From 834afc60876e25e0699cfdf017a4e86256cc53cf Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Thu, 1 Feb 2024 13:20:35 +0000 Subject: [PATCH] build based on 43736ee --- previews/PR256/.documenter-siteinfo.json | 1 + previews/PR256/api.html | 13 + previews/PR256/assets/documenter.js | 893 ++++++++++++++++++ previews/PR256/assets/indigo.css | 88 ++ .../PR256/assets/themes/documenter-dark.css | 7 + .../PR256/assets/themes/documenter-light.css | 9 + previews/PR256/assets/themeswap.js | 84 ++ previews/PR256/assets/warner.js | 52 + previews/PR256/index.html | 20 + previews/PR256/reading_list.html | 2 + previews/PR256/search_index.js | 3 + previews/PR256/siteinfo.js | 1 + previews/PR256/terminology.pdf | Bin 0 -> 416554 bytes 13 files changed, 1173 insertions(+) create mode 100644 previews/PR256/.documenter-siteinfo.json create mode 100644 previews/PR256/api.html create mode 100644 previews/PR256/assets/documenter.js create mode 100644 previews/PR256/assets/indigo.css create mode 100644 previews/PR256/assets/themes/documenter-dark.css create mode 100644 previews/PR256/assets/themes/documenter-light.css create mode 100644 previews/PR256/assets/themeswap.js create mode 100644 previews/PR256/assets/warner.js create mode 100644 previews/PR256/index.html create mode 100644 previews/PR256/reading_list.html create mode 100644 previews/PR256/search_index.js create mode 100644 previews/PR256/siteinfo.js create mode 100644 previews/PR256/terminology.pdf diff --git a/previews/PR256/.documenter-siteinfo.json b/previews/PR256/.documenter-siteinfo.json new file mode 100644 index 00000000..0ff02952 --- /dev/null +++ b/previews/PR256/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.11.0-DEV.1437","generation_timestamp":"2024-02-01T13:20:29","documenter_version":"1.1.2"}} \ No newline at end of file diff --git a/previews/PR256/api.html b/previews/PR256/api.html new file mode 100644 index 00000000..9c580a49 --- /dev/null +++ b/previews/PR256/api.html @@ -0,0 +1,13 @@ + +API · Diffractor
GitHub

Diffractor

Diffractor.AbstractTangentBundle — Type
abstract type AbstractTangentBundle{N, B}; end

This type represents the N-th order (iterated) tangent bundle [1] TⁿB over some base (Riemannian) manifold B. Note that TⁿB is itself another manifold and thus in particular a vector space (over ℝ). As such, subtypes of this abstract type are expected to support the usual vector space operations.

However, beyond that, this abstract type makes no guarantee about the representation. That said, to gain intution for what this object is, it makes sense to pick some explicit bases and write down examples.

To that end, suppose that B=ℝ. Then T¹B=T¹ℝ is just our usual notion of a dual number, i.e. for some element η ∈ T¹ℝ, we may consider η = a + bϵ for real numbers (a, b) and ϵ an infinitessimal differential such that ϵ^2 = 0.

Equivalently, we may think of η as being identified with the vector (a, b) ∈ ℝ² with some additional structure. The same form essentially holds for general B, where we may write (as sets):

T¹B = {(a, b) | a ∈ B, b ∈ Tₐ B }

Note that these vectors are orthogonal to those in the underlying base space. For example, if B=ℝ², then we have:

T¹ℝ² = {([aₓ, a_y], [bₓ, b_y]) | [aₓ, a_y] ∈ ℝ², [bₓ, b_y] ∈ Tₐ ℝ² }

For convenience, we will sometimes writes these in one as:

η ∈ T ℝ²  = aₓ x̂ + a_y ŷ + bₓ ∂/∂x|_aₓ x + b_y ∂/∂y|_{a_y}
+         := aₓ x̂ + a_y ŷ + bₓ ∂/∂¹x + b_y ∂/∂¹y
+         := [aₓ, a_y] + [bₓ, b_y] ∂/∂¹
+         := a + b ∂/∂¹
+         := a + b ∂₁

These are all definitional equivalences and we will mostly work with the final form. An important thing to keep in mind though is that the subscript on ∂₁ does not refer to a dimension of the underlying base manifold (for which we will rarely pick an explicit basis here), but rather tags the basis of the tangent bundle.

Let us iterate this construction to second order. We have:

T²B = T¹(T¹B) = { (α, β) | α ∈ T¹B, β ∈ T_α T¹B }
+              = { ((a, b), (c, d)) | a ∈ B, b ∈ Tₐ B, c ∈ Tₐ B, d ∈ T²ₐ B}

(where in the last equality we used the linearity of the tangent vector).

Following our above notation, we will canonically write such an element as:

  a + b ∂₁ + c ∂₂ + d ∂₂ ∂₁
+= a + b ∂₁ + c ∂₂ + d ∂₁ ∂₂

It is worth noting that there still only is one base point a of the underlying manifold and thus TⁿB is a vector bundle over B for all N.

Further Reading

[1] https://en.wikipedia.org/wiki/Tangent_bundle

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Diffractor.ExplicitTangent — Type
struct ExplicitTangent{P}

A fully explicit coordinate representation of the tangent space, represented by a vector of 2^N-1 partials.

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Diffractor.Jet — Type
struct Jet{T, N}

Represents the truncated (N-1)-th order Taylor series

f(a) + (x-a)f'(a) + 1/2(x-a)^2f''(a) + ...

Coefficients are stored in unscaled form. For a jet j, several operations are supported:

  1. Indexing j[i] returns fᵢ
  2. Evaluation j(x) semantically evaluates the truncated taylor series at x. However, evaluation is restricted to be precisely at a - the additional information in the taylor series is only available through derivatives. Mathematically this corresponds to an infinitessimal ball around a.
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Diffractor.TangentBundle — Type
struct TangentBundle{N, B, P}

Represents a tangent bundle as an explicit primal together with some representation of the tangent space.

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Diffractor.TaylorTangent — Type
struct TaylorTangent{C}

The taylor bundle construction mods out the full N-th order tangent bundle by the equivalence relation that coefficients of like-order basis elements be equal, i.e. rather than a generic element

a + b ∂₁ + c ∂₂ + d ∂₃ + e ∂₂ ∂₁ + f ∂₃ ∂₁ + g ∂₃ ∂₂ + h ∂₃ ∂₂ ∂₁

we have a tuple (c₀, c₁, c₂, c₃) corresponding to the full element

c₀ + c₁ ∂₁ + c₁ ∂₂ + c₁ ∂₃ + c₂ ∂₂ ∂₁ + c₂ ∂₃ ∂₁ + c₂ ∂₃ ∂₂ + c₃ ∂₃ ∂₂ ∂₁

i.e.

c₀ + c₁ (∂₁ + ∂₂ + ∂₃) + c₂ (∂₂ ∂₁ + ∂₃ ∂₁ + ∂₃ ∂₂) + c₃ ∂₃ ∂₂ ∂₁

This restriction forms a submanifold of the original manifold. The naming is by analogy with the (truncated) Taylor series

c₀ + c₁ x + 1/2 c₂ x² + 1/3! c₃ x³ + O(x⁴)
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Diffractor.UniformTangent — Type
struct UniformTangent

Represents an N-th order tangent bundle with all unform partials. Particularly useful for representing singleton values.

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Diffractor.∂xⁿ — Type
∂xⁿ{N}(x)

For x in a one dimensional manifold, map x to the trivial, unital, Nth order tangent bundle. It should hold that ∀x ⟨∂ⁿ{1}x(x), dx(x)⟩ = 1

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Diffractor.∂⃖ — Type
∂⃖{N}

∂⃖{N} is the reverse-mode AD optic functor of order N. A call (::∂⃖{N})(f, args...) corresponds to ∂⃖ⁿ f(args...) in the linear encoding of an N-optic (see the terminology guide for definitions of these terms).

In general (::∂⃖{N})(f, args...) will return a tuple of the original primal value f(args...) (in rare cases primitives may modify the primal value - in general we will ignore this rare complication for the purposes of clear documentation) and an optic continuation λ. The interpretation of this continuation depends on the order of the functor:

For example, ∂⃖{1} computes first derivatives. In particular, for a function f, ∂⃖{1}(f, args...) will return the tuple (f(args...), f⋆) (read "f upper-star").

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Diffractor.∂☆ — Type
∂☆{N}

∂☆{N} is the forward-mode AD functor of order N. A call (::∂☆{N})(f, args...) evaluating a function f: A -> B is lifted to its pushforward on the N-th order tangent bundle f⋆: Tⁿ A -> Tⁿ B.

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Diffractor.∇ — Type
∇(f, args...)

Computes the gradient ∇f(x, y, z...) (at (x, y, z...)). In particular, the return value will be a tuple of partial derivatives (∂f/∂x, ∂f/∂y, ∂f/∂z...).

Curried version

Alternatively, ∇ may be curried, essentially giving the gradient as a function:

Examples

julia> using Diffractor: ∇
+
+julia> map(∇(*), (1,2,3), (4,5,6))
+((4.0, 1.0), (5.0, 2.0), (6.0, 3.0))

The derivative ∂f/∂f

Note that since in Julia, there is no distinction between functions and values, there is in principle a partial derivative with respect to the function itself. However, said partial derivative is dropped by this interface. It is however available using the lower level ∂⃖ if desired. This interaction can also be used to obtain gradients with respect to only some of the arguments by using a closure:

∇((x,z)->f(x,y,z))(x, z) # returns (∂f/∂x, ∂f/∂z)

Though of course the same can be obtained by simply indexing the resulting tuple (in well-inferred code there should not be a performance difference between these two options).

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Diffractor.:' — Method
f'

This is a convenience syntax for taking the derivative of a function f: ℝ -> ℝ. In particular, for such a function f'(x) will be the first derivative of f at x (and similar for f''(x) and second derivatives and so on.)

Note that the syntax conflicts with the Base definition for the adjoint of a matrix and thus is not enabled by default. To use it, add the following to the top of your module:

using Diffractor: var"'"

It is also available using the @∂ macro:

@∂ f'(x)
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Diffractor.bundle — Function
bundle(primal, tangent)

Wraps a primal up with a tangent into the appropriate kind of AbstractBundle{1}. This is more or less the Diffractor equivelent of ForwardDiff.jl's Dual type.

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Diffractor.destructure — Method

for a TaylorTangent{N, <:Tuple} this breaks it up unto 1 TaylorTangent{N} for each element of the primal tuple

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Diffractor.dx — Method
dx(x)

dx represents the trival differential one-form of a one dimensional Riemannian manifold M. In particular, it is a section of the cotangent bundle of M, meaning it may be evaluted at a point x of M to obtain an element of the cotangent space T*ₓ M to M at x. We impose no restrictions on the representations of either the manifold itself or the cotangent space.

By default, the only implementation provided identifies T*ₓ ℝ ≃ ℝ, keeping watever type is used to represent ℝ. i.e.

dx(x::Real) = one(x)

However, users may provide additional overloads for custom representations of one dimensional Riemannian manifolds.

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Diffractor.find_end_of_phi_block — Method
find_end_of_phi_block(ir::IRCode, start_search_idx::Int)

Finds the last index within the same basic block, on or after the start_search_idx which is not within a phi block. A phi-block is a run on PhiNodes or nothings that must be the first statements within the basic block.

If start_search_idx is not within a phi block to begin with, then just returns start_search_idx

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Diffractor.forward_diff_no_inf! — Method
forward_diff_no_inf!(ir::IRCode, to_diff::Vector{Pair{SSAValue,Int}}; visit_custom!, transform!)

Internal method which generates the code for forward mode diffentiation

  • ir the IR being differnetation

  • to_diff: collection of all SSA values for which the derivative is to be taken, paired with the order (first deriviative, second derivative etc)

  • visit_custom!(ir::IRCode, ssa, order::Int, recurse::Bool) -> Bool:

	decides if the custom `transform!` should be applied to a `stmt` or not
+	Default: `false` for all statements
  • transform!(ir::IRCode, ssa::SSAValue, order::Int) mutates ir to do a custom tranformation.
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Diffractor.jet_taylor_ev — Method
jet_taylor_ev(::Val{}, jet, taylor)

Generates a closed form arithmetic expression for the N-th component of the action of a 1d jet (of order at least N) on a maximally symmetric (i.e. taylor) tangent bundle element. In particular, if we represent both the jet and the taylor tangent bundle element by their associated canonical taylor series:

j = j₀ + j₁ (x - a) + j₂ 1/2 (x - a)^2 + ... + jₙ 1/n! (x - a)^n
+t = t₀ + t₁ (x - t₀) + t₂ 1/2 (x - t₀)^2 + ... + tₙ 1/n! (x - t₀)^n

then the action of evaluating j on t, is some other taylor series

t′ = a + t′₁ (x - a) + t′₂ 1/2 (x - a)^2 + ... + t′ₙ 1/n! (x - a)^n

The t′ᵢ can be found by explicitly plugging in t for every x and expanding out, dropping terms of orders that are higher. This computes closed form expressions for the t′ᵢ that are hopefully easier on the compiler.

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Diffractor.@∂ — Macro
@∂

Convenice macro for writing partial derivatives. E.g. The expression:

@∂ f(∂x, ∂y)

Will compute the partial derivative ∂^2 f/∂x∂y at (x, y)`. And similarly

@∂ f(∂²x, ∂y)

will compute the derivative ∂^3 f/∂x^2 ∂y at (x,y).

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diff --git a/previews/PR256/assets/documenter.js b/previews/PR256/assets/documenter.js new file mode 100644 index 00000000..58deef09 --- /dev/null +++ b/previews/PR256/assets/documenter.js @@ -0,0 +1,893 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'minisearch': 'https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +window.MathJax = { + "tex": { + "inlineMath": [ + [ + "$", + "$" + ], + [ + "\\(", + "\\)" + ] + ], + "macros": { + "Re": "{\\operatorname{Re}}", + "ip": [ + "{\\left\\langle #1, #2 \\right\\rangle}", + 2 + ], + "tr": "{\\operatorname{tr}}", + "Im": "{\\operatorname{Im}}" + }, + "tags": "ams" + }, + "options": { + "ignoreHtmlClass": "tex2jax_ignore", + "processHtmlClass": "tex2jax_process" + } +} +; + +(function () { + var script = document.createElement('script'); + script.src = 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-svg.js'; + script.async = true; + document.head.appendChild(script); +})(); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function () { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'minisearch'], function($, minisearch) { + +// In general, most search related things will have "search" as a prefix. +// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +let results = []; +let timer = undefined; + +let data = documenterSearchIndex["docs"].map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; +}); + +// list below is the lunr 2.1.3 list minus the intersect with names(Base) +// (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) +// ideally we'd just filter the original list but it's not available as a variable +const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", +]); + +let index = new minisearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with search results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + boost: { title: 100 }, + fuzzy: 2, + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + tokenize: (string) => string.split(/[\s\-\.]+/), + }, +}); + +index.addAll(data); + +let filters = [...new Set(data.map((x) => x.category))]; +var modal_filters = make_modal_body_filters(filters); +var filter_results = []; + +$(document).on("keyup", ".documenter-search-input", function (event) { + // Adding a debounce to prevent disruptions from super-speed typing! + debounce(() => update_search(filter_results), 300); +}); + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + $(this).removeClass("search-filter-selected"); + } else { + $(this).addClass("search-filter-selected"); + } + + // Adding a debounce to prevent disruptions from crazy clicking! + debounce(() => get_filters(), 300); +}); + +/** + * A debounce function, takes a function and an optional timeout in milliseconds + * + * @function callback + * @param {number} timeout + */ +function debounce(callback, timeout = 300) { + clearTimeout(timer); + timer = setTimeout(callback, timeout); +} + +/** + * Make/Update the search component + * + * @param {string[]} selected_filters + */ +function update_search(selected_filters = []) { + let initial_search_body = ` +
Type something to get started!
+ `; + + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + results = index.search(querystring, { + filter: (result) => { + // Filtering results + if (selected_filters.length === 0) { + return result.score >= 1; + } else { + return ( + result.score >= 1 && selected_filters.includes(result.category) + ); + } + }, + }); + + let search_result_container = ``; + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + results.forEach(function (result) { + if (result.location) { + // Checking for duplication of results for the same page + if (!links.includes(result.location)) { + search_results += make_search_result(result, querystring); + count++; + } + + links.push(result.location); + } + }); + + let result_count = `
${count} result(s)
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + filter_results = []; + modal_filters = make_modal_body_filters(filters, filter_results); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(initial_search_body); + } +} + +/** + * Make the modal filter html + * + * @param {string[]} filters + * @param {string[]} selected_filters + * @returns string + */ +function make_modal_body_filters(filters, selected_filters = []) { + let str = ``; + + filters.forEach((val) => { + if (selected_filters.includes(val)) { + str += `${val}`; + } else { + str += `${val}`; + } + }); + + let filter_html = ` +
+ Filters: + ${str} +
+ `; + + return filter_html; +} + +/** + * Make the result component given a minisearch result data object and the value of the search input as queryString. + * To view the result object structure, refer: https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ +function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`\\b${querystring}\\b`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`\\b${querystring}\\b`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${result.title}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; +} + +/** + * Get selected filters, remake the filter html and lastly update the search modal + */ +function get_filters() { + let ele = $(".search-filters .search-filter-selected").get(); + filter_results = ele.map((x) => $(x).text().toLowerCase()); + modal_filters = make_modal_body_filters(filters, filter_results); + update_search(filter_results); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+`; + +let initial_search_body = ` +
Type something to get started!
+`; + +let search_modal_footer = ` + +`; + +$(document.body).append( + ` + + ` +); + +document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); +}); + +document.querySelector(".close-search-modal").addEventListener("click", () => { + closeModal(); +}); + +$(document).on("click", ".search-result-link", function () { + closeModal(); +}); + +document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; +}); + +// Functions to open and close a modal +function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); +} + +function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); +} + +document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/previews/PR256/assets/indigo.css b/previews/PR256/assets/indigo.css new file mode 100644 index 00000000..7dafd68a --- /dev/null +++ b/previews/PR256/assets/indigo.css @@ -0,0 +1,88 @@ +@font-face { + font-family: JuliaMono; + src: local("JuliaMono"), url("https://cdn.jsdelivr.net/gh/cormullion/juliamono/webfonts/JuliaMono-Regular.woff2"); } + +html.theme--documenter-dark pre, +html.theme--documenter-dark code { + font-family: "JuliaMono"; } + +html:not(.theme--documenter-dark) body #documenter a { + color: #4595D1; } + +html:not(.theme--documenter-dark) body #documenter a:hover, html:not(.theme--documenter-dark) body #documenter a:focus { + color: #194E82; } + +html:not(.theme--documenter-dark) body #documenter .docs-sidebar { + box-shadow: none; + color: #FFFFFF; + background-color: #194E82; } + html:not(.theme--documenter-dark) body #documenter .docs-sidebar .docs-package-name a, html:not(.theme--documenter-dark) body #documenter .docs-sidebar .docs-package-name a:hover { + color: #FFFFFF; } + html:not(.theme--documenter-dark) body #documenter .docs-sidebar ul.docs-menu { + border-top: none; } + html:not(.theme--documenter-dark) body #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal .tocitem:hover, html:not(.theme--documenter-dark) body #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem:hover, html:not(.theme--documenter-dark) body #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem, html:not(.theme--documenter-dark) body #documenter .docs-sidebar ul.docs-menu .tocitem:hover { + color: #FFFFFF; + background-color: #4595D1; } + html:not(.theme--documenter-dark) body #documenter .docs-sidebar ul.docs-menu .tocitem { + color: #FFFFFF; + background: none; } + html:not(.theme--documenter-dark) body #documenter .docs-sidebar ul.docs-menu li.is-active { + border-top: none; + border-bottom: none; } + html:not(.theme--documenter-dark) body #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal { + margin: 0; + border-top: none; } + html:not(.theme--documenter-dark) body #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal li { + margin-top: 0; } + html:not(.theme--documenter-dark) body #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal .tocitem { + color: #194E82; + background-color: #FFFFFF; + padding: 0.5em; + padding-left: 1em; } + +html:not(.theme--documenter-dark) body #documenter article#documenter-page a.docs-heading-anchor { + color: #194E82; } + +html:not(.theme--documenter-dark) body #documenter pre, html:not(.theme--documenter-dark) body #documenter code { + color: inherit; + font-family: "JuliaMono"; } + html:not(.theme--documenter-dark) body #documenter pre .hljs-meta, html:not(.theme--documenter-dark) body #documenter code .hljs-meta { + color: #4595D1; } + html:not(.theme--documenter-dark) body #documenter pre .hljs-keyword, html:not(.theme--documenter-dark) body #documenter code .hljs-keyword { + color: #194E82; } + +.admonition.is-category-terminology { + background-color: #FFFEDD; + border-color: #FFEC8B; } + .admonition.is-category-terminology > .admonition-header { + background-color: #FFEC8B; + color: black; } + .admonition.is-category-terminology > .admonition-header:before { + content: "Terminology: "; + font-family: inherit; + font-weight: bold; } + +html.theme--documenter-dark .admonition.is-category-terminology { + border-color: #FFEC8B; } + +details { + padding-left: 1rem; + padding-right: 1rem; + padding-bottom: 1rem; + background: aliceblue; } + +html.theme--documenter-dark details { + background: #282f2f; } + +.video-container { + position: relative; + width: 100%; + padding-bottom: 56.25%; } + +.video-container > iframe { + position: absolute; + top: 0; + left: 0; + width: 100%; + height: 100%; + border: 0; } diff --git a/previews/PR256/assets/themes/documenter-dark.css b/previews/PR256/assets/themes/documenter-dark.css new file mode 100644 index 00000000..ec054ecc --- /dev/null +++ b/previews/PR256/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ +html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select select,html.theme--documenter-dark .textarea,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:.4em;box-shadow:none;display:inline-flex;font-size:1rem;height:2.5em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.5em - 1px);padding-left:calc(0.75em - 1px);padding-right:calc(0.75em - 1px);padding-top:calc(0.5em - 1px);position:relative;vertical-align:top}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus,html.theme--documenter-dark .pagination-ellipsis:focus,html.theme--documenter-dark .file-cta:focus,html.theme--documenter-dark .file-name:focus,html.theme--documenter-dark .select select:focus,html.theme--documenter-dark .textarea:focus,html.theme--documenter-dark .input:focus,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:focus,html.theme--documenter-dark .button:focus,html.theme--documenter-dark .is-focused.pagination-previous,html.theme--documenter-dark .is-focused.pagination-next,html.theme--documenter-dark .is-focused.pagination-link,html.theme--documenter-dark .is-focused.pagination-ellipsis,html.theme--documenter-dark .is-focused.file-cta,html.theme--documenter-dark .is-focused.file-name,html.theme--documenter-dark .select select.is-focused,html.theme--documenter-dark .is-focused.textarea,html.theme--documenter-dark .is-focused.input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--documenter-dark .is-focused.button,html.theme--documenter-dark .pagination-previous:active,html.theme--documenter-dark .pagination-next:active,html.theme--documenter-dark .pagination-link:active,html.theme--documenter-dark .pagination-ellipsis:active,html.theme--documenter-dark .file-cta:active,html.theme--documenter-dark .file-name:active,html.theme--documenter-dark .select select:active,html.theme--documenter-dark .textarea:active,html.theme--documenter-dark .input:active,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:active,html.theme--documenter-dark .button:active,html.theme--documenter-dark .is-active.pagination-previous,html.theme--documenter-dark .is-active.pagination-next,html.theme--documenter-dark .is-active.pagination-link,html.theme--documenter-dark .is-active.pagination-ellipsis,html.theme--documenter-dark .is-active.file-cta,html.theme--documenter-dark .is-active.file-name,html.theme--documenter-dark .select select.is-active,html.theme--documenter-dark .is-active.textarea,html.theme--documenter-dark 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.textarea,html.theme--documenter-dark fieldset[disabled] .input,html.theme--documenter-dark fieldset[disabled] #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark #documenter .docs-sidebar fieldset[disabled] form.docs-search>input,fieldset[disabled] html.theme--documenter-dark .button,html.theme--documenter-dark fieldset[disabled] .button{cursor:not-allowed}html.theme--documenter-dark .tabs,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .breadcrumb,html.theme--documenter-dark .file,html.theme--documenter-dark .button,.is-unselectable{-webkit-touch-callout:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none}html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after,html.theme--documenter-dark 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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.button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter 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#documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter 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img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4 img,html.theme--documenter-dark .image.is-3by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--documenter-dark .image.is-2by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--documenter-dark .image.is-2by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--documenter-dark .image.is-3by5 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--documenter-dark .image.is-3by5 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--documenter-dark .image.is-9by16 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--documenter-dark .image.is-9by16 .has-ratio,html.theme--documenter-dark #documenter 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Gets put into the tag.. +function set_theme_from_local_storage() { + // Initialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if (window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the users preference is for dark color scheme + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === true; + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } + // If we find a matching theme (and it's not the default), we'll set active to non-null + if (themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if (themename !== theme) disabled.push(ss); + } + var activeTheme = null; + if (active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } + } + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); + } +} +set_theme_from_local_storage(); diff --git a/previews/PR256/assets/warner.js b/previews/PR256/assets/warner.js new file mode 100644 index 00000000..3f6f5d00 --- /dev/null +++ b/previews/PR256/assets/warner.js @@ -0,0 +1,52 @@ +function maybeAddWarning() { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return; + } + + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return; + } + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return; + } + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement("meta"); + meta.name = "robots"; + meta.content = "noindex"; + + document.getElementsByTagName("head")[0].appendChild(meta); + } + + const div = document.createElement("div"); + div.classList.add("outdated-warning-overlay"); + const closer = document.createElement("button"); + closer.classList.add("outdated-warning-closer", "delete"); + closer.addEventListener("click", function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE; + div.innerHTML = + 'This documentation is not for the latest stable release, but for either the development version or an older release.
Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); +} else { + maybeAddWarning(); +} diff --git a/previews/PR256/index.html b/previews/PR256/index.html new file mode 100644 index 00000000..6e5bc0a2 --- /dev/null +++ b/previews/PR256/index.html @@ -0,0 +1,20 @@ + +Introduction · Diffractor
GitHub

Diffractor

Next-generation AD

PDF containing the terminology

Getting Started

⚠️This certainly has bugs and issues. Please open issues on Diffractor.jl, or AbstractDifferentiation.jl as appropriate.⚠️

Diffractor's public API is via AbstractDifferentiation.jl. Please see the AbstractDifferentiation.jl docs for detailed usage.

julia> using Diffractor: DiffractorForwardBackend
+
+julia> using AbstractDifferentiation: derivative, jacobian
+
+julia> derivative(DiffractorForwardBackend(), +, 1.5, 10.0)
+(1.0, 1.0)
+
+julia> derivative(DiffractorForwardBackend(), *, 1.5, 10.0)
+(10.0, 1.5)
+
+julia> jacobian(DiffractorForwardBackend(), prod, [1.5, 2.5, 10.0]) |> only
+1×3 Matrix{Float64}:
+ 25.0  15.0  3.75
+
+julia> jacobian(DiffractorForwardBackend(), identity, [1.5, 2.5, 10.0]) |> only
+3×3 Matrix{Float64}:
+ 1.0  0.0  0.0
+ 0.0  1.0  0.0
+ 0.0  0.0  1.0
diff --git a/previews/PR256/reading_list.html b/previews/PR256/reading_list.html new file mode 100644 index 00000000..38f39462 --- /dev/null +++ b/previews/PR256/reading_list.html @@ -0,0 +1,2 @@ + +Reading List · Diffractor
GitHub

This is a list of references I found useful while thinking about Diffractor. If you are new to Julia, AD or Diffractor and are primarily intersted in Diffractor, how it works, how to use it, or even the general Diffractor theory, this is probably not the list for you. As always in the literature, some of these references use terms differently from how they are used in Diffractor (as well as being inconsistent with each other). Additionally, many of these references are quite dense and though I've found small nuggets of insight in each, excavating those took many hours. Also, these are not introductory texts. If you've not taken an introductory differential geometry course, I would recommend looking for that first. Don't feel bad if some of these references read like like nonsense. It often reads that way to me too.

Reading on Optics

  • "Categories of Optics" - Mitchell Riley - https://arxiv.org/abs/1809.00738

The original paper on optics. Good background for understanding the optics terminology.

Readings on First Order Differential Geometry

  • "Introduction to Smooth Manifolds" John M. Lee

Chapter 11 "The Cotangent Bundle" is useful for a reference on the theory of cotangent bundles, which corresponds to the structure of reverse mode AD through the optical equivalence. Also a useful general reference for Differential Geomtry.

  • "Natural Operations in Differential Geometry" - Ivan Kolář

I recommend Chapter IV. "Jets and Natural bundles"

Readings on Higher Order Differential Geometry

  • "Second Order Tangent Vectors in Riemannian Geometry", Fisher and Laquer, J. Korean Math Soc 36 (1999)

This one is quite good. I recommend reading the first half at least and tracing through the definitions. This corresponds fairly closely to notion of iterated tangent spaces as implemented in Diffractor.

  • "The Geometry of Jet Bundles" D. J. Saunders

I recommend reading Chapter 5 "Second order Jet bundles", though of course some earlier chapters may be useful to understand this chapter. I'm not 100% happy with the notation, but it gives good intuition.

diff --git a/previews/PR256/search_index.js b/previews/PR256/search_index.js new file mode 100644 index 00000000..c3e02d87 --- /dev/null +++ b/previews/PR256/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api.html","page":"API","title":"API","text":"CurrentModule = Diffractor","category":"page"},{"location":"api.html#Diffractor","page":"API","title":"Diffractor","text":"","category":"section"},{"location":"api.html","page":"API","title":"API","text":"","category":"page"},{"location":"api.html","page":"API","title":"API","text":"Modules = [Diffractor]","category":"page"},{"location":"api.html#Diffractor.AbstractTangentBundle","page":"API","title":"Diffractor.AbstractTangentBundle","text":"abstract type AbstractTangentBundle{N, B}; end\n\nThis type represents the N-th order (iterated) tangent bundle [1] TⁿB over some base (Riemannian) manifold B. Note that TⁿB is itself another manifold and thus in particular a vector space (over ℝ). As such, subtypes of this abstract type are expected to support the usual vector space operations.\n\nHowever, beyond that, this abstract type makes no guarantee about the representation. That said, to gain intution for what this object is, it makes sense to pick some explicit bases and write down examples.\n\nTo that end, suppose that B=ℝ. Then T¹B=T¹ℝ is just our usual notion of a dual number, i.e. for some element η ∈ T¹ℝ, we may consider η = a + bϵ for real numbers (a, b) and ϵ an infinitessimal differential such that ϵ^2 = 0.\n\nEquivalently, we may think of η as being identified with the vector (a, b) ∈ ℝ² with some additional structure. The same form essentially holds for general B, where we may write (as sets):\n\nT¹B = {(a, b) | a ∈ B, b ∈ Tₐ B }\n\nNote that these vectors are orthogonal to those in the underlying base space. For example, if B=ℝ², then we have:\n\nT¹ℝ² = {([aₓ, a_y], [bₓ, b_y]) | [aₓ, a_y] ∈ ℝ², [bₓ, b_y] ∈ Tₐ ℝ² }\n\nFor convenience, we will sometimes writes these in one as:\n\nη ∈ T ℝ² = aₓ x̂ + a_y ŷ + bₓ ∂/∂x|_aₓ x + b_y ∂/∂y|_{a_y}\n := aₓ x̂ + a_y ŷ + bₓ ∂/∂¹x + b_y ∂/∂¹y\n := [aₓ, a_y] + [bₓ, b_y] ∂/∂¹\n := a + b ∂/∂¹\n := a + b ∂₁\n\nThese are all definitional equivalences and we will mostly work with the final form. An important thing to keep in mind though is that the subscript on ∂₁ does not refer to a dimension of the underlying base manifold (for which we will rarely pick an explicit basis here), but rather tags the basis of the tangent bundle.\n\nLet us iterate this construction to second order. We have:\n\nT²B = T¹(T¹B) = { (α, β) | α ∈ T¹B, β ∈ T_α T¹B }\n = { ((a, b), (c, d)) | a ∈ B, b ∈ Tₐ B, c ∈ Tₐ B, d ∈ T²ₐ B}\n\n(where in the last equality we used the linearity of the tangent vector).\n\nFollowing our above notation, we will canonically write such an element as:\n\n a + b ∂₁ + c ∂₂ + d ∂₂ ∂₁\n= a + b ∂₁ + c ∂₂ + d ∂₁ ∂₂\n\nIt is worth noting that there still only is one base point a of the underlying manifold and thus TⁿB is a vector bundle over B for all N.\n\nFurther Reading\n\n[1] https://en.wikipedia.org/wiki/Tangent_bundle\n\n\n\n\n\n","category":"type"},{"location":"api.html#Diffractor.ExplicitTangent","page":"API","title":"Diffractor.ExplicitTangent","text":"struct ExplicitTangent{P}\n\nA fully explicit coordinate representation of the tangent space, represented by a vector of 2^N-1 partials.\n\n\n\n\n\n","category":"type"},{"location":"api.html#Diffractor.Jet","page":"API","title":"Diffractor.Jet","text":"struct Jet{T, N}\n\nRepresents the truncated (N-1)-th order Taylor series\n\nf(a) + (x-a)f'(a) + 1/2(x-a)^2f''(a) + ...\n\nCoefficients are stored in unscaled form. For a jet j, several operations are supported:\n\nIndexing j[i] returns fᵢ\nEvaluation j(x) semantically evaluates the truncated taylor series at x. However, evaluation is restricted to be precisely at a - the additional information in the taylor series is only available through derivatives. Mathematically this corresponds to an infinitessimal ball around a.\n\n\n\n\n\n","category":"type"},{"location":"api.html#Diffractor.TangentBundle","page":"API","title":"Diffractor.TangentBundle","text":"struct TangentBundle{N, B, P}\n\nRepresents a tangent bundle as an explicit primal together with some representation of the tangent space.\n\n\n\n\n\n","category":"type"},{"location":"api.html#Diffractor.TaylorTangent","page":"API","title":"Diffractor.TaylorTangent","text":"struct TaylorTangent{C}\n\nThe taylor bundle construction mods out the full N-th order tangent bundle by the equivalence relation that coefficients of like-order basis elements be equal, i.e. rather than a generic element\n\na + b ∂₁ + c ∂₂ + d ∂₃ + e ∂₂ ∂₁ + f ∂₃ ∂₁ + g ∂₃ ∂₂ + h ∂₃ ∂₂ ∂₁\n\nwe have a tuple (c₀, c₁, c₂, c₃) corresponding to the full element\n\nc₀ + c₁ ∂₁ + c₁ ∂₂ + c₁ ∂₃ + c₂ ∂₂ ∂₁ + c₂ ∂₃ ∂₁ + c₂ ∂₃ ∂₂ + c₃ ∂₃ ∂₂ ∂₁\n\ni.e.\n\nc₀ + c₁ (∂₁ + ∂₂ + ∂₃) + c₂ (∂₂ ∂₁ + ∂₃ ∂₁ + ∂₃ ∂₂) + c₃ ∂₃ ∂₂ ∂₁\n\nThis restriction forms a submanifold of the original manifold. The naming is by analogy with the (truncated) Taylor series\n\nc₀ + c₁ x + 1/2 c₂ x² + 1/3! c₃ x³ + O(x⁴)\n\n\n\n\n\n","category":"type"},{"location":"api.html#Diffractor.UniformTangent","page":"API","title":"Diffractor.UniformTangent","text":"struct UniformTangent\n\nRepresents an N-th order tangent bundle with all unform partials. Particularly useful for representing singleton values.\n\n\n\n\n\n","category":"type"},{"location":"api.html#Diffractor.zero_bundle","page":"API","title":"Diffractor.zero_bundle","text":"(::zero_bundle{N})(primal)\n\nCreates a bundle with a zero tangent.\n\n\n\n\n\n","category":"type"},{"location":"api.html#Diffractor.∂xⁿ","page":"API","title":"Diffractor.∂xⁿ","text":"∂xⁿ{N}(x)\n\nFor x in a one dimensional manifold, map x to the trivial, unital, Nth order tangent bundle. It should hold that ∀x ⟨∂ⁿ{1}x(x), dx(x)⟩ = 1\n\n\n\n\n\n","category":"type"},{"location":"api.html#Diffractor.∂⃖","page":"API","title":"Diffractor.∂⃖","text":"∂⃖{N}\n\n∂⃖{N} is the reverse-mode AD optic functor of order N. A call (::∂⃖{N})(f, args...) corresponds to ∂⃖ⁿ f(args...) in the linear encoding of an N-optic (see the terminology guide for definitions of these terms).\n\nIn general (::∂⃖{N})(f, args...) will return a tuple of the original primal value f(args...) (in rare cases primitives may modify the primal value - in general we will ignore this rare complication for the purposes of clear documentation) and an optic continuation λ. The interpretation of this continuation depends on the order of the functor:\n\nFor example, ∂⃖{1} computes first derivatives. In particular, for a function f, ∂⃖{1}(f, args...) will return the tuple (f(args...), f⋆) (read \"f upper-star\").\n\n\n\n\n\n","category":"type"},{"location":"api.html#Diffractor.∂☆","page":"API","title":"Diffractor.∂☆","text":"∂☆{N}\n\n∂☆{N} is the forward-mode AD functor of order N. A call (::∂☆{N})(f, args...) evaluating a function f: A -> B is lifted to its pushforward on the N-th order tangent bundle f⋆: Tⁿ A -> Tⁿ B.\n\n\n\n\n\n","category":"type"},{"location":"api.html#Diffractor.∇","page":"API","title":"Diffractor.∇","text":"∇(f, args...)\n\nComputes the gradient ∇f(x, y, z...) (at (x, y, z...)). In particular, the return value will be a tuple of partial derivatives (∂f/∂x, ∂f/∂y, ∂f/∂z...).\n\nCurried version\n\nAlternatively, ∇ may be curried, essentially giving the gradient as a function:\n\nExamples\n\njulia> using Diffractor: ∇\n\njulia> map(∇(*), (1,2,3), (4,5,6))\n((4.0, 1.0), (5.0, 2.0), (6.0, 3.0))\n\nThe derivative ∂f/∂f\n\nNote that since in Julia, there is no distinction between functions and values, there is in principle a partial derivative with respect to the function itself. However, said partial derivative is dropped by this interface. It is however available using the lower level ∂⃖ if desired. This interaction can also be used to obtain gradients with respect to only some of the arguments by using a closure:\n\n∇((x,z)->f(x,y,z))(x, z) # returns (∂f/∂x, ∂f/∂z)\n\nThough of course the same can be obtained by simply indexing the resulting tuple (in well-inferred code there should not be a performance difference between these two options).\n\n\n\n\n\n","category":"type"},{"location":"api.html#Diffractor.:'-Tuple{Any}","page":"API","title":"Diffractor.:'","text":"f'\n\nThis is a convenience syntax for taking the derivative of a function f: ℝ -> ℝ. In particular, for such a function f'(x) will be the first derivative of f at x (and similar for f''(x) and second derivatives and so on.)\n\nNote that the syntax conflicts with the Base definition for the adjoint of a matrix and thus is not enabled by default. To use it, add the following to the top of your module:\n\nusing Diffractor: var\"'\"\n\nIt is also available using the @∂ macro:\n\n@∂ f'(x)\n\n\n\n\n\n","category":"method"},{"location":"api.html#Diffractor.bundle","page":"API","title":"Diffractor.bundle","text":"bundle(primal, tangent)\n\nWraps a primal up with a tangent into the appropriate kind of AbstractBundle{1}. This is more or less the Diffractor equivelent of ForwardDiff.jl's Dual type.\n\n\n\n\n\n","category":"function"},{"location":"api.html#Diffractor.destructure-Union{Tuple{Diffractor.TangentBundle{N, B, Diffractor.TaylorTangent{P}} where P}, Tuple{B}, Tuple{N}} where {N, B<:Tuple}","page":"API","title":"Diffractor.destructure","text":"for a TaylorTangent{N, <:Tuple} this breaks it up unto 1 TaylorTangent{N} for each element of the primal tuple\n\n\n\n\n\n","category":"method"},{"location":"api.html#Diffractor.dx-Tuple{Real}","page":"API","title":"Diffractor.dx","text":"dx(x)\n\ndx represents the trival differential one-form of a one dimensional Riemannian manifold M. In particular, it is a section of the cotangent bundle of M, meaning it may be evaluted at a point x of M to obtain an element of the cotangent space T*ₓ M to M at x. We impose no restrictions on the representations of either the manifold itself or the cotangent space.\n\nBy default, the only implementation provided identifies T*ₓ ℝ ≃ ℝ, keeping watever type is used to represent ℝ. i.e.\n\ndx(x::Real) = one(x)\n\nHowever, users may provide additional overloads for custom representations of one dimensional Riemannian manifolds.\n\n\n\n\n\n","category":"method"},{"location":"api.html#Diffractor.find_end_of_phi_block-Tuple{Core.Compiler.IRCode, Int64}","page":"API","title":"Diffractor.find_end_of_phi_block","text":"find_end_of_phi_block(ir::IRCode, start_search_idx::Int)\n\nFinds the last index within the same basic block, on or after the start_search_idx which is not within a phi block. A phi-block is a run on PhiNodes or nothings that must be the first statements within the basic block.\n\nIf start_search_idx is not within a phi block to begin with, then just returns start_search_idx\n\n\n\n\n\n","category":"method"},{"location":"api.html#Diffractor.forward_diff_no_inf!-Tuple{Core.Compiler.IRCode, Vector{Pair{Core.SSAValue, Int64}}}","page":"API","title":"Diffractor.forward_diff_no_inf!","text":"forward_diff_no_inf!(ir::IRCode, to_diff::Vector{Pair{SSAValue,Int}}; visit_custom!, transform!)\n\nInternal method which generates the code for forward mode diffentiation\n\nir the IR being differnetation\nto_diff: collection of all SSA values for which the derivative is to be taken, paired with the order (first deriviative, second derivative etc)\nvisit_custom!(ir::IRCode, ssa, order::Int, recurse::Bool) -> Bool:\n\n\tdecides if the custom `transform!` should be applied to a `stmt` or not\n\tDefault: `false` for all statements\n\ntransform!(ir::IRCode, ssa::SSAValue, order::Int) mutates ir to do a custom tranformation.\n\n\n\n\n\n","category":"method"},{"location":"api.html#Diffractor.jet_taylor_ev-Union{Tuple{N}, Tuple{Val{N}, Any, Any}} where N","page":"API","title":"Diffractor.jet_taylor_ev","text":"jet_taylor_ev(::Val{}, jet, taylor)\n\nGenerates a closed form arithmetic expression for the N-th component of the action of a 1d jet (of order at least N) on a maximally symmetric (i.e. taylor) tangent bundle element. In particular, if we represent both the jet and the taylor tangent bundle element by their associated canonical taylor series:\n\nj = j₀ + j₁ (x - a) + j₂ 1/2 (x - a)^2 + ... + jₙ 1/n! (x - a)^n\nt = t₀ + t₁ (x - t₀) + t₂ 1/2 (x - t₀)^2 + ... + tₙ 1/n! (x - t₀)^n\n\nthen the action of evaluating j on t, is some other taylor series\n\nt′ = a + t′₁ (x - a) + t′₂ 1/2 (x - a)^2 + ... + t′ₙ 1/n! (x - a)^n\n\nThe t′ᵢ can be found by explicitly plugging in t for every x and expanding out, dropping terms of orders that are higher. This computes closed form expressions for the t′ᵢ that are hopefully easier on the compiler.\n\n\n\n\n\n","category":"method"},{"location":"api.html#Diffractor.@∂-Tuple{Any}","page":"API","title":"Diffractor.@∂","text":"@∂\n\nConvenice macro for writing partial derivatives. E.g. The expression:\n\n@∂ f(∂x, ∂y)\n\nWill compute the partial derivative ∂^2 f/∂x∂y at (x, y)`. And similarly\n\n@∂ f(∂²x, ∂y)\n\nwill compute the derivative ∂^3 f/∂x^2 ∂y at (x,y).\n\n\n\n\n\n","category":"macro"},{"location":"reading_list.html","page":"Reading List","title":"Reading List","text":"This is a list of references I found useful while thinking about Diffractor. If you are new to Julia, AD or Diffractor and are primarily intersted in Diffractor, how it works, how to use it, or even the general Diffractor theory, this is probably not the list for you. As always in the literature, some of these references use terms differently from how they are used in Diffractor (as well as being inconsistent with each other). Additionally, many of these references are quite dense and though I've found small nuggets of insight in each, excavating those took many hours. Also, these are not introductory texts. If you've not taken an introductory differential geometry course, I would recommend looking for that first. Don't feel bad if some of these references read like like nonsense. It often reads that way to me too.","category":"page"},{"location":"reading_list.html#Reading-on-Optics","page":"Reading List","title":"Reading on Optics","text":"","category":"section"},{"location":"reading_list.html","page":"Reading List","title":"Reading List","text":"\"Categories of Optics\" - Mitchell Riley - https://arxiv.org/abs/1809.00738","category":"page"},{"location":"reading_list.html","page":"Reading List","title":"Reading List","text":"The original paper on optics. Good background for understanding the optics terminology.","category":"page"},{"location":"reading_list.html#Readings-on-First-Order-Differential-Geometry","page":"Reading List","title":"Readings on First Order Differential Geometry","text":"","category":"section"},{"location":"reading_list.html","page":"Reading List","title":"Reading List","text":"\"Introduction to Smooth Manifolds\" John M. Lee","category":"page"},{"location":"reading_list.html","page":"Reading List","title":"Reading List","text":"Chapter 11 \"The Cotangent Bundle\" is useful for a reference on the theory of cotangent bundles, which corresponds to the structure of reverse mode AD through the optical equivalence. Also a useful general reference for Differential Geomtry.","category":"page"},{"location":"reading_list.html","page":"Reading List","title":"Reading List","text":"\"Natural Operations in Differential Geometry\" - Ivan Kolář","category":"page"},{"location":"reading_list.html","page":"Reading List","title":"Reading List","text":"I recommend Chapter IV. \"Jets and Natural bundles\"","category":"page"},{"location":"reading_list.html#Readings-on-Higher-Order-Differential-Geometry","page":"Reading List","title":"Readings on Higher Order Differential Geometry","text":"","category":"section"},{"location":"reading_list.html","page":"Reading List","title":"Reading List","text":"\"Second Order Tangent Vectors in Riemannian Geometry\", Fisher and Laquer, J. Korean Math Soc 36 (1999)","category":"page"},{"location":"reading_list.html","page":"Reading List","title":"Reading List","text":"This one is quite good. I recommend reading the first half at least and tracing through the definitions. This corresponds fairly closely to notion of iterated tangent spaces as implemented in Diffractor.","category":"page"},{"location":"reading_list.html","page":"Reading List","title":"Reading List","text":"\"The Geometry of Jet Bundles\" D. J. Saunders","category":"page"},{"location":"reading_list.html","page":"Reading List","title":"Reading List","text":"I recommend reading Chapter 5 \"Second order Jet bundles\", though of course some earlier chapters may be useful to understand this chapter. I'm not 100% happy with the notation, but it gives good intuition.","category":"page"},{"location":"index.html#Diffractor","page":"Introduction","title":"Diffractor","text":"","category":"section"},{"location":"index.html","page":"Introduction","title":"Introduction","text":"Next-generation AD","category":"page"},{"location":"index.html","page":"Introduction","title":"Introduction","text":"PDF containing the terminology","category":"page"},{"location":"index.html#Getting-Started","page":"Introduction","title":"Getting Started","text":"","category":"section"},{"location":"index.html","page":"Introduction","title":"Introduction","text":"⚠️This certainly has bugs and issues. Please open issues on Diffractor.jl, or AbstractDifferentiation.jl as appropriate.⚠️","category":"page"},{"location":"index.html","page":"Introduction","title":"Introduction","text":"Diffractor's public API is via AbstractDifferentiation.jl. Please see the AbstractDifferentiation.jl docs for detailed usage.","category":"page"},{"location":"index.html","page":"Introduction","title":"Introduction","text":"julia> using Diffractor: DiffractorForwardBackend\n\njulia> using AbstractDifferentiation: derivative, jacobian\n\njulia> derivative(DiffractorForwardBackend(), +, 1.5, 10.0)\n(1.0, 1.0)\n\njulia> derivative(DiffractorForwardBackend(), *, 1.5, 10.0)\n(10.0, 1.5)\n\njulia> jacobian(DiffractorForwardBackend(), prod, [1.5, 2.5, 10.0]) |> only\n1×3 Matrix{Float64}:\n 25.0 15.0 3.75\n\njulia> jacobian(DiffractorForwardBackend(), identity, [1.5, 2.5, 10.0]) |> only\n3×3 Matrix{Float64}:\n 1.0 0.0 0.0\n 0.0 1.0 0.0\n 0.0 0.0 1.0","category":"page"}] +} diff --git a/previews/PR256/siteinfo.js b/previews/PR256/siteinfo.js new file mode 100644 index 00000000..0cbcc2b9 --- /dev/null +++ b/previews/PR256/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR256"; diff --git a/previews/PR256/terminology.pdf 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