maximum,
replicate,
toList,
- zipWith
- )
+ zipWith )
import Data.Vector.Fixed.Cont ( Arity, arity )
import Linear.Vector ( Vec, delete, element_sum )
import Normed ( Normed(..) )
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