diff --git a/Project.toml b/Project.toml index 8f5cb798..f49738cc 100644 --- a/Project.toml +++ b/Project.toml @@ -7,6 +7,7 @@ version = "0.10.6" DataInterpolations = "82cc6244-b520-54b8-b5a6-8a565e85f1d0" FastDifferentiation = "eb9bf01b-bf85-4b60-bf87-ee5de06c00be" InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240" +IrrationalConstants = "92d709cd-6900-40b7-9082-c6be49f344b6" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" Logging = "56ddb016-857b-54e1-b83d-db4d58db5568" MacroTools = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09" @@ -26,9 +27,9 @@ ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210" SymbolicUtils = "d1185830-fcd6-423d-90d6-eec64667417b" Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7" -[extensions] -PostNewtonianForwardDiffExt = ["ForwardDiff"] -PostNewtonianSymbolicsExt = ["Symbolics", "SymbolicUtils"] +# [extensions] +# PostNewtonianForwardDiffExt = ["ForwardDiff"] +# PostNewtonianSymbolicsExt = ["Symbolics", "SymbolicUtils"] [compat] Aqua = "0.8" @@ -40,6 +41,7 @@ FileIO = "1.16.3" ForwardDiff = "0.10.38, 1" HDF5 = "0.17.2" InteractiveUtils = "1" +IrrationalConstants = "0.2.4" LinearAlgebra = "1" Logging = "1" MacroTools = "0.5.10" diff --git a/docs/Project.toml b/docs/Project.toml index 8a25f2f5..d7fec299 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -1,5 +1,7 @@ [deps] Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" +DocumenterCitations = "daee34ce-89f3-4625-b898-19384cb65244" +DocumenterMermaid = "a078cd44-4d9c-4618-b545-3ab9d77f9177" LiveServer = "16fef848-5104-11e9-1b77-fb7a48bbb589" PlotlyJS = "f0f68f2c-4968-5e81-91da-67840de0976a" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" diff --git a/docs/make.jl b/docs/make.jl index bbabee6b..bf2accb3 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -1,6 +1,7 @@ using PostNewtonian using Symbolics # To document the extension using Documenter +using DocumenterMermaid DocMeta.setdocmeta!( PostNewtonian, :DocTestSetup, :(using PostNewtonian); recursive=true, warn=false @@ -33,6 +34,7 @@ makedocs(; "GWFrames" => "interface/gwframes.md", ], "Internals" => [ + "Code diagram" => "internals/code_diagram.md", "Code structure" => "internals/code_structure.md", "internals/pn_systems.md", "internals/fundamental_variables.md", diff --git a/docs/src/interface/high-level.md b/docs/src/interface/high-level.md index 0bf595c6..e6d94463 100644 --- a/docs/src/interface/high-level.md +++ b/docs/src/interface/high-level.md @@ -53,9 +53,9 @@ using Plots # Requires also installing `Plots` in your project plotlyjs() # hide default(size=(800,480), linewidth=2, leg=:top) # hide -plot(inspiral.t, inspiral[:χ⃗₁ˣ], label=raw"$\vec{\chi}_1^x$") -plot!(inspiral.t, inspiral[:χ⃗₁ʸ], label=raw"$\vec{\chi}_1^y$") -plot!(inspiral.t, inspiral[:χ⃗₁ᶻ], label=raw"$\vec{\chi}_1^z$") +plot(inspiral.t, inspiral[:χ₁ˣ], label=raw"$\vec{\chi}_1^x$") +plot!(inspiral.t, inspiral[:χ₁ʸ], label=raw"$\vec{\chi}_1^y$") +plot!(inspiral.t, inspiral[:χ₁ᶻ], label=raw"$\vec{\chi}_1^z$") plot!(xlabel="Time (𝑀)", ylabel="Dimensionless spin components") savefig("inspiral_spins.html"); nothing # hide ``` @@ -78,7 +78,7 @@ They can be accessed by their symbols, like the spins above, or by their number in this list. To access the `i`th variable at time step `j`, use `sol[i, j]`. You can also use colons: `sol[i, :]` is a vector of the `i`th variable at all times, and `sol[:, j]` is a vector of all the data at time step `j`. For -example, `inspiral[:χ⃗₁ˣ]` could also be written as `inspiral[3, :]`. +example, `inspiral[:χ₁ˣ]` could also be written as `inspiral[3, :]`. By default, the output of `orbital_evolution` is just the time steps to which the adaptive ODE integrator happened to step. If you know that you want the diff --git a/docs/src/interface/symbolics.md b/docs/src/interface/symbolics.md index 06da77b9..9df9afd6 100644 --- a/docs/src/interface/symbolics.md +++ b/docs/src/interface/symbolics.md @@ -23,7 +23,7 @@ symbols as usual: julia> using PostNewtonian, Symbolics julia> symbolic_pnsystem = PostNewtonian.SymbolicPNSystem() -PostNewtonian.SymbolicPNSystem{Vector{Num}, 9223372036854775805//2, Num}(Num[M₁, M₂, χ⃗₁ˣ, χ⃗₁ʸ, χ⃗₁ᶻ, χ⃗₂ˣ, χ⃗₂ʸ, χ⃗₂ᶻ, Rʷ, Rˣ, Rʸ, Rᶻ, v, Φ], Λ₁, Λ₂) +PostNewtonian.SymbolicPNSystem{Vector{Num}, 9223372036854775805//2, Num}(Num[M₁, M₂, χ₁ˣ, χ₁ʸ, χ₁ᶻ, χ₂ˣ, χ₂ʸ, χ₂ᶻ, Rʷ, Rˣ, Rʸ, Rᶻ, v, Φ], Λ₁, Λ₂) julia> v = PostNewtonian.v(symbolic_pnsystem) v diff --git a/docs/src/internals/code_diagram.md b/docs/src/internals/code_diagram.md new file mode 100644 index 00000000..816f53ea --- /dev/null +++ b/docs/src/internals/code_diagram.md @@ -0,0 +1,167 @@ +## Possibilities for Code Structure + +### `StaticArrays.FieldVector` + +This is a nice idea. Given a `struct` with a series of fields, making +it a subtype of `FieldVector` makes it an `SVector` or `MVector` +(depending on whether it is immutable or mutable). The fields can be +accessed by the names you give them, but everything else is like a +nicely completed `StaticArray`, which is handled well by all the SciML +packages. So, for example, we would define `BBH` as + +```julia +using StaticArrays: FieldVector + +struct BBH{T, PNOrder} <: FieldVector{14, T} + M₁::T + M₂::T + χ⃗₁::T + χ₁ˣ::T + χ₁ʸ::T + χ₁ᶻ::T + χ⃗₂::T + χ₂ˣ::T + χ₂ʸ::T + χ₂ᶻ::T + R::T + Rʷ::T + Rˣ::T + Rʸ::T + Rᶻ::T + v::T + Φ::T +end +``` + +The big disadvantage is that it is not possible to contain non-state +variables in the `struct` — for example, the tidal coupling +parameters. Making them into state variables would make the ODE +system larger than it needs to be. Making them into type parameters +would be bad design, lengthening compile times. I don't see any other +way to incorporate them into the `struct`, so this option is +discarded. + +### `LabelledArrays` + +This is a nice design, and works well with SciML. But it doesn't +allow any other metadata — even `PNOrder`, which would be possible +with `FieldVector`. So this is discarded. + +### Emulating `LabelledArrays`' use of `Syms` + +Part of the type of a `LabelledArray` is a `Syms` object, which is a +`Tuple` of `Symbol`s. I could basically reimplement this for +`PNSystem`s, which could bring a great deal of flexibility. For +example, if a `PNSystem` has an `e` field, it must be an eccentric +system. So, in principle, we could dispatch on `Syms`. This seems +clunky to me. Also, it would remove our ability to further +specialize, unless we defined adequate abstract super types. I don't +have a solid argument against this, but I think it would be better to +just define a `symbols` function for each subtype. + +### Make `symbols` as function of type, and emulate `LabelledArrays` features + +This will be a lot of work, but basically copying all the methods of +`LabelledArrays` seems like the way to go. + +### Separate types for mutable and immutable systems + +I think it would be too much work to maintain two separate types for +each of the `PNSystem`s, one mutable and one immutable. Probably +better to just store the container type as a type parameter, and test +whether that container `ismutabletype` — for example, inside +`setindex!`, we could test and raise a more informative error if the +system `!ismutabletype`. + +## Diagram + +```mermaid +flowchart TB + %% define each layer as its own box + subgraph Core["core
Building blocks of the code"] + + end + subgraph Systems["pn_systems
Types encoding various binaries"] + end + subgraph Literature["literature
Modules for each reference containing pieces of PN expressions"] + end + subgraph Expressions["pn_expressions
Functions for computing physical quantities"] + end + subgraph Interface["interface
High-level functions for users to call"] + end + + %% draw the arrows in build‐order + Core --> Systems + Systems --> Literature + Literature --> Expressions + Expressions --> Interface +``` + +- PostNewtonian + - interface: high-level functions for users to call + - orbital_evolution + - waveform + - pn + - pn_expressions: functions for computing physical quantities + - flux + - energy + - angular_momentum + - precession + - dynamics + - waveforms + - literature: modules for each reference containing pieces of PN expressions + - common variables + - Ref1 + - import fundamental variables + - import common variables + - define variables not in common variables + - write individual expressions as separate functions with `@pn_expression` + - pn_systems: types encoding various binaries + - PNSystem + - AbstractBBHSystem + - QuasicircularBBH + - QuasisphericalBBH + - EccentricNonspinningBBH + - BBH + - AbstractBHNSSystem + - BHNS + - AbstractNSNSSystem + - NSNS + - core: the building blocks of the code + - PNExpression + - PNReference + - PNExpansion + - PNTerm + +- `PNSystem` + - Define abstract subtypes: + - `AbstractBBHSystem` + - `QuasicircularBBH` + - `QuasisphericalBBH` + - `EccentricNonspinningBBH` + +- `PNExpression` +- `PNExpansion` +- `PNTerm` + +- literature + - common variables + - each reference + - directory and module named by bibtex key + - modules are imported directly under top-level `PostNewtonian` + - explicitly import any fundamental variables used in the expressions + - import variables that are defined the same as the common variables + - define variables that are not defined in the common variables + - write individuals + +- PN expressions + - Assemble functions for high-level quantities like flux, etc. + - Inside each function, simply call the expressions from the + literature, prepending with module name. + +`@pn_expression` will + +1. look for symbols in the expression, and for any that matches a function + name in the current module, add a `let` binding for that symbol to equal + the function called on the `pnsystem` argument. diff --git a/docs/src/internals/utilities.md b/docs/src/internals/utilities.md index 8228433d..6386a4ee 100644 --- a/docs/src/internals/utilities.md +++ b/docs/src/internals/utilities.md @@ -90,11 +90,6 @@ and replace them with the appropriate float values. ```@docs PostNewtonian.γₑ PostNewtonian.ζ3 -PostNewtonian.ln2 -PostNewtonian.ln3 -PostNewtonian.ln5 -PostNewtonian.ln³╱₂ -PostNewtonian.ln⁵╱₂ ``` ## Truncated series diff --git a/docs/src/references.bib b/docs/src/references.bib new file mode 100644 index 00000000..a0d6fb41 --- /dev/null +++ b/docs/src/references.bib @@ -0,0 +1,34 @@ +@article{Blanchet2024, + title = {{Post-Newtonian} theory for gravitational waves}, + volume = {27}, + issn = {1433-8351}, + url = {https://doi.org/10.1007/s41114-024-00050-z}, + doi = {10.1007/s41114-024-00050-z}, + number = {1}, + journal = {Living Reviews in Relativity}, + author = {Blanchet, Luc}, + month = jul, + year = {2024}, +} + +@article{TaylorPoisson2008, + title = {Nonrotating black hole in a {post-Newtonian} tidal environment}, + volume = {78}, + issn = {1550-7998, 1550-2368}, + url = {http://arxiv.org/abs/0806.3052}, + doi = {10.1103/PhysRevD.78.084016}, + number = {8}, + journal = {Physical Review D}, + author = {Taylor, Stephanne and Poisson, Eric}, + month = oct, + year = {2008}, +} + +@misc{Trestini2025, + title = {The Schott term in the binding energy for compact binaries on circular orbits at fourth {post-Newtonian} order}, + url = {http://arxiv.org/abs/2504.13245}, + doi = {10.48550/arXiv.2504.13245}, + author = {Trestini, David}, + month = apr, + year = {2025}, +} diff --git a/ext/PostNewtonianSymbolicsExt.jl b/ext/PostNewtonianSymbolicsExt.jl index a8d0a1b5..c7cd1b31 100644 --- a/ext/PostNewtonianSymbolicsExt.jl +++ b/ext/PostNewtonianSymbolicsExt.jl @@ -19,10 +19,9 @@ import PostNewtonian: causes_domain_error!, prepare_pn_order, order_index, + iscall, + isadd, 𝓔′, - apply_to_first_add!, - flatten_add!, - flatten_mul!, pn_expression, pn_expansion, @pn_expansion, @@ -44,13 +43,9 @@ import PostNewtonian: X₁, X₂, ln, - ln2, - ln3, - ln5, ζ3, γₑ, _efficient_vector -#apply_to_first_add!, flatten_add!, pn_expression, using RuntimeGeneratedFunctions: init, @RuntimeGeneratedFunction init(@__MODULE__) @@ -59,6 +54,46 @@ function _efficient_vector(N, ::Type{Symbolics.Num}) return Symbolics.variables(string(gensym()), 1:N) end +### Moved from src/core/utilities/misc.jl + +""" + flatten_binary!(expr, symbols) + +Flatten nested binary operations — that is, apply associativity repeatedly. +""" +function flatten_binary!(expr, symbols) + while iscall(expr, symbols) && any(x -> iscall(x, symbols), expr.args[2:end]) + args = expr.args[2:end] + i₊ = findfirst(x -> iscall(x, symbols), args) + args′ = [first(symbols); args[1:(i₊ - 1)]; args[i₊].args[2:end]; args[(i₊ + 1):end]] + expr.args[:] = args′[1:length(expr.args)] + append!(expr.args, args′[(1 + length(expr.args)):end]) + end + return expr +end + +flatten_add!(expr) = flatten_binary!(expr, ((+), :+)) +flatten_mul!(expr) = flatten_binary!(expr, ((*), :*)) + +""" + apply_to_first_add!(expr, func) + +Apply `func` to the first sub-expression found in a "prewalk"-traversal of `expr` that +satisfies [`isadd`](@ref). If `func` acts in place, so does this function. In either case, +the expression should be returned. +""" +function apply_to_first_add!(expr, func) + found_add = false + MacroTools.prewalk(expr) do x + if !found_add && isadd(x) + found_add = true + func(x) + else + x + end + end +end + ### Moved from src/utilities/macros.jl hold(x) = x @@ -68,7 +103,7 @@ Symbolics.derivative(::typeof(hold), args::NTuple{1,Any}, ::Val{1}) = 1 function unhold(expr) MacroTools.postwalk(expr) do x m = MacroTools.trymatch(:(f_(i_)), x) - m === nothing || m[:f] !== hold ? x : Symbol(m[:i]) + m ≡ nothing || m[:f] !== hold ? x : Symbol(m[:i]) end end @@ -260,10 +295,10 @@ end causes_domain_error!(u̇, ::PNSystem{VT}) where {VT<:Vector{Symbolics.Num}} = false function SymbolicPNSystem(PNOrder=typemax(Int)) - Symbolics.@variables M₁ M₂ χ⃗₁ˣ χ⃗₁ʸ χ⃗₁ᶻ χ⃗₂ˣ χ⃗₂ʸ χ⃗₂ᶻ Rʷ Rˣ Rʸ Rᶻ v Φ Λ₁ Λ₂ + Symbolics.@variables M₁ M₂ χ₁ˣ χ₁ʸ χ₁ᶻ χ₂ˣ χ₂ʸ χ₂ᶻ Rʷ Rˣ Rʸ Rᶻ v Φ Λ₁ Λ₂ ET = typeof(M₁) return SymbolicPNSystem{Vector{ET},prepare_pn_order(PNOrder),ET}( - [M₁, M₂, χ⃗₁ˣ, χ⃗₁ʸ, χ⃗₁ᶻ, χ⃗₂ˣ, χ⃗₂ʸ, χ⃗₂ᶻ, Rʷ, Rˣ, Rʸ, Rᶻ, v, Φ], Λ₁, Λ₂ + [M₁, M₂, χ₁ˣ, χ₁ʸ, χ₁ᶻ, χ₂ˣ, χ₂ʸ, χ₂ᶻ, Rʷ, Rˣ, Rʸ, Rᶻ, v, Φ], Λ₁, Λ₂ ) end diff --git a/sources/PNpedia/.gitignore b/sources/PNpedia/.gitignore new file mode 100644 index 00000000..d239ddcb --- /dev/null +++ b/sources/PNpedia/.gitignore @@ -0,0 +1 @@ +PNpedia diff --git a/sources/PNpedia/Project.toml b/sources/PNpedia/Project.toml new file mode 100644 index 00000000..4cffcc42 --- /dev/null +++ b/sources/PNpedia/Project.toml @@ -0,0 +1,3 @@ +[deps] +PythonCall = "6099a3de-0909-46bc-b1f4-468b9a2dfc0d" +SymPyPythonCall = "bc8888f7-b21e-4b7c-a06a-5d9c9496438c" diff --git a/sources/PNpedia/README.md b/sources/PNpedia/README.md new file mode 100644 index 00000000..e03ab610 --- /dev/null +++ b/sources/PNpedia/README.md @@ -0,0 +1,13 @@ +# PNpedia + +This directory contains code to translate results from David +Trestini's [PNpedia](https://github.com/davidtrestini/PNpedia) — which +are given as `.txt` files containing Mathematica output — into Julia +code. + +Though it is `.gitignore`d, to run the code you should first clone +PNpedia into this directory, so that the files are available + +```bash +git clone https://github.com/davidtrestini/PNpedia.git +``` diff --git a/sources/PNpedia/characters.html b/sources/PNpedia/characters.html new file mode 100644 index 00000000..80ccc0b6 --- /dev/null +++ b/sources/PNpedia/characters.html @@ -0,0 +1,20 @@ +

The Wolfram Language not only has systemwide support for arbitrary Unicode characters, but also includes nearly a thousand carefully designed characters for mathematical notation and technical presentation—all fully integrated into the Wolfram Language's input, output, and graphics.

nnn or \[Name] — named character (e.g. α, a, ∖[Alpha])

Insert ▶ Special Character — palette of all named special characters

Wolfram Language Syntax »

∞  ▪  °  ▪  π  ▪  ×  ▪    ▪    ▪  ∫  ▪    ▪  ∂  ▪  ∈  ▪    ▪    ▪    ▪  〚  ▪  〛  ▪  ...

\[Degree]  ▪  \[ImaginaryI]  ▪  \[Times]  ▪  \[Element]  ▪  \[Rule]  ▪  ...

Greek Letters »

α  ▪  β  ▪  θ  ▪  ϑ  ▪  ϕ  ▪  ω  ▪  Δ  ▪  Ψ  ▪  Ω  ▪  Ϡ  ▪  ...

\[Alpha]  ▪  \[CurlyTheta]  ▪  \[CapitalDelta]  ▪  \[Sampi]  ▪  ...

Notational Alphabets »

  ▪    ▪    ▪    ▪    ▪    ▪  a  ▪  A  ▪  ℵ  ▪  ...

\[ScriptA]  ▪  \[ScriptCapitalA]  ▪  \[GothicA]  ▪  \[FormalA]  ▪  \[Aleph]  ▪  ...

Mathematical Notation »

∫  ▪  ∑  ▪  ∂  ▪  ∇  ▪  ∀  ▪  ⋂  ▪  ≡  ▪  ≳  ▪  ∠  ▪  ∈  ▪  ∅  ▪  ⋀  ▪  ⊕  ▪  ...

\[Integral]  ▪  \[Sum]  ▪  \[Del]  ▪  \[ForAll]  ▪  \[CirclePlus]  ▪  ...

Arrows & Arrow-Like Forms »

→  ▪  ⟶  ▪  ⇒  ▪  ⟹  ▪  ↔  ▪  ↕  ▪  ⇀  ▪  ⇂  ▪  ⇥  ▪  ⇌  ▪  ⊣  ▪  ...

\[RightArrow]  ▪  \[LongRightArrow]  ▪  \[DoubleRightArrow]  ▪  \[LeftRightArrow]  ▪  ...

Textual Forms »

–  ▪  —  ▪  ⋯  ▪  •  ▪    ▪  †  ▪  ✓  ▪  “  ▪  ”  ▪  ¿  ▪  ©  ▪  ...

\[Dash]  ▪  \[LongDash]  ▪  \[Bullet]  ▪  \[Copyright]  ▪  ...

Currency, Units, and Special Notations »

€  ▪  £  ▪  µ  ▪  Å  ▪  ℏ  ▪  ♂  ▪  ♃  ▪  ♪  ▪  ♮  ▪  ♣  ▪  \[WhiteKnight]  ▪  ...

\[Euro]  ▪  \[Sterling]  ▪  \[Micro]  ▪  \[Mars]  ▪  \[Natural]  ▪  ...

User Interfaces & Documentation »

▶  ▪  »  ▪    ▪    ▪    ▪  ↵  ▪  ⌘  ▪  ...

Shapes, Icons, etc. »

■  ▪  ●  ▪    ▪  □  ▪  ◆  ▪  ☺  ▪    ▪    ▪  ...

\[FilledSquare]  ▪  \[EmptySquare]  ▪  \[HappySmiley]  ▪  ...

Non-Printing Characters »

\[ThinSpace]  ▪  \[NonBreakingSpace]  ▪  \[InvisibleComma]  ▪  \[AlignmentMarker]  ▪  ...

International Characters »

é  ▪  ö  ▪  à  ▪  á  ▪  â  ▪  ã  ▪  ä  ▪  å  ▪  ç  ▪  č  ▪  ø  ▪  æ  ▪  ß  ▪  ...

\[EAcute]  ▪  \[ODoubleDot]  ▪  \[CHacek]  ▪  ...

Formal Symbols »

a  ▪  A  ▪  ω  ▪  ...

\[FormalA]  ▪  \[FormalCapitalA]  ▪  \[FormalOmega]  ▪  ...

FullForm — show characters in their full named form

\.nn, \:nnnn, \|nnnnnn — enter forms with hex values corresponding to Unicode code points

\alpha, &Alpha;, etc. — enter TeX, HTML, SGML, etc. forms

ToCharacterCode  ▪  FromCharacterCode  ▪  CharacterRange

StringToByteArray  ▪  ByteArrayToString

Alphabet

+
+

+ Alphabet[] +

+

gives a list of the lowercase letters a through z in the English alphabet.

+
+
+

+ Alphabet[type] +

+

gives the alphabet for the language or class type.

+
+
+

+ Alphabet[type,prop] +

+

gives the alphabet defined by prop for the language or class type .

+
+
— alphabets for different scripts

diff --git a/sources/PNpedia/test.jl b/sources/PNpedia/test.jl new file mode 100644 index 00000000..70138be7 --- /dev/null +++ b/sources/PNpedia/test.jl @@ -0,0 +1,96 @@ +raw""" + +We need to parse Mathematica expressions in Julia, using SymPy's parsing capabilities. +Unfortunately, at the moment, there is a bug in SymPy + + https://github.com/sympy/sympy/issues/27868 + +that prevents it from parsing, e.g., `Sqrt[2]*σ`, which does occur in these expressions. +There is a PR at + + https://github.com/sympy/sympy/pull/27876 + +that claims to fix this, but it has not been merged yet. + +Also, David Trestini has evidently used `FullForm` to output the Mathematica to TXT files, +which translates the Greek letters to their full names — e.g., `ν` becomes `\[Nu]` — which +sympy cannot parse. Specifically, `FullForm` encodes its output as "PrintableASCII". + +There are some packages that may be useful for translating quite generally (in descending +order of how up-to-date I would guess they are): + + * `pygments-mathematica` + * `mathics-scanner` + * `FoxySheep2` + +I'm wondering if it's worthwhile to to write a translator by getting all possible identifier +letters in Python, using + + import sys + [c for c in map(chr, range(sys.maxunicode+1)) if ("_"+c).isidentifier()] + +Then, we can take that into Mathematica, run each through `FullForm`, and create a JSON file +or something that we can read in with Python to replace the identifiers. There are 139,463 +such identifiers — some of which may not output at all with `FullForm`, and some of which +(not many) will be output exactly as input, so don't need to be included. + +Note that Python's spec for identifiers lives at + + https://docs.python.org/3/reference/lexical_analysis.html#identifiers + +A few useful pieces of information I glean from that: + +> Within the ASCII range (U+0001..U+007F), the valid characters for identifiers include the +> uppercase and lowercase letters A through Z, the underscore _ and, except for the first +> character, the digits 0 through 9. + +> All identifiers are converted into the normal form NFKC while parsing; comparison of +> identifiers is based on NFKC. + +I suppose it's possible that some of these things that map to the same character in NFKC +could come up, and be encoded differently in Mathematica. In that case, the output of the +"translate-to-python" function would be able to output different characters that map to the +same character in NFKC, but that's just a problem with how python works, so I don't know +that we can do anything about it. Maybe warn about it? + + +One problem is unicode's combining characters, some of which + +""" + +using Pkg +Pkg.activate(@__DIR__) + +import SymPyPythonCall +import PythonCall + +greek_replacements = ( + raw"\[Nu]" => "ν", + raw"\[Delta]" => "δ", + raw"\[Tau]" => "τ", + raw"\[Chi]" => "χ", + raw"\[Sigma]" => "σ", + raw"\[Kappa]" => "κ", + raw"\[Lambda]" => "λ", +) + +const parse_mathematica = PythonCall.pyimport( + "sympy.parsing.mathematica" => "parse_mathematica" +) + +s = replace( + raw"((1594323*I)/4480)*Sqrt[Pi/4199]*x^(9/2)*\[Nu]*(\[Delta] - 6*\[Delta]*\[Nu] + 10*\[Delta]*\[Nu]^2 - 4*\[Delta]*\[Nu]^3)", + greek_replacements..., +) + +ex = parse_mathematica(s)#, Dict("EllipticE[x]"=>"elliptic_e(x)")) + +const elliptic_e = PythonCall.pyimport( + "sympy.functions.special.elliptic_integrals" => "elliptic_e" +) + +s = raw"(Sqrt[Pi])/(2*EllipticE[m])" +s = raw"((1594323*I)/4480)*Sqrt[Pi/4199]*x^(9/2)*\[Nu]*(\[Delta] - 6*\[Delta]*\[Nu] + 10*\[Delta]*\[Nu]^2 - 4*\[Delta]*\[Nu]^3)" +ex = parse_mathematica(s)#, Dict("EllipticE[x]"=>"elliptic_e(x)")) + +ex.args[2].args[0].args diff --git a/sources/parse-literature/.python-version b/sources/parse-literature/.python-version new file mode 100644 index 00000000..e4fba218 --- /dev/null +++ b/sources/parse-literature/.python-version @@ -0,0 +1 @@ +3.12 diff --git a/sources/parse-literature/README.md b/sources/parse-literature/README.md new file mode 100644 index 00000000..e69de29b diff --git a/sources/parse-literature/main.py b/sources/parse-literature/main.py new file mode 100644 index 00000000..839cdad8 --- /dev/null +++ b/sources/parse-literature/main.py @@ -0,0 +1,6 @@ +def main(): + print("Hello from parse-literature!") + + +if __name__ == "__main__": + main() diff --git a/sources/parse-literature/pyproject.toml b/sources/parse-literature/pyproject.toml new file mode 100644 index 00000000..5beb3793 --- /dev/null +++ b/sources/parse-literature/pyproject.toml @@ -0,0 +1,10 @@ +[project] +name = "parse-literature" +version = 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"https://files.pythonhosted.org/packages/a9/e9/dec1970a136784ebb1cf7f1381ab3cf3d2c4ae6ab0ad0f0d8bcc1e2787c7/xdis-6.1.4-py39-none-any.whl", hash = "sha256:b98fc10371a7ba3036ae5f8958ec8da3ec8c45115da2404e1fb561abeec323ac", size = 224077, upload-time = "2025-05-26T15:26:47.11Z" }, +] diff --git a/src/PostNewtonian.jl b/src/PostNewtonian.jl index d4859708..de5c3d74 100644 --- a/src/PostNewtonian.jl +++ b/src/PostNewtonian.jl @@ -1,214 +1,37 @@ module PostNewtonian -# Always explicitly address functions similar to functions defined in this package, -# which come from these packages: +using Base: @propagate_inbounds +using FastDifferentiation: FastDifferentiation, Node as FDNode +#using InlineExports: @public, @export # See below +using IrrationalConstants: @irrational using MacroTools: MacroTools -using FastDifferentiation: FastDifferentiation -using RuntimeGeneratedFunctions: RuntimeGeneratedFunctions - -# Otherwise, we just explicitly import specific functions: -using DataInterpolations: CubicSpline -using InteractiveUtils: methodswith -using LinearAlgebra: mul! -using Random: AbstractRNG, default_rng -using Quaternionic: QuatVec, Rotor, abs2vec, components, normalize, ⋅, × -using SphericalFunctions: D!, Diterator, Dprep, Yiterator -using OrdinaryDiffEqVerner: Vern9 -using SciMLBase: - ODEFunction, - ODEProblem, - solve, - remake, - terminate!, - CallbackSet, - DiscreteCallback, - VectorContinuousCallback, - ODESolution, - parameterless_type, - FullSpecialize, - AbstractDiffEqInterpolation, - build_solution, - get_du -using SciMLBase.ReturnCode: ReturnCode -using SymbolicIndexingInterface: SymbolCache -using RecursiveArrayTools: DiffEqArray -using StaticArrays: SVector, MVector +using Quaternionic: + Quaternionic, QuatVec, Rotor, 𝐢, 𝐣, 𝐤, abs2vec, absvec, components, normalize, ⋅, × +using StaticArrays: MVector, SVector using TestItems: @testitem -# See the "Code structure" section of the documentation for a description of the simple -# hierarchy into which this code is organized. The different levels of that hierarchy are -# reflected cleanly in the files `include`d below. - -# It's more common in PN to use `ln` — which I also prefer, as `log` seems ambiguous. -const ln = log - -include("utilities.jl") -export termination_forwards, - termination_backwards, dtmin_terminator, decreasing_v_terminator, nonfinite_terminator -using .MathConstants - -include("pn_systems.jl") -export PNSystem, pn_order, BBH, BHBH, BHNS, NSNS, BNS, FDPNSystem, fd_pnsystem - -include("pn_expansion.jl") -export PNExpansion, PNTerm, PNExpansionParameter - -include("fundamental_variables.jl") -using .FundamentalVariables -#export M₁, M₂, χ⃗₁, χ⃗₂, R, v, Φ, Λ₁, Λ₂ # Avoid clashes: don't export - -include("derived_variables.jl") -using .DerivedVariables -export total_mass, # M, # Avoid clashes: don't export nicer names for important variables - reduced_mass, # μ, - reduced_mass_ratio, # ν, - mass_difference_ratio, # δ, - mass_ratio, # q, - chirp_mass, # ℳ, - # X1, X₁, - # X2, X₂, - n_hat, - n̂, - lambda_hat, - λ̂, - ell_hat, - ℓ̂, - Omega, - Ω, - S⃗₁, - S⃗₂, - S⃗, - Σ⃗, - χ⃗, - χ⃗ₛ, - χ⃗ₐ, - chi_perp, - χₚₑᵣₚ, - chi_eff, - χₑ, - chi_p, - χₚ, - S⃗₀⁺, - S⃗₀⁻, - S₀⁺ₙ, - S₀⁻ₙ, - S₀⁺λ, - S₀⁻λ, - S₀⁺ₗ, - S₀⁻ₗ, - χ₁², - χ₂², - χ₁, - χ₂, - χ₁₂, - χ₁ₗ, - χ₂ₗ, - χₛₗ, - χₐₗ, - Sₙ, - Σₙ, - Sλ, - Σλ, - Sₗ, - Σₗ, - sₗ, - σₗ, - S₁ₙ, - S₁λ, - S₁ₗ, - S₂ₙ, - S₂λ, - S₂ₗ, - rₕ₁, - rₕ₂, - Ωₕ₁, - Ωₕ₂, - sin²θ₁, - sin²θ₂, - ϕ̇̂₁, - ϕ̇̂₂, - Î₀₁, - Î₀₂, - κ₁, - κ₂, - κ₊, - κ₋, - λ₁, - λ₂, - λ₊, - λ₋, - Λ̃, - Lambda_tilde - -include("pn_expressions.jl") -export gw_energy_flux, - 𝓕, - tidal_heating, - binding_energy, - 𝓔, - binding_energy_deriv, - 𝓔′, - Omega_p, - Ω⃗ₚ, - Omega_chi1, - Ω⃗ᵪ₁, - Omega_chi2, - Ω⃗ᵪ₂, - #𝛡, aₗ, Ω⃗ᵪ # Too obscure to bother with - γₚₙ, - inverse_separation, - γₚₙ′, - inverse_separation_deriv, - γₚₙ⁻¹, - inverse_separation_inverse, - separation, # r, - separation_deriv, # r′, - separation_dot, # ṙ, - separation_inverse, # r⁻¹, - mode_weights!, - h! - -include("dynamics.jl") -export up_down_instability, - estimated_time_to_merger, fISCO, ΩISCO, uniform_in_phase, orbital_evolution - -include("waveforms.jl") -export coorbital_waveform, - inertial_waveform, - coorbital_waveform_computation_storage, - inertial_waveform_computation_storage, - coorbital_waveform!, - inertial_waveform! - -include("compatibility_layers.jl") -export GWFrames - -include("assorted_binaries/examples.jl") -export superkick, hangup_kick -include("assorted_binaries/random.jl") -# Base.rand is the only function in that file, hence no need for exports - -include("precompilation.jl") - -include("predefinitions_Symbolics.jl") - -if !isdefined(Base, :get_extension) - using Requires -end - -@static if !isdefined(Base, :get_extension) - # COV_EXCL_START - - function __init__() - @require Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7" include( - "../ext/PostNewtonianSymbolicsExt.jl" - ) - @require ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210" include( - "../ext/PostNewtonianForwardDiffExt.jl" - ) - end - - # COV_EXCL_STOP -end +# While I wait for https://github.com/dalum/InlineExports.jl/pull/2 to be merged, we do the +# following rather than import from the package itself. Once that is merged, we can add the +# package as a dependency, uncomment the line above, remove this block, and remove the +# following file. +include("core/utilities/InlineExports.jl") +using .InlineExports: @public, @export + +# These are definitions / aliases that are common in PN literature and/or used throughout +# this package. +@public const 𝒾 = im # Type this as `\scri` +@public const γₑ = Base.MathConstants.γ # Distinguish Euler's constant from `γₚₙ = M/r` +public ζ3 # Defined and documented in `core/utilities/misc.jl` + +# We will use these types to ensure that precision is preserved in PN expressions. +@public const ExactReal = Union{Integer,Rational,AbstractIrrational} +@public const ExactNumber = Union{ExactReal,Complex{<:ExactReal}} +@public const ExactIntegerBased = Union{Integer,Rational} + +include("pn_systems/pn_systems.jl") +include("core/core.jl") +include("literature/literature.jl") +include("pn_expressions/pn_expressions.jl") +include("interface/interface.jl") end # module PostNewtonian diff --git a/src/compatibility_layers.jl b/src/compatibility_layers.jl deleted file mode 100644 index dccb1c83..00000000 --- a/src/compatibility_layers.jl +++ /dev/null @@ -1 +0,0 @@ -include("compatibility_layers/gwframes.jl") diff --git a/src/core/PNBase.jl b/src/core/PNBase.jl new file mode 100644 index 00000000..9e5872c6 --- /dev/null +++ b/src/core/PNBase.jl @@ -0,0 +1,173 @@ +public PNBase + +# Documented below so that we can list the functions in the module automatically. +baremodule PNBase + +# We want to be able to use the Base operators like `+`, `-`, `*`, `/`, and `^`, but we're +# already redefining those operators here, so we need alternative characters for them. +# Julia defines operators that can be used with equivalent precedence and as infix operators +# in this file: https://github.com/JuliaLang/julia/blob/master/src/julia-parser.scm. +# Circled versions of each will work, except for `^`, for which we use an arrow. They can +# be typed as `\oplus`, `\ominus`, `\circledast`, `\oslash`, and `\uparrow`. +using Base: Base, + as ⊕, - as ⊖, * as ⊛, / as ⊘, ^ as ↑ + +using PostNewtonian: constant_convert, PNSystem, ExactNumber, ExactIntegerBased +using PostNewtonian.InlineExports: @export +using Base: @inline + +@export @inline ln(pnsystem::PNSystem, x) = Base.log(constant_convert(pnsystem, x)) +@inline ln(x::AbstractFloat) = Base.log(x) + +@export @inline √(pnsystem::PNSystem, x) = Base.sqrt(constant_convert(pnsystem, x)) +@inline √(x::AbstractFloat) = Base.sqrt(x) + +@export @inline (+)(pnsystem::PNSystem, x, y) = ⊕(constant_convert(pnsystem, x), y) +@inline (+)(pnsystem::PNSystem, x) = constant_convert(pnsystem, x) +# @inline function (+)(pnsystem::PNSystem, w, x, y, z...) +# return ⊕(constant_convert(pnsystem, w), x, y, z...) +# end +@inline (+)(x::AbstractFloat, y::AbstractFloat) = x ⊕ y +@inline (+)(x::AbstractFloat, y::ExactNumber) = x ⊕ y +@inline (+)(x::ExactNumber, y::AbstractFloat) = x ⊕ y +@inline (+)(x::ExactIntegerBased, y::ExactIntegerBased) = x ⊕ y +@inline (+)(x::Number) = x +(+)(x, y, z, args...) = Base.afoldl(+, (x + y) + z, args...) + +@export @inline (-)(pnsystem::PNSystem, x, y) = ⊖(constant_convert(pnsystem, x), y) +@inline (-)(x::AbstractFloat, y::AbstractFloat) = x ⊖ y +@inline (-)(x::AbstractFloat, y::ExactNumber) = x ⊖ y +@inline (-)(x::ExactNumber, y::AbstractFloat) = x ⊖ y +@inline (-)(x::ExactIntegerBased, y::ExactIntegerBased) = x ⊖ y +@inline (-)(x::Number) = ⊖(x) +@inline (-)(pnsystem::PNSystem, x) = ⊖(constant_convert(pnsystem, x)) + +@export @inline (*)(pnsystem::PNSystem, x, y) = ⊛(constant_convert(pnsystem, x), y) +@inline (*)(pnsystem::PNSystem, x) = constant_convert(pnsystem, x) +# @inline function (*)(pnsystem::PNSystem, w, x, y, z...) +# return ⊛(constant_convert(pnsystem, w), x, y, z...) +# end +@inline (*)(x::AbstractFloat, y::AbstractFloat) = x ⊛ y +@inline (*)(x::AbstractFloat, y::ExactNumber) = x ⊛ y +@inline (*)(x::ExactNumber, y::AbstractFloat) = x ⊛ y +@inline (*)(x::ExactIntegerBased, y::ExactIntegerBased) = x ⊛ y +(*)(x, y, z, args...) = Base.afoldl(*, (x * y) * z, args...) + +@export @inline (/)(pnsystem::PNSystem, x, y) = ⊘(constant_convert(pnsystem, x), y) +@inline (/)(x::AbstractFloat, y::AbstractFloat) = x ⊘ y +@inline (/)(x::AbstractFloat, y::ExactNumber) = x ⊘ y +@inline (/)(x::ExactNumber, y::AbstractFloat) = x ⊘ y + +@export @inline (^)(pnsystem::PNSystem, x, n) = ↑(constant_convert(pnsystem, x), n) +@inline (^)(x::AbstractFloat, n::ExactNumber) = x ↑ n +@inline (^)(x::ExactNumber, n::AbstractFloat) = x ↑ n +@inline (^)(x::AbstractFloat, n::AbstractFloat) = x ↑ n + +# We can actually use the original definition of `//` for most purposes; we define it +# both ways here for simplicity. +@export @inline (//)(pnsystem::PNSystem, x, y) = Base.://(x, y) +@inline (//)(x, y) = Base.://(x, y) + +end # baremodule PNBase + +# COV_EXCL_START (Covered, but missed due to const-folding) +const pnbase_functions = filter(s -> isa(getfield(PNBase, s), Function), names(PNBase)) +# COV_EXCL_END + +@doc """ + PNBase + +This module provides many of the same essential functions available in Julia's `Base` +module, but restricted to operations we expect to be used in post-Newtonian contexts, so +that we can ensure that the resulting expressions are valid within that framework. This is +intended to be used inside `@pn_expression` modules. + +It is intentionally very restrictive, so that it only includes the basic arithmetic +operations that are used in post-Newtonian expressions, and even then only in modified forms +that take a `PNSystem` as the first argument. The defined operations are + + $(pnbase_functions) + +This module is not intended to be used directly, but is imported by the +[`@pn_expression`](@ref) macro, and its methods are called by [`@pn_expansion`](@ref) to +ensure that the arithmetic operations preserve the number type of the input `PNSystem`. +""" +PNBase + +@testitem "PNBase" begin + baremodule Mod + using PostNewtonian.PNBase + end + + using PostNewtonian: pnbase_functions + + const ln = log + + for NT ∈ (Float16, Float64, BigFloat) + pnsystem = BHNS(randn(NT, 15)) + Z = (1, 2, 3, 17, 31, 3//13, 47//59) + z = (Z..., ℯ, π) + + for x ∈ z + @test eval(:(Mod.:+))(pnsystem, x) isa NT + @test eval(:(Mod.:+))(pnsystem, x) == NT(x) + @test eval(:(Mod.:+))(x) == x + + @test eval(:(Mod.:-))(pnsystem, x) isa NT + @test eval(:(Mod.:-))(pnsystem, x) == -NT(x) + @test eval(:(Mod.:-))(x) == -x + + @test eval(:(Mod.:*))(pnsystem, x) isa NT + @test eval(:(Mod.:*))(pnsystem, x) == NT(x) + end + + for f ∈ (:+, :*) + op = f≡:+ ? sum : prod + for w ∈ Z, x ∈ Z, y ∈ Z + @test eval(:(Mod.$f))(pnsystem, w, x, y) isa NT + @test eval(:(Mod.$f))(pnsystem, w, x, y) == op(NT, (w, x, y)) + @test eval(:(Mod.$f))(w, x, y) ≡ op((w, x, y)) + for v ∈ Z + @test eval(:(Mod.$f))(pnsystem, v, w, x, y) isa NT + @test eval(:(Mod.$f))(pnsystem, v, w, x, y) == op(NT, (v, w, x, y)) + @test eval(:(Mod.$f))(v, w, x, y) ≡ op((v, w, x, y)) + end + end + end + + for f ∈ (:+, :-, :*, :/, :^, :ln, :√) + @test f ∈ pnbase_functions + end + for f ∈ (:+, :-, :*, :/, :^) + for x ∈ z, y ∈ z + @test eval(:(Mod.$f))(pnsystem, x, y) isa NT + @test eval(:(Mod.$f))(pnsystem, x, y) == eval(:($f))(NT(x), NT(y)) + @test eval(:(Mod.$f))(x, NT(y)) isa NT + @test eval(:(Mod.$f))(x, NT(y)) ≈ eval(:($f))(NT(x), NT(y)) + @test eval(:(Mod.$f))(NT(x), y) isa NT + @test eval(:(Mod.$f))(NT(x), y) ≈ eval(:($f))(NT(x), NT(y)) + @test eval(:(Mod.$f))(NT(x), NT(y)) isa NT + @test eval(:(Mod.$f))(NT(x), NT(y)) == eval(:($f))(NT(x), NT(y)) + end + end + for f ∈ (:+, :-, :*, ://) + for x ∈ Z, y ∈ Z + @test typeof(eval(:(Mod.$f))(x, y)) ≡ typeof(eval(:($f))(x, y)) + @test eval(:(Mod.$f))(x, y) == eval(:($f))(x, y) + end + end + for x ∈ Z, y ∈ Z + @test typeof(eval(:(Mod.://))(pnsystem, x, y)) ≡ typeof(x // y) + @test eval(:(Mod.://))(pnsystem, x, y) == x // y + end + for f ∈ (:ln, :√) + for x ∈ z + @test eval(:(Mod.$f))(pnsystem, x) isa NT + @test eval(:(Mod.$f))(pnsystem, x) == eval(:($f))(NT(x)) + @test eval(:(Mod.$f))(NT(x)) == eval(:($f))(NT(x)) + end + for x ∈ Z + @test_throws MethodError eval(:(Mod.$f))((x)) + end + end + end +end diff --git a/src/pn_expansion.jl b/src/core/PNExpansion.jl similarity index 52% rename from src/pn_expansion.jl rename to src/core/PNExpansion.jl index 070186da..44bf561d 100644 --- a/src/pn_expansion.jl +++ b/src/core/PNExpansion.jl @@ -1,3 +1,19 @@ +# We enclose all of this in a `baremodule` so that we can isolate Base operations, and use +# PNBase operations by default. +baremodule PNExpansions + +# See explanation in `PNBase.jl` for why we use these operators. +using Base: Base, NTuple, ntuple, Val, Vector, @doc, @raw_str, @assert, @inbounds, @__dot__, + (:), eltype, promote_type, isbitstype, min, max, one, zero, + ==, ≤, <, >, ÷, + as ⊕, - as ⊖, * as ⊛, / as ⊘, ^ as ↑ + +using PostNewtonian: PostNewtonian +using PostNewtonian.PNBase +using PostNewtonian.PNTerms +using PostNewtonian.InlineExports: @export, @public +using StaticArrays: MVector, SVector +import FastDifferentiation + # This a utility that allow us to interoperate with FastDifferentiation.Node and other # Number types. function _efficient_vector(::Val{N}, ::Val{T}) where {N,T} @@ -39,67 +55,61 @@ The `N` parameter is not related to the PN order; it is just used by Julia to kn elements are currently in the coefficients, but is required to be 1 ≤ N ≤ NMax. """ -struct PNExpansion{N,T,NMax} +@public struct PNExpansion{N,T,NMax} coeffs::NTuple{N,T} function PNExpansion{N,T,NMax}(coeffs) where {N,T,NMax} if N < 1 - throw(ArgumentError("`N=$N` must be >0.")) + throw(ArgumentError("`N=$N` must be greater than 0.")) # COV_EXCL_LINE end if N > NMax - throw(ArgumentError("`N=$N` must be <`NMax=$NMax`.")) + throw(ArgumentError("`N=$N` must be less than `NMax=$NMax`.")) # COV_EXCL_LINE end return new{N,T,NMax}(coeffs) end function PNExpansion(coeffs::NTuple{N,T}, NMax) where {N,T} if N < 1 - throw(ArgumentError("`N=$N` must be >0.")) + throw(ArgumentError("`N=$N` must be greater than 0.")) end if N > NMax - throw(ArgumentError("`N=$N` must be <`NMax=$NMax`.")) + throw(ArgumentError("`N=$N` must be less than `NMax=$NMax`.")) # COV_EXCL_LINE end return new{N,T,NMax}(coeffs) end end -pn_order(::PNExpansion{N,T,NMax}) where {N,T,NMax} = (NMax - 1)//2 +Base.Tuple(pn::PNExpansion) = pn.coeffs +SVector(pn::PNExpansion) = SVector(pn.coeffs) + +PostNewtonian.pn_order(::PNExpansion{N,T,NMax}) where {N,T,NMax} = (NMax ⊖ 1)//2 Base.getindex(pn::PNExpansion, i::Int) = pn.coeffs[i] -Base.length(pn::PNExpansion) = length(pn.coeffs) -Base.eltype(pn::PNExpansion) = eltype(pn.coeffs) +Base.length(pn::PNExpansion) = Base.length(pn.coeffs) +Base.eltype(pn::PNExpansion) = Base.eltype(pn.coeffs) function Base.sum(pn_expansion::PNExpansion{N,T,NMax}) where {N,T,NMax} - return sum(pn_expansion[i] for i ∈ 1:N, init ∈ zero(T)) + return Base.sum(pn_expansion.coeffs; init=zero(T)) end -function Base.:+(pn::PNExpansion{N,T1,NMax}, x::T2) where {N,T1,NMax,T2<:Number} +function PNBase.:+(pn::PNExpansion{N,T1,NMax}, x::T2) where {N,T1,NMax,T2<:Number} T3 = promote_type(T1, T2) return PNExpansion(ntuple(i -> i == 1 ? pn[1] + x : T3(pn[i]), Val(N)), NMax) end -Base.:+(x::T, pn::PNExpansion) where {T<:Number} = pn + x -function Base.:-(pn::PNExpansion{N,T,NMax}) where {N,T,NMax} - return PNExpansion{N,T,NMax}((-).(pn.coeffs)) -end +PNBase.:+(x::T, pn::PNExpansion) where {T<:Number} = PNBase.:+(pn, x) -function Base.:*(pn::PNExpansion{N,T1,NMax}, x::T2) where {N,T1,NMax,T2<:Number} - T3 = promote_type(T1, T2) - return PNExpansion{N,T3,NMax}(@. T3(pn.coeffs * x)) -end -Base.:*(x::T, pn::PNExpansion) where {T<:Number} = pn * x - -function Base.:+( +function PNBase.:+( pn1::PNExpansion{N1,T1,NMax1}, pn2::PNExpansion{N2,T2,NMax2} ) where {N1,N2,T1,T2,NMax1,NMax2} throw( ArgumentError( - "`PNExpansion` addition is only defined for objects of the same PN order." * + "`PNExpansion` addition is only defined for objects of the same PN order." ⊛ "\nGot NMax1=$(NMax1) and NMax2=$(NMax2).", ), ) end -function Base.:+( +function PNBase.:+( pn1::PNExpansion{N1,T1,NMax}, pn2::PNExpansion{N2,T2,NMax} ) where {N1,N2,T1,T2,NMax} if N1 > N2 @@ -114,161 +124,27 @@ function sum_term( ) where {N1,N2,T1,T2,NMax} T3 = promote_type(T1, T2) if i ≤ N1 - return T3(pn1.coeffs[i] + pn2.coeffs[i]) + return T3(pn1.coeffs[i] ⊕ pn2.coeffs[i]) else return T3(pn2.coeffs[i]) end end -function Base.:*( - pn1::PNExpansion{N1,T1,NMax1}, pn2::PNExpansion{N2,T2,NMax2} -) where {N1,N2,T1,T2,NMax1,NMax2} - throw( - ArgumentError( - "`PNExpansion` multiplication is only defined for objects of the same PN order." * - "\nGot NMax1=$(NMax1) and NMax2=$(NMax2).", - ), - ) -end - -function Base.:*( - pn1::PNExpansion{N1,T1,NMax}, pn2::PNExpansion{N2,T2,NMax} -) where {N1,N2,T1,T2,NMax} - if N1 > N2 - return pn2 * pn1 - else - N3 = min(N1 + N2 - 1, NMax) - PNExpansion(ntuple(i -> product_term(i, pn1, pn2), Val(N3)), NMax) - end -end - -function product_term( - i, pn1::PNExpansion{N1,T1,NMax}, pn2::PNExpansion{N2,T2,NMax} -) where {N1,N2,T1,T2,NMax} - T3 = promote_type(T1, T2) - return sum( - pn1.coeffs[j] * pn2.coeffs[i - j + 1] for - j ∈ max(1, i - N2 + 1):min(i, N1), init ∈ zero(T3) - ) -end - -Base.:/(p::PNExpansion, x::Number) = p * (1 / x) - -function FastDifferentiation.derivative( - pn_expansion::PNExpansion{N,T,NMax}, fd_node::FastDifferentiation.Node -) where {N,T,NMax} - return PNExpansion( - ntuple(i -> FastDifferentiation.derivative(pn_expansion[i], fd_node), Val(N)), NMax - ) -end - -Base.Tuple(pn::PNExpansion) = pn.coeffs -SVector(pn::PNExpansion) = SVector(pn.coeffs) - -""" - PNTerm{T,PNOrder,c⁻¹Exponent} - -This object represents a single term in a PNExpansion. It has a single field: `coeff`, -which is the coefficient of the term. The type parameter `T` is the type of the -coefficient. The type parameter `PNOrder` is a half-integer (just as in -[`PNSystem`](@ref)s) representing the PN order of the expansion. And the type parameter -`c⁻¹Exponent` is an integer representing the exponent of the PN expansion parameter ``1/c``. - -`PNTerm`s can be multiplied and divided by scalars and exponentiated by integers, to produce -another `PNTerm`. They can also be added to other `PNTerm`s to produce a `PNExpansion`. - -A simple way to define a `PNTerm` or a `PNExpansion` is to define the PN expansion parameter -```julia -c = PNExpansionParameter(pnsystem) -``` -and use that naturally in formulas, as in -```julia -e = 1 + (v/c)^2 * (-ν/12 - 3//4) + (v/c)^4 * (-ν^2/24 + 19ν/8 - 27//8) -``` -Any exponent higher than the desired `PNOrder` will be automatically set to zero. - -Useful facts: - - `v` has order `1/c` - - `x` has order `1/c^2` - - `γ` has order `1/c^2` - - `1/r` has order `1/c^2` - -""" -struct PNTerm{T,PNOrder,c⁻¹Exponent} - coeff::T - - function PNTerm{T,PNOrder,c⁻¹Exponent}(coeff) where {T,PNOrder,c⁻¹Exponent} - if c⁻¹Exponent > 2PNOrder - coeff = zero(coeff) - end - return new{T,PNOrder,c⁻¹Exponent}(coeff) - end - function PNTerm{T,PNOrder}(c⁻¹exp::Int, coeff) where {T,PNOrder} - if c⁻¹exp > 2PNOrder - coeff = zero(coeff) - end - return new{T,PNOrder,c⁻¹exp}(coeff) - end -end - -Base.length(pn::PNTerm) = 1 -Base.eltype(pn::PNTerm{T}) where {T} = T -c⁻¹exp(pn::PNTerm{T,PNOrder,c⁻¹Exponent}) where {T,PNOrder,c⁻¹Exponent} = c⁻¹Exponent - -function Base.sum(pn::PNTerm) - return pn.coeff -end - -function Base.:+(pn::PNTerm) - return pn -end - -function Base.inv(term::PNTerm{T,PNOrder,c⁻¹Exponent}) where {T,PNOrder,c⁻¹Exponent} - return PNTerm{T,PNOrder}(-c⁻¹exp(term), inv(term.coeff)) -end - -function Base.:^(term::PNTerm{T,PNOrder,c⁻¹Exponent}, n::Int) where {T,PNOrder,c⁻¹Exponent} - coeff = term.coeff^n - return PNTerm{typeof(coeff),PNOrder}(c⁻¹exp(term) * n, coeff) -end - -function Base.:*( - x::Number, term::PNTerm{T,PNOrder,c⁻¹Exponent} -) where {T,PNOrder,c⁻¹Exponent} - coeff = x * term.coeff - return PNTerm{typeof(coeff),PNOrder,c⁻¹Exponent}(coeff) -end -Base.:*(term::PNTerm, x::Number) = x * term - -function Base.:/( - term::PNTerm{T,PNOrder,c⁻¹Exponent}, x::Number -) where {T,PNOrder,c⁻¹Exponent} - coeff = term.coeff / x - return PNTerm{typeof(coeff),PNOrder,c⁻¹Exponent}(coeff) -end - -function Base.:/( - x::Number, term::PNTerm{T,PNOrder,c⁻¹Exponent} -) where {T,PNOrder,c⁻¹Exponent} - coeff = x / term.coeff - return PNTerm{typeof(coeff),PNOrder}(-c⁻¹exp(term), coeff) -end - -function Base.:+( +function PNBase.:+( x::T1, term::PNTerm{T2,PNOrder,c⁻¹Exponent} ) where {T1<:Number,T2,PNOrder,c⁻¹Exponent} if c⁻¹exp(term) < 0 throw( ArgumentError( - "Cannot add a `PNTerm` with a negative exponent: " * - "c⁻¹exp(term)=$(c⁻¹exp(term))." * + "Cannot add a `PNTerm` with a negative exponent: " ⊛ + "c⁻¹exp(term)=$(c⁻¹exp(term))." ⊛ "\nResult will be a `PNExpansion`, which cannot store positive exponents.", ), ) end T = promote_type(T1, T2) - N₀ = c⁻¹exp(term) + 1 - NMax = Int(2PNOrder + 1) + N₀ = c⁻¹exp(term) ⊕ 1 + NMax = Int(2 ⊛ PNOrder ⊕ 1) N = min(N₀, NMax) coeffs = _efficient_vector(Val(N), Val(T)) coeffs .= zero(T) @@ -278,36 +154,17 @@ function Base.:+( end return PNExpansion{N,T,NMax}(Tuple(coeffs)) end -Base.:+(term::PNTerm, x::Number) = x + term - -function Base.:-(term::PNTerm{T,PNOrder,c⁻¹Exponent}) where {T,PNOrder,c⁻¹Exponent} - return PNTerm{T,PNOrder,c⁻¹Exponent}(-term.coeff) -end - -function Base.:*( - term1::PNTerm{T1,PNOrder,c⁻¹E1}, term2::PNTerm{T2,PNOrder,c⁻¹E2} -) where {T1,T2,PNOrder,c⁻¹E1,c⁻¹E2} - c⁻¹Exponent = c⁻¹exp(term1) + c⁻¹exp(term2) - coeff = term1.coeff * term2.coeff - return PNTerm{typeof(coeff),PNOrder,c⁻¹Exponent}(coeff) -end -function Base.:/( - term1::PNTerm{T1,PNOrder,c⁻¹E1}, term2::PNTerm{T2,PNOrder,c⁻¹E2} -) where {T1,T2,PNOrder,c⁻¹E1,c⁻¹E2} - c⁻¹Exponent = c⁻¹E1 - c⁻¹E2 - coeff = term1.coeff / term2.coeff - return PNTerm{typeof(coeff),PNOrder,c⁻¹Exponent}(coeff) -end +PNBase.:+(term::PNTerm, x::Number) = PNBase.:+(x, term) -function Base.:+( +function PNBase.:+( term1::PNTerm{T1,PNOrder,c⁻¹E1}, term2::PNTerm{T2,PNOrder,c⁻¹E2} ) where {T1,T2,PNOrder,c⁻¹E1,c⁻¹E2} if c⁻¹exp(term1) < 0 throw( ArgumentError( - "Cannot add a `PNTerm` with a negative exponent: " * - "c⁻¹exp(term1)=$(c⁻¹exp(term1))." * + "Cannot add a `PNTerm` with a negative exponent: " ⊛ + "c⁻¹exp(term1)=$(c⁻¹exp(term1))." ⊛ "\nResult will be a `PNExpansion`, which cannot store positive exponents.", ), ) @@ -315,16 +172,16 @@ function Base.:+( if c⁻¹exp(term2) < 0 throw( ArgumentError( - "Cannot add a `PNTerm` with a negative exponent: " * - "c⁻¹exp(term2)=$(c⁻¹exp(term2))." * + "Cannot add a `PNTerm` with a negative exponent: " ⊛ + "c⁻¹exp(term2)=$(c⁻¹exp(term2))." ⊛ "\nResult will be a `PNExpansion`, which cannot store positive exponents.", ), ) end T = promote_type(T1, T2) - N1₀ = c⁻¹exp(term1) + 1 - N2₀ = c⁻¹exp(term2) + 1 - NMax = Int(2PNOrder + 1) + N1₀ = c⁻¹exp(term1) ⊕ 1 + N2₀ = c⁻¹exp(term2) ⊕ 1 + NMax = Int(2 ⊛ PNOrder ⊕ 1) N = min(max(N1₀, N2₀), NMax) coeffs = _efficient_vector(Val(N), Val(T)) coeffs .= zero(T) @@ -337,22 +194,20 @@ function Base.:+( return PNExpansion{N,T,NMax}(Tuple(coeffs)) end -Base.:-(term1::PNTerm, term2::PNTerm) = term1 + (-term2) - -function Base.:+( +function PNBase.:+( term::PNTerm{T1,PNOrder,c⁻¹E1}, expansion::PNExpansion{N2,T2,NMax2} ) where {T1,PNOrder,c⁻¹E1,N2,T2,NMax2} if c⁻¹exp(term) < 0 throw( ArgumentError( - "Cannot add a `PNTerm` with a negative exponent: " * - "c⁻¹exp(term)=$(c⁻¹exp(term))." * + "Cannot add a `PNTerm` with a negative exponent: " ⊛ + "c⁻¹exp(term)=$(c⁻¹exp(term))." ⊛ "\nResult will be a `PNExpansion`, which cannot store positive exponents.", ), ) end - N1 = c⁻¹exp(term) + 1 - NMax1 = Int(2PNOrder + 1) + N1 = c⁻¹exp(term) ⊕ 1 + NMax1 = Int(2 ⊛ PNOrder ⊕ 1) NMax = min(NMax1, NMax2) N = min(max(N1, N2), NMax) T = promote_type(T1, T2) @@ -368,31 +223,76 @@ function Base.:+( end return PNExpansion{N,T,NMax}(Tuple(coeffs)) end -Base.:+(expansion::PNExpansion, term::PNTerm) = term + expansion -Base.:-(term::PNTerm, x::Number) = term + (-x) -Base.:-(x::Number, term::PNTerm) = x + (-term) -Base.:-(term::PNTerm, expansion::PNExpansion) = term + (-expansion) -Base.:-(expansion::PNExpansion, term::PNTerm) = expansion + (-term) -Base.:-(x::Number, expansion::PNExpansion) = x + (-expansion) -Base.:-(expansion::PNExpansion, x::Number) = expansion + (-x) +PNBase.:+(expansion::PNExpansion, term::PNTerm) = PNBase.:+(term, expansion) + +PNBase.:-(term1::PNTerm, term2::PNTerm) = PNBase.:+(term1, -term2) +PNBase.:-(term::PNTerm, x::Number) = PNBase.:+(term, -x) +PNBase.:-(x::Number, term::PNTerm) = PNBase.:+(x, -term) +PNBase.:-(term::PNTerm, expansion::PNExpansion) = PNBase.:+(term, -expansion) +PNBase.:-(expansion::PNExpansion, term::PNTerm) = PNBase.:+(expansion, -term) +PNBase.:-(x::Number, expansion::PNExpansion) = PNBase.:+(x, -expansion) +PNBase.:-(expansion::PNExpansion, x::Number) = PNBase.:+(expansion, -x) + +function PNBase.:-(pn::PNExpansion{N,T,NMax}) where {N,T,NMax} + return PNExpansion{N,T,NMax}((-).(pn.coeffs)) +end + +function PNBase.:*(pn::PNExpansion{N,T1,NMax}, x::T2) where {N,T1,NMax,T2<:Number} + T3 = promote_type(T1, T2) + return PNExpansion{N,T3,NMax}(@. T3(pn.coeffs * x)) +end + +PNBase.:*(x::T, pn::PNExpansion) where {T<:Number} = PNBase.:*(pn, x) + +function PNBase.:*( + pn1::PNExpansion{N1,T1,NMax1}, pn2::PNExpansion{N2,T2,NMax2} +) where {N1,N2,T1,T2,NMax1,NMax2} + throw( + ArgumentError( + "`PNExpansion` multiplication is only defined for objects of the same PN order." ⊛ + "\nGot NMax1=$(NMax1) and NMax2=$(NMax2).", + ), + ) +end + +function PNBase.:*( + pn1::PNExpansion{N1,T1,NMax}, pn2::PNExpansion{N2,T2,NMax} +) where {N1,N2,T1,T2,NMax} + if N1 > N2 + return PNBase.:*(pn2, pn1) + else + N3 = min(N1 + N2 - 1, NMax) + PNExpansion(ntuple(i -> product_term(i, pn1, pn2), Val(N3)), NMax) + end +end + +function product_term( + i, pn1::PNExpansion{N1,T1,NMax}, pn2::PNExpansion{N2,T2,NMax} +) where {N1,N2,T1,T2,NMax} + T3 = promote_type(T1, T2) + return Base.sum( + pn1.coeffs[j] ⊛ pn2.coeffs[i - j + 1] for j ∈ max(1, i - N2 + 1):min(i, N1); + init=zero(T3), + ) +end -function Base.:*( +function PNBase.:*( expansion::PNExpansion{N1,T1,NMax1}, term::PNTerm{T2,PNOrder,c⁻¹E2} ) where {N1,T1,NMax1,T2,PNOrder,c⁻¹E2} ΔN = c⁻¹exp(term) # Note that ΔN may be negative! - NMax2 = Int(2PNOrder + 1) + NMax2 = Int(2 ⊛ PNOrder ⊕ 1) NMax = min(NMax1, NMax2) - N = min(max(N1, N1 + ΔN), NMax) + N = min(max(N1, N1 ⊕ ΔN), NMax) # Check that no terms from expansion will be lost to negative PN orders - @inbounds for i ∈ 1:min(max(0, -ΔN), N1) + @inbounds for i ∈ 1:min(max(0, ⊖(ΔN)), N1) if !iszero(expansion[i]) throw( ArgumentError( - "Cannot multiply `PNExpansion` by `PNTerm` with negative exponent: " * - "c⁻¹exp(term)=$(c⁻¹exp(term))." * - "\nResult will be a `PNExpansion`, which cannot store positive exponents.", + "Cannot multiply `PNExpansion` by `PNTerm` with negative exponent: " ⊛ + "c⁻¹exp(term)=$(c⁻¹exp(term)).\nThe result will be a `PNExpansion`, " ⊛ + "which cannot store positive exponents.", ), ) end @@ -401,24 +301,88 @@ function Base.:*( T = promote_type(T1, T2) coeffs = _efficient_vector(Val(N), Val(T)) coeffs .= zero(T) - @inbounds for i ∈ max(1, 1 - ΔN):min(N1, N - ΔN) - coeffs[i + ΔN] = expansion[i] * term.coeff + @inbounds for i ∈ max(1, 1 ⊖ ΔN):min(N1, N ⊖ ΔN) + coeffs[i ⊕ ΔN] = expansion[i] ⊛ term.coeff end return PNExpansion{N,T,NMax}(Tuple(coeffs)) end -Base.:*(term::PNTerm, expansion::PNExpansion) = expansion * term + +PNBase.:*(term::PNTerm, expansion::PNExpansion) = PNBase.:*(expansion, term) # (a, b, c, d, e, f, g) * (c⁻¹^2) = (0, 0, a, b, c, d, e) -Base.:/(expansion::PNExpansion, term::PNTerm) = expansion * inv(term) +PNBase.:/(expansion::PNExpansion, x) = PNBase.:*(expansion, Base.inv(x)) -""" - PNExpansionParameter(pnsystem) +# Note that an PNExpansion is really a *relative* expansion in `1/c` — *not* `v` or `x`. +# Therefore, the correct derivative with respect to any variable (other than `c`, which we +# never differentiate with respect to) extends to just derivatives of the coefficients, +# without any change to the exponent of `1/c`. +function FastDifferentiation.derivative( + pn_expansion::PNExpansion{N,T,NMax}, fd_node::FastDifferentiation.Node +) where {N,T,NMax} + return PNExpansion( + ntuple(i -> FastDifferentiation.derivative(pn_expansion[i], fd_node), Val(N)), NMax + ) +end -Create a [`PNTerm`](@ref) object representing the post-Newtonian expansion parameter ``c``. -This can be used to automatically create more complicated `PNTerm`s, which combine to form a -[`PNExpansion`](@ref). This is a simple but effective way to write PN formulas while -automatically tracking the PN order of each term. -""" -function PNExpansionParameter(::PNSystem{ST,PNOrder}) where {ST,PNOrder} - return PNTerm{eltype(ST),PNOrder}(-1, one(eltype(ST))) +end # baremodule PNExpansions + +@testitem "PNExpansion algebra" begin + using Base: Base, one, zero, <, ÷, + as ⊕, - as ⊖, * as ⊛, / as ⊘, ^ as ↑ + using StaticArrays: MVector, SVector + using Symbolics: @variables, simplify, substitute + using PostNewtonian.PNBase: ln, (√), (+), (-), (*), (/), (//), (^) + using PostNewtonian.PNExpansions: PNExpansion + + # Test edge cases + @test_throws ArgumentError PNExpansion{0, Float64, 1}(()) + @test_throws ArgumentError PNExpansion{2, Float64, 1}((1.2, 3.4)) + @test_throws ArgumentError PNExpansion((), 0) + @test_throws ArgumentError PNExpansion((1.2, 3.4), 1) + + for N1 ∈ 1:9 + # Test conversions + coeffs = ntuple(i -> i + 1.0, N1) + for NMax ∈ N1:(N1 ⊕ 3) + expansion = PNExpansion(coeffs, NMax) + @test Base.Tuple(expansion) == coeffs + @test SVector(expansion) == SVector(coeffs) + @test Base.eltype(expansion) == Float64 + @test Base.length(expansion) == N1 + for i ∈ 1:N1 + @test expansion[i] == coeffs[i] + end + end + + for N2 ∈ 1:9 + for NMax ∈ max(N1, N2):(N1 ⊕ N2 ⊕ 3) + + @variables c⁻¹ x[1:N1] y[1:N2] z + poly(e::PNExpansion) = sum(e[i] ⊛ c⁻¹↑(i ⊖ 1) for i ∈ 1:length(e)) + eˣ = PNExpansion(tuple(x...), NMax) + eʸ = PNExpansion(tuple(y...), NMax) + + # Test sums + polysum = simplify(poly(eˣ + eʸ); expand=true) + sumpoly = simplify(poly(eˣ) ⊕ poly(eʸ); expand=true) + Δ = simplify(polysum ⊖ sumpoly; expand=true) + @test iszero(Δ) + @test_throws ArgumentError eˣ + PNExpansion(tuple(z, x...), NMax ⊕ 1) + @test_throws ArgumentError PNExpansion(tuple(z, x...), NMax ⊕ 1) + eˣ + + # Test products + polyprod = simplify(poly(eˣ * eʸ); expand=true) + prodpoly = simplify( + substitute( + simplify(poly(eˣ) ⊛ poly(eʸ); expand=true), + Dict([c⁻¹↑n => 0 for n ∈ NMax:(2NMax ⊕ 3)]), + ); + expand=true, + ) + Δ = simplify(polyprod ⊖ prodpoly; expand=true) + @test iszero(Δ) + @test_throws ArgumentError eˣ * PNExpansion(tuple(z, x...), NMax ⊕ 1) + @test_throws ArgumentError PNExpansion(tuple(z, x...), NMax ⊕ 1) * eˣ + end + end + end end diff --git a/src/core/PNTerm.jl b/src/core/PNTerm.jl new file mode 100644 index 00000000..e5b5ad5a --- /dev/null +++ b/src/core/PNTerm.jl @@ -0,0 +1,309 @@ +# We enclose all of this in a `baremodule` so that we can isolate Base operations, and use +# PNBase operations by default. +baremodule PNTerms + +# See explanation in `PNBase.jl` for why we use these operators. +using Base: Base, @doc, @assert, one, zero, >, ÷, + as ⊕, - as ⊖, * as ⊛, / as ⊘, ^ as ↑ + +import PostNewtonian: constant_convert +using PostNewtonian: PostNewtonian, PNSystem +using PostNewtonian.InlineExports: @export +using PostNewtonian.PNBase + + +""" + PNTerm{T,PNOrder,c⁻¹Exponent} + +This object represents a single term in a PNExpansion. It has a single field: `coeff`, +which is the coefficient of the term. The type parameter `T` is the type of the +coefficient. The type parameter `PNOrder` is a half-integer (just as in +[`PNSystem`](@ref)s) representing the PN order of the expansion. And the type parameter +`c⁻¹Exponent` is an integer representing the exponent of the PN expansion parameter ``1/c``. + +`PNTerm`s can be multiplied and divided by scalars and exponentiated by integers, to produce +another `PNTerm`. They can also be added to other `PNTerm`s to produce a `PNExpansion`. + +A simple way to define a `PNTerm` or a `PNExpansion` is to define the PN expansion parameter +```julia +c = PNExpansionParameter(pnsystem) +``` +and use that naturally in formulas, as in +```julia +e = 1 + (v/c)^2 * (-ν/12 - 3//4) + (v/c)^4 * (-ν^2/24 + 19ν/8 - 27//8) +``` +Any exponent higher than the desired `PNOrder` will be automatically set to zero. + +Useful facts: + - `v` has order `1/c` + - `x` has order `1/c^2` + - `γ` has order `1/c^2` + - `1/r` has order `1/c^2` + +""" +@export struct PNTerm{T,PNOrder,c⁻¹Exponent} + coeff::T + + function PNTerm{T,PNOrder,c⁻¹Exponent}(coeff) where {T,PNOrder,c⁻¹Exponent} + if c⁻¹Exponent > 2 ⊛ PNOrder + coeff = zero(coeff) + end + return new{T,PNOrder,c⁻¹Exponent}(coeff) + end + function PNTerm{T,PNOrder}(c⁻¹exp::Int, coeff) where {T,PNOrder} + if c⁻¹exp > 2 ⊛ PNOrder + coeff = zero(coeff) + end + return new{T,PNOrder,c⁻¹exp}(coeff) + end +end + +""" + PNExpansionParameter(pnsystem) + +Create a [`PNTerm`](@ref) object representing the post-Newtonian expansion parameter ``c``. +This can be used to automatically create more complicated `PNTerm`s, which combine to form a +[`PNExpansion`](@ref). This is a simple but effective way to write PN formulas while +automatically tracking the PN order of each term. +""" +@export function PNExpansionParameter(::T) where {NT,PNOrder,T<:PNSystem{NT,PNOrder}} + return PNTerm{NT,PNOrder}(-1, one(T)) +end + +Base.length(pn::PNTerm) = 1 # COV_EXCL_LINE (Covered, but missed due to const-folding) +Base.eltype(pn::PNTerm{T}) where {T} = T + +@export c⁻¹exp(pn::PNTerm{T,PNOrder,c⁻¹Exponent}) where {T,PNOrder,c⁻¹Exponent} = + c⁻¹Exponent + +function PostNewtonian.constant_convert( + pn::P, term::T +) where {NT,PNOrder,P<:PNSystem{NT,PNOrder},T<:PNTerm{NT,PNOrder}} + term +end + +### NOTE: Adding or subtracting multiple `PNTerm`s will produce a `PNExpansion`, which +### is defined in `PNExpansion.jl`. The following additive functions are just unary. + +function Base.sum(term::PNTerm) + return term.coeff +end + +function PNBase.:+(term::PNTerm) + return term +end + +function PNBase.:-(term::PNTerm{T,PNOrder,c⁻¹Exponent}) where {T,PNOrder,c⁻¹Exponent} + return PNTerm{T,PNOrder,c⁻¹Exponent}(⊖(term.coeff)) +end + +function Base.inv(term::PNTerm{T,PNOrder,c⁻¹Exponent}) where {T,PNOrder,c⁻¹Exponent} + return PNTerm{T,PNOrder}(⊖(c⁻¹Exponent), Base.inv(term.coeff)) +end + +function PNBase.:√(term::PNTerm{T,PNOrder,c⁻¹Exponent}) where {T,PNOrder,c⁻¹Exponent} + @assert Base.iseven(c⁻¹Exponent) "Only half-integer PN orders are supported." + return PNTerm{T,PNOrder}(c⁻¹Exponent ÷ 2, Base.sqrt(term.coeff)) +end + +function PNBase.:^( + term::PNTerm{T,PNOrder,c⁻¹Exponent}, n::Int +) where {T,PNOrder,c⁻¹Exponent} + coeff = term.coeff↑n + return PNTerm{typeof(coeff),PNOrder}(c⁻¹exp(term) ⊛ n, coeff) +end + +function PNBase.:*( + term1::PNTerm{T1,PNOrder,c⁻¹E1}, term2::PNTerm{T2,PNOrder,c⁻¹E2} +) where {T1,T2,PNOrder,c⁻¹E1,c⁻¹E2} + c⁻¹Exponent = c⁻¹exp(term1) ⊕ c⁻¹exp(term2) + coeff = term1.coeff ⊛ term2.coeff + return PNTerm{typeof(coeff),PNOrder,c⁻¹Exponent}(coeff) +end + +function PNBase.:*( + x::Number, term::PNTerm{T,PNOrder,c⁻¹Exponent} +) where {T,PNOrder,c⁻¹Exponent} + coeff = x ⊛ term.coeff + return PNTerm{typeof(coeff),PNOrder,c⁻¹Exponent}(coeff) +end + +PNBase.:*(term::PNTerm, x::Number) = PNBase.:*(x, term) + +function PNBase.:/( + term1::PNTerm{T1,PNOrder,c⁻¹E1}, term2::PNTerm{T2,PNOrder,c⁻¹E2} +) where {T1,T2,PNOrder,c⁻¹E1,c⁻¹E2} + c⁻¹Exponent = c⁻¹E1 ⊖ c⁻¹E2 + coeff = term1.coeff ⊘ term2.coeff + return PNTerm{typeof(coeff),PNOrder,c⁻¹Exponent}(coeff) +end + +function PNBase.:/( + term::PNTerm{T,PNOrder,c⁻¹Exponent}, x::Number +) where {T,PNOrder,c⁻¹Exponent} + coeff = term.coeff ⊘ x + return PNTerm{typeof(coeff),PNOrder,c⁻¹Exponent}(coeff) +end + +function PNBase.:/( + x::Number, term::PNTerm{T,PNOrder,c⁻¹Exponent} +) where {T,PNOrder,c⁻¹Exponent} + coeff = x ⊘ term.coeff + return PNTerm{typeof(coeff),PNOrder}(⊖(c⁻¹exp(term)), coeff) +end + +end # baremodule PNTerms + +@testitem "PNTerm algebra" begin + using Base: Base, one, zero, <, ÷, + as ⊕, - as ⊖, * as ⊛, / as ⊘, ^ as ↑ + using DoubleFloats: Double64 + using PostNewtonian: PostNewtonian, pn_order + using PostNewtonian.PNBase: ln, (√), (+), (-), (*), (/), (//), (^) + using PostNewtonian.PNTerms: PNTerm, PNExpansionParameter, c⁻¹exp, PNBase, constant_convert + using PostNewtonian.PNExpansions: PNExpansion + + for T ∈ [Float64, Float16, Double64] + pn = BBH(randn(T, 14), 9//2) + pn[:v] = /(pn, 1, 5) + c = PNExpansionParameter(pn) + z = zero(T) + x = /(pn, 6, 5) + y = /(pn, 17, 5) + w = /(pn, 28, 5) + v = /(pn, 27, 13) + + # Test behavior of `c` as the basic PNTerm + for (term, c⁻¹exponent, coeff) ∈ ( + (c, -1, 1), + (c^2, -2, 1), + (x * c^2, -2, x), + (c^2 * x, -2, x), + (c^2 / x, -2, 1 / x), + ((x * c)^2, -2, x^2), + ((x * c^2) / c^4, 2, x), + ((x * c^2) / c^-4, -6, x), + ((x / c^2) / c^4, 6, x), + ((x / c^2) * (y / c^4), 6, x * y), + ) + @test c⁻¹exp(term) == c⁻¹exponent + @test term.coeff == coeff + @test term.coeff isa eltype(pn) + @test length(term) == 1 + @test eltype(term) ≡ T + end + + # Test PNExpressions + @test_throws ArgumentError PNExpansion((), 0) + for (expr, expected) ∈ ( + (w - (x - y / c), (w - x, y)), + (w - (x / c - y), (w + y, -x)), + (x - y / c, (x, -y)), + (x / c - y, (-y, x)), + (x / c^6 + y / c, (z, y, z, z, z, z, x)), + (x / c^6 + y / c + w / c^10, (z, y, z, z, z, z, x, z, z, z)), + (x / c^6 - y / c, (z, -y, z, z, z, z, x)), + (x / c^6 - y / c - w, (-w, -y, z, z, z, z, x)), + (x / c^6 - y / c - w / c^10, (z, -y, z, z, z, z, x, z, z, z)), + (x / c^6 - (y / c - w), (w, -y, z, z, z, z, x)), + (x / c^6 - (y / c - w / c^10), (z, -y, z, z, z, z, x, z, z, z)), + (-(x / c^6) - y / c, (z, -y, z, z, z, z, -x)), + (-(x / c^6) - y / c - w, (-w, -y, z, z, z, z, -x)), + (-(x / c^6) - y / c - w / c^10, (z, -y, z, z, z, z, -x, z, z, z)), + ((x * c^2) / c^4 + y / c, (z, y, x)), + ((x * c^2) / c^4 + y / c + w, (w, y, x)), + ((x * c^2) / c^9 + y / c + w, (w, y, z, z, z, z, z, x)), + (w + (x * c^2) / c^4 + y / c, (w, y, x)), + (w + (x * c^2) / c^9 + y / c, (w, y, z, z, z, z, z, x)), + (w + ((x * c^2) / c^4 + y / c), (w, y, x)), + (w + ((x * c^2) / c^9 + y / c), (w, y, z, z, z, z, z, x)), + (((x * c^2) / c^4 + y / c + w) / c^3, (z, z, z, w, y, x)), + (((x * c^2) / c^4 + y / c + w) / c^5, (z, z, z, z, z, w, y, x)), + (((x * c^2) / c^7 + y / c + w) / c^5, (z, z, z, z, z, w, y, z, z, z)), + (v * (((x * c^2) / c^4 + y / c + w) / c^3), v .* (z, z, z, w, y, x)), + ((((x * c^2) / c^4 + y / c + w) / c^3) * v, v .* (z, z, z, w, y, x)), + ((((x * c^2) / c^4 + y / c + w) / c^3) / v, (z, z, z, w, y, x) .* (1 / v)), + ) + @test expr.coeffs == expected + @test pn_order(expr) == pn_order(pn) + @test sum(expr) == sum(expected) + @test eltype(expr) ≡ T + end + + # Can't make a PNExpression with positive exponents + @test_throws ArgumentError x * c + y + @test_throws ArgumentError x * c + y / c + @test_throws ArgumentError x * c^2 + y + @test_throws ArgumentError x * c^2 + y / c + @test_throws ArgumentError y + x * c + @test_throws ArgumentError y / c + x * c + @test_throws ArgumentError y + x * c^2 + @test_throws ArgumentError y / c + x * c^2 + @test_throws ArgumentError x * c^2 + (y / c + z / c^2) + end + + pn = BBH(randn(14), 2//1) + + # constant_convert should just return the term + t0 = PNTerm{Float64,2//1}(0, 5.0) + @test constant_convert(pn, t0) ≡ t0 + + # Base.sum + @test sum(t0) == 5.0 + + # unary + (PNBase.+) + t1 = PNTerm{Float64,2}(1, 2.5) + @test +t1 ≡ t1 + + # unary - (PNBase.-) + t1n = -t1 + @test c⁻¹exp(t1n) == c⁻¹exp(t1) + @test t1n.coeff == -2.5 + + # inv + ti = inv(t1) + @test c⁻¹exp(ti) == -c⁻¹exp(t1) + @test ti.coeff == 1/2.5 + + # sqrt on even exponent + t2 = PNTerm{Float64,2}(2, 4.0) + ts = √(t2) + @test c⁻¹exp(ts) == 1 + @test ts.coeff == 2.0 + + # sqrt on odd exponent should error + t3 = PNTerm{Float64,2}(1, 9.0) + @test_throws AssertionError √(t3) + + # power + tp = t1 ^ 3 + @test c⁻¹exp(tp) == 3*c⁻¹exp(t1) + @test tp.coeff == 2.5^3 + + # multiply term * term + ta = PNTerm{Float64,2}(1, 2.0) + tb = PNTerm{Float64,2}(2, 3.0) + tab = ta * tb + @test c⁻¹exp(tab) == 3 + @test tab.coeff == 6.0 + + # scalar * term and term * scalar + ts1 = 4.0 * ta + ts2 = ta * 4.0 + @test c⁻¹exp(ts1) == c⁻¹exp(ta) + @test ts1.coeff == 8.0 + @test ts2.coeff == 8.0 + + # term / term + td = tb / ta + @test c⁻¹exp(td) == 1 # 2 - 1 + @test td.coeff == 1.5 + + # term / scalar + td1 = tb / 2.0 + @test c⁻¹exp(td1) == c⁻¹exp(tb) + @test td1.coeff == 1.5 + + # scalar / term + td2 = 12.0 / ta + @test c⁻¹exp(td2) == -1 # -c⁻¹exp(ta) + @test td2.coeff == 6.0 +end diff --git a/src/core/core.jl b/src/core/core.jl new file mode 100644 index 00000000..134df618 --- /dev/null +++ b/src/core/core.jl @@ -0,0 +1,20 @@ +# This directory provides the core functionality for the post-Newtonian framework — things +# that we will use to build out the rest of the code. As such, it is full of little coding +# details that are important for understanding the detailed structure of the code, but not +# for understanding the physics that code is representing. + +# These are low-level utilities. +include("utilities/misc.jl") +include("utilities/truncated_series_monoid.jl") +include("utilities/truncated_series_inversion.jl") + +# These are types and modules that help to build the post-Newtonian framework. +include("PNBase.jl") +include("PNTerm.jl") +include("PNExpansion.jl") +import PostNewtonian.PNTerms: PNExpansionParameter + +# These macros effectively form the interface used directly in the rest of the code. +include("pn_expansion.jl") +include("pn_expression.jl") +include("pn_reference.jl") diff --git a/src/core/pn_expansion.jl b/src/core/pn_expansion.jl new file mode 100644 index 00000000..8ebb2c7b --- /dev/null +++ b/src/core/pn_expansion.jl @@ -0,0 +1,133 @@ +@doc raw""" + @pn_expansion pnsystem expansion + +Mark `expansion` as a post-Newtonian expansion, to be truncated at the order given by the +`pnsystem`. + +!!! warning + + The symbols `c`, `x`, `γₚₙ`, and `γ` are all considered to be PN-expansion terms inside + the expression passed to this macro. If present inside the expression, this macro will + multiply each by the appropriate power of + [`PNExpansionParameter(pnsystem)`](@ref PNExpansionParameter) to ensure that the + expansion is truncated correctly. + +Note that we generally interpret this PN order as a *relative* PN order. For example, the +expression for [gravitational-wave energy flux](@ref 𝓕) looks like +```math +\mathcal{F} = \frac{32c^5}{5G} \nu^2 \left(\frac{v}{c}\right)^{10} +\left[1 - \left(\frac{ν}{12} + \frac{3}{4}\right) \left(\frac{v}{c}\right)^2 + \ldots\right] +``` +Here, the part in square brackets is the expansion in terms of *relative* PN order, with the +1 representing the relative 0-pN term, the ``(v/c)^2`` term being the relative 1-pN term, +etc. So in the code, we apply `@pn_expansion` to the part in square brackets: +```julia +32c^5 / 5G * ν^2 * (v / c)^10 * @pn_expansion(1 - (ν/12 + 3/4) * (v/c)^2 + ...) +``` +Note that the entire expression is written inside a function that is modified by the +[`@pn_expression`](@ref) macro, which automatically inserts the `pnsystem` argument to this +`@pn_expansion` call, so you generally should not have to worry about it. + +This macro gathers terms in `expansion` by the powers of ``1/c`` involved, zeroing out any +terms with powers of ``1/c`` higher than (twice) the `pnsystem`'s `PNOrder` parameter, and +combine the terms using the `PNExpansionReducer` specified in argument of the function that +includes this macro call. + +The expansion and truncation are achieved by multiplying `c` by a +[`PNExpansionParameter(pnsystem)`](@ref PNExpansionParameter), which is just a +[`PNTerm`](@ref) with a coefficient of 1 and a `c⁻¹Exponent` of -1. This redefinition +happens inside a `let` block created by this macro so that it doesn't interfere with any +`c`s on the outside. For example, in the flux expression above, the `c`s in `32c^5 / 5G * +ν^2 * (v / c)^10` are outside the scope of the macro, so even if we set `c=2` above that +line the expansion will still be correctly truncated, and the value of `c` will be +preserved. + +In the literature, some PN expansions do not *explicitly* use the `c` parameter, but instead +define the expansion in terms of the dimensionless parameters [`x`](@ref) or [`γₚₙ`](@ref), +which include powers of `c` in their definitions. Thus, if these symbols are present inside +the expression passed to this macro, they will be multiplied by the appropriate power of +`PNExpansionParameter`. The literature simply uses `γ`, rather than the more explicit `γₚₙ` +we use here, so `γ` will be treated the same as `γₚₙ`. + +Euler's constant — sometimes called the Euler–Mascheroni constant, and distinct from Euler's +*number* ``e`` — is usually denoted by `γ` (including in Julia's own `Base.MathConstants`), +but is distinguished in the post-Newtonian literature by the subscript "E", and is defined +in this package as [`γₑ`](@ref). + +!!! note + + Because `x` and `γₚₙ` are "of order" ``1/c^2``, their exponents are generally + half-integers in any expansion. Evaluating a term like `x^(7/2)` generically will be + relatively inefficient, requiring a floating-point division, the logarithm of `x`, a + floating-point multiplication, and exponentiation. Compared to a single square-root and + integer exponentiation, this is slow. Moreover, it does not work well with the + [`PNTerm`](@ref) mechanism. So another thing this macro does is search for terms like + `x^(7/2)` and convert them to `(√x)^7`, and similarly for `γₚₙ` and `γ`. This only + works for explicit half-integers, rather than variables that may be half-integers. +""" +@public macro pn_expansion(pnsystem, expr) + expansion_parameters = Expr[] + if MacroTools.inexpr(expr, :c) + push!(expansion_parameters, :(c = c * PNExpansionParameter($pnsystem))) + end + if MacroTools.inexpr(expr, :x) + push!(expansion_parameters, :(x = x / PNExpansionParameter($pnsystem)^2)) + expr = MacroTools.postwalk(expr) do ex + MacroTools.@capture(ex, x^(n_Int/2)) || return ex + return :((√x)^$n) + end + end + if MacroTools.inexpr(expr, :γₚₙ) + push!(expansion_parameters, :(γₚₙ = γₚₙ / PNExpansionParameter($pnsystem)^2)) + expr = MacroTools.postwalk(expr) do ex + MacroTools.@capture(ex, γₚₙ^(n_Int/2)) || return ex + return :((√γₚₙ)^$n) + end + end + if MacroTools.inexpr(expr, :γ) + push!(expansion_parameters, :(γ = γ / PNExpansionParameter($pnsystem)^2)) + expr = MacroTools.postwalk(expr) do ex + MacroTools.@capture(ex, γ^(n_Int/2)) || return ex + return :((√γ)^$n) + end + end + if isempty(expansion_parameters) + error("No expansion parameters found in `@pn_expansion`.") + end + return esc(MacroTools.unblock(quote + let $(expansion_parameters...) + PNExpansionReducer($expr) + end + end)) +end + +@testitem "@pn_expansion" begin + using PostNewtonian: @pn_expansion + using MacroTools + + input = @macroexpand @pn_expansion pnsystem ( + 1 - (ν/12 + 3/4) * (v/c)^2 + 4x^3 + 5x^(7/2) + ) + output = MacroTools.unblock( + quote + let c = c * PNExpansionParameter(pnsystem), + x = x / PNExpansionParameter(pnsystem)^2 + + PNExpansionReducer(1 - (ν/12 + 3/4) * (v/c)^2 + 4x^3 + 5(√x)^7) + end + end, + ) + @test MacroTools.striplines(input) == MacroTools.striplines(output) + + input = @macroexpand @pn_expansion pnsystem (1 - (ν/12 + 3/4)γ + 4γₚₙ^3 + 5γₚₙ^(7/2)) + output = MacroTools.unblock( + quote + let γₚₙ = γₚₙ / PNExpansionParameter(pnsystem)^2, + γ = γ / PNExpansionParameter(pnsystem)^2 + + PNExpansionReducer(1 - (ν/12 + 3/4)γ + 4γₚₙ^3 + 5(√γₚₙ)^7) + end + end, + ) + @test MacroTools.striplines(input) == MacroTools.striplines(output) +end diff --git a/src/core/pn_expression.jl b/src/core/pn_expression.jl new file mode 100644 index 00000000..02221265 --- /dev/null +++ b/src/core/pn_expression.jl @@ -0,0 +1,316 @@ +""" + @pn_expression [arg_index=1] func + +This macro makes it easier to define post-Newtonian expressions. + +The optional first argument to this macro is `arg_index`, which just tells us which argument +to the function `func` is a `PNSystem` — defaulting to the first argument. For example, the +variables defined in [`PostNewtonian.FundamentalVariables`](@ref "Fundamental variables") +all take a single argument of `pnsystem`, which is used to compute the values for those +variables; this macro just needs to know where to find `pnsystem`. + +The required argument to this macro is a function the will compute some values related to +the `pnsystem`. + +Once it has this information, there are three types of transformations the macro will make: + + 1. If either `PNExpansionReducer` or `@pn_expansion` is used in the expression, this adds a + keyword argument `pn_expansion_reducer::Val{PNExpansionReducer}=Val(sum)` to the + function signature. This is used to determine how to reduce the PN expansion terms. + The default is `Val(sum)`, which will just return a single number, but `Val(identity)` + can be used to return the expansion. The reducing function can be used inside the main + function as `PNExpansionReducer`, and will be automatically used inside any + `@pn_expansion`. + 2. For every function defined in the module where this macro is called that takes a single + `PNSystem` argument, this macro will look for the name of that function inside the + expression. If it finds any such names, it will replace them with the corresponding + calls to the function with `pnsystem` as the argument. For example, you can simply use + the symbols `M₁` or `μ` in your code, rather than calling them as [`M₁(pnsystem)`](@ref + M₁) or [`μ(pnsystem)`](@ref μ) every time they appear. To be more explicit, this is + achieved by defining the relevant quantities in a `let` block placed around the body of + `func`, so that the values may be used efficiently without recomputation. If you need + to use one of those functions with different arguments, you'll need to address them + explicitly with the module name — as in `PostNewtonian.v(;Ω, M)`. + 3. Insert the `pnsystem` argument as the first argument to each occurrence of + `@pn_expansion` that needs it. + +For example, we might write a function like this: +```julia +@pn_expression function f(pnsystem) + 5μ/c^2 * @pn_expansion(1 + 4(v/c)^2) +end +``` +That is effectively rewritten by this macro as +```julia +function f(pnsystem, ::Val{PNExpansionReducer}=Val(sum)) where {PNExpansionReducer} + let μ=μ(pnsystem), c=c(pnsystem), v=v(pnsystem) + 5μ/c^2 * @pn_expansion pnsystem (1 + 4(v/c)^2) + end +end +``` +The [`@pn_expansion`](@ref) macro is further expanded so that the final result looks like +```julia +function f(pnsystem, ::Val{PNExpansionReducer}=Val(sum)) where {PNExpansionReducer} + let μ=μ(pnsystem), c=c(pnsystem), v=v(pnsystem) + 5μ/c^2 * ( + let c=PNExpansionParameter(pnsystem) + PNExpansionReducer(1 + 4(v/c)^2) + end + ) + end +end +``` +Moreover, this expression should itself be defined within an [`@pn_reference`](@ref) module, +which preserves the precision of the `pnsystem`, so that we can define `pnsystem` with, +e.g., `Float16` or `BigFloat` numbers, and natural expressions like `2π` or `4/3` won't +automatically be converted to `Float64` and spoil the requested precision. +""" +@public macro pn_expression(arg_index, func=:(nothing)) + # Note that macros secretly get two extra variables: `__module__` and `__source__`. + # These refer to the place where the macro was called. The second is useful for + # debugging, but the first is crucial here, because it lets us see what's defined in the + # module in which this macro was used. + + # First, we just search for everything defined in the module where this macro is called. + all_names = if VERSION < v"1.12.0-beta1" + # See the warning in `@pn_reference` for why we should avoid `using` on Julia <1.12 + names(__module__; all=true, imported=true) + else + names(__module__; all=true, imported=true, usings=true) + end + + # Next, we narrow that list down to callable objects defined in the `__module__` where + # this macro was used. Specifically, we filter for those objects that take one + # `PNSystem`, and nothing else, as an argument. These will be valid targets for + # replacement in the body that `@pn_expression` is applied to. + pnsystem_functions = filter( + function (name) + if isdefined(__module__, name) + f = getfield(__module__, name) + if isa(f, Base.Callable) + if !isempty(methods(f, Tuple{PNSystem})) + return true + end + end + end + return false + end, all_names + ) + + # Now, we pass that information along to the function that actually modifies our code + return esc(pn_expression(arg_index, func, pnsystem_functions, __module__, __source__)) +end + +function pn_expression(arg_index, func, pnsystem_functions, __module__, __source__) + # Handle the default argument + if func ≡ :(nothing) + arg_index, func = 1, arg_index + end + + # Check to make sure that `arg_index` is an integer; we'll check that it's valid below. + if !isa(arg_index, Integer) + error( + "The optional argument to `@pn_expression` must be an integer, not " * + "$(typeof(arg_index))\nThe incorrect application is at $(__source__).", + ) + end + + # Check to make sure that `func` is a function-definition expression + if !MacroTools.isdef(func) + error( + "The `@pn_expression` macro can only be applied to function definitions.\n" * + "The incorrect application is at $(__source__).", + ) + end + + # MacroTools has this nice function to parse function definitions so we can operate on + # each piece separately. + splitfunc = MacroTools.splitdef(func) + + # Check that the argument index is valid + if arg_index < 1 || arg_index > length(splitfunc[:args]) + error( + "Invalid argument index $arg_index for function $(splitfunc[:name]); " * + "it must be between 1 and $(length(splitfunc[:args]))\n" * + "The incorrect application is at $(__source__).", + ) + end + + # Get the name of the PNSystem argument + pnsystem = MacroTools.namify(splitfunc[:args][arg_index]) + + # Add `pnsystem` as the argument to each @pn_expansion call... + new_body = MacroTools.postwalk(splitfunc[:body]) do x + if MacroTools.isexpr(x, :macrocall) && + x.args[1] == Symbol("@pn_expansion") && + !isa(x.args[end - 1], Symbol) # ...unless there's already one there + x′ = deepcopy(x) + insert!(x′.args, length(x′.args), pnsystem) + x′ + else + x + end + end + + # Expand all the macros inside the body + new_body = macroexpand(__module__, new_body; recursive=true) + + # If `PNExpansionReducer` is or will be in the body of the function, we need to make + # sure it is included in the function signature. + if MacroTools.inexpr(new_body, :(@pn_expansion)) || + MacroTools.inexpr(new_body, :(PNExpansionReducer)) + + # Just so we don't accidentally add it twice, make sure it's not already in the + # function signature. + if !any(MacroTools.inexpr.(splitfunc[:kwargs], :(PNExpansionReducer))) + # Append a keyword argument `pn_expansion_reducer` to the function signature, + # with default value `Val(sum)`. The `Val` parameter is captured as + # `PNExpansionReducer`, which we can then use in the body of the function — + # specifically, it is automatically used by the `@pn_expansion` macro. + splitfunc[:kwargs] = [ + splitfunc[:kwargs] + :( + $(Expr( + :kw, + :(pn_expansion_reducer::Val{PNExpansionReducer}), + :(Val(Base.sum)), + )) + ) + ] + + # Add `PNExpansionReducer` to the `where` clause + splitfunc[:whereparams] = (splitfunc[:whereparams]..., :PNExpansionReducer) + end + end + + # Look for any of the `pnsystem_functions` in the body of the function and prepare an + # entry for the `let` block that will surround the body on output. + pnsystem_function_exprs = [ + :($s = $s($pnsystem)) for + s ∈ filter(s -> MacroTools.inexpr(new_body, s), pnsystem_functions) + ] + + # Walk the expression tree and find all function calls to any of the + # `pnbase_functions`, and insert `pnsystem` as the first argument. + new_body = MacroTools.postwalk(new_body) do x + if iscall(x, pnbase_functions) + insert!(x.args, 2, (pnsystem)) + x + else + x + end + end + + # Include the `let` statements so that the functions can all be used as plain symbols + # without having to call them on `pnsystem`, but we do so without burying it in a code + # block. + new_body = MacroTools.unblock(quote + #@fastmath + let $(pnsystem_function_exprs...) + $(MacroTools.unblock(new_body)) + end + end) + + # Replace the old body with the new one + splitfunc[:body] = new_body + + # And reassemble the function definition + return MacroTools.combinedef(splitfunc) +end + +@testitem "@pn_expression" begin + using MacroTools + + baremodule Mod + # These are the expressions added by `@pn_reference` + using Base: Base, Val + eval(x::Expr) = Core.eval(Base.@__MODULE__, x) + include(p::AbstractString) = Base.include(Base.@__MODULE__, p) + using PostNewtonian: PostNewtonian, @pn_expression, @pn_expansion, 𝒾, γₑ, ζ3 + using PostNewtonian.PNBase + + # Below are what we would normally write manually + import PostNewtonian: M₁, M₂, χ₁ˣ, χ₁ʸ, χ₁ᶻ, v, Φ + const x = Base.://(7, 2) + f(pnsys::PostNewtonian.PNSystem) = x + @pn_expression function g(pnsy) + f + M₁ + end + @pn_expression h(pns) = f - M₂ + @pn_expression function i(pn) + f * χ₁ˣ * γₑ + end + @pn_expression function j(pnsyst) + f / χ₁ʸ + end + @pn_expression function k(pnsyste) + f ^ χ₁ᶻ + end + @pn_expression function l(pnsystm) + f * ln(v) * ζ3 + end + @pn_expression function m(pnsystem) + √f * Φ + end + + const expr1 = Base.@macroexpand @pn_expression function n(pnsystem) + l * f * ln(v) * ζ3 + m * Φ / c + end + + const expr2 = Base.@macroexpand @pn_expression function n(pnsystem) + @pn_expansion l * f * ln(v) * ζ3 + m * Φ / c + end + + end # baremodule Mod + + import .Mod + + const ln = log + + output1 = :( + function n(pnsystem;) + let f=f(pnsystem), l=l(pnsystem), m=m(pnsystem), v=v(pnsystem), Φ=Φ(pnsystem) + + pnsystem + + pnsystem * l * f * ln(pnsystem, v) * ζ3 + + /(pnsystem, pnsystem * m * Φ, c) + end + end + ) + @test MacroTools.striplines(Mod.expr1) == MacroTools.striplines(output1) + + # Because the `c...` in the `let c...` statement is actually in a block, we have to do + # this little `c2` hack, so our explicit version resembles the generated version. + c2 = [:(c = pnsystem * c * PNExpansionParameter(pnsystem))] + output2 = :( + function n( + pnsystem; pn_expansion_reducer::Val{PNExpansionReducer}=Val(Base.sum) + ) where {PNExpansionReducer} + let f=f(pnsystem), l=l(pnsystem), m=m(pnsystem), v=v(pnsystem), Φ=Φ(pnsystem) + + let $(c2...) + PNExpansionReducer( + pnsystem + + pnsystem * l * f * ln(pnsystem, v) * ζ3 + + /(pnsystem, pnsystem * m * Φ, c), + ) + end + end + end + ) + @test MacroTools.striplines(Mod.expr2) == MacroTools.striplines(output2) + + for NT ∈ (Float16, Float64, BigFloat) + pnsystem = BHNS(NT.(1:15)) + for v ∈ (:g, :h, :i, :j, :k, :l, :m) + @test eval(:(Mod.$v))(pnsystem) isa NT + end + @test Mod.g(pnsystem) == NT(7//2) + pnsystem[:M₁] + @test Mod.h(pnsystem) == NT(7//2) - pnsystem[:M₂] + @test Mod.i(pnsystem) == NT(7//2) * pnsystem[:χ₁ˣ] * PostNewtonian.γₑ + @test Mod.j(pnsystem) == NT(7//2) / pnsystem[:χ₁ʸ] + @test Mod.k(pnsystem) == NT(7//2) ^ pnsystem[:χ₁ᶻ] + @test Mod.l(pnsystem) == NT(7//2) * log(pnsystem[:v]) * PostNewtonian.ζ3 + @test Mod.m(pnsystem) == √(NT(7//2)) * pnsystem[:Φ] + end +end diff --git a/src/core/pn_reference.jl b/src/core/pn_reference.jl new file mode 100644 index 00000000..a2ec6598 --- /dev/null +++ b/src/core/pn_reference.jl @@ -0,0 +1,195 @@ +""" +This file defines the `@pn_reference` macro, which is used to create a module for a specific +Post-Newtonian reference. Its purpose is to *un*define even the most basic operations, such +as addition, multiplication, and so on, to ensure that all operations are sufficiently +overridden by `@pn_expression`. For example, integer division `1/3` will result in a +`Float64` by default. But `@pn_expression` will extract the number type `NT` of the +`pnsystem` argument, and redefine integer division to return something compatible with `NT` +instead — possibly a `Double64` or `Sympy` expression, for example. + +The [julia docs +say](https://docs.julialang.org/en/v1/manual/modules/#Default-top-level-definitions-and-bare-modules) +that a standard module is essentially this: + +```julia +baremodule Mod + +using Base + +eval(x) = Core.eval(Mod, x) +include(p) = Base.include(Mod, p) + +... + +end +``` +We just want to replace that `using` with `import`. This will ensure that only operations +that are already handled by `@pn_expression` will be defined; if they aren't, there will be +an error. + +Similarly, we want the author to *have to* define every single variable to be used in the PN +expression. In most cases, the variable can just be imported from `common_variables` under +its own name. There may be cases, however, where the name needs to change, or a variable +needs to be defined just in the given module. One prominent example is that some authors +use `η` where we use `ν`. In any case, this will make it easier for `@pn_expression` to +look through the current module for symbols that appear in the expression that need to be +replaced with a call to that function. + +""" + +function pn_reference(expr, __module__, __source__) + # A module `Expr` has head `:module` and three arguments: + # 1. a boolean indicating if this is a module (true) as opposed to a baremodule (false) + # 2. the module name (a `Symbol`) + # 3. the module body (an `Expr` with head `:block`) + if MacroTools.isexpr(expr, :module) + # Check to make sure that this module is structured exactly as expected + if length(expr.args) ≠ 3 + error( + "Found a module expression with $(length(expr.args)) arguments:\n" * + "$(expr)", + ) + end + if ! MacroTools.isexpr(expr.args[1], Bool) + error("Found a module expression with a non-boolean flag: $(expr.args[1])") + end + if ! MacroTools.isexpr(expr.args[2], Symbol, :symbol) + error( + "Found a module expression with a non-symbol name: $(expr.args[2])\n" * + "$(expr)", + ) + end + if ! MacroTools.isexpr(expr.args[3], :block) + error("Found a module expression with a non-block body: $(dump(expr.args[3]))") + end + + # Warn if the module uses `using` on Julia < 1.12 + if VERSION < v"1.12.0-beta1" && any( + arg -> hasproperty(arg, :head) && getproperty(arg, :head) ≡ :using, + expr.args[3].args, + ) + @warn "Prefer `import` inside `@pn_reference` modules on Julia<1.12\n" * + "You are defining a `@pn_reference` module that uses `using` at\n" * + "`$(__source__)`.\n" * + "Due to a limitation in Julia 1.11 and earlier, you must use `import`\n" * + "rather than `using` to import function names that you want to use in a\n" * + "`@pn_expression`." + end + + # Now, we assemble the new module, mostly by prepending some imports to the contents + module_name = expr.args[2] + module_body = expr.args[3].args + public = VERSION ≥ v"1.11.0-beta1" ? Expr(:public, module_name) : :() + new_module = quote + $public + Base.@__doc__ baremodule $(module_name) + using Base: Base, Val, π, @raw_str, @doc + eval(x::Expr) = Core.eval($(module_name), x) + include(p::AbstractString) = Base.include($(module_name), p) + using PostNewtonian: + @pn_expression, @pn_expansion, PNExpansionParameter, 𝒾, γₑ, ζ3 + using PostNewtonian.PNBase + $(module_body...) + end + end + + # Finally, we return this as a `:toplevel` expression, to ensure that it is + # not buried in some block that causes an error. + return Expr(:toplevel, new_module) + else + error("@pn_reference can only be used with module expressions, not `$expr`") + end +end + +""" + @pn_reference + +Create a module for a specific Post-Newtonian reference. + +!!! warning + + Due to limitations of Julia versions less than 1.12, you *must* use `import` instead of + `using` to import variables inside the module created by `@pn_reference`, or they won't + be available to `@pn_expression`. + +The purposes of this macro are: + + 1. To isolate the code for each reference, allowing for different notations such as + `η` or `ν` for the reduced mass ratio, or for subtly different definitions of + fundamental quantities like spin. + 2. To require that all functions and variables used in the expressions defined in the + module are explicitly imported or defined, to minimize the chance of accidentally + using incorrect definitions. + 3. To preserve precision relevant to the number type of the input `PNSystem` + by redefining basic operations such as addition, multiplication, and so on. + +Different sources in the literature may use different notations for the same variables, so +enclosing definitions related to a particular reference in a module allows us to use the +appropriate notation within that module while still interfacing with this package and its +conventions outside of the module. For example, some authors use `η` to denote the +symmetric mass ratio whereas this package uses `ν`. We can import this with `using +..PostNewtonian: ν as η` inside the module, and then use `η` in the expressions defined +inside that module, to resemble the reference. But when any expression using `η` is called +from outside the module, the choice of variable used inside that expression will not affect +the result. + +This macro transforms the module to which it is applied, so that unlike a normal module that +effectively includes `using Base` — which allows access to such basic operations as +addition, multiplication, and so on — it instead includes `import Base`. It also includes +`using PostNewtonian: @pn_expression, @pn_expansion`, the first of which redefines the basic +operations — at least those used in post-Newtonian expressions — to account for the number +type relevant to the input `PNSystem`. By not importing the basic operations from `Base`, +we ensure that only those redefined by `@pn_expression` are available in the module, which +ensures that they preserve the number type. If any are missing, `@pn_expression` should be +extended. + +""" +@public macro pn_reference(ex) + esc(pn_reference(ex, __module__, __source__)) +end + +@testitem "@pn_reference" begin + using MacroTools: MacroTools + using PostNewtonian: @pn_reference + + input = @macroexpand @pn_reference module Einstein1918 + import PostNewtonian: G, c, M, χ⃗₁, χ⃗₂, v, pn_order + import Quaternionic: absvec + @pn_expression χ₁(pnsystem) = absvec(χ⃗₁) + @pn_expression χ₂(pnsystem) = absvec(χ⃗₂) + const x = 3 + module InnerMod + const z = 4 + end + import .InnerMod: z + @pn_expression function y(pnsystem) + G*M/c^3 * @pn_expansion(x + χ₁ + χ₂ + z*(v/c)) + end + end + + output = quote + baremodule Einstein1918 + using Base: Base, Val, π, @raw_str, @doc + eval(x::Expr) = Core.eval(Einstein1918, x) + include(p::AbstractString) = Base.include(Einstein1918, p) + using PostNewtonian: @pn_expression, @pn_expansion, PNExpansionParameter, 𝒾, γₑ, ζ3 + using PostNewtonian.PNBase + + import PostNewtonian: G, c, M, χ⃗₁, χ⃗₂, v, pn_order + import Quaternionic: absvec + @pn_expression χ₁(pnsystem) = absvec(χ⃗₁) + @pn_expression χ₂(pnsystem) = absvec(χ⃗₂) + const x = 3 + module InnerMod + const z = 4 + end + import .InnerMod: z + @pn_expression function y(pnsystem) + G*M/c^3 * @pn_expansion(x + χ₁ + χ₂ + z*(v/c)) + end + end + end + + @test MacroTools.striplines(input).args[1].args[2].args[2] == + MacroTools.striplines(output).args[1] +end diff --git a/src/core/utilities/InlineExports.jl b/src/core/utilities/InlineExports.jl new file mode 100644 index 00000000..7ce6408e --- /dev/null +++ b/src/core/utilities/InlineExports.jl @@ -0,0 +1,304 @@ +# NOTE: This file borrows from the `InlineExports.jl` package, which is licensed under the +# MIT License. The original source can be found at https://github.com/dalum/InlineExports.jl + +module NoExport + +import Base: @__doc__ + +export @export, @public + +eval(quote + """ + @export + + No-op. Used to disable inline exports. + """ + macro $(Symbol("export"))(expr::Expr) + return esc(expr) + end +end) + +""" + @public + +No-op. Used to disable inline public macro. +""" +macro public(expr::Expr) + return esc(expr) +end + +end # module NoExport + +module InlineExports + +import Base: @__doc__ + +export @export, @public + +eval(quote + """ + @export + + Return the expression with all bindings exported. + + ``` + julia> module M + using InlineExports + @export begin + const a = 2 + abstract type S <: Number end + struct T <: S + val + end + end + @export f(x::TT) where {TT<:S} = x.val^2 + end + M + + julia> using .M + + julia> f(T(a)) + 4 + ``` + """ + macro $(Symbol("export"))(expr::Expr) + return handle(expr, :export) + end +end) + +@static if VERSION < v"1.11" + using ..NoExport: @public +else + """ + @public + + Return the expression with all bindings marked as public. + + ``` + julia> module M + using InlineExports + @public begin + const a = 2 + abstract type S <: Number end + struct T <: S + val + end + end + @public f(x::TT) where {TT<:S} = x.val^2 + end + M + + julia> using .M + + julia> M.f(M.T(M.a)) + 4 + ``` + """ + macro public(expr::Expr) + return handle(expr, :public) + end +end + +function handle(expr::Expr, export_or_public::Symbol) + r = handle(expr) + ep = if r isa Symbol + Expr(export_or_public, r) + else + Expr(export_or_public, r...) + end + # COV_EXCL_START + return esc(quote + $ep + Base.@__doc__ $expr + end) + # COV_EXCL_END +end + +handle(::Any) = nothing +handle(x::Symbol) = x +handle(expr::Expr) = handle(Val(expr.head), expr) + +handle(::Val{:block}, expr) = filter(x -> x !== nothing, map(handle, expr.args)) +handle(::Val{:const}, expr) = handle(expr.args[1]) +handle(::Val{:(::)}, expr) = handle(expr.args[1]) +handle(::Val{:(=)}, expr) = handle(expr.args[1]) +handle(::Val{:function}, expr) = handle(expr.args[1]) +handle(::Val{:where}, expr) = handle(expr.args[1]) +handle(::Val{:macro}, expr) = Symbol("@", handle(expr.args[1])) +handle(::Val{:struct}, expr) = handle(expr.args[2]) +handle(::Union{Val{:abstract},Val{:primitive}}, expr) = handle(expr.args[1]) + +handle(::Val{:<:}, expr) = handle(expr.args[1]) +handle(::Val{:curly}, expr) = handle(expr.args[1]) +handle(::Val{:call}, expr) = handle(expr.args[1]) +function handle(::Val{:macrocall}, expr) + if expr.args[1]==Symbol("@doc") || + (expr.args[1] == Core.GlobalRef(Core, Symbol("@doc"))) + if length(expr.args) != 4 + # COV_EXCL_START + error("@doc expression found with $(length(expr.args)) args:\n$expr") + # COV_EXCL_END + end + handle(expr.args[4]) + else + filter(x -> x !== nothing, map(handle, expr.args[3:end])) + end +end + +end # module InlineExports + +@testitem "InlineExports" begin + using Markdown: @doc_str + + module Bla + using PostNewtonian.InlineExports: @export, @public + + @export macro garble(expr::Expr) + return esc(expr) + end + + @public macro gorble(expr::Expr) + return esc(expr) + end + + @export abstract type Flork{T} end + @public abstract type Flark{T} end + + @export m::Int = 3 + @public n::Int = 4 + + @export @eval :evala + @public @eval :evalb + + @export function funca(x) + x^2 + end + @public function funcb(x) + x^3 + end + + @export begin + "`const a` doc" + const a = 2 + "`abstract type S` doc" + abstract type S <: Number end + "`struct T` doc" + struct T <: S + val + end + end + """ + f(x) + + Here a doc! + """ + @export f(x::TT) where {TT<:S} = x.val^2 + + @public begin + "`const b` doc" + const b = 3 + "`abstract type U` doc" + abstract type U <: Number end + "`struct V` doc" + struct V <: U + val + end + end + """ + g(x) + + There a doc! + """ + @public g(x::VV) where {VV<:U} = x.val^3 + + begin + "`const c` doc" + const c = 5 + "`abstract type W` doc" + abstract type W <: Number end + "`struct X` doc" + struct X <: W + val + end + end + """ + h(x) + + Everywhere a doc, doc! + """ + h(x::XX) where {XX<:W} = x.val^5 + + end # module Bla + + using .Bla + + @test (@macroexpand @garble x=3) == :(x=3) + @test (@macroexpand Bla.@gorble y=4) == :(y=4) + + @test m isa Int + @test m == 3 + @test Bla.n isa Int + @test Bla.n == 4 + + # @test hasproperty(Bla, :evala) + # @test hasproperty(Bla, :evalb) + + @test funca(3) == 9 + @test Bla.funcb(3) == 27 + + @test f(T(a)) == 4 + @test Bla.g(Bla.V(Bla.b)) == 27 + @test Bla.h(Bla.X(Bla.c)) == 3125 + + @test Base.isexported(Bla, :a) + @test Base.isexported(Bla, :S) + @test Base.isexported(Bla, :T) + @test Base.isexported(Bla, :f) + @test !Base.isexported(Bla, :b) + @test !Base.isexported(Bla, :U) + @test !Base.isexported(Bla, :V) + @test !Base.isexported(Bla, :g) + @test !Base.isexported(Bla, :c) + @test !Base.isexported(Bla, :W) + @test !Base.isexported(Bla, :X) + @test !Base.isexported(Bla, :h) + + @test Base.ispublic(Bla, :a) + @test Base.ispublic(Bla, :S) + @test Base.ispublic(Bla, :T) + @test Base.ispublic(Bla, :f) + @test Base.ispublic(Bla, :b) + @test Base.ispublic(Bla, :U) + @test Base.ispublic(Bla, :V) + @test Base.ispublic(Bla, :g) + @test !Base.ispublic(Bla, :c) + @test !Base.ispublic(Bla, :W) + @test !Base.ispublic(Bla, :X) + @test !Base.ispublic(Bla, :h) + + @test Base.hasproperty(Bla, :a) + @test Base.hasproperty(Bla, :S) + @test Base.hasproperty(Bla, :T) + @test Base.hasproperty(Bla, :f) + @test Base.hasproperty(Bla, :b) + @test Base.hasproperty(Bla, :U) + @test Base.hasproperty(Bla, :V) + @test Base.hasproperty(Bla, :g) + # @test Base.hasproperty(Bla, :c) # This group evaluates to false for some reason! + # @test Base.hasproperty(Bla, :W) # But that's true even for modules that have nothing + # @test Base.hasproperty(Bla, :X) # to do with `InlineExports`?! + # @test Base.hasproperty(Bla, :h) # Anyway, we used them in tests above... 🤷 + + @test repr(@doc(Bla.a)) == "`const a` doc\n" + @test repr(@doc(Bla.b)) == "`const b` doc\n" + @test repr(@doc(Bla.c)) == "`const c` doc\n" + @test repr(@doc(Bla.S)) == "`abstract type S` doc\n" + @test repr(@doc(Bla.U)) == "`abstract type U` doc\n" + @test repr(@doc(Bla.W)) == "`abstract type W` doc\n" + @test repr(@doc(Bla.T)) == "`struct T` doc\n" + @test repr(@doc(Bla.V)) == "`struct V` doc\n" + @test repr(@doc(Bla.X)) == "`struct X` doc\n" + @test repr(@doc(Bla.f)) == """```\nf(x)\n```\n\nHere a doc!\n""" + @test repr(@doc(Bla.g)) == """```\ng(x)\n```\n\nThere a doc!\n""" + @test repr(@doc(Bla.h)) == """```\nh(x)\n```\n\nEverywhere a doc, doc!\n""" +end diff --git a/src/core/utilities/misc.jl b/src/core/utilities/misc.jl new file mode 100644 index 00000000..189ba40a --- /dev/null +++ b/src/core/utilities/misc.jl @@ -0,0 +1,134 @@ +# Declared public in src/PostNewtonian.jl +@irrational ζ3 1.2020569031595942 big"1.20205690315959428539973816151144999076498629234049888179227155534183820578631309018645587360933525814619915" +""" + ζ3 + apery + +[Apéry's constant](https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_constant) is +defined as ``ζ(3)``, where ``ζ`` is the Riemann zeta function. This is OEIS +sequence [A002117](https://oeis.org/A002117). + +```julia-repl +julia> PostNewtonian.apery +ζ3 = 1.2020569031595... + +julia> PostNewtonian.ζ3 +ζ3 = 1.2020569031595... + +julia> sum((1:10_000_000).^-3) +1.2020569031595896 +``` +""" +ζ3 # We document it this way because `@irrational` cannot handle docstrings. + +# Declared public in src/PostNewtonian.jl +@doc raw""" + γₑ + +[Euler's constant](https://en.wikipedia.org/wiki/Euler%27s_constant) (also known as the +Euler–Mascheroni constant) is defined as the limit as ``n \to \infty`` of the difference +between the ``n``th partial sum of the harmonic series and ``\log(n)``. This is OEIS +sequence [A001620](https://oeis.org/A001620). + +This is distinct from the Euler's *number* ``e``, which is defined as the limit as ``n \to +\infty`` of the sum of ``1/n!``. + +Note that it is usually denoted simply as `γ` in the broader literature (and in Julia's own +`Base.MathConstants`), but that symbol is used in the post-Newtonian literature for the +quantity denoted in this package as [`γₚₙ`](@ref). To distinguish between the two, the PN +literature uses ``\gamma_\mathrm{E}`` for Euler's constant. (There is no Unicode subscript +"E", so we use "e" instead.) + +```julia-repl +julia> PostNewtonian.γₑ +γₑ = 0.5772156649015... + +julia> n=10_000_000; sum(1 ./ (1:n))-log(n) +0.5772157149015307 +``` +""" +γₑ # We document it here because docs don't fit nicely in the main file where it's defined. + +""" + value(x) + +Return `x` or the value wrapped by the `Dual` number `x` +""" +@public value(x::T) where {T} = hasfield(T, :value) ? getfield(x, :value) : x + +""" + iscall(x, symbols) + +Return `true` if the `Expr` `x` is a call to any element of `symbols`. +""" +iscall(x, symbols) = MacroTools.isexpr(x, :call) && x.args[1] ∈ symbols + +""" + isadd(x) + +Return `true` if the `Expr` `x` is a call to `(+)` or `:+`. +""" +isadd(x) = iscall(x, ((+), :+)) + +""" + ismul(x) + +Return `true` if the `Expr` `x` is a call to `(*)` or `:*`. +""" +ismul(x) = iscall(x, ((*), :*)) + +@testitem "core.misc" begin + using DoubleFloats + using ForwardDiff: Dual + using PostNewtonian: ζ3, γₑ, value, iscall, isadd, ismul + + # ζ3 formula + @test ζ3 ≈ sum((1:10_000_000) .^ -3) + + # γₑ formula + N = 10_000_000 + δγₑ = 1/2N + @test γₑ ≈ sum(1 ./ (1:N)) - log(N) - δγₑ + + # value + struct Dummy + value + end + struct Dummier + valuet + end + for T ∈ (Float16, Float32, Float64, Double16, Double32, Double64, BigFloat) + x = T(big"1.2") + @test value(x) isa T + @test value(x) == x + d = Dummy(x) + @test value(d) isa T + @test value(d) == x + dr = Dummier(x) + @test value(dr) isa Dummier + @test value(dr) == dr + v = (T(big"3.4"), T(big"5.6"), T(big"7.8")) + for i ∈ eachindex(v) + ẋ = Dual{:Taggo}(x, v[begin:i]) + @test value(ẋ) isa T + @test value(ẋ) == x + end + end + + # iscall and friends + @test iscall(:(log(1.2)), (:log,)) + @test iscall(:(log(1.2)), (:log, :sin)) + @test !iscall(:(log(1.2)), (:sin,)) + @test isadd(:(1 + 2)) + @test isadd(:(1 + 2c + 3c^2)) + @test isadd(:(1 + (2n + 3m))) + @test isadd(Expr(:call, :+, 1, 2)) + @test isadd(Expr(:call, (+), 1, 2)) + @test !isadd(:(1 * 2)) + @test ismul(:(1 * 2)) + @test ismul(:(1 * 2c * 3c^2)) + @test ismul(:(1 * (2c * 3d))) + @test ismul(Expr(:call, :*, 1, 2)) + @test ismul(Expr(:call, (*), 1, 2)) + @test !ismul(:(1 + 2)) +end diff --git a/src/utilities/truncated_series_inversion.jl b/src/core/utilities/truncated_series_inversion.jl similarity index 98% rename from src/utilities/truncated_series_inversion.jl rename to src/core/utilities/truncated_series_inversion.jl index 31eaa50b..48265f71 100644 --- a/src/utilities/truncated_series_inversion.jl +++ b/src/core/utilities/truncated_series_inversion.jl @@ -16,7 +16,7 @@ This function is essentially a helper function for the [`lagrange_inversion`](@r function. """ -function x╱f_mod_xⁿ⁻¹(a::NTuple{N,T}) where {N,T} +@public function x╱f_mod_xⁿ⁻¹(a::NTuple{N,T}) where {N,T} b = zeros(MVector{N,typeof(inv(a[1]))}) b[1] = inv(a[1]) for i ∈ 2:N @@ -113,7 +113,7 @@ This function is essentially a helper function for the [`lagrange_inversion`](@r function. """ -function hⁱ✖h_mod_xⁿ⁻¹(hⁱ::NTuple{N,T}, h::NTuple{N,T}) where {N,T} +@public function hⁱ✖h_mod_xⁿ⁻¹(hⁱ::NTuple{N,T}, h::NTuple{N,T}) where {N,T} hⁱ⁺¹ = zeros(MVector{N,T}) for i ∈ 1:N hⁱ⁺¹[i] = sum((hⁱ[j] * h[i - j + 1] for j ∈ 1:i)) @@ -394,7 +394,7 @@ actually be beneficial in practice, so we stick with the basic algorithm here would not be too difficult to implement if needed. """ -function lagrange_inversion(a::NTuple{N,T}) where {N,T} +@public function lagrange_inversion(a::NTuple{N,T}) where {N,T} h = x╱f_mod_xⁿ⁻¹(a) f⁻¹ = zeros(MVector{N,typeof(h[end] / 2)}) hⁱ = h # Create storage for the loop diff --git a/src/core/utilities/truncated_series_monoid.jl b/src/core/utilities/truncated_series_monoid.jl new file mode 100644 index 00000000..c23ec022 --- /dev/null +++ b/src/core/utilities/truncated_series_monoid.jl @@ -0,0 +1,294 @@ +@doc raw""" + truncated_series_inverse(a) + truncated_series_inverse!(b, a) + +Given the coefficients `a` of a series, find the coefficients `b` of the *multiplicative* +inverse of that series, up to the order of the original series. That is, if +```math +A \colonequals \sum_{i=0}^n a_{i} v^i, +``` +then we return the coefficients `b` of the series +```math +B \colonequals \sum_{i=0}^n b_{i} v^i +``` +such that +```math +A\, B = 1 + \mathcal{O}(v^{n+1}). +``` + +See [`lagrange_inversion`](@ref) for the *compositional* inverse (a.k.a. reversion), which +returns the coefficients of ``f^{-1}`` such that ``f^{-1}(f(v)) = v + +\mathcal{O}(v^{n+1})``. + +Note that this function returns the *coefficients* of the inverse, rather than its value. +This is relevant for use in [`truncated_series_product`](@ref) and +[`truncated_series_ratio`](@ref) — the latter of which just combines the former with this +function. + +!!! note + + This function requires that the constant term (`a[1]`) be nonzero. If you have a series + that starts at a higher term — say, ``v^n`` for ``n>0`` — you should factor out the + ``v^n``, and multiply the series resulting from this function by ``v^{-n}``. + +## Explanation + +The inverse coefficients can be computed fairly easily by induction. Start by defining +```math +b_0 = 1/a_0. +``` +Now, assuming that we've computed all coefficients up to and including ``b_{i}``, we can +compute ``b_{i+1}`` from the condition that the term proportional to ``v^{i+1}`` in the +product of the series and its inverse must be zero. That coefficient of that term is +clearly given by the sum of all pairs of coefficients ``a_j b_{i+1-j}`` for +``j=0,1,\ldots,i+1``: +```math +\sum_{j=0}^{i+1} a_j b_{i+1-j} = a_0 b_{i+1} + \sum_{j=1}^{i+1} a_j b_{i+1-j}. +``` +Setting this last expression to zero, using the value of ``b_0`` above, and rearranging, we +have +```math +b_{i+1} = -b_0\sum_{j=1}^{i} a_j b_{i+1-j}. +``` +""" +@public function truncated_series_inverse(a::AbstractVector) + b = similar(a) + return truncated_series_inverse!(b, a) +end + +function truncated_series_inverse(a::NTuple{N,T}) where {N,T} + b = MVector{N,T}(undef) + truncated_series_inverse!(b, SVector{N,T}(a)) + return Tuple(b) +end + +@public function truncated_series_inverse!(b, a) + # We fake 0-based indexing by using `begin + i` for `i ∈ 0:n`. + @assert length(b) == length(a) + n = length(a) - 1 + @inbounds @fastmath if n ≥ 0 + b[begin + 0] = inv(a[begin + 0]) + end + @inbounds @fastmath for i ∈ 0:(n - 1) + b[begin + i + 1] = + -b[begin + 0] * sum( + (a[begin + j] * b[begin + i + 1 - j] for j ∈ 1:(i + 1)); + init=zero(eltype(a)), + ) + end + return b +end + +@doc raw""" + truncated_series_product(a, b, v) + +Evaluate the truncated product of the series `a` and `b`, which are expanded in powers of +`v`. + +Note that this function returns the *value* of the summation, rather than its coefficients. + +Here we define the series in terms of the coefficients `a` and `b` as +```math +A \colonequals \sum_{i=0}^n a_{i} v^i +\qquad +B \colonequals \sum_{i=0}^n b_{i} v^i, +``` +and return the *value* of the product ``A\, B`` truncated at ``v^n``. + +Internally, the sums are performed using `evalpoly`. + +See also [`truncated_series_ratio`](@ref). +""" +@public function truncated_series_product(a, b, v) + @assert length(a) == length(b) + N = length(a) - 1 + if N < 0 + return zero(v) + end + AB = b[begin + N] * a[begin + 0] + for n ∈ (N - 1):-1:0 + AB = muladd( + v, AB, b[begin + n] * evalpoly(v, @view a[(begin + 0):(begin + (N - n))]) + ) + end + return AB +end + +function truncated_series_product(a::NTuple{NT,T}, b, v) where {NT,T} + @assert length(a) == length(b) + N = length(a) - 1 + if N < 0 + return zero(v) + end + AB = b[begin + N] * a[begin + 0] + for n ∈ (N - 1):-1:0 + AB = muladd(v, AB, b[begin + n] * evalpoly(v, a[(begin + 0):(begin + (N - n))])) + end + return AB +end + +@doc raw""" + truncated_series_ratio(a, b, v) + +Evaluate the truncated ratio of the series `a` and `b`, which are expanded in powers of `v`. + +Note that this function returns the *value* of the summation, rather than its coefficients. + +Here we define the series in terms of the coefficients `a` and `b` as +```math +A \colonequals \sum_{i=0}^n a_{i} v^i +\qquad +B \colonequals \sum_{i=0}^n b_{i} v^i, +``` +and return the *value* of the ratio ``A / B`` truncated at ``v^n``. + +This function simply combines [`truncated_series_product`](@ref) and +[`truncated_series_inverse`](@ref). +""" +@public function truncated_series_ratio(a, b, v) + return truncated_series_product(a, truncated_series_inverse(b), v) +end + +@doc raw""" + truncated_series_ratio(a, b) + +Evaluate the truncated ratio of the series `a` and `b` at expansion value 1. + +This is relevant when the expansion is not in the dynamic variable `v`, for example, but in +powers of ``1/c`` as in post-Newtonian expansions. (That is, when the `v` dependence is +already included in the input coefficients.) + +This is different from `truncated_series_ratio(a, b, 1)` in that `a` and `b` may have +different lengths, and it should be somewhat more efficient. +""" +function truncated_series_ratio(a::NTuple{N1,T1}, b::NTuple{N2,T2}) where {N1,N2,T1,T2} + if N1 == 0 && N2 == 0 + throw( + ArgumentError( + "In `truncated_series_ratio(a,b)`, both arguments have length 0; " * + "this is not allowed.", + ), + ) + end + if N2 == 0 + throw( + ArgumentError( + "In `truncated_series_ratio(a,b)`, argument `b` has length 0; " * + "this is not allowed.", + ), + ) + end + if N1 == 0 + return zero(T2) + end + + N = max(N1, N2) + T = promote_type(T1, T2) + + # The uppercase `N`s represent the number of terms in the tuples, while the lowercase + # `n`s represent the highest index of the terms. + n1, n2, n = N1 - 1, N2 - 1, N - 1 + + # Next, we compute the same thing as `truncated_series_inverse` except that we truncate + # this inverse series at `n`, instead of `n2`. Specifically, the differences are that + # (1) the range of iteration over `i` extends to `(n-1)` instead of `(n2-1)`, and (2) + # the range of iteration over `j` extends to `min(i+1, n2)` instead of `(i+1)`. + b⁻¹ = MVector{N,T}(undef) + @inbounds @fastmath begin + b⁻¹[begin + 0] = inv(b[begin + 0]) + for i ∈ 0:(n - 1) + b⁻¹[begin + i + 1] = + -b⁻¹[begin + 0] * sum( + (b[begin + j] * b⁻¹[begin + i + 1 - j] for j ∈ 1:min((i + 1), n2)); + init=zero(T), + ) + end + + # Now, we do the same thing as `truncated_series_product`, except that we account + # for the fact that `a` may not be as long as `b⁻¹`, and we are assuming `v=1`. + a╱b = zero(T) + for i1 ∈ 0:n1 + a╱b += a[begin + i1] * sum((b⁻¹[begin + i2] for i2 ∈ 0:(n - i1)); init=zero(T)) + end + a╱b + end +end + +@testitem "truncated_series_ratio(a,b)" begin + using Random + using DoubleFloats + using StaticArrays: SVector + import PostNewtonian: + truncated_series_inverse, truncated_series_ratio, truncated_series_product + Random.seed!(123) + + # truncated_series_product tests + # N < 0, empty vectors => always zero + @test truncated_series_product((), (), 3.14) == 0.0 + @test truncated_series_product(Float64[], Float64[], 3.14) == 0.0 + + # N = 0, single‐term series => a0*b0 + a0, b0 = 2.5, -1.5 + @test truncated_series_product([a0], [b0], 42) == a0 * b0 + + # N = 1, two‐term series with vector inputs + a = [1.0, 2.0] # 1 + 2v + b = [3.0, 4.0] # 3 + 4v + v = 5.0 + # (1 + 2v)*(3 + 4v) = 3 + (6+4)v + ··, truncate ⇒ 3 +10⋅5 = 53 + @test truncated_series_product(a, b, v) == 53.0 + + # same with tuple dispatch + @test truncated_series_product(Tuple(a), Tuple(b), v) == 53.0 + + # truncated_series_ratio edge cases + # N2 == 0 (empty b) must throw ArgumentError + a = (1.0, 2.0, 3.0) + a_empty = () + b_empty = () + @test_throws ArgumentError truncated_series_ratio(a, b_empty) + @test_throws ArgumentError truncated_series_ratio(a_empty, b_empty) + + # N1 == 0 (empty a) returns zero of promoted type + a_empty = () + b = (5, -2) + @test truncated_series_ratio(a_empty, b) ≡ + zero(promote_type(eltype(a_empty), eltype(b))) + + for T ∈ [Float32, Float64, Double64] + for N ∈ 1:15 + A = rand(T, N) + A[1] = one(T) + rand(T) / 100 + local a = Tuple(A) + x = rand(T) + ϵ = eps(sum(a) * N) + for N1 ∈ 1:N + expected = sum(truncated_series_inverse(a)) + unit = zeros(T, N1) + unit[1] = one(T) + @test truncated_series_ratio(Tuple(unit), a) ≈ expected rtol = ϵ + end + @test truncated_series_ratio(a, a) ≈ 1 rtol = ϵ + @test truncated_series_ratio(a, x .* a) ≈ 1 / x rtol = ϵ + @test truncated_series_ratio(x .* a, a) ≈ x rtol = ϵ + + c = Tuple(rand(T, N)) + @test truncated_series_ratio(c, a) ≈ + truncated_series_ratio(SVector(c), SVector(a), 1) rtol = ϵ + + for Nzero ∈ 2:N + cshort = c[begin:(Nzero - 1)] + czeros = (cshort..., (zero(T) for i ∈ Nzero:N)...) + #! format: off + @test truncated_series_ratio(cshort, a) ≈ + truncated_series_ratio(czeros, a) atol=2eps(T) rtol=2eps(T) + + ashort = a[begin:(Nzero - 1)] + azeros = (ashort..., (zero(T) for i ∈ Nzero:N)...) + @test truncated_series_ratio(c, ashort) ≈ + truncated_series_ratio(c, azeros) atol=2eps(T) rtol=2eps(T) + #! format: on + end + end + end +end diff --git a/src/derived_variables.jl b/src/derived_variables.jl deleted file mode 100644 index 9091c887..00000000 --- a/src/derived_variables.jl +++ /dev/null @@ -1,81 +0,0 @@ -module DerivedVariables - -using ..PostNewtonian: VecOrPNSystem -using ..PostNewtonian.FundamentalVariables -using Quaternionic: 𝐢, 𝐣, 𝐤, QuatVec, ⋅, ×, abs2vec, absvec - -include("derived_variables/mass_combinations.jl") -export total_mass, - M, - reduced_mass, - μ, - reduced_mass_ratio, - ν, - mass_difference_ratio, - δ, - mass_ratio, - q, - chirp_mass, - ℳ, - X1, - X₁, - X2, - X₂ - -include("derived_variables/orbital_elements.jl") -export n_hat, n̂, lambda_hat, λ̂, ell_hat, ℓ̂, Omega, Ω, lnv - -include("derived_variables/spin_combinations.jl") -export S⃗₁, - S⃗₂, - S⃗, - Σ⃗, - χ⃗, - χ⃗ₛ, - χ⃗ₐ, - chi_perp, - χₚₑᵣₚ, - χₑ, - chi_eff, - χₚ, - chi_p, - S⃗₀⁺, - S⃗₀⁻, - S₀⁺ₙ, - S₀⁻ₙ, - S₀⁺λ, - S₀⁻λ, - S₀⁺ₗ, - S₀⁻ₗ, - χ₁², - χ₂², - χ₁, - χ₂, - χ₁₂, - χ₁ₗ, - χ₂ₗ, - χₛₗ, - χₐₗ, - Sₙ, - Σₙ, - Sλ, - Σλ, - Sₗ, - Σₗ, - sₗ, - σₗ, - S₁ₙ, - S₁λ, - S₁ₗ, - S₂ₙ, - S₂λ, - S₂ₗ - -include("derived_variables/horizons.jl") -export rₕ₁, - rₕ₂, Ωₕ₁, Ωₕ₂, sin²θ₁, sin²θ₂, ϕ̇̂₁, ϕ̇̂₂, Î₀₁, Î₀₂, κ₁, κ₂, κ₊, κ₋, λ₁, λ₂, λ₊, λ₋ - -include("derived_variables/tidal_coupling.jl") -export Λ̃, Lambda_tilde - -end diff --git a/src/dynamics.jl b/src/dynamics.jl deleted file mode 100644 index e03d7e17..00000000 --- a/src/dynamics.jl +++ /dev/null @@ -1,3 +0,0 @@ -include("dynamics/up_down_instability.jl") -include("dynamics/right_hand_sides.jl") -include("dynamics/orbital_evolution.jl") diff --git a/src/fundamental_variables.jl b/src/fundamental_variables.jl deleted file mode 100644 index db75b10d..00000000 --- a/src/fundamental_variables.jl +++ /dev/null @@ -1,163 +0,0 @@ -module FundamentalVariables - -using ..PostNewtonian -using ..PostNewtonian: PNSystem, BHNS, NSNS, FDPNSystem -using ..PostNewtonian: M₁index, M₂index, χ⃗₁indices, χ⃗₂indices, Rindices, vindex, Φindex -using Quaternionic: Quaternionic, QuatVec, Rotor - -export M₁, M₂, χ⃗₁, χ⃗₂, R, v, Φ, Λ₁, Λ₂, M1, M2, chi1, chi2, Phi, Lambda1, Lambda2 - -## NOTE: -## This indices used below are intimately bound to choices made in the definitions of -## the various `PNSystem`s. Any changes there must be mirrored here, and vice versa. - -""" - M₁(pnsystem) - M1(pnsystem) - -Mass of object 1 in this system. -""" -M₁(s::PNSystem) = M₁(s.state) -M₁(state::AbstractVector) = @inbounds state[M₁index] -const M1 = M₁ - -""" - M₂(pnsystem) - M2(pnsystem) - -Mass of object 2 in this system. -""" -M₂(s::PNSystem) = M₂(s.state) -M₂(state::AbstractVector) = @inbounds state[M₂index] -const M2 = M₂ - -""" - χ⃗₁(pnsystem) - chi1(pnsystem) - -Dimensionless spin vector of object 1 in this system, as a `QuatVec`. -""" -χ⃗₁(s::PNSystem) = χ⃗₁(s.state) -χ⃗₁(state::AbstractVector) = @inbounds QuatVec(view(state, χ⃗₁indices)...) -const chi1 = χ⃗₁ - -""" - χ⃗₂(pnsystem) - chi2(pnsystem) - -Dimensionless spin vector of object 2 in this system, as a `QuatVec`. -""" -χ⃗₂(s::PNSystem) = χ⃗₂(s.state) -χ⃗₂(state::AbstractVector) = @inbounds QuatVec(view(state, χ⃗₂indices)...) -const chi2 = χ⃗₂ - -""" - R(pnsystem) - -Orientation of the binary, as a `Rotor`. - -At any instant, the binary is represented by the right-handed triad ``(n̂, λ̂, ℓ̂)``, where -[``n̂``](@ref PostNewtonian.n̂) is the unit vector pointing from object 2 to object 1, and -the instantaneous velocities of the binary's elements are in the ``n̂``-``λ̂`` plane. This -`Rotor` will rotate the ``x̂`` vector to be along ``n̂``, the ``ŷ`` vector to be along -``λ̂``, and the ``ẑ`` vector to be along ``ℓ̂``. - -Note that the angular velocity associated to `R` is given by ``Ω⃗ = 2 Ṙ R̄ = Ω ℓ̂ + ϖ n̂``. -(Any component of ``Ω⃗`` along ``λ̂`` would violate the condition that the velocities be in -the ``n̂``-``λ̂`` plane.) Here, the scalar quantity ``Ω`` is the orbital angular frequency, -and ``ϖ`` is the precession angular frequency. - -See also [`n̂`](@ref PostNewtonian.n̂), [`λ̂`](@ref PostNewtonian.λ̂), [`ℓ̂`](@ref -PostNewtonian.ℓ̂), [`Ω`](@ref PostNewtonian.Ω), and [`𝛡`](@ref PostNewtonian.𝛡)``=ϖ n̂``. -""" -R(s::PNSystem) = R(s.state) -R(state::AbstractVector) = @inbounds Rotor(view(state, Rindices)...) - -@doc raw""" - v(pnsystem) - v(;Ω, M=1) - -Post-Newtonian velocity parameter. This is related to the orbital angular frequency -``\Omega`` as -```math -v \colonequals (M\,\Omega)^{1/3}, -``` -where ``M`` is the total mass of the binary. - -Note that if you want to pass the value ``Ω`` (rather than a `PNSystem`), you must pass it -as a keyword argument — as in `v(Ω=0.1)`. - -See also [`Ω`](@ref). -""" -v(s::PNSystem) = v(s.state) -v(state::AbstractVector) = @inbounds state[vindex] -v(; Ω, M=1) = ∛(M * Ω) - -""" - Φ(pnsystem) - Phi(pnsystem) - -Integrated orbital phase of the system. It is computed as the integral of [`Ω`](@ref). -""" -Φ(s::PNSystem) = Φ(s.state) -Φ(state::AbstractVector) = @inbounds state[Φindex] -const Phi = Φ - -@doc raw""" - Λ₁(pnsystem) - Lambda1(pnsystem) - -Quadrupolar tidal-coupling parameter of object 1 in this system. - -We imagine object 1 begin placed in an (adiabatic) external field with Newtonian potential -``\phi``, resulting in a tidal field measured by ``\partial_i \partial_j \phi`` evaluated at -the center of mass of the object. This induces a quadrupole moment ``Q_{ij}`` in object 1, -which can be related to the tidal field as -```math -Q_{ij} = -\frac{G^4}{c^{10}} \Lambda_1 M_1^5 \partial_i \partial_j \phi, -``` -where ``M_1`` is the mass of object 1. This tidal-coupling parameter ``\Lambda_1`` can be -related to the Love number ``k_2`` (where the subscript 2 refers to the fact that this is -for the ``\ell=2`` quadrupole, rather than object 2) as -```math -\Lambda_1 = \frac{2}{3} \frac{c^{10}}{G^5} \frac{R_1^5}{M_1^5} k_2, -``` -where ``R_1`` is the radius of object 1. Note that ``\Lambda_1`` is dimensionless. For -black holes, it is precisely zero; for neutron stars it may range up to 1; more exotic -objects may have significantly larger values. - -Note that — as of this writing — only `NSNS` systems can have a nonzero value for this -quantity. (`BHNS` systems can only have a nonzero value for ``\Lambda_2``.) All other -types return `0`, which Julia can use to eliminate code that would then be 0. Thus, it is -safe and efficient to use this quantity in any PN expression that specializes on the type of -`pnsystem`. - -See also [`Λ₂`](@ref) and [`Λ̃`](@ref). -""" -Λ₁(pn::PNSystem) = zero(eltype(pn)) -Λ₁(pn::NSNS) = pn.Λ₁ -Λ₁(pn::FDPNSystem) = pn.Λ₁ -const Lambda1 = Λ₁ - -@doc raw""" - Λ₂(pnsystem) - Lambda2(pnsystem) - -Quadrupolar tidal coupling parameter of object 2 in this system. - -See [`Λ₁`](@ref) for details about the definition, swapping "object 1" with "object 2". - -Note that — as of this writing — only `BHNS` and `NSNS` systems can have a nonzero value for -this quantity. All other types return `0`, which Julia can use to eliminate code that would -then be 0. Thus, it is safe and efficient to use this quantity in any PN expression that -specializes on the type of `pnsystem`. - -See also [`Λ₁`](@ref) and [`Λ̃`](@ref). -""" -Λ₂(pn::PNSystem) = zero(eltype(pn)) -Λ₂(pn::BHNS) = pn.Λ₂ -Λ₂(pn::NSNS) = pn.Λ₂ -Λ₂(pn::FDPNSystem) = pn.Λ₂ -const Lambda2 = Λ₂ - -end diff --git a/src/assorted_binaries/examples.jl b/src/interface/assorted_binaries/examples.jl similarity index 100% rename from src/assorted_binaries/examples.jl rename to src/interface/assorted_binaries/examples.jl diff --git a/src/assorted_binaries/random.jl b/src/interface/assorted_binaries/random.jl similarity index 100% rename from src/assorted_binaries/random.jl rename to src/interface/assorted_binaries/random.jl diff --git a/src/compatibility_layers/gwframes.jl b/src/interface/compatibility_layers/gwframes.jl similarity index 98% rename from src/compatibility_layers/gwframes.jl rename to src/interface/compatibility_layers/gwframes.jl index ad848c38..343bca4d 100644 --- a/src/compatibility_layers/gwframes.jl +++ b/src/interface/compatibility_layers/gwframes.jl @@ -231,8 +231,8 @@ function PNWaveform( frame=transpose(stack(solution[[:Rʷ, :Rˣ, :Rʸ, :Rᶻ]])), M1=solution[:M₁], M2=solution[:M₂], - chi1=transpose(stack(solution[[:χ⃗₁ˣ, :χ⃗₁ʸ, :χ⃗₁ᶻ]])), - chi2=transpose(stack(solution[[:χ⃗₂ˣ, :χ⃗₂ʸ, :χ⃗₂ᶻ]])), + chi1=transpose(stack(solution[[:χ₁ˣ, :χ₁ʸ, :χ₁ᶻ]])), + chi2=transpose(stack(solution[[:χ₂ˣ, :χ₂ʸ, :χ₂ᶻ]])), v=solution[:v], Phi=solution[:Φ], ) diff --git a/src/utilities/combine_solutions.jl b/src/interface/dynamics/combine_solutions.jl similarity index 100% rename from src/utilities/combine_solutions.jl rename to src/interface/dynamics/combine_solutions.jl diff --git a/src/dynamics/orbital_evolution.jl b/src/interface/dynamics/orbital_evolution.jl similarity index 98% rename from src/dynamics/orbital_evolution.jl rename to src/interface/dynamics/orbital_evolution.jl index 19d7af07..684a9883 100644 --- a/src/dynamics/orbital_evolution.jl +++ b/src/interface/dynamics/orbital_evolution.jl @@ -227,12 +227,12 @@ The evolved variables, in order, are * `M₁`: Mass of black hole 1 * `M₂`: Mass of black hole 2 - * `χ⃗₁ˣ`: ``x`` component of dimensionless spin of black hole 1 - * `χ⃗₁ʸ`: ``y`` component... - * `χ⃗₁ᶻ`: ``z`` component... - * `χ⃗₂ˣ`: ``x`` component of dimensionless spin of black hole 2 - * `χ⃗₂ʸ`: ``y`` component... - * `χ⃗₂ᶻ`: ``z`` component... + * `χ₁ˣ`: ``x`` component of dimensionless spin of black hole 1 + * `χ₁ʸ`: ``y`` component... + * `χ₁ᶻ`: ``z`` component... + * `χ₂ˣ`: ``x`` component of dimensionless spin of black hole 2 + * `χ₂ʸ`: ``y`` component... + * `χ₂ᶻ`: ``z`` component... * `Rʷ`: Scalar component of frame rotor * `Rˣ`: ``x`` component... * `Rʸ`: ``y`` component... diff --git a/src/dynamics/right_hand_sides.jl b/src/interface/dynamics/right_hand_sides.jl similarity index 96% rename from src/dynamics/right_hand_sides.jl rename to src/interface/dynamics/right_hand_sides.jl index b221da22..fa783fca 100644 --- a/src/dynamics/right_hand_sides.jl +++ b/src/interface/dynamics/right_hand_sides.jl @@ -37,12 +37,12 @@ end Ṙ = Ω⃗ * R / 2 u̇[M₁index] = Ṁ₁ u̇[M₂index] = Ṁ₂ - u̇[χ⃗₁ˣindex] = χ⃗̇₁.x - u̇[χ⃗₁ʸindex] = χ⃗̇₁.y - u̇[χ⃗₁ᶻindex] = χ⃗̇₁.z - u̇[χ⃗₂ˣindex] = χ⃗̇₂.x - u̇[χ⃗₂ʸindex] = χ⃗̇₂.y - u̇[χ⃗₂ᶻindex] = χ⃗̇₂.z + u̇[χ₁ˣindex] = χ⃗̇₁.x + u̇[χ₁ʸindex] = χ⃗̇₁.y + u̇[χ₁ᶻindex] = χ⃗̇₁.z + u̇[χ₂ˣindex] = χ⃗̇₂.x + u̇[χ₂ʸindex] = χ⃗̇₂.y + u̇[χ₂ᶻindex] = χ⃗̇₂.z u̇[Rʷindex] = Ṙ.w u̇[Rˣindex] = Ṙ.x u̇[Rʸindex] = Ṙ.y diff --git a/src/utilities/termination_criteria.jl b/src/interface/dynamics/termination_criteria.jl similarity index 100% rename from src/utilities/termination_criteria.jl rename to src/interface/dynamics/termination_criteria.jl diff --git a/src/dynamics/up_down_instability.jl b/src/interface/dynamics/up_down_instability.jl similarity index 100% rename from src/dynamics/up_down_instability.jl rename to src/interface/dynamics/up_down_instability.jl diff --git a/src/interface/interface.jl b/src/interface/interface.jl new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/src/interface/interface.jl @@ -0,0 +1 @@ + diff --git a/src/interface/orbital_evolution.jl b/src/interface/orbital_evolution.jl new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/src/interface/orbital_evolution.jl @@ -0,0 +1 @@ + diff --git a/src/interface/pn.jl b/src/interface/pn.jl new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/src/interface/pn.jl @@ -0,0 +1 @@ + diff --git a/src/waveforms.jl b/src/interface/waveform.jl similarity index 100% rename from src/waveforms.jl rename to src/interface/waveform.jl diff --git a/src/literature/Blanchet2024.jl b/src/literature/Blanchet2024.jl new file mode 100644 index 00000000..95db07a2 --- /dev/null +++ b/src/literature/Blanchet2024.jl @@ -0,0 +1,81 @@ +@doc raw""" +Expressions from [Blanchet2024](@cite) + +This package mostly derives its notation from that paper. The main exception is that +Blanchet uses the symbol ``m`` for mass and ``\mathup{M}`` for ADM mass, while we reserve +``m`` for the azimuthal number of spin-weighted spherical harmonics, and use ``M`` for mass +instead. (ADM mass does not appear in this package as of this writing.) + +In Sec. 3.2.4, Blanchet defines the total mass ``m=m₁+m₂``, the relative mass difference +``\Delta = (m₁ - m₂) / m``, the reduced mass ``μ = m₁ m₂ / m``, and the symmetric mass ratio +``ν ≡ \mu/m = m₁ m₂ / m²``. He also poses ``X₁ = m₁ / m`` and ``X₂ = m₂ / m`` so that ``Δ = +X₁ - X₂`` and ``ν = X₁ X₂``. + +In Eq. (369), he defines +```math +\gamma = \frac{GM}{rc^2}. +``` + +In Eq. (375), he defines the "frequency-related parameter" +```math +x = \left(\frac{GM\Omega}{c^3}\right)^{2/3}, +``` +Note that this ``\Omega`` is "the orbital frequency [...] of the circular orbit as measured +by a distant observer." He does not define this completely, except to say that it is the +frequency associated with the asymptotic Killing vector field "in any natural coordinate +system which respects the helical symmetry" for an idealized circular system. + +[Trestini2025](@cite) describes roughly the same frequency as the "waveform frequency" Ω, +and uses "orbital frequency" ω to refer to — presumably — the coordinate frequency. + +""" +@pn_reference module Blanchet2024 + +import PostNewtonian: G, c, x, ν, γₑ + +""" + Eq483(pnsystem) + +Quasi-circular non-spinning 4.5PN energy flux terms. + +As given in Eq. (483) of [Blanchet2024](@cite), this expression includes "contributions from +tails, iterated tails, and tails-of-memory", but no contributions from spin. + +""" +@pn_expression function Eq483(pnsystem) + ℱ = + (32c^5 / 5G * ν * x^5) * @pn_expansion( + 1 + + (-1247/336 - 35/12 * ν)x + + (4π)x^(3/2) + + (-44711/9072 + 9271/504 * ν + 65/18 * ν^2)x^2 + + (-8191/672 - 583/24 * ν)π * x^(5/2) + + ( + 6643739519/69854400 + 16/3 * π^2 / 3 - 1712/105 * γₑ - + 856/105 * ln(16x) + (-134543/7776 + 41/48 * π^2)ν - 94403/3024 * ν^2 - + 775/324 * ν^3 + )x^3 + + (-16285/504 + 214745/1728 * ν + 193385/3024 * ν^2)π * x^(7/2) + + ( + -323105549467/3178375200 + 232597/4410 * γₑ - 1369/126 * π^2 + + 39931/294 * ln(2) - 47385/1568 * ln(3) + + 232597/8820 * ln(x) + + ( + -1452202403629/1466942400 + 41478/245 * γₑ - 267127/4608 * π^2 + + 479062/2205 * ln(2) + + 47385/392 * ln(3) + + 20739/245 * ln(x) + )ν + + (1607125/6804 - 3157/384 * π^2)ν^2 + + 6875/504 * ν^3 + + 5/6 * ν^4 + )x^4 + + ( + 265978667519/745113600 - 6848/105 * γₑ - 3424/105 * ln(16x) + + (2062241/22176 + 41/12 * π^2)ν - 133112905/290304 * ν^2 - + 3719141/38016 * ν^3 + )π * x^(9/2) + ) +end + +end # module Blanchet2024 diff --git a/src/literature/Einstein1918.jl b/src/literature/Einstein1918.jl new file mode 100644 index 00000000..f1ea0f56 --- /dev/null +++ b/src/literature/Einstein1918.jl @@ -0,0 +1,9 @@ +@pn_reference module Einstein1918 + +import PostNewtonian: G, c, M₁, M₂, χ⃗₁, χ⃗₂, R, v, Φ, χₛ + +# import common variables +# define variables not in common variables +# write individual expressions as separate functions with `@pn_expression` + +end diff --git a/src/literature/TaylorPoisson2008.jl b/src/literature/TaylorPoisson2008.jl new file mode 100644 index 00000000..bcb56584 --- /dev/null +++ b/src/literature/TaylorPoisson2008.jl @@ -0,0 +1,20 @@ +@doc raw""" +Expressions from [TaylorPoisson2008](@cite) + +Note that there are expressions in the paper that could probably be used pretty easily to +generalize to precessing and/or eccentric systems. +""" +@pn_reference module TaylorPoisson2008 + +import PostNewtonian: G, c, v, M₁ as m₁, M₂ as m₂, M as m, r, χ₁ₗ as χ₁, χ₂ₗ as χ₂ + +# These are defined in the text below Eq. (9.5), though I've added subscripts to identify +# them as applying to the first and second bodies, respectively. +ϵ₁(pnsystem) = Base.sign(χ₁(pnsystem)) +ϵ₂(pnsystem) = Base.sign(χ₂(pnsystem)) + +@pn_expression function Eq_9_4(pnsystem) end + +@pn_expression function Eq_9_7(pnsystem) end + +end # module TaylorPoisson2008 diff --git a/src/literature/Trestini2025.jl b/src/literature/Trestini2025.jl new file mode 100644 index 00000000..53fb89e8 --- /dev/null +++ b/src/literature/Trestini2025.jl @@ -0,0 +1,24 @@ +@doc raw""" +Expressions from [Trestini2025](@cite) + +""" +@pn_reference module Trestini2025 + +import PostNewtonian: G, c, v, M₁ as m₁, M₂ as m₂, M as m, r, χ₁ₗ as χ₁, χ₂ₗ as χ₂ + +""" + ℵ₈(pnsystem) + +4PN tidal dissipation coefficient + +As given in the text below Eqs. (7.3) of [Trestini2025](@cite). Trestini defines ℵ₂ₙ as the + +> tidal dissipation (or black hole absorption) coefficient entering at the ``n``PN order +> beyond the leading, quadrupolar flux ('aleph' stands for 'absorption'). +""" +@pn_expression ℵ₈(pnsystem) = 1 - 4ν + 2ν^2 + +# Eq. (7.3a) +@pn_expression ℱₑᴴ(pnsystem) = 32c^5 * ν^2 / 5G * ℵ₈ * y^9 + +end # module Trestini2025 diff --git a/src/derived_variables/horizons.jl b/src/literature/common_variables/horizons.jl similarity index 87% rename from src/derived_variables/horizons.jl rename to src/literature/common_variables/horizons.jl index bc34154d..3e45a4bf 100644 --- a/src/derived_variables/horizons.jl +++ b/src/literature/common_variables/horizons.jl @@ -7,7 +7,7 @@ As defined on page 2, line 4, of [Alvi (2001)](https://doi.org/10.1103/PhysRevD.64.104020). See the documentation section on ["Horizons"](@ref Horizons) for more details. """ -rₕ₁(s::VecOrPNSystem) = M₁(s) * (1 + √(1 - min(χ₁²(s), 1))) +@public rₕ₁(s::PNSystem) = M₁(s) * (1 + √(1 - min(χ₁²(s), 1))) """ rₕ₂(s) @@ -18,7 +18,7 @@ As defined on page 2, line 4, of [Alvi (2001)](https://doi.org/10.1103/PhysRevD.64.104020). See the documentation section on ["Horizons"](@ref Horizons) for more details. """ -rₕ₂(s::VecOrPNSystem) = M₂(s) * (1 + √(1 - min(χ₂²(s), 1))) +@public rₕ₂(s::PNSystem) = M₂(s) * (1 + √(1 - min(χ₂²(s), 1))) """ Ωₕ₁(s) @@ -29,7 +29,7 @@ As defined on page 2, line 5, of [Alvi (2001)](https://doi.org/10.1103/PhysRevD.64.104020). See the documentation section on ["Horizons"](@ref Horizons) for more details. """ -Ωₕ₁(s::VecOrPNSystem) = χ₁(s) / 2rₕ₁(s) +@public Ωₕ₁(s::PNSystem) = χ₁(s) / 2rₕ₁(s) """ Ωₕ₂(s) @@ -40,7 +40,7 @@ As defined on page 2, line 5, of [Alvi (2001)](https://doi.org/10.1103/PhysRevD.64.104020). See the documentation section on ["Horizons"](@ref Horizons) for more details. """ -Ωₕ₂(s::VecOrPNSystem) = χ₂(s) / 2rₕ₂(s) +@public Ωₕ₂(s::PNSystem) = χ₂(s) / 2rₕ₂(s) """ sin²θ₁(s) @@ -50,7 +50,7 @@ Sine-squared of angle between spin of black hole 1 and vector to black hole 2. Compare to Eq. (18) of [Alvi (2001)](https://doi.org/10.1103/PhysRevD.64.104020). See the documentation section on ["Horizons"](@ref Horizons) for more details. """ -function sin²θ₁(s::VecOrPNSystem) +@public function sin²θ₁(s::PNSystem) let χ₁² = χ₁²(s) ifelse(iszero(χ₁²), one(χ₁²), abs2vec(n̂(s) × χ⃗₁(s)) / χ₁²) end @@ -64,7 +64,7 @@ Sine-squared of angle between spin of black hole 2 and vector to black hole 1. Compare to Eq. (18) of [Alvi (2001)](https://doi.org/10.1103/PhysRevD.64.104020). See the documentation section on ["Horizons"](@ref Horizons) for more details. """ -function sin²θ₂(s::VecOrPNSystem) +@public function sin²θ₂(s::PNSystem) let χ₂² = χ₂²(s) ifelse(iszero(χ₂²), one(χ₂²), abs2vec(n̂(s) × χ⃗₂(s)) / χ₂²) end @@ -83,7 +83,7 @@ that depend on this. See the documentation section on ["Horizons"](@ref Horizons) for more details. """ -function ϕ̇̂₁(s::VecOrPNSystem) +@public function ϕ̇̂₁(s::PNSystem) let χ₁ = χ₁(s), sin²θ₁ = sin²θ₁(s), M = M(s) ifelse( iszero(χ₁), @@ -106,7 +106,7 @@ that depend on this. See the documentation section on ["Horizons"](@ref Horizons) for more details. """ -function ϕ̇̂₂(s::VecOrPNSystem) +@public function ϕ̇̂₂(s::PNSystem) let χ₂ = χ₂(s), sin²θ₂ = sin²θ₂(s), M = M(s) ifelse( iszero(χ₂), @@ -125,7 +125,7 @@ This is the moment divided by ``ν^2 v^{12}``, as given by Eq. (10) of [Alvi (2001)](https://doi.org/10.1103/PhysRevD.64.104020). See the documentation section on ["Horizons"](@ref Horizons) for more details. """ -function Î₀₁(s::VecOrPNSystem) +@public function Î₀₁(s::PNSystem) let χ₁² = χ₁²(s), sin²θ₁ = sin²θ₁(s) (16rₕ₁(s) / 5M(s)^2) * M₁(s)^3 * sin²θ₁ * (1 - 3//4 * χ₁² + 15//4 * χ₁² * sin²θ₁) end @@ -140,7 +140,7 @@ This is the moment divided by ``ν^2 v^{12}``, as given by Eq. (10) of [Alvi (2001)](https://doi.org/10.1103/PhysRevD.64.104020). See the documentation section on ["Horizons"](@ref Horizons) for more details. """ -function Î₀₂(s::VecOrPNSystem) +@public function Î₀₂(s::PNSystem) let χ₂² = χ₂²(s), sin²θ₂ = sin²θ₂(s) (16rₕ₂(s) / 5M(s)^2) * M₂(s)^3 * sin²θ₂ * (1 - 3//4 * χ₂² + 15//4 * χ₂² * sin²θ₂) end @@ -155,7 +155,7 @@ The "quadrupolar polarisability" of object 1 used by [Bohé et al. Note that Bohé et al. refer to the closely related (and co-authored) [Marsat (2014)](https://arxiv.org/abs/1411.4118), who notes above Eq. (4.7) that this is denoted ``C_{\mathrm{ES}^2}`` in [Levi and Steinhoff (2014)](https://arxiv.org/abs/1410.2601), who -in turn notes that "we can set ... the Wilson coefficients ``C_{\mathrm{ES}^2} = +in turn note that "we can set ... the Wilson coefficients ``C_{\mathrm{ES}^2} = C_{\mathrm{BS}^3} = 1`` for the black hole case." However, a very similar constant ``\kappa_A`` is used in Eq. (2.1) of [Buonanno et al. @@ -173,7 +173,7 @@ See also [`λ₁`](@ref). quantity may also be related to [`λ₁`](@ref). Pull requests or issues with more information are welcome. """ -function κ₁(s::VecOrPNSystem) +@public function κ₁(s::PNSystem) return 1 end @@ -183,7 +183,7 @@ end The "quadrupolar polarisability" of object 2 used by [Bohé et al. (2015)](https://arxiv.org/abs/1501.01529). See [`κ₁`](@ref) for more details. """ -function κ₂(s::VecOrPNSystem) +@public function κ₂(s::PNSystem) return 1 end @@ -193,7 +193,7 @@ end Equal to [`κ₁`](@ref)` + `[`κ₂`](@ref); defined below Eq. (3.28) of [Bohé et al. (2015)](https://arxiv.org/abs/1501.01529). """ -function κ₊(s::VecOrPNSystem) +@public function κ₊(s::PNSystem) return κ₁(s) + κ₂(s) end @@ -203,7 +203,7 @@ end Equal to [`κ₁`](@ref)` - `[`κ₂`](@ref); defined below Eq. (3.28) of [Bohé et al. (2015)](https://arxiv.org/abs/1501.01529). """ -function κ₋(s::VecOrPNSystem) +@public function κ₋(s::PNSystem) return κ₁(s) - κ₂(s) end @@ -212,8 +212,8 @@ end The "quadrupolar polarisability" of object 1 used by [Marsat (2014)](https://arxiv.org/abs/1411.4118), who notes above Eq. (4.11) that this is denoted -``C_{\mathrm{BS}^2}`` in [Levi and Steinhoff (2014)](https://arxiv.org/abs/1410.2601), who -in turn notes that "we can set ... the Wilson coefficients ``C_{\mathrm{ES}^2} = +``C_{\mathrm{BS}^3}`` in [Levi and Steinhoff (2014)](https://arxiv.org/abs/1410.2601), who +in turn note that "we can set ... the Wilson coefficients ``C_{\mathrm{ES}^2} = C_{\mathrm{BS}^3} = 1`` for the black hole case." See also [`κ₁`](@ref). @@ -226,7 +226,7 @@ See also [`κ₁`](@ref). quantity may also be related to [`λ₁`](@ref). Pull requests or issues with more information are welcome. """ -function λ₁(s::VecOrPNSystem) +@public function λ₁(s::PNSystem) return 1 end @@ -236,7 +236,7 @@ end The "quadrupolar polarisability" of object 2 used by [Bohé et al. (2015)](https://arxiv.org/abs/1501.01529). See [`λ₁`](@ref) for more details. """ -function λ₂(s::VecOrPNSystem) +@public function λ₂(s::PNSystem) return 1 end @@ -246,7 +246,7 @@ end Equal to [`λ₁`](@ref)` + `[`λ₂`](@ref); defined below Eq. (3.28) of [Bohé et al. (2015)](https://arxiv.org/abs/1501.01529). """ -function λ₊(s::VecOrPNSystem) +@public function λ₊(s::PNSystem) return λ₁(s) + λ₂(s) end @@ -256,6 +256,6 @@ end Equal to [`λ₁`](@ref)` - `[`λ₂`](@ref); defined below Eq. (3.28) of [Bohé et al. (2015)](https://arxiv.org/abs/1501.01529). """ -function λ₋(s::VecOrPNSystem) +@public function λ₋(s::PNSystem) return λ₁(s) - λ₂(s) end diff --git a/src/derived_variables/mass_combinations.jl b/src/literature/common_variables/mass_combinations.jl similarity index 65% rename from src/derived_variables/mass_combinations.jl rename to src/literature/common_variables/mass_combinations.jl index 95044df1..30cef306 100644 --- a/src/derived_variables/mass_combinations.jl +++ b/src/literature/common_variables/mass_combinations.jl @@ -6,9 +6,9 @@ Compute the total mass ``M₁+M₂``. """ -M(M₁, M₂) = M₁ + M₂ -M(s::VecOrPNSystem) = M(M₁(s), M₂(s)) -const total_mass = M +@public M(M₁, M₂) = M₁ + M₂ +M(s::PNSystem) = M(M₁(s), M₂(s)) +@public const total_mass = M """ μ(pnsystem) @@ -18,9 +18,9 @@ const total_mass = M Compute the reduced mass ``(M₁ M₂)/(M₁+M₂)``. """ -μ(M₁, M₂) = (M₁ * M₂) / (M₁ + M₂) -μ(s::VecOrPNSystem) = μ(M₁(s), M₂(s)) -const reduced_mass = μ +@public μ(M₁, M₂) = (M₁ * M₂) / (M₁ + M₂) +μ(s::PNSystem) = μ(M₁(s), M₂(s)) +@public const reduced_mass = μ """ ν(pnsystem) @@ -32,10 +32,10 @@ Compute the reduced mass ratio ``(M₁ M₂)/(M₁+M₂)^2``. Note that the denominator is squared, unlike in the reduced mass [`μ`](@ref). """ -ν(M₁, M₂) = (M₁ * M₂) / (M₁ + M₂)^2 -ν(s::VecOrPNSystem) = ν(M₁(s), M₂(s)) +@public ν(M₁, M₂) = (M₁ * M₂) / (M₁ + M₂)^2 +ν(s::PNSystem) = ν(M₁(s), M₂(s)) ν(; q) = q / (1 + q)^2 -const reduced_mass_ratio = ν +@public const reduced_mass_ratio = ν """ δ(pnsystem) @@ -48,10 +48,10 @@ Compute mass-difference ratio ``(M₁-M₂)/(M₁+M₂)``. Note that we do not restrict to ``M₁ ≥ M₂`` or vice versa; if you prefer that ``δ`` always be positive (or always negative), you are responsible for ensuring that. """ -δ(M₁, M₂) = (M₁ - M₂) / (M₁ + M₂) -δ(s::VecOrPNSystem) = δ(M₁(s), M₂(s)) +@public δ(M₁, M₂) = (M₁ - M₂) / (M₁ + M₂) +δ(s::PNSystem) = δ(M₁(s), M₂(s)) δ(; q) = (q - 1) / (q + 1) -const mass_difference_ratio = δ +@public const mass_difference_ratio = δ """ q(pnsystem) @@ -64,9 +64,9 @@ Compute mass ratio ``M₁/M₂``. Note that we do not restrict to ``M₁ ≥ M₂`` or vice versa; if you prefer that ``q`` always be greater than or equal to 1 (or vice versa), you are responsible for ensuring that. """ -q(M₁, M₂) = M₁ / M₂ -q(s::VecOrPNSystem) = q(M₁(s), M₂(s)) -const mass_ratio = q +@public q(M₁, M₂) = M₁ / M₂ +q(s::PNSystem) = q(M₁(s), M₂(s)) +@public const mass_ratio = q """ ℳ(pnsystem) @@ -82,9 +82,9 @@ The chirp mass is defined as \\mathcal{M} = \\frac{(M_1 M_2)^{3/5}} {(M_1 + M_2)^{1/5}}. ``` """ -ℳ(M₁, M₂) = ((M₁ * M₂)^3 / (M₁ + M₂))^(1//5) -ℳ(s::VecOrPNSystem) = ℳ(M₁(s), M₂(s)) -const chirp_mass = ℳ +@public ℳ(M₁, M₂) = ((M₁ * M₂)^3 / (M₁ + M₂))^(1//5) +ℳ(s::PNSystem) = ℳ(M₁(s), M₂(s)) +@public const chirp_mass = ℳ """ X₁(pnsystem) @@ -94,9 +94,9 @@ const chirp_mass = ℳ Compute the reduced *individual* mass ``M₁/(M₁+M₂)``. """ -X₁(M₁, M₂) = M₁ / (M₁ + M₂) -X₁(s::VecOrPNSystem) = X₁(M₁(s), M₂(s)) -const X1 = X₁ +@public X₁(M₁, M₂) = M₁ / (M₁ + M₂) +X₁(s::PNSystem) = X₁(M₁(s), M₂(s)) +@public const X1 = X₁ """ X₂(pnsystem) @@ -106,6 +106,6 @@ const X1 = X₁ Compute the reduced *individual* mass ``M₂/(M₁+M₂)``. """ -X₂(M₁, M₂) = M₂ / (M₁ + M₂) -X₂(s::VecOrPNSystem) = X₂(M₁(s), M₂(s)) -const X2 = X₂ +@public X₂(M₁, M₂) = M₂ / (M₁ + M₂) +X₂(s::PNSystem) = X₂(M₁(s), M₂(s)) +@public const X2 = X₂ diff --git a/src/derived_variables/orbital_elements.jl b/src/literature/common_variables/orbital_elements.jl similarity index 59% rename from src/derived_variables/orbital_elements.jl rename to src/literature/common_variables/orbital_elements.jl index d0e24064..29829896 100644 --- a/src/derived_variables/orbital_elements.jl +++ b/src/literature/common_variables/orbital_elements.jl @@ -10,9 +10,9 @@ The unit vector pointing from object 2 to object 1, when the frame is given by t n̂(R) = R x̂ R̄ ``` """ -n̂(R) = QuatVec(R(𝐢)) -n̂(s::VecOrPNSystem) = n̂(R(s)) -const n_hat = n̂ +@public n̂(R) = QuatVec(R(𝐢)) +n̂(s::PNSystem) = n̂(R(s)) +@public const n_hat = n̂ """ λ̂(pnsystem) @@ -27,9 +27,9 @@ the frame is given by the rotor `R`. This is equal to ``` This also completes the right-handed triple of ``(n̂, λ̂, ℓ̂)``. """ -λ̂(R) = QuatVec(R(𝐣)) -λ̂(s::VecOrPNSystem) = λ̂(R(s)) -const lambda_hat = λ̂ +@public λ̂(R) = QuatVec(R(𝐣)) +λ̂(s::PNSystem) = λ̂(R(s)) +@public const lambda_hat = λ̂ """ ℓ̂(pnsystem) @@ -43,9 +43,9 @@ given by the rotor `R`. This is equal to ℓ̂(R) = R ẑ R̄ ``` """ -ℓ̂(R) = QuatVec(R(𝐤)) -ℓ̂(s::VecOrPNSystem) = ℓ̂(R(s)) -const ell_hat = ℓ̂ +@public ℓ̂(R) = QuatVec(R(𝐤)) +ℓ̂(s::PNSystem) = ℓ̂(R(s)) +@public const ell_hat = ℓ̂ @doc raw""" Ω(pnsystem) @@ -63,8 +63,22 @@ definition* as ``` See also [`v`](@ref). """ -Ω(; v, M=1) = v^3 / M -Ω(s::VecOrPNSystem) = Ω(; v=v(s), M=M(s)) -const Omega = Ω +@public Ω(; v, M=1) = v^3 / M +Ω(s::PNSystem) = Ω(; v=v(s), M=M(s)) +@public const Omega = Ω -lnv(s::VecOrPNSystem) = ln(v(s)) +@doc raw""" + x(pnsystem) + x(;v, M=1) + +The "frequency-related parameter" defined in Eq. (375) of [Blanchet2024](@cite) as +```math +x \colonequals \left(\frac{Gm\Omega}{c^3}\right)^{2/3} +``` +where `m` is the total mass of the binary, and `Ω` is the orbital angular frequency. +This is related to the PN velocity parameter `v` as +```math +x = \left(\frac{v}{c}\right)^{2}. +``` +""" +@public x(s::PNSystem) = (v(s)/c(s))^2 diff --git a/src/derived_variables/spin_combinations.jl b/src/literature/common_variables/spin_combinations.jl similarity index 59% rename from src/derived_variables/spin_combinations.jl rename to src/literature/common_variables/spin_combinations.jl index e36b5cbe..42952dd3 100644 --- a/src/derived_variables/spin_combinations.jl +++ b/src/literature/common_variables/spin_combinations.jl @@ -3,14 +3,14 @@ Dimensionful spin vector of object 1. """ -S⃗₁(s::VecOrPNSystem) = χ⃗₁(s) * M₁(s)^2 +@public S⃗₁(s::PNSystem) = χ⃗₁(s) * M₁(s)^2 """ S⃗₂(pnsystem) Dimensionful spin vector of object 2. """ -S⃗₂(s::VecOrPNSystem) = χ⃗₂(s) * M₂(s)^2 +@public S⃗₂(s::PNSystem) = χ⃗₂(s) * M₂(s)^2 """ S⃗(pnsystem) @@ -18,8 +18,8 @@ S⃗₂(s::VecOrPNSystem) = χ⃗₂(s) * M₂(s)^2 Total (dimensionful) spin vector ``S⃗₁+S⃗₂``. """ -S⃗(M₁, M₂, χ⃗₁, χ⃗₂) = χ⃗₁ * M₁^2 + χ⃗₂ * M₂^2 -S⃗(s::VecOrPNSystem) = S⃗(M₁(s), M₂(s), χ⃗₁(s), χ⃗₂(s)) +@public S⃗(M₁, M₂, χ⃗₁, χ⃗₂) = χ⃗₁ * M₁^2 + χ⃗₂ * M₂^2 +S⃗(s::PNSystem) = S⃗(M₁(s), M₂(s), χ⃗₁(s), χ⃗₂(s)) """ Σ⃗(pnsystem) @@ -27,8 +27,8 @@ S⃗(s::VecOrPNSystem) = S⃗(M₁(s), M₂(s), χ⃗₁(s), χ⃗₂(s)) Differential spin vector ``M(a⃗₂-a⃗₁)``. """ -Σ⃗(M₁, M₂, χ⃗₁, χ⃗₂) = (M₁ + M₂) * (χ⃗₂ * M₂ - χ⃗₁ * M₁) -Σ⃗(s::VecOrPNSystem) = Σ⃗(M₁(s), M₂(s), χ⃗₁(s), χ⃗₂(s)) +@public Σ⃗(M₁, M₂, χ⃗₁, χ⃗₂) = (M₁ + M₂) * (χ⃗₂ * M₂ - χ⃗₁ * M₁) +Σ⃗(s::PNSystem) = Σ⃗(M₁(s), M₂(s), χ⃗₁(s), χ⃗₂(s)) """ χ⃗(pnsystem) @@ -36,29 +36,29 @@ Differential spin vector ``M(a⃗₂-a⃗₁)``. Normalized spin vector ``S⃗/M²``. """ -χ⃗(S⃗, M) = S⃗ / M^2 -χ⃗(s::VecOrPNSystem) = χ⃗(S⃗(s), M(s)) +@public χ⃗(S⃗, M) = S⃗ / M^2 +χ⃗(s::PNSystem) = χ⃗(S⃗(s), M(s)) """ χ⃗ₛ(M₁, M₂, χ⃗₁, χ⃗₂) Symmetric spin vector ``(χ⃗₁+χ⃗₂)/2``. """ -χ⃗ₛ(χ⃗₁, χ⃗₂) = (χ⃗₁ + χ⃗₂) / 2 +@public χ⃗ₛ(χ⃗₁, χ⃗₂) = (χ⃗₁ + χ⃗₂) / 2 χ⃗ₛ(M₁, M₂, χ⃗₁, χ⃗₂) = (χ⃗₁ + χ⃗₂) / 2 -χ⃗ₛ(s::VecOrPNSystem) = χ⃗ₛ(M₁(s), M₂(s), χ⃗₁(s), χ⃗₂(s)) +χ⃗ₛ(s::PNSystem) = χ⃗ₛ(M₁(s), M₂(s), χ⃗₁(s), χ⃗₂(s)) """ χ⃗ₐ(M₁, M₂, χ⃗₁, χ⃗₂) Antisymmetric spin vector ``(χ⃗₁-χ⃗₂)/2``. """ -χ⃗ₐ(χ⃗₁, χ⃗₂) = (χ⃗₁ - χ⃗₂) / 2 +@public χ⃗ₐ(χ⃗₁, χ⃗₂) = (χ⃗₁ - χ⃗₂) / 2 χ⃗ₐ(M₁, M₂, χ⃗₁, χ⃗₂) = (χ⃗₁ - χ⃗₂) / 2 -χ⃗ₐ(s::VecOrPNSystem) = χ⃗ₐ(M₁(s), M₂(s), χ⃗₁(s), χ⃗₂(s)) +χ⃗ₐ(s::PNSystem) = χ⃗ₐ(M₁(s), M₂(s), χ⃗₁(s), χ⃗₂(s)) -χₚₑᵣₚ(s::VecOrPNSystem) = √(χ₁²(s) - (χ₁ₗ(s))^2 + χ₂²(s) - (χ₂ₗ(s))^2) -const chi_perp = χₚₑᵣₚ +@public χₚₑᵣₚ(s::PNSystem) = √(χ₁²(s) - (χ₁ₗ(s))^2 + χ₂²(s) - (χ₂ₗ(s))^2) +@public const chi_perp = χₚₑᵣₚ @doc raw""" χₑ(s) @@ -74,10 +74,8 @@ Defined as \right) \cdot \frac{\hat{\mathbf{L}}_{\mathrm{N}}} {M}. ``` """ -function χₑ(s::VecOrPNSystem) - return (S₁ₗ(s) / M₁(s) + S₂ₗ(s) / M₂(s)) / M(s) -end -const chi_eff = χₑ +@public χₑ(s::PNSystem) = (S₁ₗ(s) / M₁(s) + S₂ₗ(s) / M₂(s)) / M(s) +@public const chi_eff = χₑ @doc raw""" χₚ(s) @@ -112,7 +110,7 @@ convention. Because it seems to be the trend, this function uses the latter definition. """ -function χₚ(s::VecOrPNSystem) +@public function χₚ(s::PNSystem) χ₁ₚₑᵣₚ = √(χ₁ₙ(s)^2 + χ₁λ(s)^2) χ₂ₚₑᵣₚ = √(χ₂ₙ(s)^2 + χ₂λ(s)^2) let q = 1 / q(s) # This is to convert to LVK's convention @@ -152,16 +150,16 @@ the case for black holes. You can define `κ₁` and `κ₂` to have other valu See also [`S⃗₀⁻`](@ref). """ -S⃗₀⁺(s::VecOrPNSystem) = S⃗₀⁺(M₁(s), M₂(s), κ₁(s), κ₂(s), S⃗₁(s), S⃗₂(s)) +@public S⃗₀⁺(s::PNSystem) = S⃗₀⁺(M₁(s), M₂(s), κ₁(s), κ₂(s), S⃗₁(s), S⃗₂(s)) function S⃗₀⁺(M₁, M₂, κ₁, κ₂, S⃗₁, S⃗₂) M = M₁ + M₂ κᵣ = (κ₁ / κ₂)^(1//4) return (M / M₁) * κᵣ * √(1 + √(1 - κ₁ * κ₂)) * S⃗₁ + (M / M₂) / κᵣ * √(1 - √(1 - κ₁ * κ₂)) * S⃗₂ end -S₀⁺ₙ(s::VecOrPNSystem) = S⃗₀⁺(M₁(s), M₂(s), κ₁(s), κ₂(s), S₁ₙ(s), S₂ₙ(s)) -S₀⁺λ(s::VecOrPNSystem) = S⃗₀⁺(M₁(s), M₂(s), κ₁(s), κ₂(s), S₁λ(s), S₂λ(s)) -S₀⁺ₗ(s::VecOrPNSystem) = S⃗₀⁺(M₁(s), M₂(s), κ₁(s), κ₂(s), S₁ₗ(s), S₂ₗ(s)) +@public S₀⁺ₙ(s::PNSystem) = S⃗₀⁺(M₁(s), M₂(s), κ₁(s), κ₂(s), S₁ₙ(s), S₂ₙ(s)) +@public S₀⁺λ(s::PNSystem) = S⃗₀⁺(M₁(s), M₂(s), κ₁(s), κ₂(s), S₁λ(s), S₂λ(s)) +@public S₀⁺ₗ(s::PNSystem) = S⃗₀⁺(M₁(s), M₂(s), κ₁(s), κ₂(s), S₁ₗ(s), S₂ₗ(s)) @doc raw""" S⃗₀⁻(s) @@ -181,38 +179,38 @@ the case for black holes. You can define `κ₁` and `κ₂` to have other valu See also [`S⃗₀⁺`](@ref). """ -S⃗₀⁻(s::VecOrPNSystem) = S⃗₀⁻(M₁(s), M₂(s), κ₁(s), κ₂(s), S⃗₁(s), S⃗₂(s)) +@public S⃗₀⁻(s::PNSystem) = S⃗₀⁻(M₁(s), M₂(s), κ₁(s), κ₂(s), S⃗₁(s), S⃗₂(s)) S⃗₀⁻(M₁, M₂, κ₁, κ₂, S⃗₁, S⃗₂) = S⃗₀⁺(M₂, M₁, κ₂, κ₁, S⃗₂, S⃗₁) -S₀⁻ₙ(s::VecOrPNSystem) = S⃗₀⁻(M₁(s), M₂(s), κ₁(s), κ₂(s), S₁ₙ(s), S₂ₙ(s)) -S₀⁻λ(s::VecOrPNSystem) = S⃗₀⁻(M₁(s), M₂(s), κ₁(s), κ₂(s), S₁λ(s), S₂λ(s)) -S₀⁻ₗ(s::VecOrPNSystem) = S⃗₀⁻(M₁(s), M₂(s), κ₁(s), κ₂(s), S₁ₗ(s), S₂ₗ(s)) - -χ₁²(s::VecOrPNSystem) = abs2vec(χ⃗₁(s)) -χ₂²(s::VecOrPNSystem) = abs2vec(χ⃗₂(s)) -χ₁(s::VecOrPNSystem) = absvec(χ⃗₁(s)) -χ₂(s::VecOrPNSystem) = absvec(χ⃗₂(s)) -χ₁₂(s::VecOrPNSystem) = χ⃗₁(s) ⋅ χ⃗₂(s) -χₛₗ(s::VecOrPNSystem) = χ⃗ₛ(s) ⋅ ℓ̂(s) -χₐₗ(s::VecOrPNSystem) = χ⃗ₐ(s) ⋅ ℓ̂(s) -χ₁ₙ(s::VecOrPNSystem) = χ⃗₁(s) ⋅ n̂(s) -χ₁λ(s::VecOrPNSystem) = χ⃗₁(s) ⋅ λ̂(s) -χ₁ₗ(s::VecOrPNSystem) = χ⃗₁(s) ⋅ ℓ̂(s) -χ₂ₙ(s::VecOrPNSystem) = χ⃗₂(s) ⋅ n̂(s) -χ₂λ(s::VecOrPNSystem) = χ⃗₂(s) ⋅ λ̂(s) -χ₂ₗ(s::VecOrPNSystem) = χ⃗₂(s) ⋅ ℓ̂(s) - -Sₙ(s::VecOrPNSystem) = S⃗(s) ⋅ n̂(s) -Σₙ(s::VecOrPNSystem) = Σ⃗(s) ⋅ n̂(s) -Sλ(s::VecOrPNSystem) = S⃗(s) ⋅ λ̂(s) -Σλ(s::VecOrPNSystem) = Σ⃗(s) ⋅ λ̂(s) -Sₗ(s::VecOrPNSystem) = S⃗(s) ⋅ ℓ̂(s) -Σₗ(s::VecOrPNSystem) = Σ⃗(s) ⋅ ℓ̂(s) -sₗ(s::VecOrPNSystem) = S⃗(s) ⋅ ℓ̂(s) / M(s)^2 -σₗ(s::VecOrPNSystem) = Σ⃗(s) ⋅ ℓ̂(s) / M(s)^2 - -S₁ₙ(s::VecOrPNSystem) = S⃗₁(s) ⋅ n̂(s) -S₁λ(s::VecOrPNSystem) = S⃗₁(s) ⋅ λ̂(s) -S₁ₗ(s::VecOrPNSystem) = S⃗₁(s) ⋅ ℓ̂(s) -S₂ₙ(s::VecOrPNSystem) = S⃗₂(s) ⋅ n̂(s) -S₂λ(s::VecOrPNSystem) = S⃗₂(s) ⋅ λ̂(s) -S₂ₗ(s::VecOrPNSystem) = S⃗₂(s) ⋅ ℓ̂(s) +@public S₀⁻ₙ(s::PNSystem) = S⃗₀⁻(M₁(s), M₂(s), κ₁(s), κ₂(s), S₁ₙ(s), S₂ₙ(s)) +@public S₀⁻λ(s::PNSystem) = S⃗₀⁻(M₁(s), M₂(s), κ₁(s), κ₂(s), S₁λ(s), S₂λ(s)) +@public S₀⁻ₗ(s::PNSystem) = S⃗₀⁻(M₁(s), M₂(s), κ₁(s), κ₂(s), S₁ₗ(s), S₂ₗ(s)) + +@public χ₁²(s::PNSystem) = abs2vec(χ⃗₁(s)) +@public χ₂²(s::PNSystem) = abs2vec(χ⃗₂(s)) +@public χ₁(s::PNSystem) = absvec(χ⃗₁(s)) +@public χ₂(s::PNSystem) = absvec(χ⃗₂(s)) +@public χ₁₂(s::PNSystem) = χ⃗₁(s) ⋅ χ⃗₂(s) +@public χₛₗ(s::PNSystem) = χ⃗ₛ(s) ⋅ ℓ̂(s) +@public χₐₗ(s::PNSystem) = χ⃗ₐ(s) ⋅ ℓ̂(s) +@public χ₁ₙ(s::PNSystem) = χ⃗₁(s) ⋅ n̂(s) +@public χ₁λ(s::PNSystem) = χ⃗₁(s) ⋅ λ̂(s) +@public χ₁ₗ(s::PNSystem) = χ⃗₁(s) ⋅ ℓ̂(s) +@public χ₂ₙ(s::PNSystem) = χ⃗₂(s) ⋅ n̂(s) +@public χ₂λ(s::PNSystem) = χ⃗₂(s) ⋅ λ̂(s) +@public χ₂ₗ(s::PNSystem) = χ⃗₂(s) ⋅ ℓ̂(s) + +@public Sₙ(s::PNSystem) = S⃗(s) ⋅ n̂(s) +@public Σₙ(s::PNSystem) = Σ⃗(s) ⋅ n̂(s) +@public Sλ(s::PNSystem) = S⃗(s) ⋅ λ̂(s) +@public Σλ(s::PNSystem) = Σ⃗(s) ⋅ λ̂(s) +@public Sₗ(s::PNSystem) = S⃗(s) ⋅ ℓ̂(s) +@public Σₗ(s::PNSystem) = Σ⃗(s) ⋅ ℓ̂(s) +@public sₗ(s::PNSystem) = S⃗(s) ⋅ ℓ̂(s) / M(s)^2 +@public σₗ(s::PNSystem) = Σ⃗(s) ⋅ ℓ̂(s) / M(s)^2 + +@public S₁ₙ(s::PNSystem) = S⃗₁(s) ⋅ n̂(s) +@public S₁λ(s::PNSystem) = S⃗₁(s) ⋅ λ̂(s) +@public S₁ₗ(s::PNSystem) = S⃗₁(s) ⋅ ℓ̂(s) +@public S₂ₙ(s::PNSystem) = S⃗₂(s) ⋅ n̂(s) +@public S₂λ(s::PNSystem) = S⃗₂(s) ⋅ λ̂(s) +@public S₂ₗ(s::PNSystem) = S⃗₂(s) ⋅ ℓ̂(s) diff --git a/src/derived_variables/tidal_coupling.jl b/src/literature/common_variables/tidal_coupling.jl similarity index 92% rename from src/derived_variables/tidal_coupling.jl rename to src/literature/common_variables/tidal_coupling.jl index 211306a6..ff172f23 100644 --- a/src/derived_variables/tidal_coupling.jl +++ b/src/literature/common_variables/tidal_coupling.jl @@ -16,7 +16,7 @@ tidal couplings ``\Lambda_1`` and ``\Lambda_2`` of the two components. See also [`Λ₁`](@ref) and [`Λ₂`](@ref). """ -Λ̃(s::VecOrPNSystem) = +@public Λ̃(s::PNSystem) = 16//13 * ((M₁(s) + 12M₂(s)) * M₁(s)^4 * Λ₁(s) + (M₂(s) + 12M₁(s)) * M₂(s)^4 * Λ₂(s)) / M(s)^5 -const Lambda_tilde = Λ̃ +@public const Lambda_tilde = Λ̃ diff --git a/src/literature/literature.jl b/src/literature/literature.jl new file mode 100644 index 00000000..2775b895 --- /dev/null +++ b/src/literature/literature.jl @@ -0,0 +1,13 @@ +# These files define functions encapsulating common variables used throughout the +# literature. Note that not every reference uses these conventions, which is why +# they must be explicitly imported to be used by `@pn_reference` modules. +include("common_variables/horizons.jl") +include("common_variables/mass_combinations.jl") +include("common_variables/orbital_elements.jl") +include("common_variables/spin_combinations.jl") +include("common_variables/tidal_coupling.jl") + +# Now we include the `@pn_reference` modules themselves, named by the bibtex keys we use for +# them in ``../references.bib`. +#include("Einstein1918.jl") +include("Blanchet2024.jl") diff --git a/src/pn_expressions.jl b/src/pn_expressions.jl deleted file mode 100644 index 5ab622e6..00000000 --- a/src/pn_expressions.jl +++ /dev/null @@ -1,7 +0,0 @@ -include("utilities/macros.jl") -include("pn_expressions/flux.jl") -include("pn_expressions/tidal_heating.jl") -include("pn_expressions/binding_energy.jl") -include("pn_expressions/separation.jl") -include("pn_expressions/precession.jl") -include("pn_expressions/mode_weights.jl") diff --git a/src/pn_expressions/angular_momentum.jl b/src/pn_expressions/angular_momentum.jl new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/src/pn_expressions/angular_momentum.jl @@ -0,0 +1 @@ + diff --git a/src/pn_expressions/binding_energy.jl b/src/pn_expressions/binding_energy.jl index f93f394d..8a4374e3 100644 --- a/src/pn_expressions/binding_energy.jl +++ b/src/pn_expressions/binding_energy.jl @@ -56,7 +56,7 @@ overall factor is used, leading to a sign difference. 77ν^4 / 31104 + 301ν^3 / 1728 + (-498449//3456 + 3157π^2 / 576)ν^2 + - (-123671//5760 + 1792ln2 / 15 + 9037π^2 / 1536 + 896γₑ / 15)ν + + (-123671//5760 + 1792ln(2) / 15 + 9037π^2 / 1536 + 896γₑ / 15)ν + 2ln(v) * (448ν / 15) ) @@ -67,9 +67,9 @@ overall factor is used, leading to a sign difference. ν^5 / 512 + 55ν^4 / 512 + (-1353π^2 / 256 + 69423//512)ν^3 + - (-21337π^2 / 1024 + 3a₆ᶜ¹ - 896ln2 / 5 - 448γₑ / 5 + 893429//2880)ν^2 + + (-21337π^2 / 1024 + 3a₆ᶜ¹ - 896ln(2) / 5 - 448γₑ / 5 + 893429//2880)ν^2 + ( - -228916843//115200 - 9976γₑ / 35 + 729ln3 / 7 - 23672ln2 / 35 + + -228916843//115200 - 9976γₑ / 35 + 729ln(3) / 7 - 23672ln(2) / 35 + 126779π^2 / 512 )ν + 2ln(v) * (-4988ν / 35 - 656ν^2 / 5) @@ -82,19 +82,19 @@ overall factor is used, leading to a sign difference. (272855π^2 / 124416 - 20543435//373248)ν^4 + ( 1232γₑ / 27 + 6634243π^2 / 110592 - 11a₆ᶜ¹ / 2 - 71700787//51840 + - 2464ln2 / 27 + 2464ln(2) / 27 )ν^3 + ( 113176680983//14515200 + 18491π^4 / 2304 + - 246004ln2 / 105 + + 246004ln(2) / 105 + 112772γₑ / 105 + a₆ᶜ¹ * 11//2 + a₇ˡⁿ¹ * 2//3 + - a₇ᶜ¹ * 11//3 - 86017789π^2 / 110592 - 2673ln3 / 14 + a₇ᶜ¹ * 11//3 - 86017789π^2 / 110592 - 2673ln(3) / 14 )ν^2 + ( - -389727504721//43545600 + 74888ln2 / 243 - 7128ln3 / 7 - + -389727504721//43545600 + 74888ln(2) / 243 - 7128ln(3) / 7 - 30809603π^4 / 786432 - 3934568γₑ / 8505 + 9118627045π^2 / 5308416 )ν + 2ln(v) * @@ -220,7 +220,7 @@ function 𝓔′code( ) 𝓔′statements[end] = 𝓔′return - if PNExpansionReducer === identity + if PNExpansionReducer ≡ identity # When `pn_expansion_reducer=Val(identity)` is passed, we return a PNExpansion NMax = Int(2PNOrder + 1) return quote diff --git a/src/pn_expressions/dynamics.jl b/src/pn_expressions/dynamics.jl new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/src/pn_expressions/dynamics.jl @@ -0,0 +1 @@ + diff --git a/src/pn_expressions/flux.jl b/src/pn_expressions/flux.jl index 000c74ac..54eef84a 100644 --- a/src/pn_expressions/flux.jl +++ b/src/pn_expressions/flux.jl @@ -39,20 +39,21 @@ overall factor is used, leading to a sign difference. (v / c)^2 * (-1247//336 - 35ν / 12) + (v / c)^3 * (4π) + (v / c)^4 * (-44711//9072 + 9271ν / 504 + 65ν^2 / 18) + - (v / c)^5 * ((-8191//672 - 583 * ν / 24)π) + + (v / c)^5 * ((-8191//672 - 583ν / 24)π) + (v / c)^6 * ( - 6643739519//69854400 + 16π^2 / 3 - 1712 * (γₑ + 2ln2 + ln(v)) / 105 + - (-134543//7776 + 41π^2 / 48)ν - 94403ν^2 / 3024 - 775ν^3 / 324 + 6643739519//69854400 + 16π^2 / 3 - + 1712 * (γₑ + 2ln(2) + ln(v)) / 105 + (-134543//7776 + 41π^2 / 48)ν - + 94403ν^2 / 3024 - 775ν^3 / 324 ) + (v / c)^7 * ((-16285//504 + 214745ν / 1728 + 193385ν^2 / 3024)π) + (v / c)^8 * ( -323105549467//3178375200 + 232597γₑ / 4410 - 1369π^2 / 126 + - 39931ln2 / 294 - 47385ln3 / 1568 + + 39931ln(2) / 294 - 47385ln(3) / 1568 + 232597ln(v) / 4410 + ( -1452202403629//1466942400 + 41478γₑ / 245 - 267127π^2 / 4608 + - 479062ln2 / 2205 + - 47385ln3 / 392 + + 479062ln(2) / 2205 + + 47385ln(3) / 392 + 41478ln(v) / 245 )ν + (1607125//6804 - 3157π^2 / 384)ν^2 + @@ -61,7 +62,7 @@ overall factor is used, leading to a sign difference. ) + (v / c)^9 * ( ( - 265978667519//745113600 - 6848 * (γₑ + 2ln2 + ln(v)) / 105 + + 265978667519//745113600 - 6848 * (γₑ + 2ln(2) + ln(v)) / 105 + (2062241//22176 + 41π^2 / 12)ν - 133112905ν^2 / 290304 - 3719141ν^3 / 38016 )π @@ -129,32 +130,32 @@ overall factor is used, leading to a sign difference. + (v / c)^10 * ( -2500861660823683//2831932303200 - 424223π^2 / 6804 - - 83217611ln2 / 1122660 + + 83217611ln(2) / 1122660 + 916628467γₑ / 7858620 + - 47385ln3 / 196 + + 47385ln(3) / 196 + 916628467ln(v) / 7858620 ) + (v / c)^11 * ( - -142155π * ln3 / 784 + + -142155π * ln(3) / 784 + 8399309750401π / 101708006400 + 177293γₑ * π / 1176 + - 8521283π * ln2 / 17640 + + 8521283π * ln(2) / 17640 + 177293π * ln(v) / 1176 ) + (v / c)^12 * ( - -271272899815409ln2 / 157329572400 - 54784π^2 * ln2 / 315 - - 246137536815857γₑ / 157329572400 - 437114506833ln3 / 789268480 - + -271272899815409ln(2) / 157329572400 - 54784π^2 * ln(2) / 315 - + 246137536815857γₑ / 157329572400 - 437114506833ln(3) / 789268480 - 256π^4 / 45 - 27392γₑ * π^2 / 315 - 27392ζ3 / 105 - - 37744140625ln5 / 260941824 + + 37744140625ln(5) / 260941824 + 1465472γₑ^2 / 11025 + - 5861888γₑ * ln2 / 11025 + - 5861888ln2^2 / 11025 + + 5861888γₑ * ln(2) / 11025 + + 5861888ln(2)^2 / 11025 + 2067586193789233570693//602387400044430000 + 3803225263π^2 / 10478160 + ln(v) * ( -246137536815857//157329572400 - 27392π^2 / 315 + 2930944γₑ / 11025 + - 5861888ln2 / 11025 + + 5861888ln(2) / 11025 + 1465472ln(v) / 11025 ) ) diff --git a/src/pn_expressions/mode_weights.jl b/src/pn_expressions/mode_weights.jl index c6187197..531e5f23 100644 --- a/src/pn_expressions/mode_weights.jl +++ b/src/pn_expressions/mode_weights.jl @@ -63,9 +63,9 @@ is from Eq. (4.15) of that reference. h[Yindex(2,1,ℓₘᵢₙ)] = h₀ * @pn_expansion( (v/c)^1 * (𝒾 * δ / 3) + (v/c)^3 * (𝒾 * δ * (-17 + 20ν) / 84) - + (v/c)^4 * ((δ * (1 + 2𝒾*π + 4ln2)) / 6) + + (v/c)^4 * ((δ * (1 + 2𝒾*π + 4ln(2))) / 6) + (v/c)^5 * (𝒾 * δ * (-172 + ν * (-2036 + 237ν)) / 1512) - + (v/c)^6 * (δ*(-34𝒾*π - 17*(1 + 4ln2) + 2ν * (353 + 6𝒾*π + 12ln2)) / 168) + + (v/c)^6 * (δ*(-34𝒾*π - 17*(1 + 4ln(2)) + 2ν * (353 + 6𝒾*π + 12ln(2))) / 168) ) h[Yindex(2,2,ℓₘᵢₙ)] = h₀ * @pn_expansion( 1 @@ -75,14 +75,14 @@ is from Eq. (4.15) of that reference. + (v/c)^5 * (-24𝒾*ν + ((-107 + 34ν)π) / 21) + (v/c)^6 * ( (27027409//646800) - 856γₑ/105 + (ν*(-834555 + ν*(-729396 + 114635ν))) / 99792 - + 41ν * π^2 / 96 + (2π*(214𝒾 + 35π))/105 - 1712ln2/105 + + 41ν * π^2 / 96 + (2π*(214𝒾 + 35π))/105 - 1712ln(2)/105 - (856//105)*ln(v) ) + (v/c)^7 * ((-2𝒾 * ν * (-501655 + 24396ν) + 15*(-2173 + 2ν*(-2459 + 560ν))π) / 11340) # Eq. (6.17) of Blanchet et al. (2023) + (v/c)^8 * ( - - 846557506853//12713500800 + 45796γₑ/2205 - 22898𝒾*π/2205 - 107π^2/63 + 45796(2ln2+ln(v))/2205 - + (-336005827477//4237833600 + 15284γₑ/441 - 219314𝒾*π/2205 - 9755*π^2/32256 + 15284(2ln2+ln(v))/441)ν + - 846557506853//12713500800 + 45796γₑ/2205 - 22898𝒾*π/2205 - 107π^2/63 + 45796(2ln(2)+ln(v))/2205 + + (-336005827477//4237833600 + 15284γₑ/441 - 219314𝒾*π/2205 - 9755*π^2/32256 + 15284(2ln(2)+ln(v))/441)ν + (256450291//7413120 - 1025*π^2/1008)ν^2 - 81579187ν^3/15567552 + 26251249ν^4/31135104 ) ) @@ -94,15 +94,15 @@ is from Eq. (4.15) of that reference. h[Yindex(3,1,ℓₘᵢₙ)] = h₀ * @pn_expansion( (v/c)^1 * (𝒾 * δ / 12√14) + (v/c)^3 * (-𝒾 * δ * (4 + ν) / 18√14) - + (v/c)^4 * (δ * (7 + 5𝒾*π + 10ln2) / 60√14) + + (v/c)^4 * (δ * (7 + 5𝒾*π + 10ln(2)) / 60√14) + (v/c)^5 * (-𝒾 * δ * (-607 + ν*(272 + 247ν)) / 2376√14) + (v/c)^6 * ( - δ * (-5𝒾 * (16 + 7ν)π + 2*(-56 + ν - 5*(16 + 7ν)*ln2)) / 360√14 + δ * (-5𝒾 * (16 + 7ν)π + 2*(-56 + ν - 5*(16 + 7ν)*ln(2))) / 360√14 ) + (v/c)^7 * ( 𝒾 * δ / 12√14 * ( - (10753397//1513512) - 2ln2*((212//105) + ln2) - (26//21)*γₑ + (π^2/6) - - 2𝒾*π*((41//105) + ln2) + (ν/8)*(-(1738843//19305) + (41//8)*π^2) + (10753397//1513512) - 2ln(2)*((212//105) + ln(2)) - (26//21)*γₑ + (π^2/6) + - 2𝒾*π*((41//105) + ln(2)) + (ν/8)*(-(1738843//19305) + (41//8)*π^2) + (327059//30888)*ν^2 - (17525//15444)*ν^3 + ln(v) * (-26//21) ) @@ -117,15 +117,15 @@ is from Eq. (4.15) of that reference. h[Yindex(3,3,ℓₘᵢₙ)] = h₀ * @pn_expansion( (v/c)^1 * (-3𝒾 * √(15//224) * δ) + (v/c)^3 * (-3𝒾 * √(15//56) * δ * (-2 + ν)) - + (v/c)^4 * (√(243//70) * δ * (-7 - 5𝒾*π + 10ln³╱₂) / 4) + + (v/c)^4 * (√(243//70) * δ * (-7 - 5𝒾*π + 10ln(3/2)) / 4) + (v/c)^5 * (-𝒾 * √(3//542080) * δ * (369 + (-3676 + 887ν)ν)) - + (v/c)^6 * (δ * (-3645𝒾 * (-8 + 3ν)π + (40824 - 96206ν + 7290*(-8 + 3ν)ln³╱₂)) / 216√210) + + (v/c)^6 * (δ * (-3645𝒾 * (-8 + 3ν)π + (40824 - 96206ν + 7290*(-8 + 3ν)ln(3/2))) / 216√210) + (v/c)^7 * ( ((-3𝒾)/4) * √(15//14) * δ * ( - (19388147//280280) + (492//35)ln³╱₂ - 18*ln³╱₂^2 - (78//7)γₑ + (3//2)π^2 - + 6𝒾 * π * (-41//35 + 3ln³╱₂) + (19388147//280280) + (492//35)ln(3/2) - 18*ln(3/2)^2 - (78//7)γₑ + (3//2)π^2 + + 6𝒾 * π * (-41//35 + 3ln(3/2)) + (-7055//3432 + 41//64 * π^2)ν - (318841//17160)ν^2 + (8237//2860)ν^3 - + ln(v) * (-(39//7) * 4ln2) + + ln(v) * (-(39//7) * 4ln(2)) ) ) ) @@ -149,7 +149,7 @@ is from Eq. (4.15) of that reference. h[Yindex(4,1,ℓₘᵢₙ)] = h₀ * @pn_expansion( (v/c)^3 * (𝒾 * δ * (1 - 2ν) / 84√10) + (v/c)^5 * (-𝒾 * δ * (404 + (-1011 + 332ν)ν) / 11088√10) - + (v/c)^6 * (δ * (64 - 1661ν - 30𝒾*(-1 + 2ν)π + 60*(1 - 2ν)ln2) / 2520√10) + + (v/c)^6 * (δ * (64 - 1661ν - 30𝒾*(-1 + 2ν)π + 60*(1 - 2ν)ln(2)) / 2520√10) ) h[Yindex(4,2,ℓₘᵢₙ)] = h₀ * @pn_expansion( (v/c)^2 * (√5 * (1 - 3ν) / 63) @@ -160,12 +160,12 @@ is from Eq. (4.15) of that reference. h[Yindex(4,3,ℓₘᵢₙ)] = h₀ * @pn_expansion( (v/c)^3 * (9𝒾 * δ * (-1 + 2ν) / 4√70) + (v/c)^5 * (3𝒾 * δ * (468 + (-1267 + 524ν)ν) / 176√70) - + (v/c)^6 * (δ * (-5184 + 16301ν + 2430𝒾*(-1 + 2ν)π + 4860*(1 - 2ν)ln³╱₂) / 360√70) + + (v/c)^6 * (δ * (-5184 + 16301ν + 2430𝒾*(-1 + 2ν)π + 4860*(1 - 2ν)ln(3/2)) / 360√70) ) h[Yindex(4,4,ℓₘᵢₙ)] = h₀ * @pn_expansion( (v/c)^2 * (8 * √(5//7) * (-1 + 3ν) / 9) + (v/c)^4 * (4 * (1779 + 5ν*(-1273 + 525ν)) / 297√35) - + (v/c)^5 * ((160*(-1 + 3ν)π + 𝒾*(336 - 1193ν + 320*(-1 + 3ν)ln2)) / 9√35) + + (v/c)^5 * ((160*(-1 + 3ν)π + 𝒾*(336 - 1193ν + 320*(-1 + 3ν)ln(2))) / 9√35) + (v/c)^6 * ((-9618039 + 7ν*(9793071 + 5ν*(-3231338 + 678291ν))) / 405405√35) ) end @@ -175,7 +175,7 @@ is from Eq. (4.15) of that reference. h[Yindex(5,1,ℓₘᵢₙ)] = h₀ * @pn_expansion( (v/c)^3 * (𝒾 * δ * (1 - 2ν) / 288√385) + (v/c)^5 * (-𝒾 * δ * (179 + 4*(-88 + ν)ν) / 11232√385) - + (v/c)^6 * (δ * (181 - 70𝒾*(-1 + 2ν)π + 140ln2 - 28ν*(313 + 10ln2)) / 20160√385) + + (v/c)^6 * (δ * (181 - 70𝒾*(-1 + 2ν)π + 140ln(2) - 28ν*(313 + 10ln(2))) / 20160√385) ) h[Yindex(5,2,ℓₘᵢₙ)] = h₀ * @pn_expansion( (v/c)^4 * ((2 + 10*(-1 + ν)ν) / 27√55) @@ -184,7 +184,7 @@ is from Eq. (4.15) of that reference. h[Yindex(5,3,ℓₘᵢₙ)] = h₀ * @pn_expansion( (v/c)^3 * (9𝒾 * √(3//110) * δ * (-1 + 2ν) / 32) + (v/c)^5 * (3𝒾 * √(3//110) * δ * (207 + 8ν*(-58 + 11ν)) / 416) - + (v/c)^6 * (δ * (-395847 + 1171828ν + 153090𝒾*(-1 + 2ν)π - 306180*(-1 + 2ν)*ln³╱₂) / 60480√330) + + (v/c)^6 * (δ * (-395847 + 1171828ν + 153090𝒾*(-1 + 2ν)π - 306180*(-1 + 2ν)*ln(3/2)) / 60480√330) ) h[Yindex(5,4,ℓₘᵢₙ)] = h₀ * @pn_expansion( (v/c)^4 * ((-32 - 160*(-1 + ν)ν) / 9√165) @@ -193,7 +193,7 @@ is from Eq. (4.15) of that reference. h[Yindex(5,5,ℓₘᵢₙ)] = h₀ * @pn_expansion( (v/c)^3 * (-625𝒾 * δ * (-1 + 2ν) / 96√66) + (v/c)^5 * (-625𝒾 * δ * (263 + 16ν*(-43 + 16ν)) / 3744√66) - + (v/c)^6 * (δ * (565625 - 1481676ν - 218750𝒾*(-1 + 2ν)π + 437500*(-1 + 2ν)ln⁵╱₂) / 6720√66) + + (v/c)^6 * (δ * (565625 - 1481676ν - 218750𝒾*(-1 + 2ν)π + 437500*(-1 + 2ν)ln(5/2)) / 6720√66) ) end diff --git a/src/pn_expressions/pn_expressions.jl b/src/pn_expressions/pn_expressions.jl new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/src/pn_expressions/pn_expressions.jl @@ -0,0 +1 @@ + diff --git a/src/pn_expressions/separation.jl b/src/pn_expressions/separation.jl index 31f1a573..cec73b4b 100644 --- a/src/pn_expressions/separation.jl +++ b/src/pn_expressions/separation.jl @@ -239,7 +239,7 @@ from the Newton iterations in [`γₚₙ′`](@ref). ) γₚₙ₀′statements[end] = γₚₙ₀′return - if PNExpansionReducer === identity + if PNExpansionReducer ≡ identity # When `pn_expansion_reducer=Val(identity)` is passed, we return a PNExpansion NMax = Int(2PNOrder + 1) return quote diff --git a/src/pn_expressions/waveform.jl b/src/pn_expressions/waveform.jl new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/src/pn_expressions/waveform.jl @@ -0,0 +1 @@ + diff --git a/src/pn_systems.jl b/src/pn_systems.jl deleted file mode 100644 index f860ded7..00000000 --- a/src/pn_systems.jl +++ /dev/null @@ -1,312 +0,0 @@ -""" - PNSystem{ST, PNOrder} - -Base type for all PN systems, such as `BBH`, `BHNS`, and `NSNS`. - -These objects encode all essential properties of the binary, including its current state. -As such, they can be used as inputs to the various [fundamental](@ref Fundamental-variables) -and [derived variables](@ref Derived-variables), as well as [PN expressions](@ref) and -[dynamics](@ref Dynamics) functions. - -All subtypes should contain a `state` vector holding all of the fundamental variables for -the given type of system. The parameter `ST` is the type of the `state` vector — for -example, `Vector{Float64}`. `PNOrder` is a `Rational` giving the order to which PN -expansions should be carried. -""" -abstract type PNSystem{ST,PNOrder} end - -const VecOrPNSystem = Union{AbstractVector,PNSystem} - -const pnsystem_symbols = ( - :M₁, :M₂, :χ⃗₁ˣ, :χ⃗₁ʸ, :χ⃗₁ᶻ, :χ⃗₂ˣ, :χ⃗₂ʸ, :χ⃗₂ᶻ, :Rʷ, :Rˣ, :Rʸ, :Rᶻ, :v, :Φ -) - -for (i, s) ∈ enumerate(pnsystem_symbols) - sindex = Symbol("$(s)index") - @eval const $sindex = $i -end - -const χ⃗₁indices = χ⃗₁ˣindex:χ⃗₁ᶻindex -const χ⃗₂indices = χ⃗₂ˣindex:χ⃗₂ᶻindex -const Rindices = Rʷindex:Rᶻindex - -Base.eltype(::Type{PNT}) where {ST,PNT<:PNSystem{ST}} = eltype(ST) -Base.one(x::T) where {T<:PNSystem} = one(T) -Base.zero(x::T) where {T<:PNSystem} = zero(T) -Base.float(x::T) where {T<:PNSystem} = float(T) -Base.one(::Type{PNT}) where {PNT<:PNSystem} = one(eltype(PNT)) -Base.zero(::Type{PNT}) where {PNT<:PNSystem} = zero(eltype(PNT)) -Base.float(::Type{PNT}) where {PNT<:PNSystem} = float(eltype(PNT)) -pn_order(::PNSystem{ST,PNOrder}) where {ST,PNOrder} = PNOrder -order_index(pn::PNSystem) = 1 + Int(2pn_order(pn)) - -""" - causes_domain_error!(u̇, p) - -Ensure that these parameters correspond to a physically valid set of PN parameters. - -If the parameters are not valid, this function should modify `u̇` to indicate that the -current step is invalid. This is done by filling `u̇` with `NaN`s, which will be detected -by the ODE solver and cause it to try a different (smaller) step size. - -Currently, the only check that is done is to test that these parameters result in a PN -parameter v>0. In the future, this function may be expanded to include other checks. -""" -function causes_domain_error!(u̇, p::PNSystem{VT}) where {VT} - if p.state[vindex] ≤ 0 # If this is expanded, document the change in the docstring. - u̇ .= convert(eltype(VT), NaN) - true - else - false - end -end - -function prepare_system(; M₁, M₂, χ⃗₁, χ⃗₂, R, v, Φ=0, PNOrder=typemax(Int)) - state = [M₁; M₂; vec(QuatVec(χ⃗₁)); vec(QuatVec(χ⃗₂)); components(Rotor(R)); v; Φ] - ST = typeof(state) - PNOrder = prepare_pn_order(PNOrder) - return (ST, PNOrder, state) -end - -function prepare_pn_order(PNOrder) - if PNOrder != typemax(Int) - round(Int, 2PNOrder)//2 - else - (typemax(Int) - 2)//2 - end -end - -""" - BBH{T, PNOrder} - -The [`PNSystem`](@ref) subtype describing a binary black hole system. - -The `state` vector here holds the fundamental variables `M₁`, `M₂`, `χ⃗₁`, `χ⃗₂`, `R`, `v`, -with the spins unpacked into three components each, and `R` unpacked into four — for a total -of 13 elements. - -Optionally, `Φ` may also be tracked as the 14th element of the `state` vector. This is just -the integral of the orbital angular frequency `Ω`, and holds little interest for general -systems beyond a convenient description of how "far" the system has evolved. -""" -struct BBH{T,PNOrder} <: PNSystem{T,PNOrder} - state::T - - BBH{T,PNOrder}(state) where {T,PNOrder} = new{T,PNOrder}(state) - function BBH(; M₁, M₂, χ⃗₁, χ⃗₂, v, R=Rotor(1), Φ=0, PNOrder=typemax(Int), kwargs...) - (T, PNOrder, state) = prepare_system(; M₁, M₂, χ⃗₁, χ⃗₂, R, v, Φ, PNOrder) - return new{T,PNOrder}(state) - end - function BBH(state; Λ₁=0, Λ₂=0, PNOrder=typemax(Int)) - @assert length(state) == 14 - @assert Λ₁ == 0 - @assert Λ₂ == 0 - return new{typeof(state),prepare_pn_order(PNOrder)}(state) - end -end -const BHBH = BBH - -""" - BHNS{T, PNOrder} - -The [`PNSystem`](@ref) subtype describing a black-hole—neutron-star binary system. - -The `state` vector is the same as for a [`BBH`](@ref). There is an additional field `Λ₂` -holding the (constant) tidal-coupling parameter of the neutron star. - -Note that the neutron star is *always* object 2 — meaning that `M₂`, `χ⃗₂`, and `Λ₂` always -refer to it; `M₁` and `χ⃗₁` always refer to the black hole. See also [`NSNS`](@ref). -""" -struct BHNS{ST,PNOrder,ET} <: PNSystem{ST,PNOrder} - state::ST - Λ₂::ET - - BHNS{T,PNOrder,ET}(state) where {T,PNOrder,ET} = new{T,PNOrder,ET}(state) - BHNS{T,PNOrder}(state) where {T,PNOrder} = new{T,PNOrder,eltype(T)}(state) - function BHNS(; - M₁, M₂, χ⃗₁, χ⃗₂, v, R=Rotor(1), Λ₂, Φ=0, PNOrder=typemax(Int), kwargs... - ) - ST, PNOrder, state = prepare_system(; M₁, M₂, χ⃗₁, χ⃗₂, R, v, Φ, PNOrder) - ET = eltype(ST) - return new{ST,PNOrder,ET}(state, convert(ET, Λ₂)) - end - function BHNS(state; Λ₂, Λ₁=0, PNOrder=typemax(Int)) - @assert length(state) == 14 - ST, PNOrder = typeof(state), prepare_pn_order(PNOrder) - ET = eltype(ST) - return new{ST,PNOrder,ET}(state, convert(ET, Λ₂)) - end -end - -""" - NSNS{T, PNOrder} - -The [`PNSystem`](@ref) subtype describing a neutron-star—neutron-star binary system. - -The `state` vector is the same as for a [`BBH`](@ref). There are two additional fields `Λ₁` -and `Λ₂` holding the (constant) tidal-coupling parameters of the neutron stars. See also -[`BHNS`](@ref). -""" -struct NSNS{ST,PNOrder,ET} <: PNSystem{ST,PNOrder} - state::ST - Λ₁::ET - Λ₂::ET - - NSNS{T,PNOrder,ET}(state) where {T,PNOrder,ET} = new{T,PNOrder,ET}(state) - NSNS{T,PNOrder}(state) where {T,PNOrder} = new{T,PNOrder,eltype(T)}(state) - function NSNS(; - M₁, M₂, χ⃗₁, χ⃗₂, v, R=Rotor(1), Λ₁, Λ₂, Φ=0, PNOrder=typemax(Int), kwargs... - ) - ST, PNOrder, state = prepare_system(; M₁, M₂, χ⃗₁, χ⃗₂, R, v, Φ, PNOrder) - ET = eltype(ST) - return new{ST,PNOrder,ET}(state, convert(ET, Λ₁), convert(ET, Λ₂)) - end - function NSNS(state; Λ₁, Λ₂, PNOrder=typemax(Int)) - @assert length(state) == 14 - ST, PNOrder = typeof(state), prepare_pn_order(PNOrder) - ET = eltype(state) - return new{ST,PNOrder,ET}(state, convert(ET, Λ₁), convert(ET, Λ₂)) - end -end -const BNS = NSNS - -""" - FDPNSystem{FT, PNOrder}(state, Λ₁, Λ₂) - -A `PNSystem` that contains information as variables from -[`FastDifferentiation.jl`](https://docs.juliahub.com/General/FastDifferentiation/stable/). - -See also [`fd_pnsystem`](@ref) for a particular instance of this type. Note that this type -also involves the type `FT`, which will be the float type of actual numbers that eventually -get fed into (and will be passed out from) functions that use this system. The correct type -of `FDPNSystem` is used in calculating `𝓔′`. -""" -struct FDPNSystem{FT,PNOrder} <: PNSystem{Vector{FastDifferentiation.Node},PNOrder} - state::Vector{FastDifferentiation.Node} - Λ₁::FastDifferentiation.Node - Λ₂::FastDifferentiation.Node - - function FDPNSystem(FT, PNOrder=typemax(Int)) - FastDifferentiation.@variables M₁ M₂ χ⃗₁ˣ χ⃗₁ʸ χ⃗₁ᶻ χ⃗₂ˣ χ⃗₂ʸ χ⃗₂ᶻ Rʷ Rˣ Rʸ Rᶻ v Φ Λ₁ Λ₂ - return new{FT,prepare_pn_order(PNOrder)}( - [M₁, M₂, χ⃗₁ˣ, χ⃗₁ʸ, χ⃗₁ᶻ, χ⃗₂ˣ, χ⃗₂ʸ, χ⃗₂ᶻ, Rʷ, Rˣ, Rʸ, Rᶻ, v, Φ], Λ₁, Λ₂ - ) - end -end -Base.eltype(::FDPNSystem{FT}) where {FT} = FT - -""" - fd_pnsystem - -A symbolic `PNSystem` that contains symbolic information for all types of `PNSystem`s. - -In particular, note that this object has (essentially) infinite `PNOrder`, has nonzero -values for quantities like `Λ₁` and `Λ₂`, and assumes that the eventual output will be in -`Float64`. If you want different choices, you may need to call [`FDPNSystem`](@ref) -yourself, or even construct a different specialized subtype of `PNSystem` (it's not hard). - -# Examples -```jldoctest -julia> using PostNewtonian: M₁, M₂, χ⃗₁, χ⃗₂, FDPNSystem - -julia> fd_pnsystem = FDPNSystem(Float64) -FDPNSystem{Float64, 9223372036854775805//2}(FastDifferentiation.Node[M₁, M₂, χ⃗₁ˣ, χ⃗₁ʸ, χ⃗₁ᶻ, χ⃗₂ˣ, χ⃗₂ʸ, χ⃗₂ᶻ, Rʷ, Rˣ, Rʸ, Rᶻ, v, Φ], Λ₁, Λ₂) - -julia> M₁(fd_pnsystem), M₂(fd_pnsystem) -(M₁, M₂) - -julia> χ⃗₁(fd_pnsystem) - + χ⃗₁ˣ𝐢 + χ⃗₁ʸ𝐣 + χ⃗₁ᶻ𝐤 - -julia> χ⃗₂(fd_pnsystem) - + χ⃗₂ˣ𝐢 + χ⃗₂ʸ𝐣 + χ⃗₂ᶻ𝐤 -``` -""" -const fd_pnsystem = FDPNSystem(Float64) - -function SVector(pnsystem::PNSystem) - return SVector{16,eltype(pnsystem)}( - pnsystem.state[1], - pnsystem.state[2], - pnsystem.state[3], - pnsystem.state[4], - pnsystem.state[5], - pnsystem.state[6], - pnsystem.state[7], - pnsystem.state[8], - pnsystem.state[9], - pnsystem.state[10], - pnsystem.state[11], - pnsystem.state[12], - pnsystem.state[13], - pnsystem.state[14], - Λ₁(pnsystem), - Λ₂(pnsystem), - ) -end -function SVector(pnsystem::FDPNSystem) - return SVector{16,FastDifferentiation.Node}( - pnsystem.state[1], - pnsystem.state[2], - pnsystem.state[3], - pnsystem.state[4], - pnsystem.state[5], - pnsystem.state[6], - pnsystem.state[7], - pnsystem.state[8], - pnsystem.state[9], - pnsystem.state[10], - pnsystem.state[11], - pnsystem.state[12], - pnsystem.state[13], - pnsystem.state[14], - Λ₁(pnsystem), - Λ₂(pnsystem), - ) -end - -@testitem "PNSystem constructors" begin - using Quaternionic - - pnA = BBH(; - M₁=1.0f0, M₂=2.0f0, χ⃗₁=Float32[3.0, 4.0, 5.0], χ⃗₂=Float32[6.0, 7.0, 8.0], v=0.23f0 - ) - @test pnA.state == - Float32[1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; 1.0; 0.0; 0.0; 0.0; 0.23; 0.0] - - pnB = BBH(; - M₁=1.0f0, - M₂=2.0f0, - χ⃗₁=Float32[3.0, 4.0, 5.0], - χ⃗₂=Float32[6.0, 7.0, 8.0], - v=0.23f0, - Φ=9.0f0, - ) - @test pnB.state == - Float32[1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; 1.0; 0.0; 0.0; 0.0; 0.23; 9.0] - - R = randn(RotorF32) - pn1 = BBH(; - M₁=1.0f0, - M₂=2.0f0, - χ⃗₁=Float32[3.0, 4.0, 5.0], - χ⃗₂=Float32[6.0, 7.0, 8.0], - R=R, - v=0.23f0, - ) - @test pn1.state ≈ [1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; components(R)...; 0.23; 0.0] - - pn2 = BBH(; - M₁=1.0f0, - M₂=2.0f0, - χ⃗₁=Float32[3.0, 4.0, 5.0], - χ⃗₂=Float32[6.0, 7.0, 8.0], - R=R, - v=0.23f0, - Φ=9.0f0, - ) - @test pn2.state ≈ [1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; components(R)...; 0.23; 9.0] - - pn1.state[end] = 9.0f0 - @test pn1.state == pn2.state -end diff --git a/src/pn_systems/BBH.jl b/src/pn_systems/BBH.jl new file mode 100644 index 00000000..3b9fc53f --- /dev/null +++ b/src/pn_systems/BBH.jl @@ -0,0 +1,127 @@ +""" + BBH{NT, ST, PNOrder} <: PNSystem{NT, ST, PNOrder} + +The [`PNSystem`](@ref) subtype describing a binary black hole system. + +The `state` vector here holds the fundamental state variables characterizing the masses, +spins, orientation, velocity, and orbital phase of the system. The spins unpacked into +three components each. The orientation is described by the four components of the `Rotor` +`R`. This gives us a total of 14 elements: + + M₁, M₂, χ₁ˣ, χ₁ʸ, χ₁ᶻ, χ₂ˣ, χ₂ʸ, χ₂ᶻ, Rʷ, Rˣ, Rʸ, Rᶻ, v, Φ + +The "orbital phase" `Φ` is tracked as the 14th element of the `state` vector. This is just +the integral of the (scalar) orbital angular frequency `Ω`, and holds little interest for +general systems beyond a convenient description of how "far" the system has evolved. For +nonprecessing systems, `Φ` would be sufficient to describe the system's position, which is +more completely described by the `Rotor` `R`. However, for precessing systems, it is +difficult to extract this quantity from `R`. +""" +@export struct BBH{NT,PNOrder,ST} <: Quasispherical{NT,PNOrder,ST} + state::ST + + function BBH{NT,PNOrder,ST}(state) where {NT,PNOrder,ST} + if eachindex(state) != Base.OneTo(14) + error( + "The `state` vector for `BBH` must be indexed from 1 to 14; " * + "input is indexed `$(eachindex(state))`.", + ) + end + new{NT,PNOrder,ST}(state) + end + function BBH(; M₁, M₂, χ⃗₁, χ⃗₂, v, R=Rotor(1), Φ=0, PNOrder=typemax(Int), Λ₁=0, Λ₂=0) + if Λ₁ != 0 || Λ₂ != 0 + error( + "`BBH` does not support tidal-coupling parameters `Λ₁` or `Λ₂`; " * + "use `BHNS` or `NSNS` instead.", + ) + end + (NT, PNOrder, state) = prepare_Quasispherical(; M₁, M₂, χ⃗₁, χ⃗₂, R, v, Φ, PNOrder) + return new{NT,PNOrder,typeof(state)}(state) + end +end +@public const BHBH = BBH + +# The following are methods of functions defined in `vector_interface.jl` and +# `state_variables.jl`, specialized for `BBH` systems. +Base.length(pnsystem::BBH) = 14 # Specialize this just for efficiency +state(pnsystem::BBH) = pnsystem.state +symbols(::Type{<:BBH}) = symbols(Quasispherical) +ascii_symbols(::Type{<:BBH}) = ascii_symbols(Quasispherical) +for (i, (symbol, ascii_symbol)) ∈ enumerate(zip(symbols(BBH), ascii_symbols(BBH))) + # We could do this manually, but this is more concise and less error-prone. + @eval begin + # Define, e.g., `M₁(pnsystem::BBH) = pnsystem.state[1]`. + $(symbol)(pnsystem::BBH) = @inbounds pnsystem.state[$i] + + # Specialize `symbol_index` for Val{:M₁}, Val{:M₂}, etc. + symbol_index(::Type{T}, ::Val{$(QuoteNode(symbol))}) where {T<:BBH} = $i + end + if symbol ≠ ascii_symbol + @eval begin + # Specialize `symbol_index` for Val{:M1}, Val{:M2}, etc. + symbol_index(::Type{T}, ::Val{$(QuoteNode(ascii_symbol))}) where {T<:BBH} = $i + end + end +end + +# Define any state-variable methods we may need for variables that are not actually in the +# state vector. +Λ₁(pnsystem::BBH) = zero(pnsystem) +Λ₂(pnsystem::BBH) = zero(pnsystem) + +@testitem "BBH constructors" begin + using PostNewtonian: state, constant_convert + using Quaternionic + + pnA = BBH(; + M₁=1.0f0, M₂=2.0f0, χ⃗₁=Float32[3.0, 4.0, 5.0], χ⃗₂=Float32[6.0, 7.0, 8.0], v=0.23f0 + ) + @test eltype(pnA) == Float32 + @test state(pnA) == + Float32[1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; 1.0; 0.0; 0.0; 0.0; 0.23; 0.0] + @test constant_convert(pnA, π) isa Float32 + @test constant_convert(pnA, π) == Float32(π) + + pnB = BBH(; + M₁=1.0f0, + M₂=2.0f0, + χ⃗₁=Float32[3.0, 4.0, 5.0], + χ⃗₂=Float32[6.0, 7.0, 8.0], + v=0.23f0, + Φ=9.0f0, + ) + @test state(pnB) == + Float32[1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; 1.0; 0.0; 0.0; 0.0; 0.23; 9.0] + @test constant_convert(pnB, π) isa Float32 + @test constant_convert(pnB, π) == Float32(π) + + R = randn(RotorF32) + pn1 = BBH(; + M₁=1.0f0, + M₂=2.0f0, + χ⃗₁=Float32[3.0, 4.0, 5.0], + χ⃗₂=Float32[6.0, 7.0, 8.0], + R=R, + v=0.23f0, + ) + @test state(pn1) ≈ [1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; components(R)...; 0.23; 0.0] + @test constant_convert(pn1, π) isa Float32 + @test constant_convert(pn1, π) == Float32(π) + + pn2 = BBH(; + M₁=1.0f0, + M₂=2.0f0, + χ⃗₁=Float32[3.0, 4.0, 5.0], + χ⃗₂=Float32[6.0, 7.0, 8.0], + R=R, + v=0.23f0, + Φ=9.0f0, + ) + @test state(pn2) ≈ [1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; components(R)...; 0.23; 9.0] + @test constant_convert(pn2, π) isa Float32 + @test constant_convert(pn2, π) == Float32(π) + + state(pn1)[end] = 9.0f0 + @test state(pn1) == state(pn2) +end diff --git a/src/pn_systems/BHNS.jl b/src/pn_systems/BHNS.jl new file mode 100644 index 00000000..a93d7653 --- /dev/null +++ b/src/pn_systems/BHNS.jl @@ -0,0 +1,168 @@ +""" + BHNS{NT, ST, PNOrder} <: PNSystem{NT, ST, PNOrder} + +The [`PNSystem`](@ref) subtype describing a black-hole—neutron-star binary system. + +The `state` vector is the same as for a [`BBH`](@ref), with an additional field `Λ₂` holding +the (constant) tidal-coupling parameter of the neutron star. + +Note that the neutron star is *always* object 2 — meaning that `M₂`, `χ⃗₂`, and `Λ₂` always +refer to it; `M₁` and `χ⃗₁` always refer to the black hole. (It's "BHNS", not "NSBH".) See +also [`NSNS`](@ref). +""" +@export struct BHNS{NT,PNOrder,ST} <: Quasispherical{NT,PNOrder,ST} + state::ST + + function BHNS{NT,PNOrder,ST}(state) where {NT,PNOrder,ST} + if eachindex(state) != Base.OneTo(15) + error( + "The `state` vector for `BHNS` must be indexed from 1 to 15; " * + "input is indexed `$(eachindex(state))`.", + ) + end + new{NT,PNOrder,ST}(state) + end + function BHNS(; M₁, M₂, χ⃗₁, χ⃗₂, v, R=Rotor(1), Φ=0, Λ₁=0, Λ₂, PNOrder=typemax(Int)) + if Λ₁ != 0 + error( + "`BHNS` does not support a tidal-coupling parameter `Λ₁` for object 1; " * + "use `NSNS` instead.", + ) + end + (NT, PNOrder, state) = prepare_Quasispherical(; M₁, M₂, χ⃗₁, χ⃗₂, R, v, Φ, PNOrder) + state = vcat(state, Λ₂) + return new{eltype(state),PNOrder,typeof(state)}(state) + end +end + +# The following are methods of functions defined in `vector_interface.jl` and +# `state_variables.jl`, specialized for `BBH` systems. +Base.length(pnsystem::BHNS) = 15 # Specialize this just for efficiency +state(pnsystem::BHNS) = pnsystem.state +function symbols(::Type{<:BHNS}) + (symbols(Quasispherical)..., :Λ₂) +end +function ascii_symbols(::Type{<:BHNS}) + (ascii_symbols(Quasispherical)..., :Lambda2) +end +for (i, (symbol, ascii_symbol)) ∈ enumerate(zip(symbols(BHNS), ascii_symbols(BHNS))) + # We could do this manually, but this is more concise and less error-prone. + @eval begin + # Define, e.g., `M₁(pnsystem::BHNS) = pnsystem.state[1]`. + $(symbol)(pnsystem::BHNS) = @inbounds pnsystem.state[$i] + + # Specialize `symbol_index` for Val{:M₁}, Val{:M₂}, etc. + symbol_index(::Type{T}, ::Val{$(QuoteNode(symbol))}) where {T<:BHNS} = $i + end + if symbol ≠ ascii_symbol + @eval begin + # Specialize `symbol_index` for Val{:M1}, Val{:M2}, etc. + symbol_index(::Type{T}, ::Val{$(QuoteNode(ascii_symbol))}) where {T<:BHNS} = $i + end + end +end + +# Define any state-variable methods we may need for variables that are not actually in the +# state vector. +Λ₁(pnsystem::BHNS) = zero(pnsystem) + +@testitem "BHNS constructors" begin + using PostNewtonian: state, constant_convert + using Quaternionic + + # minimal constructor: default Φ=0, R=Rotor(1) + pnA = BHNS( + M₁=1.0f0, + M₂=2.0f0, + χ⃗₁=Float32[3.0, 4.0, 5.0], + χ⃗₂=Float32[6.0, 7.0, 8.0], + v=0.23f0, + Λ₂=4.0f0, + ) + @test eltype(pnA) == Float32 + @test state(pnA) == Float32[ + 1.0; + 2.0; + 3.0; + 4.0; + 5.0; + 6.0; + 7.0; + 8.0; + 1.0; + 0.0; + 0.0; + 0.0; + 0.23; + 0.0; + 4.0 + ] + @test constant_convert(pnA, π) isa Float32 + @test constant_convert(pnA, π) == Float32(π) + + # explicit orbital phase + pnB = BHNS( + M₁=1.0f0, + M₂=2.0f0, + χ⃗₁=Float32[3.0, 4.0, 5.0], + χ⃗₂=Float32[6.0, 7.0, 8.0], + v=0.23f0, + Φ=9.0f0, + Λ₂=4.0f0, + ) + @test state(pnB) == Float32[ + 1.0; + 2.0; + 3.0; + 4.0; + 5.0; + 6.0; + 7.0; + 8.0; + 1.0; + 0.0; + 0.0; + 0.0; + 0.23; + 9.0; + 4.0 + ] + @test constant_convert(pnB, π) isa Float32 + @test constant_convert(pnB, π) == Float32(π) + + # custom rotor, default Φ + R = randn(RotorF32) + pn1 = BHNS( + M₁=1.0f0, + M₂=2.0f0, + χ⃗₁=Float32[3.0, 4.0, 5.0], + χ⃗₂=Float32[6.0, 7.0, 8.0], + R=R, + v=0.23f0, + Λ₂=4.0f0, + ) + @test state(pn1) ≈ + [1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; components(R)...; 0.23; 0.0; 4.0] + @test constant_convert(pn1, π) isa Float32 + @test constant_convert(pn1, π) == Float32(π) + + # custom rotor and Φ + pn2 = BHNS( + M₁=1.0f0, + M₂=2.0f0, + χ⃗₁=Float32[3.0, 4.0, 5.0], + χ⃗₂=Float32[6.0, 7.0, 8.0], + R=R, + v=0.23f0, + Φ=9.0f0, + Λ₂=4.0f0, + ) + @test state(pn2) ≈ + [1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; components(R)...; 0.23; 9.0; 4.0] + @test constant_convert(pn2, π) isa Float32 + @test constant_convert(pn2, π) == Float32(π) + + # mutating the second-to-last element (Φ) to match pn2 + pn1[end - 1] = 9.0f0 + @test state(pn1) == state(pn2) +end diff --git a/src/pn_systems/FDPNsystem.jl b/src/pn_systems/FDPNsystem.jl new file mode 100644 index 00000000..478667b2 --- /dev/null +++ b/src/pn_systems/FDPNsystem.jl @@ -0,0 +1,111 @@ +""" + FDPNSystem{NT, PN, PNOrder} <: PNSystem{Node, Vector{Node}, PNOrder} + +A `PNSystem` that contains information as variables of type `Node` from +[`FastDifferentiation.jl`](https://docs.juliahub.com/General/FastDifferentiation/stable/). + +Note that this type also involves the type parameter `PN`, which is actually the type of a +`PNSystem`, and its type parameter `NT`, which will be the number type of actual numbers +that eventually get fed into (and will be passed out from) functions that use this system. + +One important example of what this type is used for is computing the derivative of the +orbital binding energy, `𝓔′` — and in particular, for generating the corresponding function +method to apply to a given `PNSystem`. + +!!! warning + + Because of the structure of the type parameters, most methods defined for a general + `PNSystem` will use `Node` as the number type. This may be correct in many cases, but + when `Node` is applied to an integer, for example, it will generally result in a + `Float64` value, rather than the `NT` type parameter. For this reason many methods + will need to be specialized for `FDPNSystem` types, using almost the same definition, + but with the additional `FD` prefix inserted throughout. +""" +@export struct FDPNSystem{NT,PNOrder,PN<:PNSystem{NT,PNOrder}} <: + PNSystem{FDNode,PNOrder,Vector{FDNode}} + state::Vector{FDNode} + + FDPNSystem(pnsystem::PNSystem) = FDPNSystem(typeof(pnsystem)) + function FDPNSystem(::Type{PN}) where {NT,PNOrder,PN<:PNSystem{NT,PNOrder}} + return new{NT,PNOrder,PN}([FDNode(s) for s ∈ symbols(PN)]) + end +end + +state(pnsystem::FDPNSystem) = pnsystem.state + +# This is an example of where we need to specialize the method for `FDPNSystem`, as +# explained in the docstring. +Base.eltype(::FDPNSystem{FT}) where {FT} = FT + +symbols(pnsystem::FDPNSystem{NT,PNOrder,PN}) where {NT,PNOrder,PN} = symbols(PN) +symbols(::Type{T}) where {NT,PNOrder,PN,T<:FDPNSystem{NT,PNOrder,PN}} = symbols(PN) + +function symbol_index(pnsystem::FDPNSystem{NT,PNOrder,PN}, s::Symbol) where {NT,PNOrder,PN} + symbol_index(PN, Val(s)) +end +function symbol_index(::Type{T}, ::Val{S}) where {T<:FDPNSystem,S} + index = findfirst(y -> y == S, symbols(T)) + if isnothing(index) + index = findfirst(y -> y == S, ascii_symbols(T)) + end + if isnothing(index) + error( + "Type `$(T)` has no symbol `:$(S)`.\n" * + "This type's symbols are `$(symbols(T))`.\n" * + "The ASCII equivalents are `$(ascii_symbols(T))`.\n", + ) + else + index + end +end + +# These are more examples of where we need to specialize the method for `FDPNSystem`, as +# explained in the docstring. +constant_convert(::T, x::ExactNumber) where {NT,T<:FDPNSystem{NT}} = NT(x) +constant_convert(::T, x::NT) where {NT,T<:FDPNSystem{NT}} = x + +@testitem "FDPNSystem" begin + using PostNewtonian: constant_convert + @testset "BBH" begin + PNOrder = 7//2 + for NT ∈ (Float16, Float64) + bbh = BBH(randn(NT, 14), PNOrder) + fdpnsystem = FDPNSystem(bbh) + @test fdpnsystem isa FDPNSystem{eltype(bbh),PNOrder,typeof(bbh)} + @test pn_order(fdpnsystem) == PNOrder + @test eltype(fdpnsystem) == NT + @test symbols(fdpnsystem) == symbols(bbh) + @test length(fdpnsystem) == 14 + @test constant_convert(fdpnsystem, π) isa NT + @test constant_convert(fdpnsystem, π) == NT(π) + end + end + @testset "BHNS" begin + PNOrder = typemax(Int) + for NT ∈ (Float16, Float64) + bhns = BHNS(randn(NT, 15), PNOrder) + fdpnsystem = FDPNSystem(bhns) + @test fdpnsystem isa FDPNSystem{eltype(bhns),max_pn_order,typeof(bhns)} + @test pn_order(fdpnsystem) == max_pn_order + @test eltype(fdpnsystem) == NT + @test symbols(fdpnsystem) == symbols(bhns) + @test length(fdpnsystem) == 15 + @test constant_convert(fdpnsystem, π) isa NT + @test constant_convert(fdpnsystem, π) == NT(π) + end + end + @testset "NSNS" begin + PNOrder = 3.5 + for NT ∈ (Float16, Float64) + nsns = NSNS(randn(NT, 16), PNOrder) + fdpnsystem = FDPNSystem(nsns) + @test fdpnsystem isa FDPNSystem{eltype(nsns),7//2,typeof(nsns)} + @test pn_order(fdpnsystem) == 7//2 + @test eltype(fdpnsystem) == NT + @test symbols(fdpnsystem) == symbols(nsns) + @test length(fdpnsystem) == 16 + @test constant_convert(fdpnsystem, π) isa NT + @test constant_convert(fdpnsystem, π) == NT(π) + end + end +end diff --git a/src/pn_systems/NSNS.jl b/src/pn_systems/NSNS.jl new file mode 100644 index 00000000..921af0d7 --- /dev/null +++ b/src/pn_systems/NSNS.jl @@ -0,0 +1,162 @@ +""" + NSNS{NT, PNOrder, ST} <: PNSystem{NT, PNOrder, ST} + +The [`PNSystem`](@ref) subtype describing a neutron-star—neutron-star binary system. + +The `state` vector is the same as for a [`BBH`](@ref), with two additional fields `Λ₁` +and `Λ₂` holding the (constant) tidal-coupling parameters of the neutron stars. See also +[`BHNS`](@ref). +""" +@export struct NSNS{NT,PNOrder,ST} <: Quasispherical{NT,PNOrder,ST} + state::ST + + function NSNS{NT,PNOrder,ST}(state) where {NT,PNOrder,ST} + if eachindex(state) != Base.OneTo(16) + error( + "The `state` vector for `NSNS` must be indexed from 1 to 16; " * + "input is indexed `$(eachindex(state))`.", + ) + end + new{NT,PNOrder,ST}(state) + end + function NSNS(; M₁, M₂, χ⃗₁, χ⃗₂, v, R=Rotor(1), Φ=0, Λ₁, Λ₂, PNOrder=typemax(Int)) + (NT, PNOrder, state) = prepare_Quasispherical(; M₁, M₂, χ⃗₁, χ⃗₂, R, v, Φ, PNOrder) + state = vcat(state, Λ₁, Λ₂) + return new{eltype(state),PNOrder,typeof(state)}(state) + end +end +@public const BNS = NSNS + +# The following are methods of functions defined in `vector_interface.jl` and +# `state_variables.jl`, specialized for `BBH` systems. +Base.length(pnsystem::NSNS) = 16 # Specialize this just for efficiency +state(pnsystem::NSNS) = pnsystem.state +function symbols(::Type{<:NSNS}) + (symbols(Quasispherical)..., :Λ₁, :Λ₂) +end +function ascii_symbols(::Type{<:NSNS}) + (ascii_symbols(Quasispherical)..., :Lambda1, :Lambda2) +end +for (i, (symbol, ascii_symbol)) ∈ enumerate(zip(symbols(NSNS), ascii_symbols(NSNS))) + # We could do this manually, but this is more concise and less error-prone. + @eval begin + # Define, e.g., `M₁(pnsystem::NSNS) = pnsystem.state[1]`. + $(symbol)(pnsystem::NSNS) = @inbounds pnsystem.state[$i] + + # Specialize `symbol_index` for Val{:M₁}, Val{:M₂}, etc. + symbol_index(::Type{T}, ::Val{$(QuoteNode(symbol))}) where {T<:NSNS} = $i + end + if symbol ≠ ascii_symbol + @eval begin + # Specialize `symbol_index` for Val{:M1}, Val{:M2}, etc. + symbol_index(::Type{T}, ::Val{$(QuoteNode(ascii_symbol))}) where {T<:NSNS} = $i + end + end +end + +@testitem "NSNS constructors" begin + using PostNewtonian: state, constant_convert + using Quaternionic + + # minimal constructor: default Φ=0, R=Rotor(1) + pnA = NSNS( + M₁=1.0f0, + M₂=2.0f0, + χ⃗₁=Float32[3.0, 4.0, 5.0], + χ⃗₂=Float32[6.0, 7.0, 8.0], + v=0.23f0, + Λ₁=5.0f0, + Λ₂=6.0f0, + ) + @test eltype(pnA) == Float32 + @test state(pnA) == Float32[ + 1.0; + 2.0; + 3.0; + 4.0; + 5.0; + 6.0; + 7.0; + 8.0; + 1.0; + 0.0; + 0.0; + 0.0; + 0.23; + 0.0; + 5.0; + 6.0 + ] + @test constant_convert(pnA, π) isa Float32 + @test constant_convert(pnA, π) == Float32(π) + + # explicit orbital phase + pnB = NSNS( + M₁=1.0f0, + M₂=2.0f0, + χ⃗₁=Float32[3.0, 4.0, 5.0], + χ⃗₂=Float32[6.0, 7.0, 8.0], + v=0.23f0, + Φ=9.0f0, + Λ₁=5.0f0, + Λ₂=6.0f0, + ) + @test state(pnB) == Float32[ + 1.0; + 2.0; + 3.0; + 4.0; + 5.0; + 6.0; + 7.0; + 8.0; + 1.0; + 0.0; + 0.0; + 0.0; + 0.23; + 9.0; + 5.0; + 6.0 + ] + @test constant_convert(pnB, π) isa Float32 + @test constant_convert(pnB, π) == Float32(π) + + # custom rotor, default Φ + R = randn(RotorF32) + pn1 = NSNS( + M₁=1.0f0, + M₂=2.0f0, + χ⃗₁=Float32[3.0, 4.0, 5.0], + χ⃗₂=Float32[6.0, 7.0, 8.0], + R=R, + v=0.23f0, + Λ₁=5.0f0, + Λ₂=6.0f0, + ) + @test state(pn1) ≈ + [1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; components(R)...; 0.23; 0.0; 5.0; 6.0] + @test constant_convert(pn1, π) isa Float32 + @test constant_convert(pn1, π) == Float32(π) + + # custom rotor and Φ + pn2 = NSNS( + M₁=1.0f0, + M₂=2.0f0, + χ⃗₁=Float32[3.0, 4.0, 5.0], + χ⃗₂=Float32[6.0, 7.0, 8.0], + R=R, + v=0.23f0, + Φ=9.0f0, + Λ₁=5.0f0, + Λ₂=6.0f0, + ) + @test state(pn2) ≈ + [1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; components(R)...; 0.23; 9.0; 5.0; 6.0] + @test constant_convert(pn2, π) isa Float32 + @test constant_convert(pn2, π) == Float32(π) + + # mutating the second-to-last element (Φ) to match pn2 + pn1[end - 2] = 9.0f0 + @test state(pn1) == state(pn2) +end diff --git a/src/pn_systems/PNSystem.jl b/src/pn_systems/PNSystem.jl new file mode 100644 index 00000000..1cb68fd6 --- /dev/null +++ b/src/pn_systems/PNSystem.jl @@ -0,0 +1,134 @@ +""" + PNSystem{NT, PNOrder, ST} + +Base type for all PN systems, such as `BBH`, `BHNS`, and `NSNS`. + +These objects encode all essential properties of the binary, including its current state. +As such, they can be used as inputs to the various [fundamental](@ref Fundamental-variables) +and [derived variables](@ref Derived-variables), as well as [PN expressions](@ref) and +[dynamics](@ref Dynamics) functions. + +The parameter `NT` is the number type of the system, such as `Float64` or `Dual{SomeTag, +Float64, 7}`. The parameter `ST <: AbstractVector{NT}` is the type returned by the `state` +function, which probably just returns the `state` vector stored in the concrete subtype. As +such, this will probably be `MVector{N, NT}` or `SVector{N, NT}`, where `N` is the number of +elements in the state. `PNOrder` is a `Rational` giving the order to which PN expansions +should be carried out when using the given object. +""" +@export abstract type PNSystem{NT<:Number,PNOrder,ST<:AbstractVector{NT}} <: + AbstractVector{NT} end + +""" + pnsystem::PNSystem(; kwargs...) + +State-modifying copy constructor for `PNSystem` objects. + +!!! warning + + This function is slow; it should not be used in performance-critical code. + +Note that this cannot modify the type's parameters — the number type `NT`, the `PNOrder` of +the system, or the state type `ST`. However, it can modify any of the state variables by +symbol or by ASCII symbol. This function will raise an AssertionError if any of the keys in +`kwargs` is not a valid symbol for the given `PNSystem` type. + +```jldoctest +julia> using PostNewtonian: BBH + +julia> pnsystem = BBH(ones(14)/2; PNOrder=7//2) +BBH{Vector{Float64}, 7//2}([0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5]) + +julia> pnsystem2 = pnsystem(M₁=0.2, M₂=0.8, chi1x=0.1) +BBH{Vector{Float64}, 7//2}([0.2, 0.8, 0.1, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5]) +``` +""" +function (pnsystem::PNSystem{NT,PNOrder,ST})(; kwargs...) where {NT,PNOrder,ST} + all_symbols = Set(symbols(pnsystem)) ∪ Set(ascii_symbols(pnsystem)) + @assert keys(kwargs) ⊆ all_symbols ( + "PNSystem of type $(typeof(pnsystem)) does not have these symbols, which were " * + "input as keyword arguments:\n $(setdiff(keys(kwargs), all_symbols))\n" * + "Maybe you passed `String`s instead of `Symbol`s?\n" * + "The available symbols for this type are\n" * + " $(symbols(pnsystem))\n" * + "and their ASCII equivalents:\n" * + " $(ascii_symbols(pnsystem))" + ) + state = Tuple( + get(kwargs, symbol, get(kwargs, ascii_symbol, pnsystem[symbol])) for + (symbol, ascii_symbol) ∈ zip(symbols(pnsystem), ascii_symbols(pnsystem)) + ) + typeof(pnsystem)(ST(SVector(state))) +end + +""" + state(pnsystem::PNSystem) + +Return the state vector of `pnsystem`, which is a vector of fundamental variables for the +given PN system. + +Note that the built-in `PNSystem` subtypes have a `state` field that is a vector, so this +function will just return that vector. However, that may not always be true for +user-defined subtypes. + +This function should have a specialized method for each concrete subtype of `PNSystem`. +""" +@public function state(::T) where {T<:PNSystem} + error("`state` is not yet defined for PNSystem subtype `$T`.") +end + +Base.eltype(::Type{PNT}) where {NT,PNT<:PNSystem{NT}} = NT +Base.one(::Type{PNT}) where {PNT<:PNSystem} = one(eltype(PNT)) +Base.one(x::T) where {T<:PNSystem} = one(T) +Base.zero(::Type{PNT}) where {PNT<:PNSystem} = zero(eltype(PNT)) +Base.zero(x::T) where {T<:PNSystem} = zero(T) +Base.float(::Type{PNT}) where {PNT<:PNSystem} = float(eltype(PNT)) +Base.float(x::T) where {T<:PNSystem} = float(T) + +""" + symbols(pnsystem::PNSystem) + symbols(::Type{<:PNSystem}) + ascii_symbols(pnsystem::PNSystem) + ascii_symbols(::Type{<:PNSystem}) + +Return a Tuple of symbols corresponding to the variables tracked by `pnsystem`, in the order +in which they are stored in the `state` vector. + +The `ascii_symbols` function returns those symbols in ASCII form, enabling interaction with +external systems (e.g., Python) that do not support many Unicode symbols. + +These functions should have specialized methods for each concrete subtype of `PNSystem`. +For example, the `BBH` system has 14 state variables, as seen in the following example: +```jldoctest +julia> using PostNewtonian: BBH + +julia> pnsystem = BBH(randn(14); PNOrder=7//2); + +julia> symbols(pnsystem) +(:M₁, :M₂, :χ₁ˣ, :χ₁ʸ, :χ₁ᶻ, :χ₂ˣ, :χ₂ʸ, :χ₂ᶻ, :Rʷ, :Rˣ, :Rʸ, :Rᶻ, :v, :Φ) + +julia> ascii_symbols(pnsystem) +(:M1, :M2, :chi1x, :chi1y, :chi1z, :chi2x, :chi2y, :chi2z, :Rw, :Rx, :Ry, :Rz, :v, :Phi) +``` +""" +@export symbols(pnsystem::PNSystem) = symbols(typeof(pnsystem)) +function symbols(::Type{T}) where {T<:PNSystem} + error("`symbols` is not yet defined for PNSystem subtype `$T`.") +end +@export ascii_symbols(pnsystem::PNSystem) = ascii_symbols(typeof(pnsystem)) +function ascii_symbols(::Type{T}) where {T<:PNSystem} + error("`ascii_symbols` is not yet defined for PNSystem subtype `$T`.") +end + +""" + constant_convert(pnsystem, x) + +Convert `x` to the type of the constant numbers to be used with `pnsystem`. Usually, this +type will be the first template parameter. However, when that parameter is a `Dual`, for +example, we don't want to bother defining constants as `Dual`, so we will just define them +as the `Dual`'s underlying type in PostNewtonianForwardDiffExt. + +You generally will not need to call this function directly; it will be used automatically by +the [`@pn_expression`](@ref) macro. +""" +@public constant_convert(::T, x::ExactNumber) where {NT,T<:PNSystem{NT}} = NT(x) +constant_convert(::T, x::NT) where {NT,T<:PNSystem{NT}} = x diff --git a/src/pn_systems/Quasispherical.jl b/src/pn_systems/Quasispherical.jl new file mode 100644 index 00000000..cb02f779 --- /dev/null +++ b/src/pn_systems/Quasispherical.jl @@ -0,0 +1,44 @@ +# NOTE: This type is documented separately, below, so that we can call +# `symbols(Quasispherical)` and `ascii_symbols(Quasispherical)` in the docstring. +@public abstract type Quasispherical{NT,PNOrder,ST} <: PNSystem{NT,PNOrder,ST} end + +function symbols(::Type{<:Quasispherical}) + (:M₁, :M₂, :χ₁ˣ, :χ₁ʸ, :χ₁ᶻ, :χ₂ˣ, :χ₂ʸ, :χ₂ᶻ, :Rʷ, :Rˣ, :Rʸ, :Rᶻ, :v, :Φ) +end +function ascii_symbols(::Type{<:Quasispherical}) + (:M1, :M2, :chi1x, :chi1y, :chi1z, :chi2x, :chi2y, :chi2z, :Rw, :Rx, :Ry, :Rz, :v, :Phi) +end + +@doc """ + Quasispherical{NT,PNOrder,ST} <: PNSystem{NT,PNOrder,ST} + +This is an abstract type for quasispherical post-Newtonian systems. The built-in `BBH`, +`BHNS`, and `NSNS` systems subtype this. + +The quantities common to all subtypes are + + $(symbols(Quasispherical)) + +which have the ASCII equivalents + + $(ascii_symbols(Quasispherical)) + +Note `BBH` has exactly these symbols, while `BHNS` and `NSNS` have additional symbols for +tidal-coupling parameters, `Λ₁` and `Λ₂` (or `Lambda1` and `Lambda2`). +""" +Quasispherical + +function (::Type{T})(state, PNOrder=typemax(Int)) where {T<:Quasispherical} + T{eltype(state),prepare_pn_order(PNOrder),typeof(state)}(state) +end + +function prepare_Quasispherical(; M₁, M₂, χ⃗₁, χ⃗₂, R, v, Φ=0, PNOrder=typemax(Int)) + χ⃗₁ = QuatVec(χ⃗₁) + χ⃗₂ = QuatVec(χ⃗₂) + state = MVector{14}( + M₁, M₂, χ⃗₁[2], χ⃗₁[3], χ⃗₁[4], χ⃗₂[2], χ⃗₂[3], χ⃗₂[4], R[1], R[2], R[3], R[4], v, Φ + ) + NT = eltype(state) + PNOrder = prepare_pn_order(PNOrder) + return (NT, PNOrder, state) +end diff --git a/src/pn_systems/pn_order.jl b/src/pn_systems/pn_order.jl new file mode 100644 index 00000000..ff452398 --- /dev/null +++ b/src/pn_systems/pn_order.jl @@ -0,0 +1,82 @@ +""" + pn_order(pnsystem::PNSystem) + +Return the PN order of the given `pnsystem`. + +This is a `Rational{Int}` that indicates the order to which the PN expansions should be +carried out when using the given object. +""" +@export pn_order(::Type{<:PNSystem{NT,PNOrder}}) where {NT,PNOrder} = PNOrder +pn_order(pnsystem::PNSystem) = pn_order(typeof(pnsystem)) + +""" + order_index(pnsystem::PNSystem) + +Return the order index of the given `pnsystem`. + +This is defined as the (one-based) index into an iterable of PN terms starting at 0pN, then +0.5pN, etc. Specifically, this is defined as `1 + Int(2pn_order(pnsystem))`. +""" +@export order_index(pnsystem::PNSystem) = 1 + Int(2pn_order(pnsystem)) + +""" + max_pn_order + +The maximum PN order that can be used without overflowing the `Int` type. +""" +@export const max_pn_order = (typemax(Int) - 2) // 2 + +""" + prepare_pn_order(PNOrder) + +Convert the input to a half-integer of type `Rational{Int}`. + +If `PNOrder` is larger than `max_pn_order`, it is set to `max_pn_order`, to avoid overflow +when computing the order index. +""" +@public function prepare_pn_order(PNOrder) + if PNOrder < max_pn_order + round(Int, 2PNOrder) // 2 + else + max_pn_order + end +end + +@testitem "PN Orders" begin + using PostNewtonian: prepare_pn_order + + @test max_pn_order == (typemax(Int) - 2) // 2 + @test max_pn_order > 4611686018427387902 + @test max_pn_order < 4611686018427387903 + + @test prepare_pn_order(0//2) == 0//2 + @test prepare_pn_order(1//2) == 1//2 + @test prepare_pn_order(2//2) == 2//2 + @test prepare_pn_order(7//2) == 7//2 + @test prepare_pn_order(31//2) == 31//2 + + @test prepare_pn_order(0.0) == 0//2 + @test prepare_pn_order(0.5) == 1//2 + for i ∈ 0:31 + @test prepare_pn_order(i/2) == i//2 + end + + @test prepare_pn_order(0) == 0//1 + @test prepare_pn_order(1) == 1//1 + @test prepare_pn_order(2) == 2//1 + @test prepare_pn_order(7) == 7//1 + @test prepare_pn_order(31) == 31//1 + + @test prepare_pn_order(typemax(Int)) == max_pn_order + @test prepare_pn_order(typemax(Int) - 1) == max_pn_order + @test prepare_pn_order(typemax(Int) - 2) == max_pn_order + @test prepare_pn_order(typemax(Int) // 2) == max_pn_order + + for i ∈ 0:31 + bbh = BBH(randn(14), i//2) + @test order_index(bbh) == 1 + i + @test pn_order(bbh) ≈ i/2 + @test pn_order(bbh) == i//2 + @test pn_order(BBH{Float16,i//2,Vector{Float16}}) == i//2 + end +end diff --git a/src/pn_systems/pn_systems.jl b/src/pn_systems/pn_systems.jl new file mode 100644 index 00000000..1479cadd --- /dev/null +++ b/src/pn_systems/pn_systems.jl @@ -0,0 +1,9 @@ +include("PNSystem.jl") +include("pn_order.jl") +include("vector_interface.jl") +include("FDPNSystem.jl") +include("state_variables.jl") +include("Quasispherical.jl") +include("BBH.jl") +include("BHNS.jl") +include("NSNS.jl") diff --git a/src/pn_systems/state_variables.jl b/src/pn_systems/state_variables.jl new file mode 100644 index 00000000..6a00e133 --- /dev/null +++ b/src/pn_systems/state_variables.jl @@ -0,0 +1,375 @@ +""" + G(pnsystem) + +Return Newton's gravitational constant for the given `pnsystem`. + +By default, the value is one *with the same number type as `pnsystem`*. It can be +overridden for subtypes of `PNSystem` that use different units or conventions. + +However, note that this function should specialize on the number type of `pnsystem`, rather +than just returning the integer `1`, because there may be expressions with factors such as +`G/3` which will immediately convert to `Float64` if `G` is just `1`, so the result will not +have the expected precision. +""" +@public G(::PNSystem{NT}) where {NT} = one(NT) +G(::FDPNSystem{NT,PN}) where {NT,PN} = one(PN) + +""" + c(pnsystem) + +Return the speed of light for the given `pnsystem`. + +By default, the value is one *with the same number type as `pnsystem`*. It can be +overridden for subtypes of `PNSystem` that use different units or conventions. + +However, note that this function should specialize on the number type of `pnsystem`, rather +than just returning the integer `1`, because there may be expressions with factors such as +`c/3` which will immediately convert to `Float64` if `c` is just `1`, so the result will not +have the expected precision. +""" +@public c(::PNSystem{NT}) where {NT} = one(NT) +c(::FDPNSystem{NT,PN}) where {NT,PN} = one(PN) + +""" + M₁(pnsystem) + M1(pnsystem) + +Mass of object 1 in this system. +""" +@public function M₁(::T) where {T<:PNSystem} + error("M₁ is not (yet) defined for PNSystem subtype `$T`.") +end +M₁(fdpnsystem::FDPNSystem) = fdpnsystem[:M₁] +@public const M1 = M₁ + +""" + M₂(pnsystem) + M2(pnsystem) + +Mass of object 2 in this system. +""" +@public function M₂(::T) where {T<:PNSystem} + error("M₂ is not (yet) defined for PNSystem subtype `$T`.") +end +M₂(fdpnsystem::FDPNSystem) = fdpnsystem[:M₂] +@public const M2 = M₂ + +""" + χ₁ˣ(pnsystem) + chi1x(pnsystem) + +`x`-component of dimensionless spin vector of object 1 in this system, as a `QuatVec`. + +See [`χ⃗₁`](@ref) for details. +""" +@public function χ₁ˣ(::T) where {T<:PNSystem} + error("χ₁ˣ is not (yet) defined for PNSystem subtype `$T`.") +end +χ₁ˣ(fdpnsystem::FDPNSystem) = fdpnsystem[:χ₁ˣ] +@public const chi1x = χ₁ˣ + +""" + χ₁ʸ(pnsystem) + chi1y(pnsystem) + +`y`-component of dimensionless spin vector of object 1 in this system, as a `QuatVec`. + +See [`χ⃗₁`](@ref) for details. +""" +@public function χ₁ʸ(::T) where {T<:PNSystem} + error("χ₁ʸ is not (yet) defined for PNSystem subtype `$T`.") +end +χ₁ʸ(fdpnsystem::FDPNSystem) = fdpnsystem[:χ₁ʸ] +@public const chi1y = χ₁ʸ + +""" + χ₁ᶻ(pnsystem) + chi1z(pnsystem) + +`z`-component of dimensionless spin vector of object 1 in this system, as a `QuatVec`. + +See [`χ⃗₁`](@ref) for details. +""" +@public function χ₁ᶻ(::T) where {T<:PNSystem} + error("χ₁ᶻ is not (yet) defined for PNSystem subtype `$T`.") +end +χ₁ᶻ(fdpnsystem::FDPNSystem) = fdpnsystem[:χ₁ᶻ] +@public const chi1z = χ₁ᶻ + +""" + χ₂ˣ(pnsystem) + chi2x(pnsystem) + +`x`-component of dimensionless spin vector of object 2 in this system, as a `QuatVec`. + +See [`χ⃗₂`](@ref) for details. +""" +@public function χ₂ˣ(::T) where {T<:PNSystem} + error("χ₂ˣ is not (yet) defined for PNSystem subtype `$T`.") +end +χ₂ˣ(fdpnsystem::FDPNSystem) = fdpnsystem[:χ₂ˣ] +@public const chi2x = χ₂ˣ + +""" + χ₂ʸ(pnsystem) + chi2y(pnsystem) + +`y`-component of dimensionless spin vector of object 2 in this system, as a `QuatVec`. + +See [`χ⃗₂`](@ref) for details. +""" +@public function χ₂ʸ(::T) where {T<:PNSystem} + error("χ₂ʸ is not (yet) defined for PNSystem subtype `$T`.") +end +χ₂ʸ(fdpnsystem::FDPNSystem) = fdpnsystem[:χ₂ʸ] +@public const chi2y = χ₂ʸ + +""" + χ₂ᶻ(pnsystem) + chi2z(pnsystem) + +`z`-component of dimensionless spin vector of object 2 in this system, as a `QuatVec`. + +See [`χ⃗₂`](@ref) for details. +""" +@public function χ₂ᶻ(::T) where {T<:PNSystem} + error("χ₂ᶻ is not (yet) defined for PNSystem subtype `$T`.") +end +χ₂ᶻ(fdpnsystem::FDPNSystem) = fdpnsystem[:χ₂ᶻ] +@public const chi2z = χ₂ᶻ + +""" + Rʷ(pnsystem) + Rw(pnsystem) + +Scalar component of the orientation `Rotor` of the binary. + +See [`R`](@ref) for details. +""" +@public function Rʷ(::T) where {T<:PNSystem} + error("Rʷ is not (yet) defined for PNSystem subtype `$T`.") +end +Rʷ(fdpnsystem::FDPNSystem) = fdpnsystem[:Rʷ] +@public const Rw = Rʷ + +""" + Rˣ(pnsystem) + Rx(pnsystem) + +`x`-component of the orientation `Rotor` of the binary. + +See [`R`](@ref) for details. +""" +@public function Rˣ(::T) where {T<:PNSystem} + error("Rˣ is not (yet) defined for PNSystem subtype `$T`.") +end +Rˣ(fdpnsystem::FDPNSystem) = fdpnsystem[:Rˣ] +@public const Rx = Rˣ + +""" + Rʸ(pnsystem) + Ry(pnsystem) + +`y`-component of the orientation `Rotor` of the binary. + +See [`R`](@ref) for details. +""" +@public function Rʸ(::T) where {T<:PNSystem} + error("Rʸ is not (yet) defined for PNSystem subtype `$T`.") +end +Rʸ(fdpnsystem::FDPNSystem) = fdpnsystem[:Rʸ] +@public const Ry = Rʸ + +""" + Rᶻ(pnsystem) + Rz(pnsystem) + +`z`-component of the orientation `Rotor` of the binary. + +See [`R`](@ref) for details. +""" +@public function Rᶻ(::T) where {T<:PNSystem} + error("Rᶻ is not (yet) defined for PNSystem subtype `$T`.") +end +Rᶻ(fdpnsystem::FDPNSystem) = fdpnsystem[:Rᶻ] +@public const Rz = Rᶻ + +@doc raw""" + v(pnsystem) + v(;Ω, M=1) + +Post-Newtonian velocity parameter. This is related to the orbital angular frequency +``\Omega`` as +```math +v \colonequals (G\,M\,\Omega)^{1/3}, +``` +where [`M`](@ref) is the total mass of the binary, and [`G`](@ref) is the gravitational +constant. This has units of speed, so it must be divided by [`c`](@ref) to be +dimensionless. In particular, it is related to the "frequency-related parameter" +[`x`](@ref) via +```math +x = \left(\frac{v}{c}\right)^{2}. +``` + +Note that if you want to pass the value ``Ω`` (rather than a `PNSystem`), you *must* pass it +as a keyword argument — as in `v(Ω=0.1)`. + +See also [`Ω`](@ref) and [`x`](@ref). +""" +@public function v(::T) where {T<:PNSystem} + error("v is not (yet) defined for PNSystem subtype `$T`.") +end +v(fdpnsystem::FDPNSystem) = fdpnsystem[:v] +v(; Ω, M=1) = ∛(M * Ω) + +""" + Φ(pnsystem) + Phi(pnsystem) + +Integrated orbital phase of the system. It is computed as the integral of [`Ω`](@ref). +""" +@public function Φ(::T) where {T<:PNSystem} + error("Φ is not (yet) defined for PNSystem subtype `$T`.") +end +Φ(fdpnsystem::FDPNSystem) = fdpnsystem[:Φ] +@public const Phi = Φ + +@doc raw""" + Λ₁(pnsystem) + Lambda1(pnsystem) + +Quadrupolar tidal-coupling parameter of object 1 in this system. + +We imagine object 1 begin placed in an (adiabatic) external field with Newtonian potential +``\phi``, resulting in a tidal field measured by ``\partial_i \partial_j \phi`` evaluated at +the center of mass of the object. This induces a quadrupole moment ``Q_{ij}`` in object 1, +which can be related to the tidal field as +```math +Q_{ij} = -\frac{G^4}{c^{10}} \Lambda_1 M_1^5 \partial_i \partial_j \phi, +``` +where ``M_1`` is the mass of object 1. This tidal-coupling parameter ``\Lambda_1`` can be +related to the Love number ``k_2`` (where the subscript 2 refers to the fact that this is +for the ``\ell=2`` quadrupole, rather than object 2) as +```math +\Lambda_1 = \frac{2}{3} \frac{c^{10}}{G^5} \frac{R_1^5}{M_1^5} k_2, +``` +where ``R_1`` is the radius of object 1. Note that ``\Lambda_1`` is dimensionless. For +black holes, it is precisely zero; for neutron stars it may range up to 1; more exotic +objects may have significantly larger values. + +Note that — as of this writing — only `NSNS` systems can have a nonzero value for this +quantity. (`BHNS` systems can only have a nonzero value for ``\Lambda_2``.) All other +types return `0`, which Julia can use to eliminate code that would then be 0. Thus, it is +safe and efficient to use this quantity in any PN expression that specializes on the type of +`pnsystem`. + +See also [`Λ₂`](@ref) and [`Λ̃`](@ref). +""" +@public function Λ₁(::T) where {T<:PNSystem} + error("Λ₁ is not (yet) defined for PNSystem subtype `$T`.") +end +Λ₁(fdpnsystem::FDPNSystem) = fdpnsystem[:Λ₁] +@public const Lambda1 = Λ₁ + +@doc raw""" + Λ₂(pnsystem) + Lambda2(pnsystem) + +Quadrupolar tidal coupling parameter of object 2 in this system. + +See [`Λ₁`](@ref) for details about the definition, swapping "object 1" with "object 2". + +Note that — as of this writing — only `BHNS` and `NSNS` systems can have a nonzero value for +this quantity. All other types return `0`, which Julia can use to eliminate code that would +then be 0. Thus, it is safe and efficient to use this quantity in any PN expression that +specializes on the type of `pnsystem`. + +See also [`Λ₁`](@ref) and [`Λ̃`](@ref). +""" +@public function Λ₂(::T) where {T<:PNSystem} + error("Λ₂ is not (yet) defined for PNSystem subtype `$T`.") +end +Λ₂(fdpnsystem::FDPNSystem) = fdpnsystem[:Λ₂] +@public const Lambda2 = Λ₂ + +################################################################# +# Not actually state variables, but aggregates of state variables + +""" + χ⃗₁(pnsystem) + chi1(pnsystem) + +Dimensionless spin vector of object 1 in this system, as a `QuatVec`. + +See also [`χ₁ˣ`](@ref), [`χ₁ʸ`](@ref), and [`χ₁ᶻ`](@ref) for the individual components. +""" +@public function χ⃗₁(::T) where {T<:PNSystem} + QuatVec(χ₁ˣ(pnsystem), χ₁ʸ(pnsystem), χ₁ᶻ(pnsystem)) +end +@public const chi1 = χ⃗₁ + +""" + χ⃗₂(pnsystem) + chi2(pnsystem) + +Dimensionless spin vector of object 2 in this system, as a `QuatVec`. + +See also [`χ₂ˣ`](@ref), [`χ₂ʸ`](@ref), and [`χ₂ᶻ`](@ref) for the individual components. +""" +@public function χ⃗₂(::T) where {T<:PNSystem} + QuatVec(χ₂ˣ(pnsystem), χ₂ʸ(pnsystem), χ₂ᶻ(pnsystem)) +end +@public const chi2 = χ⃗₂ + +""" + R(pnsystem) + +Orientation of the binary, as a `Rotor`. + +At any instant, the binary is represented by the right-handed triad ``(n̂, λ̂, ℓ̂)``, where +[``n̂``](@ref PostNewtonian.n̂) is the unit vector pointing from object 2 to object 1, and +the instantaneous velocities of the binary's elements are in the ``n̂``-``λ̂`` plane. This +`Rotor` will rotate the ``x̂`` vector to be along ``n̂``, the ``ŷ`` vector to be along +``λ̂``, and the ``ẑ`` vector to be along ``ℓ̂``. + +Note that the angular velocity associated to `R` is given by ``Ω⃗ = 2 Ṙ R̄ = Ω ℓ̂ + ϖ n̂``. +(Any component of ``Ω⃗`` along ``λ̂`` would violate the condition that the velocities be in +the ``n̂``-``λ̂`` plane.) Here, the scalar quantity ``Ω`` is the orbital angular frequency, +and ``ϖ`` is the precession angular frequency. + +See also [`n̂`](@ref PostNewtonian.n̂), [`λ̂`](@ref PostNewtonian.λ̂), [`ℓ̂`](@ref +PostNewtonian.ℓ̂), [`Ω`](@ref PostNewtonian.Ω), and [`𝛡`](@ref PostNewtonian.𝛡)``=ϖ n̂``. +""" +@public function R(pnsystem::T) where {NT,T<:PNSystem{NT}} + # We use this explicit constructor (with type parameter) to avoid normalization + # that would probably just complicate derivatives. + Rotor{NT}(Rʷ(pnsystem), Rˣ(pnsystem), Rʸ(pnsystem), Rᶻ(pnsystem)) +end +R(fdpnsystem::FDPNSystem) = fdpnsystem[:R] + +@testitem "State variables" begin + # Test BBH, BHNS, and NSNS state variables + for pnsystem ∈ (BBH(randn(14)), BHNS(randn(15)), NSNS(randn(16))) + for (i, (s, a)) ∈ enumerate(zip(symbols(pnsystem), ascii_symbols(pnsystem))) + @test PostNewtonian.eval(s)(pnsystem) == pnsystem.state[i] + @test PostNewtonian.eval(a)(pnsystem) == pnsystem.state[i] + end + end + bbh = BBH(randn(14)) + @test PostNewtonian.Λ₁(bbh) == 0 + @test PostNewtonian.Λ₂(bbh) == 0 + @test PostNewtonian.Lambda1(bbh) == 0 + @test PostNewtonian.Lambda2(bbh) == 0 + bhns = BHNS(randn(15)) + @test PostNewtonian.Λ₁(bhns) == 0 + @test PostNewtonian.Lambda1(bhns) == 0 + + # Test FDPNSystem state variables + for pnsystem ∈ (BBH(randn(14)), BHNS(randn(15)), NSNS(randn(16))) + fdpnsystem = FDPNSystem(pnsystem) + for (i, (s, a)) ∈ enumerate(zip(symbols(pnsystem), ascii_symbols(pnsystem))) + @test PostNewtonian.eval(s)(fdpnsystem).node_value == s + @test PostNewtonian.eval(a)(fdpnsystem).node_value == s + end + end +end diff --git a/src/pn_systems/vector_interface.jl b/src/pn_systems/vector_interface.jl new file mode 100644 index 00000000..8cd0a744 --- /dev/null +++ b/src/pn_systems/vector_interface.jl @@ -0,0 +1,292 @@ +function Base.ismutable(pnsystem::PNSystem{NT,PNOrder,ST}) where {NT,PNOrder,ST} + ismutable(state(pnsystem)) +end +function Base.ismutabletype(::Type{<:PNSystem{NT,PNOrder,ST}}) where {NT,PNOrder,ST} + ismutabletype(ST) +end + +### Symbol-based indexing +""" + symbol_index(::Type{T}, s::Symbol) where {T<:PNSystem} + symbol_index(::Type{T}, ::Val{S}) where {T<:PNSystem,S} + +Return the index of the symbol `s` in the state vector of the given `PNSystem` type `T`. + +Note that the default implementation is slow; `symbol_index(::Type{T}, ::Val{s})` should be +overridden for every symbol (and ASCII equivalent, if desired) for concrete `PNSystem` +types. +""" +@export function symbol_index(::Type{T}, ::Val{S}) where {T<:PNSystem,S} + index = findfirst(y -> y == S, symbols(T)) + if isnothing(index) + index = findfirst(y -> y == S, ascii_symbols(T)) + end + if isnothing(index) + error( + "Type `$(T)` has no symbol `:$(S)`.\n" * + "This type's symbols are `$(symbols(T))`.\n" * + "The ASCII equivalents are `$(ascii_symbols(T))`.\n", + ) + else + @warn "Please define `PostNewtonian.symbol_index(::Type{$T}, ::Val{$S})`" + index + end +end +Base.getindex(pnsystem::PNSystem, s::Symbol) = getindex(pnsystem, Val(s)) +function Base.getindex(pnsystem::T, s::Val{S}) where {T<:PNSystem,S} + # If `S` is not actually a symbol in `pnsystem`, `symbol_index` will error, so we know + # that the `index` is inbounds if it returns. + index = symbol_index(T, s) + @inbounds state(pnsystem)[index] +end +Base.setindex!(pnsystem::PNSystem, v, s::Symbol) = setindex!(pnsystem, v, Val(s)) +function Base.setindex!(pnsystem::T, v, ::Val{S}) where {T<:PNSystem,S} + index = symbol_index(T, Val(S)) + @inbounds setindex!(state(pnsystem), v, index) +end + +### Interfaces: https://docs.julialang.org/en/v1/manual/interfaces +# Iteration +# Base.iterate(pnsystem::PNSystem) = iterate(state(pnsystem)) +# Base.iterate(pnsystem::PNSystem, state) = iterate(state(pnsystem), state) +Base.IteratorSize(::Type{T}) where {T<:PNSystem} = Base.HasShape{1}() +Base.length(pnsystem::PNSystem) = length(state(pnsystem)) +Base.ndims(pnsystem::PNSystem) = ndims(state(pnsystem)) +Base.size(pnsystem::PNSystem) = size(state(pnsystem)) +Base.size(pnsystem::PNSystem, dim) = size(state(pnsystem), dim) +Base.IteratorEltype(::Type{T}) where {T<:PNSystem} = Base.HasEltype() +# Base.eltype(::Type{<:PNSystem{NT}}) where {NT} = NT ## Already defined in `PNSystem.jl` +Base.isdone(pnsystem::PNSystem) = Base.isdone(state(pnsystem)) +Base.isdone(pnsystem::PNSystem, iterstate) = Base.isdone(state(pnsystem), iterstate) +# Indexing +@propagate_inbounds Base.getindex(pnsystem::PNSystem, i::T) where {T} = getindex( + state(pnsystem), i +) +@propagate_inbounds Base.setindex!(pn::PNSystem, v, i::T) where {T} = setindex!( + state(pn), v, i +) +@propagate_inbounds Base.getindex(pnsystem::PNSystem, i...) = getindex( + state(pnsystem), i... +) +@propagate_inbounds Base.setindex!(pn::PNSystem, v, i...) = setindex!(state(pn), v, i...) +Base.firstindex(pnsystem::PNSystem) = firstindex(state(pnsystem)) +Base.lastindex(pnsystem::PNSystem) = lastindex(state(pnsystem)) +Base.eachindex(pnsystem::PNSystem) = eachindex(state(pnsystem)) +# Abstract arrays +Base.IndexStyle(::Type{T}) where {T<:PNSystem} = Base.IndexLinear() +# Base.length(pnsystem::PNSystem) = length(state(pnsystem)) ## Already defined above +# Base.similar(pnsystem::PNSystem) = similar(state(pnsystem)) +Base.axes(pnsystem::PNSystem) = axes(state(pnsystem)) +# Strided Arrays +Base.strides(pnsystem::PNSystem) = strides(state(pnsystem)) +function Base.unsafe_convert(::Type{Ptr{ST}}, pnsystem::PNSystem{ST}) where {ST} + Base.unsafe_convert(Ptr{ST}, state(pnsystem)) +end +Base.elsize(::Type{<:PNSystem{T}}) where {T} = sizeof(T) +Base.stride(pnsystem::PNSystem, k::Int) = stride(state(pnsystem), k) + +# NamedTuple interface +function Base.convert(::Type{NamedTuple}, pnsystem::PNSystem{N,P,S}) where {N,P,S} + NamedTuple{symbols(pnsystem),NTuple{length(pnsystem),N}}(state(pnsystem)) +end +Base.keys(pnsystem::PNSystem) = symbols(pnsystem) +function Base.pairs(pnsystem::PNSystem{N,P,S}) where {N,P,S} + (s=>v for (s, v) ∈ zip(symbols(pnsystem), state(pnsystem))) +end + +Base.@propagate_inbounds function Base.getindex( + pnsystem::PNSystem, s::AbstractVector{Symbol} +) + # We trick broadcasting into treating `pnsystem` as a scalar by putting it into a + # 1-tuple. + getindex.((pnsystem,), s) +end + +Base.copy(pnsystem::PNSystem) = typeof(pnsystem)(copy(state(pnsystem))) +Base.copyto!(x::PNSystem, y::PNSystem) = copyto!(state(x), state(y)) + +# ##################################### +# # Broadcast +# ##################################### +# struct LAStyle{T,N,L} <: Broadcast.AbstractArrayStyle{N} end +# LAStyle{T,N,L}(x::Val{i}) where {T,N,L,i} = LAStyle{T,N,L}() +# Base.BroadcastStyle(::Type{LArray{T,N,D,L}}) where {T,N,D,L} = LAStyle{T,N,L}() +# function Base.BroadcastStyle( +# ::LabelledArrays.LAStyle{T,N,L}, ::LabelledArrays.LAStyle{E,N,L} +# ) where {T,E,N,L} +# LAStyle{promote_type(T, E),N,L}() +# end + +# @generated function labels2axes(::Val{t}) where {t} +# if t isa NamedTuple && all(x -> x isa Union{Integer,UnitRange}, values(t)) # range labelling +# (Base.OneTo(maximum(Iterators.flatten(v for v ∈ values(t)))),) +# elseif t isa NTuple{<:Any,Symbol} +# axes(t) +# else +# error( +# "$t label isn't supported for broadcasting. Try to formulate it in terms of linear indexing.", +# ) +# end +# end +# function Base.similar( +# bc::Broadcast.Broadcasted{LAStyle{T,N,L}}, ::Type{ElType} +# ) where {T,N,L,ElType} +# tmp = similar(Array{ElType}, axes(bc)) +# if axes(bc) != labels2axes(Val(L)) +# return tmp +# else +# return LArray{ElType,N,typeof(tmp),L}(tmp) +# end +# end + +# Broadcasting checks for aliasing with Base.dataids but the fallback +# for AbstractArrays is very slow. Instead, we just call dataids on the +# wrapped state +Base.dataids(pnsystem::PNSystem) = Base.dataids(state(pnsystem)) + +## Misc + +# function ArrayInterface.restructure( +# x::LArray{T,N,D,Syms}, y::LArray{T2,N2,D2,Syms} +# ) where {T,N,D,T2,N2,D2,Syms} +# reshape(y, size(x)...) +# end + +# function PreallocationTools.get_tmp( +# dc::PreallocationTools.DiffCache, u::LArray{T,N,D,Syms} +# ) where {T<:ForwardDiff.Dual,N,D,Syms} +# nelem = div(sizeof(T), sizeof(eltype(dc.dual_du))) * length(dc.du) +# if nelem > length(dc.dual_du) +# PreallocationTools.enlargedualcache!(dc, nelem) +# end +# _x = ArrayInterface.restructure(dc.du, reinterpret(T, view(dc.dual_du, 1:nelem))) +# LabelledArrays.LArray{T,N,D,Syms}(_x) +# end + +# function RecursiveArrayTools.recursive_unitless_eltype( +# a::Type{LArray{T,N,D,Syms}} +# ) where {T,N,D,Syms} +# LArray{typeof(one(T)),N,D,Syms} +# end + +@testitem "Vector interface" begin + using PostNewtonian: state + using LinearAlgebra + + for pnsystem ∈ (BBH(randn(14), 7//2), BHNS(randn(15), 7//2), NSNS(randn(16), 7//2)) + @test_throws ErrorException symbol_index(typeof(pnsystem), Val(:nonexistent_symbol)) + @test symbol_index(typeof(pnsystem), Val(:M₁)) == 1 + @test symbol_index(typeof(pnsystem), Val(:M1)) == 1 + @test pnsystem[:M₁] == pnsystem[:M1] == pnsystem[1] == pnsystem.state[1] + @test symbol_index(typeof(pnsystem), Val(:M₂)) == 2 + @test symbol_index(typeof(pnsystem), Val(:M2)) == 2 + @test pnsystem[:M₂] == pnsystem[:M2] == pnsystem[2] == pnsystem.state[2] + @test symbol_index(typeof(pnsystem), Val(:χ₁ˣ)) == 3 + @test symbol_index(typeof(pnsystem), Val(:chi1x)) == 3 + @test pnsystem[:χ₁ˣ] == pnsystem[:chi1x] == pnsystem[3] == pnsystem.state[3] + @test symbol_index(typeof(pnsystem), Val(:χ₁ʸ)) == 4 + @test symbol_index(typeof(pnsystem), Val(:chi1y)) == 4 + @test pnsystem[:χ₁ʸ] == pnsystem[:chi1y] == pnsystem[4] == pnsystem.state[4] + @test symbol_index(typeof(pnsystem), Val(:χ₁ᶻ)) == 5 + @test symbol_index(typeof(pnsystem), Val(:chi1z)) == 5 + @test pnsystem[:χ₁ᶻ] == pnsystem[:chi1z] == pnsystem[5] == pnsystem.state[5] + @test symbol_index(typeof(pnsystem), Val(:χ₂ˣ)) == 6 + @test symbol_index(typeof(pnsystem), Val(:chi2x)) == 6 + @test pnsystem[:χ₂ˣ] == pnsystem[:chi2x] == pnsystem[6] == pnsystem.state[6] + @test symbol_index(typeof(pnsystem), Val(:χ₂ʸ)) == 7 + @test symbol_index(typeof(pnsystem), Val(:chi2y)) == 7 + @test pnsystem[:χ₂ʸ] == pnsystem[:chi2y] == pnsystem[7] == pnsystem.state[7] + @test symbol_index(typeof(pnsystem), Val(:χ₂ᶻ)) == 8 + @test symbol_index(typeof(pnsystem), Val(:chi2z)) == 8 + @test pnsystem[:χ₂ᶻ] == pnsystem[:chi2z] == pnsystem[8] == pnsystem.state[8] + @test symbol_index(typeof(pnsystem), Val(:Rʷ)) == 9 + @test symbol_index(typeof(pnsystem), Val(:Rw)) == 9 + @test pnsystem[:Rʷ] == pnsystem[:Rw] == pnsystem[9] == pnsystem.state[9] + @test symbol_index(typeof(pnsystem), Val(:Rˣ)) == 10 + @test symbol_index(typeof(pnsystem), Val(:Rx)) == 10 + @test pnsystem[:Rˣ] == pnsystem[:Rx] == pnsystem[10] == pnsystem.state[10] + @test symbol_index(typeof(pnsystem), Val(:Rʸ)) == 11 + @test symbol_index(typeof(pnsystem), Val(:Ry)) == 11 + @test pnsystem[:Rʸ] == pnsystem[:Ry] == pnsystem[11] == pnsystem.state[11] + @test symbol_index(typeof(pnsystem), Val(:Rᶻ)) == 12 + @test symbol_index(typeof(pnsystem), Val(:Rz)) == 12 + @test pnsystem[:Rᶻ] == pnsystem[:Rz] == pnsystem[12] == pnsystem.state[12] + @test symbol_index(typeof(pnsystem), Val(:v)) == 13 + @test pnsystem[:v] == pnsystem[13] == pnsystem.state[13] + @test symbol_index(typeof(pnsystem), Val(:Φ)) == 14 + @test symbol_index(typeof(pnsystem), Val(:Phi)) == 14 + @test pnsystem[:Φ] == pnsystem[:Phi] == pnsystem[14] == pnsystem.state[14] + end + let + pnsystem = BHNS(randn(15), 7//2) + @test symbol_index(typeof(pnsystem), Val(:Λ₂)) == 15 + @test symbol_index(typeof(pnsystem), Val(:Lambda2)) == 15 + # @test pnsystem[:Λ₂] == pnsystem[:Lambda2] == pnsystem[15] == pnsystem.state[15] + end + let + pnsystem = NSNS(randn(16), 7//2) + @test symbol_index(typeof(pnsystem), Val(:Λ₁)) == 15 + @test symbol_index(typeof(pnsystem), Val(:Lambda1)) == 15 + @test pnsystem[:Λ₁] == pnsystem[:Lambda1] == pnsystem[15] == pnsystem.state[15] + @test symbol_index(typeof(pnsystem), Val(:Λ₂)) == 16 + @test symbol_index(typeof(pnsystem), Val(:Lambda2)) == 16 + @test pnsystem[:Λ₂] == pnsystem[:Lambda2] == pnsystem[16] == pnsystem.state[16] + end + + for FT ∈ (Float16, Float32, Float64) + for PNOrder ∈ (0, 1, 3//2, 2, 5//2, 3, 7//2, 4) + pnsystem = BBH(randn(FT, 14), PNOrder) + @test Base.ismutable(pnsystem) + @test Base.ismutabletype(typeof(pnsystem)) + @test collect(pnsystem) == state(pnsystem) + @test length(pnsystem) == 14 + @test ndims(pnsystem) == 1 + @test size(pnsystem) == (14,) + @test size(pnsystem, 1) == 14 + @test axes(pnsystem) == (Base.OneTo(14),) + @test Base.eltype(pnsystem) == FT + @test Base.eltype(typeof(pnsystem)) == FT + @test Base.eltype(state(pnsystem)) == FT + for (i, v) ∈ enumerate(pnsystem) + @test v == pnsystem[i] == pnsystem.state[i] + end + for (i, v) ∈ enumerate(symbols(pnsystem)) + pnsystem[i] = 2 + @test pnsystem[v] == 2 + @test pnsystem.state[i] == 2 + pnsystem[v] = 3 + @test pnsystem[i] == 3 + @test pnsystem.state[i] == 3 + end + @test [pnsystem[i] for i ∈ firstindex(pnsystem):lastindex(pnsystem)] == pnsystem.state + @test [pnsystem[i] for i ∈ eachindex(pnsystem)] == pnsystem.state + @test eachindex(pnsystem) == axes(pnsystem, 1) + if FT ≠ Float16 + @test state(LinearAlgebra.BLAS.scal(FT(1.2), pnsystem)) ≈ 1.2state(pnsystem) atol=0 rtol=4eps( + FT + ) + end + @test stride(pnsystem, 1) == strides(state(pnsystem))[1] + @test Base.elsize(pnsystem) == sizeof(FT) + @test Base.elsize(typeof(pnsystem)) == sizeof(FT) + nt = convert(NamedTuple, pnsystem) + for symbol ∈ symbols(pnsystem) + @test haskey(nt, symbol) + @test nt[symbol] == pnsystem[symbol] + end + @test keys(pnsystem) == symbols(pnsystem) + @test collect(pairs(pnsystem)) == + collect(k=>v for (k, v) ∈ zip(symbols(pnsystem), state(pnsystem))) + @test pnsystem[collect(symbols(pnsystem))] == state(pnsystem) + pnsystem2 = BBH(randn(FT, 14), PNOrder) + pnsystem3 = copy(pnsystem2) + @test typeof(pnsystem2) == typeof(pnsystem3) + @test pnsystem2 == pnsystem3 + @test state(pnsystem2) == state(pnsystem3) + copyto!(pnsystem, pnsystem2) + @test typeof(pnsystem) == typeof(pnsystem2) + @test pnsystem == pnsystem2 + @test state(pnsystem) == state(pnsystem2) + end + end +end diff --git a/src/predefinitions_Symbolics.jl b/src/predefinitions_Symbolics.jl index c92eb0f2..951a5b9b 100644 --- a/src/predefinitions_Symbolics.jl +++ b/src/predefinitions_Symbolics.jl @@ -37,7 +37,7 @@ julia> using Symbolics julia> using PostNewtonian: M₁, M₂, χ⃗₁, χ⃗₂, SymbolicPNSystem julia> symbolic_pnsystem = SymbolicPNSystem() -SymbolicPNSystem{Vector{Num}, 9223372036854775805//2, Num}(Num[M₁, M₂, χ⃗₁ˣ, χ⃗₁ʸ, χ⃗₁ᶻ, χ⃗₂ˣ, χ⃗₂ʸ, χ⃗₂ᶻ, Rʷ, Rˣ, Rʸ, Rᶻ, v, Φ], Λ₁, Λ₂) +SymbolicPNSystem{Vector{Num}, 9223372036854775805//2, Num}(Num[M₁, M₂, χ₁ˣ, χ₁ʸ, χ₁ᶻ, χ₂ˣ, χ₂ʸ, χ₂ᶻ, Rʷ, Rˣ, Rʸ, Rᶻ, v, Φ], Λ₁, Λ₂) julia> M₁(symbolic_pnsystem), M₂(symbolic_pnsystem) (M₁, M₂) diff --git a/src/utilities.jl b/src/utilities.jl deleted file mode 100644 index 615a5069..00000000 --- a/src/utilities.jl +++ /dev/null @@ -1,9 +0,0 @@ -include("utilities/mathconstants.jl") -include("utilities/misc.jl") -include("utilities/truncated_series_monoid.jl") -include("utilities/truncated_series_inversion.jl") -include("utilities/combine_solutions.jl") -include("utilities/termination_criteria.jl") - -# Don't include macros.jl yet; we need to get contents of `FundamentalVariables` and -# `DerivedVariables`, so that's included by `pn_expressions.jl`. diff --git a/src/utilities/macros.jl b/src/utilities/macros.jl deleted file mode 100644 index 264079da..00000000 --- a/src/utilities/macros.jl +++ /dev/null @@ -1,198 +0,0 @@ -""" - type_converter(pnsystem, x) - -Convert `x` to a type appropriate for the float type of `pnsystem`. - -This is sort of an expansion of the `convert` function, but with nicer syntax for types from -this package, including the ability to do really weird things for `SymbolicPNSystem`. It's -needed to ensure that the types of variables and constants are correct when we use them in -expressions, rather than just assuming everything is a `Float64`. -""" -function type_converter(pnsystem, x) - return convert(eltype(pnsystem), x) -end -function type_converter(::FDPNSystem{FT}, x) where {FT} - return x -end -function type_converter(::FDPNSystem{FT}, x::Integer) where {FT} - return convert(FT, x) -end -function type_converter(::FDPNSystem{FT}, x::Rational) where {FT} - return convert(FT, x) -end -function type_converter(::FDPNSystem{FT}, x::AbstractIrrational) where {FT} - return convert(FT, x) -end - -fundamental_variables = methodswith(PNSystem, FundamentalVariables) -fundamental_quaternionic_variables = [ - m for m ∈ methodswith(AbstractVector, FundamentalVariables) if m.name ∈ [:χ⃗₁, :χ⃗₂, :R] -] -derived_variables = methodswith(VecOrPNSystem, DerivedVariables) -pnvariables = map(v -> v.name, [fundamental_variables; derived_variables]) - -irrationals = unique( - [ - find_symbols_of_type(Base.MathConstants, Irrational) - find_symbols_of_type(MathConstants, Irrational) - ], -) - -# This should include all the unary functions that we want to use in any PN expression. -unary_funcs = [:√, :sqrt, :log, :ln, :sin, :cos] -# unary_funcs = Dict( -# :√ => :(Base.sqrt), -# :sqrt => :(Base.sqrt), -# :log => :(Base.log), -# :ln => :(Base.log), -# ) - -# for (expr, f) ∈ pairs(unary_funcs) -# if expr ∈ (:sqrt, :ln) # These are just aliases, so avoid redefinitions -# continue -# end -# @eval begin -# $f(::Type{T}, x) where T = $f(x) -# $f(::Type{T}, x::Int) where T = $f(T(x)) -# $f(::Type{T}, x::Rational) where T = $f(T(x)) -# $f(::Type{T}, x::Irrational) where T = $f(T(x)) -# end -# end - -function pn_expression(pnsystem::Symbol, body) - # Look for variables in `body` that we need to treat specially, and write exprs to do - # so. These three are described as bullet points in the docstring of `@pn_expression`. - pnvariables_exprs = [ - :($v = $v($pnsystem)) for v ∈ filter(v -> MacroTools.inexpr(body, v), pnvariables) - ] - irrationals_exprs = [ - :($v = type_converter($pnsystem, $v)) for - v ∈ filter(v -> MacroTools.inexpr(body, v), irrationals) - ] - unary_funcs_exprs = [ - :($v = (x -> $v(type_converter($pnsystem, x)))) for - v ∈ filter(v -> MacroTools.inexpr(body, v), unary_funcs) - ] - - exprs = [ - pnvariables_exprs - irrationals_exprs - unary_funcs_exprs - ] - - # Next, add pnsystem as the argument to each @pn_expansion call - new_body = MacroTools.unblock( - macroexpand( - @__MODULE__, - MacroTools.postwalk(body) do x - if MacroTools.isexpr(x, :macrocall) && - x.args[1] == Symbol("@pn_expansion") && - !isa(x.args[end - 1], Symbol) - x′ = deepcopy(x) - insert!(x′.args, length(x′.args), pnsystem) - x′ - else - x - end - end; - recursive=true, - ), - ) - - # Finally, just wrap `new_body` in a `let` block, where we include exprs created above. - # Also include the definitions `c=G=1` (to be overwritten inside any `@pn_expansion`). - full_body = MacroTools.unblock(quote - let c=G=one(pnsystem) - #@fastmath - let $(exprs...) - $(new_body) - end - end - end) - return full_body -end - -function pn_expression(arg_index::Integer, func) - splitfunc = MacroTools.splitdef(func) - pnsystem = MacroTools.namify(splitfunc[:args][arg_index]) - splitfunc[:kwargs] = [ - splitfunc[:kwargs] - :($(Expr(:kw, :(pn_expansion_reducer::Val{PNExpansionReducer}), :(Val(sum))))) - ] - splitfunc[:whereparams] = (splitfunc[:whereparams]..., :PNExpansionReducer) - splitfunc[:body] = pn_expression(pnsystem, splitfunc[:body]) - return MacroTools.combinedef(splitfunc) -end - -""" - @pn_expression [arg_index=1] func - -This macro takes the function `func`, looks for various symbols inside that function, and if -present defines them appropriately inside that function. - -The first argument to this macro is `arg_index`, which just tells us which argument to the -function `func` is a `PNSystem`. For example, the variables defined in -[`PostNewtonian.FundamentalVariables`](@ref "Fundamental variables") all take a single -argument of `pnsystem`, which is used to compute the values for those variables; this macro -just needs to know where to find `pnsystem`. - -Once it has this information, there are five types of transformations it will make: - - 1. Adds a keyword argument `pn_expansion_reducer::Val{PNExpansionReducer}=Val(sum)` to the - function signature. This is used to determine how to reduce the PN expansion terms. - The default is `Val(sum)`, which will just return a single number, but `Val(identity)` - can be used to return the expansion. This should be used inside the function as - `PNExpansionReducer`, and will be automatically used inside any `@pn_expansion`. - 2. For every [fundamental](@ref "Fundamental variables") or [derived](@ref "Derived - variables") variable, the name of that variable used in the body of `func` will be - replaced by its value when called with `pnsystem`. For example, you can simply use the - symbols `M₁` or `μ` in your code, rather than calling them as [`M₁(pnsystem)`](@ref M₁) - or [`μ(pnsystem)`](@ref μ) every time they appear. - 3. Every `Irrational` defined in `Base.MathConstants` or `PostNewtonian.MathConstants` will - be transformed to the `eltype` of `pnsystem`. This lets you naturally use such - constants in expressions like `2π/3` without automatically converting to `Float64`. - 4. Each of a short list of functions given by `unary_funcs` in `utilities/macros.jl` will - first convert their arguments to the `eltype` of `pnsystem`. In particular, you can use - expressions like `√10` or `ln(2)` without the result being converted to a `Float64`. - 5. Insert the `pnsystem` argument as the first argument to each occurrence of - `@pn_expansion` that needs it. - -To be more explicit, the first three are achieved by defining the relevant quantities in a -`let` block placed around the body of `func`, so that the values may be used efficiently -without recomputation. - -If you need to use one of the fundamental- or derived-variable functions as arguments of -values other than those encapsulated in `pnsystem`, you'll need to address them explicitly -with the module name — as in `PostNewtonian.v(;Ω, M)`. -""" -macro pn_expression(func) - return esc(pn_expression(1, func)) -end - -macro pn_expression(arg_index, func) - return esc(pn_expression(arg_index, func)) -end - -""" - @pn_expansion [pnsystem] expansion - -Gather terms in `expansion` by the powers of ``1/c`` involved, zeroing out any terms with -powers of ``1/c`` higher than the `pnsystem`'s `PNOrder` parameter, and combine the terms -using the `PNExpansionReducer` specified in argument of the function that includes this -macro call. - -This expansion is achieved by setting — inside a `let` block created by this macro — - -Note that the `pnsystem` argument can be inserted automatically by [`@pn_expression`](@ref). -""" -macro pn_expansion(pnsystem, expr) - return esc(pn_expansion(pnsystem, expr)) -end - -function pn_expansion(pnsystem, expr) - quote - let c = PNExpansionParameter($pnsystem) - PNExpansionReducer($expr) - end - end -end diff --git a/src/utilities/mathconstants.jl b/src/utilities/mathconstants.jl deleted file mode 100644 index df235b82..00000000 --- a/src/utilities/mathconstants.jl +++ /dev/null @@ -1,183 +0,0 @@ -module MathConstants - -export log2, - ln2, - log3, - ln3, - log5, - ln5, - log3halves, - log³╱₂, - ln³╱₂, - log5halves, - log⁵╱₂, - ln⁵╱₂, - apery, - ζ3, - γₑ, - 𝒾 - -Base.@irrational ln2 0.6931471805599453 log2 -Base.@irrational γₑ 0.57721566490153286061 euler -Base.@irrational ln3 1.0986122886681097 big"1.098612288668109691395245236922525704647490557822749451734694333637494293218608966873615754813732088787970029" -Base.@irrational ln5 1.6094379124341003 big"1.60943791243410037460075933322618763952560135426851772191264789147417898770765776463013387809317961" -Base.@irrational ln³╱₂ 0.4054651081081644 big"0.40546510810816438197801311546434913657199042346249419761401432414410067124891425126775242781731340" -Base.@irrational ln⁵╱₂ 0.9162907318741551 big"0.91629073187415506518352721176801107145010121990826246779196788198078536573796304902427055109676092" -Base.@irrational ζ3 1.2020569031595942 big"1.20205690315959428539973816151144999076498629234049888179227155534183820578631309018645587360933525814619915" -const 𝒾 = im - -# When defining @irrationals, if the third argument is a symbol, it is expected to name an -# existing constant compiled into MPFR, with prefix `mpfr_const_`, which is a very limited -# set. All MPFR constants except `log2` already exist in `Base.MathConstants`. Otherwise, -# that third argument should be a literal BigFloat; it cannot be a variable name. - -@doc raw""" - γₑ - -[Euler's constant](https://en.wikipedia.org/wiki/Euler%27s_constant) (also known as the -Euler–Mascheroni constant) is defined as the limit as ``n \to \infty`` of the difference -between the ``n``th partial sum of the harmonic series and ``\log(n)``. This is OEIS -sequence [A001620](https://oeis.org/A001620). - -```julia-repl -julia> PostNewtonian.γₑ -γₑ = 0.5772156649015... - -julia> n=10_000_000; sum(1 ./ (1:n))-log(n) -0.5772157149015307 -``` -""" -γₑ - -""" - ζ3 - apery - -[Apéry's constant](https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_constant) is -defined as ``ζ(3)``, where ``ζ`` is the Riemann zeta function. This is OEIS -sequence [A002117](https://oeis.org/A002117). - -```julia-repl -julia> PostNewtonian.apery -ζ3 = 1.2020569031595... - -julia> PostNewtonian.ζ3 -ζ3 = 1.2020569031595... - -julia> sum((1:10_000_000).^-3) -1.2020569031595896 -``` -""" -ζ3 -const apery = ζ3 - -""" - ln2 - log2 - -The natural logarithm of 2. This is OEIS sequence -[A002162](https://oeis.org/A002162). - -```julia-repl -julia> PostNewtonian.ln2 -ln2 = 0.6931471805599... - -julia> exp(PostNewtonian.ln2) -2.0 - -julia> exp(big(PostNewtonian.ln2)) -2.0 -``` -""" -ln2 -const log2 = ln2 - -""" - ln3 - log3 - -The natural logarithm of 3. This is OEIS sequence -[A002391](https://oeis.org/A002391). - -```julia-repl -julia> PostNewtonian.ln3 -ln3 = 1.0986122886681... - -julia> exp(PostNewtonian.ln3) -3.0000000000000004 - -julia> exp(big(PostNewtonian.ln3)) -3.0 -``` -""" -ln3 -const log3 = ln3 - -""" - ln5 - log5 - -The natural logarithm of 5. This is OEIS sequence -[A016628](https://oeis.org/A016628). - -```julia-repl -julia> PostNewtonian.ln5 -ln5 = 1.6094379124341... - -julia> exp(PostNewtonian.ln5) -4.999999999999999 - -julia> exp(big(PostNewtonian.ln5)) -5.0 -``` -""" -ln5 -const log5 = ln5 - -""" - ln³╱₂ - log³╱₂ - log3halves - -The natural logarithm of 3//2. This is OEIS sequence -[A016578](https://oeis.org/A016578). - -```julia-repl -julia> PostNewtonian.ln³╱₂ -ln³╱₂ = 0.4054651081081... - -julia> exp(PostNewtonian.ln³╱₂) -1.5 - -julia> exp(big(PostNewtonian.ln³╱₂)) -1.5 -``` -""" -ln³╱₂ -const log³╱₂ = ln³╱₂ -const log3halves = ln³╱₂ - -""" - ln⁵╱₂ - log⁵╱₂ - log5halves - -The natural logarithm of 5//2. This is OEIS sequence -[A016579](https://oeis.org/A016579). - -```julia-repl -julia> PostNewtonian.ln⁵╱₂ -ln⁵╱₂ = 0.9162907318741... - -julia> exp(PostNewtonian.ln⁵╱₂) -2.5 - -julia> exp(big(PostNewtonian.ln⁵╱₂)) -2.5 -``` -""" -ln⁵╱₂ -const log⁵╱₂ = ln⁵╱₂ -const log5halves = ln⁵╱₂ - -end diff --git a/src/utilities/misc.jl b/src/utilities/misc.jl deleted file mode 100644 index 2f8671d1..00000000 --- a/src/utilities/misc.jl +++ /dev/null @@ -1,76 +0,0 @@ -""" - value(x) - -Return `x` or the value wrapped by the `Dual` number `x` -""" -value(x) = hasproperty(x, :value) ? getproperty(x, :value) : x - -""" - find_symbols_of_type(mod, T) - -Given a module `mod` (not just its name, but the actual imported module), find all objects -inside that module that are instances of the given type `T`. The returned quantity is a -vector of `Symbol`s. -""" -function find_symbols_of_type(mod, T) - return filter(n -> getproperty(mod, n) isa T, names(mod)) -end - -""" - iscall(x, symbols) - -Return `true` if the `Expr` `x` is a call to any element of `symbols`. -""" -iscall(x, symbols) = MacroTools.isexpr(x, :call) && x.args[1] ∈ symbols - -""" - isadd(x) - -Return `true` if the `Expr` `x` is a call to `(+)` or `:+`. -""" -isadd(x) = iscall(x, ((+), :+)) - -""" - ismul(x) - -Return `true` if the `Expr` `x` is a call to `(*)` or `:*`. -""" -ismul(x) = iscall(x, ((*), :*)) - -""" - flatten_binary!(expr, symbols) - -Flatten nested binary operations — that is, apply associativity repeatedly. -""" -function flatten_binary!(expr, symbols) - while iscall(expr, symbols) && any(x -> iscall(x, symbols), expr.args[2:end]) - args = expr.args[2:end] - i₊ = findfirst(x -> iscall(x, symbols), args) - args′ = [first(symbols); args[1:(i₊ - 1)]; args[i₊].args[2:end]; args[(i₊ + 1):end]] - expr.args[:] = args′[1:length(expr.args)] - append!(expr.args, args′[(1 + length(expr.args)):end]) - end - return expr -end - -flatten_add!(expr) = flatten_binary!(expr, ((+), :+)) -flatten_mul!(expr) = flatten_binary!(expr, ((*), :*)) - -""" - apply_to_first_add!(expr, func) - -Apply `func` to the first sub-expression found in a "prewalk"-traversal of `expr` that -satisfies [`isadd`](@ref). If `func` acts in place, so does this function. In either case, -the expression should be returned. -""" -function apply_to_first_add!(expr, func) - found_add = false - MacroTools.prewalk(expr) do x - if !found_add && isadd(x) - found_add = true - func(x) - else - x - end - end -end diff --git a/src/utilities/truncated_series_monoid.jl b/src/utilities/truncated_series_monoid.jl deleted file mode 100644 index 97615e9c..00000000 --- a/src/utilities/truncated_series_monoid.jl +++ /dev/null @@ -1,214 +0,0 @@ -@doc raw""" - truncated_series_inverse(a) - truncated_series_inverse!(b, a) - -Given the coefficients `a` of a series, find the coefficients `b` of the *multiplicative* -inverse of that series, up to the order of the original series. That is, if -```math -A \colonequals \sum_{i=0}^n a_{i-1} v^i, -``` -then we return the coefficients `b` of the series -```math -B \colonequals \sum_{i=0}^n b_{i-1} v^i -``` -such that -```math -A\, B = 1 + \mathcal{O}(v^{n+1}). -``` - -See [`lagrange_inversion`](@ref) for the *compositional* inverse (a.k.a. reversion), which -returns the coefficients of ``f^{-1}`` such that ``f^{-1}(f(v)) = v + -\mathcal{O}(v^{n+1})``. - -Note that this function returns the *coefficients* of the inverse, rather than its value. -This is relevant for use in [`truncated_series_product`](@ref) and -[`truncated_series_ratio`](@ref) — the latter of which just combines the former with this -function. - -For example, suppose the input coefficients represent the series -```math -A \colonequals \sum_{i=0}^n a_{i-1} v^i. -``` -(Remember that Julia's indexing is 1-based, so we subtract 1 to get the index of the -coefficient of ``v^i``.) Then we return the coefficients `b` of the series -```math -B \colonequals \sum_{i=0}^n b_{i-1} v^i -``` -such that -```math -A\, B = 1 + \mathcal{O}(v^{n+1}). -``` - -!!! note - This function requires that `a[1]` be nonzero. If you have a series that starts at - a higher term — say, ``v^n`` for ``n>0`` — you should factor out the ``v^n``, and - multiply the series resulting from this function by ``v^{-n}``. - -## Explanation - -The inverse coefficients can be computed fairly easily by induction. Start by defining -```math -b_0 = 1/a_0. -``` -Now, assuming that we've computed all coefficients up to and including ``b_{i}``, we can -compute ``b_{i+1}`` from the condition that the term proportional to ``v^{i+1}`` in the -product of the series and its inverse must be zero. This gives -```math -b_{i+1} = -b_0\sum_{j=1}^{i} a_j b_{i-j}. -``` -""" -function truncated_series_inverse(a::AbstractVector) - b = similar(a) - return truncated_series_inverse!(b, a) -end - -function truncated_series_inverse(a::NTuple{N,T}) where {N,T} - b = MVector{N,T}(undef) - truncated_series_inverse!(b, SVector{N,T}(a)) - return Tuple(b) -end - -function truncated_series_inverse!(b, a) - @assert length(b) == length(a) - n = length(a) - @inbounds @fastmath if n > 0 - b[0 + 1] = inv(a[0 + 1]) - end - @inbounds @fastmath for i ∈ 0:(n - 2) - b[i + 1 + 1] = - -b[0 + 1] * - sum((a[j + 1] * b[i + 1 - j + 1] for j ∈ 1:(i + 1)); init=zero(eltype(a))) - end - return b -end - -@doc raw""" - truncated_series_product(a, b, v) - -Evaluate the truncated product of the series `a` and `b`, which are expanded in powers of -`v`. - -Note that this function returns the *value* of the summation, rather than its coefficients. - -Here we define the series in terms of the coefficients `a` and `b` as -```math -A \colonequals \sum_{i=0}^n a_{i-1} v^i -\qquad -B \colonequals \sum_{i=0}^n b_{i-1} v^i, -``` -and return the *value* of the product ``A\, B`` truncated at ``v^n``. - -Internally, the sums are performed using `evalpoly`. - -See also [`truncated_series_ratio`](@ref). -""" -function truncated_series_product(a, b, v) - @assert length(a) == length(b) - N = length(a) - 1 - if N < 0 - return zero(v) - end - ex = b[N + 1] * a[1] - for n ∈ (N - 1):-1:0 - ex = muladd(v, ex, b[n + 1] * evalpoly(v, @view a[1:((N - n) + 1)])) - end - return ex -end - -function truncated_series_product(a::NTuple{N,T}, b, v) where {N,T} - @assert length(a) == length(b) - if N < 1 - return zero(v) - end - ex = b[N] * a[1] - for n ∈ (N - 2):-1:0 - ex = muladd(v, ex, b[n + 1] * evalpoly(v, a[1:((N - n - 1) + 1)])) - end - return ex -end - -@doc raw""" - truncated_series_ratio(a, b, v) - -Evaluate the truncated ratio of the series `a` and `b`, which are expanded in powers of `v`. - -Note that this function returns the *value* of the summation, rather than its coefficients. - -Here we define the series in terms of the coefficients `a` and `b` as -```math -A \colonequals \sum_{i=0}^n a_{i-1} v^i -\qquad -B \colonequals \sum_{i=0}^n b_{i-1} v^i, -``` -and return the *value* of the ratio ``A / B`` truncated at ``v^n``. - -This function simply combines [`truncated_series_product`](@ref) and -[`truncated_series_inverse`](@ref). -""" -function truncated_series_ratio(a, b, v) - return truncated_series_product(a, truncated_series_inverse(b), v) -end - -@doc raw""" - truncated_series_ratio(a, b) - -Evaluate the truncated ratio of the series `a` and `b`, evaluated at expansion value 1. -This is relevant when the expansion is not in the dynamic variable `v`, for example, but in -powers of ``1/c`` as in post-Newtonian expansions. (That is, when the `v` dependence is -already include in the input coefficients.) -""" -function truncated_series_ratio(a::NTuple{N1,T1}, b::NTuple{N2,T2}) where {N1,N2,T1,T2} - N = max(N1, N2) - T = promote_type(T1, T2) - if N2 == 0 - throw(DomainError("truncated_series_ratio(a,b): b must have at least one term")) - elseif N1 == 0 - return zero(T) - end - b⁻¹ = MVector{N,T}(undef) - - @inbounds @fastmath begin - b⁻¹[0 + 1] = inv(b[0 + 1]) - for i ∈ 0:(N2 - 2) - b⁻¹[i + 1 + 1] = - -b⁻¹[0 + 1] * - sum((b[j + 1] * b⁻¹[i + 1 - j + 1] for j ∈ 1:(i + 1)); init=zero(T)) - end - for i ∈ (N2 - 1):(N - 2) - b⁻¹[i + 1 + 1] = - -b⁻¹[0 + 1] * - sum((b[j + 1] * b⁻¹[i + 1 - j + 1] for j ∈ 1:(N2 - 1)); init=zero(T)) - end - - a╱b = zero(T) - for i1 ∈ 1:N1 - a╱b += a[i1] * sum((b⁻¹[i2] for i2 ∈ 1:(N - i1 + 1)); init=zero(T)) - end - a╱b - end -end - -@testitem "truncated_series_ratio(a,b)" begin - using Random - using DoubleFloats - import PostNewtonian: truncated_series_inverse, truncated_series_ratio - Random.seed!(123) - for T ∈ [Float32, Float64, Double64] - for N ∈ 1:20 - A = rand(T, N) - A[1] = one(T) + rand(T) / 100 - a = Tuple(A) - x = rand(T) - ϵ = sum(a) * N * eps(T) - for N1 ∈ 1:N - expected = sum(truncated_series_inverse(a)) - unit = zeros(T, N1) - unit[1] = one(T) - @test truncated_series_ratio(Tuple(unit), a) ≈ expected rtol = ϵ - end - @test truncated_series_ratio(a, a) ≈ 1 rtol = ϵ - @test truncated_series_ratio(a, x .* a) ≈ 1 / x rtol = ϵ - @test truncated_series_ratio(x .* a, a) ≈ x rtol = ϵ - end - end -end diff --git a/test/aqua.jl b/test/aqua.jl index 9308612c..7c4d8fd6 100644 --- a/test/aqua.jl +++ b/test/aqua.jl @@ -9,9 +9,9 @@ end @testitem "ExplicitImports tests" begin using ExplicitImports: ExplicitImports - @test ExplicitImports.check_no_implicit_imports(PostNewtonian) === nothing - @test ExplicitImports.check_all_explicit_imports_via_owners(PostNewtonian) === nothing - @test_broken ExplicitImports.check_all_explicit_imports_are_public(PostNewtonian) === + @test ExplicitImports.check_no_implicit_imports(PostNewtonian) ≡ nothing + @test ExplicitImports.check_all_explicit_imports_via_owners(PostNewtonian) ≡ nothing + @test_broken ExplicitImports.check_all_explicit_imports_are_public(PostNewtonian) ≡ nothing @test ExplicitImports.check_no_stale_explicit_imports( PostNewtonian; @@ -32,9 +32,6 @@ end :χ⃗₂, :ℳ, :ln, - :ln2, - :ln3, - :ln5, :order_index, :γₑ, :ζ3, @@ -44,11 +41,10 @@ end :SVector, :Node, ), - ) === nothing - @test ExplicitImports.check_all_qualified_accesses_via_owners(PostNewtonian) === nothing - @test_broken ExplicitImports.check_all_qualified_accesses_are_public(PostNewtonian) === + ) ≡ nothing + @test ExplicitImports.check_all_qualified_accesses_via_owners(PostNewtonian) ≡ nothing + @test_broken ExplicitImports.check_all_qualified_accesses_are_public(PostNewtonian) ≡ + nothing + @test ExplicitImports.check_no_self_qualified_accesses(PostNewtonian; ignore=(:Ω, :v)) ≡ nothing - @test ExplicitImports.check_no_self_qualified_accesses( - PostNewtonian; ignore=(:Ω, :v) - ) === nothing end diff --git a/test/binding_energy_reference.jl b/test/binding_energy_reference.jl index cc7a89c4..2618c20f 100644 --- a/test/binding_energy_reference.jl +++ b/test/binding_energy_reference.jl @@ -36,8 +36,8 @@ function be(pnsystem, deriv) λ₊ = PostNewtonian.λ₊(pnsystem), λ₋ = PostNewtonian.λ₋(pnsystem), π = PostNewtonian.type_converter(pnsystem, π), - ln2 = PostNewtonian.type_converter(pnsystem, PostNewtonian.ln2), - ln3 = PostNewtonian.type_converter(pnsystem, PostNewtonian.ln3), + ln2 = PostNewtonian.type_converter(pnsystem, PostNewtonian.ln(2)), + ln3 = PostNewtonian.type_converter(pnsystem, PostNewtonian.ln(3)), γₑ = PostNewtonian.type_converter(pnsystem, PostNewtonian.γₑ), ln = (x -> log(PostNewtonian.type_converter(pnsystem, x))), pn_order = PostNewtonian.pn_order(pnsystem) @@ -55,7 +55,7 @@ function be(pnsystem, deriv) 77ν^4 / 31104 + 301ν^3 / 1728 + (-498449//3456 + 3157π^2 / 576)ν^2 + - (-123671//5760 + 1792ln2 / 15 + 9037π^2 / 1536 + 896γₑ / 15)ν + (-123671//5760 + 1792ln(2) / 15 + 9037π^2 / 1536 + 896γₑ / 15)ν ) eˡⁿ[8] = (448ν / 15) diff --git a/test/orbital_evolution.jl b/test/orbital_evolution.jl index 8bddeb76..603e8976 100644 --- a/test/orbital_evolution.jl +++ b/test/orbital_evolution.jl @@ -81,7 +81,7 @@ sol_np = orbital_evolution( M₁, M₂, QuatVec(0, 0, χ⃗₁.z), QuatVec(0, 0, χ⃗₂.z), Ωᵢ; Ω₁, Rᵢ, quiet=true ) - for c ∈ [:χ⃗₁ˣ, :χ⃗₁ʸ, :χ⃗₂ˣ, :χ⃗₂ʸ, :Rˣ, :Rʸ] + for c ∈ [:χ₁ˣ, :χ₁ʸ, :χ₂ˣ, :χ₂ʸ, :Rˣ, :Rʸ] @test all(sol_np[c] .== 0) end diff --git a/test/pn_expansion.jl b/test/pn_expansion.jl deleted file mode 100644 index 8497a302..00000000 --- a/test/pn_expansion.jl +++ /dev/null @@ -1,120 +0,0 @@ -@testitem "PNTerm algebra" begin - using DoubleFloats - using PostNewtonian: PNExpansion - - for T ∈ [Float64, Float16, Double64] - pn = rand(BBH; v=T(1) / 5, PNOrder=9//2) - c = PNExpansionParameter(pn) - z = zero(T) - x = T(6) / 5 - y = T(17) / 5 - w = T(28) / 5 - v = T(27) / 13 - - # Test behavior of `c` as the basic PNTerm - for (term, c⁻¹exponent, coeff) ∈ ( - (c, -1, 1), - (c^2, -2, 1), - (x * c^2, -2, x), - (c^2 * x, -2, x), - (c^2 / x, -2, 1 / x), - ((x * c)^2, -2, x^2), - ((x * c^2) / c^4, 2, x), - ((x * c^2) / c^-4, -6, x), - ((x / c^2) / c^4, 6, x), - ((x / c^2) * (y / c^4), 6, x * y), - ) - @test PostNewtonian.c⁻¹exp(term) == c⁻¹exponent - @test term.coeff == coeff - @test term.coeff isa eltype(pn) - @test length(term) == 1 - @test eltype(term) === T - end - - # Test PNExpressions - @test_throws ArgumentError PNExpansion((), 0) - for (expr, expected) ∈ ( - (w - (x - y / c), (w - x, y)), - (w - (x / c - y), (w + y, -x)), - (x - y / c, (x, -y)), - (x / c - y, (-y, x)), - (x / c^6 + y / c, (z, y, z, z, z, z, x)), - (x / c^6 + y / c + w / c^10, (z, y, z, z, z, z, x, z, z, z)), - (x / c^6 - y / c, (z, -y, z, z, z, z, x)), - (x / c^6 - y / c - w, (-w, -y, z, z, z, z, x)), - (x / c^6 - y / c - w / c^10, (z, -y, z, z, z, z, x, z, z, z)), - (x / c^6 - (y / c - w), (w, -y, z, z, z, z, x)), - (x / c^6 - (y / c - w / c^10), (z, -y, z, z, z, z, x, z, z, z)), - (-(x / c^6) - y / c, (z, -y, z, z, z, z, -x)), - (-(x / c^6) - y / c - w, (-w, -y, z, z, z, z, -x)), - (-(x / c^6) - y / c - w / c^10, (z, -y, z, z, z, z, -x, z, z, z)), - ((x * c^2) / c^4 + y / c, (z, y, x)), - ((x * c^2) / c^4 + y / c + w, (w, y, x)), - ((x * c^2) / c^9 + y / c + w, (w, y, z, z, z, z, z, x)), - (w + (x * c^2) / c^4 + y / c, (w, y, x)), - (w + (x * c^2) / c^9 + y / c, (w, y, z, z, z, z, z, x)), - (w + ((x * c^2) / c^4 + y / c), (w, y, x)), - (w + ((x * c^2) / c^9 + y / c), (w, y, z, z, z, z, z, x)), - (((x * c^2) / c^4 + y / c + w) / c^3, (z, z, z, w, y, x)), - (((x * c^2) / c^4 + y / c + w) / c^5, (z, z, z, z, z, w, y, x)), - (((x * c^2) / c^7 + y / c + w) / c^5, (z, z, z, z, z, w, y, z, z, z)), - (v * (((x * c^2) / c^4 + y / c + w) / c^3), v .* (z, z, z, w, y, x)), - ((((x * c^2) / c^4 + y / c + w) / c^3) * v, v .* (z, z, z, w, y, x)), - ((((x * c^2) / c^4 + y / c + w) / c^3) / v, (z, z, z, w, y, x) .* (1 / v)), - ) - @test expr.coeffs == expected - @test pn_order(expr) == pn_order(pn) - @test sum(expr) == sum(expected) - @test eltype(expr) === T - end - - # Can't make a PNExpression with positive exponents - @test_throws ArgumentError x * c + y - @test_throws ArgumentError x * c + y / c - @test_throws ArgumentError x * c^2 + y - @test_throws ArgumentError x * c^2 + y / c - @test_throws ArgumentError y + x * c - @test_throws ArgumentError y / c + x * c - @test_throws ArgumentError y + x * c^2 - @test_throws ArgumentError y / c + x * c^2 - @test_throws ArgumentError x * c^2 + (y / c + z / c^2) - end -end - -@testitem "PNExpansion algebra" begin - using Symbolics - using PostNewtonian: PNExpansion - - for N1 ∈ 1:9 - for N2 ∈ 1:9 - for NMax ∈ max(N1, N2):(N1 + N2 + 3) - @variables c⁻¹ x[1:N1] y[1:N2] z - poly(e::PNExpansion) = sum(e[i] * c⁻¹^(i - 1) for i ∈ 1:length(e)) - eˣ = PNExpansion(tuple(x...), NMax) - eʸ = PNExpansion(tuple(y...), NMax) - - # Test sums - polysum = simplify(poly(eˣ + eʸ); expand=true) - sumpoly = simplify(poly(eˣ) + poly(eʸ); expand=true) - Δ = simplify(polysum - sumpoly; expand=true) - @test iszero(Δ) - @test_throws ArgumentError eˣ + PNExpansion(tuple(z, x...), NMax + 1) - @test_throws ArgumentError PNExpansion(tuple(z, x...), NMax + 1) + eˣ - - # Test products - polyprod = simplify(poly(eˣ * eʸ); expand=true) - prodpoly = simplify( - substitute( - simplify(poly(eˣ) * poly(eʸ); expand=true), - Dict([c⁻¹^n => 0 for n ∈ NMax:(2NMax + 3)]), - ); - expand=true, - ) - Δ = simplify(polyprod - prodpoly; expand=true) - @test iszero(Δ) - @test_throws ArgumentError eˣ * PNExpansion(tuple(z, x...), NMax + 1) - @test_throws ArgumentError PNExpansion(tuple(z, x...), NMax + 1) * eˣ - end - end - end -end