ad-4.3.2.1: Automatic Differentiation

Copyright(c) Edward Kmett 2010-2015
LicenseBSD3
Maintainerekmett@gmail.com
Stabilityexperimental
PortabilityGHC only
Safe HaskellNone
LanguageHaskell2010

Numeric.AD.Mode.Sparse

Contents

Description

Higher order derivatives via a "dual number tower".

Synopsis

Documentation

data AD s a Source #

Instances

Bounded a => Bounded (AD s a) Source # 

Methods

minBound :: AD s a #

maxBound :: AD s a #

Enum a => Enum (AD s a) Source # 

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] #

Eq a => Eq (AD s a) Source # 

Methods

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

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

Floating a => Floating (AD s a) Source # 

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 #

Fractional a => Fractional (AD s a) Source # 

Methods

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

recip :: AD s a -> AD s a #

fromRational :: Rational -> AD s a #

Num a => Num (AD s a) Source # 

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 #

Ord a => Ord (AD s a) Source # 

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 #

Read a => Read (AD s a) Source # 

Methods

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

readList :: ReadS [AD s a] #

readPrec :: ReadPrec (AD s a) #

readListPrec :: ReadPrec [AD s a] #

Real a => Real (AD s a) Source # 

Methods

toRational :: AD s a -> Rational #

RealFloat a => RealFloat (AD s a) Source # 

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 #

RealFrac a => RealFrac (AD s a) Source # 

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) Source # 

Methods

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

show :: AD s a -> String #

showList :: [AD s a] -> ShowS #

Erf a => Erf (AD s a) Source # 

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) Source # 

Methods

inverf :: AD s a -> AD s a #

inverfc :: AD s a -> AD s a #

invnormcdf :: AD s a -> AD s a #

Mode a => Mode (AD s a) Source # 

Associated Types

type Scalar (AD s a) :: * Source #

Methods

isKnownConstant :: AD s a -> Bool Source #

isKnownZero :: AD s a -> Bool Source #

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

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

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

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

zero :: AD s a Source #

type Scalar (AD s a) Source # 
type Scalar (AD s a) = Scalar a

data Sparse a Source #

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 - 1) distinct nth partial derivatives of a function with k inputs.

Instances

(Num a, Bounded a) => Bounded (Sparse a) # 

Methods

minBound :: Sparse a #

maxBound :: Sparse a #

(Num a, Enum a) => Enum (Sparse a) # 

Methods

succ :: Sparse a -> Sparse a #

pred :: Sparse a -> Sparse a #

toEnum :: Int -> Sparse a #

fromEnum :: Sparse a -> Int #

enumFrom :: Sparse a -> [Sparse a] #

enumFromThen :: Sparse a -> Sparse a -> [Sparse a] #

enumFromTo :: Sparse a -> Sparse a -> [Sparse a] #

enumFromThenTo :: Sparse a -> Sparse a -> Sparse a -> [Sparse a] #

(Num a, Eq a) => Eq (Sparse a) # 

Methods

(==) :: Sparse a -> Sparse a -> Bool #

(/=) :: Sparse a -> Sparse a -> Bool #

Floating a => Floating (Sparse a) # 

Methods

pi :: Sparse a #

exp :: Sparse a -> Sparse a #

log :: Sparse a -> Sparse a #

sqrt :: Sparse a -> Sparse a #

(**) :: Sparse a -> Sparse a -> Sparse a #

logBase :: Sparse a -> Sparse a -> Sparse a #

sin :: Sparse a -> Sparse a #

cos :: Sparse a -> Sparse a #

tan :: Sparse a -> Sparse a #

asin :: Sparse a -> Sparse a #

acos :: Sparse a -> Sparse a #

atan :: Sparse a -> Sparse a #

sinh :: Sparse a -> Sparse a #

cosh :: Sparse a -> Sparse a #

tanh :: Sparse a -> Sparse a #

asinh :: Sparse a -> Sparse a #

acosh :: Sparse a -> Sparse a #

atanh :: Sparse a -> Sparse a #

log1p :: Sparse a -> Sparse a #

expm1 :: Sparse a -> Sparse a #

log1pexp :: Sparse a -> Sparse a #

log1mexp :: Sparse a -> Sparse a #

Fractional a => Fractional (Sparse a) # 

Methods

(/) :: Sparse a -> Sparse a -> Sparse a #

recip :: Sparse a -> Sparse a #

fromRational :: Rational -> Sparse a #

Data a => Data (Sparse a) Source # 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Sparse a -> c (Sparse a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sparse a) #

toConstr :: Sparse a -> Constr #

dataTypeOf :: Sparse a -> DataType #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Sparse a)) #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sparse a)) #

gmapT :: (forall b. Data b => b -> b) -> Sparse a -> Sparse a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sparse a -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sparse a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Sparse a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Sparse a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sparse a -> m (Sparse a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sparse a -> m (Sparse a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sparse a -> m (Sparse a) #

Num a => Num (Sparse a) # 

Methods

(+) :: Sparse a -> Sparse a -> Sparse a #

(-) :: Sparse a -> Sparse a -> Sparse a #

(*) :: Sparse a -> Sparse a -> Sparse a #

negate :: Sparse a -> Sparse a #

abs :: Sparse a -> Sparse a #

signum :: Sparse a -> Sparse a #

fromInteger :: Integer -> Sparse a #

(Num a, Ord a) => Ord (Sparse a) # 

Methods

compare :: Sparse a -> Sparse a -> Ordering #

(<) :: Sparse a -> Sparse a -> Bool #

(<=) :: Sparse a -> Sparse a -> Bool #

(>) :: Sparse a -> Sparse a -> Bool #

(>=) :: Sparse a -> Sparse a -> Bool #

max :: Sparse a -> Sparse a -> Sparse a #

min :: Sparse a -> Sparse a -> Sparse a #

Real a => Real (Sparse a) # 

Methods

toRational :: Sparse a -> Rational #

RealFloat a => RealFloat (Sparse a) # 
RealFrac a => RealFrac (Sparse a) # 

Methods

properFraction :: Integral b => Sparse a -> (b, Sparse a) #

truncate :: Integral b => Sparse a -> b #

round :: Integral b => Sparse a -> b #

ceiling :: Integral b => Sparse a -> b #

floor :: Integral b => Sparse a -> b #

Show a => Show (Sparse a) Source # 

Methods

showsPrec :: Int -> Sparse a -> ShowS #

show :: Sparse a -> String #

showList :: [Sparse a] -> ShowS #

Erf a => Erf (Sparse a) # 

Methods

erf :: Sparse a -> Sparse a #

erfc :: Sparse a -> Sparse a #

erfcx :: Sparse a -> Sparse a #

normcdf :: Sparse a -> Sparse a #

InvErf a => InvErf (Sparse a) # 

Methods

inverf :: Sparse a -> Sparse a #

inverfc :: Sparse a -> Sparse a #

invnormcdf :: Sparse a -> Sparse a #

Num a => Mode (Sparse a) Source # 

Associated Types

type Scalar (Sparse a) :: * Source #

Num a => Jacobian (Sparse a) Source # 

Associated Types

type D (Sparse a) :: * Source #

Methods

unary :: (Scalar (Sparse a) -> Scalar (Sparse a)) -> D (Sparse a) -> Sparse a -> Sparse a Source #

lift1 :: (Scalar (Sparse a) -> Scalar (Sparse a)) -> (D (Sparse a) -> D (Sparse a)) -> Sparse a -> Sparse a Source #

lift1_ :: (Scalar (Sparse a) -> Scalar (Sparse a)) -> (D (Sparse a) -> D (Sparse a) -> D (Sparse a)) -> Sparse a -> Sparse a Source #

binary :: (Scalar (Sparse a) -> Scalar (Sparse a) -> Scalar (Sparse a)) -> D (Sparse a) -> D (Sparse a) -> Sparse a -> Sparse a -> Sparse a Source #

lift2 :: (Scalar (Sparse a) -> Scalar (Sparse a) -> Scalar (Sparse a)) -> (D (Sparse a) -> D (Sparse a) -> (D (Sparse a), D (Sparse a))) -> Sparse a -> Sparse a -> Sparse a Source #

lift2_ :: (Scalar (Sparse a) -> Scalar (Sparse a) -> Scalar (Sparse a)) -> (D (Sparse a) -> D (Sparse a) -> D (Sparse a) -> (D (Sparse a), D (Sparse a))) -> Sparse a -> Sparse a -> Sparse a Source #

Num a => Grad (Sparse a) [a] (a, [a]) a Source # 

Methods

pack :: Sparse a -> [Sparse a] -> Sparse a Source #

unpack :: ([a] -> [a]) -> [a] Source #

unpack' :: ([a] -> (a, [a])) -> (a, [a]) Source #

Num a => Grads (Sparse a) (Cofree [] a) a Source # 

Methods

packs :: Sparse a -> [Sparse a] -> Sparse a Source #

unpacks :: ([a] -> Cofree [] a) -> Cofree [] a Source #

Grads i o a => Grads (Sparse a -> i) (a -> o) a Source # 

Methods

packs :: (Sparse a -> i) -> [Sparse a] -> Sparse a Source #

unpacks :: ([a] -> Cofree [] a) -> a -> o Source #

Grad i o o' a => Grad (Sparse a -> i) (a -> o) (a -> o') a Source # 

Methods

pack :: (Sparse a -> i) -> [Sparse a] -> Sparse a Source #

unpack :: ([a] -> [a]) -> a -> o Source #

unpack' :: ([a] -> (a, [a])) -> a -> o' Source #

type Scalar (Sparse a) Source # 
type Scalar (Sparse a) = a
type D (Sparse a) Source # 
type D (Sparse a) = Sparse a

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

Embed a constant

Sparse Gradients

grad :: (Traversable f, Num a) => (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> f a Source #

grad' :: (Traversable f, Num a) => (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> (a, f a) Source #

grads :: (Traversable f, Num a) => (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> Cofree f a Source #

gradWith :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> f b Source #

gradWith' :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> (a, f b) Source #

Sparse Jacobians (synonyms)

jacobian :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (f a) Source #

jacobian' :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (a, f a) Source #

jacobianWith :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (f b) Source #

jacobianWith' :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (a, f b) Source #

jacobians :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (Cofree f a) Source #

Sparse Hessians

hessian :: (Traversable f, Num a) => (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> f (f a) Source #

hessian' :: (Traversable f, Num a) => (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> (a, f (a, f a)) Source #

hessianF :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (f (f a)) Source #

hessianF' :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (a, f (a, f a)) Source #