Safe Haskell	None
Language	Haskell98

Numeric.LAPACK.Permutation

Synopsis

data Permutation sh
newtype Shape sh = Shape sh
newtype Element sh = Element CInt
size :: Permutation sh -> sh
identity :: C sh => sh -> Permutation sh
data Inversion
- = NonInverted
- | Inverted
fromPivots :: C sh => Inversion -> Vector (Shape sh) (Element sh) -> Permutation sh
toPivots :: C sh => Inversion -> Permutation sh -> Vector sh (Element sh)
toMatrix :: (C sh, Floating a) => Permutation sh -> Square sh a
data Sign
- = Positive
- | Negative
determinant :: C sh => Permutation sh -> Sign
numberFromSign :: Floating a => Sign -> a
transpose :: C sh => Permutation sh -> Permutation sh
inversionFromTransposition :: Transposition -> Inversion
multiply :: (C sh, Eq sh) => Permutation sh -> Permutation sh -> Permutation sh
apply :: (C vert, C horiz, C height, Eq height, C width, Floating a) => Inversion -> Permutation height -> Full vert horiz height width a -> Full vert horiz height width a

Documentation

data Permutation sh Source #

Instances

Instances details

(C sh, Show sh) => Show (Permutation sh) Source #
Instance details Defined in Numeric.LAPACK.Permutation.Private Methods showsPrec :: Int -> Permutation sh -> ShowS # show :: Permutation sh -> String # showList :: [Permutation sh] -> ShowS #
Box (Permutation sh) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Type Associated Types type HeightOf (Permutation sh) Source # type WidthOf (Permutation sh) Source # Methods height :: Matrix (Permutation sh) a -> HeightOf (Permutation sh) Source # width :: Matrix (Permutation sh) a -> WidthOf (Permutation sh) Source #
C sh => FormatMatrix (Permutation sh) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Type Methods formatMatrix :: (Floating a, Output out) => String -> Matrix (Permutation sh) a -> out Source #
C sh => Format (Permutation sh) Source #
Instance details Defined in Numeric.LAPACK.Format Methods format :: Output out => String -> Permutation sh -> out Source #
Indexed size => Indexed (Permutation size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Indexed Methods (#!) :: Floating a => Matrix (Permutation size) a -> (Index (HeightOf (Permutation size)), Index (WidthOf (Permutation size))) -> a Source #
C sh => SquareShape (Permutation sh) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Class Methods toSquare :: (HeightOf (Permutation sh) ~ sh0, Floating a) => Matrix (Permutation sh) a -> Square sh0 a Source # identityOrder :: (HeightOf (Permutation sh) ~ sh0, Floating a) => Order -> sh0 -> Matrix (Permutation sh) a takeDiagonal :: (HeightOf (Permutation sh) ~ sh0, Floating a) => Matrix (Permutation sh) a -> Vector sh0 a Source #
C shape => Complex (Permutation shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Class Methods conjugate :: Floating a => Matrix (Permutation shape) a -> Matrix (Permutation shape) a Source # fromReal :: Floating a => Matrix (Permutation shape) (RealOf a) -> Matrix (Permutation shape) a Source # toComplex :: Floating a => Matrix (Permutation shape) a -> Matrix (Permutation shape) (ComplexOf a) Source #
C shape => Power (Permutation shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Methods square :: Floating a => Matrix (Permutation shape) a -> Matrix (Permutation shape) a Source # power :: Floating a => Int -> Matrix (Permutation shape) a -> Matrix (Permutation shape) a Source #
C shape => MultiplySquare (Permutation shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Methods transposableSquare :: (HeightOf (Permutation shape) ~ height, Eq height, C width, C vert, C horiz, Floating a) => Transposition -> Matrix (Permutation shape) a -> Full vert horiz height width a -> Full vert horiz height width a squareFull :: (HeightOf (Permutation shape) ~ height, Eq height, C width, C vert, C horiz, Floating a) => Matrix (Permutation shape) a -> Full vert horiz height width a -> Full vert horiz height width a fullSquare :: (WidthOf (Permutation shape) ~ width, Eq width, C height, C vert, C horiz, Floating a) => Full vert horiz height width a -> Matrix (Permutation shape) a -> Full vert horiz height width a
C shape => MultiplyVector (Permutation shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Methods matrixVector :: (WidthOf (Permutation shape) ~ width, Eq width, Floating a) => Matrix (Permutation shape) a -> Vector width a -> Vector (HeightOf (Permutation shape)) a vectorMatrix :: (HeightOf (Permutation shape) ~ height, Eq height, Floating a) => Vector height a -> Matrix (Permutation shape) a -> Vector (WidthOf (Permutation shape)) a
C shape => Inverse (Permutation shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Divide Methods inverse :: Floating a => Matrix (Permutation shape) a -> Matrix (Permutation shape) a Source #
C shape => Solve (Permutation shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Divide Methods solve :: (HeightOf (Permutation shape) ~ height, Eq height, C width, C vert, C horiz, Floating a) => Transposition -> Matrix (Permutation shape) a -> Full vert horiz height width a -> Full vert horiz height width a Source # solveRight :: (HeightOf (Permutation shape) ~ height, Eq height, C width, C vert, C horiz, Floating a) => Matrix (Permutation shape) a -> Full vert horiz height width a -> Full vert horiz height width a Source # solveLeft :: (WidthOf (Permutation shape) ~ width, Eq width, C height, C vert, C horiz, Floating a) => Full vert horiz height width a -> Matrix (Permutation shape) a -> Full vert horiz height width a Source #
C shape => Determinant (Permutation shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Divide Methods determinant :: Floating a => Matrix (Permutation shape) a -> a Source #
(C shapeA, Eq shapeA, shapeA ~ shapeB, C shapeB) => Multiply (Permutation shapeA) (Permutation shapeB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Permutation shapeA) (Permutation shapeB) Methods matrixMatrix :: Floating a => Matrix (Permutation shapeA) a -> Matrix (Permutation shapeB) a -> Matrix (Multiplied (Permutation shapeA) (Permutation shapeB)) a
(C sh, Show sh) => Show (Matrix (Permutation sh) a) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Type Methods showsPrec :: Int -> Matrix (Permutation sh) a -> ShowS # show :: Matrix (Permutation sh) a -> String # showList :: [Matrix (Permutation sh) a] -> ShowS #
type HeightOf (Permutation sh) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Type type HeightOf (Permutation sh) = sh
type WidthOf (Permutation sh) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Type type WidthOf (Permutation sh) = sh
newtype Matrix (Permutation sh) a Source #
Instance details Defined in Numeric.LAPACK.Matrix.Type newtype Matrix (Permutation sh) a = Permutation (Permutation sh)

newtype Shape sh Source #

Constructors

Shape sh

Instances

Instances details

Eq sh => Eq (Shape sh) Source #
Instance details Defined in Numeric.LAPACK.Permutation.Private Methods (==) :: Shape sh -> Shape sh -> Bool # (/=) :: Shape sh -> Shape sh -> Bool #
Show sh => Show (Shape sh) Source #
Instance details Defined in Numeric.LAPACK.Permutation.Private Methods showsPrec :: Int -> Shape sh -> ShowS # show :: Shape sh -> String # showList :: [Shape sh] -> ShowS #
C sh => C (Shape sh) Source #
Instance details Defined in Numeric.LAPACK.Permutation.Private Methods size :: Shape sh -> Int # uncheckedSize :: Shape sh -> Int #
C sh => Indexed (Shape sh) Source #
Instance details Defined in Numeric.LAPACK.Permutation.Private Associated Types type Index (Shape sh) # Methods indices :: Shape sh -> [Index (Shape sh)] # offset :: Shape sh -> Index (Shape sh) -> Int # uncheckedOffset :: Shape sh -> Index (Shape sh) -> Int # inBounds :: Shape sh -> Index (Shape sh) -> Bool # sizeOffset :: Shape sh -> (Int, Index (Shape sh) -> Int) # uncheckedSizeOffset :: Shape sh -> (Int, Index (Shape sh) -> Int) #
C sh => InvIndexed (Shape sh) Source #
Instance details Defined in Numeric.LAPACK.Permutation.Private Methods indexFromOffset :: Shape sh -> Int -> Index (Shape sh) # uncheckedIndexFromOffset :: Shape sh -> Int -> Index (Shape sh) #
type Index (Shape sh) Source #
Instance details Defined in Numeric.LAPACK.Permutation.Private type Index (Shape sh) = Element sh

newtype Element sh Source #

Constructors

Element CInt

Instances

Instances details

Eq (Element sh) Source #
Instance details Defined in Numeric.LAPACK.Permutation.Private Methods (==) :: Element sh -> Element sh -> Bool # (/=) :: Element sh -> Element sh -> Bool #
Show (Element sh) Source #
Instance details Defined in Numeric.LAPACK.Permutation.Private Methods showsPrec :: Int -> Element sh -> ShowS # show :: Element sh -> String # showList :: [Element sh] -> ShowS #
Storable (Element sh) Source #
Instance details Defined in Numeric.LAPACK.Permutation.Private Methods sizeOf :: Element sh -> Int # alignment :: Element sh -> Int # peekElemOff :: Ptr (Element sh) -> Int -> IO (Element sh) # pokeElemOff :: Ptr (Element sh) -> Int -> Element sh -> IO () # peekByteOff :: Ptr b -> Int -> IO (Element sh) # pokeByteOff :: Ptr b -> Int -> Element sh -> IO () # peek :: Ptr (Element sh) -> IO (Element sh) # poke :: Ptr (Element sh) -> Element sh -> IO () #

size :: Permutation sh -> sh Source #

identity :: C sh => sh -> Permutation sh Source #

data Inversion Source #

Constructors

NonInverted
Inverted

Instances

Instances details

Bounded Inversion Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods minBound :: Inversion # maxBound :: Inversion #
Enum Inversion Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods succ :: Inversion -> Inversion # pred :: Inversion -> Inversion # toEnum :: Int -> Inversion # fromEnum :: Inversion -> Int # enumFrom :: Inversion -> [Inversion] # enumFromThen :: Inversion -> Inversion -> [Inversion] # enumFromTo :: Inversion -> Inversion -> [Inversion] # enumFromThenTo :: Inversion -> Inversion -> Inversion -> [Inversion] #
Eq Inversion Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods (==) :: Inversion -> Inversion -> Bool # (/=) :: Inversion -> Inversion -> Bool #
Show Inversion Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods showsPrec :: Int -> Inversion -> ShowS # show :: Inversion -> String # showList :: [Inversion] -> ShowS #
Semigroup Inversion Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods (<>) :: Inversion -> Inversion -> Inversion # sconcat :: NonEmpty Inversion -> Inversion # stimes :: Integral b => b -> Inversion -> Inversion #
Monoid Inversion Source #
Instance details Defined in Numeric.LAPACK.Matrix.Modifier Methods mempty :: Inversion # mappend :: Inversion -> Inversion -> Inversion # mconcat :: [Inversion] -> Inversion #

fromPivots :: C sh => Inversion -> Vector (Shape sh) (Element sh) -> Permutation sh Source #

QC.forAll QC.arbitraryBoundedEnum $ \inv -> QC.forAll (QC.arbitrary >>= genPivots) $ \xs -> Array.toList xs == Array.toList (Perm.toPivots inv (Perm.fromPivots inv xs))

toPivots :: C sh => Inversion -> Permutation sh -> Vector sh (Element sh) Source #

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

data Sign Source #

Constructors

Positive
Negative

Instances

Instances details

Bounded Sign Source #
Instance details Defined in Numeric.LAPACK.Permutation.Private Methods minBound :: Sign # maxBound :: Sign #
Enum Sign Source #
Instance details Defined in Numeric.LAPACK.Permutation.Private Methods succ :: Sign -> Sign # pred :: Sign -> Sign # toEnum :: Int -> Sign # fromEnum :: Sign -> Int # enumFrom :: Sign -> [Sign] # enumFromThen :: Sign -> Sign -> [Sign] # enumFromTo :: Sign -> Sign -> [Sign] # enumFromThenTo :: Sign -> Sign -> Sign -> [Sign] #
Eq Sign Source #
Instance details Defined in Numeric.LAPACK.Permutation.Private Methods (==) :: Sign -> Sign -> Bool # (/=) :: Sign -> Sign -> Bool #
Show Sign Source #
Instance details Defined in Numeric.LAPACK.Permutation.Private Methods showsPrec :: Int -> Sign -> ShowS # show :: Sign -> String # showList :: [Sign] -> ShowS #
Semigroup Sign Source #
Instance details Defined in Numeric.LAPACK.Permutation.Private Methods (<>) :: Sign -> Sign -> Sign # sconcat :: NonEmpty Sign -> Sign # stimes :: Integral b => b -> Sign -> Sign #
Monoid Sign Source #
Instance details Defined in Numeric.LAPACK.Permutation.Private Methods mempty :: Sign # mappend :: Sign -> Sign -> Sign # mconcat :: [Sign] -> Sign #

determinant :: C sh => Permutation sh -> Sign Source #

QC.forAll genPerm2 $ \(p0,p1) -> determinant (multiply p0 p1) == determinant p0 <> determinant p1

numberFromSign :: Floating a => Sign -> a Source #

numberFromSign s == (-1)^fromEnum s

transpose :: C sh => Permutation sh -> Permutation sh Source #

QC.forAll genPerm2 $ \(p0,p1) -> equating (Array.toList . Perm.toPivots NonInverted) (transpose $ multiply p0 p1) (multiply (transpose p1) (transpose p0))

inversionFromTransposition :: Transposition -> Inversion Source #

multiply :: (C sh, Eq sh) => Permutation sh -> Permutation sh -> Permutation sh Source #

apply :: (C vert, C horiz, C height, Eq height, C width, Floating a) => Inversion -> Permutation height -> Full vert horiz height width a -> Full vert horiz height width a Source #