From: Michael Orlitzky Date: Tue, 4 Feb 2014 07:18:09 +0000 (-0500) Subject: Add type synonyms for column/row matrices. X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=4e464a486bef07db44de9c3d3fae0c8094401b09;p=numerical-analysis.git Add type synonyms for column/row matrices. Add row' and column' functions that do what you'd expect only they return Mats instead of Vecs like their un-prime counterparts. --- diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs index 5562e92..34920b4 100644 --- a/src/Linear/Matrix.hs +++ b/src/Linear/Matrix.hs @@ -61,13 +61,36 @@ 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 + instance (Eq a) => Eq (Mat m n a) where -- | Compare a row at a time. -- @@ -150,6 +173,14 @@ 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 +189,12 @@ 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 +592,24 @@ 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 +655,7 @@ 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