{-# LANGUAGE BangPatterns, FlexibleContexts #-}-- |-- Module : Statistics.Transform-- Copyright : (c) 2011 Bryan O'Sullivan-- License : BSD3---- Maintainer : bos@serpentine.com-- Stability : experimental-- Portability : portable---- Fourier-related transformations of mathematical functions.---- These functions are written for simplicity and correctness, not-- speed. If you need a fast FFT implementation for your application,-- you should strongly consider using a library of FFTW bindings-- instead.moduleStatistics.Transform(-- * Type synonymsCD -- * Discrete cosine transform,dct ,dct_ ,idct ,idct_ -- * Fast Fourier transform,fft ,ifft )whereimportControl.Monad(when)importControl.Monad.ST(ST)importData.Bits(shiftL,shiftR)importData.Complex(Complex(..),conjugate,realPart)importNumeric.SpecFunctions(log2)importqualifiedData.Vector.GenericasGimportqualifiedData.Vector.Generic.MutableasMimportqualifiedData.Vector.UnboxedasUimportqualifiedData.VectorasVtypeCD =ComplexDouble-- | Discrete cosine transform (DCT-II).dct ::(G.Vectorv CD ,G.Vectorv Double,G.Vectorv Int)=>v Double->v Doubledct :: forall (v :: * -> *).
(Vector v CD, Vector v Double, Vector v Int) =>
v Double -> v Double
dct =v CD -> v Double
forall (v :: * -> *).
(Vector v CD, Vector v Double, Vector v Int) =>
v CD -> v Double
dctWorker (v CD -> v Double) -> (v Double -> v CD) -> v Double -> v Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(Double -> CD) -> v Double -> v CD
forall (v :: * -> *) a b.
(Vector v a, Vector v b) =>
(a -> b) -> v a -> v b
G.map(Double -> Double -> CD
forall a. a -> a -> Complex a
:+Double
0){-# INLINABLEdct #-}{-# SPECIAlIZEdct ::U.VectorDouble->U.VectorDouble#-}{-# SPECIAlIZEdct ::V.VectorDouble->V.VectorDouble#-}-- | Discrete cosine transform (DCT-II). Only real part of vector is-- transformed, imaginary part is ignored.dct_ ::(G.Vectorv CD ,G.Vectorv Double,G.Vectorv Int)=>v CD ->v Doubledct_ :: forall (v :: * -> *).
(Vector v CD, Vector v Double, Vector v Int) =>
v CD -> v Double
dct_ =v CD -> v Double
forall (v :: * -> *).
(Vector v CD, Vector v Double, Vector v Int) =>
v CD -> v Double
dctWorker (v CD -> v Double) -> (v CD -> v CD) -> v CD -> v Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(CD -> CD) -> v CD -> v CD
forall (v :: * -> *) a b.
(Vector v a, Vector v b) =>
(a -> b) -> v a -> v b
G.map(\(Double
i :+Double
_)->Double
i Double -> Double -> CD
forall a. a -> a -> Complex a
:+Double
0){-# INLINABLEdct_ #-}{-# SPECIAlIZEdct_ ::U.VectorCD ->U.VectorDouble#-}{-# SPECIAlIZEdct_ ::V.VectorCD ->V.VectorDouble#-}dctWorker ::(G.Vectorv CD ,G.Vectorv Double,G.Vectorv Int)=>v CD ->v Double{-# INLINEdctWorker #-}dctWorker :: forall (v :: * -> *).
(Vector v CD, Vector v Double, Vector v Int) =>
v CD -> v Double
dctWorker v CD
xs -- length 1 is special cased because shuffle algorithms fail for it.|v CD -> Int
forall (v :: * -> *) a. Vector v a => v a -> Int
G.lengthv CD
xs Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
==Int
1=(CD -> Double) -> v CD -> v Double
forall (v :: * -> *) a b.
(Vector v a, Vector v b) =>
(a -> b) -> v a -> v b
G.map((Double
2Double -> Double -> Double
forall a. Num a => a -> a -> a
*)(Double -> Double) -> (CD -> Double) -> CD -> Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.CD -> Double
forall a. Complex a -> a
realPart)v CD
xs |v CD -> Bool
forall (v :: * -> *) a. Vector v a => v a -> Bool
vectorOK v CD
xs =(CD -> Double) -> v CD -> v Double
forall (v :: * -> *) a b.
(Vector v a, Vector v b) =>
(a -> b) -> v a -> v b
G.mapCD -> Double
forall a. Complex a -> a
realPart(v CD -> v Double) -> v CD -> v Double
forall a b. (a -> b) -> a -> b
$(CD -> CD -> CD) -> v CD -> v CD -> v CD
forall (v :: * -> *) a b c.
(Vector v a, Vector v b, Vector v c) =>
(a -> b -> c) -> v a -> v b -> v c
G.zipWithCD -> CD -> CD
forall a. Num a => a -> a -> a
(*)v CD
weights (v CD -> v CD
forall (v :: * -> *). Vector v CD => v CD -> v CD
fft v CD
interleaved )|Bool
otherwise=[Char] -> v Double
forall a. HasCallStack => [Char] -> a
error[Char]
"Statistics.Transform.dct: bad vector length"whereinterleaved :: v CD
interleaved =v CD -> v Int -> v CD
forall (v :: * -> *) a.
(HasCallStack, Vector v a, Vector v Int) =>
v a -> v Int -> v a
G.backpermutev CD
xs (v Int -> v CD) -> v Int -> v CD
forall a b. (a -> b) -> a -> b
$Int -> Int -> Int -> v Int
forall (v :: * -> *) a. (Vector v a, Enum a) => a -> a -> a -> v a
G.enumFromThenToInt
0Int
2(Int
len Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
2)v Int -> v Int -> v Int
forall (v :: * -> *) a. Vector v a => v a -> v a -> v a
G.++Int -> Int -> Int -> v Int
forall (v :: * -> *) a. (Vector v a, Enum a) => a -> a -> a -> v a
G.enumFromThenTo(Int
len Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
1)(Int
len Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
3)Int
1weights :: v CD
weights =CD -> v CD -> v CD
forall (v :: * -> *) a. Vector v a => a -> v a -> v a
G.consCD
2(v CD -> v CD) -> ((Int -> CD) -> v CD) -> (Int -> CD) -> v CD
forall b c a. (b -> c) -> (a -> b) -> a -> c
.Int -> (Int -> CD) -> v CD
forall (v :: * -> *) a. Vector v a => Int -> (Int -> a) -> v a
G.generate(Int
len Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
1)((Int -> CD) -> v CD) -> (Int -> CD) -> v CD
forall a b. (a -> b) -> a -> b
$\Int
x ->CD
2CD -> CD -> CD
forall a. Num a => a -> a -> a
*CD -> CD
forall a. Floating a => a -> a
exp((Double
0Double -> Double -> CD
forall a. a -> a -> Complex a
:+(-Double
1))CD -> CD -> CD
forall a. Num a => a -> a -> a
*Int -> CD
fi (Int
x Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1)CD -> CD -> CD
forall a. Num a => a -> a -> a
*CD
forall a. Floating a => a
piCD -> CD -> CD
forall a. Fractional a => a -> a -> a
/(CD
2CD -> CD -> CD
forall a. Num a => a -> a -> a
*CD
n ))wheren :: CD
n =Int -> CD
fi Int
len len :: Int
len =v CD -> Int
forall (v :: * -> *) a. Vector v a => v a -> Int
G.lengthv CD
xs -- | Inverse discrete cosine transform (DCT-III). It's inverse of-- 'dct' only up to scale parameter:---- > (idct . dct) x = (* length x)idct ::(G.Vectorv CD ,G.Vectorv Double)=>v Double->v Doubleidct :: forall (v :: * -> *).
(Vector v CD, Vector v Double) =>
v Double -> v Double
idct =v CD -> v Double
forall (v :: * -> *).
(Vector v CD, Vector v Double) =>
v CD -> v Double
idctWorker (v CD -> v Double) -> (v Double -> v CD) -> v Double -> v Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(Double -> CD) -> v Double -> v CD
forall (v :: * -> *) a b.
(Vector v a, Vector v b) =>
(a -> b) -> v a -> v b
G.map(Double -> Double -> CD
forall a. a -> a -> Complex a
:+Double
0){-# INLINABLEidct #-}{-# SPECIAlIZEidct ::U.VectorDouble->U.VectorDouble#-}{-# SPECIAlIZEidct ::V.VectorDouble->V.VectorDouble#-}-- | Inverse discrete cosine transform (DCT-III). Only real part of vector is-- transformed, imaginary part is ignored.idct_ ::(G.Vectorv CD ,G.Vectorv Double)=>v CD ->v Doubleidct_ :: forall (v :: * -> *).
(Vector v CD, Vector v Double) =>
v CD -> v Double
idct_ =v CD -> v Double
forall (v :: * -> *).
(Vector v CD, Vector v Double) =>
v CD -> v Double
idctWorker (v CD -> v Double) -> (v CD -> v CD) -> v CD -> v Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(CD -> CD) -> v CD -> v CD
forall (v :: * -> *) a b.
(Vector v a, Vector v b) =>
(a -> b) -> v a -> v b
G.map(\(Double
i :+Double
_)->Double
i Double -> Double -> CD
forall a. a -> a -> Complex a
:+Double
0){-# INLINABLEidct_ #-}{-# SPECIAlIZEidct_ ::U.VectorCD ->U.VectorDouble#-}{-# SPECIAlIZEidct_ ::V.VectorCD ->V.VectorDouble#-}idctWorker ::(G.Vectorv CD ,G.Vectorv Double)=>v CD ->v Double{-# INLINEidctWorker #-}idctWorker :: forall (v :: * -> *).
(Vector v CD, Vector v Double) =>
v CD -> v Double
idctWorker v CD
xs |v CD -> Bool
forall (v :: * -> *) a. Vector v a => v a -> Bool
vectorOK v CD
xs =Int -> (Int -> Double) -> v Double
forall (v :: * -> *) a. Vector v a => Int -> (Int -> a) -> v a
G.generateInt
len Int -> Double
interleave |Bool
otherwise=[Char] -> v Double
forall a. HasCallStack => [Char] -> a
error[Char]
"Statistics.Transform.dct: bad vector length"whereinterleave :: Int -> Double
interleave Int
z |Int -> Bool
forall a. Integral a => a -> Bool
evenInt
z =v Double
vals v Double -> Int -> Double
forall (v :: * -> *) a. Vector v a => v a -> Int -> a
`G.unsafeIndex`Int -> Int
halve Int
z |Bool
otherwise=v Double
vals v Double -> Int -> Double
forall (v :: * -> *) a. Vector v a => v a -> Int -> a
`G.unsafeIndex`(Int
len Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int -> Int
halve Int
z Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
1)vals :: v Double
vals =(CD -> Double) -> v CD -> v Double
forall (v :: * -> *) a b.
(Vector v a, Vector v b) =>
(a -> b) -> v a -> v b
G.mapCD -> Double
forall a. Complex a -> a
realPart(v CD -> v Double) -> (v CD -> v CD) -> v CD -> v Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.v CD -> v CD
forall (v :: * -> *). Vector v CD => v CD -> v CD
ifft (v CD -> v Double) -> v CD -> v Double
forall a b. (a -> b) -> a -> b
$(CD -> CD -> CD) -> v CD -> v CD -> v CD
forall (v :: * -> *) a b c.
(Vector v a, Vector v b, Vector v c) =>
(a -> b -> c) -> v a -> v b -> v c
G.zipWithCD -> CD -> CD
forall a. Num a => a -> a -> a
(*)v CD
weights v CD
xs weights :: v CD
weights =CD -> v CD -> v CD
forall (v :: * -> *) a. Vector v a => a -> v a -> v a
G.consCD
n (v CD -> v CD) -> v CD -> v CD
forall a b. (a -> b) -> a -> b
$Int -> (Int -> CD) -> v CD
forall (v :: * -> *) a. Vector v a => Int -> (Int -> a) -> v a
G.generate(Int
len Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
1)((Int -> CD) -> v CD) -> (Int -> CD) -> v CD
forall a b. (a -> b) -> a -> b
$\Int
x ->CD
2CD -> CD -> CD
forall a. Num a => a -> a -> a
*CD
n CD -> CD -> CD
forall a. Num a => a -> a -> a
*CD -> CD
forall a. Floating a => a -> a
exp((Double
0Double -> Double -> CD
forall a. a -> a -> Complex a
:+Double
1)CD -> CD -> CD
forall a. Num a => a -> a -> a
*Int -> CD
fi (Int
x Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1)CD -> CD -> CD
forall a. Num a => a -> a -> a
*CD
forall a. Floating a => a
piCD -> CD -> CD
forall a. Fractional a => a -> a -> a
/(CD
2CD -> CD -> CD
forall a. Num a => a -> a -> a
*CD
n ))wheren :: CD
n =Int -> CD
fi Int
len len :: Int
len =v CD -> Int
forall (v :: * -> *) a. Vector v a => v a -> Int
G.lengthv CD
xs -- | Inverse fast Fourier transform.ifft ::G.Vectorv CD =>v CD ->v CD ifft :: forall (v :: * -> *). Vector v CD => v CD -> v CD
ifft v CD
xs |v CD -> Bool
forall (v :: * -> *) a. Vector v a => v a -> Bool
vectorOK v CD
xs =(CD -> CD) -> v CD -> v CD
forall (v :: * -> *) a b.
(Vector v a, Vector v b) =>
(a -> b) -> v a -> v b
G.map((CD -> CD -> CD
forall a. Fractional a => a -> a -> a
/Int -> CD
fi (v CD -> Int
forall (v :: * -> *) a. Vector v a => v a -> Int
G.lengthv CD
xs ))(CD -> CD) -> (CD -> CD) -> CD -> CD
forall b c a. (b -> c) -> (a -> b) -> a -> c
.CD -> CD
forall a. Num a => Complex a -> Complex a
conjugate)(v CD -> v CD) -> (v CD -> v CD) -> v CD -> v CD
forall b c a. (b -> c) -> (a -> b) -> a -> c
.v CD -> v CD
forall (v :: * -> *). Vector v CD => v CD -> v CD
fft (v CD -> v CD) -> (v CD -> v CD) -> v CD -> v CD
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(CD -> CD) -> v CD -> v CD
forall (v :: * -> *) a b.
(Vector v a, Vector v b) =>
(a -> b) -> v a -> v b
G.mapCD -> CD
forall a. Num a => Complex a -> Complex a
conjugate(v CD -> v CD) -> v CD -> v CD
forall a b. (a -> b) -> a -> b
$v CD
xs |Bool
otherwise=[Char] -> v CD
forall a. HasCallStack => [Char] -> a
error[Char]
"Statistics.Transform.ifft: bad vector length"{-# INLINABLEifft #-}{-# SPECIAlIZEifft ::U.VectorCD ->U.VectorCD #-}{-# SPECIAlIZEifft ::V.VectorCD ->V.VectorCD #-}-- | Radix-2 decimation-in-time fast Fourier transform.fft ::G.Vectorv CD =>v CD ->v CD fft :: forall (v :: * -> *). Vector v CD => v CD -> v CD
fft v CD
v |v CD -> Bool
forall (v :: * -> *) a. Vector v a => v a -> Bool
vectorOK v CD
v =(forall s. ST s (Mutable v s CD)) -> v CD
forall (v :: * -> *) a.
Vector v a =>
(forall s. ST s (Mutable v s a)) -> v a
G.create((forall s. ST s (Mutable v s CD)) -> v CD)
-> (forall s. ST s (Mutable v s CD)) -> v CD
forall a b. (a -> b) -> a -> b
$doMutable v s CD
mv <-v CD -> ST s (Mutable v (PrimState (ST s)) CD)
forall (m :: * -> *) (v :: * -> *) a.
(PrimMonad m, Vector v a) =>
v a -> m (Mutable v (PrimState m) a)
G.thawv CD
v Mutable v s CD -> ST s ()
forall (v :: * -> * -> *) s. MVector v CD => v s CD -> ST s ()
mfft Mutable v s CD
mv Mutable v s CD -> ST s (Mutable v s CD)
forall a. a -> ST s a
forall (m :: * -> *) a. Monad m => a -> m a
returnMutable v s CD
mv |Bool
otherwise=[Char] -> v CD
forall a. HasCallStack => [Char] -> a
error[Char]
"Statistics.Transform.fft: bad vector length"{-# INLINABLEfft #-}{-# SPECIAlIZEfft ::U.VectorCD ->U.VectorCD #-}{-# SPECIAlIZEfft ::V.VectorCD ->V.VectorCD #-}-- Vector length must be power of two. It's not checkedmfft ::(M.MVectorv CD )=>v s CD ->STs (){-# INLINEmfft #-}mfft :: forall (v :: * -> * -> *) s. MVector v CD => v s CD -> ST s ()
mfft v s CD
vec =Int -> Int -> ST s ()
forall {m :: * -> *}.
(PrimState m ~ s, PrimMonad m) =>
Int -> Int -> m ()
bitReverse Int
0Int
0wherebitReverse :: Int -> Int -> m ()
bitReverse Int
i Int
j |Int
i Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
==Int
len Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
1=Int -> Int -> m ()
forall {m :: * -> *}.
(PrimState m ~ s, PrimMonad m) =>
Int -> Int -> m ()
stage Int
0Int
1|Bool
otherwise=doBool -> m () -> m ()
forall (f :: * -> *). Applicative f => Bool -> f () -> f ()
when(Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<Int
j )(m () -> m ()) -> m () -> m ()
forall a b. (a -> b) -> a -> b
$v (PrimState m) CD -> Int -> Int -> m ()
forall (m :: * -> *) (v :: * -> * -> *) a.
(HasCallStack, PrimMonad m, MVector v a) =>
v (PrimState m) a -> Int -> Int -> m ()
M.swapv s CD
v (PrimState m) CD
vec Int
i Int
j letinner :: Int -> Int -> m ()
inner Int
k Int
l |Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<=Int
l =Int -> Int -> m ()
inner (Int
k Int -> Int -> Int
forall a. Bits a => a -> Int -> a
`shiftR`Int
1)(Int
l Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
k )|Bool
otherwise=Int -> Int -> m ()
bitReverse (Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1)(Int
l Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
k )Int -> Int -> m ()
inner (Int
len Int -> Int -> Int
forall a. Bits a => a -> Int -> a
`shiftR`Int
1)Int
j stage :: Int -> Int -> m ()
stage Int
l !Int
l1 |Int
l Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
==Int
m =() -> m ()
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return()|Bool
otherwise=dolet!l2 :: Int
l2 =Int
l1 Int -> Int -> Int
forall a. Bits a => a -> Int -> a
`shiftL`Int
1!e :: Double
e =-Double
6.283185307179586Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegralInt
l2 flight :: Int -> Double -> m ()
flight Int
j !Double
a |Int
j Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
==Int
l1 =Int -> Int -> m ()
stage (Int
l Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1)Int
l2 |Bool
otherwise=doletbutterfly :: Int -> m ()
butterfly Int
i |Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>=Int
len =Int -> Double -> m ()
flight (Int
j Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1)(Double
a Double -> Double -> Double
forall a. Num a => a -> a -> a
+Double
e )|Bool
otherwise=doleti1 :: Int
i1 =Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
l1 Double
xi1 :+Double
yi1 <-v (PrimState m) CD -> Int -> m CD
forall (m :: * -> *) (v :: * -> * -> *) a.
(HasCallStack, PrimMonad m, MVector v a) =>
v (PrimState m) a -> Int -> m a
M.readv s CD
v (PrimState m) CD
vec Int
i1 let!c :: Double
c =Double -> Double
forall a. Floating a => a -> a
cosDouble
a !s :: Double
s =Double -> Double
forall a. Floating a => a -> a
sinDouble
a d :: CD
d =(Double
c Double -> Double -> Double
forall a. Num a => a -> a -> a
*Double
xi1 Double -> Double -> Double
forall a. Num a => a -> a -> a
-Double
s Double -> Double -> Double
forall a. Num a => a -> a -> a
*Double
yi1 )Double -> Double -> CD
forall a. a -> a -> Complex a
:+(Double
s Double -> Double -> Double
forall a. Num a => a -> a -> a
*Double
xi1 Double -> Double -> Double
forall a. Num a => a -> a -> a
+Double
c Double -> Double -> Double
forall a. Num a => a -> a -> a
*Double
yi1 )CD
ci <-v (PrimState m) CD -> Int -> m CD
forall (m :: * -> *) (v :: * -> * -> *) a.
(HasCallStack, PrimMonad m, MVector v a) =>
v (PrimState m) a -> Int -> m a
M.readv s CD
v (PrimState m) CD
vec Int
i v (PrimState m) CD -> Int -> CD -> m ()
forall (m :: * -> *) (v :: * -> * -> *) a.
(HasCallStack, PrimMonad m, MVector v a) =>
v (PrimState m) a -> Int -> a -> m ()
M.writev s CD
v (PrimState m) CD
vec Int
i1 (CD
ci CD -> CD -> CD
forall a. Num a => a -> a -> a
-CD
d )v (PrimState m) CD -> Int -> CD -> m ()
forall (m :: * -> *) (v :: * -> * -> *) a.
(HasCallStack, PrimMonad m, MVector v a) =>
v (PrimState m) a -> Int -> a -> m ()
M.writev s CD
v (PrimState m) CD
vec Int
i (CD
ci CD -> CD -> CD
forall a. Num a => a -> a -> a
+CD
d )Int -> m ()
butterfly (Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
l2 )Int -> m ()
butterfly Int
j Int -> Double -> m ()
flight Int
0Double
0len :: Int
len =v s CD -> Int
forall (v :: * -> * -> *) a s. MVector v a => v s a -> Int
M.lengthv s CD
vec m :: Int
m =Int -> Int
log2Int
len ------------------------------------------------------------------ Helpers----------------------------------------------------------------fi ::Int->CD fi :: Int -> CD
fi =Int -> CD
forall a b. (Integral a, Num b) => a -> b
fromIntegralhalve ::Int->Inthalve :: Int -> Int
halve =(Int -> Int -> Int
forall a. Bits a => a -> Int -> a
`shiftR`Int
1)vectorOK ::G.Vectorv a =>v a ->Bool{-# INLINEvectorOK #-}vectorOK :: forall (v :: * -> *) a. Vector v a => v a -> Bool
vectorOK v a
v =(Int
1Int -> Int -> Int
forall a. Bits a => a -> Int -> a
`shiftL`Int -> Int
log2Int
n )Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
==Int
n wheren :: Int
n =v a -> Int
forall (v :: * -> *) a. Vector v a => v a -> Int
G.lengthv a
v