maximum,
replicate,
toList,
- zipWith
- )
-import Data.Vector.Fixed.Cont (Arity, arity)
-import Linear.Vector
-import Normed
+ zipWith )
+import Data.Vector.Fixed.Cont ( Arity, arity )
+import Linear.Vector ( Vec, delete, element_sum )
+import Normed ( Normed(..) )
import NumericPrelude hiding ( (*), abs )
import qualified NumericPrelude as NP ( (*) )
import qualified Algebra.Absolute as Absolute ( C )
import Algebra.Absolute ( abs )
-import qualified Algebra.Additive as Additive
-import qualified Algebra.Algebraic as Algebraic
-import Algebra.Algebraic (root)
-import qualified Algebra.Ring as Ring
-import qualified Algebra.Module as Module
-import qualified Algebra.RealRing as RealRing
-import qualified Algebra.ToRational as ToRational
-import qualified Algebra.Transcendental as Transcendental
-import qualified Prelude as P
+import qualified Algebra.Additive as Additive ( C )
+import qualified Algebra.Algebraic as Algebraic ( C )
+import Algebra.Algebraic ( root )
+import qualified Algebra.Ring as Ring ( C )
+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 )
data Mat m n a = (Arity m, Arity n) => Mat (Vec m (Vec n a))
type Mat1 a = Mat N1 N1 a
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 -> Mat m N1 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
=> 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