From faa2cc022298ab1a7411e6285109263fae755457 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Wed, 1 Jan 2025 14:07:40 +0000 Subject: [PATCH] build based on 0741315 --- dev/.documenter-siteinfo.json | 2 +- dev/API/ActuaryUtilities/index.html | 2 +- dev/API/FinanceCore/index.html | 38 +-- dev/assets/documenter.js | 370 +++++++++++---------- dev/assets/themes/catppuccin-frappe.css | 1 + dev/assets/themes/catppuccin-latte.css | 1 + dev/assets/themes/catppuccin-macchiato.css | 1 + dev/assets/themes/catppuccin-mocha.css | 1 + dev/assets/themes/documenter-dark.css | 4 +- dev/assets/themes/documenter-light.css | 2 +- dev/financial_math/index.html | 18 +- dev/index.html | 4 +- dev/risk_measures/c718784f.png | Bin 0 -> 93512 bytes dev/risk_measures/e82f221a.png | Bin 93496 -> 0 bytes dev/risk_measures/index.html | 22 +- dev/search_index.js | 2 +- dev/upgrade/index.html | 4 +- dev/utilities/index.html | 36 +- 18 files changed, 272 insertions(+), 236 deletions(-) create mode 100644 dev/assets/themes/catppuccin-frappe.css create mode 100644 dev/assets/themes/catppuccin-latte.css create mode 100644 dev/assets/themes/catppuccin-macchiato.css create mode 100644 dev/assets/themes/catppuccin-mocha.css create mode 100644 dev/risk_measures/c718784f.png delete mode 100644 dev/risk_measures/e82f221a.png diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 7cac057..6589782 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2024-04-18T04:22:09","documenter_version":"1.4.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2025-01-01T14:07:35","documenter_version":"1.8.0"}} \ No newline at end of file diff --git a/dev/API/ActuaryUtilities/index.html b/dev/API/ActuaryUtilities/index.html index 8a72a3d..61032b3 100644 --- a/dev/API/ActuaryUtilities/index.html +++ b/dev/API/ActuaryUtilities/index.html @@ -1,2 +1,2 @@ -ActuaryUtilities · ActuaryUtilities.jl
+ActuaryUtilities · ActuaryUtilities.jl
diff --git a/dev/API/FinanceCore/index.html b/dev/API/FinanceCore/index.html index dbeabee..641da0b 100644 --- a/dev/API/FinanceCore/index.html +++ b/dev/API/FinanceCore/index.html @@ -1,10 +1,10 @@ -FinanceCore (re-exported) · ActuaryUtilities.jl

FinanceCore API Reference

Exported API

FinanceCore.Cashflow — Type
Cashflow(amount,time)

A Cahflow{A,B} is a contract that pays an amount at time.

Cashflows can be:

  • negated with the unary - operator.
  • added/subtracted together but note that the time must be isapprox equal.
  • multiplied/divided by a scalar.

Supertype Hierarchy ≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

Cashflow{A<:Real, B<:Timepoint} <: FinanceCore.AbstractContract <: Any
source
FinanceCore.Composite — Type
Composite(A,B)

Summary ≡≡≡≡≡≡≡≡≡

struct Composite{A, B}

A Composite{A,B} is a contract that is composed of two other contracts of type A and type B. The maturity of the composite is the maximum of the maturities of the two components.

It is used to assemble arbitrarily complex contracts from simpler ones.

Fields ≡≡≡≡≡≡≡≡

a :: A
-b :: B

Supertype Hierarchy ≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

Composite{A, B} <: FinanceCore.AbstractContract <: Any
source
FinanceCore.Continuous — Type
Continuous()

A type representing continuous interest compounding frequency.

Examples

julia> Rate(0.01,Continuous())
-Rate(0.01, Continuous())

See also: Periodic

source
FinanceCore.Periodic — Type
Periodic(frequency)

A type representing periodic interest compounding with the given frequency.

frequency will be converted to an Integer, and will round up to 8 decimal places (otherwise will throw an InexactError).

Examples

Creating a semi-annual bond equivalent yield:

julia> Rate(0.01,Periodic(2))
-Rate(0.01, Periodic(2))

See also: Continuous

source
FinanceCore.Periodic — Method
Periodic(rate,frequency)

A convenience constructor for Rate(rate,Periodic(frequency)).

Examples

Creating a semi-annual bond equivalent yield:

julia> Periodic(0.01,2)
-Rate(0.01, Periodic(2))

See also: Continuous

source
FinanceCore.Quote — Type
Quote(price,instrument)

The price(<:Real) is the observed value , and the instrument is the instrument/contract that the price is for.

This can be used, e.g., to calibrate a valuation model to prices for the given instruments - see FinanceModels.jl for more details.

source
FinanceCore.Rate — Method
Rate(rate[,frequency=1])
+FinanceCore (re-exported) · ActuaryUtilities.jl        
         
 
FinanceCore API Reference
Exported API
FinanceCore.Cashflow — Type
Cashflow(amount,time)
A Cahflow{A,B} is a contract that pays an amount at time. 
Cashflows can be:
  • negated with the unary - operator. 
  • added/subtracted together but note that the time must be isapprox equal.
  • multiplied/divided by a scalar.
Supertype Hierarchy ≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
Cashflow{A<:Real, B<:Timepoint} <: FinanceCore.AbstractContract <: Any
source
FinanceCore.Composite — Type
Composite(A,B)
Summary ≡≡≡≡≡≡≡≡≡
struct Composite{A, B}
A Composite{A,B} is a contract that is composed of two other contracts of type A and type B.  The maturity of the composite is the maximum of the maturities of the two components. 
It is used to assemble arbitrarily complex contracts from simpler ones.
Fields ≡≡≡≡≡≡≡≡
a :: A
+b :: B
Supertype Hierarchy ≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
Composite{A, B} <: FinanceCore.AbstractContract <: Any
source
FinanceCore.Continuous — Type
Continuous()
A type representing continuous interest compounding frequency.
Examples
julia> Rate(0.01,Continuous())
+Rate(0.01, Continuous())
See also: Periodic
source
FinanceCore.Periodic — Type
Periodic(frequency)
A type representing periodic interest compounding with the given frequency. 
frequency will be converted to an Integer, and will round up to 8 decimal places (otherwise will throw an InexactError). 
Examples
Creating a semi-annual bond equivalent yield:
julia> Rate(0.01,Periodic(2))
+Rate(0.01, Periodic(2))
See also: Continuous
source
FinanceCore.Periodic — Method
Periodic(rate,frequency)
A convenience constructor for Rate(rate,Periodic(frequency)).
Examples
Creating a semi-annual bond equivalent yield:
julia> Periodic(0.01,2)
+Rate(0.01, Periodic(2))
See also: Continuous
source
FinanceCore.Quote — Type
Quote(price,instrument)
The price(<:Real) is the observed value , and the instrument is the instrument/contract that the price is for.
This can be used, e.g., to calibrate a valuation model to prices for the given instruments - see FinanceModels.jl for more details.
source
FinanceCore.Rate — Method
Rate(rate[,frequency=1])
 Rate(rate,frequency::Frequency)
Rate is a type that encapsulates an interest rate along with its compounding frequency.
Periodic rates can be constructed via Rate(rate,frequency) or Rate(rate,Periodic(frequency)). If not given a second argument, Rate(rate) is equivalent to Rate(rate,Periodic(1)).
Continuous rates can be constructed via Rate(rate, Inf) or Rate(rate,Continuous()).
Examples
julia> Rate(0.01,Continuous())
 Rate(0.01, Continuous())
 
@@ -34,53 +34,53 @@
 
 julia> Rate(0.01,Inf)
 Rate(0.01, Continuous())
-
source
FinanceCore.amount — Method
amount(x)
If is an object with an amount component (e.g. a Cashflow), will retrun that amount component, otherwise just x.
Examples
julia> FinanceCore.amount(Cashflow(1.,3.))
+
source
FinanceCore.amount — Method
amount(x)
If is an object with an amount component (e.g. a Cashflow), will retrun that amount component, otherwise just x.
Examples
julia> FinanceCore.amount(Cashflow(1.,3.))
 1.0
 
 julia> FinanceCore.amount(1.)
-1.0
source
FinanceCore.internal_rate_of_return — Method
internal_rate_of_return(cashflows::vector)::Rate
 internal_rate_of_return(cashflows::Vector, timepoints::Vector)::Rate
Calculate the internalrateof_return with given timepoints. If no timepoints given, will assume that a series of equally spaced cashflows, assuming the first cashflow occurring at time zero and subsequent elements at time 1, 2, 3, ..., n. 
Returns a Rate type with periodic compounding once per period (e.g. annual effective if the timepoints given represent years). Get the scalar rate by calling Yields.rate() on the result.
Example
julia> internal_rate_of_return([-100,110],[0,1]) # e.g. cashflows at time 0 and 1
 0.10000000001652906
 julia> internal_rate_of_return([-100,110]) # implied the same as above
-0.10000000001652906
Solver notes
Will try to return a root within the range [-2,2]. If the fast solver does not find one matching this condition, then a more robust search will be performed over the [.99,2] range.
The solution returned will be in the range [-2,2], but may not be the one nearest zero. For a slightly slower, but more robust version, call ActuaryUtilities.irr_robust(cashflows,timepoints) directly.
source
FinanceCore.irr — Function
irr(cashflows::vector)
+0.10000000001652906
Solver notes
Will try to return a root within the range [-2,2]. If the fast solver does not find one matching this condition, then a more robust search will be performed over the [.99,2] range.
The solution returned will be in the range [-2,2], but may not be the one nearest zero. For a slightly slower, but more robust version, call ActuaryUtilities.irr_robust(cashflows,timepoints) directly.
source
FinanceCore.irr — Function
irr(cashflows::vector)
 irr(cashflows::Vector, timepoints::Vector)
 
-An alias for `internal_rate_of_return`.
source
FinanceCore.present_value — Method
present_value(yield_model, cashflows[, timepoints=pairs(cashflows)])
Discount the cashflows vector at the given yield_model,  with the cashflows occurring at the times specified in timepoints. If no timepoints given, assumes that cashflows happen at the indices of the cashflows.
If your timepoints are dates, you can convert them into a floating point representation of the time interval using DayCounts.jl.
Examples
julia> present_value(0.1, [10,20],[0,1])
+An alias for `internal_rate_of_return`.
source
FinanceCore.present_value — Method
present_value(yield_model, cashflows[, timepoints=pairs(cashflows)])
Discount the cashflows vector at the given yield_model,  with the cashflows occurring at the times specified in timepoints. If no timepoints given, assumes that cashflows happen at the indices of the cashflows.
If your timepoints are dates, you can convert them into a floating point representation of the time interval using DayCounts.jl.
Examples
julia> present_value(0.1, [10,20],[0,1])
 28.18181818181818
 julia> present_value(Continuous(0.1), [10,20],[0,1])
 28.096748360719193
 julia> present_value(Continuous(0.1), [10,20],[1,2])
 25.422989241919232
 julia> present_value(Continuous(0.1), [10,20])
-25.422989241919232
source
FinanceCore.rate — Method
rate(r::Rate)
Returns the untyped scalar interest rate represented by the Rate.
Examples
julia> r =Continuous(0.03)
+25.422989241919232
source
FinanceCore.rate — Method
rate(r::Rate)
Returns the untyped scalar interest rate represented by the Rate.
Examples
julia> r =Continuous(0.03)
 Yields.Rate{Float64, Continuous}(0.03, Continuous())
 
 julia> rate(r)
-0.03
source
FinanceCore.timepoint — Method
timepoint(x,t)
If x is an object with a defined time component (e.g. a Cashflow), will return that time component, otherwise will return t. This is useful in handling situations where you want to handle either Cashflows or separate amount and time vectors.
Example
julia> FinanceCore.timepoint(Cashflow(1.,3.),"ignored")
+0.03
source
FinanceCore.timepoint — Method
timepoint(x,t)
If x is an object with a defined time component (e.g. a Cashflow), will return that time component, otherwise will return t. This is useful in handling situations where you want to handle either Cashflows or separate amount and time vectors.
Example
julia> FinanceCore.timepoint(Cashflow(1.,3.),"ignored")
 3.0
 
 julia> FinanceCore.timepoint(1.,4.)
-4.0
source
Unexported API
FinanceCore.Timepoint — Type
Timepoint(a)
Summary ≡≡≡≡≡≡≡≡≡
Timepoint is a type alias for Union{T,Dates.Date} that can be used to represent a point in time. It can be either a Dates.Date or a Real number. If defined as a real number, the interpretation is the number of (fractional) periods since time zero.
Currently, the usage of Dates.Date is not well supported across the JuliaActuary ecosystem but this type is in place such that it can be built upon further.
Supertype Hierarchy ≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
Timepoint{T} = Union{T,Dates.Date} <: Any
source
Base.:* — Method
*(Yields.Rate, T)
-*(T, Yields.Rate)
The multiplication of a Rate with a scalar will inherit the type of the Rate, or the first argument's type if both are Rates.
source
Unexported API
FinanceCore.Timepoint — Type
Timepoint(a)
Summary ≡≡≡≡≡≡≡≡≡
Timepoint is a type alias for Union{T,Dates.Date} that can be used to represent a point in time. It can be either a Dates.Date or a Real number. If defined as a real number, the interpretation is the number of (fractional) periods since time zero.
Currently, the usage of Dates.Date is not well supported across the JuliaActuary ecosystem but this type is in place such that it can be built upon further.
Supertype Hierarchy ≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
Timepoint{T} = Union{T,Dates.Date} <: Any
source
Base.:* — Method
*(Yields.Rate, T)
+*(T, Yields.Rate)
The multiplication of a Rate with a scalar will inherit the type of the Rate, or the first argument's type if both are Rates.
source
Base.:+ — Method
+(Yields.Rate, T<:Real)
 +(T<:Real, Yields.Rate)
 +(Yields.Rate,Yields.Rate)
The addition of a rate with a number will inherit the type of the Rate, or the first argument's type if both are Rates.
Examples
julia> Yields.Periodic(0.01,2) + Yields.Periodic(0.04,2)
 Yields.Rate{Float64, Yields.Periodic}(0.05000000000000004, Yields.Periodic(2))
 
 julia> Yields.Periodic(0.04,2) + 0.01
-Yields.Rate{Float64, Yields.Periodic}(0.05, Yields.Periodic(2))
source
Base.:- — Method
-(Yields.Rate, T<:Real)
+Yields.Rate{Float64, Yields.Periodic}(0.05, Yields.Periodic(2))
source
Base.:- — Method
-(Yields.Rate, T<:Real)
 -(T<:Real, Yields.Rate)
 -(Yields.Rate, Yields.Rate)
The addition of a rate with a number will inherit the type of the Rate, or the first argument's type if both are Rates.
Examples
julia> Yields.Periodic(0.04,2) - Yields.Periodic(0.01,2)
 Yields.Rate{Float64, Yields.Periodic}(0.030000000000000214, Yields.Periodic(2))
 
 julia> Yields.Periodic(0.04,2) - 0.01
 Yields.Rate{Float64, Yields.Periodic}(0.03, Yields.Periodic(2))
-
source
Base.:/ — Method
/(x::Yields.Rate, y::Real)
The division of a Rate with a scalar will inherit the type of the Rate, or the first argument's type if both are Rates.
source
Base.:< — Method
<(x::Rate,y::Rate)
Convert the second argument to the periodicity of the first and compare the scalar rate values to determine if the first argument has a lower force of interest than the second.
Examples
julia> Yields.Periodic(0.03,100) < Yields.Continuous(0.03)
-true
source
Base.:> — Method
>(Rate,Rate)
Convert the second argument to the periodicity of the first and compare the scalar rate values to determine if the first argument has a greater force of interest than the second.
Examples
julia> Yields.Periodic(0.03,100) > Yields.Continuous(0.03)
-false
source
Base.convert — Method
convert(cf::Frequency,r::Rate)
Returns a Rate with an equivalent discount but represented with a different compounding frequency.
Examples
julia> r = Rate(Periodic(12),0.01)
+
source
Base.:/ — Method
/(x::Yields.Rate, y::Real)
The division of a Rate with a scalar will inherit the type of the Rate, or the first argument's type if both are Rates.
source
Base.:< — Method
<(x::Rate,y::Rate)
Convert the second argument to the periodicity of the first and compare the scalar rate values to determine if the first argument has a lower force of interest than the second.
Examples
julia> Yields.Periodic(0.03,100) < Yields.Continuous(0.03)
+true
source
Base.:> — Method
>(Rate,Rate)
Convert the second argument to the periodicity of the first and compare the scalar rate values to determine if the first argument has a greater force of interest than the second.
Examples
julia> Yields.Periodic(0.03,100) > Yields.Continuous(0.03)
+false
source
Base.convert — Method
convert(cf::Frequency,r::Rate)
Returns a Rate with an equivalent discount but represented with a different compounding frequency.
Examples
julia> r = Rate(Periodic(12),0.01)
 Rate(0.01, Periodic(12))
 
 julia> convert(Periodic(1),r)
 Rate(0.010045960887181016, Periodic(1))
 
 julia> convert(Continuous(),r)
-Rate(0.009995835646701251, Continuous())
source
Please open an issue if you encounter any issues or confusion with the package.

+Rate(0.009995835646701251, Continuous())
source

Please open an issue if you encounter any issues or confusion with the package.

diff --git a/dev/assets/documenter.js b/dev/assets/documenter.js index c6562b5..7d68cd8 100644 --- a/dev/assets/documenter.js +++ b/dev/assets/documenter.js @@ -77,30 +77,35 @@ 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 { - $(this) - .find(".docstring-article-toggle-button") - .removeClass("fa-chevron-right") - .addClass("fa-chevron-down"); +$(document).on( + "click", + ".docstring .docstring-article-toggle-button", + function () { + let articleToggleTitle = "Expand docstring"; + const parent = $(this).parent(); + + debounce(() => { + if (parent.siblings("section").is(":visible")) { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); - articleToggleTitle = "Collapse docstring"; - } + articleToggleTitle = "Collapse docstring"; + } - $(this) - .find(".docstring-article-toggle-button") - .prop("title", articleToggleTitle); - $(this).siblings("section").slideToggle(); - }); -}); + parent + .children(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + parent.siblings("section").slideToggle(); + }); + } +); $(document).on("click", ".docs-article-toggle-button", function (event) { let articleToggleTitle = "Expand docstring"; @@ -110,7 +115,7 @@ $(document).on("click", ".docs-article-toggle-button", function (event) { debounce(() => { if (isExpanded) { $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); - $(".docstring-article-toggle-button") + $("a.docstring-article-toggle-button") .removeClass("fa-chevron-down") .addClass("fa-chevron-right"); @@ -119,7 +124,7 @@ $(document).on("click", ".docs-article-toggle-button", function (event) { $(".docstring section").slideUp(animationSpeed); } else { $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); - $(".docstring-article-toggle-button") + $("a.docstring-article-toggle-button") .removeClass("fa-chevron-right") .addClass("fa-chevron-down"); @@ -484,6 +489,14 @@ function worker_function(documenterSearchIndex, documenterBaseURL, filters) { : string || ""; } + /** + * RegX escape function from MDN + * Refer: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ + function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + } + /** * Make the result component given a minisearch result data object and the value * of the search input as queryString. To view the result object structure, refer: @@ -502,8 +515,8 @@ function worker_function(documenterSearchIndex, documenterBaseURL, filters) { if (result.page !== "") { display_link += ` (${result.page})`; } - - let textindex = new RegExp(`${querystring}`, "i").exec(result.text); + searchstring = escapeRegExp(querystring); + let textindex = new RegExp(`${searchstring}`, "i").exec(result.text); let text = textindex !== null ? result.text.slice( @@ -520,7 +533,7 @@ function worker_function(documenterSearchIndex, documenterBaseURL, filters) { let display_result = text.length ? "..." + text.replace( - new RegExp(`${escape(querystring)}`, "i"), // For first occurrence + new RegExp(`${escape(searchstring)}`, "i"), // For first occurrence '$&' ) + "..." @@ -566,6 +579,7 @@ function worker_function(documenterSearchIndex, documenterBaseURL, filters) { // Only return relevant results return result.score >= 1; }, + combineWith: "AND", }); // Pre-filter to deduplicate and limit to 200 per category to the extent @@ -598,176 +612,194 @@ function worker_function(documenterSearchIndex, documenterBaseURL, filters) { }; } -// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! -const filters = [ - ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), -]; -const worker_str = - "(" + - worker_function.toString() + - ")(" + - JSON.stringify(documenterSearchIndex["docs"]) + - "," + - JSON.stringify(documenterBaseURL) + - "," + - JSON.stringify(filters) + - ")"; -const worker_blob = new Blob([worker_str], { type: "text/javascript" }); -const worker = new Worker(URL.createObjectURL(worker_blob)); - /////// SEARCH MAIN /////// -// Whether the worker is currently handling a search. This is a boolean -// as the worker only ever handles 1 or 0 searches at a time. -var worker_is_running = false; - -// The last search text that was sent to the worker. This is used to determine -// if the worker should be launched again when it reports back results. -var last_search_text = ""; - -// The results of the last search. This, in combination with the state of the filters -// in the DOM, is used compute the results to display on calls to update_search. -var unfiltered_results = []; - -// Which filter is currently selected -var selected_filter = ""; - -$(document).on("input", ".documenter-search-input", function (event) { - if (!worker_is_running) { - launch_search(); - } -}); - -function launch_search() { - worker_is_running = true; - last_search_text = $(".documenter-search-input").val(); - worker.postMessage(last_search_text); -} - -worker.onmessage = function (e) { - if (last_search_text !== $(".documenter-search-input").val()) { - launch_search(); - } else { - worker_is_running = false; - } - - unfiltered_results = e.data; - update_search(); -}; +function runSearchMainCode() { + // `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! + const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), + ]; + const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; + const worker_blob = new Blob([worker_str], { type: "text/javascript" }); + const worker = new Worker(URL.createObjectURL(worker_blob)); + + // Whether the worker is currently handling a search. This is a boolean + // as the worker only ever handles 1 or 0 searches at a time. + var worker_is_running = false; + + // The last search text that was sent to the worker. This is used to determine + // if the worker should be launched again when it reports back results. + var last_search_text = ""; + + // The results of the last search. This, in combination with the state of the filters + // in the DOM, is used compute the results to display on calls to update_search. + var unfiltered_results = []; + + // Which filter is currently selected + var selected_filter = ""; + + $(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } + }); -$(document).on("click", ".search-filter", function () { - if ($(this).hasClass("search-filter-selected")) { - selected_filter = ""; - } else { - selected_filter = $(this).text().toLowerCase(); + function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); } - // This updates search results and toggles classes for UI: - update_search(); -}); + worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } -/** - * Make/Update the search component - */ -function update_search() { - let querystring = $(".documenter-search-input").val(); + unfiltered_results = e.data; + update_search(); + }; - if (querystring.trim()) { - if (selected_filter == "") { - results = unfiltered_results; + $(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; } else { - results = unfiltered_results.filter((result) => { - return selected_filter == result.category.toLowerCase(); - }); + selected_filter = $(this).text().toLowerCase(); } - let search_result_container = ``; - let modal_filters = make_modal_body_filters(); - let search_divider = `
`; + // This updates search results and toggles classes for UI: + update_search(); + }); - if (results.length) { - let links = []; - let count = 0; - let search_results = ""; - - for (var i = 0, n = results.length; i < n && count < 200; ++i) { - let result = results[i]; - if (result.location && !links.includes(result.location)) { - search_results += result.div; - count++; - links.push(result.location); - } - } + /** + * Make/Update the search component + */ + function update_search() { + let querystring = $(".documenter-search-input").val(); - if (count == 1) { - count_str = "1 result"; - } else if (count == 200) { - count_str = "200+ results"; + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; } else { - count_str = count + " results"; + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); } - let result_count = `
${count_str}
`; - search_result_container = ` + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = `
${modal_filters} ${search_divider} - ${result_count} -
- ${search_results} -
-
+
0 result(s)
+ +
No result found!
`; - } else { - search_result_container = ` -
- ${modal_filters} - ${search_divider} -
0 result(s)
-
-
No result found!
- `; - } + } - if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { - $(".search-modal-card-body").removeClass("is-justify-content-center"); - } + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } - $(".search-modal-card-body").html(search_result_container); - } else { - if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { - $(".search-modal-card-body").addClass("is-justify-content-center"); + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); } + } - $(".search-modal-card-body").html(` -
Type something to get started!
- `); + /** + * Make the modal filter html + * + * @returns string + */ + function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; } } -/** - * Make the modal filter html - * - * @returns string - */ -function make_modal_body_filters() { - let str = filters - .map((val) => { - if (selected_filter == val.toLowerCase()) { - return `${val}`; - } else { - return `${val}`; - } - }) - .join(""); - - return ` -
- Filters: - ${str} -
`; +function waitUntilSearchIndexAvailable() { + // It is possible that the documenter.js script runs before the page + // has finished loading and documenterSearchIndex gets defined. + // So we need to wait until the search index actually loads before setting + // up all the search-related stuff. + if (typeof documenterSearchIndex !== "undefined") { + runSearchMainCode(); + } else { + console.warn("Search Index not available, waiting"); + setTimeout(waitUntilSearchIndexAvailable, 1000); + } } +// The actual entry point to the search code +waitUntilSearchIndexAvailable(); + }) //////////////////////////////////////////////////////////////////////////////// require(['jquery'], function($) { diff --git a/dev/assets/themes/catppuccin-frappe.css b/dev/assets/themes/catppuccin-frappe.css new file mode 100644 index 0000000..32e3f00 --- /dev/null +++ b/dev/assets/themes/catppuccin-frappe.css @@ -0,0 +1 @@ +html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link,html.theme--catppuccin-frappe .pagination-ellipsis,html.theme--catppuccin-frappe .file-cta,html.theme--catppuccin-frappe .file-name,html.theme--catppuccin-frappe .select select,html.theme--catppuccin-frappe .textarea,html.theme--catppuccin-frappe .input,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-frappe .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--catppuccin-frappe .pagination-previous:focus,html.theme--catppuccin-frappe .pagination-next:focus,html.theme--catppuccin-frappe 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.docstring>section>a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #8caaee #8caaee !important}html.theme--catppuccin-frappe .button.is-primary.is-inverted.is-outlined[disabled],html.theme--catppuccin-frappe .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-primary.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-frappe .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-primary.is-light,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.docs-sourcelink{background-color:#edf2fc;color:#153a8e}html.theme--catppuccin-frappe .button.is-primary.is-light:hover,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.docs-sourcelink:hover,html.theme--catppuccin-frappe .button.is-primary.is-light.is-hovered,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.is-hovered.docs-sourcelink{background-color:#e2eafb;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-primary.is-light:active,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.docs-sourcelink:active,html.theme--catppuccin-frappe .button.is-primary.is-light.is-active,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.is-active.docs-sourcelink{background-color:#d7e1f9;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-link{background-color:#8caaee;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-link:hover,html.theme--catppuccin-frappe .button.is-link.is-hovered{background-color:#81a2ec;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-link:focus,html.theme--catppuccin-frappe 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.button.is-link.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-link.is-outlined{background-color:transparent;border-color:#8caaee;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-outlined:hover,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-link.is-outlined:focus,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-focused{background-color:#8caaee;border-color:#8caaee;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #8caaee #8caaee !important}html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-link.is-outlined{background-color:transparent;border-color:#8caaee;box-shadow:none;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8caaee #8caaee !important}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-light{background-color:#edf2fc;color:#153a8e}html.theme--catppuccin-frappe .button.is-link.is-light:hover,html.theme--catppuccin-frappe .button.is-link.is-light.is-hovered{background-color:#e2eafb;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-link.is-light:active,html.theme--catppuccin-frappe .button.is-link.is-light.is-active{background-color:#d7e1f9;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:hover,html.theme--catppuccin-frappe .button.is-info.is-hovered{background-color:#78c4b9;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:focus,html.theme--catppuccin-frappe .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:focus:not(:active),html.theme--catppuccin-frappe .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(129,200,190,0.25)}html.theme--catppuccin-frappe .button.is-info:active,html.theme--catppuccin-frappe .button.is-info.is-active{background-color:#6fc0b5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:#81c8be;box-shadow:none}html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-focused{background-color:#81c8be;border-color:#81c8be;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-light{background-color:#f1f9f8;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:hover,html.theme--catppuccin-frappe .button.is-info.is-light.is-hovered{background-color:#e8f5f3;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:active,html.theme--catppuccin-frappe .button.is-info.is-light.is-active{background-color:#dff1ef;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-success{background-color:#a6d189;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:hover,html.theme--catppuccin-frappe .button.is-success.is-hovered{background-color:#9fcd80;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:focus,html.theme--catppuccin-frappe .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:focus:not(:active),html.theme--catppuccin-frappe .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,209,137,0.25)}html.theme--catppuccin-frappe .button.is-success:active,html.theme--catppuccin-frappe .button.is-success.is-active{background-color:#98ca77;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success{background-color:#a6d189;border-color:#a6d189;box-shadow:none}html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-outlined:hover,html.theme--catppuccin-frappe 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.button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-light{background-color:#f4f9f0;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:hover,html.theme--catppuccin-frappe .button.is-success.is-light.is-hovered{background-color:#edf6e7;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:active,html.theme--catppuccin-frappe .button.is-success.is-light.is-active{background-color:#e6f2de;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:hover,html.theme--catppuccin-frappe .button.is-warning.is-hovered{background-color:#e3c386;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus,html.theme--catppuccin-frappe .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus:not(:active),html.theme--catppuccin-frappe .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(229,200,144,0.25)}html.theme--catppuccin-frappe .button.is-warning:active,html.theme--catppuccin-frappe .button.is-warning.is-active{background-color:#e0be7b;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:#e5c890;box-shadow:none}html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-focused{background-color:#e5c890;border-color:#e5c890;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-light{background-color:#fbf7ee;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:hover,html.theme--catppuccin-frappe .button.is-warning.is-light.is-hovered{background-color:#f9f2e4;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:active,html.theme--catppuccin-frappe .button.is-warning.is-light.is-active{background-color:#f6edda;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:hover,html.theme--catppuccin-frappe .button.is-danger.is-hovered{background-color:#e57779;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus,html.theme--catppuccin-frappe .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus:not(:active),html.theme--catppuccin-frappe .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(231,130,132,0.25)}html.theme--catppuccin-frappe .button.is-danger:active,html.theme--catppuccin-frappe .button.is-danger.is-active{background-color:#e36d6f;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:#e78284;box-shadow:none}html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-focused{background-color:#e78284;border-color:#e78284;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-light{background-color:#fceeee;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:hover,html.theme--catppuccin-frappe .button.is-danger.is-light.is-hovered{background-color:#fae3e4;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:active,html.theme--catppuccin-frappe .button.is-danger.is-light.is-active{background-color:#f8d8d9;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-frappe .button.is-small:not(.is-rounded),html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .button.is-normal{font-size:1rem}html.theme--catppuccin-frappe .button.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .button.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button{background-color:#737994;border-color:#626880;box-shadow:none;opacity:.5}html.theme--catppuccin-frappe .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-frappe .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-frappe .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-frappe .button.is-static{background-color:#292c3c;border-color:#626880;color:#838ba7;box-shadow:none;pointer-events:none}html.theme--catppuccin-frappe .button.is-rounded,html.theme--catppuccin-frappe #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--catppuccin-frappe .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-frappe .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-frappe .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-frappe .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-frappe .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-frappe .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-frappe .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-frappe .buttons.has-addons .button:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-frappe .buttons.has-addons .button:focus,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused,html.theme--catppuccin-frappe .buttons.has-addons .button:active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-frappe .buttons.has-addons .button:focus:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-frappe .buttons.has-addons .button:active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-frappe .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .buttons.is-centered{justify-content:center}html.theme--catppuccin-frappe .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-frappe .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-frappe .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--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-frappe .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-frappe .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-frappe .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-frappe .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-frappe .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-frappe .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-frappe .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-frappe .content li+li{margin-top:0.25em}html.theme--catppuccin-frappe .content p:not(:last-child),html.theme--catppuccin-frappe .content dl:not(:last-child),html.theme--catppuccin-frappe .content ol:not(:last-child),html.theme--catppuccin-frappe .content ul:not(:last-child),html.theme--catppuccin-frappe .content blockquote:not(:last-child),html.theme--catppuccin-frappe .content pre:not(:last-child),html.theme--catppuccin-frappe .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-frappe .content h1,html.theme--catppuccin-frappe .content h2,html.theme--catppuccin-frappe .content h3,html.theme--catppuccin-frappe .content h4,html.theme--catppuccin-frappe .content h5,html.theme--catppuccin-frappe .content h6{color:#c6d0f5;font-weight:600;line-height:1.125}html.theme--catppuccin-frappe .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-frappe .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-frappe .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-frappe .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-frappe .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-frappe .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-frappe .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-frappe .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-frappe .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-frappe .content blockquote{background-color:#292c3c;border-left:5px solid #626880;padding:1.25em 1.5em}html.theme--catppuccin-frappe .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-frappe .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-frappe .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-frappe .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-frappe .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-frappe .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-frappe .content ul ul ul{list-style-type:square}html.theme--catppuccin-frappe .content dd{margin-left:2em}html.theme--catppuccin-frappe .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-frappe .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-frappe .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-frappe .content figure img{display:inline-block}html.theme--catppuccin-frappe .content figure figcaption{font-style:italic}html.theme--catppuccin-frappe .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-frappe .content sup,html.theme--catppuccin-frappe .content sub{font-size:75%}html.theme--catppuccin-frappe .content table{width:100%}html.theme--catppuccin-frappe .content table td,html.theme--catppuccin-frappe .content table th{border:1px solid #626880;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-frappe .content table th{color:#b0bef1}html.theme--catppuccin-frappe .content table th:not([align]){text-align:inherit}html.theme--catppuccin-frappe .content table thead td,html.theme--catppuccin-frappe .content table thead th{border-width:0 0 2px;color:#b0bef1}html.theme--catppuccin-frappe .content table tfoot td,html.theme--catppuccin-frappe .content table tfoot th{border-width:2px 0 0;color:#b0bef1}html.theme--catppuccin-frappe .content table tbody tr:last-child td,html.theme--catppuccin-frappe .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-frappe .content .tabs li+li{margin-top:0}html.theme--catppuccin-frappe .content.is-small,html.theme--catppuccin-frappe #documenter 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select:not([multiple]){padding-right:2.5em}html.theme--catppuccin-frappe .select select[multiple]{height:auto;padding:0}html.theme--catppuccin-frappe .select select[multiple] option{padding:0.5em 1em}html.theme--catppuccin-frappe .select:not(.is-multiple):not(.is-loading):hover::after{border-color:#99d1db}html.theme--catppuccin-frappe .select.is-white:not(:hover)::after{border-color:#fff}html.theme--catppuccin-frappe .select.is-white select{border-color:#fff}html.theme--catppuccin-frappe .select.is-white select:hover,html.theme--catppuccin-frappe .select.is-white select.is-hovered{border-color:#f2f2f2}html.theme--catppuccin-frappe .select.is-white select:focus,html.theme--catppuccin-frappe .select.is-white select.is-focused,html.theme--catppuccin-frappe .select.is-white select:active,html.theme--catppuccin-frappe .select.is-white select.is-active{box-shadow:0 0 0 0.125em rgba(255,255,255,0.25)}html.theme--catppuccin-frappe 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select.is-focused,html.theme--catppuccin-frappe .select.is-dark select:active,html.theme--catppuccin-frappe .content kbd.select select:active,html.theme--catppuccin-frappe .select.is-dark select.is-active,html.theme--catppuccin-frappe .content kbd.select select.is-active{box-shadow:0 0 0 0.125em rgba(65,69,89,0.25)}html.theme--catppuccin-frappe .select.is-primary:not(:hover)::after,html.theme--catppuccin-frappe .docstring>section>a.select.docs-sourcelink:not(:hover)::after{border-color:#8caaee}html.theme--catppuccin-frappe .select.is-primary select,html.theme--catppuccin-frappe .docstring>section>a.select.docs-sourcelink select{border-color:#8caaee}html.theme--catppuccin-frappe .select.is-primary select:hover,html.theme--catppuccin-frappe .docstring>section>a.select.docs-sourcelink select:hover,html.theme--catppuccin-frappe .select.is-primary select.is-hovered,html.theme--catppuccin-frappe .docstring>section>a.select.docs-sourcelink select.is-hovered{border-color:#769aeb}html.theme--catppuccin-frappe .select.is-primary select:focus,html.theme--catppuccin-frappe .docstring>section>a.select.docs-sourcelink select:focus,html.theme--catppuccin-frappe .select.is-primary select.is-focused,html.theme--catppuccin-frappe .docstring>section>a.select.docs-sourcelink select.is-focused,html.theme--catppuccin-frappe .select.is-primary select:active,html.theme--catppuccin-frappe .docstring>section>a.select.docs-sourcelink select:active,html.theme--catppuccin-frappe .select.is-primary select.is-active,html.theme--catppuccin-frappe .docstring>section>a.select.docs-sourcelink select.is-active{box-shadow:0 0 0 0.125em rgba(140,170,238,0.25)}html.theme--catppuccin-frappe .select.is-link:not(:hover)::after{border-color:#8caaee}html.theme--catppuccin-frappe .select.is-link select{border-color:#8caaee}html.theme--catppuccin-frappe .select.is-link select:hover,html.theme--catppuccin-frappe .select.is-link select.is-hovered{border-color:#769aeb}html.theme--catppuccin-frappe .select.is-link select:focus,html.theme--catppuccin-frappe .select.is-link select.is-focused,html.theme--catppuccin-frappe .select.is-link select:active,html.theme--catppuccin-frappe .select.is-link select.is-active{box-shadow:0 0 0 0.125em rgba(140,170,238,0.25)}html.theme--catppuccin-frappe .select.is-info:not(:hover)::after{border-color:#81c8be}html.theme--catppuccin-frappe .select.is-info select{border-color:#81c8be}html.theme--catppuccin-frappe .select.is-info select:hover,html.theme--catppuccin-frappe .select.is-info select.is-hovered{border-color:#6fc0b5}html.theme--catppuccin-frappe .select.is-info select:focus,html.theme--catppuccin-frappe .select.is-info select.is-focused,html.theme--catppuccin-frappe .select.is-info select:active,html.theme--catppuccin-frappe .select.is-info select.is-active{box-shadow:0 0 0 0.125em rgba(129,200,190,0.25)}html.theme--catppuccin-frappe 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a.navbar-item:focus,html.theme--catppuccin-frappe a.navbar-item:focus-within,html.theme--catppuccin-frappe a.navbar-item:hover,html.theme--catppuccin-frappe a.navbar-item.is-active,html.theme--catppuccin-frappe .navbar-link:focus,html.theme--catppuccin-frappe .navbar-link:focus-within,html.theme--catppuccin-frappe .navbar-link:hover,html.theme--catppuccin-frappe .navbar-link.is-active{background-color:rgba(0,0,0,0);color:#8caaee}html.theme--catppuccin-frappe .navbar-item{flex-grow:0;flex-shrink:0}html.theme--catppuccin-frappe .navbar-item img{max-height:1.75rem}html.theme--catppuccin-frappe .navbar-item.has-dropdown{padding:0}html.theme--catppuccin-frappe .navbar-item.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .navbar-item.is-tab{border-bottom:1px solid transparent;min-height:4rem;padding-bottom:calc(0.5rem - 1px)}html.theme--catppuccin-frappe .navbar-item.is-tab:focus,html.theme--catppuccin-frappe .navbar-item.is-tab:hover{background-color:rgba(0,0,0,0);border-bottom-color:#8caaee}html.theme--catppuccin-frappe .navbar-item.is-tab.is-active{background-color:rgba(0,0,0,0);border-bottom-color:#8caaee;border-bottom-style:solid;border-bottom-width:3px;color:#8caaee;padding-bottom:calc(0.5rem - 3px)}html.theme--catppuccin-frappe .navbar-content{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .navbar-link:not(.is-arrowless){padding-right:2.5em}html.theme--catppuccin-frappe .navbar-link:not(.is-arrowless)::after{border-color:#fff;margin-top:-0.375em;right:1.125em}html.theme--catppuccin-frappe .navbar-dropdown{font-size:0.875rem;padding-bottom:0.5rem;padding-top:0.5rem}html.theme--catppuccin-frappe .navbar-dropdown .navbar-item{padding-left:1.5rem;padding-right:1.5rem}html.theme--catppuccin-frappe .navbar-divider{background-color:rgba(0,0,0,0.2);border:none;display:none;height:2px;margin:0.5rem 0}@media screen and (max-width: 1055px){html.theme--catppuccin-frappe 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a.navbar-item:hover{background-color:rgba(0,0,0,0);color:#838ba7}html.theme--catppuccin-frappe .navbar-dropdown a.navbar-item.is-active{background-color:rgba(0,0,0,0);color:#8caaee}.navbar.is-spaced html.theme--catppuccin-frappe .navbar-dropdown,html.theme--catppuccin-frappe .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--catppuccin-frappe .navbar-dropdown.is-right{left:auto;right:0}html.theme--catppuccin-frappe .navbar-divider{display:block}html.theme--catppuccin-frappe .navbar>.container .navbar-brand,html.theme--catppuccin-frappe .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--catppuccin-frappe .navbar>.container .navbar-menu,html.theme--catppuccin-frappe .container>.navbar 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body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--catppuccin-frappe a.navbar-item.is-active,html.theme--catppuccin-frappe .navbar-link.is-active{color:#8caaee}html.theme--catppuccin-frappe a.navbar-item.is-active:not(:focus):not(:hover),html.theme--catppuccin-frappe .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--catppuccin-frappe .navbar-item.has-dropdown:focus .navbar-link,html.theme--catppuccin-frappe .navbar-item.has-dropdown:hover .navbar-link,html.theme--catppuccin-frappe .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--catppuccin-frappe .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--catppuccin-frappe .pagination{font-size:1rem;margin:-.25rem}html.theme--catppuccin-frappe .pagination.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--catppuccin-frappe .pagination.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .pagination.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .pagination.is-rounded .pagination-previous,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination .pagination-previous,html.theme--catppuccin-frappe .pagination.is-rounded .pagination-next,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination .pagination-next{padding-left:1em;padding-right:1em;border-radius:9999px}html.theme--catppuccin-frappe .pagination.is-rounded .pagination-link,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination .pagination-link{border-radius:9999px}html.theme--catppuccin-frappe .pagination,html.theme--catppuccin-frappe .pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link,html.theme--catppuccin-frappe .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link{border-color:#626880;color:#8caaee;min-width:2.5em}html.theme--catppuccin-frappe .pagination-previous:hover,html.theme--catppuccin-frappe .pagination-next:hover,html.theme--catppuccin-frappe .pagination-link:hover{border-color:#737994;color:#99d1db}html.theme--catppuccin-frappe .pagination-previous:focus,html.theme--catppuccin-frappe .pagination-next:focus,html.theme--catppuccin-frappe .pagination-link:focus{border-color:#737994}html.theme--catppuccin-frappe .pagination-previous:active,html.theme--catppuccin-frappe .pagination-next:active,html.theme--catppuccin-frappe .pagination-link:active{box-shadow:inset 0 1px 2px 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768px){html.theme--catppuccin-frappe .pagination{flex-wrap:wrap}html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .pagination-list li{flex-grow:1;flex-shrink:1}}@media screen and (min-width: 769px),print{html.theme--catppuccin-frappe .pagination-list{flex-grow:1;flex-shrink:1;justify-content:flex-start;order:1}html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link,html.theme--catppuccin-frappe .pagination-ellipsis{margin-bottom:0;margin-top:0}html.theme--catppuccin-frappe .pagination-previous{order:2}html.theme--catppuccin-frappe .pagination-next{order:3}html.theme--catppuccin-frappe .pagination{justify-content:space-between;margin-bottom:0;margin-top:0}html.theme--catppuccin-frappe .pagination.is-centered .pagination-previous{order:1}html.theme--catppuccin-frappe .pagination.is-centered 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.button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:hover,html.theme--catppuccin-latte .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus,html.theme--catppuccin-latte .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus:not(:active),html.theme--catppuccin-latte .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-latte .button.is-black:active,html.theme--catppuccin-latte .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:hover,html.theme--catppuccin-latte .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus,html.theme--catppuccin-latte .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus:not(:active),html.theme--catppuccin-latte .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-latte .button.is-light:active,html.theme--catppuccin-latte .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-latte .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted:hover,html.theme--catppuccin-latte .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-outlined:hover,html.theme--catppuccin-latte .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-light.is-outlined:focus,html.theme--catppuccin-latte .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark,html.theme--catppuccin-latte .content kbd.button{background-color:#ccd0da;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:hover,html.theme--catppuccin-latte .content kbd.button:hover,html.theme--catppuccin-latte .button.is-dark.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-hovered{background-color:#c5c9d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:focus,html.theme--catppuccin-latte .content kbd.button:focus,html.theme--catppuccin-latte .button.is-dark.is-focused,html.theme--catppuccin-latte .content kbd.button.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:focus:not(:active),html.theme--catppuccin-latte .content kbd.button:focus:not(:active),html.theme--catppuccin-latte .button.is-dark.is-focused:not(:active),html.theme--catppuccin-latte .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(204,208,218,0.25)}html.theme--catppuccin-latte .button.is-dark:active,html.theme--catppuccin-latte .content kbd.button:active,html.theme--catppuccin-latte .button.is-dark.is-active,html.theme--catppuccin-latte .content kbd.button.is-active{background-color:#bdc2cf;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark[disabled],html.theme--catppuccin-latte .content kbd.button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button{background-color:#ccd0da;border-color:#ccd0da;box-shadow:none}html.theme--catppuccin-latte .button.is-dark.is-inverted,html.theme--catppuccin-latte .content kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-focused{background-color:#ccd0da;border-color:#ccd0da;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-primary,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:hover,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#125ef4;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:focus,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:focus,html.theme--catppuccin-latte .button.is-primary.is-focused,html.theme--catppuccin-latte .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:focus:not(:active),html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--catppuccin-latte 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.docstring>section>a.button.is-inverted.docs-sourcelink{background-color:#fff;color:#1e66f5}html.theme--catppuccin-latte .button.is-primary.is-inverted:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-hovered.docs-sourcelink{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-primary.is-inverted[disabled],html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-primary.is-inverted,fieldset[disabled] html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.docs-sourcelink{background-color:#fff;border-color:transparent;box-shadow:none;color:#1e66f5}html.theme--catppuccin-latte .button.is-primary.is-loading::after,html.theme--catppuccin-latte 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.button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-success.is-light{background-color:#f1fbef;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:hover,html.theme--catppuccin-latte .button.is-success.is-light.is-hovered{background-color:#e8f8e5;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:active,html.theme--catppuccin-latte .button.is-success.is-light.is-active{background-color:#e0f5db;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:hover,html.theme--catppuccin-latte .button.is-warning.is-hovered{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus,html.theme--catppuccin-latte .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus:not(:active),html.theme--catppuccin-latte .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(223,142,29,0.25)}html.theme--catppuccin-latte .button.is-warning:active,html.theme--catppuccin-latte .button.is-warning.is-active{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:#df8e1d;box-shadow:none}html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-focused{background-color:#df8e1d;border-color:#df8e1d;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-light{background-color:#fdf6ed;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:hover,html.theme--catppuccin-latte .button.is-warning.is-light.is-hovered{background-color:#fbf1e2;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:active,html.theme--catppuccin-latte .button.is-warning.is-light.is-active{background-color:#faebd6;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:hover,html.theme--catppuccin-latte .button.is-danger.is-hovered{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus,html.theme--catppuccin-latte .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus:not(:active),html.theme--catppuccin-latte .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(210,15,57,0.25)}html.theme--catppuccin-latte .button.is-danger:active,html.theme--catppuccin-latte .button.is-danger.is-active{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:#d20f39;box-shadow:none}html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-focused{background-color:#d20f39;border-color:#d20f39;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-light{background-color:#feecf0;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:hover,html.theme--catppuccin-latte .button.is-danger.is-light.is-hovered{background-color:#fde0e6;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:active,html.theme--catppuccin-latte .button.is-danger.is-light.is-active{background-color:#fcd4dd;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-latte .button.is-small:not(.is-rounded),html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .button.is-normal{font-size:1rem}html.theme--catppuccin-latte .button.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .button.is-large{font-size:1.5rem}html.theme--catppuccin-latte .button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button{background-color:#9ca0b0;border-color:#acb0be;box-shadow:none;opacity:.5}html.theme--catppuccin-latte .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-latte .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-latte .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-latte .button.is-static{background-color:#e6e9ef;border-color:#acb0be;color:#8c8fa1;box-shadow:none;pointer-events:none}html.theme--catppuccin-latte .button.is-rounded,html.theme--catppuccin-latte #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--catppuccin-latte .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-latte .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-latte .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-latte .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-latte .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-latte .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-latte .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-latte .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-latte .buttons.has-addons .button:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-latte .buttons.has-addons .button:focus,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused,html.theme--catppuccin-latte .buttons.has-addons .button:active,html.theme--catppuccin-latte .buttons.has-addons .button.is-active,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-latte .buttons.has-addons .button:focus:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-latte .buttons.has-addons .button:active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-latte .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .buttons.is-centered{justify-content:center}html.theme--catppuccin-latte .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-latte .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-latte .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--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-latte .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-latte .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-latte .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-latte .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-latte .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-latte .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-latte .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-latte .content li+li{margin-top:0.25em}html.theme--catppuccin-latte .content p:not(:last-child),html.theme--catppuccin-latte .content dl:not(:last-child),html.theme--catppuccin-latte .content ol:not(:last-child),html.theme--catppuccin-latte .content ul:not(:last-child),html.theme--catppuccin-latte .content blockquote:not(:last-child),html.theme--catppuccin-latte .content pre:not(:last-child),html.theme--catppuccin-latte .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-latte .content h1,html.theme--catppuccin-latte .content h2,html.theme--catppuccin-latte .content h3,html.theme--catppuccin-latte .content h4,html.theme--catppuccin-latte .content h5,html.theme--catppuccin-latte .content h6{color:#4c4f69;font-weight:600;line-height:1.125}html.theme--catppuccin-latte .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-latte .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-latte .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-latte .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-latte .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-latte .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-latte .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-latte .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-latte .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-latte .content blockquote{background-color:#e6e9ef;border-left:5px solid #acb0be;padding:1.25em 1.5em}html.theme--catppuccin-latte .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-latte .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-latte .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-latte .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-latte .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-latte .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-latte .content ul ul ul{list-style-type:square}html.theme--catppuccin-latte .content dd{margin-left:2em}html.theme--catppuccin-latte 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th:not([align]){text-align:inherit}html.theme--catppuccin-latte .content table thead td,html.theme--catppuccin-latte .content table thead th{border-width:0 0 2px;color:#41445a}html.theme--catppuccin-latte .content table tfoot td,html.theme--catppuccin-latte .content table tfoot th{border-width:2px 0 0;color:#41445a}html.theme--catppuccin-latte .content table tbody tr:last-child td,html.theme--catppuccin-latte .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-latte .content .tabs li+li{margin-top:0}html.theme--catppuccin-latte .content.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-latte .content.is-normal{font-size:1rem}html.theme--catppuccin-latte .content.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .content.is-large{font-size:1.5rem}html.theme--catppuccin-latte 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#documenter .docs-sidebar form.docs-search>input.file{font-size:.75rem}html.theme--catppuccin-latte .file.is-normal{font-size:1rem}html.theme--catppuccin-latte .file.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .file.is-medium .file-icon .fa{font-size:21px}html.theme--catppuccin-latte .file.is-large{font-size:1.5rem}html.theme--catppuccin-latte .file.is-large .file-icon .fa{font-size:28px}html.theme--catppuccin-latte .file.has-name .file-cta{border-bottom-right-radius:0;border-top-right-radius:0}html.theme--catppuccin-latte .file.has-name .file-name{border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .file.has-name.is-empty .file-cta{border-radius:.4em}html.theme--catppuccin-latte .file.has-name.is-empty .file-name{display:none}html.theme--catppuccin-latte .file.is-boxed .file-label{flex-direction:column}html.theme--catppuccin-latte .file.is-boxed .file-cta{flex-direction:column;height:auto;padding:1em 3em}html.theme--catppuccin-latte .file.is-boxed .file-name{border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-boxed .file-icon{height:1.5em;width:1.5em}html.theme--catppuccin-latte .file.is-boxed .file-icon .fa{font-size:21px}html.theme--catppuccin-latte .file.is-boxed.is-small .file-icon .fa,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-boxed .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .file.is-boxed.is-medium .file-icon .fa{font-size:28px}html.theme--catppuccin-latte .file.is-boxed.is-large .file-icon .fa{font-size:35px}html.theme--catppuccin-latte .file.is-boxed.has-name .file-cta{border-radius:.4em .4em 0 0}html.theme--catppuccin-latte .file.is-boxed.has-name .file-name{border-radius:0 0 .4em .4em;border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-centered{justify-content:center}html.theme--catppuccin-latte .file.is-fullwidth .file-label{width:100%}html.theme--catppuccin-latte .file.is-fullwidth .file-name{flex-grow:1;max-width:none}html.theme--catppuccin-latte .file.is-right{justify-content:flex-end}html.theme--catppuccin-latte .file.is-right .file-cta{border-radius:0 .4em .4em 0}html.theme--catppuccin-latte .file.is-right .file-name{border-radius:.4em 0 0 .4em;border-width:1px 0 1px 1px;order:-1}html.theme--catppuccin-latte .file-label{align-items:stretch;display:flex;cursor:pointer;justify-content:flex-start;overflow:hidden;position:relative}html.theme--catppuccin-latte .file-label:hover .file-cta{background-color:#c5c9d5;color:#41445a}html.theme--catppuccin-latte .file-label:hover .file-name{border-color:#a5a9b8}html.theme--catppuccin-latte .file-label:active .file-cta{background-color:#bdc2cf;color:#41445a}html.theme--catppuccin-latte .file-label:active .file-name{border-color:#9ea2b3}html.theme--catppuccin-latte .file-input{height:100%;left:0;opacity:0;outline:none;position:absolute;top:0;width:100%}html.theme--catppuccin-latte .file-cta,html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-radius:.4em;font-size:1em;padding-left:1em;padding-right:1em;white-space:nowrap}html.theme--catppuccin-latte .file-cta{background-color:#ccd0da;color:#4c4f69}html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-style:solid;border-width:1px 1px 1px 0;display:block;max-width:16em;overflow:hidden;text-align:inherit;text-overflow:ellipsis}html.theme--catppuccin-latte .file-icon{align-items:center;display:flex;height:1em;justify-content:center;margin-right:.5em;width:1em}html.theme--catppuccin-latte .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .label{color:#41445a;display:block;font-size:1rem;font-weight:700}html.theme--catppuccin-latte .label:not(:last-child){margin-bottom:0.5em}html.theme--catppuccin-latte .label.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.label{font-size:.75rem}html.theme--catppuccin-latte .label.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .label.is-large{font-size:1.5rem}html.theme--catppuccin-latte .help{display:block;font-size:.75rem;margin-top:0.25rem}html.theme--catppuccin-latte .help.is-white{color:#fff}html.theme--catppuccin-latte .help.is-black{color:#0a0a0a}html.theme--catppuccin-latte .help.is-light{color:#f5f5f5}html.theme--catppuccin-latte .help.is-dark,html.theme--catppuccin-latte .content kbd.help{color:#ccd0da}html.theme--catppuccin-latte .help.is-primary,html.theme--catppuccin-latte .docstring>section>a.help.docs-sourcelink{color:#1e66f5}html.theme--catppuccin-latte .help.is-link{color:#1e66f5}html.theme--catppuccin-latte .help.is-info{color:#179299}html.theme--catppuccin-latte .help.is-success{color:#40a02b}html.theme--catppuccin-latte .help.is-warning{color:#df8e1d}html.theme--catppuccin-latte .help.is-danger{color:#d20f39}html.theme--catppuccin-latte .field:not(:last-child){margin-bottom:0.75rem}html.theme--catppuccin-latte .field.has-addons{display:flex;justify-content:flex-start}html.theme--catppuccin-latte .field.has-addons .control:not(:last-child){margin-right:-1px}html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .button,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .select select{border-radius:0}html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .select select{border-bottom-right-radius:0;border-top-right-radius:0}html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .select select{border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-hovered:not([disabled]){z-index:2}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]){z-index:3}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]):hover{z-index:4}html.theme--catppuccin-latte .field.has-addons .control.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .field.has-addons.has-addons-centered{justify-content:center}html.theme--catppuccin-latte .field.has-addons.has-addons-right{justify-content:flex-end}html.theme--catppuccin-latte .field.has-addons.has-addons-fullwidth .control{flex-grow:1;flex-shrink:0}html.theme--catppuccin-latte .field.is-grouped{display:flex;justify-content:flex-start}html.theme--catppuccin-latte .field.is-grouped>.control{flex-shrink:0}html.theme--catppuccin-latte .field.is-grouped>.control:not(:last-child){margin-bottom:0;margin-right:.75rem}html.theme--catppuccin-latte .field.is-grouped>.control.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .field.is-grouped.is-grouped-centered{justify-content:center}html.theme--catppuccin-latte .field.is-grouped.is-grouped-right{justify-content:flex-end}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline{flex-wrap:wrap}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline>.control:last-child,html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline>.control:not(:last-child){margin-bottom:0.75rem}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline:last-child{margin-bottom:-0.75rem}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline:not(:last-child){margin-bottom:0}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .field.is-horizontal{display:flex}}html.theme--catppuccin-latte .field-label .label{font-size:inherit}@media screen and (max-width: 768px){html.theme--catppuccin-latte .field-label{margin-bottom:0.5rem}}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .field-label{flex-basis:0;flex-grow:1;flex-shrink:0;margin-right:1.5rem;text-align:right}html.theme--catppuccin-latte .field-label.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.field-label{font-size:.75rem;padding-top:0.375em}html.theme--catppuccin-latte .field-label.is-normal{padding-top:0.375em}html.theme--catppuccin-latte .field-label.is-medium{font-size:1.25rem;padding-top:0.375em}html.theme--catppuccin-latte .field-label.is-large{font-size:1.5rem;padding-top:0.375em}}html.theme--catppuccin-latte .field-body .field .field{margin-bottom:0}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .field-body{display:flex;flex-basis:0;flex-grow:5;flex-shrink:1}html.theme--catppuccin-latte .field-body .field{margin-bottom:0}html.theme--catppuccin-latte .field-body>.field{flex-shrink:1}html.theme--catppuccin-latte .field-body>.field:not(.is-narrow){flex-grow:1}html.theme--catppuccin-latte .field-body>.field:not(:last-child){margin-right:.75rem}}html.theme--catppuccin-latte .control{box-sizing:border-box;clear:both;font-size:1rem;position:relative;text-align:inherit}html.theme--catppuccin-latte .control.has-icons-left .input:focus~.icon,html.theme--catppuccin-latte .control.has-icons-left #documenter .docs-sidebar form.docs-search>input:focus~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-left form.docs-search>input:focus~.icon,html.theme--catppuccin-latte .control.has-icons-left .select:focus~.icon,html.theme--catppuccin-latte .control.has-icons-right .input:focus~.icon,html.theme--catppuccin-latte .control.has-icons-right #documenter .docs-sidebar form.docs-search>input:focus~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-right form.docs-search>input:focus~.icon,html.theme--catppuccin-latte .control.has-icons-right .select:focus~.icon{color:#ccd0da}html.theme--catppuccin-latte .control.has-icons-left .input.is-small~.icon,html.theme--catppuccin-latte .control.has-icons-left #documenter .docs-sidebar form.docs-search>input~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-left form.docs-search>input~.icon,html.theme--catppuccin-latte .control.has-icons-left .select.is-small~.icon,html.theme--catppuccin-latte .control.has-icons-right .input.is-small~.icon,html.theme--catppuccin-latte .control.has-icons-right #documenter .docs-sidebar form.docs-search>input~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-right form.docs-search>input~.icon,html.theme--catppuccin-latte .control.has-icons-right .select.is-small~.icon{font-size:.75rem}html.theme--catppuccin-latte .control.has-icons-left .input.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-left #documenter .docs-sidebar form.docs-search>input.is-medium~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-left form.docs-search>input.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-left .select.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-right .input.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-right #documenter .docs-sidebar form.docs-search>input.is-medium~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-right form.docs-search>input.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-right .select.is-medium~.icon{font-size:1.25rem}html.theme--catppuccin-latte .control.has-icons-left 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kbd.button.is-outlined{background-color:transparent;border-color:#363a4f;box-shadow:none;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-macchiato .content 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.button.is-info.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-focused{background-color:#8bd5ca;border-color:#8bd5ca;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-outlined{background-color:transparent;border-color:#8bd5ca;box-shadow:none;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-light{background-color:#f0faf8;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:hover,html.theme--catppuccin-macchiato .button.is-info.is-light.is-hovered{background-color:#e7f6f4;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:active,html.theme--catppuccin-macchiato .button.is-info.is-light.is-active{background-color:#ddf3f0;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:hover,html.theme--catppuccin-macchiato .button.is-success.is-hovered{background-color:#9ed78c;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus,html.theme--catppuccin-macchiato .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus:not(:active),html.theme--catppuccin-macchiato .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,218,149,0.25)}html.theme--catppuccin-macchiato .button.is-success:active,html.theme--catppuccin-macchiato .button.is-success.is-active{background-color:#96d382;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:#a6da95;box-shadow:none}html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-focused{background-color:#a6da95;border-color:#a6da95;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-light{background-color:#f2faf0;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:hover,html.theme--catppuccin-macchiato .button.is-success.is-light.is-hovered{background-color:#eaf6e6;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:active,html.theme--catppuccin-macchiato .button.is-success.is-light.is-active{background-color:#e2f3dd;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:hover,html.theme--catppuccin-macchiato .button.is-warning.is-hovered{background-color:#eccf94;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus,html.theme--catppuccin-macchiato .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus:not(:active),html.theme--catppuccin-macchiato .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(238,212,159,0.25)}html.theme--catppuccin-macchiato .button.is-warning:active,html.theme--catppuccin-macchiato .button.is-warning.is-active{background-color:#eaca89;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:#eed49f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-focused{background-color:#eed49f;border-color:#eed49f;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-light{background-color:#fcf7ee;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:hover,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-hovered{background-color:#faf2e3;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:active,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-active{background-color:#f8eed8;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:hover,html.theme--catppuccin-macchiato .button.is-danger.is-hovered{background-color:#eb7c8c;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus,html.theme--catppuccin-macchiato .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus:not(:active),html.theme--catppuccin-macchiato .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(237,135,150,0.25)}html.theme--catppuccin-macchiato .button.is-danger:active,html.theme--catppuccin-macchiato .button.is-danger.is-active{background-color:#ea7183;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:#ed8796;box-shadow:none}html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-focused{background-color:#ed8796;border-color:#ed8796;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-light{background-color:#fcedef;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:hover,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-hovered{background-color:#fbe2e6;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:active,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-active{background-color:#f9d7dc;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-small:not(.is-rounded),html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .button.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .button.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .button.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button{background-color:#6e738d;border-color:#5b6078;box-shadow:none;opacity:.5}html.theme--catppuccin-macchiato .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-macchiato .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-macchiato .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-macchiato .button.is-static{background-color:#1e2030;border-color:#5b6078;color:#8087a2;box-shadow:none;pointer-events:none}html.theme--catppuccin-macchiato .button.is-rounded,html.theme--catppuccin-macchiato #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--catppuccin-macchiato .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-macchiato .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-macchiato .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-macchiato .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-macchiato .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-macchiato .buttons.are-small 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.container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-macchiato .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-macchiato .content li+li{margin-top:0.25em}html.theme--catppuccin-macchiato .content p:not(:last-child),html.theme--catppuccin-macchiato .content dl:not(:last-child),html.theme--catppuccin-macchiato .content ol:not(:last-child),html.theme--catppuccin-macchiato .content ul:not(:last-child),html.theme--catppuccin-macchiato .content blockquote:not(:last-child),html.theme--catppuccin-macchiato .content pre:not(:last-child),html.theme--catppuccin-macchiato .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-macchiato .content h1,html.theme--catppuccin-macchiato .content h2,html.theme--catppuccin-macchiato .content h3,html.theme--catppuccin-macchiato .content h4,html.theme--catppuccin-macchiato .content h5,html.theme--catppuccin-macchiato .content 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ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-macchiato .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-macchiato .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-macchiato .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-macchiato .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-macchiato .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-macchiato .content ul ul ul{list-style-type:square}html.theme--catppuccin-macchiato .content dd{margin-left:2em}html.theme--catppuccin-macchiato .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-macchiato 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form.docs-search>input.is-active{box-shadow:0 0 0 0.125em rgba(255,255,255,0.25)}html.theme--catppuccin-macchiato .is-black.textarea,html.theme--catppuccin-macchiato .is-black.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black{border-color:#0a0a0a}html.theme--catppuccin-macchiato .is-black.textarea:focus,html.theme--catppuccin-macchiato .is-black.input:focus,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:focus,html.theme--catppuccin-macchiato .is-black.is-focused.textarea,html.theme--catppuccin-macchiato .is-black.is-focused.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--catppuccin-macchiato .is-black.textarea:active,html.theme--catppuccin-macchiato .is-black.input:active,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:active,html.theme--catppuccin-macchiato 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html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-link.is-light{background-color:#ebf3fe;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:hover,html.theme--catppuccin-mocha .button.is-link.is-light.is-hovered{background-color:#dfebfe;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:active,html.theme--catppuccin-mocha .button.is-link.is-light.is-active{background-color:#d3e3fd;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:hover,html.theme--catppuccin-mocha .button.is-info.is-hovered{background-color:#8adfd1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus,html.theme--catppuccin-mocha .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus:not(:active),html.theme--catppuccin-mocha .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(148,226,213,0.25)}html.theme--catppuccin-mocha .button.is-info:active,html.theme--catppuccin-mocha .button.is-info.is-active{background-color:#80ddcd;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:#94e2d5;box-shadow:none}html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-focused{background-color:#94e2d5;border-color:#94e2d5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-light{background-color:#effbf9;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:hover,html.theme--catppuccin-mocha .button.is-info.is-light.is-hovered{background-color:#e5f8f5;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:active,html.theme--catppuccin-mocha .button.is-info.is-light.is-active{background-color:#dbf5f1;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:hover,html.theme--catppuccin-mocha .button.is-success.is-hovered{background-color:#9de097;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus,html.theme--catppuccin-mocha .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus:not(:active),html.theme--catppuccin-mocha .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,227,161,0.25)}html.theme--catppuccin-mocha .button.is-success:active,html.theme--catppuccin-mocha .button.is-success.is-active{background-color:#93dd8d;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:#a6e3a1;box-shadow:none}html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-focused{background-color:#a6e3a1;border-color:#a6e3a1;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-light{background-color:#f0faef;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:hover,html.theme--catppuccin-mocha .button.is-success.is-light.is-hovered{background-color:#e7f7e5;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:active,html.theme--catppuccin-mocha .button.is-success.is-light.is-active{background-color:#def4dc;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:hover,html.theme--catppuccin-mocha .button.is-warning.is-hovered{background-color:#f8dea3;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus,html.theme--catppuccin-mocha .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus:not(:active),html.theme--catppuccin-mocha .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(249,226,175,0.25)}html.theme--catppuccin-mocha .button.is-warning:active,html.theme--catppuccin-mocha .button.is-warning.is-active{background-color:#f7d997;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:#f9e2af;box-shadow:none}html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-focused{background-color:#f9e2af;border-color:#f9e2af;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-light{background-color:#fef8ec;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:hover,html.theme--catppuccin-mocha .button.is-warning.is-light.is-hovered{background-color:#fdf4e0;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:active,html.theme--catppuccin-mocha .button.is-warning.is-light.is-active{background-color:#fcf0d4;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:hover,html.theme--catppuccin-mocha .button.is-danger.is-hovered{background-color:#f27f9f;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus,html.theme--catppuccin-mocha .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus:not(:active),html.theme--catppuccin-mocha .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(243,139,168,0.25)}html.theme--catppuccin-mocha .button.is-danger:active,html.theme--catppuccin-mocha .button.is-danger.is-active{background-color:#f17497;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:#f38ba8;box-shadow:none}html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-focused{background-color:#f38ba8;border-color:#f38ba8;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-light{background-color:#fdedf1;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:hover,html.theme--catppuccin-mocha .button.is-danger.is-light.is-hovered{background-color:#fce1e8;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:active,html.theme--catppuccin-mocha .button.is-danger.is-light.is-active{background-color:#fbd5e0;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-mocha .button.is-small:not(.is-rounded),html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .button.is-normal{font-size:1rem}html.theme--catppuccin-mocha .button.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .button.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .button[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button{background-color:#6c7086;border-color:#585b70;box-shadow:none;opacity:.5}html.theme--catppuccin-mocha .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-mocha .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-mocha .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-mocha .button.is-static{background-color:#181825;border-color:#585b70;color:#7f849c;box-shadow:none;pointer-events:none}html.theme--catppuccin-mocha .button.is-rounded,html.theme--catppuccin-mocha #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--catppuccin-mocha .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-mocha .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-mocha .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-mocha .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-mocha .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-mocha .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-mocha .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-mocha .buttons.has-addons .button:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-mocha .buttons.has-addons .button:focus,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused,html.theme--catppuccin-mocha .buttons.has-addons .button:active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-mocha .buttons.has-addons .button:focus:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-mocha .buttons.has-addons .button:active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-mocha .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-mocha .buttons.is-centered{justify-content:center}html.theme--catppuccin-mocha .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-mocha .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-mocha .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--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-mocha .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-mocha .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-mocha .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-mocha .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-mocha .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-mocha .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-mocha .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-mocha .content li+li{margin-top:0.25em}html.theme--catppuccin-mocha .content p:not(:last-child),html.theme--catppuccin-mocha .content dl:not(:last-child),html.theme--catppuccin-mocha .content ol:not(:last-child),html.theme--catppuccin-mocha .content ul:not(:last-child),html.theme--catppuccin-mocha .content blockquote:not(:last-child),html.theme--catppuccin-mocha .content pre:not(:last-child),html.theme--catppuccin-mocha .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-mocha .content h1,html.theme--catppuccin-mocha .content h2,html.theme--catppuccin-mocha .content h3,html.theme--catppuccin-mocha .content h4,html.theme--catppuccin-mocha .content h5,html.theme--catppuccin-mocha .content h6{color:#cdd6f4;font-weight:600;line-height:1.125}html.theme--catppuccin-mocha .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-mocha .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-mocha .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-mocha .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-mocha .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-mocha .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-mocha .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-mocha .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-mocha .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-mocha .content blockquote{background-color:#181825;border-left:5px solid #585b70;padding:1.25em 1.5em}html.theme--catppuccin-mocha .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-mocha .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-mocha .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-mocha .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-mocha .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-mocha .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-mocha .content ul ul ul{list-style-type:square}html.theme--catppuccin-mocha .content dd{margin-left:2em}html.theme--catppuccin-mocha .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-mocha .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-mocha .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-mocha .content figure img{display:inline-block}html.theme--catppuccin-mocha .content figure figcaption{font-style:italic}html.theme--catppuccin-mocha .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-mocha .content sup,html.theme--catppuccin-mocha .content sub{font-size:75%}html.theme--catppuccin-mocha .content table{width:100%}html.theme--catppuccin-mocha .content table td,html.theme--catppuccin-mocha .content table th{border:1px solid #585b70;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-mocha .content table th{color:#b8c5ef}html.theme--catppuccin-mocha .content table th:not([align]){text-align:inherit}html.theme--catppuccin-mocha .content table thead td,html.theme--catppuccin-mocha .content table thead th{border-width:0 0 2px;color:#b8c5ef}html.theme--catppuccin-mocha .content table tfoot td,html.theme--catppuccin-mocha .content table tfoot th{border-width:2px 0 0;color:#b8c5ef}html.theme--catppuccin-mocha .content table tbody tr:last-child td,html.theme--catppuccin-mocha .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-mocha .content .tabs li+li{margin-top:0}html.theme--catppuccin-mocha .content.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-mocha .content.is-normal{font-size:1rem}html.theme--catppuccin-mocha .content.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .content.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-mocha .icon.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-mocha .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-mocha .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-mocha .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-mocha .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-mocha .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-mocha .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-mocha div.icon-text{display:flex}html.theme--catppuccin-mocha .image,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-mocha .image img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-mocha .image img.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-mocha .image.is-fullwidth,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-mocha .image.is-square img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-mocha .image.is-square .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-mocha .image.is-1by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar 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.has-ratio,html.theme--catppuccin-mocha .image.is-5by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-mocha .image.is-5by3 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-mocha .image.is-16by9 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-mocha .image.is-16by9 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-mocha .image.is-2by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-mocha .image.is-2by1 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-mocha .image.is-3by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-mocha 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img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-mocha .image.is-3by5 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-mocha .image.is-9by16 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-mocha .image.is-9by16 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-mocha .image.is-1by2 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-mocha .image.is-1by2 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-mocha .image.is-1by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-mocha .image.is-1by3 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-mocha .image.is-square,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--catppuccin-mocha .image.is-1by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--catppuccin-mocha .image.is-5by4,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--catppuccin-mocha .image.is-4by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--catppuccin-mocha .image.is-3by2,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--catppuccin-mocha .image.is-5by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--catppuccin-mocha .image.is-16by9,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--catppuccin-mocha .image.is-2by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--catppuccin-mocha .image.is-3by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--catppuccin-mocha .image.is-4by5,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--catppuccin-mocha .image.is-3by4,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--catppuccin-mocha .image.is-2by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--catppuccin-mocha .image.is-3by5,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--catppuccin-mocha .image.is-9by16,html.theme--catppuccin-mocha #documenter 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.button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:hover,html.theme--documenter-dark .button.is-light.is-hovered{background-color:#e5eaec;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus,html.theme--documenter-dark .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus:not(:active),html.theme--documenter-dark .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(236,240,241,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#dde4e6;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:#ecf0f1;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#ecf0f1;border-color:#ecf0f1;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(40,47,47,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#1d2122;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:#282f2f;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content 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 kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus:not(:active),html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--documenter-dark .button.is-primary.is-focused:not(:active),html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink:not(:active){box-shadow:0 0 0 0.125em rgba(55,90,127,0.25)}html.theme--documenter-dark .button.is-primary:active,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:active,html.theme--documenter-dark .button.is-primary.is-active,html.theme--documenter-dark .docstring>section>a.button.is-active.docs-sourcelink{background-color:#2f4d6d;border-color:transparent;color:#fff}html.theme--documenter-dark 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.docstring>section>a.button.is-inverted.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-inverted.docs-sourcelink{background-color:#fff;border-color:transparent;box-shadow:none;color:#375a7f}html.theme--documenter-dark .button.is-primary.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-loading.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#375a7f;color:#375a7f}html.theme--documenter-dark .button.is-primary.is-outlined:hover,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-outlined.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#375a7f;border-color:#375a7f;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #375a7f #375a7f !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined[disabled],html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#375a7f;box-shadow:none;color:#375a7f}html.theme--documenter-dark 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.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 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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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.button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(40,47,47,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#1d2122;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content 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kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content 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 kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark 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.docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#375a7f;border-color:#375a7f;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #375a7f #375a7f !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined[disabled],html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#375a7f;box-shadow:none;color:#375a7f}html.theme--documenter-dark 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.button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-link.is-outlined{background-color:transparent;border-color:#1abc9c;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-outlined:hover,html.theme--documenter-dark .button.is-link.is-outlined.is-hovered,html.theme--documenter-dark .button.is-link.is-outlined:focus,html.theme--documenter-dark .button.is-link.is-outlined.is-focused{background-color:#1abc9c;border-color:#1abc9c;color:#fff}html.theme--documenter-dark .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #1abc9c #1abc9c !important}html.theme--documenter-dark .button.is-link.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-outlined{background-color:transparent;border-color:#1abc9c;box-shadow:none;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #1abc9c #1abc9c !important}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-link.is-light{background-color:#edfdf9;color:#15987e}html.theme--documenter-dark .button.is-link.is-light:hover,html.theme--documenter-dark .button.is-link.is-light.is-hovered{background-color:#e2fbf6;border-color:transparent;color:#15987e}html.theme--documenter-dark .button.is-link.is-light:active,html.theme--documenter-dark .button.is-link.is-light.is-active{background-color:#d7f9f3;border-color:transparent;color:#15987e}html.theme--documenter-dark .button.is-info{background-color:#3c5dcd;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info:hover,html.theme--documenter-dark .button.is-info.is-hovered{background-color:#3355c9;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info:focus,html.theme--documenter-dark .button.is-info.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info:focus:not(:active),html.theme--documenter-dark .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(60,93,205,0.25)}html.theme--documenter-dark .button.is-info:active,html.theme--documenter-dark .button.is-info.is-active{background-color:#3151bf;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info{background-color:#3c5dcd;border-color:#3c5dcd;box-shadow:none}html.theme--documenter-dark .button.is-info.is-inverted{background-color:#fff;color:#3c5dcd}html.theme--documenter-dark .button.is-info.is-inverted:hover,html.theme--documenter-dark .button.is-info.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#3c5dcd}html.theme--documenter-dark .button.is-info.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-info.is-outlined{background-color:transparent;border-color:#3c5dcd;color:#3c5dcd}html.theme--documenter-dark .button.is-info.is-outlined:hover,html.theme--documenter-dark .button.is-info.is-outlined.is-hovered,html.theme--documenter-dark .button.is-info.is-outlined:focus,html.theme--documenter-dark .button.is-info.is-outlined.is-focused{background-color:#3c5dcd;border-color:#3c5dcd;color:#fff}html.theme--documenter-dark .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #3c5dcd #3c5dcd !important}html.theme--documenter-dark .button.is-info.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-info.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info.is-outlined{background-color:transparent;border-color:#3c5dcd;box-shadow:none;color:#3c5dcd}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#3c5dcd}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #3c5dcd #3c5dcd !important}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-info.is-light{background-color:#eff2fb;color:#3253c3}html.theme--documenter-dark .button.is-info.is-light:hover,html.theme--documenter-dark .button.is-info.is-light.is-hovered{background-color:#e5e9f8;border-color:transparent;color:#3253c3}html.theme--documenter-dark .button.is-info.is-light:active,html.theme--documenter-dark .button.is-info.is-light.is-active{background-color:#dae1f6;border-color:transparent;color:#3253c3}html.theme--documenter-dark .button.is-success{background-color:#259a12;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:hover,html.theme--documenter-dark .button.is-success.is-hovered{background-color:#228f11;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:focus,html.theme--documenter-dark .button.is-success.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:focus:not(:active),html.theme--documenter-dark .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(37,154,18,0.25)}html.theme--documenter-dark .button.is-success:active,html.theme--documenter-dark .button.is-success.is-active{background-color:#20830f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success{background-color:#259a12;border-color:#259a12;box-shadow:none}html.theme--documenter-dark .button.is-success.is-inverted{background-color:#fff;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#259a12}html.theme--documenter-dark .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#259a12;color:#259a12}html.theme--documenter-dark .button.is-success.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-outlined.is-focused{background-color:#259a12;border-color:#259a12;color:#fff}html.theme--documenter-dark .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #259a12 #259a12 !important}html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#259a12;box-shadow:none;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #259a12 #259a12 !important}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-success.is-light{background-color:#effded;color:#2ec016}html.theme--documenter-dark .button.is-success.is-light:hover,html.theme--documenter-dark .button.is-success.is-light.is-hovered{background-color:#e5fce1;border-color:transparent;color:#2ec016}html.theme--documenter-dark .button.is-success.is-light:active,html.theme--documenter-dark .button.is-success.is-light.is-active{background-color:#dbfad6;border-color:transparent;color:#2ec016}html.theme--documenter-dark .button.is-warning{background-color:#f4c72f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning:hover,html.theme--documenter-dark .button.is-warning.is-hovered{background-color:#f3c423;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning:focus,html.theme--documenter-dark .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning:focus:not(:active),html.theme--documenter-dark .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(244,199,47,0.25)}html.theme--documenter-dark .button.is-warning:active,html.theme--documenter-dark .button.is-warning.is-active{background-color:#f3c017;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning{background-color:#f4c72f;border-color:#f4c72f;box-shadow:none}html.theme--documenter-dark .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#f4c72f;color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-outlined.is-focused{background-color:#f4c72f;border-color:#f4c72f;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f4c72f #f4c72f !important}html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#f4c72f;box-shadow:none;color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f4c72f #f4c72f !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fefaec;color:#8c6e07}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fdf7e0;border-color:transparent;color:#8c6e07}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fdf3d3;border-color:transparent;color:#8c6e07}html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:hover,html.theme--documenter-dark .button.is-danger.is-hovered{background-color:#c13930;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus,html.theme--documenter-dark .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus:not(:active),html.theme--documenter-dark .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(203,60,51,0.25)}html.theme--documenter-dark .button.is-danger:active,html.theme--documenter-dark .button.is-danger.is-active{background-color:#b7362e;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:#cb3c33;box-shadow:none}html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-outlined.is-focused{background-color:#cb3c33;border-color:#cb3c33;color:#fff}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;box-shadow:none;color:#cb3c33}html.theme--documenter-dark 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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:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}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 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.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 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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 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Theme: Default Description: Original highlight.js style Author: (c) Ivan Sagalaev diff --git a/dev/financial_math/index.html b/dev/financial_math/index.html index 30a8f3b..733464d 100644 --- a/dev/financial_math/index.html +++ b/dev/financial_math/index.html @@ -1,5 +1,5 @@ -Financial Math · ActuaryUtilities.jl

Financial Math Submodule

Provides a set of common routines in financial maths.

Quickstart

cfs = [5, 5, 105]
+Financial Math · ActuaryUtilities.jl        
         
 
Financial Math Submodule
Provides a set of common routines in financial maths.
Quickstart
cfs = [5, 5, 105]
 times    = [1, 2, 3]
 
 discount_rate = 0.03
@@ -7,7 +7,7 @@
 present_value(discount_rate, cfs, times)           # 105.65
 duration(Macaulay(), discount_rate, cfs, times)    #   2.86
 duration(discount_rate, cfs, times)                #   2.78
-convexity(discount_rate, cfs, times)               #  10.62
API
Exported API
ActuaryUtilities.FinancialMath.KeyRate — Type
KeyRate(timepoints,shift=0.001)
A convenience constructor for KeyRateZero. 
Extended Help
KeyRateZero is chosen as the default constructor because it has more attractive properties than KeyRatePar:
  • rates after the key timepoint remain unaffected by the shift
    • e.g. this causes a 6-year zero coupon bond would have a negative duration if the 5-year par rate was used
source
ActuaryUtilities.FinancialMath.KeyRatePar — Type
KeyRatePar(timepoint,shift=0.001) <: KeyRateDuration
Shift the par curve by the given amount at the given timepoint. Use in conjunction with duration to calculate the key rate duration. 
Unlike other duration statistics which are computed using analytic derivatives, KeyRateDurations are computed via a shift-and-compute the yield curve approach.
KeyRatePar is more commonly reported (than KeyRateZero) in the fixed income markets, even though the latter has more analytically attractive properties. See the discussion of KeyRateDuration in the FinanceModels.jl docs.
source
ActuaryUtilities.FinancialMath.KeyRateZero — Type
KeyRateZero(timepoint,shift=0.001) <: KeyRateDuration
Shift the par curve by the given amount at the given timepoint. Use in conjunction with duration to calculate the key rate duration.
Unlike other duration statistics which are computed using analytic derivatives, KeyRateDuration is computed via a shift-and-compute the yield curve approach.
KeyRateZero is less commonly reported (than KeyRatePar) in the fixed income markets, even though the latter has more analytically attractive properties. See the discussion of KeyRateDuration in the FinanceModels.jl docs.
source
ActuaryUtilities.FinancialMath.breakeven — Function
breakeven(yield, cashflows::Vector)
+convexity(discount_rate, cfs, times)               #  10.62
API
Exported API
ActuaryUtilities.FinancialMath.KeyRate — Type
KeyRate(timepoints,shift=0.001)
A convenience constructor for KeyRateZero. 
Extended Help
KeyRateZero is chosen as the default constructor because it has more attractive properties than KeyRatePar:
  • rates after the key timepoint remain unaffected by the shift
    • e.g. this causes a 6-year zero coupon bond would have a negative duration if the 5-year par rate was used
source
ActuaryUtilities.FinancialMath.KeyRatePar — Type
KeyRatePar(timepoint,shift=0.001) <: KeyRateDuration
Shift the par curve by the given amount at the given timepoint. Use in conjunction with duration to calculate the key rate duration. 
Unlike other duration statistics which are computed using analytic derivatives, KeyRateDurations are computed via a shift-and-compute the yield curve approach.
KeyRatePar is more commonly reported (than KeyRateZero) in the fixed income markets, even though the latter has more analytically attractive properties. See the discussion of KeyRateDuration in the FinanceModels.jl docs.
source
ActuaryUtilities.FinancialMath.KeyRateZero — Type
KeyRateZero(timepoint,shift=0.001) <: KeyRateDuration
Shift the par curve by the given amount at the given timepoint. Use in conjunction with duration to calculate the key rate duration.
Unlike other duration statistics which are computed using analytic derivatives, KeyRateDuration is computed via a shift-and-compute the yield curve approach.
KeyRateZero is less commonly reported (than KeyRatePar) in the fixed income markets, even though the latter has more analytically attractive properties. See the discussion of KeyRateDuration in the FinanceModels.jl docs.
source
ActuaryUtilities.FinancialMath.breakeven — Function
breakeven(yield, cashflows::Vector)
 breakeven(yield, cashflows::Vector,times::Vector)
Calculate the time when the accumulated cashflows breakeven given the yield.
Assumptions:
  • cashflows occur at the end of the period
  • cashflows evenly spaced with the first one occuring at time zero if times not given
Returns nothing if cashflow stream never breaks even.
julia> breakeven(0.10, [-10,1,2,3,4,8])
 5
 
@@ -16,7 +16,7 @@
 
 julia> breakeven(0.10, [-10,-15,2,3,4,8]) # returns the `nothing` value
 
-
source
ActuaryUtilities.FinancialMath.convexity — Method
convexity(yield,cfs,times)
 convexity(yield,valuation_function)
Calculates the convexity.     - yield should be a fixed effective yield (e.g. 0.05).     - times may be omitted and it will assume cfs are evenly spaced beginning at the end of the first period.
Examples
Using vectors of cashflows and times
julia> times = 1:5
 julia> cfs = [0,0,0,0,100]
 julia> duration(0.03,cfs,times)
@@ -33,15 +33,15 @@
 4.854368932038835
 julia> convexity(0.03,my_lump_sum_value)
 28.277877274012617
-
source
ActuaryUtilities.FinancialMath.moic — Method
moic(cashflows<:AbstractArray)
The multiple on invested capital ("moic") is the un-discounted sum of distributions divided by the sum of the contributions. The function assumes that negative numbers in the array represent contributions and positive numbers represent distributions.
Examples
julia> moic([-10,20,30])
-5.0
source
ActuaryUtilities.FinancialMath.present_values — Function
present_values(interest, cashflows, timepoints)
Efficiently calculate a vector representing the present value of the given cashflows at each period prior to the given timepoint.
Examples
julia> present_values(0.00, [1,1,1])
+
source
ActuaryUtilities.FinancialMath.moic — Method
moic(cashflows<:AbstractArray)
The multiple on invested capital ("moic") is the un-discounted sum of distributions divided by the sum of the contributions. The function assumes that negative numbers in the array represent contributions and positive numbers represent distributions.
Examples
julia> moic([-10,20,30])
+5.0
source
ActuaryUtilities.FinancialMath.present_values — Function
present_values(interest, cashflows, timepoints)
Efficiently calculate a vector representing the present value of the given cashflows at each period prior to the given timepoint.
Examples
julia> present_values(0.00, [1,1,1])
 [3,2,1]
 
 julia> present_values(ForwardYield([0.1,0.2]), [10,20],[0,1]) # after `using FinanceModels`
 2-element Vector{Float64}:
  28.18181818181818
- 18.18181818181818
source
ActuaryUtilities.FinancialMath.price — Method
price(...)
The absolute value of the present_value(...). 
Extended help
Using price can be helpful if the directionality of the value doesn't matter. For example, in the common usage, duration is more interested in the change in price than present value, so price is used there.
source
ActuaryUtilities.FinancialMath.spread — Function
spread(curve1,curve2,cashflows)
Return the solved-for constant spread to add to curve1 in order to equate the discounted cashflows with curve2
Examples
spread(0.04, 0.05, cfs)
-Rate{Float64, Periodic}(0.010000000000000009, Periodic(1))
source
ActuaryUtilities.FinancialMath.price — Method
price(...)
The absolute value of the present_value(...). 
Extended help
Using price can be helpful if the directionality of the value doesn't matter. For example, in the common usage, duration is more interested in the change in price than present value, so price is used there.
source
ActuaryUtilities.FinancialMath.spread — Function
spread(curve1,curve2,cashflows)
Return the solved-for constant spread to add to curve1 in order to equate the discounted cashflows with curve2
Examples
spread(0.04, 0.05, cfs)
+Rate{Float64, Periodic}(0.010000000000000009, Periodic(1))
source
ActuaryUtilities.duration — Method
duration(keyrate::KeyRateDuration,curve,cashflows)    
 duration(keyrate::KeyRateDuration,curve,cashflows,timepoints)
 duration(keyrate::KeyRateDuration,curve,cashflows,timepoints,krd_points)
Calculate the key rate duration by shifting the zero (not par) curve by the kwarg shift at the timepoint specified by a KeyRateDuration(time).
The approach is to carve up the curve into krd_points (default is the unit steps between 1 and  the last timepoint of the casfhlows). The  zero rate corresponding to the timepoint within the KeyRateDuration is shifted by shift (specified by the KeyRateZero or KeyRatePar constructors. A new curve is created from the shifted rates. This means that the  "width" of the shifted section is ± 1 time period, unless specific points are specified via krd_points.
The curve may be any FinanceModels.jl curve (e.g. does not have to be a curve constructed via FinanceModels.Zero(...)).
!!! Experimental: Due to the paucity of examples in the literature, this feature does not have unit tests like the rest of JuliaActuary functionality. Additionally, the API may change in a future major/minor version update.
Examples
julia> riskfree_maturities = [0.5, 1.0, 1.5, 2.0];
 
@@ -53,7 +53,7 @@
 
 julia> duration(KeyRate(1),rf_curve,cfs)
 8.932800152336995
-
Extended Help
Key Rate Duration is not a well specified topic in the literature and in practice. The reference below suggest that shocking the par curve is more common  in practice, but that the zero curve produces more consistent results. Future versions may support shifting the par curve.
References: 
source
ActuaryUtilities.duration — Method
duration(Macaulay(),interest_rate,cfs,times)
+
Extended Help
Key Rate Duration is not a well specified topic in the literature and in practice. The reference below suggest that shocking the par curve is more common  in practice, but that the zero curve produces more consistent results. Future versions may support shifting the par curve.
References: 
source
ActuaryUtilities.duration — Method
duration(Macaulay(),interest_rate,cfs,times)
 duration(Modified(),interest_rate,cfs,times)
 duration(DV01(),interest_rate,cfs,times)
 duration(interest_rate,cfs,times)             # Modified Duration
@@ -84,4 +84,4 @@
 4.854368932038835
 julia> convexity(0.03,my_lump_sum_value)
 28.277877274012617
-
source
Unexported API

+
source

Unexported API

diff --git a/dev/index.html b/dev/index.html index 6183664..1acb83b 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,5 +1,5 @@ -Overview · ActuaryUtilities.jl

Quickstart

cfs = [5, 5, 105]
+Overview · ActuaryUtilities.jl        
         
 
Quickstart
cfs = [5, 5, 105]
 times    = [1, 2, 3]
 
 discount_rate = 0.03
@@ -16,4 +16,4 @@
 discount(r,cashflows)
  • convert between rates with:
r = Rate(0.05,Periodic(1));
 
 convert(Periodic(2),  r)   # convert to compounded twice per timestep
-convert(Continuous(2),r)   # convert to compounded twice per timestep
For more on Rates, see FinanceCore.jl. FinanceModels.jl also provides a rich and flexible set of yield models to use.
Documentation
Full documentation is available here.
Examples
Interactive, basic cashflow analysis
See JuliaActuary.org for instructions on running this example.
Simple cashflow analysis with ActuaryUtilities.jl
Useful tips
Functions often use a mix of interest_rates, cashflows, and timepoints. When calling functions, the general order of the arguments is 1) interest rates, 2) cashflows, and 3) timepoints.

+convert(Continuous(2),r)   # convert to compounded twice per timestep

For more on Rates, see FinanceCore.jl. FinanceModels.jl also provides a rich and flexible set of yield models to use.

Documentation

Full documentation is available here.

Examples

Interactive, basic cashflow analysis

See JuliaActuary.org for instructions on running this example.

Simple cashflow analysis with ActuaryUtilities.jl

Useful tips

Functions often use a mix of interest_rates, cashflows, and timepoints. When calling functions, the general order of the arguments is 1) interest rates, 2) cashflows, and 3) timepoints.

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Risk Measures

Quickstart

outcomes = rand(100)
+Risk Measures · ActuaryUtilities.jl        
         
 
Risk Measures
Quickstart
outcomes = rand(100)
 
 # direct usage
 VaR(0.90)(outcomes) # ≈ 0.90  
@@ -9,8 +9,8 @@
 # construct a reusable object (functor)
 rm = VaR(0.90)
 
-rm(outcomes) # ≈ 0.90
Introduction
Risk measures encompass the set of functions that map a set of outcomes to an output value characterizing the associated riskiness of those outcomes. As is usual when attempting to compress information (e.g. condensing information into a single value), there are multiple ways we can charactize this riskiness.
Coherence & Other Desirable Properties
Further, it is desireable that a risk measure has certain properties, and risk measures that meet the first four criteria are called "Coherent" in the literature.  From "An Introduction to Risk Measures for Actuarial Applications" (Hardy), she describes as follows:
Using $H$ as a risk measure and $X$ as the associated risk distribution:
1. Translation Invariance
For any non-random $c$
%$H(X + c) = H(X) + c$% This means that adding a constant amount (positive or negative) to a risk adds the same amount to the risk measure. It also implies that the risk measure for a non-random loss, with known value c, say, is just the amount of the loss c.
2. Positive Homogeneity
For any non-random $λ > 0$:
\[H(λX) = λH(X)\]
This axiom implies that changing the units of loss does not change the risk measure.
3. Subadditivity
For any two random losses $X$ and $Y$,
\[H(X + Y) ≤ H(X) + H(Y)\]
It should not be possible to reduce the economic capital required (or the appropriate premium) for a risk by splitting it into constituent parts. Or, in other words, diversification (ie consolidating risks) cannot make the risk greater, but it might make the risk smaller if the risks are less than perfectly correlated.
4. Monotonicity
If $Pr(X ≤ Y) = 1$ then $H(X) ≤ H(Y)$.
If one risk is always bigger then another, the risk measures should be similarly ordered.
Other Properties
In "Properties of Distortion Risk Measures" (Balbás, Garrido, Mayoral) also note other properties of interest:
Complete
Completeness is the property that the distortion function associated with the risk measure produces a unique mapping between the original risk's survial function $S(x)$ and the distorted  $S*(x)$ for each $x$. See Distortion Risk Measures for more detail on this.
In practice, this means that a non-complete risk measure ignores some part of the risk distribution (e.g. CTE and VaR don't use the full distribution and have the same)
Exhaustive
A risk measure is "exhaustive" if it is coherent and complete.
Adaptable
A risk measure is "adapted" or "adaptable" if its distortion function (ee Distortion Risk Measures).$g$:
1. $g$ is strictly concave, that is $g$ is strictly decreasing. 
-2. $lim_{u\to0+} g\prime(u) = \inf and lim_{u\to1-} g\prime(u) = 0.
Adaptive risk measures are exhaustive but the converse is not true.
Summary of Risk Measure Properties
MeasureCoherentCompleteExhaustiveAdaptableCondition 2
VaRNoNoNoNoNo
CTEYesNoNoNoNo
DualPower $(y > 1)$YesYesYesNoYes
ProportionalHazard $(γ > 1)$YesYesYesNoYes
WangTransformYesYesYesYesYes
Distortion Risk Measures
Distortion Risk Measures (Wikipedia Link) are a way of remapping the probabilities of a risk distribution in order to compute a risk measure $H$ on the risk distribution $X$.
Adapting Wang (2002), there are two key components:
Distortion Function $g(u)$
This remaps values in the [0,1] range to another value in the [0,1] range, and in $H$ below, operates on the survival function $S$ and $F=1-S$.
Let $g:[0,1]\to[0,1]$ be an increasing function with $g(0)=0$ and $g(1)=1$. The transform $F^*(x)=g(F(x))$ defines a distorted probability distribution, where "$g$" is called a distortion function.
Note that $F^*$ and $F$ are equivalent probability measures if and only if $g:[0,1]\to[0,1]$ is continuous and one-to-one. Definition 4.2. We define a family of distortion risk-measures using the mean-value under the distorted probability $F^*(x)=g(F(x))$:
Risk Measure Integration
To calculate a risk measure $H$, we integrate the distorted $F$ across all possible values in the risk distribution (i.e. $x \in X$):
\[H(X) = E^*(X) = - \int_{-\infty}^0 g(F(x))dx + \int_0^{+\infty}[1-g(F(x))]dx\]
That is, the risk measure ($H$) is equal to the expected value of the distortion of the risk ditribution ($E^*(X)$).
Examples
Basic Usage
outcomes = rand(100)
+rm(outcomes) # ≈ 0.90
Introduction
Risk measures encompass the set of functions that map a set of outcomes to an output value characterizing the associated riskiness of those outcomes. As is usual when attempting to compress information (e.g. condensing information into a single value), there are multiple ways we can characterize this riskiness.
Coherence & Other Desirable Properties
Further, it is desirable that a risk measure has certain properties, and risk measures that meet the first four criteria are called "Coherent" in the literature.  From "An Introduction to Risk Measures for Actuarial Applications" (Hardy), she describes as follows:
Using $H$ as a risk measure and $X$ as the associated risk distribution:
1. Translation Invariance
For any non-random $c$
%$H(X + c) = H(X) + c$% This means that adding a constant amount (positive or negative) to a risk adds the same amount to the risk measure. It also implies that the risk measure for a non-random loss, with known value c, say, is just the amount of the loss c.
2. Positive Homogeneity
For any non-random $λ > 0$:
\[H(λX) = λH(X)\]
This axiom implies that changing the units of loss does not change the risk measure.
3. Subadditivity
For any two random losses $X$ and $Y$,
\[H(X + Y) ≤ H(X) + H(Y)\]
It should not be possible to reduce the economic capital required (or the appropriate premium) for a risk by splitting it into constituent parts. Or, in other words, diversification (ie consolidating risks) cannot make the risk greater, but it might make the risk smaller if the risks are less than perfectly correlated.
4. Monotonicity
If $Pr(X ≤ Y) = 1$ then $H(X) ≤ H(Y)$.
If one risk is always bigger then another, the risk measures should be similarly ordered.
Other Properties
In "Properties of Distortion Risk Measures" (Balbás, Garrido, Mayoral) also note other properties of interest:
Complete
Completeness is the property that the distortion function associated with the risk measure produces a unique mapping between the original risk's survival function $S(x)$ and the distorted  $S*(x)$ for each $x$. See Distortion Risk Measures for more detail on this.
In practice, this means that a non-complete risk measure ignores some part of the risk distribution (e.g. CTE and VaR don't use the full distribution and have the same)
Exhaustive
A risk measure is "exhaustive" if it is coherent and complete.
Adaptable
A risk measure is "adapted" or "adaptable" if its distortion function (ee Distortion Risk Measures). $g$:
1. $g$ is strictly concave, that is $g$ is strictly decreasing. 
+2. $lim_{u\to0+} g\prime(u) = \inf and lim_{u\to1-} g\prime(u) = 0.
Adaptive risk measures are exhaustive but the converse is not true.
Summary of Risk Measure Properties
MeasureCoherentCompleteExhaustiveAdaptableCondition 2
VaRNoNoNoNoNo
CTEYesNoNoNoNo
DualPower $(y > 1)$YesYesYesNoYes
ProportionalHazard $(γ > 1)$YesYesYesNoYes
WangTransformYesYesYesYesYes
Distortion Risk Measures
Distortion Risk Measures (Wikipedia Link) are a way of remapping the probabilities of a risk distribution in order to compute a risk measure $H$ on the risk distribution $X$.
Adapting Wang (2002), there are two key components:
Distortion Function $g(u)$
This remaps values in the [0,1] range to another value in the [0,1] range, and in $H$ below, operates on the survival function $S$ and $F=1-S$.
Let $g:[0,1]\to[0,1]$ be an increasing function with $g(0)=0$ and $g(1)=1$. The transform $F^*(x)=g(F(x))$ defines a distorted probability distribution, where "$g$" is called a distortion function.
Note that $F^*$ and $F$ are equivalent probability measures if and only if $g:[0,1]\to[0,1]$ is continuous and one-to-one. Definition 4.2. We define a family of distortion risk-measures using the mean-value under the distorted probability $F^*(x)=g(F(x))$:
Risk Measure Integration
To calculate a risk measure $H$, we integrate the distorted $F$ across all possible values in the risk distribution (i.e. $x \in X$):
\[H(X) = E^*(X) = - \int_{-\infty}^0 g(F(x))dx + \int_0^{+\infty}[1-g(F(x))]dx\]
That is, the risk measure ($H$) is equal to the expected value of the distortion of the risk distribution ($E^*(X)$).
Examples
Basic Usage
outcomes = rand(100)
 
 # direct usage
 VaR(0.90)(outcomes) # ≈ 0.90  
@@ -83,7 +83,7 @@
     axislegend(ax,position=:lt)
 
         f
-end
Example block output
API
Exported API
ActuaryUtilities.RiskMeasures.CTE — Type
CTE(α)::RiskMeasure
+end
Example block output
API
Exported API
ActuaryUtilities.RiskMeasures.CTE — Type
CTE(α)::RiskMeasure
 CTE(α)(risk)::T (where T is the type of values sampled in risk)
The Conditional Tail Expectation (CTE) at level α is the expected value of the risk distribution above the αth quantile. risk can be a univariate distribution or an array of outcomes. Assumes more positive values are higher risk measures, so a higher p will return a more positive number.
CTE(α) returns a functor which can then be called on a risk distribution.
Parameters
  • α: [0,1.0) 
Examples
julia> CTE(0.95)(rand(1000))
 0.9766218612020593
 
@@ -91,8 +91,8 @@
 CTE{Float64}(0.95)
 
 julia> rm(rand(1000))
-0.9739835010268733
source
ActuaryUtilities.RiskMeasures.DualPower — Type
DualPower(v)::RiskMeasure
-DualPower(v)(risk)::T (where T is the type of values sampled in risk)
The Dual Power distortion risk measure is defined as $1 - (1 - x)^v$, where x is the cumulative distribution function (CDF) of the risk distribution and v is a positive parameter. risk can be a univariate distribution or an array of outcomes.
DualPower(v) returns a functor which can then be called on a risk distribution.
source
ActuaryUtilities.RiskMeasures.DualPower — Type
DualPower(v)::RiskMeasure
+DualPower(v)(risk)::T (where T is the type of values sampled in risk)
The Dual Power distortion risk measure is defined as $1 - (1 - x)^v$, where x is the cumulative distribution function (CDF) of the risk distribution and v is a positive parameter. risk can be a univariate distribution or an array of outcomes.
DualPower(v) returns a functor which can then be called on a risk distribution.
source
ActuaryUtilities.RiskMeasures.ProportionalHazard — Type
ProportionalHazard(y)::RiskMeasure
 ProportionalHazard(y)(risk)::T (where T is the type of values sampled in risk)
The Proportional Hazard distortion risk measure is defined as $x^(1/y)$, where x is the cumulative distribution function (CDF) of the risk distribution and y is a positive parameter. risk can be a univariate distribution or an array of outcomes. ProportionalHazard(y) returns a functor which can then be called on a risk distribution.
Examples
julia> ProportionalHazard(2)(rand(1000))
 0.6659603556774121
 
@@ -100,7 +100,7 @@
 ProportionalHazard{Int64}(2)
 
 julia> rm(rand(1000))
-0.6710587338367799
source
ActuaryUtilities.RiskMeasures.VaR — Type
 VaR(α)::RiskMeasure
  VaR(α)(risk)::T (where T is the type of values sampled in `risk`)
The αth quantile of the risk distribution is the Value at Risk, or αth quantile. risk can be a univariate distribution or an array of outcomes. Assumes more positive values are higher risk measures, so a higher p will return a more positive number. For a discrete risk, the VaR returned is the first value above the αth percentile.
VaR(α) returns a functor which can then be called on a risk distribution.
Parameters
  • α: [0,1.0) 
Examples
julia> VaR(0.95)(rand(1000))
 0.9561843082268024
 
@@ -108,7 +108,7 @@
 VaR{Float64}(0.95)
 
 julia> rm(rand(1000))
-0.9597070153670079
source
ActuaryUtilities.RiskMeasures.WangTransform — Type
WangTransform(α)::RiskMeasure
 WangTransform(α)(risk)::T (where T is the type of values sampled in risk)
The Wang Transform is a distortion risk measure that transforms the cumulative distribution function (CDF) of the risk distribution using a normal distribution with mean Φ⁻¹(α) and standard deviation 1. risk can be a univariate distribution or an array of outcomes.
WangTransform(α) returns a functor which can then be called on a risk distribution.
Parameters
  • α: [0,1.0]
In the literature, sometimes λ is used where $\lambda = \Phi^{-1}(\alpha)$.
Examples
julia> WangTransform(0.95)(rand(1000))
 0.8799465543360105
 
@@ -116,7 +116,7 @@
 WangTransform{Float64}(0.95)
 
 julia> rm(rand(1000))
-0.8892245759705852
References
  • "A Risk Measure That Goes Beyond Coherence", Shaun S. Wang, 2002
source
Unexported API
Unexported API
ActuaryUtilities.RiskMeasures.Expectation — Type
Expectation()::RiskMeasure
 Expectation()(risk)::T (where T is the type of values sampled in `risk`)
The expected value of the risk.
Expectation() returns a functor which can then be called on a risk distribution.
Examples
julia> RiskMeasures.Expectation(rand(1000))
 0.4793223308812537
 
@@ -124,5 +124,5 @@
 ActuaryUtilities.RiskMeasures.Expectation()
 
 julia> rm(rand(1000))
-0.4941708036889741
source
ActuaryUtilities.RiskMeasures.cdf_func — Method
cdf_function(risk)
Returns the appropriate cumulative distribution function depending on the type, specifically:
cdf_func(S::AbstractArray{<:Real}) = StatsBase.ecdf(S)
-cdf_func(S::Distributions.UnivariateDistribution) = x -> Distributions.cdf(S, x)
source

+0.4941708036889741
source
ActuaryUtilities.RiskMeasures.cdf_func — Method
cdf_function(risk)

Returns the appropriate cumulative distribution function depending on the type, specifically:

cdf_func(S::AbstractArray{<:Real}) = StatsBase.ecdf(S)
+cdf_func(S::Distributions.UnivariateDistribution) = x -> Distributions.cdf(S, x)
source
diff --git a/dev/search_index.js b/dev/search_index.js index 2cfe5e2..d43598d 100644 --- a/dev/search_index.js +++ b/dev/search_index.js @@ -1,3 +1,3 @@ var documenterSearchIndex = {"docs": -[{"location":"risk_measures/#Risk-Measures","page":"Risk Measures","title":"Risk Measures","text":"","category":"section"},{"location":"risk_measures/#Quickstart","page":"Risk Measures","title":"Quickstart","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"outcomes = rand(100)\n\n# direct usage\nVaR(0.90)(outcomes) # ≈ 0.90 \nCTE(0.90)(outcomes) # ≈ 0.95 \nWangTransform(0.90)(outcomes) # ≈ 0.81\n\n# construct a reusable object (functor)\nrm = VaR(0.90)\n\nrm(outcomes) # ≈ 0.90","category":"page"},{"location":"risk_measures/#Introduction","page":"Risk Measures","title":"Introduction","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Risk measures encompass the set of functions that map a set of outcomes to an output value characterizing the associated riskiness of those outcomes. As is usual when attempting to compress information (e.g. condensing information into a single value), there are multiple ways we can charactize this riskiness.","category":"page"},{"location":"risk_measures/#Coherence-and-Other-Desirable-Properties","page":"Risk Measures","title":"Coherence & Other Desirable Properties","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Further, it is desireable that a risk measure has certain properties, and risk measures that meet the first four criteria are called \"Coherent\" in the literature. From \"An Introduction to Risk Measures for Actuarial Applications\" (Hardy), she describes as follows:","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Using H as a risk measure and X as the associated risk distribution:","category":"page"},{"location":"risk_measures/#1.-Translation-Invariance","page":"Risk Measures","title":"1. Translation Invariance","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"For any non-random c","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"%H(X + c) = H(X) + c% This means that adding a constant amount (positive or negative) to a risk adds the same amount to the risk measure. It also implies that the risk measure for a non-random loss, with known value c, say, is just the amount of the loss c.","category":"page"},{"location":"risk_measures/#2.-Positive-Homogeneity","page":"Risk Measures","title":"2. Positive Homogeneity","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"For any non-random λ 0:","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"H(λX) = λH(X)","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"This axiom implies that changing the units of loss does not change the risk measure.","category":"page"},{"location":"risk_measures/#3.-Subadditivity","page":"Risk Measures","title":"3. Subadditivity","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"For any two random losses X and Y,","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"H(X + Y) H(X) + H(Y)","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"It should not be possible to reduce the economic capital required (or the appropriate premium) for a risk by splitting it into constituent parts. Or, in other words, diversification (ie consolidating risks) cannot make the risk greater, but it might make the risk smaller if the risks are less than perfectly correlated.","category":"page"},{"location":"risk_measures/#4.-Monotonicity","page":"Risk Measures","title":"4. Monotonicity","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"If Pr(X Y) = 1 then H(X) H(Y).","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"If one risk is always bigger then another, the risk measures should be similarly ordered.","category":"page"},{"location":"risk_measures/#Other-Properties","page":"Risk Measures","title":"Other Properties","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"In \"Properties of Distortion Risk Measures\" (Balbás, Garrido, Mayoral) also note other properties of interest:","category":"page"},{"location":"risk_measures/#Complete","page":"Risk Measures","title":"Complete","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Completeness is the property that the distortion function associated with the risk measure produces a unique mapping between the original risk's survial function S(x) and the distorted S*(x) for each x. See Distortion Risk Measures for more detail on this.","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"In practice, this means that a non-complete risk measure ignores some part of the risk distribution (e.g. CTE and VaR don't use the full distribution and have the same)","category":"page"},{"location":"risk_measures/#Exhaustive","page":"Risk Measures","title":"Exhaustive","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"A risk measure is \"exhaustive\" if it is coherent and complete.","category":"page"},{"location":"risk_measures/#Adaptable","page":"Risk Measures","title":"Adaptable","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"A risk measure is \"adapted\" or \"adaptable\" if its distortion function (ee Distortion Risk Measures).g:","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"1. $g$ is strictly concave, that is $g$ is strictly decreasing. \n2. $lim_{u\\to0+} g\\prime(u) = \\inf and lim_{u\\to1-} g\\prime(u) = 0.","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Adaptive risk measures are exhaustive but the converse is not true.","category":"page"},{"location":"risk_measures/#Summary-of-Risk-Measure-Properties","page":"Risk Measures","title":"Summary of Risk Measure Properties","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Measure Coherent Complete Exhaustive Adaptable Condition 2\nVaR No No No No No\nCTE Yes No No No No\nDualPower (y 1) Yes Yes Yes No Yes\nProportionalHazard (γ 1) Yes Yes Yes No Yes\nWangTransform Yes Yes Yes Yes Yes","category":"page"},{"location":"risk_measures/#Distortion-Risk-Measures","page":"Risk Measures","title":"Distortion Risk Measures","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Distortion Risk Measures (Wikipedia Link) are a way of remapping the probabilities of a risk distribution in order to compute a risk measure H on the risk distribution X.","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Adapting Wang (2002), there are two key components:","category":"page"},{"location":"risk_measures/#Distortion-Function-g(u)","page":"Risk Measures","title":"Distortion Function g(u)","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"This remaps values in the [0,1] range to another value in the [0,1] range, and in H below, operates on the survival function S and F=1-S.","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Let g01to01 be an increasing function with g(0)=0 and g(1)=1. The transform F^*(x)=g(F(x)) defines a distorted probability distribution, where \"g\" is called a distortion function.","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Note that F^* and F are equivalent probability measures if and only if g01to01 is continuous and one-to-one. Definition 4.2. We define a family of distortion risk-measures using the mean-value under the distorted probability F^*(x)=g(F(x)):","category":"page"},{"location":"risk_measures/#Risk-Measure-Integration","page":"Risk Measures","title":"Risk Measure Integration","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"To calculate a risk measure H, we integrate the distorted F across all possible values in the risk distribution (i.e. x in X):","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"H(X) = E^*(X) = - int_-infty^0 g(F(x))dx + int_0^+infty1-g(F(x))dx","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"That is, the risk measure (H) is equal to the expected value of the distortion of the risk ditribution (E^*(X)).","category":"page"},{"location":"risk_measures/#Examples","page":"Risk Measures","title":"Examples","text":"","category":"section"},{"location":"risk_measures/#Basic-Usage","page":"Risk Measures","title":"Basic Usage","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"outcomes = rand(100)\n\n# direct usage\nVaR(0.90)(outcomes) # ≈ 0.90 \nCTE(0.90)(outcomes) # ≈ 0.95 \nWangTransform(0.90)(outcomes) # ≈ 0.81\n\n# construct a reusable object (functor)\nrm = VaR(0.90)\n\nrm(outcomes) # ≈ 0.90","category":"page"},{"location":"risk_measures/#Comparison","page":"Risk Measures","title":"Comparison","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"We will generate a random outcome and show how the risk measures behave:","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"using Distributions\nusing ActuaryUtilities\nusing CairoMakie\n\noutcomes = Weibull(1,5)\n# or this could be discrete outcomes as in the next line\n#outcomes = rand(LogNormal(2,10)*100,2000) \n\nαs= range(0.00,0.99;length=100)\n\nlet \n f = Figure()\n ax = Axis(f[1,1],\n xlabel=\"α\",\n ylabel=\"Loss\",\n title = \"Comparison of Risk Measures\",\n xgridvisible=false,\n ygridvisible=false,\n )\n\n lines!(ax,\n αs,\n [quantile(outcomes, α) for α in αs],\n label = \"Quantile α of Outcome\",\n color = :grey10,\n linewidth = 3,\n )\n \n lines!(ax,\n αs,\n [VaR(α)(outcomes) for α in αs],\n label = \"VaR(α)\",\n linestyle=:dash\n )\n lines!(ax,\n αs,\n [CTE(α)(outcomes) for α in αs],\n label = \"CTE(α)\",\n )\n lines!(ax,\n αs[2:end],\n [WangTransform(α)(outcomes) for α in αs[2:end]],\n label = \"WangTransform(α)\",\n )\n lines!(ax,\n αs,\n [ProportionalHazard(2)(outcomes) for α in αs],\n label = \"ProportionalHazard(2)\",\n )\n \n lines!(ax,\n αs,\n [DualPower(2)(outcomes) for α in αs],\n label = \"DualPower(2)\",\n )\n lines!(ax,\n αs,\n [RiskMeasures.Expectation()(outcomes) for α in αs],\n label = \"Expectation\",\n )\n axislegend(ax,position=:lt)\n\n f\nend","category":"page"},{"location":"risk_measures/#API","page":"Risk Measures","title":"API","text":"","category":"section"},{"location":"risk_measures/#Exported-API","page":"Risk Measures","title":"Exported API","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Modules = [ActuaryUtilities.RiskMeasures]\nPrivate = false","category":"page"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.CTE","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.CTE","text":"CTE(α)::RiskMeasure\nCTE(α)(risk)::T (where T is the type of values sampled in risk)\n\nThe Conditional Tail Expectation (CTE) at level α is the expected value of the risk distribution above the αth quantile. risk can be a univariate distribution or an array of outcomes. Assumes more positive values are higher risk measures, so a higher p will return a more positive number.\n\nCTE(α) returns a functor which can then be called on a risk distribution.\n\nParameters\n\nα: [0,1.0) \n\nExamples\n\njulia> CTE(0.95)(rand(1000))\n0.9766218612020593\n\njulia> rm = CTE(0.95)\nCTE{Float64}(0.95)\n\njulia> rm(rand(1000))\n0.9739835010268733\n\n\n\n\n\n","category":"type"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.ConditionalTailExpectation","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.ConditionalTailExpectation","text":"CTE\n\n\n\n\n\n","category":"type"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.DualPower","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.DualPower","text":"DualPower(v)::RiskMeasure\nDualPower(v)(risk)::T (where T is the type of values sampled in risk)\n\nThe Dual Power distortion risk measure is defined as 1 - (1 - x)^v, where x is the cumulative distribution function (CDF) of the risk distribution and v is a positive parameter. risk can be a univariate distribution or an array of outcomes.\n\nDualPower(v) returns a functor which can then be called on a risk distribution.\n\n\n\n\n\n","category":"type"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.ProportionalHazard","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.ProportionalHazard","text":"ProportionalHazard(y)::RiskMeasure\nProportionalHazard(y)(risk)::T (where T is the type of values sampled in risk)\n\nThe Proportional Hazard distortion risk measure is defined as x^(1y), where x is the cumulative distribution function (CDF) of the risk distribution and y is a positive parameter. risk can be a univariate distribution or an array of outcomes. ProportionalHazard(y) returns a functor which can then be called on a risk distribution.\n\nExamples\n\njulia> ProportionalHazard(2)(rand(1000))\n0.6659603556774121\n\njulia> rm = ProportionalHazard(2)\nProportionalHazard{Int64}(2)\n\njulia> rm(rand(1000))\n0.6710587338367799\n\n\n\n\n\n","category":"type"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.VaR","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.VaR","text":" VaR(α)::RiskMeasure\n VaR(α)(risk)::T (where T is the type of values sampled in `risk`)\n\nThe αth quantile of the risk distribution is the Value at Risk, or αth quantile. risk can be a univariate distribution or an array of outcomes. Assumes more positive values are higher risk measures, so a higher p will return a more positive number. For a discrete risk, the VaR returned is the first value above the αth percentile.\n\nVaR(α) returns a functor which can then be called on a risk distribution.\n\nParameters\n\nα: [0,1.0) \n\nExamples\n\njulia> VaR(0.95)(rand(1000))\n0.9561843082268024\n\njulia> rm = VaR(0.95)\nVaR{Float64}(0.95)\n\njulia> rm(rand(1000))\n0.9597070153670079\n\n\n\n\n\n","category":"type"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.ValueAtRisk","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.ValueAtRisk","text":"VaR\n\n\n\n\n\n","category":"type"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.WangTransform","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.WangTransform","text":"WangTransform(α)::RiskMeasure\nWangTransform(α)(risk)::T (where T is the type of values sampled in risk)\n\nThe Wang Transform is a distortion risk measure that transforms the cumulative distribution function (CDF) of the risk distribution using a normal distribution with mean Φ⁻¹(α) and standard deviation 1. risk can be a univariate distribution or an array of outcomes.\n\nWangTransform(α) returns a functor which can then be called on a risk distribution.\n\nParameters\n\nα: [0,1.0]\n\nIn the literature, sometimes λ is used where lambda = Phi^-1(alpha).\n\nExamples\n\njulia> WangTransform(0.95)(rand(1000))\n0.8799465543360105\n\njulia> rm = WangTransform(0.95)\nWangTransform{Float64}(0.95)\n\njulia> rm(rand(1000))\n0.8892245759705852\n\nReferences\n\n\"A Risk Measure That Goes Beyond Coherence\", Shaun S. Wang, 2002\n\n\n\n\n\n","category":"type"},{"location":"risk_measures/#Unexported-API","page":"Risk Measures","title":"Unexported API","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Modules = [ActuaryUtilities.RiskMeasures]\nPublic = false","category":"page"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.Expectation","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.Expectation","text":"Expectation()::RiskMeasure\nExpectation()(risk)::T (where T is the type of values sampled in `risk`)\n\nThe expected value of the risk.\n\nExpectation() returns a functor which can then be called on a risk distribution.\n\nExamples\n\njulia> RiskMeasures.Expectation(rand(1000))\n0.4793223308812537\n\njulia> rm = RiskMeasures.Expectation()\nActuaryUtilities.RiskMeasures.Expectation()\n\njulia> rm(rand(1000))\n0.4941708036889741\n\n\n\n\n\n","category":"type"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.cdf_func-Tuple{AbstractArray{<:Real}}","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.cdf_func","text":"cdf_function(risk)\n\nReturns the appropriate cumulative distribution function depending on the type, specifically:\n\ncdf_func(S::AbstractArray{<:Real}) = StatsBase.ecdf(S)\ncdf_func(S::Distributions.UnivariateDistribution) = x -> Distributions.cdf(S, x)\n\n\n\n\n\n","category":"method"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.g-Tuple{ActuaryUtilities.RiskMeasures.RiskMeasure, Any}","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.g","text":"g(rm::RiskMeasure,x)\n\nThe probability distortion function associated with the given risk measure.\n\nSee Distortion Function g(u)\n\n\n\n\n\n","category":"method"},{"location":"API/ActuaryUtilities/#ActuaryUtilities-API-Reference","page":"ActuaryUtilities","title":"ActuaryUtilities API Reference","text":"","category":"section"},{"location":"API/ActuaryUtilities/","page":"ActuaryUtilities","title":"ActuaryUtilities","text":"Modules = [ActuaryUtilities]","category":"page"},{"location":"API/ActuaryUtilities/#Exported-API","page":"ActuaryUtilities","title":"Exported API","text":"","category":"section"},{"location":"API/ActuaryUtilities/","page":"ActuaryUtilities","title":"ActuaryUtilities","text":"Modules = [ActuaryUtilities]\nPrivate = false","category":"page"},{"location":"API/ActuaryUtilities/#Unexported-API","page":"ActuaryUtilities","title":"Unexported API","text":"","category":"section"},{"location":"API/ActuaryUtilities/","page":"ActuaryUtilities","title":"ActuaryUtilities","text":"Modules = [ActuaryUtilities]\nPublic = false","category":"page"},{"location":"API/ActuaryUtilities/","page":"ActuaryUtilities","title":"ActuaryUtilities","text":"Please open an issue if you encounter any issues or confusion with the package.","category":"page"},{"location":"financial_math/#Financial-Math-Submodule","page":"Financial Math","title":"Financial Math Submodule","text":"","category":"section"},{"location":"financial_math/","page":"Financial Math","title":"Financial Math","text":"Provides a set of common routines in financial maths.","category":"page"},{"location":"financial_math/#Quickstart","page":"Financial Math","title":"Quickstart","text":"","category":"section"},{"location":"financial_math/","page":"Financial Math","title":"Financial Math","text":"cfs = [5, 5, 105]\ntimes = [1, 2, 3]\n\ndiscount_rate = 0.03\n\npresent_value(discount_rate, cfs, times) # 105.65\nduration(Macaulay(), discount_rate, cfs, times) # 2.86\nduration(discount_rate, cfs, times) # 2.78\nconvexity(discount_rate, cfs, times) # 10.62","category":"page"},{"location":"financial_math/#API","page":"Financial Math","title":"API","text":"","category":"section"},{"location":"financial_math/#Exported-API","page":"Financial Math","title":"Exported API","text":"","category":"section"},{"location":"financial_math/","page":"Financial Math","title":"Financial Math","text":"Modules = [ActuaryUtilities.FinancialMath]\nPrivate = false","category":"page"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.KeyRate","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.KeyRate","text":"KeyRate(timepoints,shift=0.001)\n\nA convenience constructor for KeyRateZero. \n\nExtended Help\n\nKeyRateZero is chosen as the default constructor because it has more attractive properties than KeyRatePar:\n\nrates after the key timepoint remain unaffected by the shift\ne.g. this causes a 6-year zero coupon bond would have a negative duration if the 5-year par rate was used\n\n\n\n\n\n","category":"type"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.KeyRatePar","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.KeyRatePar","text":"KeyRatePar(timepoint,shift=0.001) <: KeyRateDuration\n\nShift the par curve by the given amount at the given timepoint. Use in conjunction with duration to calculate the key rate duration. \n\nUnlike other duration statistics which are computed using analytic derivatives, KeyRateDurations are computed via a shift-and-compute the yield curve approach.\n\nKeyRatePar is more commonly reported (than KeyRateZero) in the fixed income markets, even though the latter has more analytically attractive properties. See the discussion of KeyRateDuration in the FinanceModels.jl docs.\n\n\n\n\n\n","category":"type"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.KeyRateZero","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.KeyRateZero","text":"KeyRateZero(timepoint,shift=0.001) <: KeyRateDuration\n\nShift the par curve by the given amount at the given timepoint. Use in conjunction with duration to calculate the key rate duration.\n\nUnlike other duration statistics which are computed using analytic derivatives, KeyRateDuration is computed via a shift-and-compute the yield curve approach.\n\nKeyRateZero is less commonly reported (than KeyRatePar) in the fixed income markets, even though the latter has more analytically attractive properties. See the discussion of KeyRateDuration in the FinanceModels.jl docs.\n\n\n\n\n\n","category":"type"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.breakeven","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.breakeven","text":"breakeven(yield, cashflows::Vector)\nbreakeven(yield, cashflows::Vector,times::Vector)\n\nCalculate the time when the accumulated cashflows breakeven given the yield.\n\nAssumptions:\n\ncashflows occur at the end of the period\ncashflows evenly spaced with the first one occuring at time zero if times not given\n\nReturns nothing if cashflow stream never breaks even.\n\njulia> breakeven(0.10, [-10,1,2,3,4,8])\n5\n\njulia> breakeven(0.10, [-10,15,2,3,4,8])\n1\n\njulia> breakeven(0.10, [-10,-15,2,3,4,8]) # returns the `nothing` value\n\n\n\n\n\n\n\n","category":"function"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.convexity-Tuple{Any, Any, Any}","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.convexity","text":"convexity(yield,cfs,times)\nconvexity(yield,valuation_function)\n\nCalculates the convexity. - yield should be a fixed effective yield (e.g. 0.05). - times may be omitted and it will assume cfs are evenly spaced beginning at the end of the first period.\n\nExamples\n\nUsing vectors of cashflows and times\n\njulia> times = 1:5\njulia> cfs = [0,0,0,0,100]\njulia> duration(0.03,cfs,times)\n4.854368932038834\njulia> duration(Macaulay(),0.03,cfs,times)\n5.0\njulia> duration(Modified(),0.03,cfs,times)\n4.854368932038835\njulia> convexity(0.03,cfs,times)\n28.277877274012614\n\n\nUsing any given value function: \n\njulia> lump_sum_value(amount,years,i) = amount / (1 + i ) ^ years\njulia> my_lump_sum_value(i) = lump_sum_value(100,5,i)\njulia> duration(0.03,my_lump_sum_value)\n4.854368932038835\njulia> convexity(0.03,my_lump_sum_value)\n28.277877274012617\n\n\n\n\n\n\n","category":"method"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.moic-Tuple{T} where T<:AbstractArray","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.moic","text":"moic(cashflows<:AbstractArray)\n\nThe multiple on invested capital (\"moic\") is the un-discounted sum of distributions divided by the sum of the contributions. The function assumes that negative numbers in the array represent contributions and positive numbers represent distributions.\n\nExamples\n\njulia> moic([-10,20,30])\n5.0\n\n\n\n\n\n","category":"method"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.present_values","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.present_values","text":"present_values(interest, cashflows, timepoints)\n\nEfficiently calculate a vector representing the present value of the given cashflows at each period prior to the given timepoint.\n\nExamples\n\njulia> present_values(0.00, [1,1,1])\n[3,2,1]\n\njulia> present_values(ForwardYield([0.1,0.2]), [10,20],[0,1]) # after `using FinanceModels`\n2-element Vector{Float64}:\n 28.18181818181818\n 18.18181818181818\n\n\n\n\n\n","category":"function"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.price-Tuple{Any, Any}","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.price","text":"price(...)\n\nThe absolute value of the present_value(...). \n\nExtended help\n\nUsing price can be helpful if the directionality of the value doesn't matter. For example, in the common usage, duration is more interested in the change in price than present value, so price is used there.\n\n\n\n\n\n","category":"method"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.spread","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.spread","text":"spread(curve1,curve2,cashflows)\n\nReturn the solved-for constant spread to add to curve1 in order to equate the discounted cashflows with curve2\n\nExamples\n\nspread(0.04, 0.05, cfs)\nRate{Float64, Periodic}(0.010000000000000009, Periodic(1))\n\n\n\n\n\n","category":"function"},{"location":"financial_math/#ActuaryUtilities.duration-Tuple{ActuaryUtilities.FinancialMath.KeyRateDuration, Vararg{Any, 4}}","page":"Financial Math","title":"ActuaryUtilities.duration","text":"duration(keyrate::KeyRateDuration,curve,cashflows) \nduration(keyrate::KeyRateDuration,curve,cashflows,timepoints)\nduration(keyrate::KeyRateDuration,curve,cashflows,timepoints,krd_points)\n\nCalculate the key rate duration by shifting the zero (not par) curve by the kwarg shift at the timepoint specified by a KeyRateDuration(time).\n\nThe approach is to carve up the curve into krd_points (default is the unit steps between 1 and the last timepoint of the casfhlows). The zero rate corresponding to the timepoint within the KeyRateDuration is shifted by shift (specified by the KeyRateZero or KeyRatePar constructors. A new curve is created from the shifted rates. This means that the \"width\" of the shifted section is ± 1 time period, unless specific points are specified via krd_points.\n\nThe curve may be any FinanceModels.jl curve (e.g. does not have to be a curve constructed via FinanceModels.Zero(...)).\n\n!!! Experimental: Due to the paucity of examples in the literature, this feature does not have unit tests like the rest of JuliaActuary functionality. Additionally, the API may change in a future major/minor version update.\n\nExamples\n\njulia> riskfree_maturities = [0.5, 1.0, 1.5, 2.0];\n\njulia> riskfree = [0.05, 0.058, 0.064,0.068];\n\njulia> rf_curve = FinanceModels.Zero(riskfree,riskfree_maturities);\n\njulia> cfs = [10,10,10,10,10];\n\njulia> duration(KeyRate(1),rf_curve,cfs)\n8.932800152336995\n\n\nExtended Help\n\nKey Rate Duration is not a well specified topic in the literature and in practice. The reference below suggest that shocking the par curve is more common in practice, but that the zero curve produces more consistent results. Future versions may support shifting the par curve.\n\nReferences: \n\nQuant Finance Stack Exchange: To compute key rate duration, shall I use par curve or zero curve?\n(Financial Exam Help 123](http://www.financialexamhelp123.com/key-rate-duration/)\n\n\n\n\n\n","category":"method"},{"location":"financial_math/#ActuaryUtilities.duration-Tuple{Macaulay, Any, Any, Any}","page":"Financial Math","title":"ActuaryUtilities.duration","text":"duration(Macaulay(),interest_rate,cfs,times)\nduration(Modified(),interest_rate,cfs,times)\nduration(DV01(),interest_rate,cfs,times)\nduration(interest_rate,cfs,times) # Modified Duration\nduration(interest_rate,valuation_function) # Modified Duration\n\nCalculates the Macaulay, Modified, or DV01 duration. times may be ommitted and the valuation will assume evenly spaced cashflows starting at the end of the first period.\n\nNote that the calculated duration will depend on the periodicity convention of the interest_rate: a Periodic yield (or yield model with that convention) will be a slightly different computed duration than a Continous which follows from the present value differing according to the periodicity.\n\nWhen not given Modified() or Macaulay() as an argument, will default to Modified().\n\nModified duration: the relative change per point of yield change.\nMacaulay: the cashflow-weighted average time.\nDV01: the absolute change per basis point (hundredth of a percentage point).\n\nExamples\n\nUsing vectors of cashflows and times\n\njulia> times = 1:5;\n\njulia> cfs = [0,0,0,0,100];\n\njulia> duration(0.03,cfs,times)\n4.854368932038835\n\njulia> duration(Periodic(0.03,1),cfs,times)\n4.854368932038835\n\njulia> duration(Continuous(0.03),cfs,times)\n5.0\n\njulia> duration(Macaulay(),0.03,cfs,times)\n5.0\n\njulia> duration(Modified(),0.03,cfs,times)\n4.854368932038835\n\njulia> convexity(0.03,cfs,times)\n28.277877274012614\n\n\nUsing any given value function: \n\njulia> lump_sum_value(amount,years,i) = amount / (1 + i ) ^ years\njulia> my_lump_sum_value(i) = lump_sum_value(100,5,i)\njulia> duration(0.03,my_lump_sum_value)\n4.854368932038835\njulia> convexity(0.03,my_lump_sum_value)\n28.277877274012617\n\n\n\n\n\n\n","category":"method"},{"location":"financial_math/#Unexported-API","page":"Financial Math","title":"Unexported API","text":"","category":"section"},{"location":"financial_math/","page":"Financial Math","title":"Financial Math","text":"Modules = [ActuaryUtilities.FinancialMath]\nPublic = false","category":"page"},{"location":"upgrade/#Version-Upgrade-Guide","page":"Upgrade from Prior Versions","title":"Version Upgrade Guide","text":"","category":"section"},{"location":"upgrade/#v3-to-v4","page":"Upgrade from Prior Versions","title":"v3 to v4","text":"","category":"section"},{"location":"upgrade/#Overview","page":"Upgrade from Prior Versions","title":"Overview","text":"","category":"section"},{"location":"upgrade/","page":"Upgrade from Prior Versions","title":"Upgrade from Prior Versions","text":"The shape and API of the package is mostly unchanged. The changes that have made fall into a few categores:","category":"page"},{"location":"upgrade/","page":"Upgrade from Prior Versions","title":"Upgrade from Prior Versions","text":"Accommodating FinanceModels.jl, the next-generation version of Yields.jl.\nSimplifying the API, generally making function calls require more specific arguments to avoid ambiguity\nAccommodating the new Cashflow type which makes modeling heterogeneous assets and liabilities simpler.","category":"page"},{"location":"upgrade/#API-Changes","page":"Upgrade from Prior Versions","title":"API Changes","text":"","category":"section"},{"location":"upgrade/","page":"Upgrade from Prior Versions","title":"Upgrade from Prior Versions","text":"Breaking: The functions europut and eurocall have been moved to FinanceModels\nBreaking: Previously, the first argument to present_value or present_values would be interpreted as a set of Periodic(1) one-period forward rates if a vector of real values was passed. Users should explicitly create the yield model first, instead of relying on the implicit conversion:","category":"page"},{"location":"upgrade/","page":"Upgrade from Prior Versions","title":"Upgrade from Prior Versions","text":"# old \npv([0.05,0.1], cfs) \n\n# new\nusing FinanceModels\ny = fit(Spline.Linear(),ForwardYields([0.05,0.1]),Bootstrap())\npv(y,cfs)\n","category":"page"},{"location":"utilities/#Utilities-submodule","page":"Other Utilities","title":"Utilities submodule","text":"","category":"section"},{"location":"utilities/","page":"Other Utilities","title":"Other Utilities","text":"Provides miscellaneous routines common in actuarial and financial work.","category":"page"},{"location":"utilities/#API","page":"Other Utilities","title":"API","text":"","category":"section"},{"location":"utilities/#Exported-API","page":"Other Utilities","title":"Exported API","text":"","category":"section"},{"location":"utilities/","page":"Other Utilities","title":"Other Utilities","text":"Utilities.duration\nUtilities.years_between\nUtilities.accum_offset","category":"page"},{"location":"utilities/#ActuaryUtilities.duration","page":"Other Utilities","title":"ActuaryUtilities.duration","text":"duration(d1::Date, d2::Date)\n\nCompute the duration given two dates, which is the number of years since the first date. The interval [0,1) is defined as having duration 1. Can return negative durations if second argument is before the first.\n\njulia> issue_date = Date(2018,9,30);\n\njulia> duration(issue_date , Date(2019,9,30) ) \n2\njulia> duration(issue_date , issue_date) \n1\njulia> duration(issue_date , Date(2018,10,1) ) \n1\njulia> duration(issue_date , Date(2019,10,1) ) \n2\njulia> duration(issue_date , Date(2018,6,30) ) \n0\njulia> duration(Date(2018,9,30),Date(2017,6,30)) \n-1\n\n\n\n\n\nduration(Macaulay(),interest_rate,cfs,times)\nduration(Modified(),interest_rate,cfs,times)\nduration(DV01(),interest_rate,cfs,times)\nduration(interest_rate,cfs,times) # Modified Duration\nduration(interest_rate,valuation_function) # Modified Duration\n\nCalculates the Macaulay, Modified, or DV01 duration. times may be ommitted and the valuation will assume evenly spaced cashflows starting at the end of the first period.\n\nNote that the calculated duration will depend on the periodicity convention of the interest_rate: a Periodic yield (or yield model with that convention) will be a slightly different computed duration than a Continous which follows from the present value differing according to the periodicity.\n\nWhen not given Modified() or Macaulay() as an argument, will default to Modified().\n\nModified duration: the relative change per point of yield change.\nMacaulay: the cashflow-weighted average time.\nDV01: the absolute change per basis point (hundredth of a percentage point).\n\nExamples\n\nUsing vectors of cashflows and times\n\njulia> times = 1:5;\n\njulia> cfs = [0,0,0,0,100];\n\njulia> duration(0.03,cfs,times)\n4.854368932038835\n\njulia> duration(Periodic(0.03,1),cfs,times)\n4.854368932038835\n\njulia> duration(Continuous(0.03),cfs,times)\n5.0\n\njulia> duration(Macaulay(),0.03,cfs,times)\n5.0\n\njulia> duration(Modified(),0.03,cfs,times)\n4.854368932038835\n\njulia> convexity(0.03,cfs,times)\n28.277877274012614\n\n\nUsing any given value function: \n\njulia> lump_sum_value(amount,years,i) = amount / (1 + i ) ^ years\njulia> my_lump_sum_value(i) = lump_sum_value(100,5,i)\njulia> duration(0.03,my_lump_sum_value)\n4.854368932038835\njulia> convexity(0.03,my_lump_sum_value)\n28.277877274012617\n\n\n\n\n\n\nduration(keyrate::KeyRateDuration,curve,cashflows) \nduration(keyrate::KeyRateDuration,curve,cashflows,timepoints)\nduration(keyrate::KeyRateDuration,curve,cashflows,timepoints,krd_points)\n\nCalculate the key rate duration by shifting the zero (not par) curve by the kwarg shift at the timepoint specified by a KeyRateDuration(time).\n\nThe approach is to carve up the curve into krd_points (default is the unit steps between 1 and the last timepoint of the casfhlows). The zero rate corresponding to the timepoint within the KeyRateDuration is shifted by shift (specified by the KeyRateZero or KeyRatePar constructors. A new curve is created from the shifted rates. This means that the \"width\" of the shifted section is ± 1 time period, unless specific points are specified via krd_points.\n\nThe curve may be any FinanceModels.jl curve (e.g. does not have to be a curve constructed via FinanceModels.Zero(...)).\n\n!!! Experimental: Due to the paucity of examples in the literature, this feature does not have unit tests like the rest of JuliaActuary functionality. Additionally, the API may change in a future major/minor version update.\n\nExamples\n\njulia> riskfree_maturities = [0.5, 1.0, 1.5, 2.0];\n\njulia> riskfree = [0.05, 0.058, 0.064,0.068];\n\njulia> rf_curve = FinanceModels.Zero(riskfree,riskfree_maturities);\n\njulia> cfs = [10,10,10,10,10];\n\njulia> duration(KeyRate(1),rf_curve,cfs)\n8.932800152336995\n\n\nExtended Help\n\nKey Rate Duration is not a well specified topic in the literature and in practice. The reference below suggest that shocking the par curve is more common in practice, but that the zero curve produces more consistent results. Future versions may support shifting the par curve.\n\nReferences: \n\nQuant Finance Stack Exchange: To compute key rate duration, shall I use par curve or zero curve?\n(Financial Exam Help 123](http://www.financialexamhelp123.com/key-rate-duration/)\n\n\n\n\n\n","category":"function"},{"location":"utilities/#ActuaryUtilities.Utilities.years_between","page":"Other Utilities","title":"ActuaryUtilities.Utilities.years_between","text":"Years_Between(d1::Date, d2::Date)\n\nCompute the number of integer years between two dates, with the first date typically before the second. Will return negative number if first date is after the second. Use third argument to indicate if calendar anniversary should count as a full year.\n\nExamples\n\njulia> d1 = Date(2018,09,30);\n\njulia> d2 = Date(2019,09,30);\n\njulia> d3 = Date(2019,10,01);\n\njulia> years_between(d1,d3) \n1\njulia> years_between(d1,d2,false) # same month/day but `false` overlap\n0 \njulia> years_between(d1,d2) # same month/day but `true` overlap\n1 \njulia> years_between(d1,d2) # using default `true` overlap\n1 \n\n\n\n\n\n","category":"function"},{"location":"utilities/#ActuaryUtilities.Utilities.accum_offset","page":"Other Utilities","title":"ActuaryUtilities.Utilities.accum_offset","text":"accum_offset(x; op=*, init=1.0)\n\nA shortcut for the common operation wherein a vector is scanned with an operation, but has an initial value and the resulting array is offset from the traditional accumulate. \n\nThis is a common pattern when calculating things like survivorship given a mortality vector and you want the first value of the resulting vector to be 1.0, and the second value to be 1.0 * x[1], etc.\n\nTwo keyword arguments:\n\nop is the binary (two argument) operator you want to use, such as * or +\ninit is the initial value in the returned array\n\nExamples\n\njulia> accum_offset([0.9, 0.8, 0.7])\n3-element Array{Float64,1}:\n 1.0\n 0.9\n 0.7200000000000001\n\njulia> accum_offset(1:5) # the product of elements 1:n, with the default `1` as the first value\n5-element Array{Int64,1}:\n 1\n 1\n 2\n 6\n 24\n\njulia> accum_offset(1:5,op=+)\n5-element Array{Int64,1}:\n 1\n 2\n 4\n 7\n 11\n\n\n\n\n\n\n","category":"function"},{"location":"API/FinanceCore/#FinanceCore-API-Reference","page":"FinanceCore (re-exported)","title":"FinanceCore API Reference","text":"","category":"section"},{"location":"API/FinanceCore/","page":"FinanceCore (re-exported)","title":"FinanceCore (re-exported)","text":"Modules = [FinanceCore]","category":"page"},{"location":"API/FinanceCore/#Exported-API","page":"FinanceCore (re-exported)","title":"Exported API","text":"","category":"section"},{"location":"API/FinanceCore/","page":"FinanceCore (re-exported)","title":"FinanceCore (re-exported)","text":"Modules = [FinanceCore]\nPrivate = false","category":"page"},{"location":"API/FinanceCore/#FinanceCore.Cashflow","page":"FinanceCore (re-exported)","title":"FinanceCore.Cashflow","text":"Cashflow(amount,time)\n\nA Cahflow{A,B} is a contract that pays an amount at time. \n\nCashflows can be:\n\nnegated with the unary - operator. \nadded/subtracted together but note that the time must be isapprox equal.\nmultiplied/divided by a scalar.\n\nSupertype Hierarchy ≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡\n\nCashflow{A<:Real, B<:Timepoint} <: FinanceCore.AbstractContract <: Any\n\n\n\n\n\n","category":"type"},{"location":"API/FinanceCore/#FinanceCore.Composite","page":"FinanceCore (re-exported)","title":"FinanceCore.Composite","text":"Composite(A,B)\n\nSummary ≡≡≡≡≡≡≡≡≡\n\nstruct Composite{A, B}\n\nA Composite{A,B} is a contract that is composed of two other contracts of type A and type B. The maturity of the composite is the maximum of the maturities of the two components. \n\nIt is used to assemble arbitrarily complex contracts from simpler ones.\n\nFields ≡≡≡≡≡≡≡≡\n\na :: A\nb :: B\n\nSupertype Hierarchy ≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡\n\nComposite{A, B} <: FinanceCore.AbstractContract <: Any\n\n\n\n\n\n","category":"type"},{"location":"API/FinanceCore/#FinanceCore.Continuous","page":"FinanceCore (re-exported)","title":"FinanceCore.Continuous","text":"Continuous()\n\nA type representing continuous interest compounding frequency.\n\nExamples\n\njulia> Rate(0.01,Continuous())\nRate(0.01, Continuous())\n\nSee also: Periodic\n\n\n\n\n\n","category":"type"},{"location":"API/FinanceCore/#FinanceCore.Continuous-Tuple{Any}","page":"FinanceCore (re-exported)","title":"FinanceCore.Continuous","text":"julia> Continuous(0.01)\nRate(0.01, Continuous())\n\nSee also: Periodic\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#FinanceCore.Periodic","page":"FinanceCore (re-exported)","title":"FinanceCore.Periodic","text":"Periodic(frequency)\n\nA type representing periodic interest compounding with the given frequency. \n\nfrequency will be converted to an Integer, and will round up to 8 decimal places (otherwise will throw an InexactError). \n\nExamples\n\nCreating a semi-annual bond equivalent yield:\n\njulia> Rate(0.01,Periodic(2))\nRate(0.01, Periodic(2))\n\nSee also: Continuous\n\n\n\n\n\n","category":"type"},{"location":"API/FinanceCore/#FinanceCore.Periodic-Tuple{Any, Any}","page":"FinanceCore (re-exported)","title":"FinanceCore.Periodic","text":"Periodic(rate,frequency)\n\nA convenience constructor for Rate(rate,Periodic(frequency)).\n\nExamples\n\nCreating a semi-annual bond equivalent yield:\n\njulia> Periodic(0.01,2)\nRate(0.01, Periodic(2))\n\nSee also: Continuous\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#FinanceCore.Quote","page":"FinanceCore (re-exported)","title":"FinanceCore.Quote","text":"Quote(price,instrument)\n\nThe price(<:Real) is the observed value , and the instrument is the instrument/contract that the price is for.\n\nThis can be used, e.g., to calibrate a valuation model to prices for the given instruments - see FinanceModels.jl for more details.\n\n\n\n\n\n","category":"type"},{"location":"API/FinanceCore/#FinanceCore.Rate-Tuple{Any}","page":"FinanceCore (re-exported)","title":"FinanceCore.Rate","text":"Rate(rate[,frequency=1])\nRate(rate,frequency::Frequency)\n\nRate is a type that encapsulates an interest rate along with its compounding frequency.\n\nPeriodic rates can be constructed via Rate(rate,frequency) or Rate(rate,Periodic(frequency)). If not given a second argument, Rate(rate) is equivalent to Rate(rate,Periodic(1)).\n\nContinuous rates can be constructed via Rate(rate, Inf) or Rate(rate,Continuous()).\n\nExamples\n\njulia> Rate(0.01,Continuous())\nRate(0.01, Continuous())\n\njulia> Continuous(0.01)\nRate(0.01, Continuous())\n\njulia> Continuous()(0.01)\nRate(0.01, Continuous())\n\njulia> Rate(0.01,Periodic(2))\nRate(0.01, Periodic(2))\n\njulia> Periodic(0.01,2)\nRate(0.01, Periodic(2))\n\njulia> Periodic(2)(0.01)\nRate(0.01, Periodic(2))\n\njulia> Rate(0.01)\nRate(0.01, Periodic(1))\n\njulia> Rate(0.01,2)\nRate(0.01, Periodic(2))\n\njulia> Rate(0.01,Periodic(4))\nRate(0.01, Periodic(4))\n\njulia> Rate(0.01,Inf)\nRate(0.01, Continuous())\n\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#FinanceCore.amount-Tuple{C} where C<:Cashflow","page":"FinanceCore (re-exported)","title":"FinanceCore.amount","text":"amount(x)\n\nIf is an object with an amount component (e.g. a Cashflow), will retrun that amount component, otherwise just x.\n\nExamples\n\njulia> FinanceCore.amount(Cashflow(1.,3.))\n1.0\n\njulia> FinanceCore.amount(1.)\n1.0\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#FinanceCore.internal_rate_of_return-Tuple{Any}","page":"FinanceCore (re-exported)","title":"FinanceCore.internal_rate_of_return","text":"internal_rate_of_return(cashflows::vector)::Rate\ninternal_rate_of_return(cashflows::Vector, timepoints::Vector)::Rate\n\nCalculate the internalrateof_return with given timepoints. If no timepoints given, will assume that a series of equally spaced cashflows, assuming the first cashflow occurring at time zero and subsequent elements at time 1, 2, 3, ..., n. \n\nReturns a Rate type with periodic compounding once per period (e.g. annual effective if the timepoints given represent years). Get the scalar rate by calling Yields.rate() on the result.\n\nExample\n\njulia> internal_rate_of_return([-100,110],[0,1]) # e.g. cashflows at time 0 and 1\n0.10000000001652906\njulia> internal_rate_of_return([-100,110]) # implied the same as above\n0.10000000001652906\n\nSolver notes\n\nWill try to return a root within the range [-2,2]. If the fast solver does not find one matching this condition, then a more robust search will be performed over the [.99,2] range.\n\nThe solution returned will be in the range [-2,2], but may not be the one nearest zero. For a slightly slower, but more robust version, call ActuaryUtilities.irr_robust(cashflows,timepoints) directly.\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#FinanceCore.irr","page":"FinanceCore (re-exported)","title":"FinanceCore.irr","text":"irr(cashflows::vector)\nirr(cashflows::Vector, timepoints::Vector)\n\nAn alias for `internal_rate_of_return`.\n\n\n\n\n\n","category":"function"},{"location":"API/FinanceCore/#FinanceCore.present_value-Tuple{Any, Any, Any}","page":"FinanceCore (re-exported)","title":"FinanceCore.present_value","text":"present_value(yield_model, cashflows[, timepoints=pairs(cashflows)])\n\nDiscount the cashflows vector at the given yield_model, with the cashflows occurring at the times specified in timepoints. If no timepoints given, assumes that cashflows happen at the indices of the cashflows.\n\nIf your timepoints are dates, you can convert them into a floating point representation of the time interval using DayCounts.jl.\n\nExamples\n\njulia> present_value(0.1, [10,20],[0,1])\n28.18181818181818\njulia> present_value(Continuous(0.1), [10,20],[0,1])\n28.096748360719193\njulia> present_value(Continuous(0.1), [10,20],[1,2])\n25.422989241919232\njulia> present_value(Continuous(0.1), [10,20])\n25.422989241919232\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#FinanceCore.rate-Tuple{Rate}","page":"FinanceCore (re-exported)","title":"FinanceCore.rate","text":"rate(r::Rate)\n\nReturns the untyped scalar interest rate represented by the Rate.\n\nExamples\n\njulia> r =Continuous(0.03)\nYields.Rate{Float64, Continuous}(0.03, Continuous())\n\njulia> rate(r)\n0.03\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#FinanceCore.timepoint-Union{Tuple{C}, Tuple{C, Any}} where C<:Cashflow","page":"FinanceCore (re-exported)","title":"FinanceCore.timepoint","text":"timepoint(x,t)\n\nIf x is an object with a defined time component (e.g. a Cashflow), will return that time component, otherwise will return t. This is useful in handling situations where you want to handle either Cashflows or separate amount and time vectors.\n\nExample\n\njulia> FinanceCore.timepoint(Cashflow(1.,3.),\"ignored\")\n3.0\n\njulia> FinanceCore.timepoint(1.,4.)\n4.0\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#Unexported-API","page":"FinanceCore (re-exported)","title":"Unexported API","text":"","category":"section"},{"location":"API/FinanceCore/","page":"FinanceCore (re-exported)","title":"FinanceCore (re-exported)","text":"Modules = [FinanceCore]\nPublic = false","category":"page"},{"location":"API/FinanceCore/#FinanceCore.Timepoint","page":"FinanceCore (re-exported)","title":"FinanceCore.Timepoint","text":"Timepoint(a)\n\nSummary ≡≡≡≡≡≡≡≡≡\n\nTimepoint is a type alias for Union{T,Dates.Date} that can be used to represent a point in time. It can be either a Dates.Date or a Real number. If defined as a real number, the interpretation is the number of (fractional) periods since time zero.\n\nCurrently, the usage of Dates.Date is not well supported across the JuliaActuary ecosystem but this type is in place such that it can be built upon further.\n\nSupertype Hierarchy ≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡\n\nTimepoint{T} = Union{T,Dates.Date} <: Any\n\n\n\n\n\n","category":"type"},{"location":"API/FinanceCore/#Base.:*-Union{Tuple{T}, Tuple{N}, Tuple{Rate{N, T}, Real}} where {N, T<:Continuous}","page":"FinanceCore (re-exported)","title":"Base.:*","text":"*(Yields.Rate, T)\n*(T, Yields.Rate)\n\nThe multiplication of a Rate with a scalar will inherit the type of the Rate, or the first argument's type if both are Rates.\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#Base.:+-Union{Tuple{T}, Tuple{N}, Tuple{Rate{N, T}, Real}} where {N, T<:Continuous}","page":"FinanceCore (re-exported)","title":"Base.:+","text":"+(Yields.Rate, T<:Real)\n+(T<:Real, Yields.Rate)\n+(Yields.Rate,Yields.Rate)\n\nThe addition of a rate with a number will inherit the type of the Rate, or the first argument's type if both are Rates.\n\nExamples\n\njulia> Yields.Periodic(0.01,2) + Yields.Periodic(0.04,2)\nYields.Rate{Float64, Yields.Periodic}(0.05000000000000004, Yields.Periodic(2))\n\njulia> Yields.Periodic(0.04,2) + 0.01\nYields.Rate{Float64, Yields.Periodic}(0.05, Yields.Periodic(2))\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#Base.:--Union{Tuple{T}, Tuple{N}, Tuple{Rate{N, T}, Real}} where {N, T<:Continuous}","page":"FinanceCore (re-exported)","title":"Base.:-","text":"-(Yields.Rate, T<:Real)\n-(T<:Real, Yields.Rate)\n-(Yields.Rate, Yields.Rate)\n\nThe addition of a rate with a number will inherit the type of the Rate, or the first argument's type if both are Rates.\n\nExamples\n\njulia> Yields.Periodic(0.04,2) - Yields.Periodic(0.01,2)\nYields.Rate{Float64, Yields.Periodic}(0.030000000000000214, Yields.Periodic(2))\n\njulia> Yields.Periodic(0.04,2) - 0.01\nYields.Rate{Float64, Yields.Periodic}(0.03, Yields.Periodic(2))\n\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#Base.:/-Union{Tuple{T}, Tuple{N}, Tuple{Rate{N, T}, Real}} where {N, T<:Continuous}","page":"FinanceCore (re-exported)","title":"Base.:/","text":"/(x::Yields.Rate, y::Real)\n\nThe division of a Rate with a scalar will inherit the type of the Rate, or the first argument's type if both are Rates.\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#Base.:<-Union{Tuple{U}, Tuple{T}, Tuple{T, U}} where {T<:Rate, U<:Rate}","page":"FinanceCore (re-exported)","title":"Base.:<","text":"<(x::Rate,y::Rate)\n\nConvert the second argument to the periodicity of the first and compare the scalar rate values to determine if the first argument has a lower force of interest than the second.\n\nExamples\n\njulia> Yields.Periodic(0.03,100) < Yields.Continuous(0.03)\ntrue\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#Base.:>-Union{Tuple{U}, Tuple{T}, Tuple{T, U}} where {T<:Rate, U<:Rate}","page":"FinanceCore (re-exported)","title":"Base.:>","text":">(Rate,Rate)\n\nConvert the second argument to the periodicity of the first and compare the scalar rate values to determine if the first argument has a greater force of interest than the second.\n\nExamples\n\njulia> Yields.Periodic(0.03,100) > Yields.Continuous(0.03)\nfalse\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#Base.convert-Union{Tuple{T}, Tuple{T, Rate}} where T<:FinanceCore.Frequency","page":"FinanceCore (re-exported)","title":"Base.convert","text":"convert(cf::Frequency,r::Rate)\n\nReturns a Rate with an equivalent discount but represented with a different compounding frequency.\n\nExamples\n\njulia> r = Rate(Periodic(12),0.01)\nRate(0.01, Periodic(12))\n\njulia> convert(Periodic(1),r)\nRate(0.010045960887181016, Periodic(1))\n\njulia> convert(Continuous(),r)\nRate(0.009995835646701251, Continuous())\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/","page":"FinanceCore (re-exported)","title":"FinanceCore (re-exported)","text":"Please open an issue if you encounter any issues or confusion with the package.","category":"page"},{"location":"#Quickstart","page":"Overview","title":"Quickstart","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"cfs = [5, 5, 105]\ntimes = [1, 2, 3]\n\ndiscount_rate = 0.03\n\npresent_value(discount_rate, cfs, times) # 105.65\nduration(Macaulay(), discount_rate, cfs, times) # 2.86\nduration(discount_rate, cfs, times) # 2.78\nconvexity(discount_rate, cfs, times) # 10.62","category":"page"},{"location":"#Features","page":"Overview","title":"Features","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"A collection of common functions/manipulations used in Actuarial Calculations.","category":"page"},{"location":"#Financial-Maths","page":"Overview","title":"Financial Maths","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"duration:\nCalculate the Macaulay, Modified, or DV01 durations for a set of cashflows\nCalculate the KeyRate(time) (a.k.a. KeyRateZero)duration or KeyRatePar(time) duration\nconvexity for price sensitivity\nFlexible interest rate models via the FinanceModels.jl package.\ninternal_rate_of_return or irr to calculate the IRR given cashflows (including at timepoints like Excel's XIRR)\nbreakeven to calculate the breakeven time for a set of cashflows\naccum_offset to calculate accumulations like survivorship from a mortality vector\nspread will calculate the spread needed between two yield curves to equate a set of cashflows","category":"page"},{"location":"#Risk-Measures","page":"Overview","title":"Risk Measures","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"Calculate risk measures for a given vector of risks:\nCTE for the Conditional Tail Expectation\nVaR for the percentile/Value at Risk\nWangTransform for the Wang Transformation\nProportionalHazard for proportional hazards\nDualPower for dual power measure","category":"page"},{"location":"#Insurance-mechanics","page":"Overview","title":"Insurance mechanics","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"duration:\nCalculate the duration given an issue date and date (a.k.a. policy duration)","category":"page"},{"location":"#Typed-Rates","page":"Overview","title":"Typed Rates","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"functions which return a rate/yield will return a FinanceCore.Rate object. E.g. irr(cashflows) will return a Rate(0.05,Periodic(1)) instead of just a 0.05 (float64) to convey the compounding frequency. This is compatible across the JuliaActuary ecosystem and can be used anywhere you would otherwise use a simple floating point rate.","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"A couple of other notes:","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"rate(...) will return the scalar rate value from a Rate struct:","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"julia> r = Rate(0.05,Periodic(1));\n\njulia> rate(r) \n0.05","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"You can still pass a simple floating point rate to various methods. E.g. these two are the same (the default compounding convention is periodic once per period):","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"discount(0.05,cashflows)\n\nr = Rate(0.05,Periodic(1));\ndiscount(r,cashflows)","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"convert between rates with:","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"r = Rate(0.05,Periodic(1));\n\nconvert(Periodic(2), r) # convert to compounded twice per timestep\nconvert(Continuous(2),r) # convert to compounded twice per timestep","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"For more on Rates, see FinanceCore.jl. FinanceModels.jl also provides a rich and flexible set of yield models to use.","category":"page"},{"location":"#Documentation","page":"Overview","title":"Documentation","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"Full documentation is available here.","category":"page"},{"location":"#Examples","page":"Overview","title":"Examples","text":"","category":"section"},{"location":"#Interactive,-basic-cashflow-analysis","page":"Overview","title":"Interactive, basic cashflow analysis","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"See JuliaActuary.org for instructions on running this example.","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"(Image: Simple cashflow analysis with ActuaryUtilities.jl)","category":"page"},{"location":"#Useful-tips","page":"Overview","title":"Useful tips","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"Functions often use a mix of interest_rates, cashflows, and timepoints. When calling functions, the general order of the arguments is 1) interest rates, 2) cashflows, and 3) timepoints.","category":"page"}] +[{"location":"risk_measures/#Risk-Measures","page":"Risk Measures","title":"Risk Measures","text":"","category":"section"},{"location":"risk_measures/#Quickstart","page":"Risk Measures","title":"Quickstart","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"outcomes = rand(100)\n\n# direct usage\nVaR(0.90)(outcomes) # ≈ 0.90 \nCTE(0.90)(outcomes) # ≈ 0.95 \nWangTransform(0.90)(outcomes) # ≈ 0.81\n\n# construct a reusable object (functor)\nrm = VaR(0.90)\n\nrm(outcomes) # ≈ 0.90","category":"page"},{"location":"risk_measures/#Introduction","page":"Risk Measures","title":"Introduction","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Risk measures encompass the set of functions that map a set of outcomes to an output value characterizing the associated riskiness of those outcomes. As is usual when attempting to compress information (e.g. condensing information into a single value), there are multiple ways we can characterize this riskiness.","category":"page"},{"location":"risk_measures/#Coherence-and-Other-Desirable-Properties","page":"Risk Measures","title":"Coherence & Other Desirable Properties","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Further, it is desirable that a risk measure has certain properties, and risk measures that meet the first four criteria are called \"Coherent\" in the literature. From \"An Introduction to Risk Measures for Actuarial Applications\" (Hardy), she describes as follows:","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Using H as a risk measure and X as the associated risk distribution:","category":"page"},{"location":"risk_measures/#1.-Translation-Invariance","page":"Risk Measures","title":"1. Translation Invariance","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"For any non-random c","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"%H(X + c) = H(X) + c% This means that adding a constant amount (positive or negative) to a risk adds the same amount to the risk measure. It also implies that the risk measure for a non-random loss, with known value c, say, is just the amount of the loss c.","category":"page"},{"location":"risk_measures/#2.-Positive-Homogeneity","page":"Risk Measures","title":"2. Positive Homogeneity","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"For any non-random λ 0:","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"H(λX) = λH(X)","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"This axiom implies that changing the units of loss does not change the risk measure.","category":"page"},{"location":"risk_measures/#3.-Subadditivity","page":"Risk Measures","title":"3. Subadditivity","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"For any two random losses X and Y,","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"H(X + Y) H(X) + H(Y)","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"It should not be possible to reduce the economic capital required (or the appropriate premium) for a risk by splitting it into constituent parts. Or, in other words, diversification (ie consolidating risks) cannot make the risk greater, but it might make the risk smaller if the risks are less than perfectly correlated.","category":"page"},{"location":"risk_measures/#4.-Monotonicity","page":"Risk Measures","title":"4. Monotonicity","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"If Pr(X Y) = 1 then H(X) H(Y).","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"If one risk is always bigger then another, the risk measures should be similarly ordered.","category":"page"},{"location":"risk_measures/#Other-Properties","page":"Risk Measures","title":"Other Properties","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"In \"Properties of Distortion Risk Measures\" (Balbás, Garrido, Mayoral) also note other properties of interest:","category":"page"},{"location":"risk_measures/#Complete","page":"Risk Measures","title":"Complete","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Completeness is the property that the distortion function associated with the risk measure produces a unique mapping between the original risk's survival function S(x) and the distorted S*(x) for each x. See Distortion Risk Measures for more detail on this.","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"In practice, this means that a non-complete risk measure ignores some part of the risk distribution (e.g. CTE and VaR don't use the full distribution and have the same)","category":"page"},{"location":"risk_measures/#Exhaustive","page":"Risk Measures","title":"Exhaustive","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"A risk measure is \"exhaustive\" if it is coherent and complete.","category":"page"},{"location":"risk_measures/#Adaptable","page":"Risk Measures","title":"Adaptable","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"A risk measure is \"adapted\" or \"adaptable\" if its distortion function (ee Distortion Risk Measures). g:","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"1. $g$ is strictly concave, that is $g$ is strictly decreasing. \n2. $lim_{u\\to0+} g\\prime(u) = \\inf and lim_{u\\to1-} g\\prime(u) = 0.","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Adaptive risk measures are exhaustive but the converse is not true.","category":"page"},{"location":"risk_measures/#Summary-of-Risk-Measure-Properties","page":"Risk Measures","title":"Summary of Risk Measure Properties","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Measure Coherent Complete Exhaustive Adaptable Condition 2\nVaR No No No No No\nCTE Yes No No No No\nDualPower (y 1) Yes Yes Yes No Yes\nProportionalHazard (γ 1) Yes Yes Yes No Yes\nWangTransform Yes Yes Yes Yes Yes","category":"page"},{"location":"risk_measures/#Distortion-Risk-Measures","page":"Risk Measures","title":"Distortion Risk Measures","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Distortion Risk Measures (Wikipedia Link) are a way of remapping the probabilities of a risk distribution in order to compute a risk measure H on the risk distribution X.","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Adapting Wang (2002), there are two key components:","category":"page"},{"location":"risk_measures/#Distortion-Function-g(u)","page":"Risk Measures","title":"Distortion Function g(u)","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"This remaps values in the [0,1] range to another value in the [0,1] range, and in H below, operates on the survival function S and F=1-S.","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Let g01to01 be an increasing function with g(0)=0 and g(1)=1. The transform F^*(x)=g(F(x)) defines a distorted probability distribution, where \"g\" is called a distortion function.","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Note that F^* and F are equivalent probability measures if and only if g01to01 is continuous and one-to-one. Definition 4.2. We define a family of distortion risk-measures using the mean-value under the distorted probability F^*(x)=g(F(x)):","category":"page"},{"location":"risk_measures/#Risk-Measure-Integration","page":"Risk Measures","title":"Risk Measure Integration","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"To calculate a risk measure H, we integrate the distorted F across all possible values in the risk distribution (i.e. x in X):","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"H(X) = E^*(X) = - int_-infty^0 g(F(x))dx + int_0^+infty1-g(F(x))dx","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"That is, the risk measure (H) is equal to the expected value of the distortion of the risk distribution (E^*(X)).","category":"page"},{"location":"risk_measures/#Examples","page":"Risk Measures","title":"Examples","text":"","category":"section"},{"location":"risk_measures/#Basic-Usage","page":"Risk Measures","title":"Basic Usage","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"outcomes = rand(100)\n\n# direct usage\nVaR(0.90)(outcomes) # ≈ 0.90 \nCTE(0.90)(outcomes) # ≈ 0.95 \nWangTransform(0.90)(outcomes) # ≈ 0.81\n\n# construct a reusable object (functor)\nrm = VaR(0.90)\n\nrm(outcomes) # ≈ 0.90","category":"page"},{"location":"risk_measures/#Comparison","page":"Risk Measures","title":"Comparison","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"We will generate a random outcome and show how the risk measures behave:","category":"page"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"using Distributions\nusing ActuaryUtilities\nusing CairoMakie\n\noutcomes = Weibull(1,5)\n# or this could be discrete outcomes as in the next line\n#outcomes = rand(LogNormal(2,10)*100,2000) \n\nαs= range(0.00,0.99;length=100)\n\nlet \n f = Figure()\n ax = Axis(f[1,1],\n xlabel=\"α\",\n ylabel=\"Loss\",\n title = \"Comparison of Risk Measures\",\n xgridvisible=false,\n ygridvisible=false,\n )\n\n lines!(ax,\n αs,\n [quantile(outcomes, α) for α in αs],\n label = \"Quantile α of Outcome\",\n color = :grey10,\n linewidth = 3,\n )\n \n lines!(ax,\n αs,\n [VaR(α)(outcomes) for α in αs],\n label = \"VaR(α)\",\n linestyle=:dash\n )\n lines!(ax,\n αs,\n [CTE(α)(outcomes) for α in αs],\n label = \"CTE(α)\",\n )\n lines!(ax,\n αs[2:end],\n [WangTransform(α)(outcomes) for α in αs[2:end]],\n label = \"WangTransform(α)\",\n )\n lines!(ax,\n αs,\n [ProportionalHazard(2)(outcomes) for α in αs],\n label = \"ProportionalHazard(2)\",\n )\n \n lines!(ax,\n αs,\n [DualPower(2)(outcomes) for α in αs],\n label = \"DualPower(2)\",\n )\n lines!(ax,\n αs,\n [RiskMeasures.Expectation()(outcomes) for α in αs],\n label = \"Expectation\",\n )\n axislegend(ax,position=:lt)\n\n f\nend","category":"page"},{"location":"risk_measures/#API","page":"Risk Measures","title":"API","text":"","category":"section"},{"location":"risk_measures/#Exported-API","page":"Risk Measures","title":"Exported API","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Modules = [ActuaryUtilities.RiskMeasures]\nPrivate = false","category":"page"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.CTE","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.CTE","text":"CTE(α)::RiskMeasure\nCTE(α)(risk)::T (where T is the type of values sampled in risk)\n\nThe Conditional Tail Expectation (CTE) at level α is the expected value of the risk distribution above the αth quantile. risk can be a univariate distribution or an array of outcomes. Assumes more positive values are higher risk measures, so a higher p will return a more positive number.\n\nCTE(α) returns a functor which can then be called on a risk distribution.\n\nParameters\n\nα: [0,1.0) \n\nExamples\n\njulia> CTE(0.95)(rand(1000))\n0.9766218612020593\n\njulia> rm = CTE(0.95)\nCTE{Float64}(0.95)\n\njulia> rm(rand(1000))\n0.9739835010268733\n\n\n\n\n\n","category":"type"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.ConditionalTailExpectation","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.ConditionalTailExpectation","text":"CTE\n\n\n\n\n\n","category":"type"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.DualPower","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.DualPower","text":"DualPower(v)::RiskMeasure\nDualPower(v)(risk)::T (where T is the type of values sampled in risk)\n\nThe Dual Power distortion risk measure is defined as 1 - (1 - x)^v, where x is the cumulative distribution function (CDF) of the risk distribution and v is a positive parameter. risk can be a univariate distribution or an array of outcomes.\n\nDualPower(v) returns a functor which can then be called on a risk distribution.\n\n\n\n\n\n","category":"type"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.ProportionalHazard","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.ProportionalHazard","text":"ProportionalHazard(y)::RiskMeasure\nProportionalHazard(y)(risk)::T (where T is the type of values sampled in risk)\n\nThe Proportional Hazard distortion risk measure is defined as x^(1y), where x is the cumulative distribution function (CDF) of the risk distribution and y is a positive parameter. risk can be a univariate distribution or an array of outcomes. ProportionalHazard(y) returns a functor which can then be called on a risk distribution.\n\nExamples\n\njulia> ProportionalHazard(2)(rand(1000))\n0.6659603556774121\n\njulia> rm = ProportionalHazard(2)\nProportionalHazard{Int64}(2)\n\njulia> rm(rand(1000))\n0.6710587338367799\n\n\n\n\n\n","category":"type"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.VaR","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.VaR","text":" VaR(α)::RiskMeasure\n VaR(α)(risk)::T (where T is the type of values sampled in `risk`)\n\nThe αth quantile of the risk distribution is the Value at Risk, or αth quantile. risk can be a univariate distribution or an array of outcomes. Assumes more positive values are higher risk measures, so a higher p will return a more positive number. For a discrete risk, the VaR returned is the first value above the αth percentile.\n\nVaR(α) returns a functor which can then be called on a risk distribution.\n\nParameters\n\nα: [0,1.0) \n\nExamples\n\njulia> VaR(0.95)(rand(1000))\n0.9561843082268024\n\njulia> rm = VaR(0.95)\nVaR{Float64}(0.95)\n\njulia> rm(rand(1000))\n0.9597070153670079\n\n\n\n\n\n","category":"type"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.ValueAtRisk","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.ValueAtRisk","text":"VaR\n\n\n\n\n\n","category":"type"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.WangTransform","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.WangTransform","text":"WangTransform(α)::RiskMeasure\nWangTransform(α)(risk)::T (where T is the type of values sampled in risk)\n\nThe Wang Transform is a distortion risk measure that transforms the cumulative distribution function (CDF) of the risk distribution using a normal distribution with mean Φ⁻¹(α) and standard deviation 1. risk can be a univariate distribution or an array of outcomes.\n\nWangTransform(α) returns a functor which can then be called on a risk distribution.\n\nParameters\n\nα: [0,1.0]\n\nIn the literature, sometimes λ is used where lambda = Phi^-1(alpha).\n\nExamples\n\njulia> WangTransform(0.95)(rand(1000))\n0.8799465543360105\n\njulia> rm = WangTransform(0.95)\nWangTransform{Float64}(0.95)\n\njulia> rm(rand(1000))\n0.8892245759705852\n\nReferences\n\n\"A Risk Measure That Goes Beyond Coherence\", Shaun S. Wang, 2002\n\n\n\n\n\n","category":"type"},{"location":"risk_measures/#Unexported-API","page":"Risk Measures","title":"Unexported API","text":"","category":"section"},{"location":"risk_measures/","page":"Risk Measures","title":"Risk Measures","text":"Modules = [ActuaryUtilities.RiskMeasures]\nPublic = false","category":"page"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.Expectation","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.Expectation","text":"Expectation()::RiskMeasure\nExpectation()(risk)::T (where T is the type of values sampled in `risk`)\n\nThe expected value of the risk.\n\nExpectation() returns a functor which can then be called on a risk distribution.\n\nExamples\n\njulia> RiskMeasures.Expectation(rand(1000))\n0.4793223308812537\n\njulia> rm = RiskMeasures.Expectation()\nActuaryUtilities.RiskMeasures.Expectation()\n\njulia> rm(rand(1000))\n0.4941708036889741\n\n\n\n\n\n","category":"type"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.cdf_func-Tuple{AbstractArray{<:Real}}","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.cdf_func","text":"cdf_function(risk)\n\nReturns the appropriate cumulative distribution function depending on the type, specifically:\n\ncdf_func(S::AbstractArray{<:Real}) = StatsBase.ecdf(S)\ncdf_func(S::Distributions.UnivariateDistribution) = x -> Distributions.cdf(S, x)\n\n\n\n\n\n","category":"method"},{"location":"risk_measures/#ActuaryUtilities.RiskMeasures.g-Tuple{ActuaryUtilities.RiskMeasures.RiskMeasure, Any}","page":"Risk Measures","title":"ActuaryUtilities.RiskMeasures.g","text":"g(rm::RiskMeasure,x)\n\nThe probability distortion function associated with the given risk measure.\n\nSee Distortion Function g(u)\n\n\n\n\n\n","category":"method"},{"location":"API/ActuaryUtilities/#ActuaryUtilities-API-Reference","page":"ActuaryUtilities","title":"ActuaryUtilities API Reference","text":"","category":"section"},{"location":"API/ActuaryUtilities/","page":"ActuaryUtilities","title":"ActuaryUtilities","text":"Modules = [ActuaryUtilities]","category":"page"},{"location":"API/ActuaryUtilities/#Exported-API","page":"ActuaryUtilities","title":"Exported API","text":"","category":"section"},{"location":"API/ActuaryUtilities/","page":"ActuaryUtilities","title":"ActuaryUtilities","text":"Modules = [ActuaryUtilities]\nPrivate = false","category":"page"},{"location":"API/ActuaryUtilities/#Unexported-API","page":"ActuaryUtilities","title":"Unexported API","text":"","category":"section"},{"location":"API/ActuaryUtilities/","page":"ActuaryUtilities","title":"ActuaryUtilities","text":"Modules = [ActuaryUtilities]\nPublic = false","category":"page"},{"location":"API/ActuaryUtilities/","page":"ActuaryUtilities","title":"ActuaryUtilities","text":"Please open an issue if you encounter any issues or confusion with the package.","category":"page"},{"location":"financial_math/#Financial-Math-Submodule","page":"Financial Math","title":"Financial Math Submodule","text":"","category":"section"},{"location":"financial_math/","page":"Financial Math","title":"Financial Math","text":"Provides a set of common routines in financial maths.","category":"page"},{"location":"financial_math/#Quickstart","page":"Financial Math","title":"Quickstart","text":"","category":"section"},{"location":"financial_math/","page":"Financial Math","title":"Financial Math","text":"cfs = [5, 5, 105]\ntimes = [1, 2, 3]\n\ndiscount_rate = 0.03\n\npresent_value(discount_rate, cfs, times) # 105.65\nduration(Macaulay(), discount_rate, cfs, times) # 2.86\nduration(discount_rate, cfs, times) # 2.78\nconvexity(discount_rate, cfs, times) # 10.62","category":"page"},{"location":"financial_math/#API","page":"Financial Math","title":"API","text":"","category":"section"},{"location":"financial_math/#Exported-API","page":"Financial Math","title":"Exported API","text":"","category":"section"},{"location":"financial_math/","page":"Financial Math","title":"Financial Math","text":"Modules = [ActuaryUtilities.FinancialMath]\nPrivate = false","category":"page"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.KeyRate","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.KeyRate","text":"KeyRate(timepoints,shift=0.001)\n\nA convenience constructor for KeyRateZero. \n\nExtended Help\n\nKeyRateZero is chosen as the default constructor because it has more attractive properties than KeyRatePar:\n\nrates after the key timepoint remain unaffected by the shift\ne.g. this causes a 6-year zero coupon bond would have a negative duration if the 5-year par rate was used\n\n\n\n\n\n","category":"type"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.KeyRatePar","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.KeyRatePar","text":"KeyRatePar(timepoint,shift=0.001) <: KeyRateDuration\n\nShift the par curve by the given amount at the given timepoint. Use in conjunction with duration to calculate the key rate duration. \n\nUnlike other duration statistics which are computed using analytic derivatives, KeyRateDurations are computed via a shift-and-compute the yield curve approach.\n\nKeyRatePar is more commonly reported (than KeyRateZero) in the fixed income markets, even though the latter has more analytically attractive properties. See the discussion of KeyRateDuration in the FinanceModels.jl docs.\n\n\n\n\n\n","category":"type"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.KeyRateZero","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.KeyRateZero","text":"KeyRateZero(timepoint,shift=0.001) <: KeyRateDuration\n\nShift the par curve by the given amount at the given timepoint. Use in conjunction with duration to calculate the key rate duration.\n\nUnlike other duration statistics which are computed using analytic derivatives, KeyRateDuration is computed via a shift-and-compute the yield curve approach.\n\nKeyRateZero is less commonly reported (than KeyRatePar) in the fixed income markets, even though the latter has more analytically attractive properties. See the discussion of KeyRateDuration in the FinanceModels.jl docs.\n\n\n\n\n\n","category":"type"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.breakeven","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.breakeven","text":"breakeven(yield, cashflows::Vector)\nbreakeven(yield, cashflows::Vector,times::Vector)\n\nCalculate the time when the accumulated cashflows breakeven given the yield.\n\nAssumptions:\n\ncashflows occur at the end of the period\ncashflows evenly spaced with the first one occuring at time zero if times not given\n\nReturns nothing if cashflow stream never breaks even.\n\njulia> breakeven(0.10, [-10,1,2,3,4,8])\n5\n\njulia> breakeven(0.10, [-10,15,2,3,4,8])\n1\n\njulia> breakeven(0.10, [-10,-15,2,3,4,8]) # returns the `nothing` value\n\n\n\n\n\n\n\n","category":"function"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.convexity-Tuple{Any, Any, Any}","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.convexity","text":"convexity(yield,cfs,times)\nconvexity(yield,valuation_function)\n\nCalculates the convexity. - yield should be a fixed effective yield (e.g. 0.05). - times may be omitted and it will assume cfs are evenly spaced beginning at the end of the first period.\n\nExamples\n\nUsing vectors of cashflows and times\n\njulia> times = 1:5\njulia> cfs = [0,0,0,0,100]\njulia> duration(0.03,cfs,times)\n4.854368932038834\njulia> duration(Macaulay(),0.03,cfs,times)\n5.0\njulia> duration(Modified(),0.03,cfs,times)\n4.854368932038835\njulia> convexity(0.03,cfs,times)\n28.277877274012614\n\n\nUsing any given value function: \n\njulia> lump_sum_value(amount,years,i) = amount / (1 + i ) ^ years\njulia> my_lump_sum_value(i) = lump_sum_value(100,5,i)\njulia> duration(0.03,my_lump_sum_value)\n4.854368932038835\njulia> convexity(0.03,my_lump_sum_value)\n28.277877274012617\n\n\n\n\n\n\n","category":"method"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.moic-Tuple{T} where T<:AbstractArray","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.moic","text":"moic(cashflows<:AbstractArray)\n\nThe multiple on invested capital (\"moic\") is the un-discounted sum of distributions divided by the sum of the contributions. The function assumes that negative numbers in the array represent contributions and positive numbers represent distributions.\n\nExamples\n\njulia> moic([-10,20,30])\n5.0\n\n\n\n\n\n","category":"method"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.present_values","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.present_values","text":"present_values(interest, cashflows, timepoints)\n\nEfficiently calculate a vector representing the present value of the given cashflows at each period prior to the given timepoint.\n\nExamples\n\njulia> present_values(0.00, [1,1,1])\n[3,2,1]\n\njulia> present_values(ForwardYield([0.1,0.2]), [10,20],[0,1]) # after `using FinanceModels`\n2-element Vector{Float64}:\n 28.18181818181818\n 18.18181818181818\n\n\n\n\n\n","category":"function"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.price-Tuple{Any, Any}","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.price","text":"price(...)\n\nThe absolute value of the present_value(...). \n\nExtended help\n\nUsing price can be helpful if the directionality of the value doesn't matter. For example, in the common usage, duration is more interested in the change in price than present value, so price is used there.\n\n\n\n\n\n","category":"method"},{"location":"financial_math/#ActuaryUtilities.FinancialMath.spread","page":"Financial Math","title":"ActuaryUtilities.FinancialMath.spread","text":"spread(curve1,curve2,cashflows)\n\nReturn the solved-for constant spread to add to curve1 in order to equate the discounted cashflows with curve2\n\nExamples\n\nspread(0.04, 0.05, cfs)\nRate{Float64, Periodic}(0.010000000000000009, Periodic(1))\n\n\n\n\n\n","category":"function"},{"location":"financial_math/#ActuaryUtilities.duration-Tuple{ActuaryUtilities.FinancialMath.KeyRateDuration, Vararg{Any, 4}}","page":"Financial Math","title":"ActuaryUtilities.duration","text":"duration(keyrate::KeyRateDuration,curve,cashflows) \nduration(keyrate::KeyRateDuration,curve,cashflows,timepoints)\nduration(keyrate::KeyRateDuration,curve,cashflows,timepoints,krd_points)\n\nCalculate the key rate duration by shifting the zero (not par) curve by the kwarg shift at the timepoint specified by a KeyRateDuration(time).\n\nThe approach is to carve up the curve into krd_points (default is the unit steps between 1 and the last timepoint of the casfhlows). The zero rate corresponding to the timepoint within the KeyRateDuration is shifted by shift (specified by the KeyRateZero or KeyRatePar constructors. A new curve is created from the shifted rates. This means that the \"width\" of the shifted section is ± 1 time period, unless specific points are specified via krd_points.\n\nThe curve may be any FinanceModels.jl curve (e.g. does not have to be a curve constructed via FinanceModels.Zero(...)).\n\n!!! Experimental: Due to the paucity of examples in the literature, this feature does not have unit tests like the rest of JuliaActuary functionality. Additionally, the API may change in a future major/minor version update.\n\nExamples\n\njulia> riskfree_maturities = [0.5, 1.0, 1.5, 2.0];\n\njulia> riskfree = [0.05, 0.058, 0.064,0.068];\n\njulia> rf_curve = FinanceModels.Zero(riskfree,riskfree_maturities);\n\njulia> cfs = [10,10,10,10,10];\n\njulia> duration(KeyRate(1),rf_curve,cfs)\n8.932800152336995\n\n\nExtended Help\n\nKey Rate Duration is not a well specified topic in the literature and in practice. The reference below suggest that shocking the par curve is more common in practice, but that the zero curve produces more consistent results. Future versions may support shifting the par curve.\n\nReferences: \n\nQuant Finance Stack Exchange: To compute key rate duration, shall I use par curve or zero curve?\n(Financial Exam Help 123](http://www.financialexamhelp123.com/key-rate-duration/)\n\n\n\n\n\n","category":"method"},{"location":"financial_math/#ActuaryUtilities.duration-Tuple{Macaulay, Any, Any, Any}","page":"Financial Math","title":"ActuaryUtilities.duration","text":"duration(Macaulay(),interest_rate,cfs,times)\nduration(Modified(),interest_rate,cfs,times)\nduration(DV01(),interest_rate,cfs,times)\nduration(interest_rate,cfs,times) # Modified Duration\nduration(interest_rate,valuation_function) # Modified Duration\n\nCalculates the Macaulay, Modified, or DV01 duration. times may be ommitted and the valuation will assume evenly spaced cashflows starting at the end of the first period.\n\nNote that the calculated duration will depend on the periodicity convention of the interest_rate: a Periodic yield (or yield model with that convention) will be a slightly different computed duration than a Continous which follows from the present value differing according to the periodicity.\n\nWhen not given Modified() or Macaulay() as an argument, will default to Modified().\n\nModified duration: the relative change per point of yield change.\nMacaulay: the cashflow-weighted average time.\nDV01: the absolute change per basis point (hundredth of a percentage point).\n\nExamples\n\nUsing vectors of cashflows and times\n\njulia> times = 1:5;\n\njulia> cfs = [0,0,0,0,100];\n\njulia> duration(0.03,cfs,times)\n4.854368932038835\n\njulia> duration(Periodic(0.03,1),cfs,times)\n4.854368932038835\n\njulia> duration(Continuous(0.03),cfs,times)\n5.0\n\njulia> duration(Macaulay(),0.03,cfs,times)\n5.0\n\njulia> duration(Modified(),0.03,cfs,times)\n4.854368932038835\n\njulia> convexity(0.03,cfs,times)\n28.277877274012614\n\n\nUsing any given value function: \n\njulia> lump_sum_value(amount,years,i) = amount / (1 + i ) ^ years\njulia> my_lump_sum_value(i) = lump_sum_value(100,5,i)\njulia> duration(0.03,my_lump_sum_value)\n4.854368932038835\njulia> convexity(0.03,my_lump_sum_value)\n28.277877274012617\n\n\n\n\n\n\n","category":"method"},{"location":"financial_math/#Unexported-API","page":"Financial Math","title":"Unexported API","text":"","category":"section"},{"location":"financial_math/","page":"Financial Math","title":"Financial Math","text":"Modules = [ActuaryUtilities.FinancialMath]\nPublic = false","category":"page"},{"location":"upgrade/#Version-Upgrade-Guide","page":"Upgrade from Prior Versions","title":"Version Upgrade Guide","text":"","category":"section"},{"location":"upgrade/#v3-to-v4","page":"Upgrade from Prior Versions","title":"v3 to v4","text":"","category":"section"},{"location":"upgrade/#Overview","page":"Upgrade from Prior Versions","title":"Overview","text":"","category":"section"},{"location":"upgrade/","page":"Upgrade from Prior Versions","title":"Upgrade from Prior Versions","text":"The shape and API of the package is mostly unchanged. The changes that have made fall into a few categores:","category":"page"},{"location":"upgrade/","page":"Upgrade from Prior Versions","title":"Upgrade from Prior Versions","text":"Accommodating FinanceModels.jl, the next-generation version of Yields.jl.\nSimplifying the API, generally making function calls require more specific arguments to avoid ambiguity\nAccommodating the new Cashflow type which makes modeling heterogeneous assets and liabilities simpler.","category":"page"},{"location":"upgrade/#API-Changes","page":"Upgrade from Prior Versions","title":"API Changes","text":"","category":"section"},{"location":"upgrade/","page":"Upgrade from Prior Versions","title":"Upgrade from Prior Versions","text":"Breaking: The functions europut and eurocall have been moved to FinanceModels\nBreaking: Previously, the first argument to present_value or present_values would be interpreted as a set of Periodic(1) one-period forward rates if a vector of real values was passed. Users should explicitly create the yield model first, instead of relying on the implicit conversion:","category":"page"},{"location":"upgrade/","page":"Upgrade from Prior Versions","title":"Upgrade from Prior Versions","text":"# old \npv([0.05,0.1], cfs) \n\n# new\nusing FinanceModels\ny = fit(Spline.Linear(),ForwardYields([0.05,0.1]),Bootstrap())\npv(y,cfs)\n","category":"page"},{"location":"utilities/#Utilities-submodule","page":"Other Utilities","title":"Utilities submodule","text":"","category":"section"},{"location":"utilities/","page":"Other Utilities","title":"Other Utilities","text":"Provides miscellaneous routines common in actuarial and financial work.","category":"page"},{"location":"utilities/#API","page":"Other Utilities","title":"API","text":"","category":"section"},{"location":"utilities/#Exported-API","page":"Other Utilities","title":"Exported API","text":"","category":"section"},{"location":"utilities/","page":"Other Utilities","title":"Other Utilities","text":"Utilities.duration\nUtilities.years_between\nUtilities.accum_offset","category":"page"},{"location":"utilities/#ActuaryUtilities.duration","page":"Other Utilities","title":"ActuaryUtilities.duration","text":"duration(Macaulay(),interest_rate,cfs,times)\nduration(Modified(),interest_rate,cfs,times)\nduration(DV01(),interest_rate,cfs,times)\nduration(interest_rate,cfs,times) # Modified Duration\nduration(interest_rate,valuation_function) # Modified Duration\n\nCalculates the Macaulay, Modified, or DV01 duration. times may be ommitted and the valuation will assume evenly spaced cashflows starting at the end of the first period.\n\nNote that the calculated duration will depend on the periodicity convention of the interest_rate: a Periodic yield (or yield model with that convention) will be a slightly different computed duration than a Continous which follows from the present value differing according to the periodicity.\n\nWhen not given Modified() or Macaulay() as an argument, will default to Modified().\n\nModified duration: the relative change per point of yield change.\nMacaulay: the cashflow-weighted average time.\nDV01: the absolute change per basis point (hundredth of a percentage point).\n\nExamples\n\nUsing vectors of cashflows and times\n\njulia> times = 1:5;\n\njulia> cfs = [0,0,0,0,100];\n\njulia> duration(0.03,cfs,times)\n4.854368932038835\n\njulia> duration(Periodic(0.03,1),cfs,times)\n4.854368932038835\n\njulia> duration(Continuous(0.03),cfs,times)\n5.0\n\njulia> duration(Macaulay(),0.03,cfs,times)\n5.0\n\njulia> duration(Modified(),0.03,cfs,times)\n4.854368932038835\n\njulia> convexity(0.03,cfs,times)\n28.277877274012614\n\n\nUsing any given value function: \n\njulia> lump_sum_value(amount,years,i) = amount / (1 + i ) ^ years\njulia> my_lump_sum_value(i) = lump_sum_value(100,5,i)\njulia> duration(0.03,my_lump_sum_value)\n4.854368932038835\njulia> convexity(0.03,my_lump_sum_value)\n28.277877274012617\n\n\n\n\n\n\nduration(keyrate::KeyRateDuration,curve,cashflows) \nduration(keyrate::KeyRateDuration,curve,cashflows,timepoints)\nduration(keyrate::KeyRateDuration,curve,cashflows,timepoints,krd_points)\n\nCalculate the key rate duration by shifting the zero (not par) curve by the kwarg shift at the timepoint specified by a KeyRateDuration(time).\n\nThe approach is to carve up the curve into krd_points (default is the unit steps between 1 and the last timepoint of the casfhlows). The zero rate corresponding to the timepoint within the KeyRateDuration is shifted by shift (specified by the KeyRateZero or KeyRatePar constructors. A new curve is created from the shifted rates. This means that the \"width\" of the shifted section is ± 1 time period, unless specific points are specified via krd_points.\n\nThe curve may be any FinanceModels.jl curve (e.g. does not have to be a curve constructed via FinanceModels.Zero(...)).\n\n!!! Experimental: Due to the paucity of examples in the literature, this feature does not have unit tests like the rest of JuliaActuary functionality. Additionally, the API may change in a future major/minor version update.\n\nExamples\n\njulia> riskfree_maturities = [0.5, 1.0, 1.5, 2.0];\n\njulia> riskfree = [0.05, 0.058, 0.064,0.068];\n\njulia> rf_curve = FinanceModels.Zero(riskfree,riskfree_maturities);\n\njulia> cfs = [10,10,10,10,10];\n\njulia> duration(KeyRate(1),rf_curve,cfs)\n8.932800152336995\n\n\nExtended Help\n\nKey Rate Duration is not a well specified topic in the literature and in practice. The reference below suggest that shocking the par curve is more common in practice, but that the zero curve produces more consistent results. Future versions may support shifting the par curve.\n\nReferences: \n\nQuant Finance Stack Exchange: To compute key rate duration, shall I use par curve or zero curve?\n(Financial Exam Help 123](http://www.financialexamhelp123.com/key-rate-duration/)\n\n\n\n\n\nduration(d1::Date, d2::Date)\n\nCompute the duration given two dates, which is the number of years since the first date. The interval [0,1) is defined as having duration 1. Can return negative durations if second argument is before the first.\n\njulia> issue_date = Date(2018,9,30);\n\njulia> duration(issue_date , Date(2019,9,30) ) \n2\njulia> duration(issue_date , issue_date) \n1\njulia> duration(issue_date , Date(2018,10,1) ) \n1\njulia> duration(issue_date , Date(2019,10,1) ) \n2\njulia> duration(issue_date , Date(2018,6,30) ) \n0\njulia> duration(Date(2018,9,30),Date(2017,6,30)) \n-1\n\n\n\n\n\n","category":"function"},{"location":"utilities/#ActuaryUtilities.Utilities.years_between","page":"Other Utilities","title":"ActuaryUtilities.Utilities.years_between","text":"Years_Between(d1::Date, d2::Date)\n\nCompute the number of integer years between two dates, with the first date typically before the second. Will return negative number if first date is after the second. Use third argument to indicate if calendar anniversary should count as a full year.\n\nExamples\n\njulia> d1 = Date(2018,09,30);\n\njulia> d2 = Date(2019,09,30);\n\njulia> d3 = Date(2019,10,01);\n\njulia> years_between(d1,d3) \n1\njulia> years_between(d1,d2,false) # same month/day but `false` overlap\n0 \njulia> years_between(d1,d2) # same month/day but `true` overlap\n1 \njulia> years_between(d1,d2) # using default `true` overlap\n1 \n\n\n\n\n\n","category":"function"},{"location":"utilities/#ActuaryUtilities.Utilities.accum_offset","page":"Other Utilities","title":"ActuaryUtilities.Utilities.accum_offset","text":"accum_offset(x; op=*, init=1.0)\n\nA shortcut for the common operation wherein a vector is scanned with an operation, but has an initial value and the resulting array is offset from the traditional accumulate. \n\nThis is a common pattern when calculating things like survivorship given a mortality vector and you want the first value of the resulting vector to be 1.0, and the second value to be 1.0 * x[1], etc.\n\nTwo keyword arguments:\n\nop is the binary (two argument) operator you want to use, such as * or +\ninit is the initial value in the returned array\n\nExamples\n\njulia> accum_offset([0.9, 0.8, 0.7])\n3-element Array{Float64,1}:\n 1.0\n 0.9\n 0.7200000000000001\n\njulia> accum_offset(1:5) # the product of elements 1:n, with the default `1` as the first value\n5-element Array{Int64,1}:\n 1\n 1\n 2\n 6\n 24\n\njulia> accum_offset(1:5,op=+)\n5-element Array{Int64,1}:\n 1\n 2\n 4\n 7\n 11\n\n\n\n\n\n\n","category":"function"},{"location":"API/FinanceCore/#FinanceCore-API-Reference","page":"FinanceCore (re-exported)","title":"FinanceCore API Reference","text":"","category":"section"},{"location":"API/FinanceCore/","page":"FinanceCore (re-exported)","title":"FinanceCore (re-exported)","text":"Modules = [FinanceCore]","category":"page"},{"location":"API/FinanceCore/#Exported-API","page":"FinanceCore (re-exported)","title":"Exported API","text":"","category":"section"},{"location":"API/FinanceCore/","page":"FinanceCore (re-exported)","title":"FinanceCore (re-exported)","text":"Modules = [FinanceCore]\nPrivate = false","category":"page"},{"location":"API/FinanceCore/#FinanceCore.Cashflow","page":"FinanceCore (re-exported)","title":"FinanceCore.Cashflow","text":"Cashflow(amount,time)\n\nA Cahflow{A,B} is a contract that pays an amount at time. \n\nCashflows can be:\n\nnegated with the unary - operator. \nadded/subtracted together but note that the time must be isapprox equal.\nmultiplied/divided by a scalar.\n\nSupertype Hierarchy ≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡\n\nCashflow{A<:Real, B<:Timepoint} <: FinanceCore.AbstractContract <: Any\n\n\n\n\n\n","category":"type"},{"location":"API/FinanceCore/#FinanceCore.Composite","page":"FinanceCore (re-exported)","title":"FinanceCore.Composite","text":"Composite(A,B)\n\nSummary ≡≡≡≡≡≡≡≡≡\n\nstruct Composite{A, B}\n\nA Composite{A,B} is a contract that is composed of two other contracts of type A and type B. The maturity of the composite is the maximum of the maturities of the two components. \n\nIt is used to assemble arbitrarily complex contracts from simpler ones.\n\nFields ≡≡≡≡≡≡≡≡\n\na :: A\nb :: B\n\nSupertype Hierarchy ≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡\n\nComposite{A, B} <: FinanceCore.AbstractContract <: Any\n\n\n\n\n\n","category":"type"},{"location":"API/FinanceCore/#FinanceCore.Continuous","page":"FinanceCore (re-exported)","title":"FinanceCore.Continuous","text":"Continuous()\n\nA type representing continuous interest compounding frequency.\n\nExamples\n\njulia> Rate(0.01,Continuous())\nRate(0.01, Continuous())\n\nSee also: Periodic\n\n\n\n\n\n","category":"type"},{"location":"API/FinanceCore/#FinanceCore.Continuous-Tuple{Any}","page":"FinanceCore (re-exported)","title":"FinanceCore.Continuous","text":"julia> Continuous(0.01)\nRate(0.01, Continuous())\n\nSee also: Periodic\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#FinanceCore.Periodic","page":"FinanceCore (re-exported)","title":"FinanceCore.Periodic","text":"Periodic(frequency)\n\nA type representing periodic interest compounding with the given frequency. \n\nfrequency will be converted to an Integer, and will round up to 8 decimal places (otherwise will throw an InexactError). \n\nExamples\n\nCreating a semi-annual bond equivalent yield:\n\njulia> Rate(0.01,Periodic(2))\nRate(0.01, Periodic(2))\n\nSee also: Continuous\n\n\n\n\n\n","category":"type"},{"location":"API/FinanceCore/#FinanceCore.Periodic-Tuple{Any, Any}","page":"FinanceCore (re-exported)","title":"FinanceCore.Periodic","text":"Periodic(rate,frequency)\n\nA convenience constructor for Rate(rate,Periodic(frequency)).\n\nExamples\n\nCreating a semi-annual bond equivalent yield:\n\njulia> Periodic(0.01,2)\nRate(0.01, Periodic(2))\n\nSee also: Continuous\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#FinanceCore.Quote","page":"FinanceCore (re-exported)","title":"FinanceCore.Quote","text":"Quote(price,instrument)\n\nThe price(<:Real) is the observed value , and the instrument is the instrument/contract that the price is for.\n\nThis can be used, e.g., to calibrate a valuation model to prices for the given instruments - see FinanceModels.jl for more details.\n\n\n\n\n\n","category":"type"},{"location":"API/FinanceCore/#FinanceCore.Rate-Tuple{Any}","page":"FinanceCore (re-exported)","title":"FinanceCore.Rate","text":"Rate(rate[,frequency=1])\nRate(rate,frequency::Frequency)\n\nRate is a type that encapsulates an interest rate along with its compounding frequency.\n\nPeriodic rates can be constructed via Rate(rate,frequency) or Rate(rate,Periodic(frequency)). If not given a second argument, Rate(rate) is equivalent to Rate(rate,Periodic(1)).\n\nContinuous rates can be constructed via Rate(rate, Inf) or Rate(rate,Continuous()).\n\nExamples\n\njulia> Rate(0.01,Continuous())\nRate(0.01, Continuous())\n\njulia> Continuous(0.01)\nRate(0.01, Continuous())\n\njulia> Continuous()(0.01)\nRate(0.01, Continuous())\n\njulia> Rate(0.01,Periodic(2))\nRate(0.01, Periodic(2))\n\njulia> Periodic(0.01,2)\nRate(0.01, Periodic(2))\n\njulia> Periodic(2)(0.01)\nRate(0.01, Periodic(2))\n\njulia> Rate(0.01)\nRate(0.01, Periodic(1))\n\njulia> Rate(0.01,2)\nRate(0.01, Periodic(2))\n\njulia> Rate(0.01,Periodic(4))\nRate(0.01, Periodic(4))\n\njulia> Rate(0.01,Inf)\nRate(0.01, Continuous())\n\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#FinanceCore.amount-Tuple{C} where C<:Cashflow","page":"FinanceCore (re-exported)","title":"FinanceCore.amount","text":"amount(x)\n\nIf is an object with an amount component (e.g. a Cashflow), will retrun that amount component, otherwise just x.\n\nExamples\n\njulia> FinanceCore.amount(Cashflow(1.,3.))\n1.0\n\njulia> FinanceCore.amount(1.)\n1.0\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#FinanceCore.internal_rate_of_return-Tuple{Any}","page":"FinanceCore (re-exported)","title":"FinanceCore.internal_rate_of_return","text":"internal_rate_of_return(cashflows::vector)::Rate\ninternal_rate_of_return(cashflows::Vector, timepoints::Vector)::Rate\n\nCalculate the internalrateof_return with given timepoints. If no timepoints given, will assume that a series of equally spaced cashflows, assuming the first cashflow occurring at time zero and subsequent elements at time 1, 2, 3, ..., n. \n\nReturns a Rate type with periodic compounding once per period (e.g. annual effective if the timepoints given represent years). Get the scalar rate by calling Yields.rate() on the result.\n\nExample\n\njulia> internal_rate_of_return([-100,110],[0,1]) # e.g. cashflows at time 0 and 1\n0.10000000001652906\njulia> internal_rate_of_return([-100,110]) # implied the same as above\n0.10000000001652906\n\nSolver notes\n\nWill try to return a root within the range [-2,2]. If the fast solver does not find one matching this condition, then a more robust search will be performed over the [.99,2] range.\n\nThe solution returned will be in the range [-2,2], but may not be the one nearest zero. For a slightly slower, but more robust version, call ActuaryUtilities.irr_robust(cashflows,timepoints) directly.\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#FinanceCore.irr","page":"FinanceCore (re-exported)","title":"FinanceCore.irr","text":"irr(cashflows::vector)\nirr(cashflows::Vector, timepoints::Vector)\n\nAn alias for `internal_rate_of_return`.\n\n\n\n\n\n","category":"function"},{"location":"API/FinanceCore/#FinanceCore.present_value-Tuple{Any, Any, Any}","page":"FinanceCore (re-exported)","title":"FinanceCore.present_value","text":"present_value(yield_model, cashflows[, timepoints=pairs(cashflows)])\n\nDiscount the cashflows vector at the given yield_model, with the cashflows occurring at the times specified in timepoints. If no timepoints given, assumes that cashflows happen at the indices of the cashflows.\n\nIf your timepoints are dates, you can convert them into a floating point representation of the time interval using DayCounts.jl.\n\nExamples\n\njulia> present_value(0.1, [10,20],[0,1])\n28.18181818181818\njulia> present_value(Continuous(0.1), [10,20],[0,1])\n28.096748360719193\njulia> present_value(Continuous(0.1), [10,20],[1,2])\n25.422989241919232\njulia> present_value(Continuous(0.1), [10,20])\n25.422989241919232\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#FinanceCore.rate-Tuple{Rate}","page":"FinanceCore (re-exported)","title":"FinanceCore.rate","text":"rate(r::Rate)\n\nReturns the untyped scalar interest rate represented by the Rate.\n\nExamples\n\njulia> r =Continuous(0.03)\nYields.Rate{Float64, Continuous}(0.03, Continuous())\n\njulia> rate(r)\n0.03\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#FinanceCore.timepoint-Union{Tuple{C}, Tuple{C, Any}} where C<:Cashflow","page":"FinanceCore (re-exported)","title":"FinanceCore.timepoint","text":"timepoint(x,t)\n\nIf x is an object with a defined time component (e.g. a Cashflow), will return that time component, otherwise will return t. This is useful in handling situations where you want to handle either Cashflows or separate amount and time vectors.\n\nExample\n\njulia> FinanceCore.timepoint(Cashflow(1.,3.),\"ignored\")\n3.0\n\njulia> FinanceCore.timepoint(1.,4.)\n4.0\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#Unexported-API","page":"FinanceCore (re-exported)","title":"Unexported API","text":"","category":"section"},{"location":"API/FinanceCore/","page":"FinanceCore (re-exported)","title":"FinanceCore (re-exported)","text":"Modules = [FinanceCore]\nPublic = false","category":"page"},{"location":"API/FinanceCore/#FinanceCore.Timepoint","page":"FinanceCore (re-exported)","title":"FinanceCore.Timepoint","text":"Timepoint(a)\n\nSummary ≡≡≡≡≡≡≡≡≡\n\nTimepoint is a type alias for Union{T,Dates.Date} that can be used to represent a point in time. It can be either a Dates.Date or a Real number. If defined as a real number, the interpretation is the number of (fractional) periods since time zero.\n\nCurrently, the usage of Dates.Date is not well supported across the JuliaActuary ecosystem but this type is in place such that it can be built upon further.\n\nSupertype Hierarchy ≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡\n\nTimepoint{T} = Union{T,Dates.Date} <: Any\n\n\n\n\n\n","category":"type"},{"location":"API/FinanceCore/#Base.:*-Union{Tuple{T}, Tuple{N}, Tuple{Rate{N, T}, Real}} where {N, T<:Continuous}","page":"FinanceCore (re-exported)","title":"Base.:*","text":"*(Yields.Rate, T)\n*(T, Yields.Rate)\n\nThe multiplication of a Rate with a scalar will inherit the type of the Rate, or the first argument's type if both are Rates.\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#Base.:+-Union{Tuple{T}, Tuple{N}, Tuple{Rate{N, T}, Real}} where {N, T<:Continuous}","page":"FinanceCore (re-exported)","title":"Base.:+","text":"+(Yields.Rate, T<:Real)\n+(T<:Real, Yields.Rate)\n+(Yields.Rate,Yields.Rate)\n\nThe addition of a rate with a number will inherit the type of the Rate, or the first argument's type if both are Rates.\n\nExamples\n\njulia> Yields.Periodic(0.01,2) + Yields.Periodic(0.04,2)\nYields.Rate{Float64, Yields.Periodic}(0.05000000000000004, Yields.Periodic(2))\n\njulia> Yields.Periodic(0.04,2) + 0.01\nYields.Rate{Float64, Yields.Periodic}(0.05, Yields.Periodic(2))\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#Base.:--Union{Tuple{T}, Tuple{N}, Tuple{Rate{N, T}, Real}} where {N, T<:Continuous}","page":"FinanceCore (re-exported)","title":"Base.:-","text":"-(Yields.Rate, T<:Real)\n-(T<:Real, Yields.Rate)\n-(Yields.Rate, Yields.Rate)\n\nThe addition of a rate with a number will inherit the type of the Rate, or the first argument's type if both are Rates.\n\nExamples\n\njulia> Yields.Periodic(0.04,2) - Yields.Periodic(0.01,2)\nYields.Rate{Float64, Yields.Periodic}(0.030000000000000214, Yields.Periodic(2))\n\njulia> Yields.Periodic(0.04,2) - 0.01\nYields.Rate{Float64, Yields.Periodic}(0.03, Yields.Periodic(2))\n\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#Base.:/-Union{Tuple{T}, Tuple{N}, Tuple{Rate{N, T}, Real}} where {N, T<:Continuous}","page":"FinanceCore (re-exported)","title":"Base.:/","text":"/(x::Yields.Rate, y::Real)\n\nThe division of a Rate with a scalar will inherit the type of the Rate, or the first argument's type if both are Rates.\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#Base.:<-Union{Tuple{U}, Tuple{T}, Tuple{T, U}} where {T<:Rate, U<:Rate}","page":"FinanceCore (re-exported)","title":"Base.:<","text":"<(x::Rate,y::Rate)\n\nConvert the second argument to the periodicity of the first and compare the scalar rate values to determine if the first argument has a lower force of interest than the second.\n\nExamples\n\njulia> Yields.Periodic(0.03,100) < Yields.Continuous(0.03)\ntrue\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#Base.:>-Union{Tuple{U}, Tuple{T}, Tuple{T, U}} where {T<:Rate, U<:Rate}","page":"FinanceCore (re-exported)","title":"Base.:>","text":">(Rate,Rate)\n\nConvert the second argument to the periodicity of the first and compare the scalar rate values to determine if the first argument has a greater force of interest than the second.\n\nExamples\n\njulia> Yields.Periodic(0.03,100) > Yields.Continuous(0.03)\nfalse\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/#Base.convert-Union{Tuple{T}, Tuple{T, Rate}} where T<:FinanceCore.Frequency","page":"FinanceCore (re-exported)","title":"Base.convert","text":"convert(cf::Frequency,r::Rate)\n\nReturns a Rate with an equivalent discount but represented with a different compounding frequency.\n\nExamples\n\njulia> r = Rate(Periodic(12),0.01)\nRate(0.01, Periodic(12))\n\njulia> convert(Periodic(1),r)\nRate(0.010045960887181016, Periodic(1))\n\njulia> convert(Continuous(),r)\nRate(0.009995835646701251, Continuous())\n\n\n\n\n\n","category":"method"},{"location":"API/FinanceCore/","page":"FinanceCore (re-exported)","title":"FinanceCore (re-exported)","text":"Please open an issue if you encounter any issues or confusion with the package.","category":"page"},{"location":"#Quickstart","page":"Overview","title":"Quickstart","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"cfs = [5, 5, 105]\ntimes = [1, 2, 3]\n\ndiscount_rate = 0.03\n\npresent_value(discount_rate, cfs, times) # 105.65\nduration(Macaulay(), discount_rate, cfs, times) # 2.86\nduration(discount_rate, cfs, times) # 2.78\nconvexity(discount_rate, cfs, times) # 10.62","category":"page"},{"location":"#Features","page":"Overview","title":"Features","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"A collection of common functions/manipulations used in Actuarial Calculations.","category":"page"},{"location":"#Financial-Maths","page":"Overview","title":"Financial Maths","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"duration:\nCalculate the Macaulay, Modified, or DV01 durations for a set of cashflows\nCalculate the KeyRate(time) (a.k.a. KeyRateZero)duration or KeyRatePar(time) duration\nconvexity for price sensitivity\nFlexible interest rate models via the FinanceModels.jl package.\ninternal_rate_of_return or irr to calculate the IRR given cashflows (including at timepoints like Excel's XIRR)\nbreakeven to calculate the breakeven time for a set of cashflows\naccum_offset to calculate accumulations like survivorship from a mortality vector\nspread will calculate the spread needed between two yield curves to equate a set of cashflows","category":"page"},{"location":"#Risk-Measures","page":"Overview","title":"Risk Measures","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"Calculate risk measures for a given vector of risks:\nCTE for the Conditional Tail Expectation\nVaR for the percentile/Value at Risk\nWangTransform for the Wang Transformation\nProportionalHazard for proportional hazards\nDualPower for dual power measure","category":"page"},{"location":"#Insurance-mechanics","page":"Overview","title":"Insurance mechanics","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"duration:\nCalculate the duration given an issue date and date (a.k.a. policy duration)","category":"page"},{"location":"#Typed-Rates","page":"Overview","title":"Typed Rates","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"functions which return a rate/yield will return a FinanceCore.Rate object. E.g. irr(cashflows) will return a Rate(0.05,Periodic(1)) instead of just a 0.05 (float64) to convey the compounding frequency. This is compatible across the JuliaActuary ecosystem and can be used anywhere you would otherwise use a simple floating point rate.","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"A couple of other notes:","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"rate(...) will return the scalar rate value from a Rate struct:","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"julia> r = Rate(0.05,Periodic(1));\n\njulia> rate(r) \n0.05","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"You can still pass a simple floating point rate to various methods. E.g. these two are the same (the default compounding convention is periodic once per period):","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"discount(0.05,cashflows)\n\nr = Rate(0.05,Periodic(1));\ndiscount(r,cashflows)","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"convert between rates with:","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"r = Rate(0.05,Periodic(1));\n\nconvert(Periodic(2), r) # convert to compounded twice per timestep\nconvert(Continuous(2),r) # convert to compounded twice per timestep","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"For more on Rates, see FinanceCore.jl. FinanceModels.jl also provides a rich and flexible set of yield models to use.","category":"page"},{"location":"#Documentation","page":"Overview","title":"Documentation","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"Full documentation is available here.","category":"page"},{"location":"#Examples","page":"Overview","title":"Examples","text":"","category":"section"},{"location":"#Interactive,-basic-cashflow-analysis","page":"Overview","title":"Interactive, basic cashflow analysis","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"See JuliaActuary.org for instructions on running this example.","category":"page"},{"location":"","page":"Overview","title":"Overview","text":"(Image: Simple cashflow analysis with ActuaryUtilities.jl)","category":"page"},{"location":"#Useful-tips","page":"Overview","title":"Useful tips","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"Functions often use a mix of interest_rates, cashflows, and timepoints. When calling functions, the general order of the arguments is 1) interest rates, 2) cashflows, and 3) timepoints.","category":"page"}] } diff --git a/dev/upgrade/index.html b/dev/upgrade/index.html index 9d9d1f2..34af487 100644 --- a/dev/upgrade/index.html +++ b/dev/upgrade/index.html @@ -1,9 +1,9 @@ -Upgrade from Prior Versions · ActuaryUtilities.jl

Version Upgrade Guide

v3 to v4

Overview

The shape and API of the package is mostly unchanged. The changes that have made fall into a few categores:

  • Accommodating FinanceModels.jl, the next-generation version of Yields.jl.
  • Simplifying the API, generally making function calls require more specific arguments to avoid ambiguity
  • Accommodating the new Cashflow type which makes modeling heterogeneous assets and liabilities simpler.

API Changes

  • Breaking: The functions europut and eurocall have been moved to FinanceModels
  • Breaking: Previously, the first argument to present_value or present_values would be interpreted as a set of Periodic(1) one-period forward rates if a vector of real values was passed. Users should explicitly create the yield model first, instead of relying on the implicit conversion:
# old 
+Upgrade from Prior Versions · ActuaryUtilities.jl        
         
 
Version Upgrade Guide
v3 to v4
Overview
The shape and API of the package is mostly unchanged. The changes that have made fall into a few categores:
  • Accommodating FinanceModels.jl, the next-generation version of Yields.jl.
  • Simplifying the API, generally making function calls require more specific arguments to avoid ambiguity
  • Accommodating the new Cashflow type which makes modeling heterogeneous assets and liabilities simpler.
API Changes
  • Breaking: The functions europut and eurocall have been moved to FinanceModels
  • Breaking: Previously, the first argument to present_value or present_values would be interpreted as a set of Periodic(1) one-period forward rates if a vector of real values was passed. Users should explicitly create the yield model first, instead of relying on the implicit conversion:
# old 
 pv([0.05,0.1], cfs)  
 
 # new
 using FinanceModels
 y = fit(Spline.Linear(),ForwardYields([0.05,0.1]),Bootstrap())
 pv(y,cfs)
-

+
diff --git a/dev/utilities/index.html b/dev/utilities/index.html index e562376..ccf641e 100644 --- a/dev/utilities/index.html +++ b/dev/utilities/index.html @@ -1,18 +1,5 @@ -Other Utilities · ActuaryUtilities.jl

Utilities submodule

Provides miscellaneous routines common in actuarial and financial work.

API

Exported API

ActuaryUtilities.duration — Function
duration(d1::Date, d2::Date)

Compute the duration given two dates, which is the number of years since the first date. The interval [0,1) is defined as having duration 1. Can return negative durations if second argument is before the first.

julia> issue_date  = Date(2018,9,30);
-
-julia> duration(issue_date , Date(2019,9,30) ) 
-2
-julia> duration(issue_date , issue_date) 
-1
-julia> duration(issue_date , Date(2018,10,1) ) 
-1
-julia> duration(issue_date , Date(2019,10,1) ) 
-2
-julia> duration(issue_date , Date(2018,6,30) ) 
-0
-julia> duration(Date(2018,9,30),Date(2017,6,30)) 
--1
source
duration(Macaulay(),interest_rate,cfs,times)
+Other Utilities · ActuaryUtilities.jl        
         
 
Utilities submodule
Provides miscellaneous routines common in actuarial and financial work.
API
Exported API
ActuaryUtilities.duration — Function
duration(Macaulay(),interest_rate,cfs,times)
 duration(Modified(),interest_rate,cfs,times)
 duration(DV01(),interest_rate,cfs,times)
 duration(interest_rate,cfs,times)             # Modified Duration
@@ -43,7 +30,7 @@
 4.854368932038835
 julia> convexity(0.03,my_lump_sum_value)
 28.277877274012617
-
source
duration(keyrate::KeyRateDuration,curve,cashflows)    
+
source
duration(keyrate::KeyRateDuration,curve,cashflows)    
 duration(keyrate::KeyRateDuration,curve,cashflows,timepoints)
 duration(keyrate::KeyRateDuration,curve,cashflows,timepoints,krd_points)
Calculate the key rate duration by shifting the zero (not par) curve by the kwarg shift at the timepoint specified by a KeyRateDuration(time).
The approach is to carve up the curve into krd_points (default is the unit steps between 1 and  the last timepoint of the casfhlows). The  zero rate corresponding to the timepoint within the KeyRateDuration is shifted by shift (specified by the KeyRateZero or KeyRatePar constructors. A new curve is created from the shifted rates. This means that the  "width" of the shifted section is ± 1 time period, unless specific points are specified via krd_points.
The curve may be any FinanceModels.jl curve (e.g. does not have to be a curve constructed via FinanceModels.Zero(...)).
!!! Experimental: Due to the paucity of examples in the literature, this feature does not have unit tests like the rest of JuliaActuary functionality. Additionally, the API may change in a future major/minor version update.
Examples
julia> riskfree_maturities = [0.5, 1.0, 1.5, 2.0];
 
@@ -55,7 +42,20 @@
 
 julia> duration(KeyRate(1),rf_curve,cfs)
 8.932800152336995
-
Extended Help
Key Rate Duration is not a well specified topic in the literature and in practice. The reference below suggest that shocking the par curve is more common  in practice, but that the zero curve produces more consistent results. Future versions may support shifting the par curve.
References: 
source
ActuaryUtilities.Utilities.years_between — Function
Years_Between(d1::Date, d2::Date)
Compute the number of integer years between two dates, with the  first date typically before the second. Will return negative number if first date is after the second. Use third argument to indicate if calendar  anniversary should count as a full year.
Examples
julia> d1 = Date(2018,09,30);
+
Extended Help
Key Rate Duration is not a well specified topic in the literature and in practice. The reference below suggest that shocking the par curve is more common  in practice, but that the zero curve produces more consistent results. Future versions may support shifting the par curve.
References: 
source
duration(d1::Date, d2::Date)
Compute the duration given two dates, which is the number of years since the first date. The interval [0,1) is defined as having  duration 1. Can return negative durations if second argument is before the first.
julia> issue_date  = Date(2018,9,30);
+
+julia> duration(issue_date , Date(2019,9,30) ) 
+2
+julia> duration(issue_date , issue_date) 
+1
+julia> duration(issue_date , Date(2018,10,1) ) 
+1
+julia> duration(issue_date , Date(2019,10,1) ) 
+2
+julia> duration(issue_date , Date(2018,6,30) ) 
+0
+julia> duration(Date(2018,9,30),Date(2017,6,30)) 
+-1
source
ActuaryUtilities.Utilities.years_between — Function
Years_Between(d1::Date, d2::Date)
Compute the number of integer years between two dates, with the  first date typically before the second. Will return negative number if first date is after the second. Use third argument to indicate if calendar  anniversary should count as a full year.
Examples
julia> d1 = Date(2018,09,30);
 
 julia> d2 = Date(2019,09,30);
 
@@ -68,7 +68,7 @@
 julia> years_between(d1,d2) # same month/day but `true` overlap
 1 
 julia> years_between(d1,d2) # using default `true` overlap
-1 
source
ActuaryUtilities.Utilities.accum_offset — Function
accum_offset(x; op=*, init=1.0)
A shortcut for the common operation wherein a vector is scanned with an operation, but has an initial value and the resulting array is offset from the traditional accumulate. 
This is a common pattern when calculating things like survivorship given a mortality vector and you want the first value of the resulting vector to be 1.0, and the second value to be 1.0 * x[1], etc.
Two keyword arguments:
  • op is the binary (two argument) operator you want to use, such as * or +
  • init is the initial value in the returned array
Examples
julia> accum_offset([0.9, 0.8, 0.7])
+1 
source
ActuaryUtilities.Utilities.accum_offset — Function
accum_offset(x; op=*, init=1.0)
A shortcut for the common operation wherein a vector is scanned with an operation, but has an initial value and the resulting array is offset from the traditional accumulate. 
This is a common pattern when calculating things like survivorship given a mortality vector and you want the first value of the resulting vector to be 1.0, and the second value to be 1.0 * x[1], etc.
Two keyword arguments:
  • op is the binary (two argument) operator you want to use, such as * or +
  • init is the initial value in the returned array
Examples
julia> accum_offset([0.9, 0.8, 0.7])
 3-element Array{Float64,1}:
  1.0
  0.9
@@ -89,4 +89,4 @@
   4
   7
  11
-
source

+
source