Numeric.AD.Mode.Sparse.Double

Higher order derivatives via a "dual number tower".

Documentation

data AD s a

Instances

Mode a => Mode (AD s a)

Defined in Numeric.AD.Internal.Type

Associated Types

type Scalar (AD s a)

Methods

isKnownConstant :: AD s a -> Bool

asKnownConstant :: AD s a -> Maybe (Scalar (AD s a))

isKnownZero :: AD s a -> Bool

auto :: Scalar (AD s a) -> AD s a

(*^) :: Scalar (AD s a) -> AD s a -> AD s a

(^*) :: AD s a -> Scalar (AD s a) -> AD s a

(^/) :: AD s a -> Scalar (AD s a) -> AD s a

zero :: AD s a

Bounded a => Bounded (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

minBound :: AD s a

maxBound :: AD s a

Enum a => Enum (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

succ :: AD s a -> AD s a

pred :: AD s a -> AD s a

toEnum :: Int -> AD s a

fromEnum :: AD s a -> Int

enumFrom :: AD s a -> [AD s a]

enumFromThen :: AD s a -> AD s a -> [AD s a]

enumFromTo :: AD s a -> AD s a -> [AD s a]

enumFromThenTo :: AD s a -> AD s a -> AD s a -> [AD s a]

Floating a => Floating (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

pi :: AD s a

exp :: AD s a -> AD s a

log :: AD s a -> AD s a

sqrt :: AD s a -> AD s a

(**) :: AD s a -> AD s a -> AD s a

logBase :: AD s a -> AD s a -> AD s a

sin :: AD s a -> AD s a

cos :: AD s a -> AD s a

tan :: AD s a -> AD s a

asin :: AD s a -> AD s a

acos :: AD s a -> AD s a

atan :: AD s a -> AD s a

sinh :: AD s a -> AD s a

cosh :: AD s a -> AD s a

tanh :: AD s a -> AD s a

asinh :: AD s a -> AD s a

acosh :: AD s a -> AD s a

atanh :: AD s a -> AD s a

log1p :: AD s a -> AD s a

expm1 :: AD s a -> AD s a

log1pexp :: AD s a -> AD s a

log1mexp :: AD s a -> AD s a

RealFloat a => RealFloat (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

floatRadix :: AD s a -> Integer

floatDigits :: AD s a -> Int

floatRange :: AD s a -> (Int, Int)

decodeFloat :: AD s a -> (Integer, Int)

encodeFloat :: Integer -> Int -> AD s a

exponent :: AD s a -> Int

significand :: AD s a -> AD s a

scaleFloat :: Int -> AD s a -> AD s a

isNaN :: AD s a -> Bool

isInfinite :: AD s a -> Bool

isDenormalized :: AD s a -> Bool

isNegativeZero :: AD s a -> Bool

isIEEE :: AD s a -> Bool

atan2 :: AD s a -> AD s a -> AD s a

Num a => Num (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

(+) :: AD s a -> AD s a -> AD s a

(-) :: AD s a -> AD s a -> AD s a

(*) :: AD s a -> AD s a -> AD s a

negate :: AD s a -> AD s a

abs :: AD s a -> AD s a

signum :: AD s a -> AD s a

fromInteger :: Integer -> AD s a

Read a => Read (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

readsPrec :: Int -> ReadS (AD s a)

readList :: ReadS [AD s a]

readPrec :: ReadPrec (AD s a)

readListPrec :: ReadPrec [AD s a]

Fractional a => Fractional (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

(/) :: AD s a -> AD s a -> AD s a

recip :: AD s a -> AD s a

fromRational :: Rational -> AD s a

Real a => Real (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

toRational :: AD s a -> Rational

RealFrac a => RealFrac (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

properFraction :: Integral b => AD s a -> (b, AD s a)

truncate :: Integral b => AD s a -> b

round :: Integral b => AD s a -> b

ceiling :: Integral b => AD s a -> b

floor :: Integral b => AD s a -> b

Show a => Show (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

showsPrec :: Int -> AD s a -> ShowS

show :: AD s a -> String

showList :: [AD s a] -> ShowS

Erf a => Erf (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

erf :: AD s a -> AD s a

erfc :: AD s a -> AD s a

erfcx :: AD s a -> AD s a

normcdf :: AD s a -> AD s a

InvErf a => InvErf (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

inverf :: AD s a -> AD s a

inverfc :: AD s a -> AD s a

invnormcdf :: AD s a -> AD s a

Eq a => Eq (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

(==) :: AD s a -> AD s a -> Bool

(/=) :: AD s a -> AD s a -> Bool

Ord a => Ord (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

compare :: AD s a -> AD s a -> Ordering

(<) :: AD s a -> AD s a -> Bool

(<=) :: AD s a -> AD s a -> Bool

(>) :: AD s a -> AD s a -> Bool

(>=) :: AD s a -> AD s a -> Bool

max :: AD s a -> AD s a -> AD s a

min :: AD s a -> AD s a -> AD s a

type Scalar (AD s a)

Defined in Numeric.AD.Internal.Type

type Scalar (AD s a) = Scalar a

data SparseDouble

We only store partials in sorted order, so the map contained in a partial will only contain partials with equal or greater keys to that of the map in which it was found. This should be key for efficiently computing sparse hessians. there are only n + k - 1 choose k distinct nth partial derivatives of a function with k inputs.

Instances

Jacobian SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

Associated Types

type D SparseDouble

Methods

unary :: (Scalar SparseDouble -> Scalar SparseDouble) -> D SparseDouble -> SparseDouble -> SparseDouble

lift1 :: (Scalar SparseDouble -> Scalar SparseDouble) -> (D SparseDouble -> D SparseDouble) -> SparseDouble -> SparseDouble

lift1_ :: (Scalar SparseDouble -> Scalar SparseDouble) -> (D SparseDouble -> D SparseDouble -> D SparseDouble) -> SparseDouble -> SparseDouble

binary :: (Scalar SparseDouble -> Scalar SparseDouble -> Scalar SparseDouble) -> D SparseDouble -> D SparseDouble -> SparseDouble -> SparseDouble -> SparseDouble

lift2 :: (Scalar SparseDouble -> Scalar SparseDouble -> Scalar SparseDouble) -> (D SparseDouble -> D SparseDouble -> (D SparseDouble, D SparseDouble)) -> SparseDouble -> SparseDouble -> SparseDouble

lift2_ :: (Scalar SparseDouble -> Scalar SparseDouble -> Scalar SparseDouble) -> (D SparseDouble -> D SparseDouble -> D SparseDouble -> (D SparseDouble, D SparseDouble)) -> SparseDouble -> SparseDouble -> SparseDouble

Mode SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

Associated Types

type Scalar SparseDouble

Methods

isKnownConstant :: SparseDouble -> Bool

asKnownConstant :: SparseDouble -> Maybe (Scalar SparseDouble)

isKnownZero :: SparseDouble -> Bool

auto :: Scalar SparseDouble -> SparseDouble

(*^) :: Scalar SparseDouble -> SparseDouble -> SparseDouble

(^*) :: SparseDouble -> Scalar SparseDouble -> SparseDouble

(^/) :: SparseDouble -> Scalar SparseDouble -> SparseDouble

zero :: SparseDouble

Data SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

Methods

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

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

toConstr :: SparseDouble -> Constr

dataTypeOf :: SparseDouble -> DataType

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

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

gmapT :: (forall b. Data b => b -> b) -> SparseDouble -> SparseDouble

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

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

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

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

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

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

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

Enum SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

Methods

succ :: SparseDouble -> SparseDouble

pred :: SparseDouble -> SparseDouble

toEnum :: Int -> SparseDouble

fromEnum :: SparseDouble -> Int

enumFrom :: SparseDouble -> [SparseDouble]

enumFromThen :: SparseDouble -> SparseDouble -> [SparseDouble]

enumFromTo :: SparseDouble -> SparseDouble -> [SparseDouble]

enumFromThenTo :: SparseDouble -> SparseDouble -> SparseDouble -> [SparseDouble]

Floating SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

Methods

pi :: SparseDouble

exp :: SparseDouble -> SparseDouble

log :: SparseDouble -> SparseDouble

sqrt :: SparseDouble -> SparseDouble

(**) :: SparseDouble -> SparseDouble -> SparseDouble

logBase :: SparseDouble -> SparseDouble -> SparseDouble

sin :: SparseDouble -> SparseDouble

cos :: SparseDouble -> SparseDouble

tan :: SparseDouble -> SparseDouble

asin :: SparseDouble -> SparseDouble

acos :: SparseDouble -> SparseDouble

atan :: SparseDouble -> SparseDouble

sinh :: SparseDouble -> SparseDouble

cosh :: SparseDouble -> SparseDouble

tanh :: SparseDouble -> SparseDouble

asinh :: SparseDouble -> SparseDouble

acosh :: SparseDouble -> SparseDouble

atanh :: SparseDouble -> SparseDouble

log1p :: SparseDouble -> SparseDouble

expm1 :: SparseDouble -> SparseDouble

log1pexp :: SparseDouble -> SparseDouble

log1mexp :: SparseDouble -> SparseDouble

RealFloat SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

Methods

floatRadix :: SparseDouble -> Integer

floatDigits :: SparseDouble -> Int

floatRange :: SparseDouble -> (Int, Int)

decodeFloat :: SparseDouble -> (Integer, Int)

encodeFloat :: Integer -> Int -> SparseDouble

exponent :: SparseDouble -> Int

significand :: SparseDouble -> SparseDouble

scaleFloat :: Int -> SparseDouble -> SparseDouble

isNaN :: SparseDouble -> Bool

isInfinite :: SparseDouble -> Bool

isDenormalized :: SparseDouble -> Bool

isNegativeZero :: SparseDouble -> Bool

isIEEE :: SparseDouble -> Bool

atan2 :: SparseDouble -> SparseDouble -> SparseDouble

Num SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

Methods

(+) :: SparseDouble -> SparseDouble -> SparseDouble

(-) :: SparseDouble -> SparseDouble -> SparseDouble

(*) :: SparseDouble -> SparseDouble -> SparseDouble

negate :: SparseDouble -> SparseDouble

abs :: SparseDouble -> SparseDouble

signum :: SparseDouble -> SparseDouble

fromInteger :: Integer -> SparseDouble

Fractional SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

Methods

(/) :: SparseDouble -> SparseDouble -> SparseDouble

recip :: SparseDouble -> SparseDouble

fromRational :: Rational -> SparseDouble

Real SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

Methods

toRational :: SparseDouble -> Rational

RealFrac SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

Methods

properFraction :: Integral b => SparseDouble -> (b, SparseDouble)

truncate :: Integral b => SparseDouble -> b

round :: Integral b => SparseDouble -> b

ceiling :: Integral b => SparseDouble -> b

floor :: Integral b => SparseDouble -> b

Show SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

Methods

showsPrec :: Int -> SparseDouble -> ShowS

show :: SparseDouble -> String

showList :: [SparseDouble] -> ShowS

Erf SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

Methods

erf :: SparseDouble -> SparseDouble

erfc :: SparseDouble -> SparseDouble

erfcx :: SparseDouble -> SparseDouble

normcdf :: SparseDouble -> SparseDouble

InvErf SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

Methods

inverf :: SparseDouble -> SparseDouble

inverfc :: SparseDouble -> SparseDouble

invnormcdf :: SparseDouble -> SparseDouble

Eq SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

Methods

(==) :: SparseDouble -> SparseDouble -> Bool

(/=) :: SparseDouble -> SparseDouble -> Bool

Ord SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

Methods

compare :: SparseDouble -> SparseDouble -> Ordering

(<) :: SparseDouble -> SparseDouble -> Bool

(<=) :: SparseDouble -> SparseDouble -> Bool

(>) :: SparseDouble -> SparseDouble -> Bool

(>=) :: SparseDouble -> SparseDouble -> Bool

max :: SparseDouble -> SparseDouble -> SparseDouble

min :: SparseDouble -> SparseDouble -> SparseDouble

Grad SparseDouble [Double] (Double, [Double])

Defined in Numeric.AD.Internal.Sparse.Double

Methods

pack :: SparseDouble -> [SparseDouble] -> SparseDouble

unpack :: ([Double] -> [Double]) -> [Double]

unpack' :: ([Double] -> (Double, [Double])) -> (Double, [Double])

Grads SparseDouble (Cofree List Double)

Defined in Numeric.AD.Internal.Sparse.Double

Methods

packs :: SparseDouble -> [SparseDouble] -> SparseDouble

unpacks :: ([Double] -> Cofree List Double) -> Cofree List Double

Grads i o => Grads (SparseDouble -> i) (Double -> o)

Defined in Numeric.AD.Internal.Sparse.Double

Methods

packs :: (SparseDouble -> i) -> [SparseDouble] -> SparseDouble

unpacks :: ([Double] -> Cofree List Double) -> Double -> o

Grad i o o' => Grad (SparseDouble -> i) (Double -> o) (Double -> o')

Defined in Numeric.AD.Internal.Sparse.Double

Methods

pack :: (SparseDouble -> i) -> [SparseDouble] -> SparseDouble

unpack :: ([Double] -> [Double]) -> Double -> o

unpack' :: ([Double] -> (Double, [Double])) -> Double -> o'

type D SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

type D SparseDouble = SparseDouble

type Scalar SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

type Scalar SparseDouble = Double

auto :: Mode t => Scalar t -> t

Embed a constant

Sparse Gradients

grad :: Traversable f => (forall s. f (AD s SparseDouble) -> AD s SparseDouble) -> f Double -> f Double

The grad function calculates the gradient of a non-scalar-to-scalar function with sparse-mode AD in a single pass.

>>> grad (\[x,y,z] -> x*y+z) [1,2,3]
[2.0,1.0,1.0]

>>> grad (\[x,y] -> x**y) [0,2]
[0.0,NaN]

grad' :: Traversable f => (forall s. f (AD s SparseDouble) -> AD s SparseDouble) -> f Double -> (Double, f Double)

grads :: Traversable f => (forall s. f (AD s SparseDouble) -> AD s SparseDouble) -> f Double -> Cofree f Double

gradWith :: Traversable f => (Double -> Double -> b) -> (forall s. f (AD s SparseDouble) -> AD s SparseDouble) -> f Double -> f b

gradWith' :: Traversable f => (Double -> Double -> b) -> (forall s. f (AD s SparseDouble) -> AD s SparseDouble) -> f Double -> (Double, f b)

Sparse Jacobians (synonyms)

jacobian :: (Traversable f, Functor g) => (forall s. f (AD s SparseDouble) -> g (AD s SparseDouble)) -> f Double -> g (f Double)

jacobian' :: (Traversable f, Functor g) => (forall s. f (AD s SparseDouble) -> g (AD s SparseDouble)) -> f Double -> g (Double, f Double)

jacobianWith :: (Traversable f, Functor g) => (Double -> Double -> b) -> (forall s. f (AD s SparseDouble) -> g (AD s SparseDouble)) -> f Double -> g (f b)

jacobianWith' :: (Traversable f, Functor g) => (Double -> Double -> b) -> (forall s. f (AD s SparseDouble) -> g (AD s SparseDouble)) -> f Double -> g (Double, f b)

jacobians :: (Traversable f, Functor g) => (forall s. f (AD s SparseDouble) -> g (AD s SparseDouble)) -> f Double -> g (Cofree f Double)

Sparse Hessians

hessian :: Traversable f => (forall s. f (AD s SparseDouble) -> AD s SparseDouble) -> f Double -> f (f Double)

hessian' :: Traversable f => (forall s. f (AD s SparseDouble) -> AD s SparseDouble) -> f Double -> (Double, f (Double, f Double))

hessianF :: (Traversable f, Functor g) => (forall s. f (AD s SparseDouble) -> g (AD s SparseDouble)) -> f Double -> g (f (f Double))

hessianF' :: (Traversable f, Functor g) => (forall s. f (AD s SparseDouble) -> g (AD s SparseDouble)) -> f Double -> g (Double, f (Double, f Double))