integration 0.1 → 0.1.1

raw patch · 2 files changed

+28/−4 lines, 2 files

Files

• Numeric/Integration/TanhSinh.hs +27/−3
• integration.cabal +1/−1

@@ -53,23 +53,28 @@   , relative -- relative error   -- * Confidence intervals   , confidence+  -- * Changes of variables+  , nonNegative+  , everywhere   ) where  import Control.Parallel.Strategies import Data.List (foldl') --- integral with an result and an estimate of the error such that (result - errorEstimate, result + errorEstimate) probably bounds the actual answer.+-- | Integral with an result and an estimate of the error such that+-- @(result - errorEstimate, result + errorEstimate)@ /probably/ bounds +-- the actual answer. data Result = Result   { result        :: {-# UNPACK #-} !Double   , errorEstimate :: {-# UNPACK #-} !Double   , evalutions    :: {-# UNPACK #-} !Int   } deriving (Read,Show,Eq,Ord) +-- | Convert a Result to a confidence interval confidence :: Result -> (Double, Double) confidence (Result a b _) = (a - b, a + b) --- TanhSinh quadrature-+-- | Filter a list of results using a specified absolute error bound absolute :: Double -> [Result] -> Result absolute targetError = go where   go [] = error "no result"@@ -78,6 +83,7 @@     | e < targetError*0.1 = r     | otherwise = absolute targetError rs +-- | Filter a list of results using a specified relative error bound relative :: Double -> [Result] -> Result relative _ [] = error "no result" relative _ [r] = r@@ -90,6 +96,24 @@ m_huge :: Double m_huge = 1/0 -- 1.7976931348623157e308 +-- | Integrate a function from 0 to infinity by using the change of variables @x = t/(1-t)@+--+-- This works /much/ better than just clipping the interval at some arbitrary large number.+nonNegative :: ((Double -> Double) -> Double -> Double -> r) -> (Double -> Double) -> r+nonNegative method f = method (\t -> f(t/(1-t))/square(1-t)) 0 1 where+  square x = x * x++-- | Integrate from -inf to inf using tanh-sinh quadrature after using the change of variables @x = tan t@+--+-- > everywhere trap (\x -> x*x*exp(-x))+--+-- This works /much/ better than just clipping the interval at arbitrary large and small numbers.++-- TODO: build a custom set of change of variable tables+everywhere :: ((Double -> Double) -> Double -> Double -> r) -> (Double -> Double) -> r+everywhere method f = method (\t -> f (tan t) * (1 + square (sec t))) (-1) 1+  where sec x = recip (cos x)+        square x = x * x  -- | Integration using a truncated trapezoid rule and tanh-sinh quadrature with a specified evaluation strategy trap' :: Strategy [Double] -> (Double -> Double) -> Double -> Double -> [Result]

@@ -1,5 +1,5 @@ name:                integration-version:             0.1+version:             0.1.1 stability:           experimental synopsis:            Fast robust numeric integration via tanh-sinh quadrature description:         Fast robust numeric integration via tanh-sinh quadrature