-- Do not edit! Automatically created with doctest-extract from src/Numeric/BLAS/Matrix/RowMajor.hs
{-# LINE 98 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}

{-# OPTIONS_GHC -XTypeOperators #-}
module Test.Float.Numeric.BLAS.Matrix.RowMajor where

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

{-# LINE 100 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
import     Test.Float.Numeric.BLAS.Vector.Slice (forSliced2)
import     Test.Float.Numeric.BLAS.Vector
       (forVector, genVector, Number_, number_, real_)
import     Test.Slice (ShapeInt, shapeInt)
--     import Test.Utility (approx)
import     qualified Numeric.BLAS.Matrix.RowMajor.Block as BlockMatrix
import     qualified Numeric.BLAS.Matrix.RowMajor.Square as Square
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.Netlib.Class as Class
import     Numeric.BLAS.Matrix.RowMajor.Block ((&===), (&|||))
import     Numeric.BLAS.Vector.Slice ((|+|))
import     Numeric.BLAS.Scalar (RealOf)
import     Numeric.Netlib.Modifier (Conjugation(NonConjugated, Conjugated))
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.Array.Comfort.Boxed as BoxedArray
import     qualified Data.Foldable as Fold
import     qualified Data.Map as Map
import     qualified Data.Set as Set
import     qualified Data.Monoid.HT as Mn
import     Data.Array.Comfort.Shape ((::+)((::+)))
import     Data.Map (Map)
import     Data.Function.HT (Id)
import     qualified Test.QuickCheck as QC
import     Test.QuickCheck ((===))

type     Matrix = Matrix.Matrix ShapeInt ShapeInt
type     Real_ = RealOf Number_

maxDim     :: Int
maxDim     = 10

forMatrix     ::
       (QC.Testable prop, QC.Arbitrary a, Class.Floating a, Show a) =>
       QC.Gen a -> (Matrix a -> prop) -> QC.Property
forMatrix     genElem =
       QC.forAllShrink
          (do height <- fmap shapeInt $ QC.choose (0,maxDim)
              width <- fmap shapeInt $ QC.choose (0,maxDim)
              genVector (height, width) genElem)
          (\a ->
             let (height@(Shape.ZeroBased h), width@(Shape.ZeroBased w)) =
                   Array.shape a in
             Mn.when (h > 0)
                [let h2 = div h 2 in
                 Array2.takeTop $
                   Array.reshape
                      (Shape.ZeroBased h2 ::+ Shape.ZeroBased (h-h2), width) a,
                 Array2.takeTop $
                   Array.reshape (Shape.ZeroBased (h-1) ::+ (), width) a]
             ++
             Mn.when (w > 0)
                [let w2 = div w 2 in
                 Array2.takeLeft $
                   Array.reshape
                      (height, Shape.ZeroBased w2 ::+ Shape.ZeroBased (w-w2)) a,
                 Array2.takeLeft $
                   Array.reshape (height, Shape.ZeroBased (w-1) ::+ ()) a])

genSplitShape     :: ShapeInt -> QC.Gen (ShapeInt ::+ ShapeInt)
genSplitShape     (Shape.ZeroBased n) = do
       k <- QC.choose (0, n)
       return $ Shape.ZeroBased k ::+ Shape.ZeroBased (n-k)

genSplitShape3     :: ShapeInt -> QC.Gen (ShapeInt ::+ ShapeInt ::+ ShapeInt)
genSplitShape3     (Shape.ZeroBased n) = do
       k <- QC.choose (0, n)
       j <- QC.choose (0, n)
       let a = min k j; b = max k j
       return $
          Shape.ZeroBased a ::+ Shape.ZeroBased (b-a) ::+ Shape.ZeroBased (n-b)

test :: DocTest.T ()
test = do
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:223: "
{-# LINE 223 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.example(
{-# LINE 223 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
    Matrix.identity (Shape.ZeroBased 0) :: Matrix.Square ShapeInt Real_
  )
  [ExpectedLine [LineChunk "StorableArray.fromList (ZeroBased {",WildCardChunk,LineChunk " 0},ZeroBased {",WildCardChunk,LineChunk " 0}) []"]]
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:225: "
{-# LINE 225 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.example(
{-# LINE 225 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
    Matrix.identity (Shape.ZeroBased 3) :: Matrix.Square ShapeInt Real_
  )
  [ExpectedLine [LineChunk "StorableArray.fromList (ZeroBased {",WildCardChunk,LineChunk " 3},ZeroBased {",WildCardChunk,LineChunk " 3}) [1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0]"]]
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:261: "
{-# LINE 261 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 261 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->

   Matrix.transpose a
   ===
   Matrix.fromRowArray
      (Matrix.height a)
      (VectorSlice.slicesVector Slice.columnArray a)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:302: "
{-# LINE 302 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.example(
{-# LINE 302 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
      
   (id :: Id (array (height, Map Char ShapeInt) Number_)) $
   Matrix.fromBlockArray
      (Map.singleton 'A' (shapeInt 2) <> Map.singleton 'B' (shapeInt 3))
      Map.empty $
   BoxedArray.fromList (Set.fromList "AB", Set.empty) []
  )
  [ExpectedLine [LineChunk "StorableArray.fromList (fromList [('A',ZeroBased {",WildCardChunk,LineChunk " 2}),('B',ZeroBased {",WildCardChunk,LineChunk " 3})],fromList []) []"]]
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:311: "
{-# LINE 311 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 311 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \block ->
   let height = Map.singleton 'A' $ fst $ Array.shape block in
   let width  = Map.singleton '1' $ snd $ Array.shape block in

   Array.reshape (height,width) block
   ===
   Array2.fromBlockArray height width
      (BoxedArray.replicate (Set.singleton 'A', Set.singleton '1') block)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:322: "
{-# LINE 322 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 322 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \blockA1 ->
   forMatrix number_ $ \blockB3 ->
   let shapeR0 = fst $ Array.shape blockA1 in
   let shapeR1 = fst $ Array.shape blockB3 in
   let shapeC0 = snd $ Array.shape blockA1 in
   QC.forAll (fmap shapeInt $ QC.choose (0,10)) $ \shapeC1 ->
   let shapeC2 = snd $ Array.shape blockB3 in
   QC.forAll (genVector (shapeR0, shapeC1) number_) $ \blockA2 ->
   QC.forAll (genVector (shapeR0, shapeC2) number_) $ \blockA3 ->
   QC.forAll (genVector (shapeR1, shapeC0) number_) $ \blockB1 ->
   QC.forAll (genVector (shapeR1, shapeC1) number_) $ \blockB2 ->

   let height = Map.fromList [('A',shapeR0),('B',shapeR1)] in
   let width  = Map.fromList [('1',shapeC0),('2',shapeC1),('3',shapeC2)] in

   Array.reshape (height,width)
      (BlockMatrix.toMatrix
         (blockA1 &||| Array2.beside blockA2 blockA3
          &===
          blockB1 &||| blockB2 &||| blockB3))
   ===
   Matrix.fromBlockArray height width
      (BoxedArray.fromList
         (Set.fromList "AB", Set.fromList "123")
         [blockA1, blockA2, blockA3,
          blockB1, blockB2, blockB3])
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:383: "
{-# LINE 383 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.example(
{-# LINE 383 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
      
   let shapeR0 = shapeInt 2; shapeR1 = shapeInt 3 in
   let shapeC0 = shapeInt 3; shapeC1 = shapeInt 2 in
   let block sh a = Array.replicate sh (a::Real_) in
   Matrix.fromBlockArray
      (Map.singleton 'A' shapeR0 <> Map.singleton 'B' shapeR1)
      (Map.singleton '1' shapeC0 <> Map.singleton '2' shapeC1) $
   BoxedArray.fromList (Set.fromList "AB", Set.fromList "12")
      [block (shapeR0,shapeC0) 0, block (shapeR0,shapeC1) 1,
       block (shapeR1,shapeC0) 2, block (shapeR1,shapeC1) 3]
  )
  [ExpectedLine [LineChunk "StorableArray.fromList (fromList [('A',ZeroBased {",WildCardChunk,LineChunk " 2}),('B',ZeroBased {",WildCardChunk,LineChunk " 3})],fromList [('1',ZeroBased {",WildCardChunk,LineChunk " 3}),('2',ZeroBased {",WildCardChunk,LineChunk " 2})]) [0.0,0.0,0.0,1.0,1.0,0.0,0.0,0.0,1.0,1.0,2.0,2.0,2.0,3.0,3.0,2.0,2.0,2.0,3.0,3.0,2.0,2.0,2.0,3.0,3.0]"]]
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:396: "
{-# LINE 396 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 396 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \blockA1 ->
   forMatrix number_ $ \blockB2 ->
   let shapeR0 = fst $ Array.shape blockA1 in
   let shapeC0 = snd $ Array.shape blockA1 in
   let shapeR1 = fst $ Array.shape blockB2 in
   let shapeC1 = snd $ Array.shape blockB2 in
   QC.forAll (genVector (shapeR0, shapeC1) number_) $ \blockA2 ->
   QC.forAll (genVector (shapeR1, shapeC0) number_) $ \blockB1 ->
   let blocked =
         BoxedArray.fromList (Set.fromList "AB", Set.fromList "12")
            [blockA1, blockA2, blockB1, blockB2] in

   Array2.fromNonEmptyBlockArray blocked
   ===
   Matrix.fromNonEmptyBlockArray blocked
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:414: "
{-# LINE 414 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 414 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \blockA1 ->
   forMatrix number_ $ \blockB2 ->
   forMatrix number_ $ \blockC3 ->
   let shapeR0 = fst $ Array.shape blockA1 in
   let shapeC0 = snd $ Array.shape blockA1 in
   let shapeR1 = fst $ Array.shape blockB2 in
   let shapeC1 = snd $ Array.shape blockB2 in
   let shapeR2 = fst $ Array.shape blockC3 in
   let shapeC2 = snd $ Array.shape blockC3 in
   QC.forAll (genVector (shapeR0, shapeC1) number_) $ \blockA2 ->
   QC.forAll (genVector (shapeR0, shapeC2) number_) $ \blockA3 ->
   QC.forAll (genVector (shapeR1, shapeC0) number_) $ \blockB1 ->
   QC.forAll (genVector (shapeR1, shapeC2) number_) $ \blockB3 ->
   QC.forAll (genVector (shapeR2, shapeC0) number_) $ \blockC1 ->
   QC.forAll (genVector (shapeR2, shapeC1) number_) $ \blockC2 ->
   let blocked =
         BoxedArray.fromList (Set.fromList "ABC", Set.fromList "123")
            [blockA1, blockA2, blockA3,
             blockB1, blockB2, blockB3,
             blockC1, blockC2, blockC3] in

   Array2.fromNonEmptyBlockArray blocked
   ===
   Matrix.fromNonEmptyBlockArray blocked
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:465: "
{-# LINE 465 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 465 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   let (height, width) = Array.shape a in
   QC.forAll (genSplitShape height) $ \splitHeight ->
      let b = Array.reshape (splitHeight, width) a in
      b === Matrix.above (Matrix.takeTop b) (Matrix.takeBottom b)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:483: "
{-# LINE 483 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 483 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   let (height, width) = Array.shape a in
   QC.forAll (genSplitShape width) $ \splitWidth ->
      let b = Array.reshape (height, splitWidth) a in
      b === Matrix.beside (Matrix.takeLeft b) (Matrix.takeRight b)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:543: "
{-# LINE 543 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 543 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   let (height, width) = Array.shape a in
   QC.forAll (genVector width number_) $ \x ->
   QC.forAll (genSplitShape width) $ \splitWidth ->
   let b = Array.reshape (height, splitWidth) a in
   let y = Array.reshape splitWidth x in

   Matrix.multiplyVectorRight b y
   ===
   Vector.add
      (Matrix.multiplyVectorRight (Matrix.takeLeft b) (Vector.takeLeft y))
      (Matrix.multiplyVectorRight (Matrix.takeRight b) (Vector.takeRight y))
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:585: "
{-# LINE 585 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 585 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \abc0 ->
   let width = Matrix.width abc0 in
   QC.forAll (genSplitShape3 width) $ \splitWidth ->
   let abc = Matrix.reshapeWidth splitWidth abc0 in

   let a = Matrix.takeLeft abc in
   let b = Matrix.takeHorizCenter abc in
   let c = Matrix.takeRight (Matrix.takeRight abc) in
   abc === BlockMatrix.toMatrix (a &||| b &||| c)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:597: "
{-# LINE 597 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 597 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \abc0 ->
   let width = Matrix.width abc0 in
   QC.forAll (genSplitShape3 width) $ \splitWidth ->
   let abc = Matrix.reshapeWidth splitWidth abc0 in

   Matrix.takeHorizCenter abc
   ===
   Array2.takeHorizCenter abc
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:625: "
{-# LINE 625 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.example(
{-# LINE 625 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
    Matrix.transpose (Array.fromList (Shape.Range 'a' 'c', shapeInt 2) [1,2,3,4,5,6::Real_])
  )
  [ExpectedLine [LineChunk "StorableArray.fromList (ZeroBased {",WildCardChunk,LineChunk "2},Range {rangeFrom = 'a', rangeTo = 'c'}) [1.0,3.0,5.0,2.0,4.0,6.0]"]]
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:628: "
{-# LINE 628 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 628 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
      forMatrix number_ $ \a -> a == Matrix.transpose (Matrix.transpose a)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:630: "
{-# LINE 630 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 630 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->

   Matrix.transpose a
   ==
   Array.reshape (Matrix.width a, Matrix.height a)
      (VectorSlice.concat
         (Fold.toList $ fmap VectorSlice.chunk $
          VectorSlice.slicesVector Slice.columnArray a))
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:641: "
{-# LINE 641 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 641 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->

   fmap VectorSlice.toVector
      (VectorSlice.slicesVector Slice.rowArray (Matrix.transpose a))
   ==
   fmap VectorSlice.toVector
      (VectorSlice.slicesVector Slice.columnArray a)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:663: "
{-# LINE 663 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 663 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forVector number_ $ \xs ->
   Matrix.tensorProduct (Left Conjugated) xs (Vector.one ())
   ===
   Matrix.singleColumn (Vector.conjugate xs)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:670: "
{-# LINE 670 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 670 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forVector number_ $ \xs ->
   Matrix.tensorProduct (Right Conjugated) (Vector.one ()) xs
   ===
   Matrix.singleRow (Vector.conjugate xs)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:677: "
{-# LINE 677 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 677 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forVector number_ $ \xs ->
   forVector number_ $ \ys ->
   QC.forAll (genVector (Array.shape ys) number_) $ \zs ->
   Matrix.multiplyVectorRight
      (Matrix.tensorProduct (Left NonConjugated) xs ys) zs
   ===
   Vector.scale (Vector.dot ys zs) xs
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:687: "
{-# LINE 687 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 687 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forVector number_ $ \xs ->
   forVector number_ $ \ys ->
   QC.forAll (genVector (Array.shape xs) number_) $ \zs ->
   Matrix.multiplyVectorLeft zs
      (Matrix.tensorProduct (Right NonConjugated) xs ys)
   ===
   Vector.scale (Vector.dot xs zs) ys
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:697: "
{-# LINE 697 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 697 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forVector number_ $ \xs ->
   forVector number_ $ \ys ->
   QC.forAll (genVector (Array.shape ys) number_) $ \zs ->
   Matrix.multiplyVectorRight
      (Matrix.tensorProduct (Right Conjugated) xs ys) zs
   ===
   Vector.scale (Vector.inner ys zs) xs
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:707: "
{-# LINE 707 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 707 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forVector number_ $ \xs ->
   forVector number_ $ \ys ->
   QC.forAll (genVector (Array.shape xs) number_) $ \zs ->
   Matrix.multiplyVectorLeft zs
      (Matrix.tensorProduct (Left Conjugated) xs ys)
   ===
   Vector.scale (Vector.inner xs zs) ys
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:768: "
{-# LINE 768 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 768 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   a === Matrix.scaleRows (VectorSlice.one (Matrix.height a)) a
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:773: "
{-# LINE 773 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 773 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forSliced2 number_ $ \x y ->
   QC.forAll (Shape.ZeroBased <$> QC.choose (1,maxDim)) $ \width ->
   QC.forAll (genVector (VectorSlice.shape x, width) number_) $ \a ->

   Matrix.scaleRows (x|+|y) a
   ===
   Matrix.scaleRows x a |+| Matrix.scaleRows y a
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:783: "
{-# LINE 783 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 783 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   QC.forAll (Shape.ZeroBased <$> QC.choose (1,maxDim)) $ \set ->
   QC.forAll (genVector (Matrix.height a, set) number_) $ \b ->
   QC.forAll (QC.elements $ Shape.indices set) $ \k ->

   Matrix.scaleRows (VectorSlice.sliceVector (Slice.column k) b) a
   ===
   Matrix.scaleRows (Matrix.takeColumn k b) a
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:819: "
{-# LINE 819 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 819 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   a === Matrix.scaleColumns (VectorSlice.one (Matrix.width a)) a
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:824: "
{-# LINE 824 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 824 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forSliced2 number_ $ \x y ->
   QC.forAll (Shape.ZeroBased <$> QC.choose (1,maxDim)) $ \height ->
   QC.forAll (genVector (height, VectorSlice.shape x) number_) $ \a ->

   Matrix.scaleColumns (x|+|y) a
   ===
   Matrix.scaleColumns x a |+| Matrix.scaleColumns y a
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:834: "
{-# LINE 834 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 834 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   QC.forAll (Shape.ZeroBased <$> QC.choose (1,maxDim)) $ \set ->
   QC.forAll (genVector (Matrix.width a, set) number_) $ \b ->
   QC.forAll (QC.elements $ Shape.indices set) $ \k ->

   Matrix.scaleColumns (VectorSlice.sliceVector (Slice.column k) b) a
   ===
   Matrix.scaleColumns (Matrix.takeColumn k b) a
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:878: "
{-# LINE 878 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 878 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   let (height, _width) = Array.shape a in
   QC.forAll (genVector height real_) $ \x ->

   Matrix.scaleRowsReal x a
   ===
   Matrix.scaleRows (Vector.fromReal x) a
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:901: "
{-# LINE 901 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 901 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   let (_height, width) = Array.shape a in
   QC.forAll (genVector width real_) $ \x ->

   Matrix.scaleColumnsReal x a
   ===
   Matrix.scaleColumns (Vector.fromReal x) a
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:946: "
{-# LINE 946 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.example(
{-# LINE 946 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
    Matrix.multiplyVectorLeft (Array.vectorFromList [3,1,4]) (Array.fromList (Shape.ZeroBased (3::Int), Shape.Range 'a' 'b') [0,1,0,0,1,0::Real_])
  )
  [ExpectedLine [LineChunk "StorableArray.fromList (Range {rangeFrom = 'a', rangeTo = 'b'}) [4.0,3.0]"]]
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:949: "
{-# LINE 949 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 949 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forVector number_ $ \xs ->
   Matrix.multiplyVectorLeft xs (Matrix.identity (Array.shape xs)) == xs
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:961: "
{-# LINE 961 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.example(
{-# LINE 961 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
    Matrix.multiplyVectorRight (Array.fromList (Shape.Range 'a' 'b', Shape.ZeroBased (3::Int)) [0,0,1,1,0,0]) (Array.vectorFromList [3,1,4::Real_])
  )
  [ExpectedLine [LineChunk "StorableArray.fromList (Range {rangeFrom = 'a', rangeTo = 'b'}) [4.0,3.0]"]]
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:963: "
{-# LINE 963 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.example(
{-# LINE 963 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
    Matrix.multiplyVectorRight (Array.fromList (Shape.Range 'a' 'b', Shape.ZeroBased (3::Int)) [2,7,1,8,2,8]) (Array.vectorFromList [3,1,4::Real_])
  )
  [ExpectedLine [LineChunk "StorableArray.fromList (Range {rangeFrom = 'a', rangeTo = 'b'}) [17.0,58.0]"]]
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:966: "
{-# LINE 966 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 966 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forVector number_ $ \xs ->
   Matrix.multiplyVectorRight (Matrix.identity (Array.shape xs)) xs === xs
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:971: "
{-# LINE 971 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 971 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   QC.forAll (genVector (snd $ Array.shape a) number_) $ \x ->
   Matrix.singleColumn (Matrix.multiplyVectorRight a x)
   ===
   Matrix.multiply a (Matrix.singleColumn x)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:979: "
{-# LINE 979 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 979 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   QC.forAll (genVector (fst $ Array.shape a) number_) $ \x ->
   QC.forAll (genVector (snd $ Array.shape a) number_) $ \y ->
   Vector.dot x (Matrix.multiplyVectorRight a y)
   ===
   Vector.dot (Matrix.multiplyVectorLeft x a) y
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:988: "
{-# LINE 988 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 988 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   QC.forAll (genVector (snd $ Array.shape a) number_) $ \x ->
   Matrix.multiplyVectorRight a x
   ===
   Matrix.multiplyVectorLeft x (Matrix.transpose a)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1004: "
{-# LINE 1004 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.example(
{-# LINE 1004 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
      
   Matrix.multiply
      (Array.fromList (shapeInt 2, shapeInt 2) [1000,100,10,1])
      (Array.fromList (shapeInt 2, shapeInt 3) [0..5::Real_])
  )
  [ExpectedLine [WildCardChunk,LineChunk " [300.0,1400.0,2500.0,3.0,14.0,25.0]"]]
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1011: "
{-# LINE 1011 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1011 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
      Matrix.multiply (Matrix.identity (Matrix.height a)) a == a
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1015: "
{-# LINE 1015 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1015 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
      Matrix.multiply a (Matrix.identity (Matrix.width a)) == a
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1019: "
{-# LINE 1019 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1019 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   forMatrix number_ $ \c ->
   QC.forAll (genVector (Matrix.width a, Matrix.height c) number_) $ \b ->
      Matrix.multiply a (Matrix.multiply b c)
      ===
      Matrix.multiply (Matrix.multiply a b) c
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1041: "
{-# LINE 1041 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1041 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->

   Matrix.sumRows a
   ===
   Matrix.multiplyVectorRight a (Vector.one $ snd $ Array.shape a)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1049: "
{-# LINE 1049 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1049 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   Vector.sum (Matrix.sumRows a)
   ===
   Vector.sum (Matrix.sumColumns a)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1056: "
{-# LINE 1056 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1056 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   QC.forAll (genVector (fst $ Array.shape a) number_) $ \x ->

   Vector.dot x (Matrix.sumRows a)
   ===
   Vector.sum (Matrix.multiplyVectorLeft x a)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1125: "
{-# LINE 1125 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1125 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->

   Matrix.sumColumns a
   ===
   Matrix.multiplyVectorLeft (Vector.one $ fst $ Array.shape a) a
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1133: "
{-# LINE 1133 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1133 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->

   Matrix.sumColumns a
   ===
   Matrix.sumRows (Matrix.transpose a)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1141: "
{-# LINE 1141 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1141 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   QC.forAll (genVector (snd $ Array.shape a) number_) $ \x ->

   Vector.dot (Matrix.sumColumns a) x
   ===
   Vector.sum (Matrix.multiplyVectorRight a x)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1183: "
{-# LINE 1183 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1183 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   QC.forAll (genVector (Array.shape a) number_) $ \b ->

   Array.toBoxed (Matrix.dotRowwise a b)
   ===
   BoxedArray.zipWith Vector.dot (Matrix.toRowArray a) (Matrix.toRowArray b)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1192: "
{-# LINE 1192 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1192 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   QC.forAll (genVector (Array.shape a) number_) $ \b ->

   Square.takeDiagonal
      (Array.mapShape (Shape.Square . fst)
         (Matrix.multiply a (Matrix.transpose b)))
   ===
   Matrix.dotRowwise a b
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1203: "
{-# LINE 1203 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1203 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   let shape = Array.shape a in
   QC.forAll (genVector shape number_) $ \b ->

   Matrix.dotRowwise a b
   ===
   Matrix.sumRows (Vector.mul a b)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1213: "
{-# LINE 1213 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1213 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   QC.forAll (genVector (Array.shape a) number_) $ \b ->

   Vector.dot a b
   ===
   Vector.sum (Matrix.dotRowwise a b)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1222: "
{-# LINE 1222 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1222 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   QC.forAll (genVector (Array.shape a) number_) $ \b ->

   Matrix.dotRowwise a b
   ===
   Matrix.dotRowwise b a
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1241: "
{-# LINE 1241 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1241 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   let shape = Array.shape a in
   QC.forAll (genVector shape number_) $ \b ->

   Matrix.innerRowwise a b
   ===
   Matrix.sumRows (Vector.mulConj a b)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1251: "
{-# LINE 1251 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1251 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   QC.forAll (genVector (Array.shape a) number_) $ \b ->

   Matrix.innerRowwise a b
   ===
   Matrix.dotRowwise (Vector.conjugate a) b
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1260: "
{-# LINE 1260 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1260 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   forMatrix number_ $ \a ->
   QC.forAll (genVector (Array.shape a) number_) $ \b ->

   Vector.inner a b
   ===
   Vector.sum (Matrix.innerRowwise a b)
  )
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1278: "
{-# LINE 1278 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.example(
{-# LINE 1278 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
      
   Matrix.kronecker
      (Array.fromList (shapeInt 2, shapeInt 2) [0,1,-1,0::Real_])
      (Array.fromList (shapeInt 2, shapeInt 3) [1..6])
  )
  [ExpectedLine [WildCardChunk,LineChunk " [0.0,0.0,0.0,1.0,2.0,3.0,0.0,0.0,0.0,4.0,5.0,6.0,-1.0,-2.0,-3.0,0.0,0.0,0.0,-4.0,-5.0,-6.0,0.0,0.0,0.0]"]]
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1285: "
{-# LINE 1285 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.example(
{-# LINE 1285 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
      
   Matrix.kronecker
      (Array.fromList (shapeInt 2, shapeInt 2) [1,2,3,4::Real_])
      (Array.fromList (shapeInt 2, shapeInt 3) [1,2,4,8,16,32])
  )
  [ExpectedLine [WildCardChunk,LineChunk " [1.0,2.0,4.0,2.0,4.0,8.0,8.0,16.0,32.0,16.0,32.0,64.0,3.0,6.0,12.0,4.0,8.0,16.0,24.0,48.0,96.0,32.0,64.0,128.0]"]]
 DocTest.printPrefix "Numeric.BLAS.Matrix.RowMajor:1292: "
{-# LINE 1292 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
 DocTest.property(
{-# LINE 1292 "src/Numeric/BLAS/Matrix/RowMajor.hs" #-}
        
   QC.forAll (QC.choose (0,5)) $ \m ->
   QC.forAll (QC.choose (0,5)) $ \n ->
      Matrix.kronecker
         (Matrix.identity (shapeInt m))
         (Matrix.identity (shapeInt n))
      ==
      (Matrix.identity (shapeInt m, shapeInt n)
         :: Matrix.Square (ShapeInt, ShapeInt) Number_)
  )