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|
{-# OPTIONS #-}
-----------------------------------------------------------------------------
{- |
Module : Numeric.GSL.Integration
Copyright : (c) Alberto Ruiz 2006
License : GPL-style
Maintainer : Alberto Ruiz (aruiz at um dot es)
Stability : provisional
Portability : uses ffi
Numerical integration routines.
<http://www.gnu.org/software/gsl/manual/html_node/Numerical-Integration.html#Numerical-Integration>
-}
-----------------------------------------------------------------------------
module Numeric.GSL.Integration (
integrateQNG,
integrateQAGS,
integrateQAGI,
integrateQAGIU,
integrateQAGIL
) where
import Foreign.C.Types
import Foreign.Marshal.Alloc(malloc, free)
import Foreign.Ptr(Ptr, FunPtr, freeHaskellFunPtr)
import Foreign.Storable(peek)
import Data.Packed.Internal(check,(//))
import System.IO.Unsafe(unsafePerformIO)
{- | conversion of Haskell functions into function pointers that can be used in the C side
-}
foreign import ccall "wrapper" mkfun:: (Double -> Ptr() -> Double) -> IO( FunPtr (Double -> Ptr() -> Double))
--------------------------------------------------------------------
{- | Numerical integration using /gsl_integration_qags/ (adaptive integration with singularities). For example:
@\> let quad = integrateQAGS 1E-9 1000
\> let f a x = x**(-0.5) * log (a*x)
\> quad (f 1) 0 1
(-3.999999999999974,4.871658632055187e-13)@
-}
integrateQAGS :: Double -- ^ precision (e.g. 1E-9)
-> Int -- ^ size of auxiliary workspace (e.g. 1000)
-> (Double -> Double) -- ^ function to be integrated on the interval (a,b)
-> Double -- ^ a
-> Double -- ^ b
-> (Double, Double) -- ^ result of the integration and error
integrateQAGS prec n f a b = unsafePerformIO $ do
r <- malloc
e <- malloc
fp <- mkfun (\x _ -> f x)
c_integrate_qags fp a b prec (fromIntegral n) r e // check "integrate_qags"
vr <- peek r
ve <- peek e
let result = (vr,ve)
free r
free e
freeHaskellFunPtr fp
return result
foreign import ccall "gsl-aux.h integrate_qags"
c_integrate_qags :: FunPtr (Double-> Ptr() -> Double) -> Double -> Double -> Double -> CInt
-> Ptr Double -> Ptr Double -> IO CInt
-----------------------------------------------------------------
{- | Numerical integration using /gsl_integration_qng/ (useful for fast integration of smooth functions). For example:
@\> let quad = integrateQNG 1E-6
\> quad (\\x -> 4\/(1+x*x)) 0 1
(3.141592653589793,3.487868498008632e-14)@
-}
integrateQNG :: Double -- ^ precision (e.g. 1E-9)
-> (Double -> Double) -- ^ function to be integrated on the interval (a,b)
-> Double -- ^ a
-> Double -- ^ b
-> (Double, Double) -- ^ result of the integration and error
integrateQNG prec f a b = unsafePerformIO $ do
r <- malloc
e <- malloc
fp <- mkfun (\x _ -> f x)
c_integrate_qng fp a b prec r e // check "integrate_qng"
vr <- peek r
ve <- peek e
let result = (vr,ve)
free r
free e
freeHaskellFunPtr fp
return result
foreign import ccall "gsl-aux.h integrate_qng"
c_integrate_qng :: FunPtr (Double-> Ptr() -> Double) -> Double -> Double -> Double
-> Ptr Double -> Ptr Double -> IO CInt
--------------------------------------------------------------------
{- | Numerical integration using /gsl_integration_qagi/ (integration over the infinite integral -Inf..Inf using QAGS).
For example:
@\> let quad = integrateQAGI 1E-9 1000
\> let f a x = exp(-a * x^2)
\> quad (f 0.5)
(2.5066282746310002,6.229215880648858e-11)@
-}
integrateQAGI :: Double -- ^ precision (e.g. 1E-9)
-> Int -- ^ size of auxiliary workspace (e.g. 1000)
-> (Double -> Double) -- ^ function to be integrated on the interval (-Inf,Inf)
-> (Double, Double) -- ^ result of the integration and error
integrateQAGI prec n f = unsafePerformIO $ do
r <- malloc
e <- malloc
fp <- mkfun (\x _ -> f x)
c_integrate_qagi fp prec (fromIntegral n) r e // check "integrate_qagi"
vr <- peek r
ve <- peek e
let result = (vr,ve)
free r
free e
freeHaskellFunPtr fp
return result
foreign import ccall "gsl-aux.h integrate_qagi"
c_integrate_qagi :: FunPtr (Double-> Ptr() -> Double) -> Double -> CInt
-> Ptr Double -> Ptr Double -> IO CInt
--------------------------------------------------------------------
{- | Numerical integration using /gsl_integration_qagiu/ (integration over the semi-infinite integral a..Inf).
For example:
@\> let quad = integrateQAGIU 1E-9 1000
\> let f a x = exp(-a * x^2)
\> quad (f 0.5) 0
(1.2533141373155001,3.114607940324429e-11)@
-}
integrateQAGIU :: Double -- ^ precision (e.g. 1E-9)
-> Int -- ^ size of auxiliary workspace (e.g. 1000)
-> (Double -> Double) -- ^ function to be integrated on the interval (a,Inf)
-> Double -- ^ a
-> (Double, Double) -- ^ result of the integration and error
integrateQAGIU prec n f a = unsafePerformIO $ do
r <- malloc
e <- malloc
fp <- mkfun (\x _ -> f x)
c_integrate_qagiu fp a prec (fromIntegral n) r e // check "integrate_qagiu"
vr <- peek r
ve <- peek e
let result = (vr,ve)
free r
free e
freeHaskellFunPtr fp
return result
foreign import ccall "gsl-aux.h integrate_qagiu"
c_integrate_qagiu :: FunPtr (Double-> Ptr() -> Double) -> Double -> Double -> CInt
-> Ptr Double -> Ptr Double -> IO CInt
--------------------------------------------------------------------
{- | Numerical integration using /gsl_integration_qagil/ (integration over the semi-infinite integral -Inf..b).
For example:
@\> let quad = integrateQAGIL 1E-9 1000
\> let f a x = exp(-a * x^2)
\> quad (f 0.5) 0
(1.2533141373155001,3.114607940324429e-11)@
-}
integrateQAGIL :: Double -- ^ precision (e.g. 1E-9)
-> Int -- ^ size of auxiliary workspace (e.g. 1000)
-> (Double -> Double) -- ^ function to be integrated on the interval (a,Inf)
-> Double -- ^ b
-> (Double, Double) -- ^ result of the integration and error
integrateQAGIL prec n f b = unsafePerformIO $ do
r <- malloc
e <- malloc
fp <- mkfun (\x _ -> f x)
c_integrate_qagil fp b prec (fromIntegral n) r e // check "integrate_qagil"
vr <- peek r
ve <- peek e
let result = (vr,ve)
free r
free e
freeHaskellFunPtr fp
return result
foreign import ccall "gsl-aux.h integrate_qagil"
c_integrate_qagil :: FunPtr (Double-> Ptr() -> Double) -> Double -> Double -> CInt
-> Ptr Double -> Ptr Double -> IO CInt
|
