X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FLinear%2FMatrix.hs;h=d166e44367e626b9d87979a4b0e9ab7b2b24e7d9;hb=3cb0f69fa38e5f46a2374d48168acf69bfc9e910;hp=7452007990e0e015c45610b03605cf6cfc642aad;hpb=1f64a1a33b2636ef2e863a0b577c8d8d50233580;p=numerical-analysis.git

diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs
index 7452007..d166e44 100644
--- 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.Cont (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.
   --
@@ -423,7 +431,7 @@ instance (Algebraic.C a,
   --   5.0
   --
   norm_p p (Mat rows) =
-    (root p') $ sum [(fromRational' $ toRational x)^p' | x <- xs]
+    (root p') $ sum [fromRational' (toRational x)^p' | x <- xs]
     where
       p' = toInteger p
       xs = concat $ V.toList $ V.map V.toList rows
@@ -512,3 +520,93 @@ angle v1 v2 =
   where
    theta = (recip norms) NP.* (v1 `dot` v2)
    norms = (norm v1) NP.* (norm v2)
+
+
+
+-- | Given a square @matrix@, return a new matrix of the same size
+--   containing only the on-diagonal entries of @matrix@. The
+--   off-diagonal entries are set to zero.
+--
+--   Examples:
+--
+--   >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+--   >>> diagonal_part m
+--   ((1,0,0),(0,5,0),(0,0,9))
+--
+diagonal_part :: (Arity m, Ring.C a)
+         => Mat m m a
+         -> Mat m m a
+diagonal_part matrix =
+  construct lambda
+  where
+    lambda i j = if i == j then matrix !!! (i,j) else 0
+
+
+-- | Given a square @matrix@, return a new matrix of the same size
+--   containing only the on-diagonal and below-diagonal entries of
+--   @matrix@. The above-diagonal entries are set to zero.
+--
+--   Examples:
+--
+--   >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+--   >>> lt_part m
+--   ((1,0,0),(4,5,0),(7,8,9))
+--
+lt_part :: (Arity m, Ring.C a)
+        => Mat m m a
+        -> Mat m m a
+lt_part matrix =
+  construct lambda
+  where
+    lambda i j = if i >= j then matrix !!! (i,j) else 0
+
+
+-- | Given a square @matrix@, return a new matrix of the same size
+--   containing only the below-diagonal entries of @matrix@. The on-
+--   and above-diagonal entries are set to zero.
+--
+--   Examples:
+--
+--   >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+--   >>> lt_part_strict m
+--   ((0,0,0),(4,0,0),(7,8,0))
+--
+lt_part_strict :: (Arity m, Ring.C a)
+        => Mat m m a
+        -> Mat m m a
+lt_part_strict matrix =
+  construct lambda
+  where
+    lambda i j = if i > j then matrix !!! (i,j) else 0
+
+
+-- | Given a square @matrix@, return a new matrix of the same size
+--   containing only the on-diagonal and above-diagonal entries of
+--   @matrix@. The below-diagonal entries are set to zero.
+--
+--   Examples:
+--
+--   >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+--   >>> ut_part m
+--   ((1,2,3),(0,5,6),(0,0,9))
+--
+ut_part :: (Arity m, Ring.C a)
+        => Mat m m a
+        -> Mat m m a
+ut_part = transpose . lt_part . transpose
+
+
+-- | Given a square @matrix@, return a new matrix of the same size
+--   containing only the above-diagonal entries of @matrix@. The on-
+--   and below-diagonal entries are set to zero.
+--
+--   Examples:
+--
+--   >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+--   >>> ut_part_strict m
+--   ((0,2,3),(0,0,6),(0,0,0))
+--
+ut_part_strict :: (Arity m, Ring.C a)
+        => Mat m m a
+        -> Mat m m a
+ut_part_strict = transpose . lt_part_strict . transpose