From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 7 Dec 2018 15:07:13 +0000 (-0500)
Subject: src/Linear/Matrix.hs: add support for zero-length columns/matrices.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=3274b18a2fb48f26e6582d9dcee11b4067230911;p=numerical-analysis.git

src/Linear/Matrix.hs: add support for zero-length columns/matrices.
---

diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs
index 4c2c7f3..e8d7180 100644
--- a/src/Linear/Matrix.hs
+++ b/src/Linear/Matrix.hs
@@ -20,6 +20,7 @@ import Data.List (intercalate)
 import Data.Vector.Fixed (
   (!),
   generate,
+  mk0,
   mk1,
   mk2,
   mk3,
@@ -27,13 +28,13 @@ import Data.Vector.Fixed (
   mk5 )
 import qualified Data.Vector.Fixed as V (
   and,
+  foldl,
   fromList,
   head,
   ifoldl,
   ifoldr,
   imap,
   map,
-  maximum,
   replicate,
   reverse,
   toList,
@@ -43,7 +44,9 @@ import Linear.Vector ( Vec, delete )
 import Naturals
 import Normed ( Normed(..) )
 
-import NumericPrelude hiding ( (*), abs )
+-- We want the "max" that works on Ord, not the one that only works on
+-- Bool/Integer from the Lattice class!
+import NumericPrelude hiding ( (*), abs, max)
 import qualified NumericPrelude as NP ( (*) )
 import qualified Algebra.Absolute as Absolute ( C )
 import Algebra.Absolute ( abs )
@@ -56,12 +59,13 @@ import qualified Algebra.Module as Module ( C )
 import qualified Algebra.RealRing as RealRing ( C )
 import qualified Algebra.ToRational as ToRational ( C )
 import qualified Algebra.Transcendental as Transcendental ( C )
-import qualified Prelude as P ( map )
+import qualified Prelude as P ( map, max)
 
 -- | 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 Mat0 a = Mat Z Z a
 type Mat1 a = Mat N1 N1 a
 type Mat2 a = Mat N2 N2 a
 type Mat3 a = Mat N3 N3 a
@@ -86,6 +90,7 @@ 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 Col0 a = Col Z a
 type Col1 a = Col N1 a
 type Col2 a = Col N2 a
 type Col3 a = Col N3 a
@@ -612,8 +617,8 @@ instance (Absolute.C a,
           Algebraic.C a,
           ToRational.C a,
           Arity m)
-         => Normed (Col (S m) a) where
-  -- | Generic p-norms for vectors in R^n that are represented as n-by-1
+         => Normed (Col m a) where
+  -- | Generic p-norms for vectors in R^m that are represented as m-by-1
   --   matrices.
   --
   --   Examples:
@@ -628,6 +633,10 @@ instance (Absolute.C a,
   --   >>> norm_p 1 v1 :: Double
   --   2.0
   --
+  --   >>> let v1 = vec0d :: Col0 Double
+  --   >>> norm v1
+  --   0.0
+  --
   norm_p p (Mat rows) =
     (root p') $ sum [fromRational' (toRational $ abs x)^p' | x <- xs]
     where
@@ -643,7 +652,8 @@ instance (Absolute.C a,
   --   5
   --
   norm_infty (Mat rows) =
-    fromRational' $ toRational $ V.maximum $ V.map V.maximum rows
+    fromRational' $ toRational
+                      $ (V.foldl P.max 0) $ V.map (V.foldl P.max 0) rows
 
 
 -- | Compute the Frobenius norm of a matrix. This essentially treats
@@ -688,6 +698,9 @@ frobenius_norm matrix =
 --   >>> fixed_point g eps u0
 --   ((1.0728549599342185),(1.0820591495686167))
 --
+vec0d :: Col0 a
+vec0d = Mat mk0
+
 vec1d :: (a) -> Col1 a
 vec1d (x) = Mat (mk1 (mk1 x))