Cybus.FinMat

core type

data FinMat ns

definition of the indices of a matrix

Instances

NS ns => Bounded (FinMat ns)

Defined in Cybus.FinMat

Methods

minBound :: FinMat ns

maxBound :: FinMat ns

NS ns => Enum (FinMat ns)

Defined in Cybus.FinMat

Methods

succ :: FinMat ns -> FinMat ns

pred :: FinMat ns -> FinMat ns

toEnum :: Int -> FinMat ns

fromEnum :: FinMat ns -> Int

enumFrom :: FinMat ns -> [FinMat ns]

enumFromThen :: FinMat ns -> FinMat ns -> [FinMat ns]

enumFromTo :: FinMat ns -> FinMat ns -> [FinMat ns]

enumFromThenTo :: FinMat ns -> FinMat ns -> FinMat ns -> [FinMat ns]

Eq (FinMat ns)

Defined in Cybus.FinMat

Methods

(==) :: FinMat ns -> FinMat ns -> Bool

(/=) :: FinMat ns -> FinMat ns -> Bool

NS ns => Num (FinMat ns)

Defined in Cybus.FinMat

Methods

(+) :: FinMat ns -> FinMat ns -> FinMat ns

(-) :: FinMat ns -> FinMat ns -> FinMat ns

(*) :: FinMat ns -> FinMat ns -> FinMat ns

negate :: FinMat ns -> FinMat ns

abs :: FinMat ns -> FinMat ns

signum :: FinMat ns -> FinMat ns

fromInteger :: Integer -> FinMat ns

Ord (FinMat ns)

Defined in Cybus.FinMat

Methods

compare :: FinMat ns -> FinMat ns -> Ordering

(<) :: FinMat ns -> FinMat ns -> Bool

(<=) :: FinMat ns -> FinMat ns -> Bool

(>) :: FinMat ns -> FinMat ns -> Bool

(>=) :: FinMat ns -> FinMat ns -> Bool

max :: FinMat ns -> FinMat ns -> FinMat ns

min :: FinMat ns -> FinMat ns -> FinMat ns

NS ns => Read (FinMat ns)

Defined in Cybus.FinMat

Methods

readsPrec :: Int -> ReadS (FinMat ns)

readList :: ReadS [FinMat ns]

readPrec :: ReadPrec (FinMat ns)

readListPrec :: ReadPrec [FinMat ns]

Show (FinMat ns)

Defined in Cybus.FinMat

Methods

showsPrec :: Int -> FinMat ns -> ShowS

show :: FinMat ns -> String

showList :: [FinMat ns] -> ShowS

Generic (FinMat ns)

Defined in Cybus.FinMat

Associated Types

type Rep (FinMat ns) :: Type -> Type

Methods

from :: FinMat ns -> Rep (FinMat ns) x

to :: Rep (FinMat ns) x -> FinMat ns

Semigroup (FinMat ns)

Defined in Cybus.FinMat

Methods

(<>) :: FinMat ns -> FinMat ns -> FinMat ns

sconcat :: NonEmpty (FinMat ns) -> FinMat ns

stimes :: Integral b => b -> FinMat ns -> FinMat ns

NS ns => Monoid (FinMat ns)

Defined in Cybus.FinMat

Methods

mempty :: FinMat ns

mappend :: FinMat ns -> FinMat ns -> FinMat ns

mconcat :: [FinMat ns] -> FinMat ns

NFData (FinMat ns)

Defined in Cybus.FinMat

Methods

rnf :: FinMat ns -> ()

NS ns => Num1 (FinMat ns)

Defined in Cybus.FinMat

Methods

toInteger1 :: FinMat ns -> Integer

fromInteger1 :: FinMat ns -> Integer -> Either String (FinMat ns)

(.+) :: Either String (FinMat ns) -> Either String (FinMat ns) -> Either String (FinMat ns)

(.-) :: Either String (FinMat ns) -> Either String (FinMat ns) -> Either String (FinMat ns)

(.*) :: Either String (FinMat ns) -> Either String (FinMat ns) -> Either String (FinMat ns)

negate1 :: Either String (FinMat ns) -> Either String (FinMat ns)

abs1 :: Either String (FinMat ns) -> Either String (FinMat ns)

signum1 :: Either String (FinMat ns) -> Either String (FinMat ns)

succ1 :: Either String (FinMat ns) -> Either String (FinMat ns)

pred1 :: Either String (FinMat ns) -> Either String (FinMat ns)

Generic1 FinMat

Defined in Cybus.FinMat

Associated Types

type Rep1 FinMat :: k -> Type

Methods

from1 :: forall (a :: k). FinMat a -> Rep1 FinMat a

to1 :: forall (a :: k). Rep1 FinMat a -> FinMat a

NS ns => FunctorWithIndex (FinMat ns) (Mat ns)

Defined in Cybus.Mat

Methods

imap :: (FinMat ns -> a -> b) -> Mat ns a -> Mat ns b

NS ns => FoldableWithIndex (FinMat ns) (Mat ns)

Defined in Cybus.Mat

Methods

ifoldMap :: Monoid m => (FinMat ns -> a -> m) -> Mat ns a -> m

ifoldMap' :: Monoid m => (FinMat ns -> a -> m) -> Mat ns a -> m

ifoldr :: (FinMat ns -> a -> b -> b) -> b -> Mat ns a -> b

ifoldl :: (FinMat ns -> b -> a -> b) -> b -> Mat ns a -> b

ifoldr' :: (FinMat ns -> a -> b -> b) -> b -> Mat ns a -> b

ifoldl' :: (FinMat ns -> b -> a -> b) -> b -> Mat ns a -> b

NS ns => TraversableWithIndex (FinMat ns) (Mat ns)

Defined in Cybus.Mat

Methods

itraverse :: Applicative f => (FinMat ns -> a -> f b) -> Mat ns a -> f (Mat ns b)

type Rep (FinMat ns)

Defined in Cybus.FinMat

type Rep (FinMat ns) = D1 ('MetaData "FinMat" "Cybus.FinMat" "cybus-0.3.0.0-2tgktn1zjvk47vpww9PCqf" 'False) (C1 ('MetaCons "FinMatUnsafe" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (NonEmpty Pos))))

type Rep1 FinMat

Defined in Cybus.FinMat

type Rep1 FinMat = D1 ('MetaData "FinMat" "Cybus.FinMat" "cybus-0.3.0.0-2tgktn1zjvk47vpww9PCqf" 'False) (C1 ('MetaCons "FinMatUnsafe" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (NonEmpty Pos))))

fmPos :: FinMat ns -> Int

accessor for the relative position within a matrix

fmNS :: FinMat ns -> NonEmpty Pos

accessor for the indices of a matrix

pattern FinMat :: forall (ns :: [Nat]). Int -> NonEmpty Pos -> FinMat ns

readonly pattern synonym for finmatrix

pattern FinMatU :: forall (ns :: [Nat]). (HasCallStack, NS ns) => Int -> NonEmpty Pos -> FinMat ns

pattern synonym for validating the finmatrix before construction but uses an extra NS constraint to check "ns"

constructors

class FinMatC is ns where

convert type level indices into a FinMat

Methods

finMatC :: FinMat ns

Instances

(TypeError ('Text "FinMatC '[] '[]: empty index 'is' and 'ns'") :: Constraint) => FinMatC ('[] :: [k]) ('[] :: [Nat])

Defined in Cybus.FinMat

Methods

finMatC :: FinMat '[]

(TypeError ('Text "FinMatC '[] (n ': ns): empty index 'is'") :: Constraint) => FinMatC ('[] :: [k]) (n ': ns)

Defined in Cybus.FinMat

Methods

finMatC :: FinMat (n ': ns)

(TypeError ('Text "FinMatC (i ': is) '[]: empty index 'ns'") :: Constraint) => FinMatC (i ': is :: [a]) ('[] :: [Nat])

Defined in Cybus.FinMat

Methods

finMatC :: FinMat '[]

(is' ~ (i ': is), ns' ~ (n ': ns), NS is', NS ns', FinMatT is' ns' 1 is' ns') => FinMatC (i ': is :: [Nat]) (n ': ns)

Defined in Cybus.FinMat

Methods

finMatC :: FinMat (n ': ns)

mkFinMat :: Int -> NonEmpty Pos -> Either String (FinMat ns)

create a FinMat value level "i" and "ns" values and validate that "i" is in range

mkFinMatC :: forall ns. NS ns => Int -> NonEmpty Pos -> Either String (FinMat ns)

create a FinMat value level "i" and "ns" values and validate against expected "ns"

finMat :: forall ns. NS ns => Int -> Either String (FinMat ns)

convenience function for conversion from Int to FinMat

toFinMatFromPos :: forall (i :: Nat) ns. (NS ns, i <! ProductT ns) => FinMat ns

create a FinMat using a relative type level index

conversions

finMatToNonEmpty :: forall ns. FinMat ns -> NonEmpty Pos

convert a FinMat into a list of indices

nonEmptyToFinMat :: forall ns. NS ns => NonEmpty Pos -> Either String (FinMat ns)

try to convert a list of indices into a FinMat

nonEmptyToFinMat' :: NonEmpty Pos -> NonEmpty Pos -> Either String (FinMat ns)

try to convert a list of indices into a FinMat

read/show methods

showFinMat :: FinMat ns -> String

pretty print FinMat

readFinMatP :: forall ns. NS ns => ReadP (FinMat ns)

reader for showFin

readFinMat :: NS ns => ReadS (FinMat ns)

reader for FinMat

showFinMat' :: forall ns. FinMat ns -> String

more detailed pretty print FinMat

miscellaneous

class NS (ns :: [Nat]) where

conversion from list of Nats to Positives

Minimal complete definition

fromNSP, nsLengthP

Methods

fromNSP :: NonEmpty Pos

fromNSTotalP :: Pos

nsLengthP :: Pos

Instances

(TypeError ('Text "NS: empty dimensions are not supported") :: Constraint) => NS ('[] :: [Nat])

Defined in Data.Pos

Methods

fromNSP :: NonEmpty Pos

fromNSTotalP :: Pos

nsLengthP :: Pos

PosC n => NS '[n]

Defined in Data.Pos

Methods

fromNSP :: NonEmpty Pos

fromNSTotalP :: Pos

nsLengthP :: Pos

(PosC n, NS (n1 ': ns)) => NS (n ': (n1 ': ns))

Defined in Data.Pos

Methods

fromNSP :: NonEmpty Pos

fromNSTotalP :: Pos

nsLengthP :: Pos

class NSRangeC i ns

constrain i within the size of the indices ie "i >= 1 && i <= LengthT ns"

Instances

(TypeError ('Text "NSRangeC '[]: empty indices") :: Constraint) => NSRangeC p ('[] :: [Nat])

Defined in Cybus.FinMat

(TypeError ('Text "NSRangeC: zero is not a valid index: index must be one or greater") :: Constraint) => NSRangeC 'Z (n ': ns)

Defined in Cybus.FinMat

NSRangeC ('S 'Z) (n ': ns)

Defined in Cybus.FinMat

(TypeError ('Text "NSRangeC: index is larger than the number of matrix indices ns") :: Constraint) => NSRangeC ('S ('S i)) '[n]

Defined in Cybus.FinMat

NSRangeC ('S i) (m ': ns) => NSRangeC ('S ('S i)) (n ': (m ': ns))

Defined in Cybus.FinMat

relPos :: Foldable1 t => t (Pos, Pos) -> (Pos, Int)

find the relative position in a matrix index

finMatFinSet :: forall i n ns. (PosC i, NSRangeC (NatToPeanoT i) ns) => FinMat ns -> Fin n -> FinMat ns

set the Fin at index "i" for the FinMat

finMatFinGet :: forall i n ns. (PosC i, NSRangeC (NatToPeanoT i) ns) => FinMat ns -> Fin n

get the Fin at index "i" from FinMat must rely on FinMat to get "n at index i "which saves us pulling "n" from the typelevel ie we can omit PosC n

lens into the matrix indices

_finMatCons :: forall n n1 ns. (NS (n1 ': ns), PosC n) => Iso' (FinMat (n ': (n1 ': ns))) (Fin n, FinMat (n1 ': ns))

iso that conses out the Fin from FinMat

_finMatFin :: forall i n ns. (PosC i, NSRangeC (NatToPeanoT i) ns) => Lens' (FinMat ns) (Fin n)

a lens for accessing the "i" index in a indices of FinMat

_i1 :: Lens' (FinMat (n ': ns)) (Fin n)

lens for index 1

_i2 :: Lens' (FinMat (n1 ': (n ': ns))) (Fin n)

lens for index 2

_i3 :: Lens' (FinMat (n1 ': (n2 ': (n ': ns)))) (Fin n)

lens for index 3

_i4 :: Lens' (FinMat (n1 ': (n2 ': (n3 ': (n ': ns))))) (Fin n)

lens for index 4

_i5 :: Lens' (FinMat (n1 ': (n2 ': (n3 ': (n4 ': (n ': ns)))))) (Fin n)

lens for index 5

_i6 :: Lens' (FinMat (n1 ': (n2 ': (n3 ': (n4 ': (n5 ': (n ': ns))))))) (Fin n)

lens for index 6

_i7 :: Lens' (FinMat (n1 ': (n2 ': (n3 ': (n4 ': (n5 ': (n6 ': (n ': ns)))))))) (Fin n)

lens for index 7

_i8 :: Lens' (FinMat (n1 ': (n2 ': (n3 ': (n4 ': (n5 ': (n6 ': (n7 ': (n ': ns))))))))) (Fin n)

lens for index 8

_i9 :: Lens' (FinMat (n1 ': (n2 ': (n3 ': (n4 ': (n5 ': (n6 ': (n7 ': (n8 ': (n ': ns)))))))))) (Fin n)

lens for index 9

_i10 :: Lens' (FinMat (n1 ': (n2 ': (n3 ': (n4 ': (n5 ': (n6 ': (n7 ': (n8 ': (n9 ': (n ': ns))))))))))) (Fin n)

lens for index 10