zipWith
)
import Data.Vector.Fixed.Boxed (Vec)
-import Data.Vector.Fixed.Internal.Arity (Arity, arity)
+import Data.Vector.Fixed.Cont (Arity, arity)
import Linear.Vector
import Normed
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.
--
-- 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
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