2 files changed, 621 insertions, 2 deletions

diff --git a/packages/base/src/Numeric/LinearAlgebra/Static.hs b/packages/base/src/Numeric/LinearAlgebra/Static/Internal.hs
index daf8d80..c9641d5 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Static.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Static/Internal.hs
@@ -14,14 +14,14 @@
 
 
 {- |
-Module      :  Numeric.LinearAlgebra.Static
+Module      :  Numeric.LinearAlgebra.Static.Internal
 Copyright   :  (c) Alberto Ruiz 2006-14
 License     :  BSD3
 Stability   :  provisional
 
 -}
 
-module Numeric.LinearAlgebra.Static where
+module Numeric.LinearAlgebra.Static.Internal where
 
 
 import GHC.TypeLits
diff --git a/packages/base/src/Numeric/LinearAlgebra/tmpStatic.hs b/packages/base/src/Numeric/LinearAlgebra/tmpStatic.hs
new file mode 100644
index 0000000..4258d6b
--- /dev/null
+++ b/packages/base/src/Numeric/LinearAlgebra/tmpStatic.hs
@@ -0,0 +1,619 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE KindSignatures #-}
+{-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE FunctionalDependencies #-}
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE EmptyDataDecls #-}
+{-# LANGUAGE Rank2Types #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE ViewPatterns #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE OverlappingInstances #-}
+{-# LANGUAGE TypeFamilies #-}
+
+
+{- |
+Module      :  Numeric.LinearAlgebra.Static
+Copyright   :  (c) Alberto Ruiz 2014
+License     :  BSD3
+Stability   :  experimental
+
+Experimental interface with statically checked dimensions.
+
+-}
+
+module Numeric.LinearAlgebra.Static(
+    -- * Vector
+    ℝ, R,
+    vec2, vec3, vec4, (&), (#), split, headTail,
+    vector,
+    linspace, range, dim,
+    -- * Matrix
+    L, Sq, build,
+    row, col, (¦),(——), splitRows, splitCols,
+    unrow, uncol,
+    tr,
+    eye,
+    diag,
+    blockAt,
+    matrix,
+    -- * Complex
+    C, M, Her, her, 𝑖,
+    -- * Products
+    (<>),(#>),(<·>),
+    -- * Linear Systems
+    linSolve, (<\>),
+    -- * Factorizations
+    svd, withCompactSVD, svdTall, svdFlat, Eigen(..),
+    withNullspace, qr,
+    -- * Misc
+    mean,
+    Disp(..), Domain(..),
+    withVector, withMatrix,
+    toRows, toColumns,
+    Sized(..), Diag(..), Sym, sym, mTm, unSym
+) where
+
+
+import GHC.TypeLits
+import Numeric.LinearAlgebra.HMatrix hiding (
+    (<>),(#>),(<·>),Konst(..),diag, disp,(¦),(——),row,col,vector,matrix,linspace,toRows,toColumns,
+    (<\>),fromList,takeDiag,svd,eig,eigSH,eigSH',eigenvalues,eigenvaluesSH,eigenvaluesSH',build,
+    qr)
+import qualified Numeric.LinearAlgebra.HMatrix as LA
+import Data.Proxy(Proxy)
+import Numeric.LinearAlgebra.Static.Internal
+import Control.Arrow((***))
+
+
+
+
+
+ud1 :: R n -> Vector ℝ
+ud1 (R (Dim v)) = v
+
+
+infixl 4 &
+(&) :: forall n . (KnownNat n, 1 <= n)
+    => R n -> ℝ -> R (n+1)
+u & x = u # (konst x :: R 1)
+
+infixl 4 #
+(#) :: forall n m . (KnownNat n, KnownNat m)
+    => R n -> R m -> R (n+m)
+(R u) # (R v) = R (vconcat u v)
+
+
+
+vec2 :: ℝ -> ℝ -> R 2
+vec2 a b = R (gvec2 a b)
+
+vec3 :: ℝ -> ℝ -> ℝ -> R 3
+vec3 a b c = R (gvec3 a b c)
+
+
+vec4 :: ℝ -> ℝ -> ℝ -> ℝ -> R 4
+vec4 a b c d = R (gvec4 a b c d)
+
+vector :: KnownNat n => [ℝ] -> R n
+vector = fromList
+
+matrix :: (KnownNat m, KnownNat n) => [ℝ] -> L m n
+matrix = fromList
+
+linspace :: forall n . KnownNat n => (ℝ,ℝ) -> R n
+linspace (a,b) = mkR (LA.linspace d (a,b))
+  where
+    d = fromIntegral . natVal $ (undefined :: Proxy n)
+
+range :: forall n . KnownNat n => R n
+range = mkR (LA.linspace d (1,fromIntegral d))
+  where
+    d = fromIntegral . natVal $ (undefined :: Proxy n)
+
+dim :: forall n . KnownNat n => R n
+dim = mkR (scalar d)
+  where
+    d = fromIntegral . natVal $ (undefined :: Proxy n)
+
+
+--------------------------------------------------------------------------------
+
+
+ud2 :: L m n -> Matrix ℝ
+ud2 (L (Dim (Dim x))) = x
+
+
+--------------------------------------------------------------------------------
+
+diag :: KnownNat n => R n -> Sq n
+diag = diagR 0
+
+eye :: KnownNat n => Sq n
+eye = diag 1
+
+--------------------------------------------------------------------------------
+
+blockAt :: forall m n . (KnownNat m, KnownNat n) =>  ℝ -> Int -> Int -> Matrix Double -> L m n
+blockAt x r c a = mkL res
+  where
+    z = scalar x
+    z1 = LA.konst x (r,c)
+    z2 = LA.konst x (max 0 (m'-(ra+r)), max 0 (n'-(ca+c)))
+    ra = min (rows a) . max 0 $ m'-r
+    ca = min (cols a) . max 0 $ n'-c
+    sa = subMatrix (0,0) (ra, ca) a
+    m' = fromIntegral . natVal $ (undefined :: Proxy m)
+    n' = fromIntegral . natVal $ (undefined :: Proxy n)
+    res = fromBlocks [[z1,z,z],[z,sa,z],[z,z,z2]]
+
+
+
+
+
+--------------------------------------------------------------------------------
+
+
+row :: R n -> L 1 n
+row = mkL . asRow . ud1
+
+--col :: R n -> L n 1
+col v = tr . row $ v
+
+unrow :: L 1 n -> R n
+unrow = mkR . head . LA.toRows . ud2
+
+--uncol :: L n 1 -> R n
+uncol v = unrow . tr $ v
+
+
+infixl 2 ——
+(——) :: (KnownNat r1, KnownNat r2, KnownNat c) => L r1 c -> L r2 c -> L (r1+r2) c
+a —— b = mkL (extract a LA.—— extract b)
+
+
+infixl 3 ¦
+-- (¦) :: (KnownNat r, KnownNat c1, KnownNat c2) => L r c1 -> L r c2 -> L r (c1+c2)
+a ¦ b = tr (tr a —— tr b)
+
+
+type Sq n  = L n n
+--type CSq n = CL n n
+
+type GL = (KnownNat n, KnownNat m) => L m n
+type GSq = KnownNat n => Sq n
+
+isKonst :: forall m n . (KnownNat m, KnownNat n) => L m n -> Maybe (ℝ,(Int,Int))
+isKonst (unwrap -> x)
+    | singleM x = Just (x `atIndex` (0,0), (m',n'))
+    | otherwise = Nothing
+  where
+    m' = fromIntegral . natVal $ (undefined :: Proxy m) :: Int
+    n' = fromIntegral . natVal $ (undefined :: Proxy n) :: Int
+
+
+isKonstC :: forall m n . (KnownNat m, KnownNat n) => M m n -> Maybe (ℂ,(Int,Int))
+isKonstC (unwrap -> x)
+    | singleM x = Just (x `atIndex` (0,0), (m',n'))
+    | otherwise = Nothing
+  where
+    m' = fromIntegral . natVal $ (undefined :: Proxy m) :: Int
+    n' = fromIntegral . natVal $ (undefined :: Proxy n) :: Int
+
+
+
+infixr 8 <>
+(<>) :: forall m k n. (KnownNat m, KnownNat k, KnownNat n) => L m k -> L k n -> L m n
+(<>) = mulR
+
+
+infixr 8 #>
+(#>) :: (KnownNat m, KnownNat n) => L m n -> R n -> R m
+(#>) = appR
+
+
+infixr 8 <·>
+(<·>) :: R n -> R n -> ℝ
+(<·>) = dotR
+
+--------------------------------------------------------------------------------
+
+class Diag m d | m -> d
+  where
+    takeDiag :: m -> d
+
+
+instance forall n . (KnownNat n) => Diag (L n n) (R n)
+  where
+    takeDiag m = mkR (LA.takeDiag (extract m))
+
+
+instance forall m n . (KnownNat m, KnownNat n, m <= n+1) => Diag (L m n) (R m)
+  where
+    takeDiag m = mkR (LA.takeDiag (extract m))
+
+
+instance forall m n . (KnownNat m, KnownNat n, n <= m+1) => Diag (L m n) (R n)
+  where
+    takeDiag m = mkR (LA.takeDiag (extract m))
+
+
+--------------------------------------------------------------------------------
+
+linSolve :: (KnownNat m, KnownNat n) => L m m -> L m n -> Maybe (L m n)
+linSolve (extract -> a) (extract -> b) = fmap mkL (LA.linearSolve a b)
+
+(<\>) :: (KnownNat m, KnownNat n, KnownNat r) => L m n -> L m r -> L n r
+(extract -> a) <\> (extract -> b) = mkL (a LA.<\> b)
+
+svd :: (KnownNat m, KnownNat n) => L m n -> (L m m, R n, L n n)
+svd (extract -> m) = (mkL u, mkR s', mkL v)
+  where
+    (u,s,v) = LA.svd m
+    s' = vjoin [s, z]
+    z = LA.konst 0 (max 0 (cols m - size s))
+
+
+svdTall :: (KnownNat m, KnownNat n, n <= m) => L m n -> (L m n, R n, L n n)
+svdTall (extract -> m) = (mkL u, mkR s, mkL v)
+  where
+    (u,s,v) = LA.thinSVD m
+
+
+svdFlat :: (KnownNat m, KnownNat n, m <= n) => L m n -> (L m m, R m, L n m)
+svdFlat (extract -> m) = (mkL u, mkR s, mkL v)
+  where
+    (u,s,v) = LA.thinSVD m
+
+--------------------------------------------------------------------------------
+
+class Eigen m l v | m -> l, m -> v
+  where
+    eigensystem :: m -> (l,v)
+    eigenvalues :: m -> l
+
+newtype Sym n = Sym (Sq n) deriving Show
+
+
+sym :: KnownNat n => Sq n -> Sym n
+sym m = Sym $ (m + tr m)/2
+
+mTm :: (KnownNat m, KnownNat n) => L m n -> Sym n
+mTm x = Sym (tr x <> x)
+
+unSym :: Sym n -> Sq n
+unSym (Sym x) = x
+
+
+𝑖 :: Sized ℂ s c => s
+𝑖 = konst iC
+
+newtype Her n = Her (M n n)
+
+her :: KnownNat n => M n n -> Her n
+her m = Her $ (m + LA.tr m)/2
+
+
+
+instance KnownNat n => Eigen (Sym n) (R n) (L n n)
+  where
+    eigenvalues (Sym (extract -> m)) =  mkR . LA.eigenvaluesSH' $ m
+    eigensystem (Sym (extract -> m)) = (mkR l, mkL v)
+      where
+        (l,v) = LA.eigSH' m
+
+instance KnownNat n => Eigen (Sq n) (C n) (M n n)
+  where
+    eigenvalues (extract -> m) = mkC . LA.eigenvalues $ m
+    eigensystem (extract -> m) = (mkC l, mkM v)
+      where
+        (l,v) = LA.eig m
+
+--------------------------------------------------------------------------------
+
+withNullspace
+    :: forall m n z . (KnownNat m, KnownNat n)
+    => L m n
+    -> (forall k . (KnownNat k) => L n k -> z)
+    -> z
+withNullspace (LA.nullspace . extract -> a) f =
+    case someNatVal $ fromIntegral $ cols a of
+       Nothing -> error "static/dynamic mismatch"
+       Just (SomeNat (_ :: Proxy k)) -> f (mkL a :: L n k)
+
+
+withCompactSVD
+    :: forall m n z . (KnownNat m, KnownNat n)
+    => L m n
+    -> (forall k . (KnownNat k) => (L m k, R k, L n k) -> z)
+    -> z
+withCompactSVD (LA.compactSVD . extract -> (u,s,v)) f =
+    case someNatVal $ fromIntegral $ size s of
+       Nothing -> error "static/dynamic mismatch"
+       Just (SomeNat (_ :: Proxy k)) -> f (mkL u :: L m k, mkR s :: R k, mkL v :: L n k)
+
+--------------------------------------------------------------------------------
+
+qr :: (KnownNat m, KnownNat n) => L m n -> (L m m, L m n)
+qr (extract -> x) = (mkL q, mkL r)
+  where
+    (q,r) = LA.qr x
+
+-- use qrRaw?
+
+--------------------------------------------------------------------------------
+
+split :: forall p n . (KnownNat p, KnownNat n, p<=n) => R n -> (R p, R (n-p))
+split (extract -> v) = ( mkR (subVector 0 p' v) ,
+                         mkR (subVector p' (size v - p') v) )
+  where
+    p' = fromIntegral . natVal $ (undefined :: Proxy p) :: Int
+
+
+headTail :: (KnownNat n, 1<=n) => R n -> (ℝ, R (n-1))
+headTail = ((!0) . extract *** id) . split
+
+
+splitRows :: forall p m n . (KnownNat p, KnownNat m, KnownNat n, p<=m) => L m n -> (L p n, L (m-p) n)
+splitRows (extract -> x) = ( mkL (takeRows p' x) ,
+                             mkL (dropRows p' x) )
+  where
+    p' = fromIntegral . natVal $ (undefined :: Proxy p) :: Int
+
+splitCols :: forall p m n. (KnownNat p, KnownNat m, KnownNat n, KnownNat (n-p), p<=n) => L m n -> (L m p, L m (n-p))
+splitCols = (tr *** tr) . splitRows . tr
+
+
+toRows :: forall m n . (KnownNat m, KnownNat n) => L m n -> [R n]
+toRows (LA.toRows . extract -> vs) = map mkR vs
+
+
+toColumns :: forall m n . (KnownNat m, KnownNat n) => L m n -> [R m]
+toColumns (LA.toColumns . extract -> vs) = map mkR vs
+
+
+--------------------------------------------------------------------------------
+
+build
+  :: forall m n . (KnownNat n, KnownNat m)
+    => (ℝ -> ℝ -> ℝ)
+    -> L m n
+build f = mkL $ LA.build (m',n') f
+  where
+    m' = fromIntegral . natVal $ (undefined :: Proxy m) :: Int
+    n' = fromIntegral . natVal $ (undefined :: Proxy n) :: Int
+
+--------------------------------------------------------------------------------
+
+withVector
+    :: forall z
+     . Vector ℝ
+    -> (forall n . (KnownNat n) => R n -> z)
+    -> z
+withVector v f =
+    case someNatVal $ fromIntegral $ size v of
+       Nothing -> error "static/dynamic mismatch"
+       Just (SomeNat (_ :: Proxy m)) -> f (mkR v :: R m)
+
+
+withMatrix
+    :: forall z
+     . Matrix ℝ
+    -> (forall m n . (KnownNat m, KnownNat n) => L m n -> z)
+    -> z
+withMatrix a f =
+    case someNatVal $ fromIntegral $ rows a of
+       Nothing -> error "static/dynamic mismatch"
+       Just (SomeNat (_ :: Proxy m)) ->
+           case someNatVal $ fromIntegral $ cols a of
+               Nothing -> error "static/dynamic mismatch"
+               Just (SomeNat (_ :: Proxy n)) ->
+                  f (mkL a :: L m n)
+
+--------------------------------------------------------------------------------
+
+class Domain field vec mat | mat -> vec field, vec -> mat field, field -> mat vec
+  where
+    mul :: forall m k n. (KnownNat m, KnownNat k, KnownNat n) => mat m k -> mat k n -> mat m n
+    app :: forall m n . (KnownNat m, KnownNat n) => mat m n -> vec n -> vec m
+    dot :: forall n . (KnownNat n) => vec n -> vec n -> field
+    cross :: vec 3 -> vec 3 -> vec 3
+    diagR ::  forall m n k . (KnownNat m, KnownNat n, KnownNat k) => field -> vec k -> mat m n
+
+
+instance Domain ℝ R L
+  where
+    mul = mulR
+    app = appR
+    dot = dotR
+    cross = crossR
+    diagR = diagRectR
+
+instance Domain ℂ C M
+  where
+    mul = mulC
+    app = appC
+    dot = dotC
+    cross = crossC
+    diagR = diagRectC
+
+--------------------------------------------------------------------------------
+
+mulR :: forall m k n. (KnownNat m, KnownNat k, KnownNat n) => L m k -> L k n -> L m n
+
+mulR (isKonst -> Just (a,(_,k))) (isKonst -> Just (b,_)) = konst (a * b * fromIntegral k)
+
+mulR (isDiag -> Just (0,a,_)) (isDiag -> Just (0,b,_)) = diagR 0 (mkR v :: R k)
+  where
+    v = a' * b'
+    n = min (size a) (size b)
+    a' = subVector 0 n a
+    b' = subVector 0 n b
+
+mulR (isDiag -> Just (0,a,_)) (extract -> b) = mkL (asColumn a * takeRows (size a) b)
+
+mulR (extract -> a) (isDiag -> Just (0,b,_)) = mkL (takeColumns (size b) a * asRow b)
+
+mulR a b = mkL (extract a LA.<> extract b)
+
+
+appR :: (KnownNat m, KnownNat n) => L m n -> R n -> R m
+appR (isDiag -> Just (0, w, _)) v = mkR (w * subVector 0 (size w) (extract v))
+appR m v = mkR (extract m LA.#> extract v)
+
+
+dotR :: R n -> R n -> ℝ
+dotR (ud1 -> u) (ud1 -> v)
+    | singleV u || singleV v = sumElements (u * v)
+    | otherwise = udot u v
+
+
+crossR :: R 3 -> R 3 -> R 3
+crossR (extract -> x) (extract -> y) = vec3 z1 z2 z3
+  where
+    z1 = x!1*y!2-x!2*y!1
+    z2 = x!2*y!0-x!0*y!2
+    z3 = x!0*y!1-x!1*y!0
+
+--------------------------------------------------------------------------------
+
+mulC :: forall m k n. (KnownNat m, KnownNat k, KnownNat n) => M m k -> M k n -> M m n
+
+mulC (isKonstC -> Just (a,(_,k))) (isKonstC -> Just (b,_)) = konst (a * b * fromIntegral k)
+
+mulC (isDiagC -> Just (0,a,_)) (isDiagC -> Just (0,b,_)) = diagR 0 (mkC v :: C k)
+  where
+    v = a' * b'
+    n = min (size a) (size b)
+    a' = subVector 0 n a
+    b' = subVector 0 n b
+
+mulC (isDiagC -> Just (0,a,_)) (extract -> b) = mkM (asColumn a * takeRows (size a) b)
+
+mulC (extract -> a) (isDiagC -> Just (0,b,_)) = mkM (takeColumns (size b) a * asRow b)
+
+mulC a b = mkM (extract a LA.<> extract b)
+
+
+appC :: (KnownNat m, KnownNat n) => M m n -> C n -> C m
+appC (isDiagC -> Just (0, w, _)) v = mkC (w * subVector 0 (size w) (extract v))
+appC m v = mkC (extract m LA.#> extract v)
+
+
+dotC :: KnownNat n => C n -> C n -> ℂ
+dotC (unwrap -> u) (unwrap -> v)
+    | singleV u || singleV v = sumElements (conj u * v)
+    | otherwise = u LA.<·> v
+
+
+crossC :: C 3 -> C 3 -> C 3
+crossC (extract -> x) (extract -> y) = mkC (LA.fromList [z1, z2, z3])
+  where
+    z1 = x!1*y!2-x!2*y!1
+    z2 = x!2*y!0-x!0*y!2
+    z3 = x!0*y!1-x!1*y!0
+
+--------------------------------------------------------------------------------
+
+diagRectR :: forall m n k . (KnownNat m, KnownNat n, KnownNat k) => ℝ -> R k -> L m n
+diagRectR x v = mkL (asRow (vjoin [scalar x, ev, zeros]))
+  where
+    ev = extract v
+    zeros = LA.konst x (max 0 ((min m' n') - size ev))
+    m' = fromIntegral . natVal $ (undefined :: Proxy m)
+    n' = fromIntegral . natVal $ (undefined :: Proxy n)
+
+
+diagRectC :: forall m n k . (KnownNat m, KnownNat n, KnownNat k) => ℂ -> C k -> M m n
+diagRectC x v = mkM (asRow (vjoin [scalar x, ev, zeros]))
+  where
+    ev = extract v
+    zeros = LA.konst x (max 0 ((min m' n') - size ev))
+    m' = fromIntegral . natVal $ (undefined :: Proxy m)
+    n' = fromIntegral . natVal $ (undefined :: Proxy n)
+
+--------------------------------------------------------------------------------
+
+mean :: (KnownNat n, 1<=n) => R n -> ℝ
+mean v = v <·> (1/dim)
+
+test :: (Bool, IO ())
+test = (ok,info)
+  where
+    ok =   extract (eye :: Sq 5) == ident 5
+           && (unwrap .unSym) (mTm sm :: Sym 3) == tr ((3><3)[1..]) LA.<> (3><3)[1..]
+           && unwrap (tm :: L 3 5) == LA.matrix 5 [1..15]
+           && thingS == thingD
+           && precS == precD
+           && withVector (LA.vector [1..15]) sumV == sumElements (LA.fromList [1..15])
+
+    info = do
+        print $ u
+        print $ v
+        print (eye :: Sq 3)
+        print $ ((u & 5) + 1) <·> v
+        print (tm :: L 2 5)
+        print (tm <> sm :: L 2 3)
+        print thingS
+        print thingD
+        print precS
+        print precD
+        print $ withVector (LA.vector [1..15]) sumV
+        splittest
+
+    sumV w = w <·> konst 1
+
+    u = vec2 3 5
+
+    𝕧 x = vector [x] :: R 1
+
+    v = 𝕧 2 & 4 & 7
+
+    tm :: GL
+    tm = lmat 0 [1..]
+
+    lmat :: forall m n . (KnownNat m, KnownNat n) => ℝ -> [ℝ] -> L m n
+    lmat z xs = mkL . reshape n' . LA.fromList . take (m'*n') $ xs ++ repeat z
+      where
+        m' = fromIntegral . natVal $ (undefined :: Proxy m)
+        n' = fromIntegral . natVal $ (undefined :: Proxy n)
+
+    sm :: GSq
+    sm = lmat 0 [1..]
+
+    thingS = (u & 1) <·> tr q #> q #> v
+      where
+        q = tm :: L 10 3
+
+    thingD = vjoin [ud1 u, 1] LA.<·> tr m LA.#> m LA.#> ud1 v
+      where
+        m = LA.matrix 3 [1..30]
+
+    precS = (1::Double) + (2::Double) * ((1 :: R 3) * (u & 6)) <·> konst 2 #> v
+    precD = 1 + 2 * vjoin[ud1 u, 6] LA.<·> LA.konst 2 (size (ud1 u) +1, size (ud1 v)) LA.#> ud1 v
+
+
+splittest
+    = do
+    let v = range :: R 7
+        a = snd (split v) :: R 4
+    print $ a
+    print $ snd . headTail . snd . headTail $ v
+    print $ first (vec3 1 2 3)
+    print $ second (vec3 1 2 3)
+    print $ third (vec3 1 2 3)
+    print $ (snd $ splitRows eye :: L 4 6)
+ where
+    first v = fst . headTail $ v
+    second v = first . snd . headTail $ v
+    third v = first . snd . headTail . snd . headTail $ v
+
+
+instance (KnownNat n', KnownNat m') => Testable (L n' m')
+  where
+    checkT _ = test
+
+