| Safe Haskell | None |
|---|
Numeric.LAPACK.Linear.LowerUpper
- 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
- data Conjugation
- 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 shSource
type Tall height width = LowerUpper Big Small height widthSource
type Wide height width = LowerUpper Small Big height widthSource
Constructors
| 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 aSource
fromMatrix :: (C vert, C horiz, C height, C width, Floating a) => Full vert horiz height width a -> LowerUpper vert horiz height width aSource
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 aSource
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 aSource
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 aSource
determinant :: (C sh, Floating a) => Square sh a -> aSource
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 aSource
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 aSource
extractL :: (C vert, C horiz, C height, C width, Floating a) => LowerUpper vert horiz height width a -> Full vert horiz height width aSource
wideExtractL :: (C horiz, C height, C width, Floating a) => LowerUpper Small horiz height width a -> UnitLower height aSource
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 aSource
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 aSource
extractU :: (C vert, C horiz, C height, C width, Floating a) => LowerUpper vert horiz height width a -> Full vert horiz height width aSource
tallExtractU :: (C vert, C height, C width, Floating a) => LowerUpper vert Small height width a -> Upper width aSource
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 aSource
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 aSource
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