Numeric.LAPACK.Permutation

Documentation

data Permutation sh

Instances

(C sh, Eq sh) => Eq (Permutation sh)

Defined in Numeric.LAPACK.Permutation.Private

Methods

(==) :: Permutation sh -> Permutation sh -> Bool

(/=) :: Permutation sh -> Permutation sh -> Bool

(C sh, Show sh) => Show (Permutation sh)

Defined in Numeric.LAPACK.Permutation.Private

Methods

showsPrec :: Int -> Permutation sh -> ShowS

show :: Permutation sh -> String

showList :: [Permutation sh] -> ShowS

C sh => Format (Permutation sh)

Defined in Numeric.LAPACK.Format

Methods

format :: Output out => Config -> Permutation sh -> out

newtype Shape sh

Constructors

Shape sh

Instances

Functor Shape

Defined in Numeric.LAPACK.Permutation.Private

Methods

fmap :: (a -> b) -> Shape a -> Shape b

(<$) :: a -> Shape b -> Shape a

Eq sh => Eq (Shape sh)

Defined in Numeric.LAPACK.Permutation.Private

Methods

(==) :: Shape sh -> Shape sh -> Bool

(/=) :: Shape sh -> Shape sh -> Bool

Show sh => Show (Shape sh)

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)

Defined in Numeric.LAPACK.Permutation.Private

Methods

size :: Shape sh -> Int

C sh => Indexed (Shape sh)

Defined in Numeric.LAPACK.Permutation.Private

Associated Types

type Index (Shape sh) :: Type

Methods

indices :: Shape sh -> [Index (Shape sh)]

offset :: Shape sh -> Index (Shape sh) -> Int

uncheckedOffset :: Shape sh -> Index (Shape sh) -> Int

unifiedOffset :: Checking check => Shape sh -> Index (Shape sh) -> Result check Int

inBounds :: Shape sh -> Index (Shape sh) -> Bool

sizeOffset :: Shape sh -> (Int, Index (Shape sh) -> Int)

uncheckedSizeOffset :: Shape sh -> (Int, Index (Shape sh) -> Int)

unifiedSizeOffset :: Checking check => Shape sh -> (Int, Index (Shape sh) -> Result check Int)

C sh => InvIndexed (Shape sh)

Defined in Numeric.LAPACK.Permutation.Private

Methods

indexFromOffset :: Shape sh -> Int -> Index (Shape sh)

uncheckedIndexFromOffset :: Shape sh -> Int -> Index (Shape sh)

unifiedIndexFromOffset :: Checking check => Shape sh -> Int -> Result check (Index (Shape sh))

type Index (Shape sh)

Defined in Numeric.LAPACK.Permutation.Private

type Index (Shape sh) = Element sh

newtype Element sh

Constructors

Element CInt

Instances

Eq (Element sh)

Defined in Numeric.LAPACK.Permutation.Private

Methods

(==) :: Element sh -> Element sh -> Bool

(/=) :: Element sh -> Element sh -> Bool

Show (Element sh)

Defined in Numeric.LAPACK.Permutation.Private

Methods

showsPrec :: Int -> Element sh -> ShowS

show :: Element sh -> String

showList :: [Element sh] -> ShowS

Storable (Element sh)

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

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

data Inversion

Constructors

NonInverted

Inverted

Instances

Bounded Inversion

Defined in Numeric.LAPACK.Matrix.Modifier

Methods

minBound :: Inversion

maxBound :: Inversion

Enum Inversion

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

Defined in Numeric.LAPACK.Matrix.Modifier

Methods

(==) :: Inversion -> Inversion -> Bool

(/=) :: Inversion -> Inversion -> Bool

Show Inversion

Defined in Numeric.LAPACK.Matrix.Modifier

Methods

showsPrec :: Int -> Inversion -> ShowS

show :: Inversion -> String

showList :: [Inversion] -> ShowS

Semigroup Inversion

Defined in Numeric.LAPACK.Matrix.Modifier

Methods

(<>) :: Inversion -> Inversion -> Inversion

sconcat :: NonEmpty Inversion -> Inversion

stimes :: Integral b => b -> Inversion -> Inversion

Monoid Inversion

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

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

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

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

data Sign

Constructors

Positive

Negative

Instances

Bounded Sign

Defined in Numeric.LAPACK.Permutation.Private

Methods

minBound :: Sign

maxBound :: Sign

Enum Sign

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

Defined in Numeric.LAPACK.Permutation.Private

Methods

(==) :: Sign -> Sign -> Bool

(/=) :: Sign -> Sign -> Bool

Show Sign

Defined in Numeric.LAPACK.Permutation.Private

Methods

showsPrec :: Int -> Sign -> ShowS

show :: Sign -> String

showList :: [Sign] -> ShowS

Semigroup Sign

Defined in Numeric.LAPACK.Permutation.Private

Methods

(<>) :: Sign -> Sign -> Sign

sconcat :: NonEmpty Sign -> Sign

stimes :: Integral b => b -> Sign -> Sign

Monoid Sign

Defined in Numeric.LAPACK.Permutation.Private

Methods

mempty :: Sign

mappend :: Sign -> Sign -> Sign

mconcat :: [Sign] -> Sign

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

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

numberFromSign :: Floating a => Sign -> a

numberFromSign s == (-1)^fromEnum s

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

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

inversionFromTransposition :: Transposition -> Inversion

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

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