-- Do not edit! Automatically created with doctest-extract from src/Numeric/BLAS/Vector/Slice.hs
{-# LINE 87 "src/Numeric/BLAS/Vector/Slice.hs" #-}

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

import qualified Test.DocTest.Driver as DocTest

{-# LINE 90 "src/Numeric/BLAS/Vector/Slice.hs" #-}
import     qualified Test.Slice as TestSlice
import     Test.ComplexFloat.Numeric.BLAS.Vector
       (maxElem, maxDim, genVector, number_, real_, complex_)
import     Test.ComplexFloat.Type (Number_)
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.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, 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 Shape 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     :: Shape.C sh => VectorSlice.T shA 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 (sh0 ::+ (sh, sh1) ::+ sh2) sh a
takeColumn     c =
       VectorSlice.slice
          (Slice.column c . Slice.left . Slice.right) . VectorSlice.fromVector

listFromSlice     ::
       (Shape.C sh, Class.Floating a) => VectorSlice.T shA 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:280: "
{-# LINE 280 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 280 "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:282: "
{-# LINE 282 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 282 "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 == cut xs)
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:314: "
{-# LINE 314 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 314 "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:315: "
{-# LINE 315 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 315 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced number_ $ \xs -> VectorSlice.inner xs xs == Scalar.fromReal (VectorSlice.norm2Squared xs))
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:398: "
{-# LINE 398 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 398 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced number_ $ \xs -> VectorSlice.sum xs == List.sum (listFromSlice xs))
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:471: "
{-# LINE 471 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 471 "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:482: "
{-# LINE 482 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 482 "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:497: "
{-# LINE 497 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 497 "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:498: "
{-# LINE 498 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 498 "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:499: "
{-# LINE 499 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 499 "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:546: "
{-# LINE 546 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 546 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced real_ $ \xs -> isNonEmpty xs ==> VectorSlice.argAbsMaximum xs == VectorSlice.argAbs1Maximum xs)
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:571: "
{-# LINE 571 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 571 "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:582: "
{-# LINE 582 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 582 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced real_ $ \xs -> isNonEmpty xs ==> VectorSlice.minimum xs == List.minimum (listFromSlice xs))
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:583: "
{-# LINE 583 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 583 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced real_ $ \xs -> isNonEmpty xs ==> VectorSlice.maximum xs == List.maximum (listFromSlice xs))
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:599: "
{-# LINE 599 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 599 "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:629: "
{-# LINE 629 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 629 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced number_ $ \xs -> VectorSlice.negate xs == VectorSlice.scale minusOne xs)
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:630: "
{-# LINE 630 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 630 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced number_ $ \xs -> VectorSlice.scale 2 xs == VectorSlice.add xs xs)
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:689: "
{-# LINE 689 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 689 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced2 number_ $ \xs ys -> VectorSlice.add xs ys == VectorSlice.add ys xs)
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:690: "
{-# LINE 690 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 690 "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:715: "
{-# LINE 715 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 715 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced number_ $ \xs -> VectorSlice.toVector xs == Vector.negate (VectorSlice.negate xs))
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:728: "
{-# LINE 728 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 728 "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:745: "
{-# LINE 745 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 745 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced2 number_ $ \xs ys -> VectorSlice.mul xs ys == VectorSlice.mul ys xs)
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:753: "
{-# LINE 753 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 753 "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:877: "
{-# LINE 877 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 877 "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)