From 2addcfb5db6721b9520e8be9942278dfc17b7021 Mon Sep 17 00:00:00 2001
From: Alberto Ruiz <aruiz@um.es>
Date: Wed, 4 Jun 2014 18:49:50 +0200
Subject: complex instances

---
 packages/base/src/Numeric/LinearAlgebra/Real.hs   | 105 +++++++++++++++++-----
 packages/base/src/Numeric/LinearAlgebra/Static.hs |   6 +-
 2 files changed, 84 insertions(+), 27 deletions(-)

(limited to 'packages/base/src/Numeric')

diff --git a/packages/base/src/Numeric/LinearAlgebra/Real.hs b/packages/base/src/Numeric/LinearAlgebra/Real.hs
index 2ff69c7..d03ca6e 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Real.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Real.hs
@@ -45,7 +45,7 @@ module Numeric.LinearAlgebra.Real(
     -- * Linear Systems
     linSolve, (<\>),
     -- * Factorizations
-    svd, svdTall, svdFlat, eig,
+    svd, svdTall, svdFlat, Eigen(..),
     -- * Pretty printing
     Disp(..),
     -- * Misc
@@ -58,8 +58,9 @@ module Numeric.LinearAlgebra.Real(
 import GHC.TypeLits
 import Numeric.HMatrix hiding (
     (<>),(#>),(<·>),Konst(..),diag, disp,(¦),(——),row,col,vect,mat,linspace,
-    (<\>),fromList,takeDiag,svd,eig)
+    (<\>),fromList,takeDiag,svd,eig,eigSH,eigSH',eigenvalues,eigenvaluesSH,eigenvaluesSH')
 import qualified Numeric.HMatrix as LA
+import Data.Packed.Internal(mbCatch)
 import Data.Proxy(Proxy)
 import Numeric.LinearAlgebra.Static
 import Text.Printf
@@ -80,6 +81,8 @@ ud1 (R (Dim v)) = v
 mkR :: Vector ℝ -> R n
 mkR = R . Dim
 
+mkC :: Vector ℂ -> C n
+mkC = C . Dim
 
 infixl 4 &
 (&) :: forall n . KnownNat n
@@ -126,17 +129,17 @@ dim = mkR (scalar d)
 
 newtype L m n = L (Dim m (Dim n (Matrix ℝ)))
 
--- newtype CL m n = CL (Dim m (Dim n (Matrix  ℂ)))
+newtype M m n = M (Dim m (Dim n (Matrix  ℂ)))
 
 ud2 :: L m n -> Matrix ℝ
 ud2 (L (Dim (Dim x))) = x
 
 
-
-
 mkL :: Matrix ℝ -> L m n
 mkL x = L (Dim (Dim x))
 
+mkM :: Matrix ℂ -> M m n
+mkM x = M (Dim (Dim x))
 
 instance forall m n . (KnownNat m, KnownNat n) => Show (L m n)
   where
@@ -150,6 +153,18 @@ instance forall m n . (KnownNat m, KnownNat n) => Show (L m n)
 
 --------------------------------------------------------------------------------
 
+instance forall n. KnownNat n => Sized ℂ (C n) (Vector ℂ)
+  where
+    konst x = mkC (LA.scalar x)
+    unwrap (C (Dim v)) = v 
+    fromList xs = C (gvect "C" xs)
+    extract (unwrap -> v)
+      | singleV v = LA.konst (v!0) d
+      | otherwise = v
+     where
+       d = fromIntegral . natVal $ (undefined :: Proxy n)
+
+
 instance forall n. KnownNat n => Sized ℝ (R n) (Vector ℝ)
   where
     konst x = mkR (LA.scalar x)
@@ -162,11 +177,12 @@ instance forall n. KnownNat n => Sized ℝ (R n) (Vector ℝ)
        d = fromIntegral . natVal $ (undefined :: Proxy n)
 
 
+
 instance forall m n . (KnownNat m, KnownNat n) => Sized ℝ (L m n) (Matrix ℝ)
   where
     konst x = mkL (LA.scalar x)
-    unwrap = ud2
     fromList = mat
+    unwrap = ud2
     extract (isDiag -> Just (z,y,(m',n'))) = diagRect z y m' n'
     extract (unwrap -> a)
         | singleM a = LA.konst (a `atIndex` (0,0)) (m',n')
@@ -175,6 +191,20 @@ instance forall m n . (KnownNat m, KnownNat n) => Sized ℝ (L m n) (Matrix ℝ)
         m' = fromIntegral . natVal $ (undefined :: Proxy m)
         n' = fromIntegral . natVal $ (undefined :: Proxy n)
 
+
+instance forall m n . (KnownNat m, KnownNat n) => Sized ℂ (M m n) (Matrix ℂ)
+  where
+    konst x = mkM (LA.scalar x)
+    fromList xs = M (gmat "M" xs)
+    unwrap (M (Dim (Dim m))) = m
+    extract (isDiagC -> Just (z,y,(m',n'))) = diagRect z y m' n'
+    extract (unwrap -> a)
+        | singleM a = LA.konst (a `atIndex` (0,0)) (m',n')
+        | otherwise = a
+      where
+        m' = fromIntegral . natVal $ (undefined :: Proxy m)
+        n' = fromIntegral . natVal $ (undefined :: Proxy n)
+
 --------------------------------------------------------------------------------
 
 diagR :: forall m n k . (KnownNat m, KnownNat n, KnownNat k) => ℝ -> R k -> L m n
@@ -225,26 +255,41 @@ instance (KnownNat m, KnownNat n) => Disp (L m n)
         let su = LA.dispf n a
         printf "L %d %d" (rows a) (cols a) >> putStr (dropWhile (/='\n') $ su)
 
+instance (KnownNat m, KnownNat n) => Disp (M m n)
+  where
+    disp n x = do
+        let a = extract x
+        let su = LA.dispcf n a
+        printf "M %d %d" (rows a) (cols a) >> putStr (dropWhile (/='\n') $ su)
+
+
 instance KnownNat n => Disp (R n)
   where
     disp n v = do
         let su = LA.dispf n (asRow $ extract v)
         putStr "R " >> putStr (tail . dropWhile (/='x') $ su)
 
+instance KnownNat n => Disp (C n)
+  where
+    disp n v = do
+        let su = LA.dispcf n (asRow $ extract v)
+        putStr "C " >> putStr (tail . dropWhile (/='x') $ su)
+
+
 --------------------------------------------------------------------------------
 
 
 row :: R n -> L 1 n
 row = mkL . asRow . ud1
 
-col :: R n -> L n 1
-col = tr . row
+--col :: R n -> L n 1
+col v = tr . row $ v
 
 unrow :: L 1 n -> R n
 unrow = mkR . head . toRows . ud2
 
-uncol :: L n 1 -> R n
-uncol = unrow . tr
+--uncol :: L n 1 -> R n
+uncol v = unrow . tr $ v
 
 
 infixl 2 ——
@@ -253,7 +298,7 @@ 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)
+-- (¦) :: (KnownNat r, KnownNat c1, KnownNat c2) => L r c1 -> L r c2 -> L r (c1+c2)
 a ¦ b = tr (tr a —— tr b)
 
 
@@ -274,7 +319,14 @@ isKonst (unwrap -> x)
 
 
 isDiag :: forall m n . (KnownNat m, KnownNat n) => L m n -> Maybe (ℝ, Vector ℝ, (Int,Int))
-isDiag (unwrap -> x)
+isDiag (L x) = isDiagg x
+
+isDiagC :: forall m n . (KnownNat m, KnownNat n) => M m n -> Maybe (ℂ, Vector ℂ, (Int,Int))
+isDiagC (M x) = isDiagg x
+
+
+isDiagg :: forall m n t . (Numeric t, KnownNat m, KnownNat n) => GM m n t -> Maybe (t, Vector t, (Int,Int))
+isDiagg (Dim (Dim x))
     | singleM x = Nothing
     | rows x == 1 && m' > 1 || cols x == 1 && n' > 1 = Just (z,yz,(m',n'))
     | otherwise = Nothing  
@@ -282,7 +334,7 @@ isDiag (unwrap -> x)
     m' = fromIntegral . natVal $ (undefined :: Proxy m) :: Int
     n' = fromIntegral . natVal $ (undefined :: Proxy n) :: Int
     v = flatten x
-    z = v!0
+    z = v `atIndex` 0
     y = subVector 1 (size v-1) v
     ny = size y
     zeros = LA.konst 0 (max 0 (min m' n' - ny))
@@ -320,9 +372,10 @@ infixr 8 <·>
     | otherwise = udot u v
 
 
-instance Transposable (L m n) (L n m)
+instance (KnownNat n, KnownNat m) => Transposable (L m n) (L n m)
   where
-    tr (ud2 -> a) = mkL (tr a)
+    tr a@(isDiag -> Just _) = mkL (extract a)
+    tr (extract -> a) = mkL (tr a)
 
 --------------------------------------------------------------------------------
 
@@ -424,11 +477,12 @@ svdFlat (extract -> m) = (mkL u, mkR s, mkL v)
 
 --------------------------------------------------------------------------------
 
-class Eig m r | m -> r
+class Eigen m l v | m -> l, m -> v
   where
-    eig :: m -> r
+    eigensystem :: m -> (l,v)
+    eigenvalues :: m -> l
     
-newtype Sym n = Sym (Sq n)
+newtype Sym n = Sym (Sq n) deriving Show
 
 --newtype Her n = Her (CSq n)
 
@@ -438,16 +492,19 @@ sym m = Sym $ (m + tr m)/2
 --her :: KnownNat n => CSq n -> Her n
 --her = undefined -- Her $ (m + tr m)/2
 
-
-instance KnownNat n => Eig (Sym n) (R n, Sq n)
+instance KnownNat n => Eigen (Sym n) (R n) (L n n)
   where
-    eig (Sym (extract -> m)) = (mkR l, mkL v)
+    eigenvalues (Sym (extract -> m)) =  mkR . LA.eigenvaluesSH' $ m
+    eigensystem (Sym (extract -> m)) = (mkR l, mkL v)
       where
-        (l,v) = eigSH m
+        (l,v) = LA.eigSH' m
 
-instance KnownNat n => Eig (Sq n) (C n)
+instance KnownNat n => Eigen (Sq n) (C n) (M n n)
   where
-    eig (extract -> m) = C . Dim . eigenvalues $ m
+    eigenvalues (extract -> m) = mkC . LA.eigenvalues $ m
+    eigensystem (extract -> m) = (mkC l, mkM v)
+      where
+        (l,v) = LA.eig m
     
 --------------------------------------------------------------------------------
 
diff --git a/packages/base/src/Numeric/LinearAlgebra/Static.hs b/packages/base/src/Numeric/LinearAlgebra/Static.hs
index 5caf6f8..6acd9a3 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Static.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Static.hs
@@ -27,7 +27,7 @@ module Numeric.LinearAlgebra.Static(
     lift1F, lift2F,
     vconcat, gvec2, gvec3, gvec4, gvect, gmat,
     Sized(..),
-    singleV, singleM
+    singleV, singleM,GM
 ) where
 
 
@@ -105,7 +105,7 @@ ud (Dim v) = v
 mkV :: forall (n :: Nat) t . t -> Dim n t
 mkV = Dim 
 
-type M m n t = Dim m (Dim n (Matrix t))
+type GM m n t = Dim m (Dim n (Matrix t))
 
 --ud2 :: Dim m (Dim n (Matrix t)) -> Matrix t
 --ud2 (Dim (Dim m)) = m
@@ -166,7 +166,7 @@ gvect st xs'
     abort info = error $ st++" "++show d++" can't be created from elements "++info
 
 
-gmat :: forall m n t . (Show t, KnownNat m, KnownNat n, Numeric t) => String -> [t] -> M m n t
+gmat :: forall m n t . (Show t, KnownNat m, KnownNat n, Numeric t) => String -> [t] -> GM m n t
 gmat st xs'
     | ok = mkM x
     | not (null rest) && null (tail rest) = abort (show xs')
-- 
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