Safe Haskell	Safe-Inferred
Language	Haskell98

Numeric.BLAS.Matrix.RowMajor

Synopsis

type Matrix height width = Array (height, width)
type Square sh = Matrix sh sh
type Vector = Array
height :: Matrix height width a -> height
width :: Matrix height width a -> width
singleRow :: Array width a -> Array2 () width a
flattenRow :: Array2 () width a -> Array width a
singleColumn :: Array height a -> Array2 height () a
flattenColumn :: Array2 height () a -> Array height a
identity :: (C sh, Floating a) => sh -> Square sh a
takeRow :: (Indexed height, C width, Index height ~ ix, Storable a) => ix -> Matrix height width a -> Vector width a
takeColumn :: (C height, Indexed width, Index width ~ ix, Floating a) => ix -> Matrix height width a -> Vector height a
fromRows :: (C width, Eq width, Storable a) => width -> [Vector width a] -> Matrix ShapeInt width a
above :: (C heightA, C heightB) => (C width, Eq width) => Storable a => Matrix heightA width a -> Matrix heightB width a -> Matrix (heightA ::+ heightB) width a
beside :: (C widthA, C widthB) => (C height, Eq height) => Storable a => Matrix height widthA a -> Matrix height widthB a -> Matrix height (widthA ::+ widthB) a
takeTop :: (C heightA, C heightB, C width, Storable a) => Matrix (heightA ::+ heightB) width a -> Matrix heightA width a
takeBottom :: (C heightA, C heightB, C width, Storable a) => Matrix (heightA ::+ heightB) width a -> Matrix heightB width a
takeLeft :: (C height, C widthA, C widthB, Storable a) => Matrix height (widthA ::+ widthB) a -> Matrix height widthA a
takeRight :: (C height, C widthA, C widthB, Storable a) => Matrix height (widthA ::+ widthB) a -> Matrix height widthB a
tensorProduct :: (C height, C width, Floating a) => Either Conjugation Conjugation -> Vector height a -> Vector width a -> Matrix height width a
decomplex :: Real a => Matrix height width (Complex a) -> Matrix height (width, ComplexShape) a
recomplex :: Real a => Matrix height (width, ComplexShape) a -> Matrix height width (Complex a)
scaleRows :: (C height, Eq height, C width, Floating a) => Vector height a -> Matrix height width a -> Matrix height width a
scaleColumns :: (C height, C width, Eq width, Floating a) => Vector width a -> Matrix height width a -> Matrix height width a
multiplyVectorLeft :: (Eq height, C height, C width, Floating a) => Vector height a -> Matrix height width a -> Vector width a
multiplyVectorRight :: (C height, C width, Eq width, Floating a) => Matrix height width a -> Vector width a -> Vector height a
data Transposable height width a
- = NonTransposed (Matrix height width a)
- | Transposed (Matrix width height a)
nonTransposed :: Matrix height width a -> Transposable height width a
transposed :: Matrix height width a -> Transposable width height a
transposeTransposable :: Transposable height width a -> Transposable width height a
multiply :: (C height, C width, C fuse, Eq fuse, Floating a) => Matrix height fuse a -> Matrix fuse width a -> Matrix height width a
multiplyTransposable :: (C height, C width, C fuse, Eq fuse, Floating a) => Transposable height fuse a -> Transposable fuse width a -> Matrix height width a
kronecker :: (C heightA, C widthA, C heightB, C widthB, Floating a) => Matrix heightA widthA a -> Matrix heightB widthB a -> Matrix (heightA, heightB) (widthA, widthB) a
kroneckerTransposable :: (C heightA, C widthA, C heightB, C widthB, Floating a) => Transposable heightA widthA a -> Transposable heightB widthB a -> Transposable (heightA, heightB) (widthA, widthB) a
kroneckerLeftTransposable :: (C heightA, C widthA, C heightB, C widthB, Floating a) => Transposable heightA widthA a -> Matrix heightB widthB a -> Matrix (heightA, heightB) (widthA, widthB) a

Documentation

type Matrix height width = Array (height, width) Source #

type Square sh = Matrix sh sh Source #

There is also Square but this would be incompatible with other matrix operations. This might be addressed in a new Matrix.Square module. But for advanced type hacks you can already use the lapack package.

type Vector = Array Source #

height :: Matrix height width a -> height Source #

width :: Matrix height width a -> width Source #

singleRow :: Array width a -> Array2 () width a #

flattenRow :: Array2 () width a -> Array width a #

singleColumn :: Array height a -> Array2 height () a #

flattenColumn :: Array2 height () a -> Array height a #

identity :: (C sh, Floating a) => sh -> Square sh a Source #

>>> Matrix.identity (Shape.ZeroBased 0) :: Matrix.Square (Shape.ZeroBased Int) Real_
StorableArray.fromList (ZeroBased {... 0},ZeroBased {... 0}) []
>>> Matrix.identity (Shape.ZeroBased 3) :: Matrix.Square (Shape.ZeroBased Int) Real_
StorableArray.fromList (ZeroBased {... 3},ZeroBased {... 3}) [1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0]

takeRow :: (Indexed height, C width, Index height ~ ix, Storable a) => ix -> Matrix height width a -> Vector width a Source #

takeColumn :: (C height, Indexed width, Index width ~ ix, Floating a) => ix -> Matrix height width a -> Vector height a Source #

fromRows :: (C width, Eq width, Storable a) => width -> [Vector width a] -> Matrix ShapeInt width a Source #

above :: (C heightA, C heightB) => (C width, Eq width) => Storable a => Matrix heightA width a -> Matrix heightB width a -> Matrix (heightA ::+ heightB) width a infixr 2 Source #

beside :: (C widthA, C widthB) => (C height, Eq height) => Storable a => Matrix height widthA a -> Matrix height widthB a -> Matrix height (widthA ::+ widthB) a infixr 3 Source #

takeTop :: (C heightA, C heightB, C width, Storable a) => Matrix (heightA ::+ heightB) width a -> Matrix heightA width a Source #

takeBottom :: (C heightA, C heightB, C width, Storable a) => Matrix (heightA ::+ heightB) width a -> Matrix heightB width a Source #

takeLeft :: (C height, C widthA, C widthB, Storable a) => Matrix height (widthA ::+ widthB) a -> Matrix height widthA a Source #

takeRight :: (C height, C widthA, C widthB, Storable a) => Matrix height (widthA ::+ widthB) a -> Matrix height widthB a Source #

tensorProduct :: (C height, C width, Floating a) => Either Conjugation Conjugation -> Vector height a -> Vector width a -> Matrix height width a Source #

Warning: Don't use conjugation. Left and Right are swapped.

decomplex :: Real a => Matrix height width (Complex a) -> Matrix height (width, ComplexShape) a Source #

recomplex :: Real a => Matrix height (width, ComplexShape) a -> Matrix height width (Complex a) Source #

scaleRows :: (C height, Eq height, C width, Floating a) => Vector height a -> Matrix height width a -> Matrix height width a Source #

scaleColumns :: (C height, C width, Eq width, Floating a) => Vector width a -> Matrix height width a -> Matrix height width a Source #

multiplyVectorLeft :: (Eq height, C height, C width, Floating a) => Vector height a -> Matrix height width a -> Vector width a Source #

>>> Matrix.multiplyVectorLeft (Array.vectorFromList [3,1,4]) (Array.fromList (Shape.ZeroBased (3::Int), Shape.Range 'a' 'b') [0,1,0,0,1,0::Real_])
StorableArray.fromList (Range {rangeFrom = 'a', rangeTo = 'b'}) [4.0,3.0]

forVector number_ $ \xs ->
   Matrix.multiplyVectorLeft xs (Matrix.identity (Array.shape xs)) == xs

multiplyVectorRight :: (C height, C width, Eq width, Floating a) => Matrix height width a -> Vector width a -> Vector height a Source #

>>> Matrix.multiplyVectorRight (Array.fromList (Shape.Range 'a' 'b', Shape.ZeroBased (3::Int)) [0,0,1,1,0,0]) (Array.vectorFromList [3,1,4::Real_])
StorableArray.fromList (Range {rangeFrom = 'a', rangeTo = 'b'}) [4.0,3.0]
>>> Matrix.multiplyVectorRight (Array.fromList (Shape.Range 'a' 'b', Shape.ZeroBased (3::Int)) [2,7,1,8,2,8]) (Array.vectorFromList [3,1,4::Real_])
StorableArray.fromList (Range {rangeFrom = 'a', rangeTo = 'b'}) [17.0,58.0]

forVector number_ $ \xs ->
   Matrix.multiplyVectorRight (Matrix.identity (Array.shape xs)) xs == xs

forMatrix number_ $ \a ->
   QC.forAll (genVector (snd $ Array.shape a) number_) $ \x ->
   Matrix.singleColumn (Matrix.multiplyVectorRight a x)
   ==
   Matrix.multiply a (Matrix.singleColumn x)

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

forMatrix number_ $ \a ->
   QC.forAll (genVector (snd $ Array.shape a) number_) $ \x ->
   Matrix.multiplyVectorRight a x
   ==
   Matrix.multiplyVectorLeft x (transpose a)

data Transposable height width a Source #

Constructors

NonTransposed (Matrix height width a)
Transposed (Matrix width height a)

Instances

Instances details

(C height, C width, Storable a, Show height, Show width, Show a) => Show (Transposable height width a) Source #
Instance details Defined in Numeric.BLAS.Matrix.RowMajor Methods showsPrec :: Int -> Transposable height width a -> ShowS # show :: Transposable height width a -> String # showList :: [Transposable height width a] -> ShowS #

nonTransposed :: Matrix height width a -> Transposable height width a Source #

transposed :: Matrix height width a -> Transposable width height a Source #

transposeTransposable :: Transposable height width a -> Transposable width height a Source #

multiply :: (C height, C width, C fuse, Eq fuse, Floating a) => Matrix height fuse a -> Matrix fuse width a -> Matrix height width a Source #

>>> Matrix.multiply
      (Array.fromList (shapeInt 2, shapeInt 2) [1000,100,10,1])
      (Array.fromList (shapeInt 2, shapeInt 3) [0..5::Real_])
... [300.0,1400.0,2500.0,3.0,14.0,25.0]

forMatrix number_ $ \a ->
      Matrix.multiply (Matrix.identity (Matrix.height a)) a == a

forMatrix number_ $ \a ->
      Matrix.multiply a (Matrix.identity (Matrix.width a)) == a

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

multiplyTransposable :: (C height, C width, C fuse, Eq fuse, Floating a) => Transposable height fuse a -> Transposable fuse width a -> Matrix height width a Source #

forMatrix number_ $ \a ->
   QC.forAll (genIdentityTrans (Matrix.height a)) $ \eye ->
      a == Matrix.multiplyTransposable eye (Matrix.nonTransposed a)

forMatrix number_ $ \a ->
   QC.forAll (genIdentityTrans (Matrix.width a)) $ \eye ->
      a == Matrix.multiplyTransposable (Matrix.nonTransposed a) eye

forMatrix number_ $ \a ->
   QC.forAll (genIdentityTrans (Matrix.width a)) $ \leftEye ->
   QC.forAll (genIdentityTrans (Matrix.height a)) $ \rightEye ->
      Matrix.multiplyTransposable leftEye (Matrix.transposed a)
      ==
      Matrix.multiplyTransposable (Matrix.transposed a) rightEye

forMatrix number_ $ \a ->
   QC.forAll (QC.choose (0,maxDim)) $ \n ->
   QC.forAll (genVector (Matrix.width a, shapeInt n) number_) $ \b ->
      transpose (Matrix.multiply a b)
      ==
      Matrix.multiplyTransposable (Matrix.transposed b) (Matrix.transposed a)

kronecker :: (C heightA, C widthA, C heightB, C widthB, Floating a) => Matrix heightA widthA a -> Matrix heightB widthB a -> Matrix (heightA, heightB) (widthA, widthB) a Source #

>>> Matrix.kronecker
      (Array.fromList (shapeInt 2, shapeInt 2) [0,1,-1,0::Real_])
      (Array.fromList (shapeInt 2, shapeInt 3) [1..6])
... [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]

>>> 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])
... [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]

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_)

kroneckerTransposable :: (C heightA, C widthA, C heightB, C widthB, Floating a) => Transposable heightA widthA a -> Transposable heightB widthB a -> Transposable (heightA, heightB) (widthA, widthB) a Source #

kroneckerLeftTransposable :: (C heightA, C widthA, C heightB, C widthB, Floating a) => Transposable heightA widthA a -> Matrix heightB widthB a -> Matrix (heightA, heightB) (widthA, widthB) a Source #