Clean up imports in FixedMatrix.hs.

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

diff --git a/src/ODE/IVP.hs b/src/ODE/IVP.hs
index 5d715a6356df5fd291c325a0b831ca469facb94e..d4876ded2dfe4994bdfb4c7841be7ef84d0a930a 100644 (file)
--- a/src/ODE/IVP.hs
+++ b/src/ODE/IVP.hs
@@ -56,6 +56,8 @@ eulers_method1 x0 y0 f h =
 --   >>> let yN = head $ reverse ys
 --   >>> abs ((exp 1) - yN) < 1/10^3
 --   True
+--   >>> head ys == y0
+--   True
 --
 eulers_method :: forall a b c. (RealFrac a, RealFrac b, Integral c)
                => a -- ^ x0, the initial point
@@ -65,19 +67,20 @@ eulers_method :: forall a b c. (RealFrac a, RealFrac b, Integral c)
                -> c -- ^ n, the number of intervals to use.
                -> [b]
 eulers_method x0 y0 xN f n =
-  go xs y0 f
+  y0 : go xs y0 f
   where
     xs = partition n x0 xN
 
     -- The 'go' function actually does all the work. It takes a list
-    -- of intervals [(x0,x1), (x1, x2)...] and peels off the first
+    -- of intervals [(v0,v1), (v1, v2)...] and peels off the first
     -- one. It then runs the single-step Euler's method on that
     -- interval, and afterwards recurses down the rest of the list.
+    --
     go :: [(a,a)] -> b -> (a -> b -> b) -> [b]
     go [] _ _ = []
-    go ((x0,x1):rest) y0 f = y1 : (go rest y1 f)
+    go ((v0,v1):rest) w0 g = w1 : (go rest w1 g)
       where
-        y1 = eulers_method1 x0 y0 f (x1 - x0)
+        w1 = eulers_method1 v0 w0 g (v1 - v0)
 
 
 -- | Perform as many iterations of Euler's method over the interval
@@ -109,4 +112,5 @@ eulers_methodH :: (RealFrac a, RealFrac b)
 eulers_methodH x0 y0 xN f h =
   eulers_method x0 y0 xN f n
   where
+    n :: Integer
     n = floor $ (xN - x0) / h