Data.Sparse.SpVector

Sparse Vector

data SpVector a

Constructors

SV

Fields

• svDim :: !Int
• svData :: !(IntM a)

Instances

Functor SpVector

Methods

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

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

Foldable SpVector

Methods

fold :: Monoid m => SpVector m -> m

foldMap :: Monoid m => (a -> m) -> SpVector a -> m

foldr :: (a -> b -> b) -> b -> SpVector a -> b

foldr' :: (a -> b -> b) -> b -> SpVector a -> b

foldl :: (b -> a -> b) -> b -> SpVector a -> b

foldl' :: (b -> a -> b) -> b -> SpVector a -> b

foldr1 :: (a -> a -> a) -> SpVector a -> a

foldl1 :: (a -> a -> a) -> SpVector a -> a

toList :: SpVector a -> [a]

null :: SpVector a -> Bool

length :: SpVector a -> Int

elem :: Eq a => a -> SpVector a -> Bool

maximum :: Ord a => SpVector a -> a

minimum :: Ord a => SpVector a -> a

sum :: Num a => SpVector a -> a

product :: Num a => SpVector a -> a

Set SpVector

Methods

liftU2 :: (a -> a -> a) -> SpVector a -> SpVector a -> SpVector a

liftI2 :: (a -> a -> b) -> SpVector a -> SpVector a -> SpVector b

FiniteDim SpVector

SpVectors form a vector space because they can be multiplied by a scalar

SpVectors are finite-dimensional vectors

Associated Types

type FDSize (SpVector :: * -> *) :: *

Methods

dim :: SpVector a -> FDSize SpVector

Elt a => SpContainer SpVector a

SpVectors are sparse containers too, i.e. any specific component may be missing (so it is assumed to be 0)

Associated Types

type ScIx (SpVector :: * -> *) :: *

Methods

scInsert :: ScIx SpVector -> a -> SpVector a -> SpVector a

scLookup :: SpVector a -> ScIx SpVector -> Maybe a

scToList :: SpVector a -> [(ScIx SpVector, a)]

(@@) :: SpVector a -> ScIx SpVector -> a

Sparse SpVector a

Methods

spy :: Fractional b => SpVector a -> b

HasData SpVector a

Associated Types

type HDData (SpVector :: * -> *) a :: *

Methods

nnz :: SpVector a -> Int

dat :: SpVector a -> HDData SpVector a

Eq a => Eq (SpVector a)

Methods

(==) :: SpVector a -> SpVector a -> Bool

(/=) :: SpVector a -> SpVector a -> Bool

Show a => Show (SpVector a)

Methods

showsPrec :: Int -> SpVector a -> ShowS

show :: SpVector a -> String

showList :: [SpVector a] -> ShowS

VectorSpace (SpVector Double)

Associated Types

type Scalar (SpVector Double) :: *

Methods

(*^) :: Scalar (SpVector Double) -> SpVector Double -> SpVector Double

VectorSpace (SpVector (Complex Double))

Associated Types

type Scalar (SpVector (Complex Double)) :: *

Methods

(*^) :: Scalar (SpVector (Complex Double)) -> SpVector (Complex Double) -> SpVector (Complex Double)

InnerSpace (SpVector Double)

Methods

(<.>) :: SpVector Double -> SpVector Double -> Scalar (SpVector Double)

InnerSpace (SpVector (Complex Double))

Methods

(<.>) :: SpVector (Complex Double) -> SpVector (Complex Double) -> Scalar (SpVector (Complex Double))

AdditiveGroup (SpVector Double)

Methods

zeroV :: SpVector Double

(^+^) :: SpVector Double -> SpVector Double -> SpVector Double

negateV :: SpVector Double -> SpVector Double

(^-^) :: SpVector Double -> SpVector Double -> SpVector Double

AdditiveGroup (SpVector (Complex Double))

Methods

zeroV :: SpVector (Complex Double)

(^+^) :: SpVector (Complex Double) -> SpVector (Complex Double) -> SpVector (Complex Double)

negateV :: SpVector (Complex Double) -> SpVector (Complex Double)

(^-^) :: SpVector (Complex Double) -> SpVector (Complex Double) -> SpVector (Complex Double)

Normed (SpVector Double)

Associated Types

type Magnitude (SpVector Double) :: *

type RealScalar (SpVector Double) :: *

Methods

norm1 :: SpVector Double -> Magnitude (SpVector Double)

norm2Sq :: SpVector Double -> Magnitude (SpVector Double)

normP :: RealScalar (SpVector Double) -> SpVector Double -> Magnitude (SpVector Double)

normalize :: RealScalar (SpVector Double) -> SpVector Double -> SpVector Double

normalize2 :: SpVector Double -> SpVector Double

normalize2' :: SpVector Double -> SpVector Double

norm2 :: SpVector Double -> Magnitude (SpVector Double)

norm2' :: SpVector Double -> Scalar (SpVector Double)

norm :: RealScalar (SpVector Double) -> SpVector Double -> Magnitude (SpVector Double)

Normed (SpVector (Complex Double))

Associated Types

type Magnitude (SpVector (Complex Double)) :: *

type RealScalar (SpVector (Complex Double)) :: *

Methods

norm1 :: SpVector (Complex Double) -> Magnitude (SpVector (Complex Double))

norm2Sq :: SpVector (Complex Double) -> Magnitude (SpVector (Complex Double))

normP :: RealScalar (SpVector (Complex Double)) -> SpVector (Complex Double) -> Magnitude (SpVector (Complex Double))

normalize :: RealScalar (SpVector (Complex Double)) -> SpVector (Complex Double) -> SpVector (Complex Double)

normalize2 :: SpVector (Complex Double) -> SpVector (Complex Double)

normalize2' :: SpVector (Complex Double) -> SpVector (Complex Double)

norm2 :: SpVector (Complex Double) -> Magnitude (SpVector (Complex Double))

norm2' :: SpVector (Complex Double) -> Scalar (SpVector (Complex Double))

norm :: RealScalar (SpVector (Complex Double)) -> SpVector (Complex Double) -> Magnitude (SpVector (Complex Double))

type ScIx SpVector

type ScIx SpVector = Int

type FDSize SpVector

type FDSize SpVector = Int

type HDData SpVector a

type HDData SpVector a

type Scalar (SpVector Double)

type Scalar (SpVector Double) = Double

type Scalar (SpVector (Complex Double))

type Scalar (SpVector (Complex Double)) = Complex Double

type MatrixType (SpVector Double)

type MatrixType (SpVector Double) = SpMatrix Double

type MatrixType (SpVector (Complex Double))

type MatrixType (SpVector (Complex Double)) = SpMatrix (Complex Double)

type Magnitude (SpVector Double)

type Magnitude (SpVector Double) = Double

type Magnitude (SpVector (Complex Double))

type Magnitude (SpVector (Complex Double)) = Double

type RealScalar (SpVector Double)

type RealScalar (SpVector Double) = Double

type RealScalar (SpVector (Complex Double))

type RealScalar (SpVector (Complex Double)) = Double

spySV :: Fractional b => SpVector a -> b

SpVector sparsity

nzSV :: SpVector a -> Int

Number of nonzeros

sizeStrSV :: SpVector a -> String

dotS :: InnerSpace (IntM t) => SpVector t -> SpVector t -> Scalar (IntM t)

dotSSafe :: (InnerSpace (IntM t), MonadThrow m) => SpVector t -> SpVector t -> m (Scalar (IntM t))

Creation

zeroSV :: Int -> SpVector a

Empty sparse vector (length n, no entries)

singletonSV :: a -> SpVector a

Singleton sparse vector (length 1)

ei :: Num a => Int -> Key -> SpVector a

Canonical basis vector in R^n

mkSpVector :: Epsilon a => Int -> IntMap a -> SpVector a

Sparse vector from an association list while discarding all zero entries

mkSpVector1 :: Int -> IntMap a -> SpVector a

mkSpVR :: Int -> [Double] -> SpVector Double

Dense real SpVector (monomorphic Double)

mkSpVC :: Int -> [Complex Double] -> SpVector (Complex Double)

Dense complex SpVector (monomorphic Double)

fromListDenseSV :: Int -> [a] -> SpVector a

Create new sparse vector, assumin 0-based, contiguous indexing

spVectorDenseIx :: Epsilon a => (Int -> a) -> UB -> [Int] -> SpVector a

Map a function over a range of indices and filter the result (indices and values) to fit in a n-long SpVector

spVectorDenseLoHi :: Epsilon a => (Int -> a) -> UB -> Int -> Int -> SpVector a

", using just the integer bounds of the interval

oneHotSVU :: Num a => Int -> IxRow -> SpVector a

one-hot encoding : `oneHotSV n k` produces a SpVector of length n having 1 at the k-th position

oneHotSV :: Num a => Int -> IxRow -> SpVector a

onesSV :: Num a => Int -> SpVector a

DENSE vector of `1`s

zerosSV :: Num a => Int -> SpVector a

DENSE vector of `0`s

Vector-related

fromVector :: Vector a -> SpVector a

Populate a SpVector with the contents of a Vector.

toVector :: SpVector a -> Vector a

Populate a Vector with the entries of a SpVector, discarding the indices (NB: loses sparsity information).

toVectorDense :: Num a => SpVector a -> Vector a

• - | Populate a Vector with the entries of a SpVector, replacing the missing entries with 0

Element insertion

insertSpVector :: Key -> a -> SpVector a -> SpVector a

insert element x at index i in a preexisting SpVector; discards out-of-bounds entries

insertSpVectorSafe :: MonadThrow m => Int -> a -> SpVector a -> m (SpVector a)

fromList

fromListSV :: Foldable t => Int -> t (Int, a) -> SpVector a

toList

toListSV :: SpVector a -> [(Key, a)]

toDenseListSV :: Num b => SpVector b -> [b]

To dense list (default = 0)

ifoldSV :: (Key -> a -> b -> b) -> b -> SpVector a -> b

Indexed fold over SpVector

Lookup

lookupSV :: Key -> SpVector a -> Maybe a

Lookup an index in a SpVector

lookupDefaultSV :: a -> Key -> SpVector a -> a

Lookup an index, return a default value if lookup fails

lookupDenseSV :: Num a => Key -> SpVector a -> a

Lookup an index in a SpVector, returns 0 if lookup fails

Sub-vectors

tailSV :: SpVector a -> SpVector a

Tail elements

headSV :: Num a => SpVector a -> a

Head element

takeSV :: Int -> SpVector a -> SpVector a

Keep the first n components of the SpVector (like take for lists)

dropSV :: Int -> SpVector a -> SpVector a

Discard the first n components of the SpVector and rebalance the keys (like drop for lists)

Keep the first n components of the SpVector (like take for lists)

rangeSV :: (Key, Key) -> SpVector a -> SpVector a

Keep a range of entries

concatSV :: SpVector a -> SpVector a -> SpVector a

Concatenate two sparse vectors

filterSV :: (a -> Bool) -> SpVector a -> SpVector a

Filter

ifilterSV :: (Int -> a -> Bool) -> SpVector a -> SpVector a

Indexed filter

Sparsify : remove almost-0 elements (|x| < eps)

sparsifySV :: Epsilon a => SpVector a -> SpVector a

Sparsify an SpVector

Orthogonal vector

orthogonalSV :: (Scalar (SpVector t) ~ t, InnerSpace (SpVector t), Fractional t) => SpVector t -> SpVector t

Generate an arbitrary (not random) vector u such that `v dot u = 0`