Safe Haskell | None |
---|---|
Language | Haskell2010 |
Metric classes
Synopsis
- class Multiplicative a => Signed a where
- class (Additive a, Additive b) => Normed a b where
- norm :: a -> b
- class Metric a b where
- distance :: a -> a -> b
- class (Eq a, Additive a, Subtractive a, MeetSemiLattice a) => Epsilon a where
- epsilon :: a
- nearZero :: a -> Bool
- aboutEqual :: a -> a -> Bool
- (~=) :: Epsilon a => a -> a -> Bool
Documentation
class Multiplicative a => Signed a where Source #
signum
from base is not an operator replicated in numhask, being such a very silly name, and preferred is the much more obvious sign
. Compare with Norm
where there is a change in codomain
abs a * sign a == a
Generalising this class tends towards size and direction (abs is the size on the one-dim number line of a vector with its tail at zero, and sign is the direction, right?).
Instances
Signed Double Source # | |
Signed Float Source # | |
Signed Int Source # | |
Signed Int8 Source # | |
Signed Int16 Source # | |
Signed Int32 Source # | |
Signed Int64 Source # | |
Signed Integer Source # | |
Signed Natural Source # | |
Signed Word Source # | |
Signed Word8 Source # | |
Signed Word16 Source # | |
Signed Word32 Source # | |
Signed Word64 Source # | |
GCDConstraints a => Signed (Ratio a) Source # | |
Signed a => Signed (Pair a) Source # | |
(Ord a, LowerBoundedField a, UpperBoundedField a, ExpField a) => Signed (LogField a) Source # | |
Signed a => Signed (Wrapped a) Source # | |
Signed a => Signed (Positive a) Source # | |
class (Additive a, Additive b) => Normed a b where Source #
Cab be Normed
norm a >= zero norm zero == zero
Note that the Normed codomain can be different to the domain.
Instances
Normed Double Double Source # | |
Normed Float Float Source # | |
Normed Int Int Source # | |
Normed Int8 Int8 Source # | |
Normed Int16 Int16 Source # | |
Normed Int32 Int32 Source # | |
Normed Int64 Int64 Source # | |
Normed Integer Integer Source # | |
Normed Natural Natural Source # | |
Normed Word Word Source # | |
Normed Word8 Word8 Source # | |
Normed Word16 Word16 Source # | |
Normed Word32 Word32 Source # | |
Normed Word64 Word64 Source # | |
Normed a a => Normed a (Positive a) Source # | |
Defined in NumHask.Data.Positive | |
(ExpField a, Normed a a) => Normed (Complex a) a Source # | |
Defined in NumHask.Data.Complex | |
(ExpField a, Normed a a) => Normed (Pair a) a Source # | |
Defined in NumHask.Data.Pair | |
GCDConstraints a => Normed (Ratio a) (Ratio a) Source # | |
Normed a a => Normed (Pair a) (Pair a) Source # | |
Normed a b => Normed (Wrapped a) (Wrapped b) Source # | |
class Metric a b where Source #
distance between numbers using L1 norm
distance a b >= zero distance a a == zero
Instances
Metric Double Double Source # | |
Metric Float Float Source # | |
Metric Int Int Source # | |
Metric Int8 Int8 Source # | |
Metric Int16 Int16 Source # | |
Metric Int32 Int32 Source # | |
Metric Int64 Int64 Source # | |
Metric Integer Integer Source # | |
Metric Natural Natural Source # | |
Metric Word Word Source # | |
Metric Word8 Word8 Source # | |
Metric Word16 Word16 Source # | |
Metric Word32 Word32 Source # | |
Metric Word64 Word64 Source # | |
(Subtractive a, Normed a a) => Metric a (Positive a) Source # | |
Defined in NumHask.Data.Positive | |
(Subtractive a, ExpField a, Normed a a) => Metric (Complex a) a Source # | |
(ExpField a, Subtractive a, Normed a a) => Metric (Pair a) a Source # | |
GCDConstraints a => Metric (Ratio a) (Ratio a) Source # | |
(Subtractive a, Normed a a) => Metric (Pair a) (Pair a) Source # | |
Metric a b => Metric (Wrapped a) (Wrapped b) Source # | |
class (Eq a, Additive a, Subtractive a, MeetSemiLattice a) => Epsilon a where Source #
Nothing
Instances
Epsilon Double Source # | |
Epsilon Float Source # | |
Epsilon Int Source # | |
Epsilon Int8 Source # | |
Epsilon Int16 Source # | |
Epsilon Int32 Source # | |
Epsilon Int64 Source # | |
Epsilon Integer Source # | |
Epsilon Word Source # | |
Epsilon Word8 Source # | |
Epsilon Word16 Source # | |
Epsilon Word32 Source # | |
Epsilon Word64 Source # | |
(Ord a, Signed a, Subtractive a, Epsilon a) => Epsilon (Complex a) Source # | |
(GCDConstraints a, MeetSemiLattice a) => Epsilon (Ratio a) Source # | |
(Subtractive a, Epsilon a) => Epsilon (Pair a) Source # | |
(Epsilon a, ExpField a, LowerBoundedField a, UpperBoundedField a, Ord a) => Epsilon (LogField a) Source # | |
Epsilon a => Epsilon (Wrapped a) Source # | |
(Epsilon a, Ord a) => Epsilon (Positive a) Source # | |