-- 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 #-}
module Test.ComplexFloat.Numeric.BLAS.Vector.Slice where

import qualified Test.DocTest.Driver as DocTest

{-# LINE 89 "src/Numeric/BLAS/Vector/Slice.hs" #-}
import     qualified Test.Slice as TestSlice
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.Monad (replicateM)
import     Control.Applicative (liftA2)

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

type     Real_ = RealOf Number_
type     Complex_ = Complex Real_

maxElem     :: Integer
maxElem     = 10

maxDim     :: Int
maxDim     = 100

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)

genVector     ::
       (Shape.C sh, Class.Floating a) =>
       sh -> QC.Gen a -> QC.Gen (Vector.Vector sh a)
genVector     shape genElem =
       fmap (Vector.fromList shape) $
       replicateM (Shape.size shape) genElem

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

real_     :: QC.Gen Real_
real_     = genNumber maxElem

complex_     :: QC.Gen Complex_
complex_     = genNumber maxElem

number_     :: QC.Gen Number_
number_     = genNumber maxElem

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:300: "
{-# LINE 300 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 300 "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:302: "
{-# LINE 302 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 302 "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:334: "
{-# LINE 334 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 334 "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:335: "
{-# LINE 335 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 335 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced number_ $ \xs -> VectorSlice.inner xs xs == Scalar.fromReal (VectorSlice.norm2Squared xs))
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:418: "
{-# LINE 418 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 418 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced number_ $ \xs -> VectorSlice.sum xs == List.sum (listFromSlice xs))
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:491: "
{-# LINE 491 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 491 "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:502: "
{-# LINE 502 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 502 "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:517: "
{-# LINE 517 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 517 "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:518: "
{-# LINE 518 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 518 "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:519: "
{-# LINE 519 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 519 "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:566: "
{-# LINE 566 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 566 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced real_ $ \xs -> isNonEmpty xs ==> VectorSlice.argAbsMaximum xs == VectorSlice.argAbs1Maximum xs)
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:591: "
{-# LINE 591 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 591 "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:602: "
{-# LINE 602 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 602 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced real_ $ \xs -> isNonEmpty xs ==> VectorSlice.minimum xs == List.minimum (listFromSlice xs))
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:603: "
{-# LINE 603 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 603 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced real_ $ \xs -> isNonEmpty xs ==> VectorSlice.maximum xs == List.maximum (listFromSlice xs))
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:619: "
{-# LINE 619 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 619 "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:649: "
{-# LINE 649 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 649 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced number_ $ \xs -> VectorSlice.negate xs == VectorSlice.scale minusOne xs)
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:650: "
{-# LINE 650 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 650 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced number_ $ \xs -> VectorSlice.scale 2 xs == VectorSlice.add xs xs)
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:709: "
{-# LINE 709 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 709 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced2 number_ $ \xs ys -> VectorSlice.add xs ys == VectorSlice.add ys xs)
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:710: "
{-# LINE 710 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 710 "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:735: "
{-# LINE 735 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 735 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced number_ $ \xs -> VectorSlice.toVector xs == Vector.negate (VectorSlice.negate xs))
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:748: "
{-# LINE 748 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 748 "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:765: "
{-# LINE 765 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 765 "src/Numeric/BLAS/Vector/Slice.hs" #-}
     (forSliced2 number_ $ \xs ys -> VectorSlice.mul xs ys == VectorSlice.mul ys xs)
 DocTest.printPrefix "Numeric.BLAS.Vector.Slice:773: "
{-# LINE 773 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 773 "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:897: "
{-# LINE 897 "src/Numeric/BLAS/Vector/Slice.hs" #-}
 DocTest.property
{-# LINE 897 "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)