Copyright	(c) Edward Kmett 2010-2021
License	BSD3
Maintainer	ekmett@gmail.com
Stability	experimental
Portability	GHC only
Safe Haskell	None
Language	Haskell2010

Numeric.AD.Internal.Sparse.Double

Description

Unsafe and often partial combinators intended for internal usage.

Handle with care.

Synopsis

newtype Monomial = Monomial (IntMap Int)
emptyMonomial :: Monomial
addToMonomial :: Int -> Monomial -> Monomial
indices :: Monomial -> [Int]
data SparseDouble
- = Sparse !Double (IntMap SparseDouble)
- | Zero
apply :: Traversable f => (f SparseDouble -> b) -> f Double -> b
vars :: Traversable f => f Double -> f SparseDouble
d :: Traversable f => f b -> SparseDouble -> f Double
d' :: Traversable f => f Double -> SparseDouble -> (Double, f Double)
ds :: Traversable f => f b -> SparseDouble -> Cofree f Double
skeleton :: Traversable f => f a -> f Int
spartial :: [Int] -> SparseDouble -> Maybe Double
partial :: [Int] -> SparseDouble -> Double
vgrad :: Grad i o o' => i -> o
vgrad' :: Grad i o o' => i -> o'
vgrads :: Grads i o => i -> o
class Grad i o o' | i -> o o', o -> i o', o' -> i o where
- pack :: i -> [SparseDouble] -> SparseDouble
- unpack :: ([Double] -> [Double]) -> o
- unpack' :: ([Double] -> (Double, [Double])) -> o'
class Grads i o | i -> o, o -> i where
- packs :: i -> [SparseDouble] -> SparseDouble
- unpacks :: ([Double] -> Cofree [] Double) -> o
terms :: Monomial -> [(Integer, Monomial, Monomial)]
primal :: SparseDouble -> Double

Documentation

newtype Monomial Source #

Constructors

Monomial (IntMap Int)

emptyMonomial :: Monomial Source #

addToMonomial :: Int -> Monomial -> Monomial Source #

indices :: Monomial -> [Int] Source #

data SparseDouble 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 distinct nth partial derivatives of a function with k inputs.

Constructors

Sparse !Double (IntMap SparseDouble)
Zero

Instances

Instances details

Enum SparseDouble Source #
Instance details 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] #
Eq SparseDouble Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double Methods (==) :: SparseDouble -> SparseDouble -> Bool # (/=) :: SparseDouble -> SparseDouble -> Bool #
Floating SparseDouble Source #
Instance details 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 #
Fractional SparseDouble Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double Methods (/) :: SparseDouble -> SparseDouble -> SparseDouble # recip :: SparseDouble -> SparseDouble # fromRational :: Rational -> SparseDouble #
Data SparseDouble Source #
Instance details 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 #
Num SparseDouble Source #
Instance details 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 #
Ord SparseDouble Source #
Instance details 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 #
Real SparseDouble Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double Methods toRational :: SparseDouble -> Rational #
RealFloat SparseDouble Source #
Instance details 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 #
RealFrac SparseDouble Source #
Instance details 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 Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double Methods showsPrec :: Int -> SparseDouble -> ShowS # show :: SparseDouble -> String # showList :: [SparseDouble] -> ShowS #
Erf SparseDouble Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double Methods erf :: SparseDouble -> SparseDouble # erfc :: SparseDouble -> SparseDouble # erfcx :: SparseDouble -> SparseDouble # normcdf :: SparseDouble -> SparseDouble #
InvErf SparseDouble Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double Methods inverf :: SparseDouble -> SparseDouble # inverfc :: SparseDouble -> SparseDouble # invnormcdf :: SparseDouble -> SparseDouble #
Mode SparseDouble Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double Associated Types type Scalar SparseDouble Source # Methods isKnownConstant :: SparseDouble -> Bool Source # asKnownConstant :: SparseDouble -> Maybe (Scalar SparseDouble) Source # isKnownZero :: SparseDouble -> Bool Source # auto :: Scalar SparseDouble -> SparseDouble Source # (^) :: Scalar SparseDouble -> SparseDouble -> SparseDouble Source # (^) :: SparseDouble -> Scalar SparseDouble -> SparseDouble Source # (^/) :: SparseDouble -> Scalar SparseDouble -> SparseDouble Source # zero :: SparseDouble Source #
Jacobian SparseDouble Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double Associated Types type D SparseDouble Source # Methods unary :: (Scalar SparseDouble -> Scalar SparseDouble) -> D SparseDouble -> SparseDouble -> SparseDouble Source # lift1 :: (Scalar SparseDouble -> Scalar SparseDouble) -> (D SparseDouble -> D SparseDouble) -> SparseDouble -> SparseDouble Source # lift1_ :: (Scalar SparseDouble -> Scalar SparseDouble) -> (D SparseDouble -> D SparseDouble -> D SparseDouble) -> SparseDouble -> SparseDouble Source # binary :: (Scalar SparseDouble -> Scalar SparseDouble -> Scalar SparseDouble) -> D SparseDouble -> D SparseDouble -> SparseDouble -> SparseDouble -> SparseDouble Source # lift2 :: (Scalar SparseDouble -> Scalar SparseDouble -> Scalar SparseDouble) -> (D SparseDouble -> D SparseDouble -> (D SparseDouble, D SparseDouble)) -> SparseDouble -> SparseDouble -> SparseDouble Source # lift2_ :: (Scalar SparseDouble -> Scalar SparseDouble -> Scalar SparseDouble) -> (D SparseDouble -> D SparseDouble -> D SparseDouble -> (D SparseDouble, D SparseDouble)) -> SparseDouble -> SparseDouble -> SparseDouble Source #
Grad SparseDouble [Double] (Double, [Double]) Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double Methods pack :: SparseDouble -> [SparseDouble] -> SparseDouble Source # unpack :: ([Double] -> [Double]) -> [Double] Source # unpack' :: ([Double] -> (Double, [Double])) -> (Double, [Double]) Source #
Grads SparseDouble (Cofree [] Double) Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double Methods packs :: SparseDouble -> [SparseDouble] -> SparseDouble Source # unpacks :: ([Double] -> Cofree [] Double) -> Cofree [] Double Source #
Grads i o => Grads (SparseDouble -> i) (Double -> o) Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double Methods packs :: (SparseDouble -> i) -> [SparseDouble] -> SparseDouble Source # unpacks :: ([Double] -> Cofree [] Double) -> Double -> o Source #
Grad i o o' => Grad (SparseDouble -> i) (Double -> o) (Double -> o') Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double Methods pack :: (SparseDouble -> i) -> [SparseDouble] -> SparseDouble Source # unpack :: ([Double] -> [Double]) -> Double -> o Source # unpack' :: ([Double] -> (Double, [Double])) -> Double -> o' Source #
type Scalar SparseDouble Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double type Scalar SparseDouble = Double
type D SparseDouble Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double type D SparseDouble = SparseDouble

apply :: Traversable f => (f SparseDouble -> b) -> f Double -> b Source #

vars :: Traversable f => f Double -> f SparseDouble Source #

d :: Traversable f => f b -> SparseDouble -> f Double Source #

d' :: Traversable f => f Double -> SparseDouble -> (Double, f Double) Source #

ds :: Traversable f => f b -> SparseDouble -> Cofree f Double Source #

skeleton :: Traversable f => f a -> f Int Source #

spartial :: [Int] -> SparseDouble -> Maybe Double Source #

partial :: [Int] -> SparseDouble -> Double Source #

vgrad :: Grad i o o' => i -> o Source #

vgrad' :: Grad i o o' => i -> o' Source #

vgrads :: Grads i o => i -> o Source #

class Grad i o o' | i -> o o', o -> i o', o' -> i o where Source #

Methods

pack :: i -> [SparseDouble] -> SparseDouble Source #

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

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

Instances

Instances details

Grad SparseDouble [Double] (Double, [Double]) Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double Methods pack :: SparseDouble -> [SparseDouble] -> SparseDouble Source # unpack :: ([Double] -> [Double]) -> [Double] Source # unpack' :: ([Double] -> (Double, [Double])) -> (Double, [Double]) Source #
Grad i o o' => Grad (SparseDouble -> i) (Double -> o) (Double -> o') Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double Methods pack :: (SparseDouble -> i) -> [SparseDouble] -> SparseDouble Source # unpack :: ([Double] -> [Double]) -> Double -> o Source # unpack' :: ([Double] -> (Double, [Double])) -> Double -> o' Source #

class Grads i o | i -> o, o -> i where Source #

Methods

packs :: i -> [SparseDouble] -> SparseDouble Source #

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

Instances

Instances details

Grads SparseDouble (Cofree [] Double) Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double Methods packs :: SparseDouble -> [SparseDouble] -> SparseDouble Source # unpacks :: ([Double] -> Cofree [] Double) -> Cofree [] Double Source #
Grads i o => Grads (SparseDouble -> i) (Double -> o) Source #
Instance details Defined in Numeric.AD.Internal.Sparse.Double Methods packs :: (SparseDouble -> i) -> [SparseDouble] -> SparseDouble Source # unpacks :: ([Double] -> Cofree [] Double) -> Double -> o Source #

terms :: Monomial -> [(Integer, Monomial, Monomial)] Source #

primal :: SparseDouble -> Double Source #