SubHask.Algebra.Vector

Dense vectors and linear algebra operations.

NOTE: This module is a prototype for what a more fully featured linear algebra module might look like. There are a number of efficiency related features that are missing. In particular, matrices will get copied more often than they need to, and only the most naive dense matrix format is currently supported. These limitations are due to using "hmatrix" as a backend (all operations should be at least as fast as in hmatrix). Future iterations will use something like "hblas" to get finer lever control.

FIXME: Shouldn't expose the constructors, but they're needed for the SubHask.Algebra.Array types.

FIXME: We shouldn't need to call out to the FFI in order to get SIMD instructions.

Documentation

data family SVector n r

The type of dynamic or statically sized vectors implemented using the FFI.

Instances

MatrixField r => Normed ((+>) (SVector k m r) (SVector k n r))

(Show r, ValidSVector Nat n r, KnownNat n) => Show (SVector Nat n r)

(Show r, Monoid r, ValidSVector Symbol n r) => Show (SVector Symbol n r)

(KnownNat n, Arbitrary r, ValidSVector Nat n r, FreeModule r, IsScalar r) => Arbitrary (SVector Nat n r)

(Arbitrary r, ValidSVector Symbol n r, FreeModule r, IsScalar r) => Arbitrary (SVector Symbol n r)

(FromField r, ValidSVector Symbol n r, IsScalar r, FreeModule r) => FromRecord (SVector Symbol n r)

(NFData r, ValidSVector Nat n r) => NFData (SVector Nat n r)

(NFData r, ValidSVector Symbol n r) => NFData (SVector Symbol n r)

(KnownNat n, ValidSVector Nat n r) => IsMutable (SVector Nat n r)

ValidSVector Symbol n r => IsMutable (SVector Symbol n r)

(KnownNat n, Monoid r, ValidLogic r, ValidSVector Nat n r, IsScalar r, FreeModule r) => IxContainer (SVector Nat n r)

(Monoid r, ValidLogic r, ValidSVector Symbol n r, IsScalar r, FreeModule r) => IxContainer (SVector Symbol n r)

(KnownNat n, ValidSVector Nat n r, ExpField r, Normed r, Ord_ r, (~) * (Logic r) Bool, IsScalar r, VectorSpace r, ValidSVector Symbol "dyn" r) => Metric (SVector Nat n r)

(ValidSVector Symbol n r, ExpField r, Normed r, Ord_ r, (~) * (Logic r) Bool, IsScalar r, VectorSpace r) => Metric (SVector Symbol n r)

(FiniteModule (SVector k n r), VectorSpace (SVector k n r), MatrixField r, ToFromVector (SVector k n r)) => TensorAlgebra (SVector k n r)

(KnownNat n, VectorSpace r, ValidSVector Nat n r, IsScalar r, ExpField r, Real r, OrdField r, MatrixField r, ValidSVector Nat n r, ValidSVector Symbol "dyn" r) => Hilbert (SVector Nat n r)

(VectorSpace r, ValidSVector Symbol n r, IsScalar r, ExpField r, Real r, OrdField r, MatrixField r) => Hilbert (SVector Symbol n r)

(KnownNat n, VectorSpace r, ValidSVector Nat n r, IsScalar r, ExpField r, Real r, ValidSVector Nat n r, ValidSVector Symbol "dyn" r) => Banach (SVector Nat n r)

(VectorSpace r, ValidSVector Symbol n r, IsScalar r, ExpField r, Real r) => Banach (SVector Symbol n r)

(KnownNat n, VectorSpace r, ValidSVector Nat n r, IsScalar r) => VectorSpace (SVector Nat n r)

(VectorSpace r, ValidSVector Symbol n r, IsScalar r) => VectorSpace (SVector Symbol n r)

(KnownNat n, FreeModule r, ValidLogic r, ValidSVector Nat n r, IsScalar r) => FiniteModule (SVector Nat n r)

(FreeModule r, ValidLogic r, ValidSVector Symbol n r, IsScalar r) => FiniteModule (SVector Symbol n r)

(KnownNat n, FreeModule r, ValidSVector Nat n r, IsScalar r) => FreeModule (SVector Nat n r)

(FreeModule r, ValidSVector Symbol n r, IsScalar r) => FreeModule (SVector Symbol n r)

(KnownNat n, Module r, ValidSVector Nat n r, IsScalar r) => Module (SVector Nat n r)

(Module r, ValidSVector Symbol n r, IsScalar r) => Module (SVector Symbol n r)

(KnownNat n, VectorSpace r, ValidSVector Nat n r, IsScalar r, ExpField r) => Normed (SVector Nat n r)

(VectorSpace r, ValidSVector Symbol n r, IsScalar r, ExpField r) => Normed (SVector Symbol n r)

(KnownNat n, Abelian r, ValidSVector Nat n r) => Abelian (SVector Nat n r)

(Monoid r, Abelian r, ValidSVector Symbol n r) => Abelian (SVector Symbol n r)

(KnownNat n, Group r, ValidSVector Nat n r) => Group (SVector Nat n r)

(Group r, ValidSVector Symbol n r) => Group (SVector Symbol n r)

(KnownNat n, Cancellative r, ValidSVector Nat n r) => Cancellative (SVector Nat n r)

(Monoid r, Cancellative r, ValidSVector Symbol n r) => Cancellative (SVector Symbol n r)

(KnownNat n, Monoid r, ValidSVector Nat n r) => Monoid (SVector Nat n r)

(Monoid r, ValidSVector Symbol n r) => Monoid (SVector Symbol n r)

(KnownNat n, Semigroup r, ValidSVector Nat n r) => Semigroup (SVector Nat n r)

(Monoid r, ValidSVector Symbol n r) => Semigroup (SVector Symbol n r)

(KnownNat n, Eq_ r, ValidLogic r, ValidSVector Nat n r) => Eq_ (SVector Nat n r)

(Eq r, Monoid r, ValidSVector Symbol n r) => Eq_ (SVector Symbol n r)

data SVector Nat = SVector_Nat (ForeignPtr r)

data SVector Symbol = SVector_Dynamic !(ForeignPtr r) !Int !Int

type (><) * * (SVector k m a) b

data Mutable m (SVector Nat n r) = Mutable_SVector_Nat (ForeignPtr r)

data Mutable m (SVector Symbol n r) = Mutable_SVector (PrimRef m (SVector Symbol n r))

type Index (SVector k n r) = Int

type Elem (SVector k n r) = Scalar r

type Scalar (SVector k n r) = Scalar r

type Logic (SVector k n r) = Logic r

type ValidElem (SVector Nat n r) e

type ValidElem (SVector Symbol n r) e

type SetElem (SVector k n r) b = SVector k n b

data family UVector n r

The type of dynamic or statically sized vectors implemented using the FFI.

Instances

(ClassicalLogic r, Eq_ r, Unbox r, Prim r, FreeModule r, IsScalar r, Prim y, Unbox y) => Constructible (UArray (Labeled' (UVector Symbol s r) y))

(ClassicalLogic r, Eq_ r, Unbox r, Prim r, FreeModule r, IsScalar r) => Constructible (UArray (UVector Symbol s r))

(ClassicalLogic r, Eq_ r, Unbox r, Prim r, FreeModule r, IsScalar r, Prim y, Unbox y) => Monoid (UArray (Labeled' (UVector Symbol s r) y))

(ClassicalLogic r, Eq_ r, Unbox r, Prim r, FreeModule r, IsScalar r) => Monoid (UArray (UVector Symbol s r))

(Show r, Monoid r, Prim r) => Show (UVector Symbol n r)

(Arbitrary r, Prim r, FreeModule r, IsScalar r) => Arbitrary (UVector Symbol n r)

(FromField r, Prim r, IsScalar r, FreeModule r) => FromRecord (UVector Symbol n r)

(NFData r, Prim r) => NFData (UVector Symbol n r)

Prim r => IsMutable (UVector Symbol n r)

(Monoid r, ValidLogic r, Prim r, IsScalar r) => IxContainer (UVector Symbol n r)

(Prim r, ExpField r, Normed r, Ord_ r, (~) * (Logic r) Bool, IsScalar r, VectorSpace r) => Metric (UVector Symbol n r)

(VectorSpace r, Prim r) => VectorSpace (UVector Symbol n r)

(FreeModule r, ValidLogic r, Prim r, IsScalar r) => FiniteModule (UVector Symbol n r)

(FreeModule r, Prim r) => FreeModule (UVector Symbol n r)

(Module r, Prim r) => Module (UVector Symbol n r)

(VectorSpace r, Prim r, IsScalar r, ExpField r) => Normed (UVector Symbol n r)

(Monoid r, Abelian r, Prim r) => Abelian (UVector Symbol n r)

(Group r, Prim r) => Group (UVector Symbol n r)

(Monoid r, Cancellative r, Prim r) => Cancellative (UVector Symbol n r)

(Monoid r, Prim r) => Monoid (UVector Symbol n r)

(Monoid r, Prim r) => Semigroup (UVector Symbol n r)

(Eq r, Monoid r, Prim r) => Eq_ (UVector Symbol n r)

data UVector Symbol = UVector_Dynamic !ByteArray !Int !Int

type (><) * k (UVector k1 n r) a = UVector k1 n ((><) * k r a)

data MVector s (Labeled' (UVector Symbol n elem) y) = UArray_Labeled'_MUVector !(MutableByteArray s) !Int !Int !Int

data MVector s (UVector Symbol n elem) = UArray_MUVector !(MutableByteArray s) !Int !Int !Int

data Mutable m (UVector Symbol n r) = Mutable_UVector (PrimRef m (UVector Symbol n r))

data Vector (Labeled' (UVector Symbol n elem) y) = UArray_Labeled'_UVector !ByteArray !Int !Int !Int

data Vector (UVector Symbol n elem) = UArray_UVector !ByteArray !Int !Int !Int

type Index (UVector k n r) = Int

type Elem (UVector k n r) = Scalar r

type Scalar (UVector k n r) = Scalar r

type Logic (UVector k n r) = Logic r

type ValidElem (UVector Symbol n r) e = ()

type SetElem (UVector k n r) b = UVector k n b

type Unbox = Unbox

data a +> b

Instances

Dagger * (+>)

Groupoid * (+>)

Category * (+>)

(MatrixField (Scalar b), Show (Scalar b)) => Show ((+>) a b)

IsMutable ((+>) a b)

(VectorSpace a, VectorSpace b) => VectorSpace ((+>) a b)

(VectorSpace a, VectorSpace b) => FreeModule ((+>) a b)

(VectorSpace a, VectorSpace b) => Module ((+>) a b)

MatrixField r => Normed ((+>) (SVector k m r) (SVector k n r))

VectorSpace a => Field ((+>) a a)

VectorSpace a => Ring ((+>) a a)

VectorSpace a => Rig ((+>) a a)

VectorSpace a => Rg ((+>) a a)

Abelian ((+>) a b)

(VectorSpace a, VectorSpace b) => Group ((+>) a b)

(VectorSpace a, VectorSpace b) => Cancellative ((+>) a b)

(VectorSpace a, VectorSpace b) => Monoid ((+>) a b)

Semigroup ((+>) a b)

(<:) (* -> * -> *) (+>) (->)

Sup (* -> * -> *) (->) (+>) (->)

Sup (* -> * -> *) (+>) (->) (->)

type ValidCategory * (+>) a

type (><) * k ((+>) a b) c

data Mutable m ((+>) a0 b0) = Mutable_AppT__AppT__ConT_SubHask_Algebra_Vector______VarT_a_1627750060____VarT_b_1627750061_ (PrimRef m ((+>) a b))

type Scalar ((+>) a b) = Scalar b

type Logic ((+>) a b) = Bool

type SMatrix r m n = SVector m r +> SVector n r

A slightly more convenient type for linear functions between SVectors

unsafeMkSMatrix :: (VectorSpace (SVector m r), VectorSpace (SVector n r), ToFromVector (SVector m r), ToFromVector (SVector n r), MatrixField r) => Int -> Int -> [r] -> SMatrix r m n

Construct an SMatrix

FFI

distance_l2_m128 :: Ptr Float -> Ptr Float -> Int -> IO Float

distance_l2_m128_SVector_Dynamic :: SVector (s :: Symbol) Float -> SVector (s :: Symbol) Float -> Float

distance_l2_m128_UVector_Dynamic :: UVector (s :: Symbol) Float -> UVector (s :: Symbol) Float -> Float

distanceUB_l2_m128 :: Ptr Float -> Ptr Float -> Int -> Float -> IO Float

distanceUB_l2_m128_SVector_Dynamic :: SVector (s :: Symbol) Float -> SVector (s :: Symbol) Float -> Float -> Float

distanceUB_l2_m128_UVector_Dynamic :: UVector (s :: Symbol) Float -> UVector (s :: Symbol) Float -> Float -> Float

Debug

safeNewByteArray :: PrimMonad m => Int -> Int -> m (MutableByteArray (PrimState m))