and,
fromList,
head,
- length,
+ ifoldl,
map,
maximum,
replicate,
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.
--
toList :: Mat m n a -> [[a]]
toList (Mat rows) = map V.toList (V.toList rows)
+
-- | Create a matrix from a nested list.
fromList :: (Arity m, Arity n) => [[a]] -> Mat m n a
fromList vs = Mat (V.fromList $ map V.fromList vs)
--- | Unsafe indexing.
+-- | Unsafe indexing. Much faster than the safe indexing.
(!!!) :: (Arity m, Arity n) => Mat m n a -> (Int, Int) -> a
-(!!!) m (i, j) = (row m i) ! j
+(!!!) (Mat rows) (i, j) = (rows ! i) ! j
+
-- | Safe indexing.
-(!!?) :: Mat m n a -> (Int, Int) -> Maybe a
-(!!?) m@(Mat rows) (i, j)
- | i < 0 || j < 0 = Nothing
- | i > V.length rows = Nothing
- | otherwise = if j > V.length (row m j)
- then Nothing
- else Just $ (row m j) ! j
+--
+-- Examples:
+--
+-- >>> let m = fromList [[1,2],[3,4]] :: Mat2 Int
+-- >>> m !!? (-1,-1)
+-- Nothing
+-- >>> m !!? (-1,0)
+-- Nothing
+-- >>> m !!? (-1,1)
+-- Nothing
+-- >>> m !!? (0,-1)
+-- Nothing
+-- >>> m !!? (0,0)
+-- Just 1
+-- >>> m !!? (0,1)
+-- Just 2
+-- >>> m !!? (1,-1)
+-- Nothing
+-- >>> m !!? (1,0)
+-- Just 3
+-- >>> m !!? (1,1)
+-- Just 4
+-- >>> m !!? (2,-1)
+-- Nothing
+-- >>> m !!? (2,0)
+-- Nothing
+-- >>> m !!? (2,1)
+-- Nothing
+-- >>> m !!? (2,2)
+-- Nothing
+--
+(!!?) :: (Arity m, Arity n) => Mat m n a -> (Int, Int) -> Maybe a
+(!!?) matrix idx =
+ ifoldl2 f Nothing matrix
+ where
+ f k l found cur = if (k,l) == idx then (Just cur) else found
-- | The number of rows in the matrix.
nrows :: forall m n a. (Arity m) => Mat m n a -> Int
nrows _ = arity (undefined :: m)
+
-- | The number of columns in the first row of the
-- matrix. Implementation stolen from Data.Vector.Fixed.length.
ncols :: forall m n a. (Arity n) => Mat m n a -> Int
ncols _ = arity (undefined :: n)
--- | Return the @i@th row of @m@. Unsafe.
-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 =
+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 =
- V.map (element j) rows
- where
- 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 =
+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
--- implementation.. it would be a little cleaner to use imap, but it
--- doesn't seem to work.
+-- implementation, but I don't see a better way.
--
-- TODO: Don't cheat with fromList.
--
-- ((1,3),(2,4))
--
transpose :: (Arity m, Arity n) => Mat m n a -> Mat n m a
-transpose m = Mat $ V.fromList column_list
+transpose matrix =
+ construct lambda
where
- column_list = [ column m i | i <- [0..(ncols m)-1] ]
+ lambda i j = matrix !!! (j,i)
-- | Is @m@ symmetric?
identity_matrix =
construct (\i j -> if i == j then (fromInteger 1) else (fromInteger 0))
+
-- | Given a positive-definite matrix @m@, computes the
-- upper-triangular matrix @r@ with (transpose r)*r == m and all
-- values on the diagonal of @r@ positive.
--
-- >>> 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:
--
-- >>> let m = fromList [[1,2],[3,4]] :: Mat2 Int
--- >>> matmap (^2) m
+-- >>> map2 (^2) m
-- ((1,4),(9,16))
--
-matmap :: (a -> b) -> Mat m n a -> Mat m n b
-matmap f (Mat rows) =
+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
projects / numerical-analysis.git / blobdiff