X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FLinear%2FMatrix.hs;h=119d77089461dfae968320c79bd1375c31d46b41;hb=342fb80c0a34bd362a51fd62989eeef462b58721;hp=c33e96691b00f9cb2c87c3332ab572a32286d10b;hpb=f9a18f9f5685f86697475529033096e8c6f6e627;p=numerical-analysis.git

diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs
index c33e966..119d770 100644
--- a/src/Linear/Matrix.hs
+++ b/src/Linear/Matrix.hs
@@ -37,6 +37,7 @@ import qualified Data.Vector.Fixed as V (
   fromList,
   head,
   ifoldl,
+  ifoldr,
   imap,
   map,
   maximum,
@@ -662,11 +663,16 @@ vec5d (v,w,x,y,z) = Mat (mk5 (mk1 v) (mk1 w) (mk1 x) (mk1 y) (mk1 z))
 scalar :: a -> Mat1 a
 scalar x = Mat (mk1 (mk1 x))
 
-dot :: (RealRing.C a, m ~ S t, Arity t)
-       => Col m a
-       -> Col m a
+-- Get the scalar value out of a 1x1 matrix.
+unscalar :: Mat1 a -> a
+unscalar (Mat rows) = V.head $ V.head rows
+
+
+dot :: (Ring.C a, Arity m)
+       => Col (S m) a
+       -> Col (S m) a
        -> a
-v1 `dot` v2 = ((transpose v1) * v2) !!! (0, 0)
+v1 `dot` v2 = unscalar $ ((transpose v1) * v2)
 
 
 -- | The angle between @v1@ and @v2@ in Euclidean space.
@@ -818,37 +824,73 @@ trace matrix =
     element_sum $ V.map V.head rows
 
 
--- | Zip together two column matrices.
+-- | Zip together two matrices.
+--
+--   TODO: don't cheat with construct (map V.zips instead).
 --
 --   Examples:
 --
 --   >>> let m1 = fromList [[1],[1],[1]] :: Col3 Int
 --   >>> let m2 = fromList [[1],[2],[3]] :: Col3 Int
---   >>> colzip m1 m2
+--   >>> zip2 m1 m2
 --   (((1,1)),((1,2)),((1,3)))
 --
-colzip :: Arity m => Col m a -> Col m a -> Col m (a,a)
-colzip c1 c2 =
+--   >>> let m1 = fromList [[1,2],[3,4]] :: Mat2 Int
+--   >>> let m2 = fromList [[1,1],[1,1]] :: Mat2 Int
+--   >>> zip2 m1 m2
+--   (((1,1),(2,1)),((3,1),(4,1)))
+--
+zip2 :: (Arity m, Arity n) => Mat m n a -> Mat m n a -> Mat m n (a,a)
+zip2 m1 m2 =
+  construct lambda
+  where
+    lambda i j = (m1 !!! (i,j), m2 !!! (i,j))
+
+
+-- | Zip together three matrices.
+--
+--   TODO: don't cheat with construct (map V.zips instead).
+--
+--   Examples:
+--
+--   >>> let m1 = fromList [[1],[1],[1]] :: Col3 Int
+--   >>> let m2 = fromList [[1],[2],[3]] :: Col3 Int
+--   >>> let m3 = fromList [[4],[5],[6]] :: Col3 Int
+--   >>> zip2three m1 m2 m3
+--   (((1,1,4)),((1,2,5)),((1,3,6)))
+--
+--   >>> let m1 = fromList [[1,2],[3,4]] :: Mat2 Int
+--   >>> let m2 = fromList [[1,1],[1,1]] :: Mat2 Int
+--   >>> let m3 = fromList [[8,2],[6,3]] :: Mat2 Int
+--   >>> zip2three m1 m2 m3
+--   (((1,1,8),(2,1,2)),((3,1,6),(4,1,3)))
+--
+zip2three :: (Arity m, Arity n)
+          => Mat m n a
+          -> Mat m n a
+          -> Mat m n a
+          -> Mat m n (a,a,a)
+zip2three m1 m2 m3 =
   construct lambda
   where
-    lambda i j = (c1 !!! (i,j), c2 !!! (i,j))
+    lambda i j = (m1 !!! (i,j), m2 !!! (i,j), m3 !!! (i,j))
 
 
--- | Zip together two column matrices using the supplied function.
+-- | Zip together two 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
+--   >>> zipwith2 (^) c1 c2
 --   ((1),(32),(729))
 --
-colzipwith :: Arity m
+zipwith2 :: Arity m
            => (a -> a -> b)
            -> Col m a
            -> Col m a
            -> Col m b
-colzipwith f c1 c2 =
+zipwith2 f c1 c2 =
   construct lambda
   where
     lambda i j = f (c1 !!! (i,j)) (c2 !!! (i,j))
@@ -870,7 +912,8 @@ map2 f (Mat rows) =
 
 
 -- | Fold over the entire matrix passing the coordinates @i@ and @j@
---   (of the row/column) to the accumulation function.
+--   (of the row/column) to the accumulation function. The fold occurs
+--   from top-left to bottom-right.
 --
 --   Examples:
 --
@@ -897,6 +940,36 @@ ifoldl2 f initial (Mat rows) =
     row_function rowinit idx r = V.ifoldl (g idx) rowinit r
 
 
+-- | Fold over the entire matrix passing the coordinates @i@ and @j@
+--   (of the row/column) to the accumulation function. The fold occurs
+--   from bottom-right to top-left.
+--
+--   The order of the arguments in the supplied function are different
+--   from those in V.ifoldr; we keep them similar to ifoldl2.
+--
+--   Examples:
+--
+--   >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+--   >>> ifoldr2 (\i j cur _ -> cur + i + j) 0 m
+--   18
+--
+ifoldr2 :: forall a b m n.
+           (Int -> Int -> b -> a -> b)
+        -> b
+        -> Mat m n a
+        -> b
+ifoldr2 f initial (Mat rows) =
+  V.ifoldr row_function initial rows
+  where
+    -- | Swap the order of arguments in @f@ so that it agrees with the
+    --   @f@ passed to ifoldl2.
+    g :: Int -> Int -> a -> b -> b
+    g w x y z = f w x z y
+
+    row_function :: Int -> Vec n a -> b -> b
+    row_function idx r rowinit = V.ifoldr (g idx) rowinit r
+
+
 -- | Map a function over a matrix of any dimensions, passing the
 --   coordinates @i@ and @j@ to the function @f@.
 --
@@ -931,3 +1004,27 @@ imap2 f (Mat rows) =
 --
 reverse2 :: (Arity m, Arity n) => Mat m n a -> Mat m n a
 reverse2 (Mat rows) = Mat $ V.reverse $ V.map V.reverse rows
+
+
+-- | Unsafely set the (i,j) element of the given matrix.
+--
+--   Examples:
+--
+--   >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+--   >>> set_idx m (1,1) 17
+--   ((1,2,3),(4,17,6),(7,8,9))
+--
+set_idx :: forall m n a.
+           (Arity m, Arity n)
+        => Mat m n a
+        -> (Int, Int)
+        -> a
+        -> Mat m n a
+set_idx matrix (i,j) newval =
+  imap2 updater matrix
+  where
+    updater :: Int -> Int -> a -> a
+    updater k l existing =
+      if k == i && l == j
+      then newval
+      else existing