Add a 2D fixed-point doctest (example) to Vector.hs.

Remove unused imports.

diff --git a/src/Matrix.hs b/src/Matrix.hs
index ea44ae968878ab1b5d1b02a7dd981e77f5446337..5b558448100c35d817a88c3ef4d4802a0709db01 100644 (file)
--- a/src/Matrix.hs
+++ b/src/Matrix.hs
@@ -9,7 +9,6 @@ where
 
 import Vector
 import Data.Vector.Fixed (
-  Arity(..),
   Dim,
   Vector,
   (!),

diff --git a/src/Vector.hs b/src/Vector.hs
index b42932c22d2058e685e3d6aa9cc2bb25422ca3cc..f55808b33f534283cf7ba432d667c72a6e565353 100644 (file)
--- a/src/Vector.hs
+++ b/src/Vector.hs
@@ -11,7 +11,6 @@ import Data.List (intercalate)
 import Data.Vector.Fixed (
   Dim,
   Fun(..),
-  N1,
   N2,
   N3,
   N4,
@@ -217,6 +216,20 @@ angle v1 v2 =
 -- constructors, so you can pattern match out the individual
 -- components.
 
+-- | Convenient constructor for 2D vectors.
+--
+--   Examples:
+--
+--   >>> import Roots.Simple
+--   >>> let h = 0.5 :: Double
+--   >>> let g1 (Vn (Vec2D x y)) = 1.0 + h*exp(-(x^2))/(1.0 + y^2)
+--   >>> let g2 (Vn (Vec2D x y)) = 0.5 + h*atan(x^2 + y^2)
+--   >>> let g u = make2d ((g1 u), (g2 u))
+--   >>> let u0 = make2d (1.0, 1.0)
+--   >>> let eps = 1/(10^9)
+--   >>> fixed_point g eps u0
+--   (1.0728549599342185,1.0820591495686167)
+--
 data Vec2D a = Vec2D a a
 type instance Dim Vec2D = N2
 instance Vector Vec2D a where