X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FIntegration%2FGaussian.hs;h=c2e4d5f684b7b5a97cb702b0a6049f88f3031b84;hb=b32831b5dde3440b85cbef62f4c47fcce0ee974f;hp=8fcca4f710d4fd918e061f475196ad3c9a2af1e5;hpb=6f237bfcd5890513cd390000c1ac8cdbdbaffb8c;p=numerical-analysis.git

diff --git a/src/Integration/Gaussian.hs b/src/Integration/Gaussian.hs
index 8fcca4f..c2e4d5f 100644
--- a/src/Integration/Gaussian.hs
+++ b/src/Integration/Gaussian.hs
@@ -24,15 +24,15 @@ import Linear.Matrix (
   Col,
   Col10,
   Mat(..),
-  colzipwith,
   construct,
+  element_sum2,
   fromList,
   identity_matrix,
-  matmap,
-  row',
-  transpose )
+  map2,
+  row,
+  transpose,
+  zipwith2 )
 import Linear.QR ( eigenvectors_symmetric )
-import Normed ( Normed(..) )
 
 
 -- | Compute the Jacobi matrix for the Legendre polynomials over
@@ -102,14 +102,12 @@ nodes_and_weights :: forall m a.
 nodes_and_weights iterations =
   (nodes, weights)
   where
-    jac = jacobi_matrix
-
     -- A shift is needed to make sure the QR algorithm
     -- converges. Since the roots (and thus eigenvalues) of orthogonal
     -- polynomials are real and distinct, there does exist a shift
     -- that will make it work. We guess lambda=1 makes it work.
 
-    shifted_jac = jac - identity_matrix
+    shifted_jac = jacobi_matrix - identity_matrix :: Mat (S m) (S m) a
     (shifted_nodes, vecs) = eigenvectors_symmetric iterations shifted_jac
 
     ones :: Col (S m) a
@@ -119,11 +117,11 @@ nodes_and_weights iterations =
     nodes = shifted_nodes + ones -- unshift the nodes
 
     -- Get the first component of each column.
-    first_components = row' vecs 0
+    first_components = row vecs 0
 
     -- Square it and multiply by 2; see the Golub-Welsch paper for
     -- this magic.
-    weights_row = matmap (\x -> (fromInteger 2)*x^2) first_components
+    weights_row = map2 (\x -> (fromInteger 2)*x^2) first_components
 
     weights = transpose $ weights_row
 
@@ -147,6 +145,7 @@ gaussian :: forall a.
 gaussian f =
   gaussian' f nodes weights
   where
+    coerce :: (ToRational.C b) => b -> a
     coerce = fromRational' . toRational
 
     nodes :: Col10 a
@@ -187,9 +186,6 @@ 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 +198,7 @@ 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 +206,7 @@ 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 = matmap f nodes
-    weighted_values = colzipwith (*) weights function_values
+    function_values = map2 f nodes
+    weighted_values = zipwith2 (*) weights function_values