X-Git-Url: http://gitweb.michael.orlitzky.com/?p=numerical-analysis.git;a=blobdiff_plain;f=src%2FLinear%2FMatrix.hs;h=34920b4f025e7e2027588ab07c14d6772b679ab2;hp=ea6bc5772422c620daa3057c0177a946442fc690;hb=4e464a486bef07db44de9c3d3fae0c8094401b09;hpb=ae914d13235a4582077a5cb2b1edd630d9c6ad62

diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs
index ea6bc57..34920b4 100644
--- a/src/Linear/Matrix.hs
+++ b/src/Linear/Matrix.hs
@@ -42,8 +42,7 @@ import qualified Data.Vector.Fixed as V (
   maximum,
   replicate,
   toList,
-  zipWith
-  )
+  zipWith )
 import Data.Vector.Fixed.Cont ( Arity, arity )
 import Linear.Vector ( Vec, delete, element_sum )
 import Normed ( Normed(..) )
@@ -62,13 +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.
   --
@@ -151,6 +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 =
@@ -159,6 +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
@@ -556,24 +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)
@@ -608,6 +644,23 @@ angle v1 v2 =
    norms = (norm v1) NP.* (norm v2)
 
 
+-- | Retrieve the diagonal elements of the given matrix as a \"column
+--   vector,\" i.e. a m-by-1 matrix. We require the matrix to be
+--   square to avoid ambiguity in the return type which would ideally
+--   have dimension min(m,n) supposing an m-by-n matrix.
+--
+--   Examples:
+--
+--   >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+--   >>> diagonal m
+--   ((1),(5),(9))
+--
+diagonal :: (Arity m) => Mat m m a -> Col m a
+diagonal matrix =
+  construct lambda
+  where
+    lambda i _ = matrix !!! (i,i)
+
 
 -- | Given a square @matrix@, return a new matrix of the same size
 --   containing only the on-diagonal entries of @matrix@. The
@@ -696,3 +749,21 @@ ut_part_strict :: (Arity m, Ring.C a)
         => Mat m m a
         -> Mat m m a
 ut_part_strict = transpose . lt_part_strict . transpose
+
+
+-- | Compute the trace of a square matrix, the sum of the elements
+--   which lie on its diagonal. We require the matrix to be
+--   square to avoid ambiguity in the return type which would ideally
+--   have dimension min(m,n) supposing an m-by-n matrix.
+--
+--   Examples:
+--
+--   >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+--   >>> trace m
+--   15
+--
+trace :: (Arity m, Ring.C a) => Mat m m a -> a
+trace matrix =
+  let (Mat rows) = diagonal matrix
+  in
+    element_sum $ V.map V.head rows