Constrain Normed instance to column vectors (m-by-1 matrices).

[numerical-analysis.git] / src / Linear / Matrix.hs

diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs
index 7452007990e0e015c45610b03605cf6cfc642aad..8490b229921becb127a7a299be47efd16ddec7e4 100644 (file)
--- a/src/Linear/Matrix.hs
+++ b/src/Linear/Matrix.hs
@@ -17,6 +17,7 @@ where
 import Data.List (intercalate)
 
 import Data.Vector.Fixed (
+  (!),
   N1,
   N2,
   N3,
@@ -33,6 +34,7 @@ import Data.Vector.Fixed (
 import qualified Data.Vector.Fixed as V (
   and,
   fromList,
+  head,
   length,
   map,
   maximum,
@@ -41,7 +43,7 @@ import qualified Data.Vector.Fixed as V (
   zipWith
   )
 import Data.Vector.Fixed.Boxed (Vec)
-import Data.Vector.Fixed.Internal (Arity, arity)
+import Data.Vector.Fixed.Internal.Arity (Arity, arity)
 import Linear.Vector
 import Normed
 
@@ -340,13 +342,21 @@ 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 +366,12 @@ 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:
 --
@@ -408,9 +417,8 @@ instance (Ring.C a, Arity m, Arity n) => Module.C a (Mat m n a) where
 
 instance (Algebraic.C a,
           ToRational.C a,
-          Arity m,
-          Arity n)
-         => Normed (Mat (S m) (S n) a) where
+          Arity m)
+         => Normed (Mat (S m) N1 a) where
   -- | Generic p-norms. The usual norm in R^n is (norm_p 2). We treat
   --   all matrices as big vectors.
   --