From: Michael Orlitzky <michael@orlitzky.com>
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