From: Michael Orlitzky <michael@orlitzky.com>
Date: Thu, 21 Feb 2013 04:08:56 +0000 (-0500)
Subject: Fix compiler warnings and doctests.
X-Git-Url: http://gitweb.michael.orlitzky.com/?p=numerical-analysis.git;a=commitdiff_plain;h=2f54e89d36e835c58efcc281741632d457859b20

Fix compiler warnings and doctests.
---

diff --git a/src/BigFloat.hs b/src/BigFloat.hs
index 0bebab9..4c57aad 100644
--- a/src/BigFloat.hs
+++ b/src/BigFloat.hs
@@ -1,7 +1,8 @@
 {-# LANGUAGE RebindableSyntax #-}
 
 module BigFloat
-  (module Data.Number.BigFloat)
+  (module Data.Number.BigFloat,
+   R)
 where
 
 import Data.Number.BigFloat
diff --git a/src/Integration/Simpson.hs b/src/Integration/Simpson.hs
index c3d59ff..c9ad414 100644
--- a/src/Integration/Simpson.hs
+++ b/src/Integration/Simpson.hs
@@ -6,10 +6,7 @@ where
 import Misc (partition)
 
 import NumericPrelude hiding (abs)
-import Algebra.Absolute (abs)
-import qualified Algebra.Field as Field
 import qualified Algebra.RealField as RealField
-import qualified Algebra.RealRing as RealRing
 import qualified Algebra.ToInteger as ToInteger
 import qualified Algebra.ToRational as ToRational
 
@@ -26,6 +23,7 @@ import qualified Algebra.ToRational as ToRational
 --   >>> simpson_1 f (-1) 1
 --   0.0
 --
+--   >>> import Algebra.Absolute (abs)
 --   >>> let f x = x^2
 --   >>> let area = simpson_1 f (-1) 1
 --   >>> abs (area - (2/3)) < 1/10^12
@@ -56,6 +54,7 @@ simpson_1 f a b =
 --
 --   Examples:
 --
+--   >>> import Algebra.Absolute (abs)
 --   >>> let f x = x^4
 --   >>> let area = simpson 10 f (-1) 1
 --   >>> abs (area - (2/5)) < 0.0001
@@ -64,6 +63,7 @@ simpson_1 f a b =
 --   Note that the convergence here is much faster than the Trapezoid
 --   rule!
 --
+--   >>> import Algebra.Absolute (abs)
 --   >>> let area = simpson 10 sin 0 pi
 --   >>> abs (area - 2) < 0.00001
 --   True
diff --git a/src/Integration/Trapezoid.hs b/src/Integration/Trapezoid.hs
index c358fef..444d92d 100644
--- a/src/Integration/Trapezoid.hs
+++ b/src/Integration/Trapezoid.hs
@@ -6,10 +6,8 @@ where
 import Misc (partition)
 
 import NumericPrelude hiding (abs)
-import Algebra.Absolute (abs)
 import qualified Algebra.Field as Field
 import qualified Algebra.RealField as RealField
-import qualified Algebra.RealRing as RealRing
 import qualified Algebra.ToInteger as ToInteger
 import qualified Algebra.ToRational as ToRational
 
@@ -48,11 +46,13 @@ trapezoid_1 f a b =
 --
 --   Examples:
 --
+--   >>> import Algebra.Absolute (abs)
 --   >>> let f x = x^2
 --   >>> let area = trapezoid 1000 f (-1) 1
 --   >>> abs (area - (2/3)) < 0.00001
 --   True
 --
+--   >>> import Algebra.Absolute (abs)
 --   >>> let area = trapezoid 1000 sin 0 pi
 --   >>> abs (area - 2) < 0.0001
 --   True
diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs
index ef0e9b6..4f2e845 100644
--- a/src/Linear/Matrix.hs
+++ b/src/Linear/Matrix.hs
@@ -16,20 +16,16 @@ import Data.Vector.Fixed (
   Vector
   )
 import qualified Data.Vector.Fixed as V (
-  Fun(..),
   N1,
   and,
-  eq,
-  foldl,
   fromList,
   length,
   map,
-  maximum,
   replicate,
   toList,
   zipWith
   )
-import Data.Vector.Fixed.Internal (Arity, arity, S, Dim)
+import Data.Vector.Fixed.Internal (Arity, arity, S)
 import Linear.Vector
 import Normed
 
@@ -37,13 +33,9 @@ import NumericPrelude hiding ((*), abs)
 import qualified NumericPrelude as NP ((*))
 import qualified Algebra.Algebraic as Algebraic
 import Algebra.Algebraic (root)
-import qualified Algebra.Absolute as Absolute
 import qualified Algebra.Additive as Additive
 import qualified Algebra.Ring as Ring
-import Algebra.Absolute (abs)
-import qualified Algebra.Field as Field
 import qualified Algebra.Module as Module
-import qualified Algebra.RealField as RealField
 import qualified Algebra.RealRing as RealRing
 import qualified Algebra.ToRational as ToRational
 import qualified Algebra.Transcendental as Transcendental
@@ -294,7 +286,7 @@ instance (Ring.C a,
          => Ring.C (Mat v w a) where
   -- The first * is ring multiplication, the second is matrix
   -- multiplication.
-  m1 * m2 = m1 * m1
+  m1 * m2 = m1 * m2
 
 
 instance (Ring.C a,
@@ -359,13 +351,13 @@ instance (Algebraic.C a,
 --
 --   >>> import Roots.Simple
 --   >>> let h = 0.5 :: Double
---   >>> let g1 (Mat (D2 (D1 x) (D1 y))) = 1.0 + h*exp(-(x^2))/(1.0 + y^2)
---   >>> let g2 (Mat (D2 (D1 x) (D1 y))) = 0.5 + h*atan(x^2 + y^2)
+--   >>> let g1 (Mat (D2 (D1 x) (D1 y))) = 1.0 + h NP.* exp(-(x^2))/(1.0 + y^2)
+--   >>> let g2 (Mat (D2 (D1 x) (D1 y))) = 0.5 + h NP.* atan(x^2 + y^2)
 --   >>> let g u = vec2d ((g1 u), (g2 u))
 --   >>> let u0 = vec2d (1.0, 1.0)
 --   >>> let eps = 1/(10^9)
 --   >>> fixed_point g eps u0
---   (1.0728549599342185,1.0820591495686167)
+--   ((1.0728549599342185),(1.0820591495686167))
 --
 vec2d :: (a,a) -> Mat D2 D1 a
 vec2d (x,y) = Mat (D2 (D1 x) (D1 y))
diff --git a/src/Linear/Vector.hs b/src/Linear/Vector.hs
index d728334..aba9e5f 100644
--- a/src/Linear/Vector.hs
+++ b/src/Linear/Vector.hs
@@ -7,7 +7,6 @@
 module Linear.Vector
 where
 
-import Data.List (intercalate)
 import Data.Vector.Fixed (
   Dim,
   Fun(..),
@@ -24,8 +23,6 @@ import qualified Data.Vector.Fixed as V (
   length,
   )
 
-import Normed
-
 
 -- * Low-dimension vector wrappers.
 --
diff --git a/src/Normed.hs b/src/Normed.hs
index 3752edc..8b48295 100644
--- a/src/Normed.hs
+++ b/src/Normed.hs
@@ -13,7 +13,6 @@ import Algebra.Absolute (abs)
 import qualified Algebra.Absolute as Absolute
 import qualified Algebra.Algebraic as Algebraic
 import qualified Algebra.RealField as RealField
-import qualified Algebra.RealRing as RealRing
 import qualified Algebra.ToInteger as ToInteger
 
 -- Since the norm is defined on a vector space, we should be able to
diff --git a/src/ODE/IVP.hs b/src/ODE/IVP.hs
index b4fd3dc..615c668 100644
--- a/src/ODE/IVP.hs
+++ b/src/ODE/IVP.hs
@@ -14,7 +14,6 @@ where
 
 import Misc (partition)
 import NumericPrelude hiding (abs)
-import Algebra.Absolute (abs)
 import qualified Algebra.Field as Field
 import qualified Algebra.ToInteger as ToInteger
 import qualified Algebra.ToRational as ToRational
@@ -54,6 +53,7 @@ eulers_method1 x0 y0 f h =
 --
 --   Examples:
 --
+--   >>> import Algebra.Absolute (abs)
 --   >>> let x0 = 0.0
 --   >>> let xN = 1.0
 --   >>> let y0 = 1.0
diff --git a/src/Roots/Fast.hs b/src/Roots/Fast.hs
index 0deb1fd..b3b5818 100644
--- a/src/Roots/Fast.hs
+++ b/src/Roots/Fast.hs
@@ -16,7 +16,6 @@ import NumericPrelude hiding (abs)
 import qualified Algebra.Absolute as Absolute
 import qualified Algebra.Additive as Additive
 import qualified Algebra.Algebraic as Algebraic
-import qualified Algebra.Field as Field
 import qualified Algebra.RealRing as RealRing
 import qualified Algebra.RealField as RealField
 
@@ -118,7 +117,7 @@ fixed_point_iterations f x0 =
 --   We also return the number of iterations required.
 --
 fixed_point_with_iterations :: (Normed a,
-                                Algebraic.C a,
+                                Additive.C a,
                                 RealField.C b,
                                 Algebraic.C b)
                             => (a -> a)  -- ^ The function @f@ to iterate.
diff --git a/src/Roots/Simple.hs b/src/Roots/Simple.hs
index d3c10cd..414b777 100644
--- a/src/Roots/Simple.hs
+++ b/src/Roots/Simple.hs
@@ -18,7 +18,6 @@ import Normed
 import qualified Roots.Fast as F
 
 import NumericPrelude hiding (abs)
-import qualified Algebra.Absolute as Absolute
 import Algebra.Absolute (abs)
 import qualified Algebra.Additive as Additive
 import qualified Algebra.Algebraic as Algebraic
@@ -89,7 +88,7 @@ bisect f a b epsilon =
 --   at x0. We delegate to the version that returns the number of
 --   iterations and simply discard the number of iterations.
 --
-fixed_point :: (Normed a, Algebraic.C a, Algebraic.C b, RealField.C b)
+fixed_point :: (Normed a, Additive.C a, Algebraic.C b, RealField.C b)
             => (a -> a) -- ^ The function @f@ to iterate.
             -> b       -- ^ The tolerance, @epsilon@.
             -> a       -- ^ The initial value @x0@.
@@ -103,7 +102,7 @@ fixed_point f epsilon x0 =
 --   @epsilon@. We delegate to the version that returns the number of
 --   iterations and simply discard the fixed point.
 fixed_point_iteration_count :: (Normed a,
-                                Algebraic.C a,
+                                Additive.C a,
                                 RealField.C b,
                                 Algebraic.C b)
                             => (a -> a) -- ^ The function @f@ to iterate.