Analysis and plotting

transform_solutions(res::Result, f::String; rules) -> Any

Takes a Result object and a string f representing a Symbolics.jl expression. Returns an array with the values of f evaluated for the respective solutions. Additional substitution rules can be specified in rules in the format ("a" => val) or (a => val)

plot_1D_solutions(res::Result; 
                    x::String, y::String, 
                    xscale="linear",yscale="linear"
                    ,plot_only=["physical"],
                    marker_classification="stable",filename=nothing, kwargs...)

Make a 1D plot of a Result object.

Keyword arguments

• x, y: Expressions to plot on as independent/dependent variables (parsed into Symbolics.jl).
• xscale, yscale: scale for x/y dimensions (e.g. "linear" or "log")
• plot_only: a list of strings corresponding to the solution classes of Result. Only solutions which belong to the listed classes are plotted.
• marker_classification: A class of the solutions (created by classify_solutions!) which is distinguished with different markers. Entering an inequality creates a new class "custom_class".
• filename: if different from nothing, plotted data and parameter values are exported to ./filename.jld2. Otherwise, data is returned as a dictionary.
• kwargs: any additional keywords arguments for the matplotlib plotting

The strings in marker_classification allows the user to stablish custom criteria for binary classification of solutions. For instance, if marker_classification = "ω^15* sqrt(u1^2 + v1^2) < 0.1", for a system with harmonic variables u1,v1, then solutions are classified as true according to that criterion and false according to its complement.

plot_1D_jacobian_eigenvalues(res::Result; x::String, physical=true, stable=false,marker_re="o",marker_im="X", filename=nothing,kwargs...)

Make a 1D plot of the Jacobian eigenvalues for each of the solutions in a Result object.

Keyword arguments

• x: The function on the x axis (a string parsed into Symbolics.jl).
• physical, stable: Booleans specifying whether unphysical and/or unstable solutions are shown.
• marker_re, marker_im: The markers to use for the Re and Im parts of the eigenvalues.
• ax: axis object from PyCall.PyObject setting the coordinate system where data will be plotted. If not given, it is created automatically.
• filename: if different from nothing, plotted data and parameter values are exported to ./filename.jld2. Otherwise, data is returned as a dictionary.

plot_2D_solutions(res::Result,ax=nothing; filename=nothing)

Make a 2D plot of each of solutions vs swept parameters for a Result object, obtained from a get_steady_states applied to a 2D parameter grid.`.

Keyword arguments

• ax: axis object from PyCall.PyObject setting the coordinate system where data will be plotted. If not given, it is created automatically.
• filename: if different from nothing, plotted data and parameter values are exported to ./filename.jld2. Otherwise, data is returned as a dictionary.
• z: The function on the z axis (a string parsed into Symbolics.jl). If z=nothing, raw solutions are displayed
• plot_only: Array of labels to filter physical solutions (e.g. "stable") and multi-solution methods if z!=nothing (e.g. maximum)

plot_2D_phase_diagram(res::Result; stable=false,observable="nsols",ax=nothing, filename=nothing)

Make a 2D phase diagram plot of each of solutions vs swept parameters for a Result object, obtained from a get_steady_states applied to a 2D parameter grid.

Keyword arguments

• stable: whether only stable solutions are depicted
• observable: reference observable to represent dynamical phases in the problem. If observable="nsols", number of solutions for each point is shown. If instead observable="binary", the result of classification of bistrings [is_stable(solution_1),is_stable(solution_2),...] is presented (see classify_binaries!(Result) function).
• filename: if different from nothing, plotted data and parameter values are exported to ./filename.jld2.Otherwise, data is returned as a dictionary.

plot_2D_phase_diagram_interactive(res::Result;
 observable="nsols",
  stable=false,nrows=2,
  ncols=2,cut_dim="1",
  cut_type="solutions",
  string_f=nothing,
  marker_classification="stable")

Interactive phase diagram of 2D solutions stored in Result. This includes a clickable version of a plot_2D_phase_diagram for a given observable and extra panels containing 1D cuts of solutions, functions of solutions, or Jacobian eigenvalues.

Keyword arguments

• observable: reference observable to represent dynamical phases in the problem. If observable="nsols", number of solutions for each point is shown. If instead observable="binary", the result of classification of bistrings[isstable(solution1),isstable(solution2),...]is presented (seeclassify_binaries!(Result)` function).
• ncols, nrows: number of rows and columns of the plot window.
• cut_dim: dimension along which 1D quantities will be calculated. cut_dim="1" (cut_dim="2") takes a cut along the horizontal (vertical) parameter dimension of the 2D plot.
• cut_type: quantity to be represented along the 1D cut. If cut_type=solutions, steady state variables are shown with a panel per Problem variable. Else if cut_type=jacobian eigenvalues, Re and Im parts of complex Jacobian eigenvalues for each solution are shown with a panel per solution. If instead cut_type=transform, functions of the solution variables passed to string_f (see below) are displayed.
• string_f: list of strings for transformed observables to be plotted in 1D when cut_type=transform, e.g. string_f=["sqrt(u1^2 + v1^2)","sqrt(u2^2 + v2^2)"] for Problem variables u1,u2,v1,v2.
• marker_classification: A class of the solutions (created by classify_solutions!) which is distinguished with different markers. Entering an inequality creates a new class "custom_class".
• ylim: vertical limits for 1D cuts