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Language	Haskell98

Numeric.LAPACK.Linear.LowerUpper

Synopsis

type LowerUpper vert horiz height width = Matrix (LU vert horiz height width)
type Square sh = LowerUpper Small Small sh sh
type Tall height width = LowerUpper Big Small height width
type Wide height width = LowerUpper Small Big height width
data Transposition
- = NonTransposed
- | Transposed
data Conjugation
- = NonConjugated
- | Conjugated
data Inversion
- = NonInverted
- | Inverted
mapExtent :: (C vertA, C horizA) => (C vertB, C horizB) => Map vertA horizA vertB horizB height width -> LowerUpper vertA horizA height width a -> LowerUpper vertB horizB height width a
fromMatrix :: (C vert, C horiz, C height, C width, Floating a) => Full vert horiz height width a -> LowerUpper vert horiz height width a
toMatrix :: (C vert, C horiz, C height, Eq height, C width, Eq width, Floating a) => LowerUpper vert horiz height width a -> Full vert horiz height width a
solve :: (C vert, C horiz, Eq height, C height, C width, Floating a) => Square height a -> Full vert horiz height width a -> Full vert horiz height width a
multiplyFull :: (C vert, C horiz, C height, Eq height, C width, C fuse, Eq fuse, Floating a) => LowerUpper vert horiz height fuse a -> Full vert horiz fuse width a -> Full vert horiz height width a
determinant :: (C sh, Floating a) => Square sh a -> a
extractP :: (C vert, C horiz, C height, C width) => Inversion -> LowerUpper vert horiz height width a -> Permutation height a
multiplyP :: (C vertA, C horizA, C vertB, C horizB, Eq height, C height, C widthA, C widthB, Floating a) => Inversion -> LowerUpper vertA horizA height widthA a -> Full vertB horizB height widthB a -> Full vertB horizB height widthB a
extractL :: (C vert, C horiz, C height, C width, Floating a) => LowerUpper vert horiz height width a -> Full vert horiz height width a
wideExtractL :: (C horiz, C height, C width, Floating a) => LowerUpper Small horiz height width a -> UnitLower height a
wideMultiplyL :: (C horizA, C vert, C horiz, C height, Eq height, C widthA, C widthB, Floating a) => Transposition -> LowerUpper Small horizA height widthA a -> Full vert horiz height widthB a -> Full vert horiz height widthB a
wideSolveL :: (C horizA, C vert, C horiz, C height, Eq height, C width, C nrhs, Floating a) => Transposition -> Conjugation -> LowerUpper Small horizA height width a -> Full vert horiz height nrhs a -> Full vert horiz height nrhs a
extractU :: (C vert, C horiz, C height, C width, Floating a) => LowerUpper vert horiz height width a -> Full vert horiz height width a
tallExtractU :: (C vert, C height, C width, Floating a) => LowerUpper vert Small height width a -> Upper width a
tallMultiplyU :: (C vertA, C vert, C horiz, C height, Eq height, C heightA, C widthB, Floating a) => Transposition -> LowerUpper vertA Small heightA height a -> Full vert horiz height widthB a -> Full vert horiz height widthB a
tallSolveU :: (C vertA, C vert, C horiz, C height, C width, Eq width, C nrhs, Floating a) => Transposition -> Conjugation -> LowerUpper vertA Small height width a -> Full vert horiz width nrhs a -> Full vert horiz width nrhs a
caseTallWide :: (C vert, C horiz, C height, C width) => LowerUpper vert horiz height width a -> Either (Tall height width a) (Wide height width a)

Documentation

type LowerUpper vert horiz height width = Matrix (LU vert horiz height width) Source #

type Square sh = LowerUpper Small Small sh sh Source #

type Tall height width = LowerUpper Big Small height width Source #

type Wide height width = LowerUpper Small Big height width Source #

data Transposition Source #

Constructors

NonTransposed
Transposed

Instances

Instances details

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

data Conjugation Source #

Constructors

NonConjugated
Conjugated

Instances

Instances details

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

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 #

mapExtent :: (C vertA, C horizA) => (C vertB, C horizB) => Map vertA horizA vertB horizB height width -> LowerUpper vertA horizA height width a -> LowerUpper vertB horizB height width a Source #

fromMatrix :: (C vert, C horiz, C height, C width, Floating a) => Full vert horiz height width a -> LowerUpper vert horiz height width a Source #

LowerUpper.fromMatrix a computes the LU decomposition of matrix a with row pivotisation.

You can reconstruct a from lu depending on whether a is tall or wide.

LU.multiplyP NonInverted lu $ LU.extractL lu ##*# LU.tallExtractU lu
LU.multiplyP NonInverted lu $ LU.wideExtractL lu #*## LU.extractU lu

toMatrix :: (C vert, C horiz, C height, Eq height, C width, Eq width, Floating a) => LowerUpper vert horiz height width a -> Full vert horiz height width a Source #

solve :: (C vert, C horiz, Eq height, C height, C width, Floating a) => Square height a -> Full vert horiz height width a -> Full vert horiz height width a Source #

multiplyFull :: (C vert, C horiz, C height, Eq height, C width, C fuse, Eq fuse, Floating a) => LowerUpper vert horiz height fuse a -> Full vert horiz fuse width a -> Full vert horiz height width a Source #

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

Caution: LU.determinant . LU.fromMatrix will fail for singular matrices.

extractP :: (C vert, C horiz, C height, C width) => Inversion -> LowerUpper vert horiz height width a -> Permutation height a Source #

multiplyP :: (C vertA, C horizA, C vertB, C horizB, Eq height, C height, C widthA, C widthB, Floating a) => Inversion -> LowerUpper vertA horizA height widthA a -> Full vertB horizB height widthB a -> Full vertB horizB height widthB a Source #

extractL :: (C vert, C horiz, C height, C width, Floating a) => LowerUpper vert horiz height width a -> Full vert horiz height width a Source #

wideExtractL :: (C horiz, C height, C width, Floating a) => LowerUpper Small horiz height width a -> UnitLower height a Source #

wideMultiplyL :: (C horizA, C vert, C horiz, C height, Eq height, C widthA, C widthB, Floating a) => Transposition -> LowerUpper Small horizA height widthA a -> Full vert horiz height widthB a -> Full vert horiz height widthB a Source #

wideMultiplyL transposed lu a multiplies the square part of lu containing the lower triangular matrix with a.

wideMultiplyL NonTransposed lu a == wideExtractL lu #*## a
wideMultiplyL Transposed lu a == Tri.transpose (wideExtractL lu) #*## a

wideSolveL :: (C horizA, C vert, C horiz, C height, Eq height, C width, C nrhs, Floating a) => Transposition -> Conjugation -> LowerUpper Small horizA height width a -> Full vert horiz height nrhs a -> Full vert horiz height nrhs a Source #

extractU :: (C vert, C horiz, C height, C width, Floating a) => LowerUpper vert horiz height width a -> Full vert horiz height width a Source #

tallExtractU :: (C vert, C height, C width, Floating a) => LowerUpper vert Small height width a -> Upper width a Source #

tallMultiplyU :: (C vertA, C vert, C horiz, C height, Eq height, C heightA, C widthB, Floating a) => Transposition -> LowerUpper vertA Small heightA height a -> Full vert horiz height widthB a -> Full vert horiz height widthB a Source #

tallMultiplyU transposed lu a multiplies the square part of lu containing the upper triangular matrix with a.

tallMultiplyU NonTransposed lu a == tallExtractU lu #*## a
tallMultiplyU Transposed lu a == Tri.transpose (tallExtractU lu) #*## a

tallSolveU :: (C vertA, C vert, C horiz, C height, C width, Eq width, C nrhs, Floating a) => Transposition -> Conjugation -> LowerUpper vertA Small height width a -> Full vert horiz width nrhs a -> Full vert horiz width nrhs a Source #

caseTallWide :: (C vert, C horiz, C height, C width) => LowerUpper vert horiz height width a -> Either (Tall height width a) (Wide height width a) Source #