intervals 0.7 → 0.7.0.1

raw patch · 7 files changed

+183/−3 lines, 7 files

Files

• CHANGELOG.markdown +4/−0
• intervals.cabal +1/−1
• src/Numeric/Interval.hs +3/−0
• src/Numeric/Interval/Internal.hs +71/−1
• src/Numeric/Interval/Kaucher.hs +49/−0
• src/Numeric/Interval/NonEmpty.hs +2/−0
• src/Numeric/Interval/NonEmpty/Internal.hs +53/−1

@@ -1,3 +1,7 @@+0.7.0.1+-------+* Removed a couple of unnecessary `Fractional` constraints.+ 0.7 --- * Corrected the definition of `mignitude`.

@@ -1,5 +1,5 @@ name:              intervals-version:           0.7+version:           0.7.0.1 synopsis:          Interval Arithmetic description:   A 'Numeric.Interval.Interval' is a closed, convex set of floating point values.

@@ -12,6 +12,7 @@ module Numeric.Interval   ( Interval   , (...)+  , (+/-)   , interval   , whole   , empty@@ -31,6 +32,8 @@   , magnitude   , mignitude   , distance+  , inflate, deflate+  , scale, symmetric   , contains   , isSubsetOf   , certainly, (<!), (<=!), (==!), (>=!), (>!)

@@ -20,6 +20,7 @@ module Numeric.Interval.Internal   ( Interval(..)   , (...)+  , (+/-)   , interval   , whole   , empty@@ -39,6 +40,8 @@   , magnitude   , mignitude   , distance+  , inflate, deflate+  , scale, symmetric   , contains   , isSubsetOf   , certainly, (<!), (<=!), (==!), (>=!), (>!)@@ -77,7 +80,11 @@   {-# INLINE foldMap #-}  infix 3 ...+infixl 6 +/- +(+/-) :: (Num a, Ord a) => a -> a -> Interval a+a +/- b = a - b ... a + b+ negInfinity :: Fractional a => a negInfinity = (-1)/0 {-# INLINE negInfinity #-}@@ -261,6 +268,69 @@ distance :: (Num a, Ord a) => Interval a -> Interval a -> a distance i1 i2 = mignitude (i1 - i2) +-- | Inflate an interval by enlarging it at both ends.+--+-- >>> inflate 3 (-1 ... 7)+-- -4 ... 10+--+-- >>> inflate (-2) (0 ... 4)+-- -2 ... 6+--+-- >>> inflate 1 empty+-- Empty+inflate :: (Num a, Ord a) => a -> Interval a -> Interval a+inflate x y = symmetric x + y++-- | Deflate an interval by shrinking it from both ends.+--+-- >>> deflate 3.0 (-4.0 ... 10.0)+-- -1.0 ... 7.0+--+-- >>> deflate 2.0 (-1.0 ... 1.0)+-- Empty+--+-- >>> deflate 1.0 empty+-- Empty+deflate :: (Fractional a, Ord a) => a -> Interval a -> Interval a+deflate _ Empty               = Empty+deflate x (I a b) | a' <= b'  = I a' b'+                  | otherwise = Empty+  where+    a' = a + x+    b' = b - x++-- | Scale an interval about its midpoint.+--+-- >>> scale 1.1 (-6.0 ... 4.0)+-- -6.5 ... 4.5+--+-- >>> scale (-2.0) (-1.0 ... 1.0)+-- Empty+--+-- >>> scale 3.0 empty+-- Empty+scale :: (Fractional a, Ord a) => a -> Interval a -> Interval a+scale _ Empty = Empty+scale x i = a ... b where+  h = x * width i / 2+  mid = midpoint i+  a = mid - h+  b = mid + h++-- | Construct a symmetric interval.+--+-- >>> symmetric 3+-- -3 ... 3+--+-- >>> symmetric (-2)+-- -2 ... 2+symmetric :: (Num a, Ord a) => a -> Interval a+symmetric x | a <= b    = I a b+            | otherwise = I b a+  where+    a = negate x+    b = x+ instance (Num a, Ord a) => Num (Interval a) where   I a b + I a' b' = (a + a') ... (b + b')   _ + _ = Empty@@ -592,7 +662,7 @@ -- -- >>> intersection (1 ... 10 :: Interval Double) (5 ... 15 :: Interval Double) -- 5.0 ... 10.0-intersection :: (Fractional a, Ord a) => Interval a -> Interval a -> Interval a+intersection :: Ord a => Interval a -> Interval a -> Interval a intersection x@(I a b) y@(I a' b')   | x /=! y   = Empty   | otherwise = I (max a a') (min b b')

@@ -38,6 +38,8 @@   , magnitude   , mignitude   , distance+  , inflate, deflate+  , scale, symmetric   , contains   , isSubsetOf   , certainly, (<!), (<=!), (==!), (>=!), (>!)@@ -272,6 +274,53 @@ -- NaN distance :: (Num a, Ord a) => Interval a -> Interval a -> a distance i1 i2 = mignitude (i1 - i2)++-- | Inflate an interval by enlarging it at both ends.+--+-- >>> inflate 3 (-1 ... 7)+-- -4 ... 10+--+-- >>> inflate (-2) (0 ... 4)+-- 2 ... 2+inflate :: (Num a, Ord a) => a -> Interval a -> Interval a+inflate x y = symmetric x + y++-- | Deflate an interval by shrinking it from both ends.+--+-- >>> deflate 3.0 (-4.0 ... 10.0)+-- -1.0 ... 7.0+--+-- >>> deflate 2.0 (-1.0 ... 1.0)+-- 1.0 ... -1.0+deflate :: (Fractional a, Ord a) => a -> Interval a -> Interval a+deflate x (I a b) = I a' b'+  where+    a' = a + x+    b' = b - x++-- | Scale an interval about its midpoint.+--+-- >>> scale 1.1 (-6.0 ... 4.0)+-- -6.5 ... 4.5+--+-- >>> scale (-2.0) (-1.0 ... 1.0)+-- 2.0 ... -2.0+scale :: (Fractional a, Ord a) => a -> Interval a -> Interval a+scale x i = I a b where+  h = x * width i / 2+  mid = midpoint i+  a = mid - h+  b = mid + h++-- | Construct a symmetric interval.+--+-- >>> symmetric 3+-- -3 ... 3+--+-- >>> symmetric (-2)+-- 2 ... -2+symmetric :: (Num a, Ord a) => a -> Interval a+symmetric x = negate x ... x  instance (Num a, Ord a) => Num (Interval a) where   I a b + I a' b' = (a + a') ... (b + b')

@@ -42,6 +42,8 @@   , certainly, (<!), (<=!), (==!), (>=!), (>!)   , possibly, (<?), (<=?), (==?), (>=?), (>?)   , clamp+  , inflate, deflate+  , scale, symmetric   , idouble   , ifloat   ) where

@@ -41,6 +41,8 @@   , certainly, (<!), (<=!), (==!), (>=!), (>!)   , possibly, (<?), (<=?), (==?), (>=?), (>?)   , clamp+  , inflate, deflate+  , scale, symmetric   , idouble   , ifloat   ) where@@ -471,7 +473,7 @@ -- -- >>> intersection (1 ... 10 :: Interval Double) (5 ... 15 :: Interval Double) -- Just (5.0 ... 10.0)-intersection :: (Fractional a, Ord a) => Interval a -> Interval a -> Maybe (Interval a)+intersection :: Ord a => Interval a -> Interval a -> Maybe (Interval a) intersection x@(I a b) y@(I a' b')   | x /=! y   = Nothing   | otherwise = Just $ I (max a a') (min b b')@@ -654,6 +656,56 @@   | x < a     = a   | x > b     = b   | otherwise = x++-- | Inflate an interval by enlarging it at both ends.+--+-- >>> inflate 3 (-1 ... 7)+-- -4 ... 10+--+-- >>> inflate (-2) (0 ... 4)+-- -2 ... 6+inflate :: (Num a, Ord a) => a -> Interval a -> Interval a+inflate x y = symmetric x + y++-- | Deflate an interval by shrinking it from both ends.+-- Note that in cases that would result in an empty interval, the result is a singleton interval at the midpoint.+--+-- >>> deflate 3.0 (-4.0 ... 10.0)+-- -1.0 ... 7.0+--+-- >>> deflate 2.0 (-1.0 ... 1.0)+-- 0.0 ... 0.0+deflate :: (Fractional a, Ord a) => a -> Interval a -> Interval a+deflate x i@(I a b) | a' <= b'  = I a' b'+                    | otherwise = singleton m+  where+    a' = a + x+    b' = b - x+    m = midpoint i++-- | Scale an interval about its midpoint.+--+-- >>> scale 1.1 (-6.0 ... 4.0)+-- -6.5 ... 4.5+--+-- >>> scale (-2.0) (-1.0 ... 1.0)+-- -2.0 ... 2.0+scale :: (Fractional a, Ord a) => a -> Interval a -> Interval a+scale x i = a ... b where+  h = x * width i / 2+  mid = midpoint i+  a = mid - h+  b = mid + h++-- | Construct a symmetric interval.+--+-- >>> symmetric 3+-- -3 ... 3+--+-- >>> symmetric (-2)+-- -2 ... 2+symmetric :: (Num a, Ord a) => a -> Interval a+symmetric x = negate x ... x  -- | id function. Useful for type specification --