From c22f72ffaa4edec587b28a7c22aa07330349fd73 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 24 Feb 2013 09:55:10 -0500
Subject: [PATCH] Get determinants working.

---
 src/Linear/Matrix.hs | 24 ++++++++++++++++--------
 1 file changed, 16 insertions(+), 8 deletions(-)

diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs
index 7452007..dbd321f 100644
--- a/src/Linear/Matrix.hs
+++ b/src/Linear/Matrix.hs
@@ -33,6 +33,7 @@ import Data.Vector.Fixed (
 import qualified Data.Vector.Fixed as V (
   and,
   fromList,
+  head,
   length,
   map,
   maximum,
@@ -340,13 +341,21 @@ class (Eq a, Ring.C a) => Determined p a where
   determinant :: (p a) -> a
 
 instance (Eq a, Ring.C a) => Determined (Mat (S Z) (S Z)) a where
-  determinant m = m !!! (0,0)
+  determinant (Mat rows) = (V.head . V.head) rows
 
-instance (Eq a, Ring.C a, Arity m) => Determined (Mat m m) a where
-  determinant _ = undefined
-
-instance (Eq a, Ring.C a, Arity n)
+instance (Eq a,
+          Ring.C a,
+          Arity n,
+          Determined (Mat (S n) (S n)) a)
          => Determined (Mat (S (S n)) (S (S n))) a where
+  -- | The recursive definition with a special-case for triangular matrices.
+  --
+  --   Examples:
+  --
+  --   >>> let m = fromList [[1,2],[3,4]] :: Mat2 Int
+  --   >>> determinant m
+  --   -1
+  --
   determinant m
     | is_triangular m = product [ m !!! (i,i) | i <- [0..(nrows m)-1] ]
     | otherwise = determinant_recursive
@@ -356,13 +365,12 @@ instance (Eq a, Ring.C a, Arity n)
           det_minor i j = determinant (minor m i j)
 
           determinant_recursive =
-            sum [ (-1)^(1+(toInteger j)) NP.* (m' 0 j) NP.* (det_minor 0 j)
+            sum [ (-1)^(toInteger j) NP.* (m' 0 j) NP.* (det_minor 0 j)
               | j <- [0..(ncols m)-1] ]
 
 
 
--- | Matrix multiplication. Our 'Num' instance doesn't define one, and
---   we need additional restrictions on the result type anyway.
+-- | Matrix multiplication.
 --
 --   Examples:
 --
-- 
2.43.2