Linear.Class

Description

Synopsis

• class AbelianGroup g where
  • (&+) :: g -> g -> g
  • (&-) :: g -> g -> g
  • neg :: g -> g
  • zero :: g
• vecSum :: AbelianGroup g => [g] -> g
• class MultSemiGroup r where
  • (.*.) :: r -> r -> r
  • one :: r
• class (AbelianGroup r, MultSemiGroup r) => Ring r
• semigroupProduct :: MultSemiGroup r => [r] -> r
• class LeftModule r m where
  • lmul :: r -> m -> m
  • (*.) :: r -> m -> m
• class RightModule m r | m -> r, r -> m where
  • rmul :: m -> r -> m
  • (.*) :: m -> r -> m
• class AbelianGroup (v a) => Vector a v where
  • mapVec :: (a -> a) -> v a -> v a
  • scalarMul :: a -> v a -> v a
  • (*&) :: a -> v a -> v a
  • (&*) :: v a -> a -> v a
• class Num a => DotProd a v where
  • (&.) :: v a -> v a -> a
  • dotprod :: v a -> v a -> a
  • normsqr :: v a -> a
  • lensqr :: v a -> a
• class (Floating a, DotProd a v) => Norm a v where
  • norm :: v a -> a
  • vlen :: v a -> a
• class CrossProd v where
  • crossprod :: v -> v -> v
  • (&^) :: v -> v -> v
• normalize :: (Vector a v, Norm a v) => v a -> v a
• distance :: (Vector a v, Norm a v) => v a -> v a -> a
• angle :: (Vector a v, Norm a v) => v a -> v a -> a
• angle' :: (Floating a, Vector a v, UnitVector a v u, DotProd a v) => u a -> u a -> a
• class (Vector a v, Norm a v) => UnitVector a v u | u -> v, v -> u where
  • mkNormal :: v a -> u a
  • toNormalUnsafe :: v a -> u a
  • fromNormal :: u a -> v a
  • fromNormalRadius :: a -> u a -> v a
• class Pointwise v where
  • pointwise :: v -> v -> v
  • (&!) :: v -> v -> v
• class Extend a u v where
  • extendZero :: u a -> v a
  • extendWith :: a -> u a -> v a
  • trim :: v a -> u a
• class Dimension a where
  • dim :: a -> Int
• class Transpose m n | m -> n, n -> m where
  • transpose :: m -> n
• class SquareMatrix m where
  • inverse :: m -> m
  • idmtx :: m
• class Tensor t v | t -> v where
  • outer :: v -> v -> t
• class Diagonal s t | t -> s where
  • diag :: s -> t
• class Determinant a m where
  • det :: m -> a
• class SquareMatrix (m a) => Orthogonal a m o | m -> o, o -> m where
  • fromOrtho :: o a -> m a
  • toOrthoUnsafe :: m a -> o a
• class (Vector a v, Orthogonal a n o, Diagonal (v a) (n a)) => Projective a v n o m p | m -> p, p -> m, p -> o, o -> p, p -> n, n -> p, p -> v, v -> p, n -> o, n -> v, v -> n where
  • fromProjective :: p a -> m a
  • toProjectiveUnsafe :: m a -> p a
  • orthogonal :: o a -> p a
  • linear :: n a -> p a
  • translation :: v a -> p a
  • scaling :: v a -> p a
• class (AbelianGroup m, SquareMatrix m) => MatrixNorms a m where
  • frobeniusNorm :: m -> a
  • matrixDistance :: m -> m -> a
  • operatorNorm :: m -> a
• project :: (Fractional a, Vector a v, DotProd a v) => v a -> v a -> v a
• project' :: (Vector a v, UnitVector a v u, Norm a v) => v a -> u a -> v a
• projectUnsafe :: (Vector a v, DotProd a v) => v a -> v a -> v a
• flipNormal :: UnitVector a v n => n a -> n a
• householder :: (Vector a v, UnitVector a v u, SquareMatrix (m a), Vector a m, Tensor (m a) (v a)) => u a -> m a
• householderOrtho :: (Vector a v, UnitVector a v u, SquareMatrix (m a), Vector a m, Tensor (m a) (v a), Orthogonal a m o) => u a -> o a

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