-- Do not edit! Automatically created with doctest-extract from private/Numeric/FFTW/Extra/Rank1/Transform.hs
{-# LINE 78 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}

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

import qualified Test.DocTest.Driver as DocTest

{-# LINE 80 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
import     Test.Numeric.FFTW.Extra.Utility
import     DocTest.Float.Numeric.FFTW.Extra.Rank1.Convolution
       (complex_, real_)
import     Numeric.FFTW.Extra.Rank1.Transform
import     Numeric.FFTW.Extra.Rank1.Convolution (arrangeMutable)
import     Numeric.FFTW.Extra.NumberTheory (divisors)
import     Numeric.FFTW.Extra.Utility (cyclicTake, padCyclic, spreadCyclic)
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.Dim2 as Array2
import     qualified Data.Array.Comfort.Storable as Array
import     qualified Data.Array.Comfort.Shape as Shape
--     import qualified Data.Foldable as Fold
--     import qualified Data.List.Match as Match
import     Data.Array.Comfort.Storable ((!), (//))
import     Data.Complex (Complex((:+)), cis)

import     qualified Test.QuickCheck as QC
import     Test.QuickCheck ((.&&.))

test :: DocTest.T ()
test = do
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:109: "
{-# LINE 109 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 109 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
        
   QC.forAll (genCyclic complex_) $ \xy ->
   let (x,y) = Vector.unzipComplex xy in
   let (fx,fy) = fourierRC2 (x,y) in
   Rank1.fourierRC x =~= fx
   .&&.
   Rank1.fourierRC y =~= fy
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:287: "
{-# LINE 287 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 287 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
        
   QC.forAll (genCyclic complex_) $ \x sign ->
   let n = Shape.size $ Array.shape x in
   QC.forAll (QC.elements $ divisors n) $ \m ->
   QC.forAll (chooseLogarithmic n) $ \mcut ->

   takeDivisorFourier sign mcut m x
   =~=
   takeShape (Shape.ZeroBased mcut) (Rank1.fourier sign x)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:348: "
{-# LINE 348 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 348 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
        
   QC.forAll (genCyclic complex_) $ \x sign ->
   let n = Shape.size $ Array.shape x in
   QC.forAll (QC.elements $ divisors n) $ \m ->
   QC.forAll (chooseLogarithmic n) $ \mcut from ->
   let shape = Shape.intervalFromShifted $ Shape.Shifted from mcut in

   takeDivisorFourierInterval sign shape m x
   =~=
   cyclicTake shape (Rank1.fourier sign x)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:385: "
{-# LINE 385 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 385 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
        
   QC.forAll (genCyclic complex_) $ \x sign ->
   let n = Shape.size $ Array.shape x in
   QC.forAll (QC.elements $ divisors n) $ \m ->
   QC.forAll (chooseLogarithmic n) $ \mcut ->

   takeDivisorFourier sign mcut m x
   =~=
   takeNonDivisorFourier sign mcut x
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:415: "
{-# LINE 415 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 415 "private/Numeric/FFTW/Extra/Rank1/Transform.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

   takeNonDivisorFourierInterval sign shape x
   =~=
   cyclicTake shape (Rank1.fourier sign x)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:465: "
{-# LINE 465 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 465 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
        
   QC.forAll (genCyclic real_) $ \x ->
   let n = Shape.cyclicSize $ Array.shape x in
   QC.forAll (QC.elements $ divisors n) $ \m ->
   QC.forAll (chooseLogarithmic n) $ \mcut ->

   takeDivisorFourierRC mcut m x
   =~=
   takeNonDivisorFourierRC mcut x
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:501: "
{-# LINE 501 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 501 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
        
   QC.forAll genVectorShape $ \shape sign ->
   let n = Shape.zeroBasedSize shape in
   QC.forAll (QC.elements $ divisors n) $ \m ->
   QC.forAll (chooseLogarithmic n) $ \mcut ->
   QC.forAll (genVectorForShape complex_ (Shape.ZeroBased mcut)) $ \x ->

   Rank1.fourier sign (padCyclic n x)
   =~=
   extendDivisorFourier sign n m x
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:559: "
{-# LINE 559 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 559 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
        
   QC.forAll genVectorShape $ \shape sign ->
   let n = Shape.zeroBasedSize shape in
   QC.forAll (QC.elements $ divisors n) $ \m ->
   QC.forAll (chooseLogarithmic n) $ \mcut from ->
   let rng = Shape.intervalFromShifted $ Shape.Shifted from mcut in
   QC.forAll (genVectorForShape complex_ rng) $ \x ->

   extendDivisorFourierInterval sign n m x
   =~=
   Rank1.fourier sign (spreadCyclic n x)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:595: "
{-# LINE 595 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 595 "private/Numeric/FFTW/Extra/Rank1/Transform.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 ->

   Rank1.fourier sign (padCyclic n x)
   =~=
   extendNonDivisorFourier sign n x
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:606: "
{-# LINE 606 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 606 "private/Numeric/FFTW/Extra/Rank1/Transform.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 ->

   takeNonDivisorFourier (Rank1.flipSign sign) m
      (extendNonDivisorFourier sign n x)
   =~=
   Vector.scaleReal (fromIntegral n) x
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:638: "
{-# LINE 638 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 638 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
        
   QC.forAll genCyclicShape $ \shape ->
   let n = Shape.cyclicSize shape in
   n>=2 QC.==>
   QC.forAll (chooseLogarithmic (n-1)) $ \m ->
   let halfShape = Spectrum.Half m in
   QC.forAll (genVectorForShape complex_ halfShape) $ \xh ->

   extendNonDivisorFourierInterval Rank1.Backward n
      (spectrumIntervalFromHalf xh)
   =~=
   Vector.fromReal (extendNonDivisorFourierCR n xh)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:652: "
{-# LINE 652 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 652 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
        
   QC.forAll genVectorShape $ \shape ->
   let n = Shape.zeroBasedSize shape in
   QC.forAll (chooseLogarithmic n) $ \m ->
   let halfShape = Spectrum.Half m in
   QC.forAll (genVectorForShape complex_ halfShape) $ \x ->

   Vector.realPart
      (Rank1.fourier Rank1.Backward
         (padCyclic n $ Array.mapShape (Shape.ZeroBased . Shape.size) $
            Vector.scaleReal 2 x // [(0, x!0)]))
   =~=
   extendNonDivisorFourierCR n x
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:667: "
{-# LINE 667 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 667 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
        
   QC.forAll genVectorShape $ \shape ->
   let n = Shape.zeroBasedSize shape in
   QC.forAll (QC.elements $ divisors n) $ \m ->
   QC.forAll (chooseLogarithmic n) $ \mcut ->
   QC.forAll (genVectorForShape complex_ (Spectrum.Half mcut)) $ \x ->

   extendDivisorFourierCR n m x
   =~=
   extendNonDivisorFourierCR n x
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:680: "
{-# LINE 680 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 680 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
        
   QC.forAll genCyclicShape $ \shape ->
   let n = Shape.cyclicSize shape in
   forChoose (0, div n 2) $ \f a b ->
   let c = -2*pi / fromIntegral n in
   let (a2,b2) = if f==0 then (a,b) else (2*a,2*b) in

   extendNonDivisorFourierCR n
      (Array.fromAssociations 0 (Spectrum.Half (2*f))
         [(f, a:+b :: Complex Float)])
   =~=
   Array.sample shape
      (\t ->
         a2 * cos (c * fromIntegral (mod (t*f) n)) +
         b2 * sin (c * fromIntegral (mod (t*f) n)))
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:743: "
{-# LINE 743 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 743 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
        
   QC.forAll genCyclicShape $ \shape sign ->
   let n = Shape.cyclicSize shape in
   QC.forAll (chooseLogarithmic n) $ \m ->
   QC.forAll (genVectorForShape complex_ (Shape.ZeroBased m)) $ \x ->

   extendNonDivisorFourier sign n x
   =~=
   extendNonDivisorFourierInterval sign n (Array.reshape (Shape.Interval 0 (m-1)) x)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:754: "
{-# LINE 754 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 754 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
        
   QC.forAll genCyclicShape $ \shape sign f a ->
   let n = Shape.cyclicSize shape in
   let cu = 2*pi / fromIntegral n in
   let c = case sign of Rank1.Forward -> -cu; Rank1.Backward -> cu in

   extendNonDivisorFourierInterval sign n
      (Array.replicate (Shape.Interval f f) (a :: Complex Float))
   =~=
   Array.sample shape (\t -> a * cis (c * fromIntegral (mod (t*f) n)))
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:766: "
{-# LINE 766 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 766 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
        
   QC.forAll genCyclicShape $ \shape sign ->
   let n = Shape.cyclicSize shape in
   n>=2 QC.==>
   forChoose (1,n-1) $ \d f0 a b ->
   let f1 = f0+d in
   let cu = 2*pi / fromIntegral n in
   let c = case sign of Rank1.Forward -> -cu; Rank1.Backward -> cu in

   extendNonDivisorFourierInterval sign n
      (Array.fromAssociations 0 (Shape.Interval f0 f1)
         [(f0,a), (f1,b :: Complex Float)])
   =~=
   Array.sample shape
      (\t ->
         a * cis (c * fromIntegral (mod (t*f0) n)) +
         b * cis (c * fromIntegral (mod (t*f1) n)))
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:872: "
{-# LINE 872 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 872 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
        
   QC.forAll genVectorShape $ \shapeShort ->
   forChoose (1,10) $ \stepSize ->
   forChoose (2,10) $ \overlap ->
   let m = stepSize * overlap in
   let window = Array.sample (Shape.ZeroBased m)
                     (\i -> sin (pi * fromIntegral i / fromIntegral m)) in
   let shape = fmap (\n -> n + mod (-n) (stepSize*overlap)) shapeShort in
   QC.forAll (genVectorForShape complex_ shape) $ \x ->
   let zeroPad = Vector.zero $ Shape.ZeroBased $ (overlap-1)*stepSize in
   let xpad = zeroPad <> x <> zeroPad in

   Vector.scaleReal (fromIntegral (m*overlap) / 2) xpad
   =~=
   shortTimeFourierBackward window overlap
      (shortTimeFourierForward window overlap xpad)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.Rank1.Transform:916: "
{-# LINE 916 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
 DocTest.property(
{-# LINE 916 "private/Numeric/FFTW/Extra/Rank1/Transform.hs" #-}
        
   QC.forAll (genVector real_) $ \dat ->
   let n = Shape.zeroBasedSize $ Array.shape dat in
   forChoose (1, min n 4) $ \overlap ->
   QC.forAll (chooseLogarithmic (div n overlap)) $ \stepSize ->
   let width = overlap * stepSize in
   let height = div n width in
   let xs = takeShape (Shape.ZeroBased height, Shape.ZeroBased width) dat in

   fromOverlappingBlocks overlap xs
   =~=
   arrangeMutable
      ((height-1 + overlap) * stepSize)
      stepSize xs (Vector.zero (Shape.ZeroBased 0))
  )