Remove assumptions on the Normed class.

[numerical-analysis.git] / src / Roots / Fast.hs

diff --git a/src/Roots/Fast.hs b/src/Roots/Fast.hs
index 5efdf3be99eec871931d18c6095333b8bd31ce83..0deb1fd6237a5909ea7d15a252f09b524093d1bf 100644 (file)
--- 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
@@ -10,8 +12,17 @@ import Data.List (find)
 
 import Normed
 
-
-has_root :: (Fractional a, Ord a, Ord b, Num b)
+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.Field as Field
+import qualified Algebra.RealRing as RealRing
+import qualified Algebra.RealField as RealField
+
+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 +62,9 @@ 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 +100,7 @@ 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 +117,10 @@ fixed_point_iterations f x0 =
 --
 --   We also return the number of iterations required.
 --
-fixed_point_with_iterations :: (Normed a, RealFrac b)
+fixed_point_with_iterations :: (Normed a,
+                                Algebraic.C a,
+                                RealField.C b,
+                                Algebraic.C b)
                             => (a -> a)  -- ^ The function @f@ to iterate.
                             -> b        -- ^ The tolerance, @epsilon@.
                             -> a        -- ^ The initial value @x0@.
@@ -133,4 +149,3 @@ 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
-