X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FRoots%2FFast.hs;h=b3b5818782fede0db3e6b465dc9186d8e29a1ca5;hb=d86da7a71b498a24b544ded9ad7191707fd0a123;hp=cda999ceab62a2fcc3b1f77e07560fb22403d6d3;hpb=ad7ad985ec59ac865483ce810603a43f180fc5ec;p=numerical-analysis.git

diff --git a/src/Roots/Fast.hs b/src/Roots/Fast.hs
index cda999c..b3b5818 100644
--- a/src/Roots/Fast.hs
+++ b/src/Roots/Fast.hs
@@ -1,3 +1,5 @@
+{-# LANGUAGE RebindableSyntax #-}
+
 -- | The Roots.Fast module contains faster implementations of the
 --   'Roots.Simple' algorithms. Generally, we will pass precomputed
 --   values to the next iteration of a function rather than passing
@@ -8,10 +10,18 @@ where
 
 import Data.List (find)
 
-import Vector
+import Normed
 
+import NumericPrelude hiding (abs)
+import qualified Algebra.Absolute as Absolute
+import qualified Algebra.Additive as Additive
+import qualified Algebra.Algebraic as Algebraic
+import qualified Algebra.RealRing as RealRing
+import qualified Algebra.RealField as RealField
 
-has_root :: (Fractional a, Ord a, Ord b, Num b)
+has_root :: (RealField.C a,
+             RealRing.C b,
+             Absolute.C b)
          => (a -> b) -- ^ The function @f@
          -> a       -- ^ The \"left\" endpoint, @a@
          -> a       -- ^ The \"right\" endpoint, @b@
@@ -51,8 +61,9 @@ has_root f a b epsilon f_of_a f_of_b =
     c = (a + b)/2
 
 
-
-bisect :: (Fractional a, Ord a, Num b, Ord b)
+bisect :: (RealField.C a,
+           RealRing.C b,
+           Absolute.C b)
        => (a -> b) -- ^ The function @f@ whose root we seek
        -> a       -- ^ The \"left\" endpoint of the interval, @a@
        -> a       -- ^ The \"right\" endpoint of the interval, @b@
@@ -88,6 +99,7 @@ bisect f a b epsilon f_of_a f_of_b
 
 
 
+
 -- | Iterate the function @f@ with the initial guess @x0@ in hopes of
 --   finding a fixed point.
 fixed_point_iterations :: (a -> a) -- ^ The function @f@ to iterate.
@@ -104,7 +116,10 @@ fixed_point_iterations f x0 =
 --
 --   We also return the number of iterations required.
 --
-fixed_point_with_iterations :: (Vector a, RealFrac b)
+fixed_point_with_iterations :: (Normed a,
+                                Additive.C a,
+                                RealField.C b,
+                                Algebraic.C b)
                             => (a -> a)  -- ^ The function @f@ to iterate.
                             -> b        -- ^ The tolerance, @epsilon@.
                             -> a        -- ^ The initial value @x0@.
@@ -115,7 +130,7 @@ fixed_point_with_iterations f epsilon x0 =
     xn = fixed_point_iterations f x0
     xn_plus_one = tail xn
 
-    abs_diff v w = norm_2 (v - w)
+    abs_diff v w = norm (v - w)
 
     -- The nth entry in this list is the absolute value of x_{n} -
     -- x_{n+1}.
@@ -133,4 +148,3 @@ fixed_point_with_iterations f epsilon x0 =
     -- "safe" since the list is infinite. We'll succeed or loop
     -- forever.
     Just winning_pair = find (\(_, diff) -> diff < epsilon) pairs
-