From 57bf4ffaa426358a03839a2b6e4075e7dc000d9f Mon Sep 17 00:00:00 2001
From: Alberto Ruiz <aruiz@um.es>
Date: Fri, 6 Jun 2014 20:01:57 +0200
Subject: norms

---
 packages/base/src/Numeric/HMatrix.hs              |  7 ++-
 packages/base/src/Numeric/LinearAlgebra/Util.hs   | 60 ++++++++++++++---------
 packages/tests/src/Numeric/LinearAlgebra/Tests.hs |  2 +-
 3 files changed, 40 insertions(+), 29 deletions(-)

diff --git a/packages/base/src/Numeric/HMatrix.hs b/packages/base/src/Numeric/HMatrix.hs
index 024e462..9d34658 100644
--- a/packages/base/src/Numeric/HMatrix.hs
+++ b/packages/base/src/Numeric/HMatrix.hs
@@ -121,8 +121,7 @@ module Numeric.HMatrix (
     orth,
 
     -- * Norms
-    norm_0, norm_1, norm_2, norm_Inf,
-    mnorm_0, mnorm_1, mnorm_2, mnorm_Inf,
+    Normed(..),
     norm_Frob, norm_nuclear,
 
     -- * Correlation and convolution
@@ -140,7 +139,7 @@ module Numeric.HMatrix (
     RealOf, ComplexOf, SingleOf, DoubleOf,
     IndexOf,
     Field,
-    Normed,
+--    Normed,
     Transposable,
     CGState(..),
     Testable(..),
@@ -152,7 +151,7 @@ import Numeric.LinearAlgebra.Data
 import Numeric.Matrix()
 import Numeric.Vector()
 import Data.Packed.Numeric hiding ((<>))
-import Numeric.LinearAlgebra.Algorithms hiding (linearSolve)
+import Numeric.LinearAlgebra.Algorithms hiding (linearSolve,Normed)
 import qualified Numeric.LinearAlgebra.Algorithms as A
 import Numeric.LinearAlgebra.Util
 import Numeric.LinearAlgebra.Random
diff --git a/packages/base/src/Numeric/LinearAlgebra/Util.hs b/packages/base/src/Numeric/LinearAlgebra/Util.hs
index aee21b8..324fb44 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Util.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Util.hs
@@ -33,8 +33,7 @@ module Numeric.LinearAlgebra.Util(
     cross,
     norm,
     ℕ,ℤ,ℝ,ℂ,𝑖,i_C, --ℍ
-    norm_1, norm_2, norm_0, norm_Inf, norm_Frob, norm_nuclear,
-    mnorm_1, mnorm_2, mnorm_0, mnorm_Inf,
+    Normed(..), norm_Frob, norm_nuclear,
     unitary,
     mt,
     (~!~),
@@ -61,7 +60,8 @@ module Numeric.LinearAlgebra.Util(
 ) where
 
 import Data.Packed.Numeric
-import Numeric.LinearAlgebra.Algorithms hiding (i)
+import Numeric.LinearAlgebra.Algorithms hiding (i,Normed)
+--import qualified Numeric.LinearAlgebra.Algorithms as A
 import Numeric.Matrix()
 import Numeric.Vector()
 import Numeric.LinearAlgebra.Random
@@ -225,37 +225,49 @@ norm :: Vector Double -> Double
 -- ^ 2-norm of real vector
 norm = pnorm PNorm2
 
-norm_2 :: Normed Vector t => Vector t -> RealOf t
-norm_2 = pnorm PNorm2
+class Normed a
+  where
+    norm_0   :: a -> ℝ
+    norm_1   :: a -> ℝ
+    norm_2   :: a -> ℝ
+    norm_Inf :: a -> ℝ
 
-norm_1 :: Normed Vector t => Vector t -> RealOf t
-norm_1 = pnorm PNorm1
 
-norm_Inf :: Normed Vector t => Vector t -> RealOf t
-norm_Inf = pnorm Infinity
+instance Normed (Vector ℝ)
+  where
+    norm_0 v = sumElements (step (abs v - scalar (eps*normInf v)))
+    norm_1 = pnorm PNorm1
+    norm_2 = pnorm PNorm2
+    norm_Inf = pnorm Infinity
 
-norm_0 :: Vector ℝ -> ℝ
-norm_0 v = sumElements (step (abs v - scalar (eps*mx)))
+instance Normed (Vector ℂ)
   where
-    mx = norm_Inf v
+    norm_0 v = sumElements (step (fst (fromComplex (abs v)) - scalar (eps*normInf v)))
+    norm_1 = pnorm PNorm1
+    norm_2 = pnorm PNorm2
+    norm_Inf = pnorm Infinity
 
-norm_Frob :: Normed Matrix t => Matrix t -> RealOf t
-norm_Frob = pnorm Frobenius
+instance Normed (Matrix ℝ)
+  where
+    norm_0 = norm_0 . flatten
+    norm_1 = pnorm PNorm1
+    norm_2 = pnorm PNorm2
+    norm_Inf = pnorm Infinity
 
-norm_nuclear :: Field t => Matrix t -> ℝ
-norm_nuclear = sumElements . singularValues
+instance Normed (Matrix ℂ)
+  where
+    norm_0 = norm_0 . flatten
+    norm_1 = pnorm PNorm1
+    norm_2 = pnorm PNorm2
+    norm_Inf = pnorm Infinity
 
-mnorm_2 :: Normed Matrix t => Matrix t -> RealOf t
-mnorm_2 = pnorm PNorm2
 
-mnorm_1 :: Normed Matrix t => Matrix t -> RealOf t
-mnorm_1 = pnorm PNorm1
+norm_Frob :: (Normed (Vector t), Element t) => Matrix t -> ℝ
+norm_Frob = norm_2 . flatten
 
-mnorm_Inf :: Normed Matrix t => Matrix t -> RealOf t
-mnorm_Inf = pnorm Infinity
+norm_nuclear :: Field t => Matrix t -> ℝ
+norm_nuclear = sumElements . singularValues
 
-mnorm_0 :: Matrix ℝ -> ℝ
-mnorm_0 = norm_0 . flatten
 
 -- | Obtains a vector in the same direction with 2-norm=1
 unitary :: Vector Double -> Vector Double
diff --git a/packages/tests/src/Numeric/LinearAlgebra/Tests.hs b/packages/tests/src/Numeric/LinearAlgebra/Tests.hs
index 02beb21..cd88a24 100644
--- a/packages/tests/src/Numeric/LinearAlgebra/Tests.hs
+++ b/packages/tests/src/Numeric/LinearAlgebra/Tests.hs
@@ -27,7 +27,7 @@ module Numeric.LinearAlgebra.Tests(
 ) where
 
 import Numeric.LinearAlgebra
-import Numeric.HMatrix hiding ((<>))
+import Numeric.HMatrix hiding ((<>),linearSolve)
 import Numeric.LinearAlgebra.Real(L)
 import Numeric.LinearAlgebra.Util(col,row)
 import Data.Packed
-- 
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