n :: *). Dim n => Proxy n -> r) -> r+reifyDimNat :: Int -> (forall (n :: Nat). KnownNat n => Proxy n -> r) -> r+reifyDimNat i f = R.reifyNat (fromIntegral i) f+{-# INLINE reifyDimNat #-}++reifyVectorNat :: forall a r. Vector a -> (forall (n :: Nat). KnownNat n => V n a -> r) -> r+reifyVectorNat v f = reifyNat (fromIntegral $ V.length v) $ \(Proxy :: Proxy n) -> f (V v :: V n a)+{-# INLINE reifyVectorNat #-}++reifyDim :: Int -> (forall (n :: Type). Dim n => Proxy n -> r) -> r reifyDim i f = R.reify i (go f) where- go :: Reifies n Int => (Proxy (ReifiedDim n) -> a) -> proxy n -> a+ go :: (Proxy (ReifiedDim n) -> a) -> proxy n -> a go g _ = g Proxy {-# INLINE reifyDim #-} -reifyVector :: forall a r. Vector a -> (forall (n :: *). Dim n => V n a -> r) -> r+reifyVector :: forall a r. Vector a -> (forall (n :: Type). Dim n => V n a -> r) -> r reifyVector v f = reifyDim (V.length v) $ \(Proxy :: Proxy n) -> f (V v :: V n a) {-# INLINE reifyVector #-} @@ -122,18 +175,75 @@ reflectDim _ = reflectDim (Proxy :: Proxy n) {-# INLINE reflectDim #-} +instance (Dim n, Semigroup a) => Semigroup (V n a) where+ (<>) = liftA2 (<>)++instance (Dim n, Monoid a) => Monoid (V n a) where+ mempty = pure mempty+#if !(MIN_VERSION_base(4,11,0))+ mappend = liftA2 mappend+#endif+ instance Functor (V n) where fmap f (V as) = V (fmap f as) {-# INLINE fmap #-} +instance WithIndex.FunctorWithIndex Int (V n) where+ imap f (V as) = V (Lens.imap f as)+ {-# INLINE imap #-}+ instance Foldable (V n) where- foldMap f (V as) = foldMap f as+ fold (V as) = fold as+ {-# INLINE fold #-}+ foldMap f (V as) = Foldable.foldMap f as {-# INLINE foldMap #-}+ foldr f z (V as) = V.foldr f z as+ {-# INLINE foldr #-}+ foldl f z (V as) = V.foldl f z as+ {-# INLINE foldl #-}+ foldr' f z (V as) = V.foldr' f z as+ {-# INLINE foldr' #-}+ foldl' f z (V as) = V.foldl' f z as+ {-# INLINE foldl' #-}+ foldr1 f (V as) = V.foldr1 f as+ {-# INLINE foldr1 #-}+ foldl1 f (V as) = V.foldl1 f as+ {-# INLINE foldl1 #-}+ length (V as) = V.length as+ {-# INLINE length #-}+ null (V as) = V.null as+ {-# INLINE null #-}+ toList (V as) = V.toList as+ {-# INLINE toList #-}+ elem a (V as) = V.elem a as+ {-# INLINE elem #-}+ maximum (V as) = V.maximum as+ {-# INLINE maximum #-}+ minimum (V as) = V.minimum as+ {-# INLINE minimum #-}+ sum (V as) = V.sum as+ {-# INLINE sum #-}+ product (V as) = V.product as+ {-# INLINE product #-} +instance WithIndex.FoldableWithIndex Int (V n) where+ ifoldMap f (V as) = ifoldMap f as+ {-# INLINE ifoldMap #-}+ instance Traversable (V n) where traverse f (V as) = V <$> traverse f as {-# INLINE traverse #-} +instance WithIndex.TraversableWithIndex Int (V n) where+ itraverse f (V as) = V <$> itraverse f as+ {-# INLINE itraverse #-}++#if !MIN_VERSION_lens(5,0,0)+instance Lens.FunctorWithIndex Int (V n) where imap = WithIndex.imap+instance Lens.FoldableWithIndex Int (V n) where ifoldMap = WithIndex.ifoldMap+instance Lens.TraversableWithIndex Int (V n) where itraverse = WithIndex.itraverse+#endif+ instance Apply (V n) where V as <.> V bs = V (V.zipWith id as bs) {-# INLINE (<.>) #-}@@ -146,15 +256,17 @@ {-# INLINE (<*>) #-} instance Bind (V n) where- V as >>- f = V $ generate (V.length as) $ \i ->- toVector (f (as `unsafeIndex` i)) `unsafeIndex` i+ V as >>- f = V $ V.generate (V.length as) $ \i ->+ toVector (f (as `V.unsafeIndex` i)) `V.unsafeIndex` i {-# INLINE (>>-) #-} instance Dim n => Monad (V n) where+#if !(MIN_VERSION_base(4,11,0)) return = V . V.replicate (reflectDim (Proxy :: Proxy n)) {-# INLINE return #-}- V as >>= f = V $ generate (reflectDim (Proxy :: Proxy n)) $ \i ->- toVector (f (as `unsafeIndex` i)) `unsafeIndex` i+#endif+ V as >>= f = V $ V.generate (reflectDim (Proxy :: Proxy n)) $ \i ->+ toVector (f (as `V.unsafeIndex` i)) `V.unsafeIndex` i {-# INLINE (>>=) #-} instance Dim n => Additive (V n) where@@ -189,20 +301,69 @@ fromRational = pure . fromRational {-# INLINE fromRational #-} +instance (Dim n, Floating a) => Floating (V n a) where+ pi = pure pi+ {-# INLINE pi #-}+ exp = fmap exp+ {-# INLINE exp #-}+ sqrt = fmap sqrt+ {-# INLINE sqrt #-}+ log = fmap log+ {-# INLINE log #-}+ V as ** V bs = V $ V.zipWith (**) as bs+ {-# INLINE (**) #-}+ logBase (V as) (V bs) = V $ V.zipWith logBase as bs+ {-# INLINE logBase #-}+ sin = fmap sin+ {-# INLINE sin #-}+ tan = fmap tan+ {-# INLINE tan #-}+ cos = fmap cos+ {-# INLINE cos #-}+ asin = fmap asin+ {-# INLINE asin #-}+ atan = fmap atan+ {-# INLINE atan #-}+ acos = fmap acos+ {-# INLINE acos #-}+ sinh = fmap sinh+ {-# INLINE sinh #-}+ tanh = fmap tanh+ {-# INLINE tanh #-}+ cosh = fmap cosh+ {-# INLINE cosh #-}+ asinh = fmap asinh+ {-# INLINE asinh #-}+ atanh = fmap atanh+ {-# INLINE atanh #-}+ acosh = fmap acosh+ {-# INLINE acosh #-}+ instance Dim n => Distributive (V n) where- distribute f = V $ V.generate (reflectDim (Proxy :: Proxy n)) $ \i -> fmap (\(V v) -> unsafeIndex v i) f+ distribute f = V $ V.generate (reflectDim (Proxy :: Proxy n)) $ \i -> fmap (\(V v) -> V.unsafeIndex v i) f {-# INLINE distribute #-} +instance Hashable a => Hashable (V n a) where+ hashWithSalt s0 (V v) =+ V.foldl' (\s a -> s `hashWithSalt` a) s0 v+ `hashWithSalt` V.length v++instance Dim n => Hashable1 (V n) where+ liftHashWithSalt h s0 (V v) =+ V.foldl' (\s a -> h s a) s0 v+ `hashWithSalt` V.length v+ {-# INLINE liftHashWithSalt #-}+ instance (Dim n, Storable a) => Storable (V n a) where sizeOf _ = reflectDim (Proxy :: Proxy n) * sizeOf (undefined:: a) {-# INLINE sizeOf #-} alignment _ = alignment (undefined :: a) {-# INLINE alignment #-} poke ptr (V xs) = Foldable.forM_ [0..reflectDim (Proxy :: Proxy n)-1] $ \i ->- pokeElemOff ptr' i (unsafeIndex xs i)+ pokeElemOff ptr' i (V.unsafeIndex xs i) where ptr' = castPtr ptr {-# INLINE poke #-}- peek ptr = V <$> generateM (reflectDim (Proxy :: Proxy n)) (peekElemOff ptr')+ peek ptr = V <$> V.generateM (reflectDim (Proxy :: Proxy n)) (peekElemOff ptr') where ptr' = castPtr ptr {-# INLINE peek #-} @@ -221,7 +382,7 @@ | V.length v == reflectDim (Proxy :: Proxy n) = Just (V v) | otherwise = Nothing -#if !(MIN_VERSION_reflection(1,3,0))+#if !(MIN_VERSION_reflection(1,3,0)) && defined(MIN_VERSION_template_haskell) data Z -- 0 data D (n :: *) -- 2n data SD (n :: *) -- 2n+1@@ -269,18 +430,19 @@ #endif instance Dim n => Representable (V n) where- type Rep (V n) = E (V n)- tabulate f = V $ generate (reflectDim (Proxy :: Proxy n)) $ \i -> f $ E $ \g (V v) ->- (\a -> V $ v V.// [(i,a)]) <$> g (unsafeIndex v i)+ type Rep (V n) = Int+ tabulate = V . V.generate (reflectDim (Proxy :: Proxy n)) {-# INLINE tabulate #-}- index xs (E l) = view l xs+ index (V xs) i = xs V.! i {-# INLINE index #-} -type instance Index (V n a) = E (V n)+type instance Index (V n a) = Int type instance IxValue (V n a) = a instance Ixed (V n a) where- ix = el+ ix i f v@(V as)+ | i < 0 || i >= V.length as = pure v+ | otherwise = vLens i f v {-# INLINE ix #-} instance Dim n => MonadZip (V n) where@@ -293,3 +455,140 @@ instance Each (V n a) (V n b) a b where each = traverse {-# INLINE each #-}++instance (Bounded a, Dim n) => Bounded (V n a) where+ minBound = pure minBound+ {-# INLINE minBound #-}+ maxBound = pure maxBound+ {-# INLINE maxBound #-}++vConstr :: Constr+vConstr = mkConstr vDataType "variadic" [] Prefix+{-# NOINLINE vConstr #-}++vDataType :: DataType+vDataType = mkDataType "Linear.V.V" [vConstr]+{-# NOINLINE vDataType #-}++instance (Typeable (V n), Typeable (V n a), Dim n, Data a) => Data (V n a) where+ gfoldl f z (V as) = z (V . V.fromList) `f` V.toList as+ toConstr _ = vConstr+ gunfold k z c = case constrIndex c of+ 1 -> k (z (V . V.fromList))+ _ -> error "gunfold"+ dataTypeOf _ = vDataType+ dataCast1 f = gcast1 f++instance Dim n => Serial1 (V n) where+ serializeWith = traverse_+ deserializeWith f = sequenceA $ pure f++instance (Dim n, Serial a) => Serial (V n a) where+ serialize = traverse_ serialize+ deserialize = sequenceA $ pure deserialize++instance (Dim n, Binary a) => Binary (V n a) where+ put = serializeWith Binary.put+ get = deserializeWith Binary.get++instance (Dim n, Serialize a) => Serialize (V n a) where+ put = serializeWith Cereal.put+ get = deserializeWith Cereal.get++instance Eq1 (V n) where+ liftEq f0 (V as0) (V bs0) = go f0 (V.toList as0) (V.toList bs0) where+ go _ [] [] = True+ go f (a:as) (b:bs) = f a b && go f as bs+ go _ _ _ = False++instance Ord1 (V n) where+ liftCompare f0 (V as0) (V bs0) = go f0 (V.toList as0) (V.toList bs0) where+ go f (a:as) (b:bs) = f a b `mappend` go f as bs+ go _ [] [] = EQ+ go _ _ [] = GT+ go _ [] _ = LT++instance Show1 (V n) where+ liftShowsPrec _ g d (V as) = showParen (d > 10) $ showString "V " . g (V.toList as)++instance Dim n => Read1 (V n) where+ liftReadsPrec _ g d = readParen (d > 10) $ \r ->+ [ (V (V.fromList as), r2)+ | ("V",r1) <- lex r+ , (as, r2) <- g r1+ , P.length as == reflectDim (Proxy :: Proxy n)+ ]++data instance U.Vector (V n a) = V_VN {-# UNPACK #-} !Int !(U.Vector a)+data instance U.MVector s (V n a) = MV_VN {-# UNPACK #-} !Int !(U.MVector s a)+instance (Dim n, U.Unbox a) => U.Unbox (V n a)++instance (Dim n, U.Unbox a) => M.MVector U.MVector (V n a) where+ {-# INLINE basicLength #-}+ {-# INLINE basicUnsafeSlice #-}+ {-# INLINE basicOverlaps #-}+ {-# INLINE basicUnsafeNew #-}+ {-# INLINE basicUnsafeRead #-}+ {-# INLINE basicUnsafeWrite #-}+ basicLength (MV_VN n _) = n+ basicUnsafeSlice m n (MV_VN _ v) = MV_VN n (M.basicUnsafeSlice (d*m) (d*n) v)+ where d = reflectDim (Proxy :: Proxy n)+ basicOverlaps (MV_VN _ v) (MV_VN _ u) = M.basicOverlaps v u+ basicUnsafeNew n = liftM (MV_VN n) (M.basicUnsafeNew (d*n))+ where d = reflectDim (Proxy :: Proxy n)+ basicUnsafeRead (MV_VN _ v) i =+ liftM V $ V.generateM d (\j -> M.basicUnsafeRead v (d*i+j))+ where d = reflectDim (Proxy :: Proxy n)+ basicUnsafeWrite (MV_VN _ v0) i (V vn0) = let d0 = V.length vn0 in go v0 vn0 d0 (d0*i) 0+ where+ go v vn d o j+ | j >= d = return ()+ | otherwise = do+ a <- liftBox $ G.basicUnsafeIndexM vn j+ M.basicUnsafeWrite v o a+ go v vn d (o+1) (j+1)+ basicInitialize (MV_VN _ v) = M.basicInitialize v+ {-# INLINE basicInitialize #-}++liftBox :: Monad m => Box a -> m a+liftBox (Box a) = return a+{-# INLINE liftBox #-}++instance (Dim n, U.Unbox a) => G.Vector U.Vector (V n a) where+ {-# INLINE basicUnsafeFreeze #-}+ {-# INLINE basicUnsafeThaw #-}+ {-# INLINE basicLength #-}+ {-# INLINE basicUnsafeSlice #-}+ {-# INLINE basicUnsafeIndexM #-}+ basicUnsafeFreeze (MV_VN n v) = liftM ( V_VN n) (G.basicUnsafeFreeze v)+ basicUnsafeThaw ( V_VN n v) = liftM (MV_VN n) (G.basicUnsafeThaw v)+ basicLength ( V_VN n _) = n+ basicUnsafeSlice m n (V_VN _ v) = V_VN n (G.basicUnsafeSlice (d*m) (d*n) v)+ where d = reflectDim (Proxy :: Proxy n)+ basicUnsafeIndexM (V_VN _ v) i =+ liftM V $ V.generateM d (\j -> G.basicUnsafeIndexM v (d*i+j))+ where d = reflectDim (Proxy :: Proxy n)++vLens :: Int -> Lens' (V n a) a+vLens i = \f (V v) -> f (v V.! i) <&> \a -> V (v V.// [(i, a)])+{-# INLINE vLens #-}++instance ( 1 <= n) => Field1 (V n a) (V n a) a a where _1 = vLens 0+instance ( 2 <= n) => Field2 (V n a) (V n a) a a where _2 = vLens 1+instance ( 3 <= n) => Field3 (V n a) (V n a) a a where _3 = vLens 2+instance ( 4 <= n) => Field4 (V n a) (V n a) a a where _4 = vLens 3+instance ( 5 <= n) => Field5 (V n a) (V n a) a a where _5 = vLens 4+instance ( 6 <= n) => Field6 (V n a) (V n a) a a where _6 = vLens 5+instance ( 7 <= n) => Field7 (V n a) (V n a) a a where _7 = vLens 6+instance ( 8 <= n) => Field8 (V n a) (V n a) a a where _8 = vLens 7+instance ( 9 <= n) => Field9 (V n a) (V n a) a a where _9 = vLens 8+instance (10 <= n) => Field10 (V n a) (V n a) a a where _10 = vLens 9+instance (11 <= n) => Field11 (V n a) (V n a) a a where _11 = vLens 10+instance (12 <= n) => Field12 (V n a) (V n a) a a where _12 = vLens 11+instance (13 <= n) => Field13 (V n a) (V n a) a a where _13 = vLens 12+instance (14 <= n) => Field14 (V n a) (V n a) a a where _14 = vLens 13+instance (15 <= n) => Field15 (V n a) (V n a) a a where _15 = vLens 14+instance (16 <= n) => Field16 (V n a) (V n a) a a where _16 = vLens 15+instance (17 <= n) => Field17 (V n a) (V n a) a a where _17 = vLens 16+instance (18 <= n) => Field18 (V n a) (V n a) a a where _18 = vLens 17+instance (19 <= n) => Field19 (V n a) (V n a) a a where _19 = vLens 18
src/Linear/V0.hs view
@@ -4,17 +4,14 @@ {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE MultiParamTypeClasses #-}-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702 {-# LANGUAGE DeriveGeneric #-} {-# LANGUAGE Trustworthy #-}-#endif+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE DeriveLift #-} -#ifndef MIN_VERSION_hashable-#define MIN_VERSION_hashable-#endif ----------------------------------------------------------------------------- -- |--- Copyright : (C) 2012-2013 Edward Kmett+-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett <ekmett@gmail.com>@@ -28,23 +25,33 @@ ) where import Control.Applicative-import Control.Lens+import Control.DeepSeq (NFData(rnf))+import Control.Lens as Lens import Control.Monad.Fix import Control.Monad.Zip+import Data.Binary -- binary+import Data.Bytes.Serial -- bytes import Data.Data import Data.Distributive import Data.Foldable-import Data.Functor.Rep+import qualified Data.Foldable.WithIndex as WithIndex import Data.Functor.Bind+import Data.Functor.Classes+import Data.Functor.Rep+import qualified Data.Functor.WithIndex as WithIndex import Data.Hashable+import Data.Hashable.Lifted import Data.Ix+#if !(MIN_VERSION_base(4,11,0)) import Data.Semigroup-import Foreign.Storable (Storable(..))-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702-import GHC.Generics (Generic) #endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706-import GHC.Generics (Generic1)+import Data.Serialize -- cereal+import qualified Data.Traversable.WithIndex as WithIndex+import qualified Data.Vector as V+import Foreign.Storable (Storable(..))+import GHC.Generics (Generic, Generic1)+#if defined(MIN_VERSION_template_haskell)+import Language.Haskell.TH.Syntax (Lift) #endif import qualified Data.Vector.Generic.Mutable as M import qualified Data.Vector.Generic as G@@ -52,10 +59,16 @@ import Linear.Metric import Linear.Epsilon import Linear.Vector+import Linear.V+import System.Random (Random(..), Uniform)+import System.Random.Stateful (UniformRange(..)) import Prelude hiding (sum) -- $setup+-- >>> import Control.Applicative -- >>> import Control.Lens+-- >>> import qualified Data.Foldable as F+-- >>> let sum xs = F.sum xs -- | A 0-dimensional vector --@@ -65,15 +78,45 @@ -- >>> V0 + V0 -- V0 ---data V0 a = V0 deriving (Eq,Ord,Show,Read,Ix,Enum,Data,Typeable-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702- ,Generic-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706- ,Generic1+data V0 a = V0 deriving (Eq,Ord,Show,Read,Ix,Enum,Data+ ,Generic,Generic1+#if defined(MIN_VERSION_template_haskell)+ ,Lift #endif ) +instance Finite V0 where+ type Size V0 = 0+ toV _ = V V.empty+ fromV _ = V0++instance Random (V0 a) where+ random g = (V0, g)+ randomR _ g = (V0, g)+ randomRs _ _ = repeat V0+ randoms _ = repeat V0++instance Uniform (V0 a) where++instance UniformRange (V0 a) where+ uniformRM (_, _) _ = pure V0++instance Serial1 V0 where+ serializeWith _ = serialize+ deserializeWith _ = deserialize++instance Serial (V0 a) where+ serialize V0 = return ()+ deserialize = return V0++instance Binary (V0 a) where+ put V0 = return ()+ get = return V0++instance Serialize (V0 a) where+ put V0 = return ()+ get = return V0+ instance Functor V0 where fmap _ V0 = V0 {-# INLINE fmap #-}@@ -83,6 +126,8 @@ instance Foldable V0 where foldMap _ V0 = mempty {-# INLINE foldMap #-}+ null _ = True+ length _ = 0 instance Traversable V0 where traverse _ V0 = pure V0@@ -90,7 +135,7 @@ instance Apply V0 where V0 <.> V0 = V0- {-@ INLINE (<.>) #-}+ {-# INLINE (<.>) #-} instance Applicative V0 where pure _ = V0@@ -98,6 +143,15 @@ V0 <*> V0 = V0 {-# INLINE (<*>) #-} +instance Semigroup (V0 a) where+ _ <> _ = V0++instance Monoid (V0 a) where+ mempty = V0+#if !(MIN_VERSION_base(4,11,0))+ mappend _ _ = V0+#endif+ instance Additive V0 where zero = V0 {-# INLINE zero #-}@@ -111,8 +165,10 @@ {-# INLINE (>>-) #-} instance Monad V0 where+#if !(MIN_VERSION_base(4,11,0)) return _ = V0 {-# INLINE return #-}+#endif V0 >>= _ = V0 {-# INLINE (>>=) #-} @@ -140,6 +196,44 @@ fromRational _ = V0 {-# INLINE fromRational #-} +instance Floating (V0 a) where+ pi = V0+ {-# INLINE pi #-}+ exp V0 = V0+ {-# INLINE exp #-}+ sqrt V0 = V0+ {-# INLINE sqrt #-}+ log V0 = V0+ {-# INLINE log #-}+ V0 ** V0 = V0+ {-# INLINE (**) #-}+ logBase V0 V0 = V0+ {-# INLINE logBase #-}+ sin V0 = V0+ {-# INLINE sin #-}+ tan V0 = V0+ {-# INLINE tan #-}+ cos V0 = V0+ {-# INLINE cos #-}+ asin V0 = V0+ {-# INLINE asin #-}+ atan V0 = V0+ {-# INLINE atan #-}+ acos V0 = V0+ {-# INLINE acos #-}+ sinh V0 = V0+ {-# INLINE sinh #-}+ tanh V0 = V0+ {-# INLINE tanh #-}+ cosh V0 = V0+ {-# INLINE cosh #-}+ asinh V0 = V0+ {-# INLINE asinh #-}+ atanh V0 = V0+ {-# INLINE atanh #-}+ acosh V0 = V0+ {-# INLINE acosh #-}+ instance Metric V0 where dot V0 V0 = 0 {-# INLINE dot #-}@@ -149,18 +243,20 @@ {-# INLINE distribute #-} instance Hashable (V0 a) where-#if (MIN_VERSION_hashable(1,2,1)) || !(MIN_VERSION_hashable(1,2,0)) hash V0 = 0 {-# INLINE hash #-}-#endif hashWithSalt s V0 = s {-# INLINE hashWithSalt #-} -instance Epsilon a => Epsilon (V0 a) where+instance Hashable1 V0 where+ liftHashWithSalt _ s V0 = s+ {-# INLINE liftHashWithSalt #-}++instance Epsilon (V0 a) where nearZero _ = True {-# INLINE nearZero #-} -instance Storable a => Storable (V0 a) where+instance Storable (V0 a) where sizeOf _ = 0 {-# INLINE sizeOf #-} alignment _ = 1@@ -170,18 +266,24 @@ peek _ = return V0 {-# INLINE peek #-} -instance FunctorWithIndex (E V0) V0 where+instance WithIndex.FunctorWithIndex (E V0) V0 where imap _ V0 = V0 {-# INLINE imap #-} -instance FoldableWithIndex (E V0) V0 where+instance WithIndex.FoldableWithIndex (E V0) V0 where ifoldMap _ V0 = mempty {-# INLINE ifoldMap #-} -instance TraversableWithIndex (E V0) V0 where+instance WithIndex.TraversableWithIndex (E V0) V0 where itraverse _ V0 = pure V0 {-# INLINE itraverse #-} +#if !MIN_VERSION_lens(5,0,0)+instance Lens.FunctorWithIndex (E V0) V0 where imap = WithIndex.imap+instance Lens.FoldableWithIndex (E V0) V0 where ifoldMap = WithIndex.ifoldMap+instance Lens.TraversableWithIndex (E V0) V0 where itraverse = WithIndex.itraverse+#endif+ instance Representable V0 where type Rep V0 = E V0 tabulate _ = V0@@ -193,7 +295,7 @@ type instance IxValue (V0 a) = a instance Ixed (V0 a) where- ix = el+ ix i = el i {-# INLINE ix #-} instance Each (V0 a) (V0 b) a b where@@ -205,14 +307,27 @@ instance U.Unbox (V0 a) instance M.MVector U.MVector (V0 a) where+ {-# INLINE basicLength #-}+ {-# INLINE basicUnsafeSlice #-}+ {-# INLINE basicOverlaps #-}+ {-# INLINE basicUnsafeNew #-}+ {-# INLINE basicUnsafeRead #-}+ {-# INLINE basicUnsafeWrite #-} basicLength (MV_V0 n) = n basicUnsafeSlice _ n _ = MV_V0 n basicOverlaps _ _ = False basicUnsafeNew n = return (MV_V0 n) basicUnsafeRead _ _ = return V0 basicUnsafeWrite _ _ _ = return ()+ basicInitialize _ = return ()+ {-# INLINE basicInitialize #-} instance G.Vector U.Vector (V0 a) where+ {-# INLINE basicUnsafeFreeze #-}+ {-# INLINE basicUnsafeThaw #-}+ {-# INLINE basicLength #-}+ {-# INLINE basicUnsafeSlice #-}+ {-# INLINE basicUnsafeIndexM #-} basicUnsafeFreeze (MV_V0 n) = return (V_V0 n) basicUnsafeThaw (V_V0 n) = return (MV_V0 n) basicLength (V_V0 n) = n@@ -226,3 +341,21 @@ instance MonadFix V0 where mfix _ = V0++instance Bounded (V0 a) where+ minBound = V0+ {-# INLINE minBound #-}+ maxBound = V0+ {-# INLINE maxBound #-}++instance NFData (V0 a) where+ rnf V0 = ()++instance Eq1 V0 where+ liftEq _ _ _ = True+instance Ord1 V0 where+ liftCompare _ _ _ = EQ+instance Show1 V0 where+ liftShowsPrec _ _ = showsPrec+instance Read1 V0 where+ liftReadsPrec _ _ = readsPrec
src/Linear/V1.hs view
@@ -8,18 +8,14 @@ {-# LANGUAGE GeneralizedNewtypeDeriving #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE ScopedTypeVariables #-}--- {-# OPTIONS_GHC -fno-warn-name-shadowing #-}-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702 {-# LANGUAGE Trustworthy #-} {-# LANGUAGE DeriveGeneric #-}-#endif+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE DeriveLift #-} -#ifndef MIN_VERSION_hashable-#define MIN_VERSION_hashable(x,y,z) 1-#endif ----------------------------------------------------------------------------- -- |--- Copyright : (C) 2012-2013 Edward Kmett,+-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett <ekmett@gmail.com>@@ -35,41 +31,53 @@ ) where import Control.Applicative+import Control.DeepSeq (NFData) import Control.Monad (liftM) import Control.Monad.Fix import Control.Monad.Zip-import Control.Lens+import Control.Lens as Lens+import Data.Binary as Binary+import Data.Bytes.Serial+import Data.Serialize as Cereal import Data.Data import Data.Distributive import Data.Foldable+import qualified Data.Foldable.WithIndex as WithIndex import Data.Functor.Bind+import Data.Functor.Classes import Data.Functor.Rep+import qualified Data.Functor.WithIndex as WithIndex import Data.Hashable+import Data.Hashable.Lifted import Data.Semigroup.Foldable+import qualified Data.Traversable.WithIndex as WithIndex+import qualified Data.Vector as V+import Linear.V import Foreign.Storable (Storable) import GHC.Arr (Ix(..))-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702-import GHC.Generics (Generic)-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706-import GHC.Generics (Generic1)+import GHC.Generics (Generic, Generic1)+#if defined(MIN_VERSION_template_haskell)+import Language.Haskell.TH.Syntax (Lift) #endif import Linear.Metric import Linear.Epsilon import Linear.Vector import Prelude hiding (sum)+import System.Random (Random(..), Uniform)+import System.Random.Stateful (UniformRange(..))+#if !(MIN_VERSION_base(4,11,0))+import Data.Semigroup+#endif import qualified Data.Vector.Generic.Mutable as M import qualified Data.Vector.Generic as G import qualified Data.Vector.Unboxed.Base as U -#ifdef HLINT--- HLint is delusional-{-# ANN module "HLint: ignore Unused LANGUAGE pragma" #-}-#endif- -- $setup+-- >>> import Control.Applicative -- >>> import Control.Lens+-- >>> import qualified Data.Foldable as F+-- >>> let sum xs = F.sum xs -- | A 1-dimensional vector --@@ -85,19 +93,30 @@ -- >>> sum (V1 2) -- 2 ---data V2 a = V2 !a !a deriving (Eq,Ord,Show,Read,Data,Typeable)+--data V2 a = V2 !a !a deriving (Eq,Ord,Show,Read,Data) newtype V1 a = V1 a- deriving (Eq,Ord,Show,Read,Data,Typeable,- Functor,Foldable,Traversable,- Epsilon,Storable-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702- ,Generic-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706- ,Generic1+ deriving (Eq,Ord,Show,Read,Data,+ Functor,Traversable,+ Epsilon,Storable,NFData+ ,Generic,Generic1+#if defined(MIN_VERSION_template_haskell)+ ,Lift #endif ) +instance Foldable V1 where+ foldMap f (V1 a) = f a+#if MIN_VERSION_base(4,13,0)+ foldMap' f (V1 a) = f a+#endif+ null _ = False+ length _ = 1++instance Finite V1 where+ type Size V1 = 1+ toV (V1 a) = V (V.singleton a)+ fromV (V v) = V1 (v V.! 0)+ instance Foldable1 V1 where foldMap1 f (V1 a) = f a {-# INLINE foldMap1 #-}@@ -108,13 +127,13 @@ instance Apply V1 where V1 f <.> V1 x = V1 (f x)- {-@ INLINE (<.>) #-}+ {-# INLINE (<.>) #-} instance Applicative V1 where pure = V1 {-# INLINE pure #-} V1 f <*> V1 x = V1 (f x)- {-@ INLINE (<*>) #-}+ {-# INLINE (<*>) #-} instance Additive V1 where zero = pure 0@@ -129,8 +148,10 @@ {-# INLINE (>>-) #-} instance Monad V1 where+#if !(MIN_VERSION_base(4,11,0)) return = V1 {-# INLINE return #-}+#endif V1 a >>= f = f a {-# INLINE (>>=) #-} @@ -158,12 +179,52 @@ fromRational = pure . fromRational {-# INLINE fromRational #-} +instance Floating a => Floating (V1 a) where+ pi = pure pi+ {-# INLINE pi #-}+ exp = fmap exp+ {-# INLINE exp #-}+ sqrt = fmap sqrt+ {-# INLINE sqrt #-}+ log = fmap log+ {-# INLINE log #-}+ (**) = liftA2 (**)+ {-# INLINE (**) #-}+ logBase = liftA2 logBase+ {-# INLINE logBase #-}+ sin = fmap sin+ {-# INLINE sin #-}+ tan = fmap tan+ {-# INLINE tan #-}+ cos = fmap cos+ {-# INLINE cos #-}+ asin = fmap asin+ {-# INLINE asin #-}+ atan = fmap atan+ {-# INLINE atan #-}+ acos = fmap acos+ {-# INLINE acos #-}+ sinh = fmap sinh+ {-# INLINE sinh #-}+ tanh = fmap tanh+ {-# INLINE tanh #-}+ cosh = fmap cosh+ {-# INLINE cosh #-}+ asinh = fmap asinh+ {-# INLINE asinh #-}+ atanh = fmap atanh+ {-# INLINE atanh #-}+ acosh = fmap acosh+ {-# INLINE acosh #-}+ instance Hashable a => Hashable (V1 a) where-#if (MIN_VERSION_hashable(1,2,1)) || !(MIN_VERSION_hashable(1,2,0)) hash (V1 a) = hash a-#endif hashWithSalt s (V1 a) = s `hashWithSalt` a +instance Hashable1 V1 where+ liftHashWithSalt h s (V1 a) = h s a+ {-# INLINE liftHashWithSalt #-}+ instance Metric V1 where dot (V1 a) (V1 b) = a * b {-# INLINE dot #-}@@ -214,23 +275,29 @@ index xs (E l) = view l xs {-# INLINE index #-} -instance FunctorWithIndex (E V1) V1 where+instance WithIndex.FunctorWithIndex (E V1) V1 where imap f (V1 a) = V1 (f ex a) {-# INLINE imap #-} -instance FoldableWithIndex (E V1) V1 where+instance WithIndex.FoldableWithIndex (E V1) V1 where ifoldMap f (V1 a) = f ex a {-# INLINE ifoldMap #-} -instance TraversableWithIndex (E V1) V1 where+instance WithIndex.TraversableWithIndex (E V1) V1 where itraverse f (V1 a) = V1 <$> f ex a {-# INLINE itraverse #-} +#if !MIN_VERSION_lens(5,0,0)+instance Lens.FunctorWithIndex (E V1) V1 where imap = WithIndex.imap+instance Lens.FoldableWithIndex (E V1) V1 where ifoldMap = WithIndex.ifoldMap+instance Lens.TraversableWithIndex (E V1) V1 where itraverse = WithIndex.itraverse+#endif+ type instance Index (V1 a) = E V1 type instance IxValue (V1 a) = a instance Ixed (V1 a) where- ix = el+ ix i = el i {-# INLINE ix #-} instance Each (V1 a) (V1 b) a b where@@ -242,14 +309,27 @@ instance U.Unbox a => U.Unbox (V1 a) instance U.Unbox a => M.MVector U.MVector (V1 a) where+ {-# INLINE basicLength #-}+ {-# INLINE basicUnsafeSlice #-}+ {-# INLINE basicOverlaps #-}+ {-# INLINE basicUnsafeNew #-}+ {-# INLINE basicUnsafeRead #-}+ {-# INLINE basicUnsafeWrite #-} basicLength (MV_V1 v) = M.basicLength v basicUnsafeSlice m n (MV_V1 v) = MV_V1 (M.basicUnsafeSlice m n v) basicOverlaps (MV_V1 v) (MV_V1 u) = M.basicOverlaps v u basicUnsafeNew n = liftM MV_V1 (M.basicUnsafeNew n) basicUnsafeRead (MV_V1 v) i = liftM V1 (M.basicUnsafeRead v i) basicUnsafeWrite (MV_V1 v) i (V1 x) = M.basicUnsafeWrite v i x+ basicInitialize (MV_V1 v) = M.basicInitialize v+ {-# INLINE basicInitialize #-} instance U.Unbox a => G.Vector U.Vector (V1 a) where+ {-# INLINE basicUnsafeFreeze #-}+ {-# INLINE basicUnsafeThaw #-}+ {-# INLINE basicLength #-}+ {-# INLINE basicUnsafeSlice #-}+ {-# INLINE basicUnsafeIndexM #-} basicUnsafeFreeze (MV_V1 v) = liftM V_V1 (G.basicUnsafeFreeze v) basicUnsafeThaw (V_V1 v) = liftM MV_V1 (G.basicUnsafeThaw v) basicLength (V_V1 v) = G.basicLength v@@ -263,3 +343,58 @@ instance MonadFix V1 where mfix f = V1 (let V1 a = f a in a)++instance Bounded a => Bounded (V1 a) where+ minBound = pure minBound+ {-# INLINE minBound #-}+ maxBound = pure maxBound+ {-# INLINE maxBound #-}++instance Serial1 V1 where+ serializeWith f (V1 a) = f a+ deserializeWith m = V1 `liftM` m++instance Serial a => Serial (V1 a) where+ serialize (V1 a) = serialize a+ deserialize = V1 `liftM` deserialize++instance Binary a => Binary (V1 a) where+ put = serializeWith Binary.put+ get = deserializeWith Binary.get++instance Serialize a => Serialize (V1 a) where+ put = serializeWith Cereal.put+ get = deserializeWith Cereal.get++instance Random a => Random (V1 a) where+ random g = case random g of (a, g') -> (V1 a, g')+ randoms g = V1 <$> randoms g+ randomR (V1 a, V1 b) g = case randomR (a, b) g of (a', g') -> (V1 a', g')+ randomRs (V1 a, V1 b) g = V1 <$> randomRs (a, b) g++instance Uniform a => Uniform (V1 a) where++instance UniformRange a => UniformRange (V1 a) where+ uniformRM (V1 a, V1 b) g = V1 <$> uniformRM (a, b) g++instance Eq1 V1 where+ liftEq f (V1 a) (V1 b) = f a b+instance Ord1 V1 where+ liftCompare f (V1 a) (V1 b) = f a b+instance Show1 V1 where+ liftShowsPrec f _ d (V1 a) = showParen (d >= 10) $ showString "V1 " . f d a+instance Read1 V1 where+ liftReadsPrec f _ = readsData $ readsUnaryWith f "V1" V1++instance Field1 (V1 a) (V1 b) a b where+ _1 f (V1 x) = V1 <$> f x++instance Semigroup a => Semigroup (V1 a) where+ (<>) = liftA2 (<>)++instance Monoid a => Monoid (V1 a) where+ mempty = pure mempty+#if !(MIN_VERSION_base(4,11,0))+ mappend = liftA2 mappend+#endif+
src/Linear/V2.hs view
@@ -2,16 +2,17 @@ {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE RankNTypes #-} {-# LANGUAGE MultiParamTypeClasses #-}--- {-# OPTIONS_GHC -fno-warn-name-shadowing #-} {-# LANGUAGE CPP #-}-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702 {-# LANGUAGE Trustworthy #-} {-# LANGUAGE DeriveGeneric #-}-#endif+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE DeriveLift #-}+ ----------------------------------------------------------------------------- -- |--- Copyright : (C) 2012-2013 Edward Kmett,+-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett <ekmett@gmail.com>@@ -24,44 +25,61 @@ ( V2(..) , R1(..) , R2(..)+ , _yx , ex, ey , perp , angle+ , unangle+ , crossZ ) where import Control.Applicative+import Control.DeepSeq (NFData(rnf)) import Control.Monad (liftM) import Control.Monad.Fix import Control.Monad.Zip-import Control.Lens hiding ((<.>))+import Control.Lens as Lens hiding ((<.>))+import Data.Binary as Binary+import Data.Bytes.Serial import Data.Data import Data.Distributive import Data.Foldable-import Data.Hashable+import qualified Data.Foldable.WithIndex as WithIndex import Data.Functor.Bind+import Data.Functor.Classes import Data.Functor.Rep+import qualified Data.Functor.WithIndex as WithIndex+import Data.Hashable+import Data.Hashable.Lifted import Data.Semigroup import Data.Semigroup.Foldable+import Data.Serialize as Cereal+import qualified Data.Traversable.WithIndex as WithIndex+import qualified Data.Vector as V import Foreign.Ptr (castPtr) import Foreign.Storable (Storable(..)) import GHC.Arr (Ix(..))-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702-import GHC.Generics (Generic)-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706-import GHC.Generics (Generic1)+import GHC.Generics (Generic, Generic1)+#if defined(MIN_VERSION_template_haskell)+import Language.Haskell.TH.Syntax (Lift) #endif import qualified Data.Vector.Generic.Mutable as M import qualified Data.Vector.Generic as G import qualified Data.Vector.Unboxed.Base as U import Linear.Metric import Linear.Epsilon+import Linear.V import Linear.Vector import Linear.V1 (R1(..),ex) import Prelude hiding (sum)+import System.Random (Random(..), Uniform)+import System.Random.Stateful (UniformRange(..)) -- $setup+-- >>> import Control.Applicative -- >>> import Control.Lens+-- >>> import qualified Data.Foldable as F+-- >>> let sum xs = F.sum xs -- | A 2-dimensional vector --@@ -78,15 +96,33 @@ -- 3 data V2 a = V2 !a !a deriving- (Eq,Ord,Show,Read,Data,Typeable-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702- ,Generic-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706- ,Generic1+ (Eq,Ord,Show,Read,Data+ ,Generic,Generic1+#if defined(MIN_VERSION_template_haskell)+ ,Lift #endif ) +instance Finite V2 where+ type Size V2 = 2+ toV (V2 a b) = V (V.fromListN 2 [a,b])+ fromV (V v) = V2 (v V.! 0) (v V.! 1)++instance Random a => Random (V2 a) where+ random g = case random g of+ (a, g') -> case random g' of+ (b, g'') -> (V2 a b, g'')+ {-# inline random #-}+ randomR (V2 a b, V2 c d) g = case randomR (a, c) g of+ (x, g') -> case randomR (b, d) g' of+ (y, g'') -> (V2 x y, g'')+ {-# inline randomR #-}++instance Uniform a => Uniform (V2 a) where++instance UniformRange a => UniformRange (V2 a) where+ uniformRM (V2 a b, V2 c d) g = V2 <$> uniformRM (a, c) g <*> uniformRM (b, d) g+ instance Functor V2 where fmap f (V2 a b) = V2 (f a) (f b) {-# INLINE fmap #-}@@ -96,6 +132,12 @@ instance Foldable V2 where foldMap f (V2 a b) = f a `mappend` f b {-# INLINE foldMap #-}+#if MIN_VERSION_base(4,13,0)+ foldMap' f (V2 a b) = f a `mappend` f b+ {-# INLINE foldMap' #-}+#endif+ null _ = False+ length _ = 2 instance Traversable V2 where traverse f (V2 a b) = V2 <$> f a <*> f b@@ -123,6 +165,10 @@ hashWithSalt s (V2 a b) = s `hashWithSalt` a `hashWithSalt` b {-# INLINE hashWithSalt #-} +instance Hashable1 V2 where+ liftHashWithSalt h s (V2 a b) = s `h` a `h` b+ {-# INLINE liftHashWithSalt #-}+ instance Additive V2 where zero = pure 0 {-# INLINE zero #-}@@ -138,8 +184,10 @@ {-# INLINE (>>-) #-} instance Monad V2 where+#if !(MIN_VERSION_base(4,11,0)) return a = V2 a a {-# INLINE return #-}+#endif V2 a b >>= f = V2 a' b' where V2 a' _ = f a V2 _ b' = f b@@ -169,6 +217,44 @@ fromRational = pure . fromRational {-# INLINE fromRational #-} +instance Floating a => Floating (V2 a) where+ pi = pure pi+ {-# INLINE pi #-}+ exp = fmap exp+ {-# INLINE exp #-}+ sqrt = fmap sqrt+ {-# INLINE sqrt #-}+ log = fmap log+ {-# INLINE log #-}+ (**) = liftA2 (**)+ {-# INLINE (**) #-}+ logBase = liftA2 logBase+ {-# INLINE logBase #-}+ sin = fmap sin+ {-# INLINE sin #-}+ tan = fmap tan+ {-# INLINE tan #-}+ cos = fmap cos+ {-# INLINE cos #-}+ asin = fmap asin+ {-# INLINE asin #-}+ atan = fmap atan+ {-# INLINE atan #-}+ acos = fmap acos+ {-# INLINE acos #-}+ sinh = fmap sinh+ {-# INLINE sinh #-}+ tanh = fmap tanh+ {-# INLINE tanh #-}+ cosh = fmap cosh+ {-# INLINE cosh #-}+ asinh = fmap asinh+ {-# INLINE asinh #-}+ atanh = fmap atanh+ {-# INLINE atanh #-}+ acosh = fmap acosh+ {-# INLINE acosh #-}+ instance Metric V2 where dot (V2 a b) (V2 c d) = a * c + b * d {-# INLINE dot #-}@@ -182,19 +268,19 @@ -- >>> V2 1 2 & _y .~ 3 -- V2 1 3 --- -- @- -- '_y' :: Lens' (t a) a- -- @- _y :: Functor f => (a -> f a) -> t a -> f (t a)+ _y :: Lens' (t a) a _y = _xy._y {-# INLINE _y #-} - -- |- -- @- -- '_xy' :: Lens' (t a) ('V2' a)- -- @- _xy :: Functor f => (V2 a -> f (V2 a)) -> t a -> f (t a)+ _xy :: Lens' (t a) (V2 a) +-- |+-- >>> V2 1 2 ^. _yx+-- V2 2 1+_yx :: R2 t => Lens' (t a) (V2 a)+_yx f = _xy $ \(V2 a b) -> f (V2 b a) <&> \(V2 b' a') -> V2 a' b'+{-# INLINE _yx #-}+ ey :: R2 t => E t ey = E _y @@ -258,34 +344,46 @@ index xs (E l) = view l xs {-# INLINE index #-} -instance FunctorWithIndex (E V2) V2 where+instance WithIndex.FunctorWithIndex (E V2) V2 where imap f (V2 a b) = V2 (f ex a) (f ey b) {-# INLINE imap #-} -instance FoldableWithIndex (E V2) V2 where+instance WithIndex.FoldableWithIndex (E V2) V2 where ifoldMap f (V2 a b) = f ex a `mappend` f ey b {-# INLINE ifoldMap #-} -instance TraversableWithIndex (E V2) V2 where+instance WithIndex.TraversableWithIndex (E V2) V2 where itraverse f (V2 a b) = V2 <$> f ex a <*> f ey b {-# INLINE itraverse #-} +#if !MIN_VERSION_lens(5,0,0)+instance Lens.FunctorWithIndex (E V2) V2 where imap = WithIndex.imap+instance Lens.FoldableWithIndex (E V2) V2 where ifoldMap = WithIndex.ifoldMap+instance Lens.TraversableWithIndex (E V2) V2 where itraverse = WithIndex.itraverse+#endif+ type instance Index (V2 a) = E V2 type instance IxValue (V2 a) = a instance Ixed (V2 a) where- ix = el+ ix i = el i {-# INLINE ix #-} instance Each (V2 a) (V2 b) a b where each = traverse {-# INLINE each #-} -data instance U.Vector (V2 a) = V_V2 !Int (U.Vector a)-data instance U.MVector s (V2 a) = MV_V2 !Int (U.MVector s a)+data instance U.Vector (V2 a) = V_V2 {-# UNPACK #-} !Int !(U.Vector a)+data instance U.MVector s (V2 a) = MV_V2 {-# UNPACK #-} !Int !(U.MVector s a) instance U.Unbox a => U.Unbox (V2 a) instance U.Unbox a => M.MVector U.MVector (V2 a) where+ {-# INLINE basicLength #-}+ {-# INLINE basicUnsafeSlice #-}+ {-# INLINE basicOverlaps #-}+ {-# INLINE basicUnsafeNew #-}+ {-# INLINE basicUnsafeRead #-}+ {-# INLINE basicUnsafeWrite #-} basicLength (MV_V2 n _) = n basicUnsafeSlice m n (MV_V2 _ v) = MV_V2 n (M.basicUnsafeSlice (2*m) (2*n) v) basicOverlaps (MV_V2 _ v) (MV_V2 _ u) = M.basicOverlaps v u@@ -299,8 +397,15 @@ do let o = 2*i M.basicUnsafeWrite v o x M.basicUnsafeWrite v (o+1) y+ basicInitialize (MV_V2 _ v) = M.basicInitialize v+ {-# INLINE basicInitialize #-} instance U.Unbox a => G.Vector U.Vector (V2 a) where+ {-# INLINE basicUnsafeFreeze #-}+ {-# INLINE basicUnsafeThaw #-}+ {-# INLINE basicLength #-}+ {-# INLINE basicUnsafeSlice #-}+ {-# INLINE basicUnsafeIndexM #-} basicUnsafeFreeze (MV_V2 n v) = liftM ( V_V2 n) (G.basicUnsafeFreeze v) basicUnsafeThaw ( V_V2 n v) = liftM (MV_V2 n) (G.basicUnsafeThaw v) basicLength ( V_V2 n _) = n@@ -320,3 +425,67 @@ angle :: Floating a => a -> V2 a angle a = V2 (cos a) (sin a)++unangle :: (Floating a, Ord a) => V2 a -> a+unangle a@(V2 ax ay) =+ let alpha = asin $ ay / norm a+ in if ax < 0+ then pi - alpha+ else alpha++-- | The Z-component of the cross product of two vectors in the XY-plane.+--+-- >>> crossZ (V2 1 0) (V2 0 1)+-- 1+crossZ :: Num a => V2 a -> V2 a -> a+crossZ (V2 x1 y1) (V2 x2 y2) = x1*y2 - y1*x2+{-# INLINE crossZ #-}++instance Bounded a => Bounded (V2 a) where+ minBound = pure minBound+ {-# INLINE minBound #-}+ maxBound = pure maxBound+ {-# INLINE maxBound #-}++instance NFData a => NFData (V2 a) where+ rnf (V2 a b) = rnf a `seq` rnf b++instance Serial1 V2 where+ serializeWith = traverse_+ deserializeWith k = V2 <$> k <*> k++instance Serial a => Serial (V2 a) where+ serialize = serializeWith serialize+ deserialize = deserializeWith deserialize++instance Binary a => Binary (V2 a) where+ put = serializeWith Binary.put+ get = deserializeWith Binary.get++instance Serialize a => Serialize (V2 a) where+ put = serializeWith Cereal.put+ get = deserializeWith Cereal.get++instance Eq1 V2 where+ liftEq f (V2 a b) (V2 c d) = f a c && f b d+instance Ord1 V2 where+ liftCompare f (V2 a b) (V2 c d) = f a c `mappend` f b d+instance Read1 V2 where+ liftReadsPrec f _ = readsData $ readsBinaryWith f f "V2" V2+instance Show1 V2 where+ liftShowsPrec f _ d (V2 a b) = showsBinaryWith f f "V2" d a b++instance Field1 (V2 a) (V2 a) a a where+ _1 f (V2 x y) = f x <&> \x' -> V2 x' y++instance Field2 (V2 a) (V2 a) a a where+ _2 f (V2 x y) = f y <&> \y' -> V2 x y'++instance Semigroup a => Semigroup (V2 a) where+ (<>) = liftA2 (<>)++instance Monoid a => Monoid (V2 a) where+ mempty = pure mempty+#if !(MIN_VERSION_base(4,11,0))+ mappend = liftA2 mappend+#endif
src/Linear/V3.hs view
@@ -2,15 +2,17 @@ {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE RankNTypes #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE CPP #-}-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702 {-# LANGUAGE Trustworthy #-} {-# LANGUAGE DeriveGeneric #-}-#endif+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE DeriveLift #-}+ ----------------------------------------------------------------------------- -- |--- Copyright : (C) 2012-2013 Edward Kmett,+-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett <ekmett@gmail.com>@@ -24,52 +26,73 @@ , cross, triple , R1(..) , R2(..)+ , _yx , R3(..)+ , _xz, _yz, _zx, _zy+ , _xzy, _yxz, _yzx, _zxy, _zyx , ex, ey, ez ) where +#if !MIN_VERSION_base(4,18,0) import Control.Applicative+#endif+import Control.DeepSeq (NFData(rnf)) import Control.Monad (liftM) import Control.Monad.Fix import Control.Monad.Zip-import Control.Lens hiding ((<.>))+import Control.Lens as Lens hiding ((<.>))+import Data.Binary as Binary -- binary+import Data.Bytes.Serial -- bytes import Data.Data import Data.Distributive import Data.Foldable+import qualified Data.Foldable.WithIndex as WithIndex import Data.Functor.Bind+import Data.Functor.Classes import Data.Functor.Rep+import qualified Data.Functor.WithIndex as WithIndex import Data.Hashable+import Data.Hashable.Lifted+#if !(MIN_VERSION_base(4,11,0)) import Data.Semigroup+#endif import Data.Semigroup.Foldable+import Data.Serialize as Cereal -- cereal+import qualified Data.Traversable.WithIndex as WithIndex+import qualified Data.Vector as V+import qualified Data.Vector.Generic.Mutable as M+import qualified Data.Vector.Generic as G+import qualified Data.Vector.Unboxed.Base as U import Foreign.Ptr (castPtr) import Foreign.Storable (Storable(..)) import GHC.Arr (Ix(..))-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702-import GHC.Generics (Generic)-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706-import GHC.Generics (Generic1)+import GHC.Generics (Generic, Generic1)+#if defined(MIN_VERSION_template_haskell)+import Language.Haskell.TH.Syntax (Lift) #endif-import qualified Data.Vector.Generic.Mutable as M-import qualified Data.Vector.Generic as G-import qualified Data.Vector.Unboxed.Base as U import Linear.Epsilon import Linear.Metric+import Linear.V import Linear.V2 import Linear.Vector+import System.Random (Random(..), Uniform)+import System.Random.Stateful (UniformRange(..)) -{-# ANN module "HLint: ignore Reduce duplication" #-}+-- $setup+-- >>> import Control.Lens hiding (index) -- | A 3-dimensional vector-data V3 a = V3 !a !a !a deriving (Eq,Ord,Show,Read,Data,Typeable-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702- ,Generic-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706- ,Generic1+data V3 a = V3 !a !a !a deriving (Eq,Ord,Show,Read,Data+ ,Generic,Generic1+#if defined(MIN_VERSION_template_haskell)+ ,Lift #endif ) +instance Finite V3 where+ type Size V3 = 3+ toV (V3 a b c) = V (V.fromListN 3 [a,b,c])+ fromV (V v) = V3 (v V.! 0) (v V.! 1) (v V.! 2) instance Functor V3 where fmap f (V3 a b c) = V3 (f a) (f b) (f c)@@ -80,7 +103,31 @@ instance Foldable V3 where foldMap f (V3 a b c) = f a `mappend` f b `mappend` f c {-# INLINE foldMap #-}+#if MIN_VERSION_base(4,13,0)+ foldMap' f (V3 a b c) = (f a `mappend` f b) `mappend` f c+ {-# INLINE foldMap' #-}+#endif+ null _ = False+ length _ = 3 +instance Random a => Random (V3 a) where+ random g = case random g of+ (a, g') -> case random g' of+ (b, g'') -> case random g'' of+ (c, g''') -> (V3 a b c, g''')+ randomR (V3 a b c, V3 a' b' c') g = case randomR (a,a') g of+ (a'', g') -> case randomR (b,b') g' of+ (b'', g'') -> case randomR (c,c') g'' of+ (c'', g''') -> (V3 a'' b'' c'', g''')++instance Uniform a => Uniform (V3 a) where++instance UniformRange a => UniformRange (V3 a) where+ uniformRM (V3 a b c, V3 a' b' c') g = V3+ <$> uniformRM (a, a') g+ <*> uniformRM (b, b') g+ <*> uniformRM (c, c') g+ instance Traversable V3 where traverse f (V3 a b c) = V3 <$> f a <*> f b <*> f c {-# INLINE traverse #-}@@ -119,8 +166,10 @@ {-# INLINE (>>-) #-} instance Monad V3 where+#if !(MIN_VERSION_base(4,11,0)) return a = V3 a a a {-# INLINE return #-}+#endif V3 a b c >>= f = V3 a' b' c' where V3 a' _ _ = f a V3 _ b' _ = f b@@ -151,10 +200,52 @@ fromRational = pure . fromRational {-# INLINE fromRational #-} +instance Floating a => Floating (V3 a) where+ pi = pure pi+ {-# INLINE pi #-}+ exp = fmap exp+ {-# INLINE exp #-}+ sqrt = fmap sqrt+ {-# INLINE sqrt #-}+ log = fmap log+ {-# INLINE log #-}+ (**) = liftA2 (**)+ {-# INLINE (**) #-}+ logBase = liftA2 logBase+ {-# INLINE logBase #-}+ sin = fmap sin+ {-# INLINE sin #-}+ tan = fmap tan+ {-# INLINE tan #-}+ cos = fmap cos+ {-# INLINE cos #-}+ asin = fmap asin+ {-# INLINE asin #-}+ atan = fmap atan+ {-# INLINE atan #-}+ acos = fmap acos+ {-# INLINE acos #-}+ sinh = fmap sinh+ {-# INLINE sinh #-}+ tanh = fmap tanh+ {-# INLINE tanh #-}+ cosh = fmap cosh+ {-# INLINE cosh #-}+ asinh = fmap asinh+ {-# INLINE asinh #-}+ atanh = fmap atanh+ {-# INLINE atanh #-}+ acosh = fmap acosh+ {-# INLINE acosh #-}+ instance Hashable a => Hashable (V3 a) where hashWithSalt s (V3 a b c) = s `hashWithSalt` a `hashWithSalt` b `hashWithSalt` c {-# INLINE hashWithSalt #-} +instance Hashable1 V3 where+ liftHashWithSalt h s (V3 a b c) = s `h` a `h` b `h` c+ {-# INLINE liftHashWithSalt #-}+ instance Metric V3 where dot (V3 a b c) (V3 d e f) = a * d + b * e + c * f {-# INLINABLE dot #-}@@ -166,16 +257,43 @@ -- | A space that distinguishes 3 orthogonal basis vectors: '_x', '_y', and '_z'. (It may have more) class R2 t => R3 t where -- |- -- @- -- '_z' :: Lens' (t a) a- -- @- _z :: Functor f => (a -> f a) -> t a -> f (t a)- -- |- -- @- -- '_xyz' :: Lens' (t a) ('V3' a)- -- @- _xyz :: Functor f => (V3 a -> f (V3 a)) -> t a -> f (t a)+ -- >>> V3 1 2 3 ^. _z+ -- 3+ _z :: Lens' (t a) a + _xyz :: Lens' (t a) (V3 a)++_xz, _yz, _zx, _zy :: R3 t => Lens' (t a) (V2 a)++_xz f = _xyz $ \(V3 a b c) -> f (V2 a c) <&> \(V2 a' c') -> V3 a' b c'+{-# INLINE _xz #-}++_yz f = _xyz $ \(V3 a b c) -> f (V2 b c) <&> \(V2 b' c') -> V3 a b' c'+{-# INLINE _yz #-}++_zx f = _xyz $ \(V3 a b c) -> f (V2 c a) <&> \(V2 c' a') -> V3 a' b c'+{-# INLINE _zx #-}++_zy f = _xyz $ \(V3 a b c) -> f (V2 c b) <&> \(V2 c' b') -> V3 a b' c'+{-# INLINE _zy #-}++_xzy, _yxz, _yzx, _zxy, _zyx :: R3 t => Lens' (t a) (V3 a)++_xzy f = _xyz $ \(V3 a b c) -> f (V3 a c b) <&> \(V3 a' c' b') -> V3 a' b' c'+{-# INLINE _xzy #-}++_yxz f = _xyz $ \(V3 a b c) -> f (V3 b a c) <&> \(V3 b' a' c') -> V3 a' b' c'+{-# INLINE _yxz #-}++_yzx f = _xyz $ \(V3 a b c) -> f (V3 b c a) <&> \(V3 b' c' a') -> V3 a' b' c'+{-# INLINE _yzx #-}++_zxy f = _xyz $ \(V3 a b c) -> f (V3 c a b) <&> \(V3 c' a' b') -> V3 a' b' c'+{-# INLINE _zxy #-}++_zyx f = _xyz $ \(V3 a b c) -> f (V3 c b a) <&> \(V3 c' b' a') -> V3 a' b' c'+{-# INLINE _zyx #-}+ ez :: R3 t => E t ez = E _z @@ -251,34 +369,46 @@ index xs (E l) = view l xs {-# INLINE index #-} -instance FunctorWithIndex (E V3) V3 where+instance WithIndex.FunctorWithIndex (E V3) V3 where imap f (V3 a b c) = V3 (f ex a) (f ey b) (f ez c) {-# INLINE imap #-} -instance FoldableWithIndex (E V3) V3 where+instance WithIndex.FoldableWithIndex (E V3) V3 where ifoldMap f (V3 a b c) = f ex a `mappend` f ey b `mappend` f ez c {-# INLINE ifoldMap #-} -instance TraversableWithIndex (E V3) V3 where+instance WithIndex.TraversableWithIndex (E V3) V3 where itraverse f (V3 a b c) = V3 <$> f ex a <*> f ey b <*> f ez c {-# INLINE itraverse #-} +#if !MIN_VERSION_lens(5,0,0)+instance Lens.FunctorWithIndex (E V3) V3 where imap = WithIndex.imap+instance Lens.FoldableWithIndex (E V3) V3 where ifoldMap = WithIndex.ifoldMap+instance Lens.TraversableWithIndex (E V3) V3 where itraverse = WithIndex.itraverse+#endif+ type instance Index (V3 a) = E V3 type instance IxValue (V3 a) = a instance Ixed (V3 a) where- ix = el+ ix i = el i {-# INLINE ix #-} instance Each (V3 a) (V3 b) a b where each = traverse {-# INLINE each #-} -data instance U.Vector (V3 a) = V_V3 !Int (U.Vector a)-data instance U.MVector s (V3 a) = MV_V3 !Int (U.MVector s a)+data instance U.Vector (V3 a) = V_V3 {-# UNPACK #-} !Int !(U.Vector a)+data instance U.MVector s (V3 a) = MV_V3 {-# UNPACK #-} !Int !(U.MVector s a) instance U.Unbox a => U.Unbox (V3 a) instance U.Unbox a => M.MVector U.MVector (V3 a) where+ {-# INLINE basicLength #-}+ {-# INLINE basicUnsafeSlice #-}+ {-# INLINE basicOverlaps #-}+ {-# INLINE basicUnsafeNew #-}+ {-# INLINE basicUnsafeRead #-}+ {-# INLINE basicUnsafeWrite #-} basicLength (MV_V3 n _) = n basicUnsafeSlice m n (MV_V3 _ v) = MV_V3 n (M.basicUnsafeSlice (3*m) (3*n) v) basicOverlaps (MV_V3 _ v) (MV_V3 _ u) = M.basicOverlaps v u@@ -294,8 +424,15 @@ M.basicUnsafeWrite v o x M.basicUnsafeWrite v (o+1) y M.basicUnsafeWrite v (o+2) z+ basicInitialize (MV_V3 _ v) = M.basicInitialize v+ {-# INLINE basicInitialize #-} instance U.Unbox a => G.Vector U.Vector (V3 a) where+ {-# INLINE basicUnsafeFreeze #-}+ {-# INLINE basicUnsafeThaw #-}+ {-# INLINE basicLength #-}+ {-# INLINE basicUnsafeSlice #-}+ {-# INLINE basicUnsafeIndexM #-} basicUnsafeFreeze (MV_V3 n v) = liftM ( V_V3 n) (G.basicUnsafeFreeze v) basicUnsafeThaw ( V_V3 n v) = liftM (MV_V3 n) (G.basicUnsafeThaw v) basicLength ( V_V3 n _) = n@@ -314,3 +451,63 @@ mfix f = V3 (let V3 a _ _ = f a in a) (let V3 _ a _ = f a in a) (let V3 _ _ a = f a in a)++instance Bounded a => Bounded (V3 a) where+ minBound = pure minBound+ {-# INLINE minBound #-}+ maxBound = pure maxBound+ {-# INLINE maxBound #-}++instance NFData a => NFData (V3 a) where+ rnf (V3 a b c) = rnf a `seq` rnf b `seq` rnf c++instance Serial1 V3 where+ serializeWith = traverse_+ deserializeWith k = V3 <$> k <*> k <*> k++instance Serial a => Serial (V3 a) where+ serialize = serializeWith serialize+ deserialize = deserializeWith deserialize++instance Binary a => Binary (V3 a) where+ put = serializeWith Binary.put+ get = deserializeWith Binary.get++instance Serialize a => Serialize (V3 a) where+ put = serializeWith Cereal.put+ get = deserializeWith Cereal.get++instance Eq1 V3 where+ liftEq k (V3 a b c) (V3 d e f) = k a d && k b e && k c f+instance Ord1 V3 where+ liftCompare k (V3 a b c) (V3 d e f) = k a d `mappend` k b e `mappend` k c f+instance Read1 V3 where+ liftReadsPrec k _ d = readParen (d > 10) $ \r ->+ [ (V3 a b c, r4)+ | ("V3",r1) <- lex r+ , (a,r2) <- k 11 r1+ , (b,r3) <- k 11 r2+ , (c,r4) <- k 11 r3+ ]+instance Show1 V3 where+ liftShowsPrec f _ d (V3 a b c) = showParen (d > 10) $+ showString "V3 " . f 11 a . showChar ' ' . f 11 b . showChar ' ' . f 11 c++instance Field1 (V3 a) (V3 a) a a where+ _1 f (V3 x y z) = f x <&> \x' -> V3 x' y z++instance Field2 (V3 a) (V3 a) a a where+ _2 f (V3 x y z) = f y <&> \y' -> V3 x y' z++instance Field3 (V3 a) (V3 a) a a where+ _3 f (V3 x y z) = f z <&> \z' -> V3 x y z'++instance Semigroup a => Semigroup (V3 a) where+ (<>) = liftA2 (<>)++instance Monoid a => Monoid (V3 a) where+ mempty = pure mempty+#if !(MIN_VERSION_base(4,11,0))+ mappend = liftA2 mappend+#endif+
src/Linear/V4.hs view
@@ -1,16 +1,18 @@ {-# LANGUAGE DeriveDataTypeable #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE RankNTypes #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE CPP #-}-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702 {-# LANGUAGE Trustworthy #-} {-# LANGUAGE DeriveGeneric #-}-#endif+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE DeriveLift #-}+ ----------------------------------------------------------------------------- -- |--- Copyright : (C) 2012-2013 Edward Kmett,+-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett <ekmett@gmail.com>@@ -24,54 +26,82 @@ , vector, point, normalizePoint , R1(..) , R2(..)+ , _yx , R3(..)+ , _xz, _yz, _zx, _zy+ , _xzy, _yxz, _yzx, _zxy, _zyx , R4(..)+ , _xw, _yw, _zw, _wx, _wy, _wz+ , _xyw, _xzw, _xwy, _xwz, _yxw, _yzw, _ywx, _ywz, _zxw, _zyw, _zwx, _zwy+ , _wxy, _wxz, _wyx, _wyz, _wzx, _wzy+ , _xywz, _xzyw, _xzwy, _xwyz, _xwzy, _yxzw , _yxwz, _yzxw, _yzwx, _ywxz+ , _ywzx, _zxyw, _zxwy, _zyxw, _zywx, _zwxy, _zwyx, _wxyz, _wxzy, _wyxz+ , _wyzx, _wzxy, _wzyx , ex, ey, ez, ew ) where +#if !MIN_VERSION_base(4,18,0) import Control.Applicative+#endif+import Control.DeepSeq (NFData(rnf)) import Control.Monad (liftM) import Control.Monad.Fix import Control.Monad.Zip-import Control.Lens hiding ((<.>))+import Control.Lens as Lens hiding ((<.>))+import Data.Binary as Binary+import Data.Bytes.Serial import Data.Data import Data.Distributive import Data.Foldable+import qualified Data.Foldable.WithIndex as WithIndex import Data.Functor.Bind+import Data.Functor.Classes import Data.Functor.Rep+import qualified Data.Functor.WithIndex as WithIndex import Data.Hashable+import Data.Hashable.Lifted+#if !(MIN_VERSION_base(4,11,0)) import Data.Semigroup+#endif import Data.Semigroup.Foldable+import Data.Serialize as Cereal+import qualified Data.Traversable.WithIndex as WithIndex+import qualified Data.Vector as V+import qualified Data.Vector.Generic.Mutable as M+import qualified Data.Vector.Generic as G+import qualified Data.Vector.Unboxed.Base as U import Foreign.Ptr (castPtr) import Foreign.Storable (Storable(..)) import GHC.Arr (Ix(..))-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702-import GHC.Generics (Generic)-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706-import GHC.Generics (Generic1)+import GHC.Generics (Generic, Generic1)+#if defined(MIN_VERSION_template_haskell)+import Language.Haskell.TH.Syntax (Lift) #endif-import qualified Data.Vector.Generic.Mutable as M-import qualified Data.Vector.Generic as G-import qualified Data.Vector.Unboxed.Base as U import Linear.Epsilon import Linear.Metric+import Linear.V import Linear.V2 import Linear.V3 import Linear.Vector+import System.Random (Random(..), Uniform)+import System.Random.Stateful (UniformRange(..)) -{-# ANN module "HLint: ignore Reduce duplication" #-}+-- $setup+-- >>> import Control.Lens hiding (index) -- | A 4-dimensional vector.-data V4 a = V4 !a !a !a !a deriving (Eq,Ord,Show,Read,Data,Typeable-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702- ,Generic-#endif-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 706- ,Generic1+data V4 a = V4 !a !a !a !a deriving (Eq,Ord,Show,Read,Data+ ,Generic,Generic1+#if defined(MIN_VERSION_template_haskell)+ ,Lift #endif ) +instance Finite V4 where+ type Size V4 = 4+ toV (V4 a b c d) = V (V.fromListN 4 [a,b,c,d])+ fromV (V v) = V4 (v V.! 0) (v V.! 1) (v V.! 2) (v V.! 3)+ instance Functor V4 where fmap f (V4 a b c d) = V4 (f a) (f b) (f c) (f d) {-# INLINE fmap #-}@@ -81,7 +111,34 @@ instance Foldable V4 where foldMap f (V4 a b c d) = f a `mappend` f b `mappend` f c `mappend` f d {-# INLINE foldMap #-}+#if MIN_VERSION_base(4,13,0)+ foldMap' f (V4 a b c d) = ((f a `mappend` f b) `mappend` f c) `mappend` f d+ {-# INLINE foldMap' #-}+#endif+ null _ = False+ length _ = 4 +instance Random a => Random (V4 a) where+ random g = case random g of+ (a, g') -> case random g' of+ (b, g'') -> case random g'' of+ (c, g''') -> case random g''' of+ (d, g'''') -> (V4 a b c d, g'''')+ randomR (V4 a b c d, V4 a' b' c' d') g = case randomR (a,a') g of+ (a'', g') -> case randomR (b,b') g' of+ (b'', g'') -> case randomR (c,c') g'' of+ (c'', g''') -> case randomR (d,d') g''' of+ (d'', g'''') -> (V4 a'' b'' c'' d'', g'''')++instance Uniform a => Uniform (V4 a) where++instance UniformRange a => UniformRange (V4 a) where+ uniformRM (V4 a b c d, V4 a' b' c' d') g = V4+ <$> uniformRM (a, a') g+ <*> uniformRM (b, b') g+ <*> uniformRM (c, c') g+ <*> uniformRM (d, d') g+ instance Traversable V4 where traverse f (V4 a b c d) = V4 <$> f a <*> f b <*> f c <*> f d {-# INLINE traverse #-}@@ -121,8 +178,10 @@ {-# INLINE (>>-) #-} instance Monad V4 where+#if !(MIN_VERSION_base(4,11,0)) return a = V4 a a a a {-# INLINE return #-}+#endif V4 a b c d >>= f = V4 a' b' c' d' where V4 a' _ _ _ = f a V4 _ b' _ _ = f b@@ -154,6 +213,44 @@ fromRational = pure . fromRational {-# INLINE fromRational #-} +instance Floating a => Floating (V4 a) where+ pi = pure pi+ {-# INLINE pi #-}+ exp = fmap exp+ {-# INLINE exp #-}+ sqrt = fmap sqrt+ {-# INLINE sqrt #-}+ log = fmap log+ {-# INLINE log #-}+ (**) = liftA2 (**)+ {-# INLINE (**) #-}+ logBase = liftA2 logBase+ {-# INLINE logBase #-}+ sin = fmap sin+ {-# INLINE sin #-}+ tan = fmap tan+ {-# INLINE tan #-}+ cos = fmap cos+ {-# INLINE cos #-}+ asin = fmap asin+ {-# INLINE asin #-}+ atan = fmap atan+ {-# INLINE atan #-}+ acos = fmap acos+ {-# INLINE acos #-}+ sinh = fmap sinh+ {-# INLINE sinh #-}+ tanh = fmap tanh+ {-# INLINE tanh #-}+ cosh = fmap cosh+ {-# INLINE cosh #-}+ asinh = fmap asinh+ {-# INLINE asinh #-}+ atanh = fmap atanh+ {-# INLINE atanh #-}+ acosh = fmap acosh+ {-# INLINE acosh #-}+ instance Metric V4 where dot (V4 a b c d) (V4 e f g h) = a * e + b * f + c * g + d * h {-# INLINE dot #-}@@ -169,19 +266,164 @@ hashWithSalt s (V4 a b c d) = s `hashWithSalt` a `hashWithSalt` b `hashWithSalt` c `hashWithSalt` d {-# INLINE hashWithSalt #-} +instance Hashable1 V4 where+ liftHashWithSalt h s (V4 a b c d) = s `h` a `h` b `h` c `h` d+ {-# INLINE liftHashWithSalt #-}+ -- | A space that distinguishes orthogonal basis vectors '_x', '_y', '_z', '_w'. (It may have more.) class R3 t => R4 t where -- |- -- @- -- '_w' :: Lens' (t a) a- -- @- _w :: Functor f => (a -> f a) -> t a -> f (t a)- -- |- -- @- -- '_xyzw' :: Lens' (t a) ('V4' a)- -- @- _xyzw :: Functor f => (V4 a -> f (V4 a)) -> t a -> f (t a)+ -- >>> V4 1 2 3 4 ^._w+ -- 4+ _w :: Lens' (t a) a+ _xyzw :: Lens' (t a) (V4 a) +_xw, _yw, _zw, _wx, _wy, _wz :: R4 t => Lens' (t a) (V2 a)+_xw f = _xyzw $ \(V4 a b c d) -> f (V2 a d) <&> \(V2 a' d') -> V4 a' b c d'+{-# INLINE _xw #-}++_yw f = _xyzw $ \(V4 a b c d) -> f (V2 b d) <&> \(V2 b' d') -> V4 a b' c d'+{-# INLINE _yw #-}++_zw f = _xyzw $ \(V4 a b c d) -> f (V2 c d) <&> \(V2 c' d') -> V4 a b c' d'+{-# INLINE _zw #-}++_wx f = _xyzw $ \(V4 a b c d) -> f (V2 d a) <&> \(V2 d' a') -> V4 a' b c d'+{-# INLINE _wx #-}++_wy f = _xyzw $ \(V4 a b c d) -> f (V2 d b) <&> \(V2 d' b') -> V4 a b' c d'+{-# INLINE _wy #-}++_wz f = _xyzw $ \(V4 a b c d) -> f (V2 d c) <&> \(V2 d' c') -> V4 a b c' d'+{-# INLINE _wz #-}++_xyw, _xzw, _xwy, _xwz, _yxw, _yzw, _ywx, _ywz, _zxw, _zyw, _zwx, _zwy, _wxy, _wxz, _wyx, _wyz, _wzx, _wzy :: R4 t => Lens' (t a) (V3 a)+_xyw f = _xyzw $ \(V4 a b c d) -> f (V3 a b d) <&> \(V3 a' b' d') -> V4 a' b' c d'+{-# INLINE _xyw #-}++_xzw f = _xyzw $ \(V4 a b c d) -> f (V3 a c d) <&> \(V3 a' c' d') -> V4 a' b c' d'+{-# INLINE _xzw #-}++_xwy f = _xyzw $ \(V4 a b c d) -> f (V3 a d b) <&> \(V3 a' d' b') -> V4 a' b' c d'+{-# INLINE _xwy #-}++_xwz f = _xyzw $ \(V4 a b c d) -> f (V3 a d c) <&> \(V3 a' d' c') -> V4 a' b c' d'+{-# INLINE _xwz #-}++_yxw f = _xyzw $ \(V4 a b c d) -> f (V3 b a d) <&> \(V3 b' a' d') -> V4 a' b' c d'+{-# INLINE _yxw #-}++_yzw f = _xyzw $ \(V4 a b c d) -> f (V3 b c d) <&> \(V3 b' c' d') -> V4 a b' c' d'+{-# INLINE _yzw #-}++_ywx f = _xyzw $ \(V4 a b c d) -> f (V3 b d a) <&> \(V3 b' d' a') -> V4 a' b' c d'+{-# INLINE _ywx #-}++_ywz f = _xyzw $ \(V4 a b c d) -> f (V3 b d c) <&> \(V3 b' d' c') -> V4 a b' c' d'+{-# INLINE _ywz #-}++_zxw f = _xyzw $ \(V4 a b c d) -> f (V3 c a d) <&> \(V3 c' a' d') -> V4 a' b c' d'+{-# INLINE _zxw #-}++_zyw f = _xyzw $ \(V4 a b c d) -> f (V3 c b d) <&> \(V3 c' b' d') -> V4 a b' c' d'+{-# INLINE _zyw #-}++_zwx f = _xyzw $ \(V4 a b c d) -> f (V3 c d a) <&> \(V3 c' d' a') -> V4 a' b c' d'+{-# INLINE _zwx #-}++_zwy f = _xyzw $ \(V4 a b c d) -> f (V3 c d b) <&> \(V3 c' d' b') -> V4 a b' c' d'+{-# INLINE _zwy #-}++_wxy f = _xyzw $ \(V4 a b c d) -> f (V3 d a b) <&> \(V3 d' a' b') -> V4 a' b' c d'+{-# INLINE _wxy #-}++_wxz f = _xyzw $ \(V4 a b c d) -> f (V3 d a c) <&> \(V3 d' a' c') -> V4 a' b c' d'+{-# INLINE _wxz #-}++_wyx f = _xyzw $ \(V4 a b c d) -> f (V3 d b a) <&> \(V3 d' b' a') -> V4 a' b' c d'+{-# INLINE _wyx #-}++_wyz f = _xyzw $ \(V4 a b c d) -> f (V3 d b c) <&> \(V3 d' b' c') -> V4 a b' c' d'+{-# INLINE _wyz #-}++_wzx f = _xyzw $ \(V4 a b c d) -> f (V3 d c a) <&> \(V3 d' c' a') -> V4 a' b c' d'+{-# INLINE _wzx #-}++_wzy f = _xyzw $ \(V4 a b c d) -> f (V3 d c b) <&> \(V3 d' c' b') -> V4 a b' c' d'+{-# INLINE _wzy #-}++_xywz, _xzyw, _xzwy, _xwyz, _xwzy, _yxzw , _yxwz, _yzxw, _yzwx, _ywxz+ , _ywzx, _zxyw, _zxwy, _zyxw, _zywx, _zwxy, _zwyx, _wxyz, _wxzy, _wyxz+ , _wyzx, _wzxy, _wzyx :: R4 t => Lens' (t a) (V4 a)+_xywz f = _xyzw $ \(V4 a b c d) -> f (V4 a b d c) <&> \(V4 a' b' d' c') -> V4 a' b' c' d'+{-# INLINE _xywz #-}++_xzyw f = _xyzw $ \(V4 a b c d) -> f (V4 a c b d) <&> \(V4 a' c' b' d') -> V4 a' b' c' d'+{-# INLINE _xzyw #-}++_xzwy f = _xyzw $ \(V4 a b c d) -> f (V4 a c d b) <&> \(V4 a' c' d' b') -> V4 a' b' c' d'+{-# INLINE _xzwy #-}++_xwyz f = _xyzw $ \(V4 a b c d) -> f (V4 a d b c) <&> \(V4 a' d' b' c') -> V4 a' b' c' d'+{-# INLINE _xwyz #-}++_xwzy f = _xyzw $ \(V4 a b c d) -> f (V4 a d c b) <&> \(V4 a' d' c' b') -> V4 a' b' c' d'+{-# INLINE _xwzy #-}++_yxzw f = _xyzw $ \(V4 a b c d) -> f (V4 b a c d) <&> \(V4 b' a' c' d') -> V4 a' b' c' d'+{-# INLINE _yxzw #-}++_yxwz f = _xyzw $ \(V4 a b c d) -> f (V4 b a d c) <&> \(V4 b' a' d' c') -> V4 a' b' c' d'+{-# INLINE _yxwz #-}++_yzxw f = _xyzw $ \(V4 a b c d) -> f (V4 b c a d) <&> \(V4 b' c' a' d') -> V4 a' b' c' d'+{-# INLINE _yzxw #-}++_yzwx f = _xyzw $ \(V4 a b c d) -> f (V4 b c d a) <&> \(V4 b' c' d' a') -> V4 a' b' c' d'+{-# INLINE _yzwx #-}++_ywxz f = _xyzw $ \(V4 a b c d) -> f (V4 b d a c) <&> \(V4 b' d' a' c') -> V4 a' b' c' d'+{-# INLINE _ywxz #-}++_ywzx f = _xyzw $ \(V4 a b c d) -> f (V4 b d c a) <&> \(V4 b' d' c' a') -> V4 a' b' c' d'+{-# INLINE _ywzx #-}++_zxyw f = _xyzw $ \(V4 a b c d) -> f (V4 c a b d) <&> \(V4 c' a' b' d') -> V4 a' b' c' d'+{-# INLINE _zxyw #-}++_zxwy f = _xyzw $ \(V4 a b c d) -> f (V4 c a d b) <&> \(V4 c' a' d' b') -> V4 a' b' c' d'+{-# INLINE _zxwy #-}++_zyxw f = _xyzw $ \(V4 a b c d) -> f (V4 c b a d) <&> \(V4 c' b' a' d') -> V4 a' b' c' d'+{-# INLINE _zyxw #-}++_zywx f = _xyzw $ \(V4 a b c d) -> f (V4 c b d a) <&> \(V4 c' b' d' a') -> V4 a' b' c' d'+{-# INLINE _zywx #-}++_zwxy f = _xyzw $ \(V4 a b c d) -> f (V4 c d a b) <&> \(V4 c' d' a' b') -> V4 a' b' c' d'+{-# INLINE _zwxy #-}++_zwyx f = _xyzw $ \(V4 a b c d) -> f (V4 c d b a) <&> \(V4 c' d' b' a') -> V4 a' b' c' d'+{-# INLINE _zwyx #-}++_wxyz f = _xyzw $ \(V4 a b c d) -> f (V4 d a b c) <&> \(V4 d' a' b' c') -> V4 a' b' c' d'+{-# INLINE _wxyz #-}++_wxzy f = _xyzw $ \(V4 a b c d) -> f (V4 d a c b) <&> \(V4 d' a' c' b') -> V4 a' b' c' d'+{-# INLINE _wxzy #-}++_wyxz f = _xyzw $ \(V4 a b c d) -> f (V4 d b a c) <&> \(V4 d' b' a' c') -> V4 a' b' c' d'+{-# INLINE _wyxz #-}++_wyzx f = _xyzw $ \(V4 a b c d) -> f (V4 d b c a) <&> \(V4 d' b' c' a') -> V4 a' b' c' d'+{-# INLINE _wyzx #-}++_wzxy f = _xyzw $ \(V4 a b c d) -> f (V4 d c a b) <&> \(V4 d' c' a' b') -> V4 a' b' c' d'+{-# INLINE _wzxy #-}++_wzyx f = _xyzw $ \(V4 a b c d) -> f (V4 d c b a) <&> \(V4 d' c' b' a') -> V4 a' b' c' d'+{-# INLINE _wzyx #-}+ ew :: R4 t => E t ew = E _w @@ -223,12 +465,14 @@ where ptr' = castPtr ptr {-# INLINE peek #-} --- | Convert a 3-dimensional affine vector into a 4-dimensional homogeneous vector.+-- | Convert a 3-dimensional affine vector into a 4-dimensional homogeneous vector,+-- i.e. sets the @w@ coordinate to 0. vector :: Num a => V3 a -> V4 a vector (V3 a b c) = V4 a b c 0 {-# INLINE vector #-} --- | Convert a 3-dimensional affine point into a 4-dimensional homogeneous vector.+-- | Convert a 3-dimensional affine point into a 4-dimensional homogeneous vector,+-- i.e. sets the @w@ coordinate to 1. point :: Num a => V3 a -> V4 a point (V3 a b c) = V4 a b c 1 {-# INLINE point #-}@@ -276,29 +520,35 @@ index xs (E l) = view l xs {-# INLINE index #-} -instance FunctorWithIndex (E V4) V4 where+instance WithIndex.FunctorWithIndex (E V4) V4 where imap f (V4 a b c d) = V4 (f ex a) (f ey b) (f ez c) (f ew d) {-# INLINE imap #-} -instance FoldableWithIndex (E V4) V4 where+instance WithIndex.FoldableWithIndex (E V4) V4 where ifoldMap f (V4 a b c d) = f ex a `mappend` f ey b `mappend` f ez c `mappend` f ew d {-# INLINE ifoldMap #-} -instance TraversableWithIndex (E V4) V4 where+instance WithIndex.TraversableWithIndex (E V4) V4 where itraverse f (V4 a b c d) = V4 <$> f ex a <*> f ey b <*> f ez c <*> f ew d {-# INLINE itraverse #-} +#if !MIN_VERSION_lens(5,0,0)+instance Lens.FunctorWithIndex (E V4) V4 where imap = WithIndex.imap+instance Lens.FoldableWithIndex (E V4) V4 where ifoldMap = WithIndex.ifoldMap+instance Lens.TraversableWithIndex (E V4) V4 where itraverse = WithIndex.itraverse+#endif+ type instance Index (V4 a) = E V4 type instance IxValue (V4 a) = a instance Ixed (V4 a) where- ix = el+ ix i = el i instance Each (V4 a) (V4 b) a b where each = traverse -data instance U.Vector (V4 a) = V_V4 !Int (U.Vector a)-data instance U.MVector s (V4 a) = MV_V4 !Int (U.MVector s a)+data instance U.Vector (V4 a) = V_V4 {-# UNPACK #-} !Int !(U.Vector a)+data instance U.MVector s (V4 a) = MV_V4 {-# UNPACK #-} !Int !(U.MVector s a) instance U.Unbox a => U.Unbox (V4 a) instance U.Unbox a => M.MVector U.MVector (V4 a) where@@ -319,6 +569,7 @@ M.basicUnsafeWrite v (o+1) y M.basicUnsafeWrite v (o+2) z M.basicUnsafeWrite v (o+3) w+ basicInitialize (MV_V4 _ v) = M.basicInitialize v instance U.Unbox a => G.Vector U.Vector (V4 a) where basicUnsafeFreeze (MV_V4 n v) = liftM ( V_V4 n) (G.basicUnsafeFreeze v)@@ -341,3 +592,67 @@ (let V4 _ a _ _ = f a in a) (let V4 _ _ a _ = f a in a) (let V4 _ _ _ a = f a in a)++instance Bounded a => Bounded (V4 a) where+ minBound = pure minBound+ {-# INLINE minBound #-}+ maxBound = pure maxBound+ {-# INLINE maxBound #-}++instance NFData a => NFData (V4 a) where+ rnf (V4 a b c d) = rnf a `seq` rnf b `seq` rnf c `seq` rnf d++instance Serial1 V4 where+ serializeWith = traverse_+ deserializeWith k = V4 <$> k <*> k <*> k <*> k++instance Serial a => Serial (V4 a) where+ serialize = serializeWith serialize+ deserialize = deserializeWith deserialize++instance Binary a => Binary (V4 a) where+ put = serializeWith Binary.put+ get = deserializeWith Binary.get++instance Serialize a => Serialize (V4 a) where+ put = serializeWith Cereal.put+ get = deserializeWith Cereal.get++instance Eq1 V4 where+ liftEq k (V4 a b c d) (V4 e f g h) = k a e && k b f && k c g && k d h+instance Ord1 V4 where+ liftCompare k (V4 a b c d) (V4 e f g h) = k a e `mappend` k b f `mappend` k c g `mappend` k d h+instance Read1 V4 where+ liftReadsPrec k _ z = readParen (z > 10) $ \r ->+ [ (V4 a b c d, r5)+ | ("V4",r1) <- lex r+ , (a,r2) <- k 11 r1+ , (b,r3) <- k 11 r2+ , (c,r4) <- k 11 r3+ , (d,r5) <- k 11 r4+ ]+instance Show1 V4 where+ liftShowsPrec f _ z (V4 a b c d) = showParen (z > 10) $+ showString "V4 " . f 11 a . showChar ' ' . f 11 b . showChar ' ' . f 11 c . showChar ' ' . f 11 d++instance Field1 (V4 a) (V4 a) a a where+ _1 f (V4 x y z w) = f x <&> \x' -> V4 x' y z w++instance Field2 (V4 a) (V4 a) a a where+ _2 f (V4 x y z w) = f y <&> \y' -> V4 x y' z w++instance Field3 (V4 a) (V4 a) a a where+ _3 f (V4 x y z w) = f z <&> \z' -> V4 x y z' w++instance Field4 (V4 a) (V4 a) a a where+ _4 f (V4 x y z w) = f w <&> \w' -> V4 x y z w'++instance Semigroup a => Semigroup (V4 a) where+ (<>) = liftA2 (<>)++instance Monoid a => Monoid (V4 a) where+ mempty = pure mempty+#if !(MIN_VERSION_base(4,11,0))+ mappend = liftA2 mappend+#endif+
src/Linear/Vector.hs view
@@ -2,15 +2,13 @@ {-# LANGUAGE TypeOperators #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE RankNTypes #-}+{-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE TypeFamilies #-}-#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702 {-# LANGUAGE Trustworthy #-} {-# LANGUAGE DefaultSignatures #-}-#define USE_GHC_GENERICS-#endif ----------------------------------------------------------------------------- -- |--- Copyright : (C) 2012 Edward Kmett+-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- Maintainer : Edward Kmett <ekmett@gmail.com> -- Stability : provisional@@ -28,7 +26,7 @@ , sumV , basis , basisFor- , kronecker+ , scaled , outer , unit ) where@@ -36,18 +34,17 @@ import Control.Applicative import Control.Lens import Data.Complex-import Data.Foldable as Foldable (Foldable, forM_, foldl')+import Data.Foldable as Foldable (forM_, foldl')+import Data.Functor.Compose+import Data.Functor.Product import Data.HashMap.Lazy as HashMap import Data.Hashable import Data.IntMap as IntMap import Data.Map as Map-import Data.Monoid (mempty)-import Data.Traversable (mapAccumL)-import Data.Vector as Vector-import Data.Vector.Mutable as Mutable-#ifdef USE_GHC_GENERICS+import qualified Data.Vector as Vector+import Data.Vector (Vector)+import qualified Data.Vector.Mutable as Mutable import GHC.Generics-#endif import Linear.Instances () -- $setup@@ -59,7 +56,6 @@ infixl 6 ^+^, ^-^ infixl 7 ^*, *^, ^/ -#ifdef USE_GHC_GENERICS class GAdditive f where gzero :: Num a => f a gliftU2 :: (a -> a -> a) -> f a -> f a -> f a@@ -81,6 +77,14 @@ gliftI2 f (a :*: b) (c :*: d) = gliftI2 f a c :*: gliftI2 f b d {-# INLINE gliftI2 #-} +instance (Additive f, GAdditive g) => GAdditive (f :.: g) where+ gzero = Comp1 $ gzero <$ (zero :: f Int)+ {-# INLINE gzero #-}+ gliftU2 f (Comp1 a) (Comp1 b) = Comp1 $ liftU2 (gliftU2 f) a b+ {-# INLINE gliftU2 #-}+ gliftI2 f (Comp1 a) (Comp1 b) = Comp1 $ liftI2 (gliftI2 f) a b+ {-# INLINE gliftI2 #-}+ instance Additive f => GAdditive (Rec1 f) where gzero = Rec1 zero {-# INLINE gzero #-}@@ -103,49 +107,39 @@ {-# INLINE gliftU2 #-} gliftI2 f (Par1 a) (Par1 b) = Par1 (f a b) {-# INLINE gliftI2 #-}-#endif - -- | A vector is an additive group with additional structure. class Functor f => Additive f where -- | The zero vector zero :: Num a => f a-#ifdef USE_GHC_GENERICS #ifndef HLINT default zero :: (GAdditive (Rep1 f), Generic1 f, Num a) => f a zero = to1 gzero #endif-#endif -- | Compute the sum of two vectors -- -- >>> V2 1 2 ^+^ V2 3 4 -- V2 4 6 (^+^) :: Num a => f a -> f a -> f a-#ifdef USE_GHC_GENERICS-#ifndef HLINT- default (^+^) :: Num a => f a -> f a -> f a (^+^) = liftU2 (+) {-# INLINE (^+^) #-}-#endif-#endif -- | Compute the difference between two vectors --- -- >>> V2 4 5 - V2 3 1+ -- >>> V2 4 5 ^-^ V2 3 1 -- V2 1 4 (^-^) :: Num a => f a -> f a -> f a-#ifdef USE_GHC_GENERICS-#ifndef HLINT- default (^-^) :: Num a => f a -> f a -> f a x ^-^ y = x ^+^ negated y- {-# INLINE (^-^) #-}-#endif-#endif -- | Linearly interpolate between two vectors.+ --+ -- /Since linear version 1.23, interpolation direction has been reversed; now/+ --+ -- > lerp 0 a b == a+ -- > lerp 1 a b == b lerp :: Num a => a -> f a -> f a -> f a- lerp alpha u v = alpha *^ u ^+^ (1 - alpha) *^ v+ lerp alpha u v = (1 - alpha) *^ u ^+^ alpha *^ v {-# INLINE lerp #-} -- | Apply a function to merge the 'non-zero' components of two vectors, unioning the rest of the values.@@ -154,13 +148,11 @@ -- -- * For a sparse vector this is equivalent to 'unionWith'. liftU2 :: (a -> a -> a) -> f a -> f a -> f a-#ifdef USE_GHC_GENERICS #ifndef HLINT default liftU2 :: Applicative f => (a -> a -> a) -> f a -> f a -> f a liftU2 = liftA2 {-# INLINE liftU2 #-} #endif-#endif -- | Apply a function to the components of two vectors. --@@ -168,14 +160,32 @@ -- -- * For a sparse vector this is equivalent to 'intersectionWith'. liftI2 :: (a -> b -> c) -> f a -> f b -> f c-#ifdef USE_GHC_GENERICS #ifndef HLINT default liftI2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c liftI2 = liftA2 {-# INLINE liftI2 #-} #endif-#endif +instance (Additive f, Additive g) => Additive (Product f g) where+ zero = Pair zero zero+ liftU2 f (Pair a b) (Pair c d) = Pair (liftU2 f a c) (liftU2 f b d)+ liftI2 f (Pair a b) (Pair c d) = Pair (liftI2 f a c) (liftI2 f b d)+ Pair a b ^+^ Pair c d = Pair (a ^+^ c) (b ^+^ d)+ Pair a b ^-^ Pair c d = Pair (a ^-^ c) (b ^-^ d)+ lerp alpha (Pair a b) (Pair c d) = Pair (lerp alpha a c) (lerp alpha b d)++instance (Additive f, Additive g) => Additive (Compose f g) where+ zero = Compose $ zero <$ (zero :: f Int)+ {-# INLINE zero #-}+ Compose a ^+^ Compose b = Compose $ liftU2 (^+^) a b+ {-# INLINE (^+^) #-}+ Compose a ^-^ Compose b = Compose $ liftU2 (^-^) a b+ {-# INLINE (^-^) #-}+ liftU2 f (Compose a) (Compose b) = Compose $ liftU2 (liftU2 f) a b+ {-# INLINE liftU2 #-}+ liftI2 f (Compose a) (Compose b) = Compose $ liftI2 (liftI2 f) a b+ {-# INLINE liftI2 #-}+ instance Additive ZipList where zero = ZipList [] {-# INLINE zero #-}@@ -183,34 +193,22 @@ {-# INLINE liftU2 #-} liftI2 = liftA2 {-# INLINE liftI2 #-}-#ifndef USE_GHC_GENERICS- (^+^) = liftU2 (+)- {-# INLINE (^+^) #-}- x ^-^ y = x ^+^ negated y- {-# INLINE (^-^) #-}-#endif instance Additive Vector where zero = mempty {-# INLINE zero #-} liftU2 f u v = case compare lu lv of LT | lu == 0 -> v- | otherwise -> modify (\ w -> Foldable.forM_ [0..lu-1] $ \i -> unsafeWrite w i $ f (unsafeIndex u i) (unsafeIndex v i)) v+ | otherwise -> Vector.modify (\ w -> Foldable.forM_ [0..lu-1] $ \i -> Mutable.unsafeWrite w i $ f (Vector.unsafeIndex u i) (Vector.unsafeIndex v i)) v EQ -> Vector.zipWith f u v GT | lv == 0 -> u- | otherwise -> modify (\ w -> Foldable.forM_ [0..lv-1] $ \i -> unsafeWrite w i $ f (unsafeIndex u i) (unsafeIndex v i)) u+ | otherwise -> Vector.modify (\ w -> Foldable.forM_ [0..lv-1] $ \i -> Mutable.unsafeWrite w i $ f (Vector.unsafeIndex u i) (Vector.unsafeIndex v i)) u where lu = Vector.length u lv = Vector.length v {-# INLINE liftU2 #-} liftI2 = Vector.zipWith {-# INLINE liftI2 #-}-#ifndef USE_GHC_GENERICS- (^+^) = liftU2 (+)- {-# INLINE (^+^) #-}- x ^-^ y = x ^+^ negated y- {-# INLINE (^-^) #-}-#endif instance Additive Maybe where zero = Nothing@@ -221,12 +219,6 @@ {-# INLINE liftU2 #-} liftI2 = liftA2 {-# INLINE liftI2 #-}-#ifndef USE_GHC_GENERICS- (^+^) = liftU2 (+)- {-# INLINE (^+^) #-}- x ^-^ y = x ^+^ negated y- {-# INLINE (^-^) #-}-#endif instance Additive [] where zero = []@@ -238,12 +230,6 @@ {-# INLINE liftU2 #-} liftI2 = Prelude.zipWith {-# INLINE liftI2 #-}-#ifndef USE_GHC_GENERICS- (^+^) = liftU2 (+)- {-# INLINE (^+^) #-}- x ^-^ y = x ^+^ negated y- {-# INLINE (^-^) #-}-#endif instance Additive IntMap where zero = IntMap.empty@@ -252,12 +238,6 @@ {-# INLINE liftU2 #-} liftI2 = IntMap.intersectionWith {-# INLINE liftI2 #-}-#ifndef USE_GHC_GENERICS- (^+^) = liftU2 (+)- {-# INLINE (^+^) #-}- x ^-^ y = x ^+^ negated y- {-# INLINE (^-^) #-}-#endif instance Ord k => Additive (Map k) where zero = Map.empty@@ -266,12 +246,6 @@ {-# INLINE liftU2 #-} liftI2 = Map.intersectionWith {-# INLINE liftI2 #-}-#ifndef USE_GHC_GENERICS- (^+^) = liftU2 (+)- {-# INLINE (^+^) #-}- x ^-^ y = x ^+^ negated y- {-# INLINE (^-^) #-}-#endif instance (Eq k, Hashable k) => Additive (HashMap k) where zero = HashMap.empty@@ -280,12 +254,6 @@ {-# INLINE liftU2 #-} liftI2 = HashMap.intersectionWith {-# INLINE liftI2 #-}-#ifndef USE_GHC_GENERICS- (^+^) = liftU2 (+)- {-# INLINE (^+^) #-}- x ^-^ y = x ^+^ negated y- {-# INLINE (^-^) #-}-#endif instance Additive ((->) b) where zero = const 0@@ -294,12 +262,6 @@ {-# INLINE liftU2 #-} liftI2 = liftA2 {-# INLINE liftI2 #-}-#ifndef USE_GHC_GENERICS- (^+^) = liftU2 (+)- {-# INLINE (^+^) #-}- x ^-^ y = x ^+^ negated y- {-# INLINE (^-^) #-}-#endif instance Additive Complex where zero = 0 :+ 0@@ -308,12 +270,6 @@ {-# INLINE liftU2 #-} liftI2 f (a :+ b) (c :+ d) = f a c :+ f b d {-# INLINE liftI2 #-}-#ifndef USE_GHC_GENERICS- (^+^) = liftU2 (+)- {-# INLINE (^+^) #-}- x ^-^ y = x ^+^ negated y- {-# INLINE (^-^) #-}-#endif instance Additive Identity where zero = Identity 0@@ -322,12 +278,6 @@ {-# INLINE liftU2 #-} liftI2 = liftA2 {-# INLINE liftI2 #-}-#ifndef USE_GHC_GENERICS- (^+^) = liftU2 (+)- {-# INLINE (^+^) #-}- x ^-^ y = x ^+^ negated y- {-# INLINE (^-^) #-}-#endif -- | Compute the negation of a vector --@@ -366,39 +316,38 @@ f ^/ a = fmap (/a) f {-# INLINE (^/) #-} --- `SetOne` builds all combinations of the filler with one value from the choices list.-data SetOne a = SetOne { _filler :: !a, choices :: [a] }-instance Functor SetOne where- fmap f (SetOne a os) = SetOne (f a) (fmap f os)-instance Applicative SetOne where- pure a = SetOne a []- SetOne f fs <*> SetOne a as = SetOne (f a) (Prelude.foldr ((:) . ($ a)) (Prelude.map f as) fs)- -- | Produce a default basis for a vector space. If the dimensionality -- of the vector space is not statically known, see 'basisFor'.-basis :: (Applicative t, Traversable t, Num a) => [t a]-basis = choices $ traverse (\a -> SetOne 0 [a]) (pure 1)+basis :: (Additive t, Traversable t, Num a) => [t a]+basis = basisFor (zero :: Additive v => v Int) -- | Produce a default basis for a vector space from which the -- argument is drawn. basisFor :: (Traversable t, Num a) => t b -> [t a]-basisFor = choices . traverse (\_ -> SetOne 0 [1])+basisFor = \t ->+ ifoldMapOf traversed ?? t $ \i _ ->+ return $+ iover traversed ?? t $ \j _ ->+ if i == j then 1 else 0+{-# INLINABLE basisFor #-} --- | Produce a diagonal matrix from a vector.-kronecker :: (Traversable t, Num a) => t a -> t (t a)-kronecker v = fillFromList (choices $ traverse (\a -> SetOne 0 [a]) v) v+-- | Produce a diagonal (scale) matrix from a vector.+--+-- >>> scaled (V2 2 3)+-- V2 (V2 2 0) (V2 0 3)+scaled :: (Traversable t, Num a) => t a -> t (t a)+scaled = \t -> iter t (\i x -> iter t (\j _ -> if i == j then x else 0))+ where+ iter :: Traversable t => t a -> (Int -> a -> b) -> t b+ iter x f = iover traversed f x+{-# INLINE scaled #-} -- | Create a unit vector. -- -- >>> unit _x :: V2 Int -- V2 1 0-unit :: (Applicative t, Num a) => ASetter' (t a) a -> t a-unit l = set' l 1 (pure 0)--fillFromList :: Traversable t => [a] -> t b -> t a-fillFromList l = snd . mapAccumL aux l- where aux (a:as) _ = (as, a)- aux [] _ = error "too few elements in takeFromList"+unit :: (Additive t, Num a) => ASetter' (t a) a -> t a+unit l = set' l 1 zero -- | Outer (tensor) product of two vectors outer :: (Functor f, Functor g, Num a) => f a -> g a -> f (g a)
− tests/Binary.hs
@@ -1,19 +0,0 @@-module Binary (tests) where-import Control.Applicative-import Data.Binary.Put-import Data.Binary.Get-import Linear-import qualified Data.ByteString.Lazy as BS-import Test.HUnit--originalVecs :: (V3 Float, V2 Char)-originalVecs = (V3 1 2 3, V2 'a' 'b')--bytes :: BS.ByteString-bytes = runPut $ do putLinear $ fst originalVecs- putLinear $ snd originalVecs--tests :: Test-tests = test [ "Serialized length" ~: BS.length bytes ~?= 3*13+2- , "Deserialization" ~: deserialized ~?= originalVecs ]- where deserialized = runGet ((,) <$> getLinear <*> getLinear) bytes
− tests/Plucker.hs
@@ -1,34 +0,0 @@-module Plucker (tests) where-import Linear-import Linear.Plucker-import Test.HUnit--ln2,ln3,ln4,ln5,ln6,ln7,ln8,ln9 :: Plucker Float-ln2 = plucker3D (V3 1 3 0) (V3 1 3 (-2)) -- starting line-ln3 = plucker3D (V3 2 3 0) (V3 2 3 (-2)) -- parallel-ln4 = plucker3D (V3 2 4 0) (V3 1 4 (-2)) -- ccw-ln5 = plucker3D (V3 (-2) 4 0) (V3 2 4 (-2)) -- cw-ln6 = plucker3D (V3 2 3 0) (V3 1 3 (-2)) -- intersect-ln7 = plucker3D (V3 1 3 0) (V3 1 3 2) -- reversed-ln8 = plucker3D (V3 0 4 4) (V3 0 (-4) (-4)) -- through origin-ln9 = Plucker 1 2 3 4 5 6 -- not a 3D line--tests :: Test-tests = test [ "parallel" ~: parallel ln2 ln3 ~?= True- , "CCW" ~: passes ln2 ln4 ~?= Counterclockwise - , "CW" ~: passes ln2 ln5 ~?= Clockwise- , "intersect1" ~: intersects ln2 ln6 ~?= True - , "intersect2" ~: intersects ln2 ln3 ~?= False- , "line equality 1" ~: Line ln2 == Line ln2 ~?= True - , "line equality 2" ~: Line ln2 == Line ln7 ~?= True - , "line equality 3" ~: Line ln2 == Ray ln7 ~?= True- , "line equality 4" ~: Ray ln2 == Line ln7 ~?= True- , "ray equality 1" ~: Ray ln2 == Ray ln7 ~?= False- , "ray equality 2" ~: Ray ln2 == Ray (3 *^ ln2) ~?= True- , "ray equality 3" ~: Ray ln2 == Ray (negate ln7) ~?= True- , "quadrance" ~: nearZero (quadranceToOrigin ln2 - 10) ~?= True- , "closest 1" ~: - nearZero (qd (V3 1 3 0) $ closestToOrigin ln2) ~?= True- , "closest 2" ~: nearZero (qd 0 $ closestToOrigin ln8) ~?= True- , "isLine 1" ~: isLine ln2 ~?= True- , "isLine 2" ~: isLine ln9 ~?= False ]
+ tests/Prop/Quaternion.hs view
@@ -0,0 +1,28 @@+{-# OPTIONS_GHC -Wno-orphans #-}+module Prop.Quaternion (tests) where++import Linear.Quaternion (Quaternion(..))+import Linear.Epsilon (nearZero)+import Linear.Vector (lerp)+import Test.QuickCheck (Arbitrary(..))+import Test.Tasty (TestTree, testGroup)+import Test.Tasty.QuickCheck (testProperty)++import Prop.V3 ()++instance Arbitrary a => Arbitrary (Quaternion a) where+ arbitrary = Quaternion <$> arbitrary <*> arbitrary++prop_lerp0 :: Quaternion Double -> Quaternion Double -> Bool+prop_lerp0 a b = nearZero (lerp 0 a b - a)++prop_lerp1 :: Quaternion Double -> Quaternion Double -> Bool+prop_lerp1 a b = nearZero (lerp 1 a b - b)++tests :: [TestTree]+tests =+ [ testGroup "lerp"+ [ testProperty "lerp 0 a b == a" prop_lerp0+ , testProperty "lerp 1 a b == b" prop_lerp1+ ]+ ]
+ tests/Prop/V3.hs view
@@ -0,0 +1,8 @@+{-# OPTIONS_GHC -Wno-orphans #-}+module Prop.V3 () where++import Linear.V3 (V3(..))+import Test.QuickCheck (Arbitrary(..))++instance Arbitrary a => Arbitrary (V3 a) where+ arbitrary = V3 <$> arbitrary <*> arbitrary <*> arbitrary
+ tests/Test.hs view
@@ -0,0 +1,24 @@+{-# LANGUAGE CPP #-}+module Main (main) where++import Test.Tasty (defaultMain, testGroup, TestTree)++import qualified Prop.Quaternion+import qualified Unit.Binary+import qualified Unit.Plucker+import qualified Unit.V++tests :: [TestTree]+tests =+ [ testGroup "Property tests"+ [ testGroup "Quaternion" Prop.Quaternion.tests+ ]+ , testGroup "Unit tests"+ [ testGroup "Binary" Unit.Binary.tests+ , testGroup "Plucker" Unit.Plucker.tests+ , testGroup "V" Unit.V.tests+ ]+ ]++main :: IO ()+main = defaultMain $ testGroup "linear" tests
+ tests/Unit/Binary.hs view
@@ -0,0 +1,20 @@+module Unit.Binary (tests) where++import Data.Binary.Put+import Data.Binary.Get+import Linear+import qualified Data.ByteString.Lazy as BS+import Test.Tasty (TestTree)+import Test.Tasty.HUnit ((@?=), testCase)++originalVecs :: (V3 Float, V2 Char)+originalVecs = (V3 1 2 3, V2 'a' 'b')++bytes :: BS.ByteString+bytes = runPut $ do putLinear $ fst originalVecs+ putLinear $ snd originalVecs++tests :: [TestTree]+tests = [ testCase "Serialized length" $ BS.length bytes @?= 3*13+2+ , testCase "Deserialization" $ deserialized @?= originalVecs ]+ where deserialized = runGet ((,) <$> getLinear <*> getLinear) bytes
+ tests/Unit/Plucker.hs view
@@ -0,0 +1,36 @@+module Unit.Plucker (tests) where+import Linear+import Linear.Plucker+import Linear.Plucker.Coincides+import Test.Tasty (TestTree)+import Test.Tasty.HUnit ((@?=), testCase)++ln2,ln3,ln4,ln5,ln6,ln7,ln8,ln9 :: Plucker Float+ln2 = plucker3D (V3 1 3 0) (V3 1 3 (-2)) -- starting line+ln3 = plucker3D (V3 2 3 0) (V3 2 3 (-2)) -- parallel+ln4 = plucker3D (V3 2 4 0) (V3 1 4 (-2)) -- ccw+ln5 = plucker3D (V3 (-2) 4 0) (V3 2 4 (-2)) -- cw+ln6 = plucker3D (V3 2 3 0) (V3 1 3 (-2)) -- intersect+ln7 = plucker3D (V3 1 3 0) (V3 1 3 2) -- reversed+ln8 = plucker3D (V3 0 4 4) (V3 0 (-4) (-4)) -- through origin+ln9 = Plucker 1 2 3 4 5 6 -- not a 3D line++tests :: [TestTree]+tests = [ testCase "parallel" $ parallel ln2 ln3 @?= True+ , testCase "CCW" $ passes ln2 ln4 @?= Counterclockwise+ , testCase "CW" $ passes ln2 ln5 @?= Clockwise+ , testCase "intersect1" $ intersects ln2 ln6 @?= True+ , testCase "intersect2" $ intersects ln2 ln3 @?= False+ , testCase "line equality 1" $ Line ln2 == Line ln2 @?= True+ , testCase "line equality 2" $ Line ln2 == Line ln7 @?= True+ , testCase "line equality 3" $ Line ln2 == Ray ln7 @?= True+ , testCase "line equality 4" $ Ray ln2 == Line ln7 @?= True+ , testCase "ray equality 1" $ Ray ln2 == Ray ln7 @?= False+ , testCase "ray equality 2" $ Ray ln2 == Ray (3 *^ ln2) @?= True+ , testCase "ray equality 3" $ Ray ln2 == Ray (negate ln7) @?= True+ , testCase "quadrance" $ nearZero (quadranceToOrigin ln2 - 10) @?= True+ , testCase "closest 1" $+ nearZero (qd (V3 1 3 0) $ closestToOrigin ln2) @?= True+ , testCase "closest 2" $ nearZero (qd 0 $ closestToOrigin ln8) @?= True+ , testCase "isLine 1" $ isLine ln2 @?= True+ , testCase "isLine 2" $ isLine ln9 @?= False ]
+ tests/Unit/V.hs view
@@ -0,0 +1,14 @@+{-# LANGUAGE DataKinds #-}+module Unit.V (tests) where++import Control.DeepSeq (rnf)+import qualified Data.Vector.Unboxed as U (fromList)+import Linear.V (V)+import Test.Tasty (TestTree)+import Test.Tasty.HUnit ((@?=), testCase)++v10 :: V 10 Int+v10 = return 5++tests :: [TestTree]+tests = [ testCase "GH124" $ rnf (U.fromList [v10]) @?= () ]
− tests/UnitTests.hs
@@ -1,12 +0,0 @@-module Main (main) where-import Test.Framework (defaultMain, testGroup, Test)-import Test.Framework.Providers.HUnit-import qualified Plucker-import qualified Binary--tests :: [Test]-tests = [ testGroup "Plucker" $ hUnitTestToTests Plucker.tests - , testGroup "Binary" $ hUnitTestToTests Binary.tests ]--main :: IO ()-main = defaultMain tests
tests/doctests.hs view
@@ -1,30 +1,19 @@+-----------------------------------------------------------------------------+-- |+-- Module : Main (doctests)+-- Copyright : (C) 2012-14 Edward Kmett+-- License : BSD-style (see the file LICENSE)+-- Maintainer : Edward Kmett <ekmett@gmail.com>+-- Stability : provisional+-- Portability : portable+--+-- This module exists to add dependencies+----------------------------------------------------------------------------- module Main where -import Build_doctests (deps)-import Control.Applicative-import Control.Monad-import Data.List-import System.Directory-import System.FilePath-import Test.DocTest- main :: IO ()-main = getSources >>= \sources -> doctest $- "-isrc"- : "-idist/build/autogen"- : "-optP-include"- : "-optPdist/build/autogen/cabal_macros.h"- : "-hide-all-packages"- : map ("-package="++) deps ++ sources--getSources :: IO [FilePath]-getSources = filter (isSuffixOf ".hs") <$> go "src"- where- go dir = do- (dirs, files) <- getFilesAndDirectories dir- (files ++) . concat <$> mapM go dirs--getFilesAndDirectories :: FilePath -> IO ([FilePath], [FilePath])-getFilesAndDirectories dir = do- c <- map (dir </>) . filter (`notElem` ["..", "."]) <$> getDirectoryContents dir- (,) <$> filterM doesDirectoryExist c <*> filterM doesFileExist c+main = do+ putStrLn "This test-suite exists only to add dependencies"+ putStrLn "To run doctests: "+ putStrLn " cabal build all --enable-tests"+ putStrLn " cabal-docspec"
− travis/cabal-apt-install
@@ -1,27 +0,0 @@-#! /bin/bash-set -eu--APT="sudo apt-get -q -y"-CABAL_INSTALL_DEPS="cabal install --only-dependencies --force-reinstall"--$APT update-$APT install dctrl-tools--# Find potential system packages to satisfy cabal dependencies-deps()-{- local M='^\([^ ]\+\)-[0-9.]\+ (.*$'- local G=' -o ( -FPackage -X libghc-\L\1\E-dev )'- local E="$($CABAL_INSTALL_DEPS "$@" --dry-run -v 2> /dev/null \- | sed -ne "s/$M/$G/p" | sort -u)"- grep-aptavail -n -sPackage \( -FNone -X None \) $E | sort -u-}--$APT install $(deps "$@") libghc-quickcheck2-dev # QuickCheck is special-$CABAL_INSTALL_DEPS "$@" # Install the rest via Hackage--if ! $APT install hlint ; then- $APT install $(deps hlint)- cabal install hlint-fi-
− travis/config
@@ -1,16 +0,0 @@--- This provides a custom ~/.cabal/config file for use when hackage is down that should work on unix------ This is particularly useful for travis-ci to get it to stop complaining--- about a broken build when everything is still correct on our end.------ This uses Luite Stegeman's mirror of hackage provided by his 'hdiff' site instead------ To enable this, uncomment the before_script in .travis.yml--remote-repo: hdiff.luite.com:http://hdiff.luite.com/packages/archive-remote-repo-cache: ~/.cabal/packages-world-file: ~/.cabal/world-build-summary: ~/.cabal/logs/build.log-remote-build-reporting: anonymous-install-dirs user-install-dirs global