mk2,
mk3,
mk4,
- mk5
- )
+ mk5 )
import qualified Data.Vector.Fixed as V (
and,
fromList,
head,
ifoldl,
+ ifoldr,
imap,
map,
maximum,
replicate,
+ reverse,
toList,
zipWith )
import Data.Vector.Fixed.Cont ( Arity, arity )
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.
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 = (c1 !!! (i,j), c2 !!! (i,j))
+ lambda i j = (m1 !!! (i,j), m2 !!! (i,j))
--- | Zip together two column matrices using the supplied function.
+-- | 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 = (m1 !!! (i,j), m2 !!! (i,j), m3 !!! (i,j))
+
+
+-- | 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))
-- | 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:
--
-- >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
--- >>> ifoldl2 (\i j cur _ -> cur + i + j) 0 m
+-- >>> ifoldl2 (\i j cur _ -> cur + i + j) 0 m
-- 18
--
ifoldl2 :: forall a b m n.
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@.
--
Mat $ V.imap g rows
where
g i = V.imap (f i)
+
+
+-- | Reverse the order of elements in a matrix.
+--
+-- Examples:
+--
+-- >>> let m1 = fromList [[1,2,3]] :: Row3 Int
+-- >>> reverse2 m1
+-- ((3,2,1))
+--
+-- >>> let m1 = vec3d (1,2,3 :: Int)
+-- >>> reverse2 m1
+-- ((3),(2),(1))
+--
+-- >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+-- >>> reverse2 m
+-- ((9,8,7),(6,5,4),(3,2,1))
+--
+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
projects / numerical-analysis.git / blobdiff