Numeric.Dimensions.Idx

Provides a data type Idx to index Dim and Idxs that enumerates through multiple dimensions.

Higher indices go first, i.e. assumed enumeration is i = i1*n1*n2*...*n(k-1) + ... + i(k-2)*n1*n2 + i(k-1)*n1 + ik This corresponds to row-first layout of matrices and multidimenional arrays.

Data types

data Idx (n :: k) where

This type is used to index a single dimension; the range of indices is from 0 to n-1.

Bundled Patterns

pattern Idx :: forall (k :: Type) (n :: k). BoundedDim n => Word -> Idx n

Convert between Word and Idx.

If the word is outside of the bounds, fails with an error (unless unsafeindices flag is turned on).

Instances

BoundedDims ds => Bounded (Idxs ds)

Defined in Numeric.Dimensions.Idx

Methods

minBound :: Idxs ds

maxBound :: Idxs ds

BoundedDim n => Bounded (Idx n)

Defined in Numeric.Dimensions.Idx

Methods

minBound :: Idx n

maxBound :: Idx n

Dimensions ds => Enum (Idxs ds)

Defined in Numeric.Dimensions.Idx

Methods

succ :: Idxs ds -> Idxs ds

pred :: Idxs ds -> Idxs ds

toEnum :: Int -> Idxs ds

fromEnum :: Idxs ds -> Int

enumFrom :: Idxs ds -> [Idxs ds]

enumFromThen :: Idxs ds -> Idxs ds -> [Idxs ds]

enumFromTo :: Idxs ds -> Idxs ds -> [Idxs ds]

enumFromThenTo :: Idxs ds -> Idxs ds -> Idxs ds -> [Idxs ds]

BoundedDim n => Enum (Idx n)

Defined in Numeric.Dimensions.Idx

Methods

succ :: Idx n -> Idx n

pred :: Idx n -> Idx n

toEnum :: Int -> Idx n

fromEnum :: Idx n -> Int

enumFrom :: Idx n -> [Idx n]

enumFromThen :: Idx n -> Idx n -> [Idx n]

enumFromTo :: Idx n -> Idx n -> [Idx n]

enumFromThenTo :: Idx n -> Idx n -> Idx n -> [Idx n]

Eq (Idxs xs)

Defined in Numeric.Dimensions.Idx

Methods

(==) :: Idxs xs -> Idxs xs -> Bool

(/=) :: Idxs xs -> Idxs xs -> Bool

Eq (Idx n)

Defined in Numeric.Dimensions.Idx

Methods

(==) :: Idx n -> Idx n -> Bool

(/=) :: Idx n -> Idx n -> Bool

BoundedDim n => Integral (Idx n)

Defined in Numeric.Dimensions.Idx

Methods

quot :: Idx n -> Idx n -> Idx n

rem :: Idx n -> Idx n -> Idx n

div :: Idx n -> Idx n -> Idx n

mod :: Idx n -> Idx n -> Idx n

quotRem :: Idx n -> Idx n -> (Idx n, Idx n)

divMod :: Idx n -> Idx n -> (Idx n, Idx n)

toInteger :: Idx n -> Integer

(Typeable n, Typeable k) => Data (Idx n)

Defined in Numeric.Dimensions.Idx

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Idx n -> c (Idx n)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Idx n)

toConstr :: Idx n -> Constr

dataTypeOf :: Idx n -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Idx n))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Idx n))

gmapT :: (forall b. Data b => b -> b) -> Idx n -> Idx n

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Idx n -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Idx n -> r

gmapQ :: (forall d. Data d => d -> u) -> Idx n -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Idx n -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Idx n -> m (Idx n)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Idx n -> m (Idx n)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Idx n -> m (Idx n)

BoundedDim n => Num (Idxs (n ': ([] :: [k])))

With this instance we can slightly reduce indexing expressions, e.g.

x ! (1 :* 2 :* 4) == x ! (1 :* 2 :* 4 :* U)

Defined in Numeric.Dimensions.Idx

Methods

(+) :: Idxs (n ': []) -> Idxs (n ': []) -> Idxs (n ': [])

(-) :: Idxs (n ': []) -> Idxs (n ': []) -> Idxs (n ': [])

(*) :: Idxs (n ': []) -> Idxs (n ': []) -> Idxs (n ': [])

negate :: Idxs (n ': []) -> Idxs (n ': [])

abs :: Idxs (n ': []) -> Idxs (n ': [])

signum :: Idxs (n ': []) -> Idxs (n ': [])

fromInteger :: Integer -> Idxs (n ': [])

BoundedDim n => Num (Idx n)

Defined in Numeric.Dimensions.Idx

Methods

(+) :: Idx n -> Idx n -> Idx n

(-) :: Idx n -> Idx n -> Idx n

(*) :: Idx n -> Idx n -> Idx n

negate :: Idx n -> Idx n

abs :: Idx n -> Idx n

signum :: Idx n -> Idx n

fromInteger :: Integer -> Idx n

Ord (Idxs xs)

Compare indices by their importance in lexicorgaphic order from the first dimension to the last dimension (the first dimension is the most significant one).

Literally,

compare a b = compare (listIdxs a) (listIdxs b)

This is the same compare rule, as for Dims. This is also consistent with offsets:

sort == sortOn fromEnum

Defined in Numeric.Dimensions.Idx

Methods

compare :: Idxs xs -> Idxs xs -> Ordering

(<) :: Idxs xs -> Idxs xs -> Bool

(<=) :: Idxs xs -> Idxs xs -> Bool

(>) :: Idxs xs -> Idxs xs -> Bool

(>=) :: Idxs xs -> Idxs xs -> Bool

max :: Idxs xs -> Idxs xs -> Idxs xs

min :: Idxs xs -> Idxs xs -> Idxs xs

Ord (Idx n)

Defined in Numeric.Dimensions.Idx

Methods

compare :: Idx n -> Idx n -> Ordering

(<) :: Idx n -> Idx n -> Bool

(<=) :: Idx n -> Idx n -> Bool

(>) :: Idx n -> Idx n -> Bool

(>=) :: Idx n -> Idx n -> Bool

max :: Idx n -> Idx n -> Idx n

min :: Idx n -> Idx n -> Idx n

BoundedDims xs => Read (Idxs xs)

Defined in Numeric.Dimensions.Idx

Methods

readsPrec :: Int -> ReadS (Idxs xs)

readList :: ReadS [Idxs xs]

readPrec :: ReadPrec (Idxs xs)

readListPrec :: ReadPrec [Idxs xs]

BoundedDim x => Read (Idx x)

Defined in Numeric.Dimensions.Idx

Methods

readsPrec :: Int -> ReadS (Idx x)

readList :: ReadS [Idx x]

readPrec :: ReadPrec (Idx x)

readListPrec :: ReadPrec [Idx x]

BoundedDim n => Real (Idx n)

Defined in Numeric.Dimensions.Idx

Methods

toRational :: Idx n -> Rational

Show (Idxs xs)

Defined in Numeric.Dimensions.Idx

Methods

showsPrec :: Int -> Idxs xs -> ShowS

show :: Idxs xs -> String

showList :: [Idxs xs] -> ShowS

Show (Idx x)

Defined in Numeric.Dimensions.Idx

Methods

showsPrec :: Int -> Idx x -> ShowS

show :: Idx x -> String

showList :: [Idx x] -> ShowS

Generic (Idx n)

Defined in Numeric.Dimensions.Idx

Associated Types

type Rep (Idx n) :: Type -> Type

Methods

from :: Idx n -> Rep (Idx n) x

to :: Rep (Idx n) x -> Idx n

Storable (Idx n)

Defined in Numeric.Dimensions.Idx

Methods

sizeOf :: Idx n -> Int

alignment :: Idx n -> Int

peekElemOff :: Ptr (Idx n) -> Int -> IO (Idx n)

pokeElemOff :: Ptr (Idx n) -> Int -> Idx n -> IO ()

peekByteOff :: Ptr b -> Int -> IO (Idx n)

pokeByteOff :: Ptr b -> Int -> Idx n -> IO ()

peek :: Ptr (Idx n) -> IO (Idx n)

poke :: Ptr (Idx n) -> Idx n -> IO ()

type Rep (Idx n)

Defined in Numeric.Dimensions.Idx

type Rep (Idx n) = D1 (MetaData "Idx" "Numeric.Dimensions.Idx" "dimensions-2.0.0.0-E3TodFh6CxsCRM2bfCokxE" True) (C1 (MetaCons "Idx'" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Word)))

type Idxs (xs :: [k]) = TypedList Idx xs

Type-level dimensional indexing with arbitrary Word values inside. Most of the operations on it require Dimensions constraint, because the Idxs itself does not store info about dimension bounds.

idxFromWord :: forall (k :: Type) (d :: k). BoundedDim d => Word -> Maybe (Idx d)

Convert an arbitrary Word to Idx.

unsafeIdxFromWord :: forall (k :: Type) (d :: k). BoundedDim d => Word -> Idx d

Convert an arbitrary Word to Idx.

If the word is outside of the bounds, fails with an error (unless unsafeindices flag is turned on).

idxToWord :: forall (k :: Type) (d :: k). Idx d -> Word

Get the value of an Idx.

listIdxs :: forall (k :: Type) (xs :: [k]). Idxs xs -> [Word]

idxsFromWords :: forall (k :: Type) (xs :: [k]). BoundedDims xs => [Word] -> Maybe (Idxs xs)