From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 2 Feb 2014 17:34:42 +0000 (-0500)
Subject: Add the Frobenius norm to Linear.Matrix.
X-Git-Url: http://gitweb.michael.orlitzky.com/?p=numerical-analysis.git;a=commitdiff_plain;h=af25e6f32f6787a747be63093adc10915ad60068

Add the Frobenius norm to Linear.Matrix.
---

diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs
index c0f56b3..66b22f9 100644
--- a/src/Linear/Matrix.hs
+++ b/src/Linear/Matrix.hs
@@ -2,6 +2,7 @@
 {-# LANGUAGE FlexibleContexts #-}
 {-# LANGUAGE FlexibleInstances #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE NoMonomorphismRestriction #-}
 {-# LANGUAGE ScopedTypeVariables #-}
 {-# LANGUAGE TypeFamilies #-}
 {-# LANGUAGE RebindableSyntax #-}
@@ -34,6 +35,7 @@ import Data.Vector.Fixed (
   )
 import qualified Data.Vector.Fixed as V (
   and,
+  foldl,
   fromList,
   head,
   length,
@@ -457,7 +459,31 @@ instance (Algebraic.C a,
     fromRational' $ toRational $ V.maximum $ V.map V.maximum rows
 
 
+-- | Compute the Frobenius norm of a matrix. This essentially treats
+--   the matrix as one long vector containing all of its entries (in
+--   any order, it doesn't matter).
+--
+--   Examples:
+--
+--   >>> let m = fromList [[1, 2, 3],[4,5,6],[7,8,9]] :: Mat3 Double
+--   >>> frobenius_norm m == sqrt 285
+--   True
+--
+--   >>> let m = fromList [[1, -1, 1],[-1,1,-1],[1,-1,1]] :: Mat3 Double
+--   >>> frobenius_norm m == 3
+--   True
+--
+frobenius_norm :: (Algebraic.C a, Ring.C a) => Mat m n a -> a
+frobenius_norm (Mat rows) =
+  sqrt $ vsum $ V.map row_sum rows
+  where
+    -- | The \"sum\" function defined in fixed-vector requires a 'Num'
+    --   constraint whereas we want to use the classes from
+    --   numeric-prelude.
+    vsum = V.foldl (+) (fromInteger 0)
 
+    -- | Square and add up the entries of a row.
+    row_sum = vsum . V.map (^2)
 
 
 -- Vector helpers. We want it to be easy to create low-dimension