In GTPSA:

• Move layer 2 implementations of "map" methods out of GTPSA and into this package? (Yes but then "parameters" in GTPSA.jl are meaningless, which might be okay, would have to move into this package, so unsure)
• Allow changing Descriptors when number variables/parameters also changes? no for now
• Documentation cleanup (fixing "Syntax" parts of gjh, etc)
• Make TPSs callable for nicer evaluation syntax and also composition

Both:

• SizedVectors required (not isbits) and confirmed is slower in tracking than regular vectors. Consider use of MVector/SVector for map fields. This is faster for small array sizes but concatenation current requires one to include all parameters in vector so may be slower for large number of parameters. Would need to Modify all lower level functions in GTPSA to also accept MVector or SVector (dense)

In NonlinearNormalForm

• cleaned Probe ctor cleanup (all kwarg? but need number vars. MVectors + numvars in type. do not require v)
• Probe for both types of trackingHow to deal with Probes? Should I overload indexing for probe struct to automatically set scalar part?
• Map ctor cleanup
• Map operators: \circ, ^, +, -
• (Bi)quaternion implementation
• Add ref column to map output
• Probe cannot just take a phase space ray... need to fix this. Etiennes way is to set x0 with scalar part of TPSA map and keep scalar part in map

For some reason, when writing (something)^(negative_number), Julia does not just call ^(something, negative_number). Instead it calls inv(something)^(-1*negative_number). This definition does not agree with FPP. For example, for a TPSAMap m, inv(m)^3 != inv(m^3). In fact inv(m)^3 is very problematic, whereas inv(m^3) is not.

This is only a problem for TPSAMaps

This is helpful since looking at the significantly nonzero terms in this matrix gives clues as to where the non-symplecticity is happening.

Because of of the bug in GTPSA, the output map length must be nn and not nv. Therefore this temporary is unnecessarily big.

After the bug is fixed the affected functions inv!, prep_comp_inv_work_low and prep_inv_work_low should be corrected. Also instead of allocating a new array for the quaternion if nv<4 instead of reusing m1x_low or whatever it was, instead just make m1x_low big enough to reuse quaternion part

Generate hamiltonian in phasors then transform back

At the time of this issue, the function gofix looks like

function gofix(xy::DAMap, order=1)
  desc = getdesc(xy)
  nv = numvars(desc)

  # 1: v = map-identity in harmonic planes, identity in spin
  v = zero(xy)
  for i=1:nv
    @inbounds v.x[i] =  xy.x[i] - mono(i,use=desc)
  end
  v.Q.q[1] = 1

  # 2: map is cut to order 2 or above
  cut!(v,v,order+1)

  # 3: map is inverted at least to order 1:
  inv!(v,v)

  # 4: a map x is created with dimension nv
  # x is zero except for the parameters and delta if coasting
  x = zero(v) # default identity in parameters
  x.Q.q[1] = 1 # identity in spin
  compose!(v,v,x)

  # 5: add back in identity
  for i=1:nv
    @inbounds v.x[i] += mono(i,use=desc)
  end

  return v
end

This is pretty fast (could be made faster by proper use of work temporaries accessible by user of inv and compose) , however this is not the easiest to read. gofix could instead be written as

function gofix(xy::DAMap, order=1)
  m = cut(xy, order+1)
  return (m-I)^-1∘zero(m)+I
end

This is much easier to understand and read, however much slower. For the best of both worlds, a macro must be implemented to convert the above easy-to-read function to its faster less-easy-to-read function. The approach could be the same as that taken for @FastGTPSA in GTPSA.jl

FPP accounts for longitudinal drift (RF off) with a special setting ndpt which treats the longitudinal as a parameter but must also satisfy poisson bracket (unlike the rest of the parameters which are just knobs). My current thinking is for NonlinearNormalForm to extend the Descriptor constructors to allow for this

What I see is:

julia> import Pkg; Pkg.add(path="https://github.com/bmad-sim/NonlinearNormalForm.jl")
Cloning git-repo https://github.com/bmad-sim/NonlinearNormalForm.jl
Updating git-repo https://github.com/bmad-sim/NonlinearNormalForm.jl
Updating registry at ~/.julia/registries/General.toml
Resolving package versions...
ERROR: Unsatisfiable requirements detected for package GTPSA_jll [a4739e29]:
GTPSA_jll [a4739e29] log:
├─possible versions are: 1.0.0-1.3.0 or uninstalled
└─restricted to versions 1.3.1-1 by GTPSA [b27dd330] — no versions left
└─GTPSA [b27dd330] log:
├─possible versions are: 0.6.1 or uninstalled
├─restricted to versions 0.5.2-0.5 by NonlinearNormalForm [05e19671] — no versions left
│ └─NonlinearNormalForm [05e19671] log:
│ ├─possible versions are: 1.0.0 or uninstalled
│ └─NonlinearNormalForm [05e19671] is fixed to version 1.0.0-DEV
└─GTPSA [b27dd330] is fixed to version 0.6.1
Stacktrace:
[1] check_constraints(graph::Pkg.Resolve.Graph)
@ Pkg.Resolve /Applications/Julia-1.10.app/Contents/Resources/julia/share/julia/stdlib/v1.10/Pkg/src/Resolve/graphtype.jl:998
[2] Pkg.Resolve.Graph(compat::Dict{…}, compat_weak::Dict{…}, uuid_to_name::Dict{…}, reqs::Dict{…}, fixed::Dict{…}, verbose::Bool, julia_version::VersionNumber)
@ Pkg.Resolve /Applications/Julia-1.10.app/Contents/Resources/julia/share/julia/stdlib/v1.10/Pkg/src/Resolve/graphtype.jl:345
[3] deps_graph(env::Pkg.Types.EnvCache, registries::Vector{…}, uuid_to_name::Dict{…}, reqs::Dict{…}, fixed::Dict{…}, julia_version::VersionNumber, installed_only::Bool)
@ Pkg.Operations /Applications/Julia-1.10.app/Contents/Resources/julia/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:586
[4] resolve_versions!(env::Pkg.Types.EnvCache, registries::Vector{…}, pkgs::Vector{…}, julia_version::VersionNumber, installed_only::Bool)
@ Pkg.Operations /Applications/Julia-1.10.app/Contents/Resources/julia/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:406
[5] targeted_resolve(env::Pkg.Types.EnvCache, registries::Vector{…}, pkgs::Vector{…}, preserve::Pkg.Types.PreserveLevel, julia_version::VersionNumber)
@ Pkg.Operations /Applications/Julia-1.10.app/Contents/Resources/julia/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:1360
[6] tiered_resolve(env::Pkg.Types.EnvCache, registries::Vector{…}, pkgs::Vector{…}, julia_version::VersionNumber, try_all_installed::Bool)
@ Pkg.Operations /Applications/Julia-1.10.app/Contents/Resources/julia/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:1349
[7] _resolve(io::Base.TTY, env::Pkg.Types.EnvCache, registries::Vector{…}, pkgs::Vector{…}, preserve::Pkg.Types.PreserveLevel, julia_version::VersionNumber)
@ Pkg.Operations /Applications/Julia-1.10.app/Contents/Resources/julia/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:1370
[8] add(ctx::Pkg.Types.Context, pkgs::Vector{…}, new_git::Set{…}; preserve::Pkg.Types.PreserveLevel, platform::Base.BinaryPlatforms.Platform)
@ Pkg.Operations /Applications/Julia-1.10.app/Contents/Resources/julia/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:1387
[9] add
@ Pkg.Operations /Applications/Julia-1.10.app/Contents/Resources/julia/share/julia/stdlib/v1.10/Pkg/src/Operations.jl:1376 [inlined]
[10] add(ctx::Pkg.Types.Context, pkgs::Vector{…}; preserve::Pkg.Types.PreserveLevel, platform::Base.BinaryPlatforms.Platform, kwargs::@kwargs{…})
@ Pkg.API /Applications/Julia-1.10.app/Contents/Resources/julia/share/julia/stdlib/v1.10/Pkg/src/API.jl:278
[11] add(pkgs::Vector{Pkg.Types.PackageSpec}; io::Base.TTY, kwargs::@kwargs{})
@ Pkg.API /Applications/Julia-1.10.app/Contents/Resources/julia/share/julia/stdlib/v1.10/Pkg/src/API.jl:159
[12] add(pkgs::Vector{Pkg.Types.PackageSpec})
@ Pkg.API /Applications/Julia-1.10.app/Contents/Resources/julia/share/julia/stdlib/v1.10/Pkg/src/API.jl:148
[13] add(; name::Nothing, uuid::Nothing, version::Nothing, url::Nothing, rev::Nothing, path::String, mode::Pkg.Types.PackageMode, subdir::Nothing, kwargs::@kwargs{})
@ Pkg.API ./boot.jl:0
[14] top-level scope
@ REPL[1]:1
Some type information was truncated. Use show(err) to see complete types.

julia>