-- Do not edit! Automatically created with doctest-extract from src/Numeric/FFTW/Extra/Rank1.hs
{-# LINE 46 "src/Numeric/FFTW/Extra/Rank1.hs" #-}

{-# OPTIONS_GHC -XTypeFamilies #-}
module DocTest.Float.Numeric.FFTW.Extra.Rank1 where

import qualified Test.DocTest.Driver as DocTest

{-# LINE 48 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
import     Test.Numeric.FFTW.Extra.Utility
import     Numeric.FFTW.Extra.Rank1
import     DocTest.Float.Numeric.FFTW.Extra.Rank1.Convolution
       (real_, complex_)
import     Numeric.FFTW.Extra.Utility
       (padShape, padCyclic, spreadCyclic, cyclicTake)
import     qualified Numeric.FFTW.Shape as Spectrum
import     qualified Numeric.FFTW.Rank1 as Rank1
import     qualified Numeric.BLAS.Vector as Vector

import     qualified Data.Array.Comfort.Storable as Array
import     qualified Data.Array.Comfort.Shape as Shape
import     qualified Data.Complex as Complex
import     Data.Array.Comfort.Storable ((//), (!))
import     Data.Complex (Complex((:+)), cis)

import     qualified Test.QuickCheck as QC

test :: DocTest.T ()
test = do
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1:98: "
{-# LINE 98 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
 DocTest.property(
{-# LINE 98 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
        
   QC.forAll (genCyclic complex_) $ \x sign ->
   QC.forAll (chooseLogarithmic (Shape.cyclicSize $ Array.shape x)) $ \m ->
   takeFourier sign (Shape.ZeroBased m) x
   =~=
   takeShape (Shape.ZeroBased m) (Rank1.fourier sign x)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1:110: "
{-# LINE 110 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
 DocTest.property(
{-# LINE 110 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
        
   QC.forAll (genCyclic complex_) $ \x sign ->
   let n = Shape.cyclicSize $ Array.shape x in
   forChoose (1,10) $ \m ->

   Rank1.fourier (Rank1.flipSign sign)
      (Array.mapShape (Shape.Cyclic . Shape.zeroBasedSize)
         (takeFourier sign (Shape.ZeroBased n) (upsample m x)))
   =~=
   Vector.scaleReal (fromIntegral n) x
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1:126: "
{-# LINE 126 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
 DocTest.property(
{-# LINE 126 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
        
   QC.forAll (genCyclic complex_) $ \x sign ->
   let n = Shape.size $ Array.shape x in
   QC.forAll (chooseLogarithmic n) $ \m from ->
   let shape = Shape.intervalFromShifted $ Shape.Shifted from m in

   takeFourier sign shape x
   =~=
   cyclicTake shape (Rank1.fourier sign x)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1:195: "
{-# LINE 195 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
 DocTest.property(
{-# LINE 195 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
        
   QC.forAll (genCyclic real_) $ \x ->
   QC.forAll (chooseLogarithmic (Shape.size $ Array.shape x)) $ \m ->

   takeFourierRC m x
   =~=
   takeShape (Spectrum.Half m) (Rank1.fourierRC x)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1:208: "
{-# LINE 208 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
 DocTest.property(
{-# LINE 208 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
        
   QC.forAll (genCyclic real_) $ \x ->
   let n = Shape.cyclicSize $ Array.shape x in
   forChoose (1,10) $ \m ->

   Rank1.fourierCR (takeFourierRC n (upsample m x))
   =~=
   Vector.scale (fromIntegral n) x
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1:225: "
{-# LINE 225 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
 DocTest.property(
{-# LINE 225 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
        
   forChoose (1,100::Int) $ \n k ->
   forChoose (1, div n 2) $ \m ->
   let c = - 2*pi / fromIntegral n in

   takeFourierRC m (Vector.unit (Shape.Cyclic n) k &:: real_)
   =~=
   Array.sample (Spectrum.Half m) (\i -> cis (c * fromIntegral (i*k)))
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1:237: "
{-# LINE 237 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
 DocTest.property(
{-# LINE 237 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
        
   forChoose (1,100::Int) $ \n k ->
   forChoose (1,n) $ \m ->
   let c = 2*pi / fromIntegral n in
   let d = 2*pi / fromIntegral m in

   Vector.fromReal
      (Rank1.fourierCR (takeFourierRC m (Vector.unit (Shape.Cyclic n) k)))
   =~=
   Array.sample (Shape.Cyclic m)
      (\j ->
         (if even m
            then let m2 = div m 2 in
                 cos (d * fromIntegral (m2*j) - c * fromIntegral (m2*k))
                    :+ 0
            else 0)
         +
         (Vector.sum $
            Array.sample (Shape.Interval (- div (m-1) 2) (div (m-1) 2))
               (\i -> cis (d * fromIntegral (i*j) - c * fromIntegral (i*k)))))
      &:: complex_
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1:269: "
{-# LINE 269 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
 DocTest.property(
{-# LINE 269 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
        
   forChoose (1,100::Int) $ \n k ->
   forChoose (1,n) $ \m ->
   let c = pi / fromIntegral (m*n) in
   let projectCentric i =
         let nm2 = div (n*m) 2
             (q,r) = divMod (i+nm2) (n*m)
         in c * fromIntegral (if even q then r-nm2 else nm2-r)
   in
   -- numerically stable version of sin (c*m1*i) / sin (c*i)
   let dirichlet :: Int -> Int -> Float
       dirichlet m1 i =
         if mod i (n*m) == 0
         then fromIntegral m1
         else sin (projectCentric (m1*i)) / sin (projectCentric i) in

   Rank1.fourierCR (takeFourierRC m (Vector.unit (Shape.Cyclic n) k))
   =~=
   Array.sample (Shape.Cyclic m)
      (\j ->
         let i = n*j - m*k
             (m1,residue) =
               if even m
               then (m-1, cos (c * fromIntegral (m*i)))
               else (m, 0)
         in residue + dirichlet m1 i)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1:380: "
{-# LINE 380 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
 DocTest.property(
{-# LINE 380 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
        
   QC.forAll genVectorShape $ \shape sign ->
   let n = Shape.zeroBasedSize shape in
   QC.forAll (chooseLogarithmic n) $ \m ->
   QC.forAll (genVectorForShape complex_ (Shape.ZeroBased m)) $ \x ->

   extendFourier sign n x
   =~=
   Rank1.fourier sign (padCyclic n x)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1:395: "
{-# LINE 395 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
 DocTest.property(
{-# LINE 395 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
        
   QC.forAll genVectorShape $ \shape sign ->
   let n = Shape.zeroBasedSize shape in
   QC.forAll (chooseLogarithmic n) $ \m from ->
   let rng = Shape.intervalFromShifted $ Shape.Shifted from m in
   QC.forAll (genVectorForShape complex_ rng) $ \x ->

   extendFourier sign n x
   =~=
   Rank1.fourier sign (spreadCyclic n x)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1:407: "
{-# LINE 407 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
 DocTest.property(
{-# LINE 407 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
        
   QC.forAll genVectorShape $ \shape sign ->
   let n = Shape.zeroBasedSize shape in
   QC.forAll (chooseLogarithmic n) $ \m ->
   QC.forAll (genVectorForShape complex_ (Shape.ZeroBased m)) $ \x ->

   extendFourier sign n x
   =~=
   extendFourier sign n
      (Array.mapShape Shape.intervalFromZeroBased x)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1:420: "
{-# LINE 420 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
 DocTest.property(
{-# LINE 420 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
        
   QC.forAll genVectorShape $ \shape ->
   let n = Shape.zeroBasedSize shape in
   n>=3 QC.==>
   QC.forAll (chooseLogarithmic (n - mod (n+1) 2)) $ \m ->
   let halfShape = Spectrum.Half m in
   QC.forAll (genVectorForShape complex_ halfShape) $ \xc ->
   let x = xc // [(0, Complex.realPart (xc!0) :+ 0)] in
   let nh = Shape.size halfShape in
   let xs = Array.reshape (Shape.ZeroBased nh) x in

   Vector.fromReal (extendFourierCR n x)
   =~=
   extendFourier Rank1.Backward n
      (Array.reshape (Shape.Interval (1-nh) (nh-1)) $
         Vector.conjugate (Vector.reverse xs) <> Vector.drop 1 xs)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1:471: "
{-# LINE 471 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
 DocTest.property(
{-# LINE 471 "src/Numeric/FFTW/Extra/Rank1.hs" #-}
        
   QC.forAll genVectorShape $ \shape ->
   let n = Shape.zeroBasedSize shape in
   QC.forAll (chooseLogarithmic n) $ \m ->
   QC.forAll (genVectorForShape complex_ (Spectrum.Half m)) $ \x ->

   Rank1.fourierCR (padShape (Spectrum.Half n) x)
   =~=
   extendFourierCR n x
  )