-- Do not edit! Automatically created with doctest-extract from src/Numeric/BLAS/Vector/Slice.hs
{-# LINE 142 "src/Numeric/BLAS/Vector/Slice.hs" #-}

{-# OPTIONS_GHC -XTypeOperators #-}
{-# OPTIONS_GHC -XGADTs #-}
module Test.Float.Numeric.BLAS.Vector.Slice where

import Test.DocTest.Base
import qualified Test.DocTest.Driver as DocTest

{-# LINE 145 "src/Numeric/BLAS/Vector/Slice.hs" #-}
import     qualified Test.Slice as TestSlice
import     Test.Float.Numeric.BLAS.Vector
       (forVector, maxElem, maxDim, genVector,
        Number_, number_, real_, complex_)
import     Test.Slice (shapeInt)
import     Test.Generator (genNumber)
import     Test.Utility (approx, approxReal)

import     qualified Numeric.BLAS.Matrix.RowMajor as Matrix
import     qualified Numeric.BLAS.Vector.Slice as VectorSlice
import     qualified Numeric.BLAS.Vector as Vector
import     qualified Numeric.BLAS.Subobject.View as View
import     qualified Numeric.BLAS.Subobject.Layout as Layout
import     qualified Numeric.BLAS.Slice as Slice
import     qualified Numeric.BLAS.Scalar as Scalar
import     qualified Numeric.Netlib.Class as Class
import     qualified Data.Array.Comfort.Storable as Array
import     qualified Data.Array.Comfort.Shape as Shape
import     qualified Data.List as List
import     Numeric.BLAS.Vector ((+++), (|+|))
import     Numeric.BLAS.Scalar (RealOf, absolute, realPart, minusOne)
import     Data.Array.Comfort.Shape ((::+)((::+)))
import     Data.Tuple.HT (mapPair)
import     Data.Complex (Complex)
import     Control.Applicative (liftA2)

import     qualified Test.QuickCheck as QC
import     Test.QuickCheck ((==>))

type     Real_ = RealOf Number_
type     Complex_ = Complex Real_

maxDim1     :: Int
maxDim1     = 10

type     ShapeInt = Shape.ZeroBased Int
type     Shape = ShapeInt ::+ (ShapeInt, ShapeInt) ::+ ShapeInt
type     Vector = Vector.Vector Shape
type     Sliced = VectorSlice.T Layout.Slice ShapeInt

genDim     :: QC.Gen Int
genDim     = QC.choose (0,maxDim)

genShapeDim     :: Int -> QC.Gen Shape
genShapeDim     numRows = do
       left <- fmap Shape.ZeroBased $ QC.choose (0,maxDim)
       right <- fmap Shape.ZeroBased $ QC.choose (0,maxDim)
       columns <- fmap Shape.ZeroBased $ QC.choose (1,maxDim1)
       return (left ::+ (Shape.ZeroBased numRows, columns) ::+ right)

genShape     :: QC.Gen Shape
genShape     = genShapeDim =<< QC.choose (0,maxDim1)

forAll_     :: (Show a) => QC.Gen a -> (a -> QC.Property) -> QC.Property
forAll_     = QC.forAll

isNonEmpty     ::
       (View.Slice lay, Shape.C sh) => VectorSlice.T lay sh a -> Bool
isNonEmpty     xs = Shape.size (VectorSlice.shape xs) > 0

takeColumn     ::
       (Shape.Indexed sh1, Shape.C sh, Shape.C sh0, Shape.C sh2) =>
       Shape.Index sh1 ->
       Vector.Vector (sh0 ::+ (sh, sh1) ::+ sh2) a ->
       VectorSlice.T Layout.Slice sh a
takeColumn     c =
       VectorSlice.sliceVector (Slice.column c . Slice.left . Slice.right)

listFromSlice     ::
       (View.Slice lay, Shape.C sh, Class.Floating a) =>
       VectorSlice.T lay sh a -> [a]
listFromSlice     = Vector.toList . VectorSlice.toVector

genSlicedDim     ::
       (Class.Floating a) =>
       Int -> QC.Gen a -> QC.Gen (Int, Vector a)
genSlicedDim     numRows genElem = do
       shape@(_::+(_rows,columns)::+_) <- genShapeDim numRows
       c <- QC.elements (Shape.indices columns)
       fmap ((,) c) $ genVector shape genElem

genSliced     ::
       (Class.Floating a) =>
       QC.Gen a -> QC.Gen (Int, Vector a)
genSliced     genElem = flip genSlicedDim genElem =<< genDim

shrinkSliced     ::
       (Shape.C sh0, Shape.Indexed sh1, QC.Arbitrary a, Class.Floating a) =>
       (Shape.Index sh1,
        Vector.Vector (ShapeInt ::+ (sh0, sh1) ::+ ShapeInt) a) ->
       [(Shape.Index sh1,
         Vector.Vector (ShapeInt ::+ (sh0, sh1) ::+ ShapeInt) a)]
shrinkSliced     (c,xs) =
       let xs0 = Vector.takeLeft xs in
       let xs1 = Vector.takeRight xs in
       let xs10 = Vector.takeLeft xs1 in
       let xs11 = Vector.takeRight xs1 in
       map (\(ysl,ysr) ->
             (c,
              Vector.autoFromList ysl +++ xs10 +++ Vector.autoFromList ysr)) $
       QC.shrink (Vector.toList xs0, Vector.toList xs11)

forSliced     ::
       (QC.Testable prop, QC.Arbitrary a, Class.Floating a, Show a) =>
       QC.Gen a -> (Sliced a -> prop) -> QC.Property
forSliced     genElem prop =
       QC.forAllShrink (genSliced genElem) shrinkSliced
          (prop . uncurry takeColumn)

genSliced2     ::
       (Class.Floating a) =>
       QC.Gen a -> QC.Gen ((Int, Vector a), (Int, Vector a))
genSliced2     genElem = do
       dim <- genDim
       liftA2 (,) (genSlicedDim dim genElem) (genSlicedDim dim genElem)

forSliced2     ::
       (QC.Testable prop, Class.Floating a, Show a) =>
       QC.Gen a -> (Sliced a -> Sliced a -> prop) -> QC.Property
forSliced2     genElem prop =
       QC.forAll (genSliced2 genElem)
          (uncurry prop . mapPair (uncurry takeColumn, uncurry takeColumn))

test :: DocTest.T ()
test = do
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:274: "
{-# LINE 274 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 274 "src/Numeric/BLAS/Vector/Slice.hs" #-}
        
   QC.forAll genShape $ \shape@(_::+(_rows,columns)::+_) ->
   QC.forAll (QC.elements (Shape.indices columns)) $ \c ->
   QC.forAll (genVector shape number_) $ \xs ->
   VectorSlice.extract (Slice.column c . Slice.left . Slice.right) xs
   ==
   Matrix.takeColumn c
      (Vector.takeLeft (Vector.takeRight (xs :: Vector Number_)))
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:284: "
{-# LINE 284 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 284 "src/Numeric/BLAS/Vector/Slice.hs" #-}
        
   forAll_ (TestSlice.genShapeSelect 4 100) $ \(TestSlice.ShapeSelect sh select) ->
   QC.forAll (genVector sh number_) $ \xs ->
   case TestSlice.instantiate sh select of
      TestSlice.Extraction slice cut ->
         VectorSlice.extract slice xs QC.=== cut xs
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:334: "
{-# LINE 334 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 334 "src/Numeric/BLAS/Vector/Slice.hs" #-}
        
   QC.forAll genShape $ \shape a ->
   VectorSlice.toVector (VectorSlice.replicate shape a)
   ==
   Vector.constant shape (a :: Number_)
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:368: "
{-# LINE 368 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 368 "src/Numeric/BLAS/Vector/Slice.hs" #-}
        
   forSliced number_ $ \xy ->
   let shape = VectorSlice.shape xy in
   QC.forAll (QC.choose (0, Shape.zeroBasedSize shape)) $ \k ->

   VectorSlice.toVector xy
   ==
   Array.reshape shape (uncurry VectorSlice.append (VectorSlice.splitAt k xy))
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:409: "
{-# LINE 409 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 409 "src/Numeric/BLAS/Vector/Slice.hs" #-}
        
   forVector number_ $ \x ->
   forVector number_ $ \y ->
   let (x1,y1) =
         VectorSlice.split $ VectorSlice.fromVector $ Vector.append x y in

   x == VectorSlice.toVector x1
   &&
   y == VectorSlice.toVector y1
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:436: "
{-# LINE 436 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.example(
{-# LINE 436 "src/Numeric/BLAS/Vector/Slice.hs" #-}
    List.map realPart $ Vector.toList $ VectorSlice.append (VectorSlice.fromVector $ Vector.autoFromList [3,1,4,1]) (VectorSlice.replicate (Shape.ZeroBased (3::Int)) (0::Number_))
  )
  [ExpectedLine [LineChunk "[3.0,1.0,4.0,1.0,0.0,0.0,0.0]"]]
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:466: "
{-# LINE 466 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.example(
{-# LINE 466 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      
   List.map realPart $ Vector.toList $
   let matrix =
         Vector.fromList (shapeInt 4, shapeInt 3) $
         map (\x -> fromInteger x :: Number_) [0 ..] in
   VectorSlice.concat $
   map
      (\k ->
         VectorSlice.chunk (VectorSlice.sliceVector (Slice.column k) matrix))
      [0,1,2]
  )
  [ExpectedLine [LineChunk "[0.0,3.0,6.0,9.0,1.0,4.0,7.0,10.0,2.0,5.0,8.0,11.0]"]]
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:479: "
{-# LINE 479 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 479 "src/Numeric/BLAS/Vector/Slice.hs" #-}
        
   QC.forAll (QC.listOf $ fmap (uncurry takeColumn) $ genSliced number_) $
      \xss ->
   map VectorSlice.toVector xss
   ==
   VectorSlice.extractMany Slice.list
      (VectorSlice.concat (map VectorSlice.chunk xss))
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:520: "
{-# LINE 520 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 520 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced2 number_ $ \xs ys -> VectorSlice.inner xs ys == Vector.dot (VectorSlice.conjugate xs) (VectorSlice.toVector ys)
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:521: "
{-# LINE 521 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 521 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced number_ $ \xs -> VectorSlice.inner xs xs == Scalar.fromReal (VectorSlice.norm2Squared xs)
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:604: "
{-# LINE 604 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 604 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced number_ $ \xs -> VectorSlice.sum xs == List.sum (listFromSlice xs)
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:677: "
{-# LINE 677 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 677 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced number_ $ \xs -> VectorSlice.normInf xs == List.maximum (0 : List.map absolute (listFromSlice xs))
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:688: "
{-# LINE 688 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 688 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced number_ $ \xs -> VectorSlice.normInf1 xs == List.maximum (0 : List.map Scalar.norm1 (listFromSlice xs))
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:706: "
{-# LINE 706 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 706 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced number_ $ \xs -> isNonEmpty xs ==> let (xi,xm) = VectorSlice.argAbsMaximum xs in VectorSlice.access xs xi == xm
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:707: "
{-# LINE 707 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 707 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced number_ $ \xs -> isNonEmpty xs ==> let (_xi,xm) = VectorSlice.argAbsMaximum xs in List.all (\x -> absolute x <= absolute xm) $ listFromSlice xs
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:708: "
{-# LINE 708 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 708 "src/Numeric/BLAS/Vector/Slice.hs" #-}
        
   forSliced number_ $ \xs ->
   forSliced number_ $ \ys ->
   isNonEmpty xs && isNonEmpty ys ==>
   let (_xi,xm) = VectorSlice.argAbsMaximum xs
       (_yi,ym) = VectorSlice.argAbsMaximum ys
       (zi,zm) = Vector.argAbsMaximum
                     (VectorSlice.toVector xs +++ VectorSlice.toVector ys) in
   case zi of
      Left _ -> xm==zm && absolute xm >= absolute ym
      Right _ -> ym==zm && absolute xm < absolute ym
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:769: "
{-# LINE 769 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 769 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced real_ $ \xs -> isNonEmpty xs ==> VectorSlice.argAbsMaximum xs == VectorSlice.argAbs1Maximum xs
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:794: "
{-# LINE 794 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 794 "src/Numeric/BLAS/Vector/Slice.hs" #-}
        
   QC.forAll genShape $ \sh@(_::+(_rows,columns)::+_) ->
   QC.forAll (QC.elements (Shape.indices columns)) $ \c ->
   QC.forAll (genVector sh $ genNumber 3) $ \xt ->
   let xs = takeColumn c xt in
   approx 1e-2
      (VectorSlice.product xs)
      (List.product (listFromSlice (xs :: Sliced Number_)))
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:813: "
{-# LINE 813 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 813 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced real_ $ \xs -> isNonEmpty xs ==> VectorSlice.minimum xs == List.minimum (listFromSlice xs)
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:814: "
{-# LINE 814 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 814 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced real_ $ \xs -> isNonEmpty xs ==> VectorSlice.maximum xs == List.maximum (listFromSlice xs)
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:830: "
{-# LINE 830 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 830 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced real_ $ \xs -> isNonEmpty xs ==> VectorSlice.limits xs == Array.limits (VectorSlice.toVector xs)
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:860: "
{-# LINE 860 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 860 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced number_ $ \xs -> VectorSlice.negate xs == VectorSlice.scale minusOne xs
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:861: "
{-# LINE 861 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 861 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced number_ $ \xs -> VectorSlice.scale 2 xs == VectorSlice.add xs xs
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:921: "
{-# LINE 921 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 921 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced2 number_ $ \xs ys -> VectorSlice.add xs ys == VectorSlice.add ys xs
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:922: "
{-# LINE 922 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 922 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced2 number_ $ \xs ys -> VectorSlice.toVector xs == VectorSlice.sub xs ys |+| VectorSlice.toVector ys
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:934: "
{-# LINE 934 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 934 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      QC.forAll number_ $ \a -> forSliced2 number_ $ \xs ys -> VectorSlice.mac a xs ys == VectorSlice.scale a xs |+| VectorSlice.toVector ys
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:953: "
{-# LINE 953 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 953 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced number_ $ \xs -> VectorSlice.toVector xs == Vector.negate (VectorSlice.negate xs)
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:966: "
{-# LINE 966 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 966 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      QC.forAll (genNumber maxElem) $ \d -> forSliced number_ $ \xs -> VectorSlice.toVector xs == Vector.raise (-d) (VectorSlice.raise d xs)
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:984: "
{-# LINE 984 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 984 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced2 number_ $ \xs ys -> VectorSlice.mul xs ys == VectorSlice.mul ys xs
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:992: "
{-# LINE 992 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 992 "src/Numeric/BLAS/Vector/Slice.hs" #-}
      forSliced2 number_ $ \xs ys -> VectorSlice.mulConj xs ys == Vector.mul (VectorSlice.conjugate xs) (VectorSlice.toVector ys)
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:1014: "
{-# LINE 1014 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 1014 "src/Numeric/BLAS/Vector/Slice.hs" #-}
        
   forSliced2 real_ $ \xs ys ->

   VectorSlice.mulReal xs ys
   ==
   VectorSlice.mul xs ys
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:1022: "
{-# LINE 1022 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 1022 "src/Numeric/BLAS/Vector/Slice.hs" #-}
        
   forSliced2 complex_ $ \xs ys ->
   let xrs = VectorSlice.realPart xs in

   VectorSlice.mulReal xrs ys
   ==
   VectorSlice.mul (VectorSlice.fromReal xrs) ys
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:1045: "
{-# LINE 1045 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 1045 "src/Numeric/BLAS/Vector/Slice.hs" #-}
        
   forSliced2 real_ $ \xs ys ->

   VectorSlice.mulRealConj xs ys
   ==
   VectorSlice.mul xs ys
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:1053: "
{-# LINE 1053 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 1053 "src/Numeric/BLAS/Vector/Slice.hs" #-}
        
   forSliced2 complex_ $ \xs ys ->
   let xrs = VectorSlice.realPart xs in

   VectorSlice.mulRealConj xrs ys
   ==
   VectorSlice.mul (VectorSlice.fromReal xrs) (VectorSlice.conjugate ys)
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:1231: "
{-# LINE 1231 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 1231 "src/Numeric/BLAS/Vector/Slice.hs" #-}
        
   forSliced complex_ $ \xs ->
   approxReal 1e-2 (VectorSlice.norm2 xs) $
   let (xrs,xis) = VectorSlice.unzipComplex xs in
   sqrt $ VectorSlice.norm2Squared xrs + VectorSlice.norm2Squared xis
  )
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:1247: "
{-# LINE 1247 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property(
{-# LINE 1247 "src/Numeric/BLAS/Vector/Slice.hs" #-}
        
   forVector number_ $ \xs ->
   let n = Shape.size $ Array.shape xs in
   QC.forAll (QC.choose (0,n)) $ \k ->
   let split = VectorSlice.fromVector $
                  Array.reshape (shapeInt k ::+ shapeInt (n-k)) xs in

   Vector.reverse xs
   QC.===
   VectorSlice.reverse (VectorSlice.slice Slice.right split)
   <>
   VectorSlice.reverse (VectorSlice.slice Slice.left split)
  )