hypergeometric 0.1.3.0 → 0.1.4.0

raw patch · 4 files changed

+42/−4 lines, 4 filesPVP ok

version bump matches the API change (PVP)

API changes (from Hackage documentation)

Files

• CHANGELOG.md +4/−0
• hypergeometric.cabal +1/−1
• src/Math/Hypergeometric.hs +3/−3
• src/Math/SpecialFunction.hs +34/−0

@@ -1,5 +1,9 @@ # hypergeometric +## 0.1.4.0++  * Add `agm`, `completeElliptic`+ ## 0.1.3.0    * Add `bessel1`

@@ -1,6 +1,6 @@ cabal-version:   1.18 name:            hypergeometric-version:         0.1.3.0+version:         0.1.4.0 license:         AGPL-3 license-file:    COPYING copyright:       Copyright: (c) 2022 Vanessa McHale

@@ -13,20 +13,20 @@ factorial :: Num a => Int -> a factorial n = product (fromIntegral <$> [1..n]) --- prop_cdf :: (Double -> Double) -> Double -> Bool--- prop_cdf f x = f x <= 1- {-# SPECIALIZE ncdf :: Double -> Double #-}+{-# SPECIALIZE ncdf :: Float -> Float #-} -- | CDF of the standard normal \( N(0,1) \) ncdf :: (Eq a, Floating a) => a -> a ncdf z = (1/2) * (1 + erf (z / sqrt 2))  {-# SPECIALIZE erf :: Double -> Double #-}+{-# SPECIALIZE erf :: Float -> Float #-} -- | [erf](https://mathworld.wolfram.com/Erf.html) erf :: (Eq a, Floating a) => a -> a erf z = (2 * z * exp (-z^(2::Int)) / sqrt pi) * hypergeometric [1] [3/2] (z^(2::Int))  {-# SPECIALIZE hypergeometric :: [Double] -> [Double] -> Double -> Double #-}+{-# SPECIALIZE hypergeometric :: [Float] -> [Float] -> Float -> Float #-} -- | \( _pF_q(a_1,\ldots,a_p;b_1,\ldots,b_q;z) = \displaystyle\sum_{n=0}^\infty\frac{(a_1)_n\cdots(a_p)_n}{(b_1)_b\cdots(b_q)_n}\frac{z^n}{n!} \) -- -- This iterates until the result stabilizes.

@@ -3,6 +3,8 @@                             , bessel1                             , gamma                             , gammaln+                            , agm+                            , completeElliptic                             , fcdf                             , chisqcdf                             , tcdf@@ -11,6 +13,7 @@ import           Math.Hypergeometric  {-# SPECIALIZE tcdf :: Double -> Double -> Double #-}+{-# SPECIALIZE tcdf :: Float -> Float -> Float #-} -- | Converges if and only if \(|x| < \sqrt{\nu} \) -- -- @since 0.1.2.0@@ -20,6 +23,8 @@      -> a tcdf 𝜈 x = 0.5 + x * gamma (0.5*(𝜈+1)) / (sqrt(pi*𝜈) * gamma(𝜈/2)) * hypergeometric [0.5, 0.5*(𝜈+1)] [1.5] (-x^(2::Int)/𝜈) +{-# SPECIALIZE bessel1 :: Double -> Double -> Double #-}+{-# SPECIALIZE bessel1 :: Float -> Float -> Float #-} -- | Bessel functions of the first kind, \( J_\alpha(x)\). -- -- @since 0.1.3.0@@ -29,8 +34,30 @@         -> a bessel1 𝛼 x = ((x/2)**𝛼/gamma(𝛼+1))*hypergeometric [] [𝛼+1] (-(x^(2::Int))/4) +{-# SPECIALIZE completeElliptic :: Double -> Double #-}+{-# SPECIALIZE completeElliptic :: Float -> Float #-}+-- | [Complete elliptic integral of the first kind](https://mathworld.wolfram.com/CompleteEllipticIntegraloftheFirstKind.html)+--+-- @since 0.1.4.0+completeElliptic :: (Ord a, Floating a) => a -> a+completeElliptic k = pi/(2*agm 1 (sqrt (1-k^(2::Int))))++{-# SPECIALIZE agm :: Double -> Double -> Double #-}+{-# SPECIALIZE agm :: Float -> Float -> Float #-}+-- | [Arithmetic-geometric mean](https://mathworld.wolfram.com/Arithmetic-GeometricMean.html)+--+-- @since 0.1.4.0+agm :: (Ord a, Floating a) => a -> a -> a+agm a b =+    let a' = (a+b)/2+        b' = sqrt(a*b)+    in if (a'-b')/b'<1e-15 && (b'-a')/b'<1e-15+        then a'+        else agm a' b'+ -- | @since 0.1.2.0 {-# SPECIALIZE chisqcdf :: Double -> Double -> Double #-}+{-# SPECIALIZE chisqcdf :: Float -> Float -> Float #-} chisqcdf :: (Floating a, Ord a)          => a -- ^ \(r\) (degrees of freedom)          -> a -- ^ \(\chi^2\)@@ -38,6 +65,7 @@ chisqcdf r x = incgamma (0.5*r) (0.5*x) / gamma (0.5*r)  {-# SPECIALIZE incgamma :: Double -> Double -> Double #-}+{-# SPECIALIZE incgamma :: Float -> Float -> Float #-} -- | \(a^{-1}x^a{}_1F_1(a;1+a;-x) \) incgamma :: (Floating a, Ord a) => a -> a -> a incgamma a x = (1/a) * x ** a * hypergeometric [a] [1+a] (-x)@@ -48,6 +76,7 @@ -- (1 2 H. _1.1) 1 hangs indefinitely  {-# SPECIALIZE incbeta :: Double -> Double -> Double -> Double #-}+{-# SPECIALIZE incbeta :: Float -> Float -> Float -> Float #-} -- | Incomplete beta function, \(|z|<1\) -- -- Calculated with \(B(z;a,b)=\displaystyle\frac{z^a}{a}{}_2F_1(a, 1-b; a+1; z)\)@@ -61,11 +90,13 @@ incbeta z a b = z**a/a * hypergeometric [a,1-b] [a+1] z  {-# SPECIALIZE regbeta :: Double -> Double -> Double -> Double #-}+{-# SPECIALIZE regbeta :: Float -> Float -> Float -> Float #-} -- | \(I(z;a,b) = \displaystyle\frac{B(z;a,b)}{B(a,b)}\) regbeta :: (Floating a, Ord a) => a -> a -> a -> a regbeta z a b = incbeta z a b / beta a b  {-# SPECIALIZE fcdf :: Double -> Double -> Double -> Double #-}+{-# SPECIALIZE fcdf :: Float -> Float -> Float -> Float #-} -- | @since 0.1.2.0 fcdf :: (Floating a, Ord a)      => a -- ^ \(n\)@@ -75,6 +106,7 @@ fcdf n m x = regbeta (n * x / (m + n * x)) (0.5 * n) (0.5 * m) -- we can use hypergeo because nx/(m+nx) < 1  {-# SPECIALIZE beta :: Double -> Double -> Double #-}+{-# SPECIALIZE beta :: Float -> Float -> Float #-} -- | \(B(x, y) = \displaystyle\frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\) -- -- This uses 'gammaln' under the hood to extend its domain somewhat.@@ -84,6 +116,7 @@ beta x y = exp (betaln x y)  {-# SPECIALIZE betaln :: Double -> Double -> Double #-}+{-# SPECIALIZE betaln :: Float -> Float -> Float #-} betaln :: (Floating a, Ord a) => a -> a -> a betaln x y = gammaln x + gammaln y - gammaln (x+y) @@ -94,6 +127,7 @@ gamma = exp . gammaln  {-# SPECIALIZE gammaln :: Double -> Double #-}+{-# SPECIALIZE gammaln :: Float -> Float #-} -- | \(\text{log} (\Gamma(z))\) -- -- Lanczos approximation.