X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FRoots%2FSimple.hs;h=03b39aeb643de47ed6546693c26346851b80b0fc;hb=af25e6f32f6787a747be63093adc10915ad60068;hp=414b77787262e608ceef4a66981a5dc5ab82cc50;hpb=2f54e89d36e835c58efcc281741632d457859b20;p=numerical-analysis.git

diff --git a/src/Roots/Simple.hs b/src/Roots/Simple.hs
index 414b777..03b39ae 100644
--- a/src/Roots/Simple.hs
+++ b/src/Roots/Simple.hs
@@ -56,7 +56,7 @@ has_root f a b epsilon =
 
 
 -- | We are given a function @f@ and an interval [a,b]. The bisection
---   method checks finds a root by splitting [a,b] in half repeatedly.
+--   method finds a root by splitting [a,b] in half repeatedly.
 --
 --   If one is found within some prescribed tolerance @epsilon@, it is
 --   returned. Otherwise, the interval [a,b] is split into two
@@ -68,8 +68,12 @@ has_root f a b epsilon =
 --
 --   Examples:
 --
---   >>> bisect cos 1 2 0.001
---   Just 1.5712890625
+--   >>> let actual = 1.5707963267948966
+--   >>> let Just root = bisect cos 1 2 0.001
+--   >>> root
+--   1.5712890625
+--   >>> abs (root - actual) < 0.001
+--   True
 --
 --   >>> bisect sin (-1) 1 0.001
 --   Just 0.0
@@ -84,6 +88,40 @@ bisect f a b epsilon =
   F.bisect f a b epsilon Nothing Nothing
 
 
+-- | We are given a function @f@ and an interval [a,b]. The trisection
+--   method finds a root by splitting [a,b] into three
+--   subintervals repeatedly.
+--
+--   If one is found within some prescribed tolerance @epsilon@, it is
+--   returned. Otherwise, the interval [a,b] is split into two
+--   subintervals [a,c] and [c,b] of equal length which are then both
+--   checked via the same process.
+--
+--   Returns 'Just' the value x for which f(x) == 0 if one is found,
+--   or Nothing if one of the preconditions is violated.
+--
+--   Examples:
+--
+--   >>> let actual = 1.5707963267948966
+--   >>> let Just root = trisect cos 1 2 0.001
+--   >>> root
+--   1.5713305898491083
+--   >>> abs (root - actual) < 0.001
+--   True
+--
+--   >>> trisect sin (-1) 1 0.001
+--   Just 0.0
+--
+trisect :: (RealField.C a, RealRing.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@
+       -> a       -- ^ The tolerance, @epsilon@
+       -> Maybe a
+trisect f a b epsilon =
+  F.trisect f a b epsilon Nothing Nothing
+
+
 -- | Find a fixed point of the function @f@ with the search starting
 --   at x0. We delegate to the version that returns the number of
 --   iterations and simply discard the number of iterations.
@@ -157,8 +195,8 @@ newton_iterations :: (Field.C a)
                     -> (a -> a) -- ^ The derivative of @f@
                     -> a       -- ^ Initial guess, x-naught
                     -> [a]
-newton_iterations f f' x0 =
-  iterate next x0
+newton_iterations f f' =
+  iterate next
   where
   next xn =
     xn - ( (f xn) / (f' xn) )
@@ -242,8 +280,8 @@ secant_iterations :: (Field.C a)
                     -> a       -- ^ Initial guess, x-naught
                     -> a       -- ^ Second initial guess, x-one
                     -> [a]
-secant_iterations f x0 x1 =
-  iterate2 g x0 x1
+secant_iterations f =
+  iterate2 g
   where
   g prev2 prev1 =
     let x_change = prev1 - prev2