Clean up imports everywhere.

[numerical-analysis.git] / src / ODE / IVP.hs

diff --git a/src/ODE/IVP.hs b/src/ODE/IVP.hs
index d4876ded2dfe4994bdfb4c7841be7ef84d0a930a..6f798f46846a44ef4006145a440f87837cf0a2cc 100644 (file)
--- a/src/ODE/IVP.hs
+++ b/src/ODE/IVP.hs
@@ -1,4 +1,5 @@
 {-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE RebindableSyntax #-}
 
 -- | Numerical solution of the initial value problem,
 --
@@ -8,11 +9,18 @@
 --   for x in [x0, xN].
 --
 
-module ODE.IVP
+module ODE.IVP (
+  eulers_method,
+  eulers_method1,
+  eulers_methodH )
 where
 
-import Misc (partition)
-
+import Misc ( partition )
+import NumericPrelude hiding ( abs )
+import qualified Algebra.Field as Field ( C )
+import qualified Algebra.ToInteger as ToInteger ( C )
+import qualified Algebra.ToRational as ToRational ( C )
+import qualified Algebra.RealField as RealField ( C )
 
 -- | A single iteration of Euler's method over the interval
 --   [$x0$, $x0$+$h$].
@@ -26,7 +34,7 @@ import Misc (partition)
 --   >>> eulers_method1 x0 y0 f h
 --   2.0
 --
-eulers_method1 :: (RealFrac a, RealFrac b)
+eulers_method1 :: (Field.C a, ToRational.C a, Field.C b)
                => a -- ^ x0, the initial point
                -> b -- ^ y0, the initial value at x0
                -> (a -> b -> b) -- ^ The function f(x,y)
@@ -35,7 +43,7 @@ eulers_method1 :: (RealFrac a, RealFrac b)
 eulers_method1 x0 y0 f h =
   y0 +  h'*y'
   where
-    h' = fromRational $ toRational h
+    h' = fromRational'$ toRational h
     y' = (f x0 y0)
 
 
@@ -48,6 +56,7 @@ eulers_method1 x0 y0 f h =
 --
 --   Examples:
 --
+--   >>> import Algebra.Absolute (abs)
 --   >>> let x0 = 0.0
 --   >>> let xN = 1.0
 --   >>> let y0 = 1.0
@@ -59,7 +68,11 @@ eulers_method1 x0 y0 f h =
 --   >>> head ys == y0
 --   True
 --
-eulers_method :: forall a b c. (RealFrac a, RealFrac b, Integral c)
+eulers_method :: forall a b c. (Field.C a,
+                                ToRational.C a,
+                                Field.C b,
+                                ToInteger.C c,
+                                Enum c)
                => a -- ^ x0, the initial point
                -> b -- ^ y0, the initial value at x0
                -> a -- ^ xN, the terminal point
@@ -102,7 +115,7 @@ eulers_method x0 y0 xN f n =
 --   >>> ys == ys'
 --   True
 --
-eulers_methodH :: (RealFrac a, RealFrac b)
+eulers_methodH :: (RealField.C a, ToRational.C a, Field.C b)
                => a -- ^ x0, the initial point
                -> b -- ^ y0, the initial value at x0
                -> a -- ^ xN, the terminal point