maximum,
replicate,
toList,
- zipWith
- )
+ zipWith )
import Data.Vector.Fixed.Cont ( Arity, arity )
import Linear.Vector ( Vec, delete, element_sum )
import Normed ( Normed(..) )
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
+
instance (Eq a) => Eq (Mat m n a) where
-- | Compare a row at a time.
--
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 =
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
-- >>> 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)
norms = (norm v1) NP.* (norm v2)
+-- | Retrieve the diagonal elements of the given matrix as a \"column
+-- vector,\" i.e. a m-by-1 matrix. We require the matrix to be
+-- square to avoid ambiguity in the return type which would ideally
+-- have dimension min(m,n) supposing an m-by-n matrix.
+--
+-- Examples:
+--
+-- >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+-- >>> diagonal m
+-- ((1),(5),(9))
+--
+diagonal :: (Arity m) => Mat m m a -> Col m a
+diagonal matrix =
+ construct lambda
+ where
+ lambda i _ = matrix !!! (i,i)
+
-- | Given a square @matrix@, return a new matrix of the same size
-- containing only the on-diagonal entries of @matrix@. The
=> Mat m m a
-> Mat m m a
ut_part_strict = transpose . lt_part_strict . transpose
+
+
+-- | Compute the trace of a square matrix, the sum of the elements
+-- which lie on its diagonal. We require the matrix to be
+-- square to avoid ambiguity in the return type which would ideally
+-- have dimension min(m,n) supposing an m-by-n matrix.
+--
+-- Examples:
+--
+-- >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+-- >>> trace m
+-- 15
+--
+trace :: (Arity m, Ring.C a) => Mat m m a -> a
+trace matrix =
+ let (Mat rows) = diagonal matrix
+ in
+ element_sum $ V.map V.head rows
projects / numerical-analysis.git / blobdiff