{-# OPTIONS_GHC -fno-warn-missing-signatures #-}

{- |
Module      :  Numeric.GSL.Integration
Copyright   :  (c) Alberto Ruiz 2006
License     :  GPL
Maintainer  :  Alberto Ruiz
Stability   :  provisional

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,
    integrateCQUAD
) where

import Foreign.C.Types
import Foreign.Marshal.Alloc(malloc, free)
import Foreign.Ptr(Ptr, FunPtr, freeHaskellFunPtr)
import Foreign.Storable(peek)
import Numeric.GSL.Internal
import System.IO.Unsafe(unsafePerformIO)

eps :: Double
eps = 1e-12

{- | conversion of Haskell functions into function pointers that can be used in the C side
-}
foreign import ccall safe "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 :: Double
-> Int
-> (Double -> Double)
-> Double
-> Double
-> (Double, Double)
integrateQAGS prec :: Double
prec n :: Int
n f :: Double -> Double
f a :: Double
a b :: Double
b = IO (Double, Double) -> (Double, Double)
forall a. IO a -> a
unsafePerformIO (IO (Double, Double) -> (Double, Double))
-> IO (Double, Double) -> (Double, Double)
forall a b. (a -> b) -> a -> b
$ do
    Ptr Double
r <- IO (Ptr Double)
forall a. Storable a => IO (Ptr a)
malloc
    Ptr Double
e <- IO (Ptr Double)
forall a. Storable a => IO (Ptr a)
malloc
    FunPtr (Double -> Ptr () -> Double)
fp <- (Double -> Ptr () -> Double)
-> IO (FunPtr (Double -> Ptr () -> Double))
mkfun (\x :: Double
x _ -> Double -> Double
f Double
x)
    FunPtr (Double -> Ptr () -> Double)
-> Double
-> Double
-> Double
-> Double
-> CInt
-> Ptr Double
-> Ptr Double
-> IO CInt
c_integrate_qags FunPtr (Double -> Ptr () -> Double)
fp Double
a Double
b Double
eps Double
prec (Int -> CInt
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n) Ptr Double
r Ptr Double
e IO CInt -> (IO CInt -> IO ()) -> IO ()
forall x y. x -> (x -> y) -> y
// String -> IO CInt -> IO ()
check "integrate_qags"
    Double
vr <- Ptr Double -> IO Double
forall a. Storable a => Ptr a -> IO a
peek Ptr Double
r
    Double
ve <- Ptr Double -> IO Double
forall a. Storable a => Ptr a -> IO a
peek Ptr Double
e
    let result :: (Double, Double)
result = (Double
vr,Double
ve)
    Ptr Double -> IO ()
forall a. Ptr a -> IO ()
free Ptr Double
r
    Ptr Double -> IO ()
forall a. Ptr a -> IO ()
free Ptr Double
e
    FunPtr (Double -> Ptr () -> Double) -> IO ()
forall a. FunPtr a -> IO ()
freeHaskellFunPtr FunPtr (Double -> Ptr () -> Double)
fp
    (Double, Double) -> IO (Double, Double)
forall (m :: * -> *) a. Monad m => a -> m a
return (Double, Double)
result

foreign import ccall safe "integrate_qags" c_integrate_qags
    :: FunPtr (Double-> Ptr() -> Double) -> 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 :: Double
-> (Double -> Double) -> Double -> Double -> (Double, Double)
integrateQNG prec :: Double
prec f :: Double -> Double
f a :: Double
a b :: Double
b = IO (Double, Double) -> (Double, Double)
forall a. IO a -> a
unsafePerformIO (IO (Double, Double) -> (Double, Double))
-> IO (Double, Double) -> (Double, Double)
forall a b. (a -> b) -> a -> b
$ do
    Ptr Double
r <- IO (Ptr Double)
forall a. Storable a => IO (Ptr a)
malloc
    Ptr Double
e <- IO (Ptr Double)
forall a. Storable a => IO (Ptr a)
malloc
    FunPtr (Double -> Ptr () -> Double)
fp <- (Double -> Ptr () -> Double)
-> IO (FunPtr (Double -> Ptr () -> Double))
mkfun (\x :: Double
x _ -> Double -> Double
f Double
x)
    FunPtr (Double -> Ptr () -> Double)
-> Double
-> Double
-> Double
-> Double
-> Ptr Double
-> Ptr Double
-> IO CInt
c_integrate_qng FunPtr (Double -> Ptr () -> Double)
fp Double
a Double
b Double
eps Double
prec Ptr Double
r Ptr Double
e  IO CInt -> (IO CInt -> IO ()) -> IO ()
forall x y. x -> (x -> y) -> y
// String -> IO CInt -> IO ()
check "integrate_qng"
    Double
vr <- Ptr Double -> IO Double
forall a. Storable a => Ptr a -> IO a
peek Ptr Double
r
    Double
ve <- Ptr Double -> IO Double
forall a. Storable a => Ptr a -> IO a
peek Ptr Double
e
    let result :: (Double, Double)
result = (Double
vr,Double
ve)
    Ptr Double -> IO ()
forall a. Ptr a -> IO ()
free Ptr Double
r
    Ptr Double -> IO ()
forall a. Ptr a -> IO ()
free Ptr Double
e
    FunPtr (Double -> Ptr () -> Double) -> IO ()
forall a. FunPtr a -> IO ()
freeHaskellFunPtr FunPtr (Double -> Ptr () -> Double)
fp
    (Double, Double) -> IO (Double, Double)
forall (m :: * -> *) a. Monad m => a -> m a
return (Double, Double)
result

foreign import ccall safe "integrate_qng" c_integrate_qng
    :: FunPtr (Double-> Ptr() -> Double) -> 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 :: Double -> Int -> (Double -> Double) -> (Double, Double)
integrateQAGI prec :: Double
prec n :: Int
n f :: Double -> Double
f = IO (Double, Double) -> (Double, Double)
forall a. IO a -> a
unsafePerformIO (IO (Double, Double) -> (Double, Double))
-> IO (Double, Double) -> (Double, Double)
forall a b. (a -> b) -> a -> b
$ do
    Ptr Double
r <- IO (Ptr Double)
forall a. Storable a => IO (Ptr a)
malloc
    Ptr Double
e <- IO (Ptr Double)
forall a. Storable a => IO (Ptr a)
malloc
    FunPtr (Double -> Ptr () -> Double)
fp <- (Double -> Ptr () -> Double)
-> IO (FunPtr (Double -> Ptr () -> Double))
mkfun (\x :: Double
x _ -> Double -> Double
f Double
x)
    FunPtr (Double -> Ptr () -> Double)
-> Double -> Double -> CInt -> Ptr Double -> Ptr Double -> IO CInt
c_integrate_qagi FunPtr (Double -> Ptr () -> Double)
fp Double
eps Double
prec (Int -> CInt
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n) Ptr Double
r Ptr Double
e IO CInt -> (IO CInt -> IO ()) -> IO ()
forall x y. x -> (x -> y) -> y
// String -> IO CInt -> IO ()
check "integrate_qagi"
    Double
vr <- Ptr Double -> IO Double
forall a. Storable a => Ptr a -> IO a
peek Ptr Double
r
    Double
ve <- Ptr Double -> IO Double
forall a. Storable a => Ptr a -> IO a
peek Ptr Double
e
    let result :: (Double, Double)
result = (Double
vr,Double
ve)
    Ptr Double -> IO ()
forall a. Ptr a -> IO ()
free Ptr Double
r
    Ptr Double -> IO ()
forall a. Ptr a -> IO ()
free Ptr Double
e
    FunPtr (Double -> Ptr () -> Double) -> IO ()
forall a. FunPtr a -> IO ()
freeHaskellFunPtr FunPtr (Double -> Ptr () -> Double)
fp
    (Double, Double) -> IO (Double, Double)
forall (m :: * -> *) a. Monad m => a -> m a
return (Double, Double)
result

foreign import ccall safe "integrate_qagi" c_integrate_qagi
    :: FunPtr (Double-> Ptr() -> Double) -> 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 :: Double -> Int -> (Double -> Double) -> Double -> (Double, Double)
integrateQAGIU prec :: Double
prec n :: Int
n f :: Double -> Double
f a :: Double
a = IO (Double, Double) -> (Double, Double)
forall a. IO a -> a
unsafePerformIO (IO (Double, Double) -> (Double, Double))
-> IO (Double, Double) -> (Double, Double)
forall a b. (a -> b) -> a -> b
$ do
    Ptr Double
r <- IO (Ptr Double)
forall a. Storable a => IO (Ptr a)
malloc
    Ptr Double
e <- IO (Ptr Double)
forall a. Storable a => IO (Ptr a)
malloc
    FunPtr (Double -> Ptr () -> Double)
fp <- (Double -> Ptr () -> Double)
-> IO (FunPtr (Double -> Ptr () -> Double))
mkfun (\x :: Double
x _ -> Double -> Double
f Double
x)
    FunPtr (Double -> Ptr () -> Double)
-> Double
-> Double
-> Double
-> CInt
-> Ptr Double
-> Ptr Double
-> IO CInt
c_integrate_qagiu FunPtr (Double -> Ptr () -> Double)
fp Double
a Double
eps Double
prec (Int -> CInt
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n) Ptr Double
r Ptr Double
e IO CInt -> (IO CInt -> IO ()) -> IO ()
forall x y. x -> (x -> y) -> y
// String -> IO CInt -> IO ()
check "integrate_qagiu"
    Double
vr <- Ptr Double -> IO Double
forall a. Storable a => Ptr a -> IO a
peek Ptr Double
r
    Double
ve <- Ptr Double -> IO Double
forall a. Storable a => Ptr a -> IO a
peek Ptr Double
e
    let result :: (Double, Double)
result = (Double
vr,Double
ve)
    Ptr Double -> IO ()
forall a. Ptr a -> IO ()
free Ptr Double
r
    Ptr Double -> IO ()
forall a. Ptr a -> IO ()
free Ptr Double
e
    FunPtr (Double -> Ptr () -> Double) -> IO ()
forall a. FunPtr a -> IO ()
freeHaskellFunPtr FunPtr (Double -> Ptr () -> Double)
fp
    (Double, Double) -> IO (Double, Double)
forall (m :: * -> *) a. Monad m => a -> m a
return (Double, Double)
result

foreign import ccall safe "integrate_qagiu" c_integrate_qagiu
    :: FunPtr (Double-> Ptr() -> Double) -> 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 :: Double -> Int -> (Double -> Double) -> Double -> (Double, Double)
integrateQAGIL prec :: Double
prec n :: Int
n f :: Double -> Double
f b :: Double
b = IO (Double, Double) -> (Double, Double)
forall a. IO a -> a
unsafePerformIO (IO (Double, Double) -> (Double, Double))
-> IO (Double, Double) -> (Double, Double)
forall a b. (a -> b) -> a -> b
$ do
    Ptr Double
r <- IO (Ptr Double)
forall a. Storable a => IO (Ptr a)
malloc
    Ptr Double
e <- IO (Ptr Double)
forall a. Storable a => IO (Ptr a)
malloc
    FunPtr (Double -> Ptr () -> Double)
fp <- (Double -> Ptr () -> Double)
-> IO (FunPtr (Double -> Ptr () -> Double))
mkfun (\x :: Double
x _ -> Double -> Double
f Double
x)
    FunPtr (Double -> Ptr () -> Double)
-> Double
-> Double
-> Double
-> CInt
-> Ptr Double
-> Ptr Double
-> IO CInt
c_integrate_qagil FunPtr (Double -> Ptr () -> Double)
fp Double
b Double
eps Double
prec (Int -> CInt
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n) Ptr Double
r Ptr Double
e IO CInt -> (IO CInt -> IO ()) -> IO ()
forall x y. x -> (x -> y) -> y
// String -> IO CInt -> IO ()
check "integrate_qagil"
    Double
vr <- Ptr Double -> IO Double
forall a. Storable a => Ptr a -> IO a
peek Ptr Double
r
    Double
ve <- Ptr Double -> IO Double
forall a. Storable a => Ptr a -> IO a
peek Ptr Double
e
    let result :: (Double, Double)
result = (Double
vr,Double
ve)
    Ptr Double -> IO ()
forall a. Ptr a -> IO ()
free Ptr Double
r
    Ptr Double -> IO ()
forall a. Ptr a -> IO ()
free Ptr Double
e
    FunPtr (Double -> Ptr () -> Double) -> IO ()
forall a. FunPtr a -> IO ()
freeHaskellFunPtr FunPtr (Double -> Ptr () -> Double)
fp
    (Double, Double) -> IO (Double, Double)
forall (m :: * -> *) a. Monad m => a -> m a
return (Double, Double)
result

foreign import ccall safe "gsl-aux.h integrate_qagil" c_integrate_qagil
    :: FunPtr (Double-> Ptr() -> Double) -> Double -> Double
    -> Double -> CInt -> Ptr Double -> Ptr Double -> IO CInt


--------------------------------------------------------------------
{- | Numerical integration using /gsl_integration_cquad/ (quadrature
for general integrands).  From the GSL manual:

@CQUAD is a new doubly-adaptive general-purpose quadrature routine
which can handle most types of singularities, non-numerical function
values such as Inf or NaN, as well as some divergent integrals. It
generally requires more function evaluations than the integration
routines in QUADPACK, yet fails less often for difficult integrands.@

For example:

>>> let quad = integrateCQUAD 1E-12 1000
>>> let f a x = exp(-a * x^2)
>>> quad (f 0.5) 2 5
(5.7025405463957006e-2,9.678874441303705e-16,95)

Unlike other quadrature methods, integrateCQUAD also returns the
number of function evaluations required.

-}

integrateCQUAD :: 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, Int) -- ^ result of the integration, error and number of function evaluations performed
integrateCQUAD :: Double
-> Int
-> (Double -> Double)
-> Double
-> Double
-> (Double, Double, Int)
integrateCQUAD prec :: Double
prec n :: Int
n f :: Double -> Double
f a :: Double
a b :: Double
b = IO (Double, Double, Int) -> (Double, Double, Int)
forall a. IO a -> a
unsafePerformIO (IO (Double, Double, Int) -> (Double, Double, Int))
-> IO (Double, Double, Int) -> (Double, Double, Int)
forall a b. (a -> b) -> a -> b
$ do
    Ptr Double
r <- IO (Ptr Double)
forall a. Storable a => IO (Ptr a)
malloc
    Ptr Double
e <- IO (Ptr Double)
forall a. Storable a => IO (Ptr a)
malloc
    Ptr Int
neval <- IO (Ptr Int)
forall a. Storable a => IO (Ptr a)
malloc
    FunPtr (Double -> Ptr () -> Double)
fp <- (Double -> Ptr () -> Double)
-> IO (FunPtr (Double -> Ptr () -> Double))
mkfun (\x :: Double
x _ -> Double -> Double
f Double
x)
    FunPtr (Double -> Ptr () -> Double)
-> Double
-> Double
-> Double
-> Double
-> CInt
-> Ptr Double
-> Ptr Double
-> Ptr Int
-> IO CInt
c_integrate_cquad FunPtr (Double -> Ptr () -> Double)
fp Double
a Double
b Double
eps Double
prec (Int -> CInt
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n) Ptr Double
r Ptr Double
e Ptr Int
neval IO CInt -> (IO CInt -> IO ()) -> IO ()
forall x y. x -> (x -> y) -> y
// String -> IO CInt -> IO ()
check "integrate_cquad"
    Double
vr <- Ptr Double -> IO Double
forall a. Storable a => Ptr a -> IO a
peek Ptr Double
r
    Double
ve <- Ptr Double -> IO Double
forall a. Storable a => Ptr a -> IO a
peek Ptr Double
e
    Int
vneval <- Ptr Int -> IO Int
forall a. Storable a => Ptr a -> IO a
peek Ptr Int
neval
    let result :: (Double, Double, Int)
result = (Double
vr,Double
ve,Int
vneval)
    Ptr Double -> IO ()
forall a. Ptr a -> IO ()
free Ptr Double
r
    Ptr Double -> IO ()
forall a. Ptr a -> IO ()
free Ptr Double
e
    Ptr Int -> IO ()
forall a. Ptr a -> IO ()
free Ptr Int
neval
    FunPtr (Double -> Ptr () -> Double) -> IO ()
forall a. FunPtr a -> IO ()
freeHaskellFunPtr FunPtr (Double -> Ptr () -> Double)
fp
    (Double, Double, Int) -> IO (Double, Double, Int)
forall (m :: * -> *) a. Monad m => a -> m a
return (Double, Double, Int)
result

foreign import ccall safe "integrate_cquad" c_integrate_cquad
    :: FunPtr (Double-> Ptr() -> Double) -> Double -> Double
    -> Double -> Double -> CInt -> Ptr Double -> Ptr Double -> Ptr Int -> IO CInt