X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FPiecewise.hs;h=59af066db58dcd3a424f12576b76e7ae6998adad;hb=cc6e96512831fd319a185b1f5ef513a19b69c853;hp=cf71d05a6615081f1fed399df8ee4a5c2716f00c;hpb=ac19cda8bbd1d4ff05673892b9566e6ca2b367ea;p=numerical-analysis.git

diff --git a/src/Piecewise.hs b/src/Piecewise.hs
index cf71d05..59af066 100644
--- a/src/Piecewise.hs
+++ b/src/Piecewise.hs
@@ -4,13 +4,16 @@ module Piecewise (
   Piecewise(..),
   evaluate,
   evaluate',
-  from_intervals )
+  from_intervals,
+  list_plot' )
 where
 
 import qualified Algebra.Additive as Additive ( C )
+import qualified Algebra.Field as Field ( C )
 import Control.Arrow ( first )
+import Misc ( partition )
 import NumericPrelude
-import qualified Prelude as P
+import Prelude ()
 
 -- | A predicate is basically a function that returns True or
 --   False. In this case, the predicate is used to determine which
@@ -38,8 +41,8 @@ data Piecewise a =
 --   point and the result is returned wrapped in a 'Just'. If the
 --   point is outside of the domain, 'Nothing' is returned.
 evaluate :: Piecewise a -> a -> Maybe a
-evaluate (Piecewise pieces) x =
-  foldl f Nothing pieces
+evaluate (Piecewise ps) x =
+  foldl f Nothing ps
   where
     f (Just y) _ = Just y
     f Nothing (p,g) = if p x then Just (g x) else Nothing
@@ -77,3 +80,27 @@ from_intervals =
   where
     f :: (a,a) -> Predicate a
     f (x1,x2) x = x1 <= x && x <= x2
+
+
+-- | Plot a piecewise function over an interval @(x0,x1)@ using
+--   'evaluate''. Return the result a list of @(x,y)@ tuples.
+--
+--   Examples:
+--
+--   >>> let p1 = ((-1,0), \x -> -x) :: ((Double,Double), Double->Double)
+--   >>> let p2 = ((0,1), \x -> x) :: ((Double,Double), Double->Double)
+--   >>> let ivs = [p1, p2]
+--   >>> let pw = from_intervals ivs
+--   >>> list_plot' pw (-2) 2 4
+--   [(-2.0,0.0),(-1.0,1.0),(0.0,-0.0),(1.0,1.0),(2.0,0.0)]
+--
+list_plot' :: (Additive.C a, Field.C a)
+           => Piecewise a
+           -> a
+           -> a
+           -> Int
+           -> [(a,a)]
+list_plot' pw x0 x1 subintervals =
+  [ (x, evaluate' pw x) | x <- nodes ]
+  where
+    nodes = x0 : (map snd $ partition subintervals x0 x1)