Add the 'ifoldl2' function to Linear.Matrix.

[numerical-analysis.git] / src / Linear / Matrix.hs

diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs
index 7c0f84a41042744b636c416dc8c3043e6b76abe6..660330245b330b840bcb848af512b7d6561e217f 100644 (file)
--- a/src/Linear/Matrix.hs
+++ b/src/Linear/Matrix.hs
@@ -37,6 +37,7 @@ import qualified Data.Vector.Fixed as V (
   and,
   fromList,
   head,
+  ifoldl,
   length,
   map,
   maximum,
@@ -91,6 +92,11 @@ type Col3 a = Col N3 a
 type Col4 a = Col N4 a
 type Col5 a = Col N5 a
 
+-- We need a big column for Gaussian quadrature.
+type N10 = S (S (S (S (S N5))))
+type Col10 a = Col N10 a
+
+
 instance (Eq a) => Eq (Mat m n a) where
   -- | Compare a row at a time.
   --
@@ -775,16 +781,36 @@ trace matrix =
 --
 --   >>> let m1 = fromList [[1],[1],[1]] :: Col3 Int
 --   >>> let m2 = fromList [[1],[2],[3]] :: Col3 Int
---   >>> zipcol m1 m2
+--   >>> colzip m1 m2
 --   (((1,1)),((1,2)),((1,3)))
 --
-zipcol :: Arity m => Col m a -> Col m a -> Col m (a,a)
-zipcol c1 c2 =
+colzip :: Arity m => Col m a -> Col m a -> Col m (a,a)
+colzip c1 c2 =
   construct lambda
   where
     lambda i j = (c1 !!! (i,j), c2 !!! (i,j))
 
 
+-- | Zip together two column matrices using the supplied function.
+--
+--   Examples:
+--
+--   >>> let c1 = fromList [[1],[2],[3]] :: Col3 Integer
+--   >>> let c2 = fromList [[4],[5],[6]] :: Col3 Integer
+--   >>> colzipwith (^) c1 c2
+--   ((1),(32),(729))
+--
+colzipwith :: Arity m
+           => (a -> a -> b)
+           -> Col m a
+           -> Col m a
+           -> Col m b
+colzipwith f c1 c2 =
+  construct lambda
+  where
+    lambda i j = f (c1 !!! (i,j)) (c2 !!! (i,j))
+
+
 -- | Map a function over a matrix of any dimensions.
 --
 --   Examples:
@@ -798,3 +824,33 @@ matmap f (Mat rows) =
   Mat $ V.map g rows
   where
     g = V.map f
+
+
+-- | Fold over the entire matrix passing the coordinates @i@ and @j@
+--   (of the row/column) to the accumulation function.
+--
+--   Examples:
+--
+--   >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+--   >>>  ifoldl2 (\i j cur _ -> cur + i + j) 0 m
+--   18
+--
+ifoldl2 :: forall a b m n.
+           (Int -> Int -> b -> a -> b)
+        -> b
+        -> Mat m n a
+        -> b
+ifoldl2 f initial (Mat rows) =
+  V.ifoldl row_function initial rows
+  where
+    -- | The order that we need this in (so that @g idx@ makes sense)
+    --   is a little funny. So that we don't need to pass weird
+    --   functions into ifoldl2, we swap the second and third
+    --   arguments of @f@ calling the result @g@.
+    g :: Int -> b -> Int -> a -> b
+    g w x y = f w y x
+
+    row_function :: b -> Int -> Vec n a -> b
+    row_function rowinit idx r = V.ifoldl (g idx) rowinit r
+
+