X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FLinear%2FMatrix.hs;h=054bb6e3afac2777ef16e200ff64b9c60a9fd3fd;hb=b64e8d2a0ef24e880265b9ba4997c3d4eb995570;hp=5562e92b7ef6101a754fbcc505eb2bf6bc22c37f;hpb=c7b6b27f4304416dcec67519b710d090850c3caa;p=numerical-analysis.git

diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs
index 5562e92..054bb6e 100644
--- 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,
@@ -61,13 +62,41 @@ import qualified Algebra.ToRational as ToRational ( C )
 import qualified Algebra.Transcendental as Transcendental ( C )
 import qualified Prelude as P ( map )
 
+-- | Our main matrix type.
 data Mat m n a = (Arity m, Arity n) => Mat (Vec m (Vec n a))
+
+-- Type synonyms for n-by-n matrices.
 type Mat1 a = Mat N1 N1 a
 type Mat2 a = Mat N2 N2 a
 type Mat3 a = Mat N3 N3 a
 type Mat4 a = Mat N4 N4 a
 type Mat5 a = Mat N5 N5 a
 
+-- | Type synonym for row vectors expressed as 1-by-n matrices.
+type Row n a = Mat N1 n a
+
+-- Type synonyms for 1-by-n row "vectors".
+type Row1 a = Row N1 a
+type Row2 a = Row N2 a
+type Row3 a = Row N3 a
+type Row4 a = Row N4 a
+type Row5 a = Row N5 a
+
+-- | Type synonym for column vectors expressed as n-by-1 matrices.
+type Col n a = Mat n N1 a
+
+-- Type synonyms for n-by-1 column "vectors".
+type Col1 a = Col N1 a
+type Col2 a = Col N2 a
+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.
   --
@@ -150,6 +179,14 @@ row :: Mat m n a -> Int -> (Vec n a)
 row (Mat rows) i = rows ! i
 
 
+-- | Return the @i@th row of @m@ as a matrix. Unsafe.
+row' :: (Arity m, Arity n) => Mat m n a -> Int -> Row n a
+row' m i =
+  construct lambda
+  where
+    lambda _ j = m !!! (i, j)
+
+
 -- | Return the @j@th column of @m@. Unsafe.
 column :: Mat m n a -> Int -> (Vec m a)
 column (Mat rows) j =
@@ -158,6 +195,12 @@ column (Mat rows) j =
     element = flip (!)
 
 
+-- | Return the @j@th column of @m@ as a matrix. Unsafe.
+column' :: (Arity m, Arity n) => Mat m n a -> Int -> Col m a
+column' m j =
+  construct lambda
+  where
+    lambda i _ = m !!! (i, j)
 
 
 -- | Transpose @m@; switch it's columns and its rows. This is a dirty
@@ -555,24 +598,24 @@ frobenius_norm (Mat rows) =
 --   >>> fixed_point g eps u0
 --   ((1.0728549599342185),(1.0820591495686167))
 --
-vec1d :: (a) -> Mat N1 N1 a
+vec1d :: (a) -> Col1 a
 vec1d (x) = Mat (mk1 (mk1 x))
 
-vec2d :: (a,a) -> Mat N2 N1 a
+vec2d :: (a,a) -> Col2 a
 vec2d (x,y) = Mat (mk2 (mk1 x) (mk1 y))
 
-vec3d :: (a,a,a) -> Mat N3 N1 a
+vec3d :: (a,a,a) -> Col3 a
 vec3d (x,y,z) = Mat (mk3 (mk1 x) (mk1 y) (mk1 z))
 
-vec4d :: (a,a,a,a) -> Mat N4 N1 a
+vec4d :: (a,a,a,a) -> Col4 a
 vec4d (w,x,y,z) = Mat (mk4 (mk1 w) (mk1 x) (mk1 y) (mk1 z))
 
-vec5d :: (a,a,a,a,a) -> Mat N5 N1 a
+vec5d :: (a,a,a,a,a) -> Col5 a
 vec5d (v,w,x,y,z) = Mat (mk5 (mk1 v) (mk1 w) (mk1 x) (mk1 y) (mk1 z))
 
 -- Since we commandeered multiplication, we need to create 1x1
 -- matrices in order to multiply things.
-scalar :: a -> Mat N1 N1 a
+scalar :: a -> Mat1 a
 scalar x = Mat (mk1 (mk1 x))
 
 dot :: (RealRing.C a, n ~ N1, m ~ S t, Arity t)
@@ -618,7 +661,7 @@ angle v1 v2 =
 --   >>> diagonal m
 --   ((1),(5),(9))
 --
-diagonal :: (Arity m) => Mat m m a -> Mat m N1 a
+diagonal :: (Arity m) => Mat m m a -> Col m a
 diagonal matrix =
   construct lambda
   where
@@ -730,3 +773,84 @@ trace matrix =
   let (Mat rows) = diagonal matrix
   in
     element_sum $ V.map V.head rows
+
+
+-- | Zip together two column matrices.
+--
+--   Examples:
+--
+--   >>> let m1 = fromList [[1],[1],[1]] :: Col3 Int
+--   >>> let m2 = fromList [[1],[2],[3]] :: Col3 Int
+--   >>> colzip m1 m2
+--   (((1,1)),((1,2)),((1,3)))
+--
+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:
+--
+--   >>> let m = fromList [[1,2],[3,4]] :: Mat2 Int
+--   >>> map2 (^2) m
+--   ((1,4),(9,16))
+--
+map2 :: (a -> b) -> Mat m n a -> Mat m n b
+map2 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
+
+