Safe Haskell	Safe-Inferred
Language	Haskell2010

Downhill.Metric

Synopsis

class Dual (Tang p) (Grad p) => MetricTensor p g where
- evalMetric :: g -> Grad p -> Tang p
- innerProduct :: g -> Grad p -> Grad p -> MScalar p
- sqrNorm :: g -> Grad p -> MScalar p

Documentation

class Dual (Tang p) (Grad p) => MetricTensor p g where Source #

MetricTensor converts gradients to vectors.

It is really inverse of a metric tensor, because it maps cotangent space into tangent space. Gradient descent doesn't need metric tensor, it needs inverse.

Minimal complete definition

evalMetric

Methods

evalMetric :: g -> Grad p -> Tang p Source #

m must be symmetric:

evalGrad x (evalMetric m y) = evalGrad y (evalMetric m x)

innerProduct :: g -> Grad p -> Grad p -> MScalar p Source #

innerProduct m x y = evalGrad x (evalMetric m y)

sqrNorm :: g -> Grad p -> MScalar p Source #

sqrNorm m x = innerProduct m x x

Instances

Instances details

MetricTensor Integer Integer Source #
Instance details Defined in Downhill.Metric Methods evalMetric :: Integer -> Grad Integer -> Tang Integer Source # innerProduct :: Integer -> Grad Integer -> Grad Integer -> MScalar Integer Source # sqrNorm :: Integer -> Grad Integer -> MScalar Integer Source #
MetricTensor Double Double Source #
Instance details Defined in Downhill.Metric Methods evalMetric :: Double -> Grad Double -> Tang Double Source # innerProduct :: Double -> Grad Double -> Grad Double -> MScalar Double Source # sqrNorm :: Double -> Grad Double -> MScalar Double Source #
MetricTensor Float Float Source #
Instance details Defined in Downhill.Metric Methods evalMetric :: Float -> Grad Float -> Tang Float Source # innerProduct :: Float -> Grad Float -> Grad Float -> MScalar Float Source # sqrNorm :: Float -> Grad Float -> MScalar Float Source #
Num a => MetricTensor (AsNum a) (AsNum a) Source #
Instance details Defined in Downhill.BVar.Num Methods evalMetric :: AsNum a -> Grad (AsNum a) -> Tang (AsNum a) Source # innerProduct :: AsNum a -> Grad (AsNum a) -> Grad (AsNum a) -> MScalar (AsNum a) Source # sqrNorm :: AsNum a -> Grad (AsNum a) -> MScalar (AsNum a) Source #
(MScalar a ~ MScalar b, MetricTensor a ma, MetricTensor b mb) => MetricTensor (a, b) (ma, mb) Source #
Instance details Defined in Downhill.Metric Methods evalMetric :: (ma, mb) -> Grad (a, b) -> Tang (a, b) Source # innerProduct :: (ma, mb) -> Grad (a, b) -> Grad (a, b) -> MScalar (a, b) Source # sqrNorm :: (ma, mb) -> Grad (a, b) -> MScalar (a, b) Source #
(MScalar a ~ MScalar b, MScalar a ~ MScalar c, MetricTensor a ma, MetricTensor b mb, MetricTensor c mc) => MetricTensor (a, b, c) (ma, mb, mc) Source #
Instance details Defined in Downhill.Metric Methods evalMetric :: (ma, mb, mc) -> Grad (a, b, c) -> Tang (a, b, c) Source # innerProduct :: (ma, mb, mc) -> Grad (a, b, c) -> Grad (a, b, c) -> MScalar (a, b, c) Source # sqrNorm :: (ma, mb, mc) -> Grad (a, b, c) -> MScalar (a, b, c) Source #