emmy.dual
This namespace contains an implementation of [[Dual]], a type that forms the basis for the forward-mode automatic differentiation implementation in emmy.
See emmy.calculus.derivative for a fleshed-out derivative implementation
using [[Dual]].
This namespace contains an implementation of [[Dual]], a type that forms the basis for the forward-mode automatic differentiation implementation in emmy. See [[emmy.calculus.derivative]] for a fleshed-out derivative implementation using [[Dual]].
bundle-elementclj/s
(bundle-element primal)(bundle-element primal tag)(bundle-element primal tangent tag)Returns a new [[Dual]] object with the supplied primal and tangent
components, and the supplied internal tag that this [[Dual]] will
carry around to prevent perturbation confusion.
If the tangent component is 0, acts as identity on primal. tangent
defaults to 1.
tag defaults to a side-effecting call to fresh-tag; you can retrieve
this unknown tag by calling tag on the returned [[Dual]].
Returns a new [[Dual]] object with the supplied `primal` and `tangent` components, and the supplied internal `tag` that this [[Dual]] will carry around to prevent perturbation confusion. If the `tangent` component is `0`, acts as identity on `primal`. `tangent` defaults to 1. `tag` defaults to a side-effecting call to [[fresh-tag]]; you can retrieve this unknown tag by calling [[tag]] on the returned [[Dual]].
compareclj/s
(compare a b)Comparator that compares [[Dual]] instances with each other or
non-differentials using only the primal of each instance. Matches the
response of equiv.
Acts as emmy.value/compare for non-differentials.
Comparator that compares [[Dual]] instances with each other or non-differentials using only the [[primal]] of each instance. Matches the response of [[equiv]]. Acts as [[emmy.value/compare]] for non-differentials.
compare-fullclj/s
(compare-full a b)Comparator that compares [[Dual]] instances with each other or
non-differentials using all tangent terms each instance. Matches the response
of eq.
Acts as emmy.value/compare for non-differentials.
Comparator that compares [[Dual]] instances with each other or non-differentials using all tangent terms each instance. Matches the response of [[eq]]. Acts as [[emmy.value/compare]] for non-differentials.
derivativeclj/s
(derivative f)Returns a single-argument function of that, when called with an argument x,
returns the derivative of f at x using forward-mode automatic
differentiation.
For numerical differentiation,
see emmy.numerical.derivative/D-numeric.
f must be built out of generic operations that know how to handle [[Dual]]
inputs in addition to any types that a normal (f x) call would present. This
restriction does not apply to operations like putting x into a container
or destructuring; just primitive function calls.
Returns a single-argument function of that, when called with an argument `x`, returns the derivative of `f` at `x` using forward-mode automatic differentiation. For numerical differentiation, see [[emmy.numerical.derivative/D-numeric]]. `f` must be built out of generic operations that know how to handle [[Dual]] inputs in addition to any types that a normal `(f x)` call would present. This restriction does _not_ apply to operations like putting `x` into a container or destructuring; just primitive function calls.
dual?clj/s
(dual? dx)Returns true if the supplied object is an instance of [[Dual]], false otherwise.
Returns true if the supplied object is an instance of [[Dual]], false otherwise.
eqclj/s
(eq _)(eq a b)(eq a b & more)For non-differentials, this is identical to emmy.value/=.
For [[Dual]] instances, equality acts on tangent components too.
If you want to ignore the tangent components, use equiv.
For non-differentials, this is identical to [[emmy.value/=]]. For [[Dual]] instances, equality acts on tangent components too. If you want to ignore the tangent components, use [[equiv]].
equivclj/s
(equiv _)(equiv a b)(equiv a b & more)Returns true if all of the supplied objects have equal primals, false
otherwise.
Use equiv if you want to compare scalars with
[[Dual]]s and ignore the tangent. If you do want to take the tangent into
account, prefer eq.
Returns true if all of the supplied objects have equal [[primal]]s, false otherwise. Use [[equiv]] if you want to compare scalars with [[Dual]]s and ignore the tangent. If you _do_ want to take the tangent into account, prefer [[eq]].
fresh-tagclj/s
(fresh-tag)Returns a new, unique tag for use by a perturbation in an automatic differentiation pass.
Returns a new, unique tag for use by a perturbation in an automatic differentiation pass.
IPerturbedclj/sprotocol
extract-idclj/s
(extract-id this id)Given an instance of [[Completed]] (or a container type with [[Completed]]
instances at its leaves) and the id of an [[emmy.tape/TapeCell]], returns
the partial derivative associated with that [[emmy.tape/TapeCell]]'s
id.
This function is an internal implementation detail of reverse-mode automatic differentiation.
Given an instance of [[Completed]] (or a container type with [[Completed]] instances at its leaves) and the `id` of an [[emmy.tape/TapeCell]], returns the partial derivative associated with that [[emmy.tape/TapeCell]]'s `id`. This function is an internal implementation detail of reverse-mode automatic differentiation.
extract-tangentclj/s
(extract-tangent this tag mode)If this is perturbed, return the tangent component paired with the
supplied tag. Else, returns ([[emmy.value/zero-like]] this).
If `this` is perturbed, return the tangent component paired with the supplied tag. Else, returns `([[emmy.value/zero-like]] this)`.
replace-tagclj/s
(replace-tag this old-tag new-tag)If this is perturbed, Returns a similar object with the perturbation
modified by replacing any appearance of old-tag with new-tag. Else,
return this.
If `this` is perturbed, Returns a similar object with the perturbation modified by replacing any appearance of `old-tag` with `new-tag`. Else, return `this`.
primalclj/s
(primal dx)(primal dx tag)If dx is an instance of [[Dual]] returns the primal component. Else, acts
as identity.
If the optional tag is supplied, [[primal-part]] acts as identity
for [[Dual]] instances with a non-matching tag.
If `dx` is an instance of [[Dual]] returns the `primal` component. Else, acts as identity. If the optional `tag` is supplied, [[primal-part]] acts as identity for [[Dual]] instances with a non-matching tag.
primal-tangent-pairclj/s
(primal-tangent-pair dx)(primal-tangent-pair dx t)Returns a pair of the primal and tangent components of the supplied dx, with
respect to the supplied tag. See the docs for primal
and tangent for more details.
primal-tangent-pair is equivalent to
[([[primal]] dx tag) ([[tangent]] dx tag)]
but slightly more efficient if you need both.
Returns a pair of the primal and tangent components of the supplied `dx`, with respect to the supplied `tag`. See the docs for [[primal]] and [[tangent]] for more details. [[primal-tangent-pair]] is equivalent to `[([[primal]] dx tag) ([[tangent]] dx tag)]` but slightly more efficient if you need both.
tagclj/s
(tag dx)If dx is an instance of [[Dual]] returns the tag component. Else, acts
as nil.
If `dx` is an instance of [[Dual]] returns the `tag` component. Else, acts as nil.
tag-active?clj/s
(tag-active? tag)Returns true if tag is an element of *active-tags* (and therefore pending
for extraction by some nested derivative), false otherwise.
Returns true if `tag` is an element of [[*active-tags*]] (and therefore pending for extraction by some nested derivative), false otherwise.
tangentclj/s
(tangent dx)(tangent dx tag)If dx is an instance of [[Dual]] returns the tangent component. Else, returns 0.
If the optional tag is supplied, [[primal-part]] returns 0 for [[Dual]]
instances with a non-matching tag.
If `dx` is an instance of [[Dual]] returns the `tangent` component. Else, returns 0. If the optional `tag` is supplied, [[primal-part]] returns 0 for [[Dual]] instances with a non-matching tag.
with-active-tagclj/s
(with-active-tag tag f args)Like apply, but conj-es tag onto the dynamic variable *active-tags*
inside the scope of f.
Returns the result of applying f to args.
Like `apply`, but conj-es `tag` onto the dynamic variable [[*active-tags*]] inside the scope of `f`. Returns the result of applying `f` to `args`.
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