From: Michael Orlitzky <michael@orlitzky.com>
Date: Wed, 19 Feb 2014 01:22:12 +0000 (-0500)
Subject: Use the element_sum2 function to sum the terms in Gaussian integration instead of... 
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=762a87a1bd7bc628ebf12263fb21566ab3aeb86f;p=numerical-analysis.git

Use the element_sum2 function to sum the terms in Gaussian integration instead of the incorrect 1-norm.
---

diff --git a/src/Integration/Gaussian.hs b/src/Integration/Gaussian.hs
index 6eb46f6..554dadc 100644
--- a/src/Integration/Gaussian.hs
+++ b/src/Integration/Gaussian.hs
@@ -25,6 +25,7 @@ import Linear.Matrix (
   Col10,
   Mat(..),
   construct,
+  element_sum2,
   fromList,
   identity_matrix,
   map2,
@@ -32,7 +33,6 @@ import Linear.Matrix (
   transpose,
   zipwith2 )
 import Linear.QR ( eigenvectors_symmetric )
-import Normed ( Normed(..) )
 
 
 -- | Compute the Jacobi matrix for the Legendre polynomials over
@@ -187,9 +187,6 @@ gaussian f =
 --   type level so this function couldn't just compute e.g. @n@ of
 --   them for you).
 --
---   The class constraints on @a@ could be loosened significantly if
---   we implemented column sum outside of the 1-norm.
---
 --   Examples:
 --
 --   >>> import Linear.Matrix ( Col5 )
@@ -202,7 +199,7 @@ gaussian f =
 --   True
 --
 gaussian' :: forall m a.
-             (Arity m, Absolute.C a, Algebraic.C a, ToRational.C a, Ring.C a)
+             (Arity m, ToRational.C a, Ring.C a)
           => (a -> a)    -- ^ The function @f@ to integrate.
           -> Col (S m) a -- ^ Column matrix of nodes
           -> Col (S m) a -- ^ Column matrix of weights
@@ -210,7 +207,7 @@ gaussian' :: forall m a.
 gaussian' f nodes weights =
   -- The one norm is just the sum of the entries, which is what we
   -- want.
-  norm_p (1::Int) weighted_values
+  element_sum2 weighted_values
   where
     function_values = map2 f nodes
     weighted_values = zipwith2 (*) weights function_values