Numeric.Clifford.NumericIntegration

Documentation

elementAdd :: C c => [c] -> [c] -> [c]

elementScale :: C a c => [a] -> [c] -> [c]

elementSub :: C c => [c] -> [c] -> [c]

elementMul :: C c => [c] -> [c] -> [c]

rk4ClassicalTableau :: (Fractional f, C f) => ButcherTableau f

implicitEulerTableau :: ButcherTableau Double

sumVector :: (Ord t1, SingI Nat t, C t1) => Vector (Multivector t t1) -> Multivector t t1

systemBroydensMethod :: (Ord f, SingI Nat n, C f) => ([Multivector n f] -> [Multivector n f]) -> [Multivector n f] -> [Multivector n f] -> [[Multivector n f]]

convergeList :: (Show f, Ord f) => [[f]] -> [f]

showOutput :: Show a => [Char] -> a -> a

convergeTolLists :: (Ord f, C f, C f, Show f, SingI d) => f -> [[Multivector d f]] -> [Multivector d f]

type RKStepper d t stateType = (Ord t, Show t, C t (Multivector d t), C t) => t -> (t -> stateType -> stateType) -> ([Multivector d t] -> stateType) -> (stateType -> [Multivector d t]) -> (t, stateType) -> (t, stateType)

data ButcherTableau f

Constructors

ButcherTableau

Fields

_tableauA :: [[f]]

_tableauB :: [f]

_tableauC :: [f]

tableauC :: forall f. Lens' (ButcherTableau f) [f]

tableauB :: forall f. Lens' (ButcherTableau f) [f]

tableauA :: forall f. Lens' (ButcherTableau f) [[f]]

type ConvergerFunction f = forall d f. [[Multivector d f]] -> [Multivector d f]

type AdaptiveStepSizeFunction f state = f -> state -> f

data RKAttribute f state

Constructors

Explicit

HamiltonianFunction

AdaptiveStepSize

Fields

sigma :: AdaptiveStepSizeFunction f state

ConvergenceTolerance

Fields

epsilon :: f

ConvergenceFunction

Fields

converger :: ConvergerFunction f

RootSolver

UseAutomaticDifferentiationForRootSolver

StartingGuessMethod

isStartingGuessMethod :: forall f_1627458391 state_1627458392. RKAttribute f_1627458391 state_1627458392 -> Bool

isUseAutomaticDifferentiationForRootSolver :: forall f_1627458391 state_1627458392. RKAttribute f_1627458391 state_1627458392 -> Bool

isRootSolver :: forall f_1627458391 state_1627458392. RKAttribute f_1627458391 state_1627458392 -> Bool

isConvergenceFunction :: forall f_1627458391 state_1627458392. RKAttribute f_1627458391 state_1627458392 -> Bool

isConvergenceTolerance :: forall f_1627458391 state_1627458392. RKAttribute f_1627458391 state_1627458392 -> Bool

isAdaptiveStepSize :: forall f_1627458391 state_1627458392. RKAttribute f_1627458391 state_1627458392 -> Bool

isHamiltonianFunction :: forall f_1627458391 state_1627458392. RKAttribute f_1627458391 state_1627458392 -> Bool

isExplicit :: forall f_1627458391 state_1627458392. RKAttribute f_1627458391 state_1627458392 -> Bool

genericRKMethod :: forall d t stateType. (Ord t, Show t, C t (Multivector d t), C t, C t, SingI d) => ButcherTableau t -> [RKAttribute t stateType] -> RKStepper d t stateType