X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FLinear%2FIteration.hs;h=6117770a52313c21546ed57e729854a7d1fc5f8c;hb=64e43e504a8716cb1784de5fc33d7f02e915e2ac;hp=7daf3b69b5f66c536d1a2567b7896fe54c972c57;hpb=613b25028368b3651bea0c801e05d9962ad9b604;p=numerical-analysis.git

diff --git a/src/Linear/Iteration.hs b/src/Linear/Iteration.hs
index 7daf3b6..6117770 100644
--- a/src/Linear/Iteration.hs
+++ b/src/Linear/Iteration.hs
@@ -1,34 +1,53 @@
+{-# LANGUAGE NoImplicitPrelude #-}
 {-# LANGUAGE ScopedTypeVariables #-}
 {-# LANGUAGE TypeFamilies #-}
 
 -- | Classical iterative methods to solve the system Ax = b.
 
-module Linear.Iteration
+module Linear.Iteration (
+  gauss_seidel_iteration,
+  gauss_seidel_iterations,
+  gauss_seidel_method,
+  jacobi_iteration,
+  jacobi_iterations,
+  jacobi_method,
+  rayleigh_quotient,
+  sor_iteration,
+  sor_iterations,
+  sor_method )
 where
 
-import Data.List (find)
-import Data.Maybe (fromJust)
-import Data.Vector.Fixed (Arity, N1, S)
-import NumericPrelude hiding ((*))
-import qualified Algebra.Algebraic as Algebraic
-import qualified Algebra.Field as Field
-import qualified Algebra.RealField as RealField
-import qualified Algebra.ToRational as ToRational
-import qualified Prelude as P
+import Data.List ( find )
+import Data.Maybe ( fromJust )
+import Data.Vector.Fixed ( Arity, N1, S )
+import NumericPrelude hiding ( (*) )
+import qualified Algebra.Algebraic as Algebraic ( C )
+import qualified Algebra.Field as Field ( C )
+import qualified Algebra.RealField as RealField ( C )
+import qualified Algebra.ToRational as ToRational ( C )
+
+import Linear.Matrix (
+  Col,
+  Mat(..),
+  (!!!),
+  (*),
+  diagonal_part,
+  dot,
+  lt_part_strict,
+  transpose )
+import Linear.System ( forward_substitute )
+import Normed ( Normed(..) )
 
-import Linear.Matrix
-import Linear.System
-import Normed
 
 -- | A generalized implementation for Jacobi, Gauss-Seidel, etc. All
 --   that we really need to know is how to construct the matrix M, so we
 --   take a function that does it as an argument.
-classical_iteration :: (Field.C a, Arity m)
-                 => (Mat m m  a -> Mat m m  a)
-                 -> Mat m m  a
-                 -> Mat m N1 a
-                 -> Mat m N1 a
-                 -> Mat m N1 a
+classical_iteration :: (Eq a, Field.C a, m ~ S n, Arity n)
+                 => (Mat m m a -> Mat m m a)
+                 -> Mat m m a
+                 -> Col m a
+                 -> Col m a
+                 -> Col m a
 classical_iteration m_function matrix b x_current =
   x_next
   where
@@ -41,8 +60,8 @@ classical_iteration m_function matrix b x_current =
 
 -- | Perform one iteration of successive over-relaxation.
 --
-sor_iteration :: forall m a.
-                 (Field.C a, Arity m)
+sor_iteration :: forall m n a.
+                 (Eq a, Field.C a, m ~ S n, Arity n)
               => a -- ^ Omega
               -> Mat m m  a -- ^ Matrix A
               -> Mat m N1 a -- ^ Vector b
@@ -61,7 +80,7 @@ sor_iteration omega =
 
 -- | Compute an infinite list of SOR iterations starting with the
 --   vector x0.
-sor_iterations :: (Field.C a, Arity m)
+sor_iterations :: (Eq a, Field.C a, m ~ S n, Arity n)
                => a
                -> Mat m m  a
                -> Mat m N1 a
@@ -72,7 +91,7 @@ sor_iterations omega matrix b =
 
 
 -- | Perform one iteration of Gauss-Seidel.
-gauss_seidel_iteration :: (Field.C a, Arity m)
+gauss_seidel_iteration :: (Eq a, Field.C a, m ~ S n, Arity n)
                        => Mat m m  a
                        -> Mat m N1 a
                        -> Mat m N1 a
@@ -82,7 +101,7 @@ gauss_seidel_iteration = sor_iteration one
 
 -- | Compute an infinite list of Gauss-Seidel iterations starting with
 --   the vector x0.
-gauss_seidel_iterations :: (Field.C a, Arity m)
+gauss_seidel_iterations :: (Eq a, Field.C a, m ~ S n, Arity n)
                         => Mat m m  a
                         -> Mat m N1 a
                         -> Mat m N1 a
@@ -97,6 +116,8 @@ gauss_seidel_iterations matrix b =
 --
 --   Examples:
 --
+--   >>> import Linear.Matrix ( Mat2, fromList, vec2d )
+--
 --   >>> let m  = fromList [[4,2],[2,2]] :: Mat2 Double
 --   >>> let x0 = vec2d (0, 0::Double)
 --   >>> let b  = vec2d (1, 1::Double)
@@ -106,7 +127,7 @@ gauss_seidel_iterations matrix b =
 --   >>> jacobi_iteration m b x1
 --   ((0.0),(0.25))
 --
-jacobi_iteration :: (Field.C a, Arity m)
+jacobi_iteration :: (Eq a, Field.C a, m ~ S n, Arity n)
                  => Mat m m  a
                  -> Mat m N1 a
                  -> Mat m N1 a
@@ -117,7 +138,7 @@ jacobi_iteration =
 
 -- | Compute an infinite list of Jacobi iterations starting with the
 --   vector x0.
-jacobi_iterations :: (Field.C a, Arity m)
+jacobi_iterations :: (Eq a, Field.C a, m ~ S n, Arity n)
                   => Mat m m  a
                   -> Mat m N1 a
                   -> Mat m N1 a
@@ -131,6 +152,8 @@ jacobi_iterations matrix b =
 --
 --   Examples:
 --
+--   >>> import Linear.Matrix ( Mat2, fromList, vec2d )
+--
 --   >>> let m  = fromList [[4,2],[2,2]] :: Mat2 Double
 --   >>> let x0 = vec2d (0, 0::Double)
 --   >>> let b  = vec2d (1, 1::Double)
@@ -160,6 +183,8 @@ jacobi_method =
 --
 --   Examples:
 --
+--   >>> import Linear.Matrix ( Mat2, fromList, vec2d )
+--
 --   >>> let m  = fromList [[4,2],[2,2]] :: Mat2 Double
 --   >>> let x0 = vec2d (0, 0::Double)
 --   >>> let b  = vec2d (1, 1::Double)
@@ -190,6 +215,8 @@ gauss_seidel_method =
 --
 --   Examples:
 --
+--   >>> import Linear.Matrix ( Mat2, fromList, vec2d )
+--
 --   >>> let m  = fromList [[4,2],[2,2]] :: Mat2 Double
 --   >>> let x0 = vec2d (0, 0::Double)
 --   >>> let b  = vec2d (1, 1::Double)
@@ -268,6 +295,8 @@ classical_method iterations_function matrix b x0 epsilon =
 --
 --   Examples:
 --
+--   >>> import Linear.Matrix ( Mat2, fromList, vec2d )
+--
 --   >>> let m = fromList [[3,1],[1,2]] :: Mat2 Rational
 --   >>> let v = vec2d (1, 1::Rational)
 --   >>> rayleigh_quotient m v