Phase space class for dimensionless equations

class non_dimensional.phase_space

Phase space object performing a parameter span for a (custom) pair of parameters using dimensionless form of equations

get_initial()

Calculate initial condition for the simulation.

If the parameter self.recalculate_initial is True, then the initial condition is recalculated, as defined in the simulation class.

If it’s False, then the previous initial condition is utilized**

Returns:

get_outname(out)

Defines the labels attributed to the various statistics that are calculated.

Parameters:out – The output matrix from the parameter sweep (e.g. self.rel_height) Returns:Label (str) (e.g. r”$Delta e$”)

get_stats(X)

Perform the simulation (with repeats as defined by the np.int self.rep), and calculate the summary statistics: the relative height (∆e), the amount (int e dx), the polarization timescale, and the number of peaks.

Parameters:X – Two-element list or array defining the values of the parameters attributed to the x or y axis Returns:Four-element array of the statistics, as defined by the order listed above.

make_param_span_plot(ax, out, xscale='log', yscale='log', percentile_lim=(0, 100), cmap=<sphinx.ext.autodoc.importer._MockObject object>, overlay_peaks=False, vlim=None)

Plot the parameter scan.

Parameters:

• ax – matplotlib axis object to plot the parameter scan onto.
• out – np.ndarray of statistics for each parameter combination (resolution x resolution). E.g. self.rel_height
• xscale – Scale of the x-axis. Must be the same as in self.perform_param_scan.
• yscale – Scale of the y-axis. Must be the same as in self.perform_param_scan.
• percentile_lim – Cut-off for the colorbar, setting the maximum and minimum percentile of the statistic for which a color is attributed.
• cmap – matplotlib.cm object e.g. matplotlib.cm.plasma
• overlay_peaks – Overlay the number of peaks for each parameter combination (i.e. to identify multi-peak regimes).

overlay_peaks(ax)

Overlay the number of peaks. Transparent if 1 or 0 peaks, or increasingly black if multi-peak solutions are frequent.

Parameters:ax – matplotlib axis object Returns:ax

perform_param_scan(xlim, ylim, xscale, yscale, resolution, xvar='lambd', yvar='epsilon', recalculate_initial=True)

Perform the parameter scan.

Saves the parameter-scan to an npy file.

Uses the joblib parallelisation package.

Parameters:

• xlim – Tuple, setting the minimum and maximum of the xvar to simulate over. If xlim = (a,b), (where a < b) then if xscale is “log”, simulate between 10^a and 10^b if xscale is “reciprocal”, simulate between 1/b and 1/a if xscale is “normal”, then simulate between a and b
• ylim – Tuple, setting the minimum and maximum of the yvar to simulate over. Same rules as xvar
• xscale – Scale of the x-axis, setting the stepping of the parameter discretization. A str: either “log”, “reciprocal” or “normal”
• yscale – Scale of y-axis. Same rules as xscale.
• resolution – Number of parameter discretisations to simulate over. Can be an np.int32, where paramter discretisation number is same in x and y axis, or a tuple of np.int32, defining the number of spatial discretisations for the x vs y axis
• xvar – str defining the x-axis attributed parameter. Must match nomencalture of the code precisely. e.g. “D_E”
• yvar – str defining the y-axis attributed parameter. Must match nomencalture of the code precisely. e.g. “E_crit”
• recalculate_initial – Recalculate the initial condition of the simulation for each repeat and each parameter combination if True. Else the first initial condition is stored and re-used.

plot_param_scan(out, xscale='log', yscale='log', percentile_lim=(0, 100), cmap=<sphinx.ext.autodoc.importer._MockObject object>, overlay_peaks=False, save=True, vlim=None)

Make full parameter scan plot. A wrapper for self.make_param_span_plot.

Saves the plot to the plots directory as a PDF.

Parameters:

• out – np.ndarray of statistics for each parameter combination (resolution x resolution). E.g. self.rel_height
• xscale – Scale of the x-axis. Must be the same as in self.perform_param_scan.
• yscale – Scale of the y-axis. Must be the same as in self.perform_param_scan.
• percentile_lim – Cut-off for the colorbar, setting the maximum and minimum percentile of the statistic for which a color is attributed.
• cmap – matplotlib.cm object e.g. matplotlib.cm.plasma
• overlay_peaks – Overlay the number of peaks for each parameter combination (i.e. to identify multi-peak regimes).

set_names(xname, yname)

Phase space considers solutions when varying two parameters. So this function sets the axis-labels of the x and y axes

Parameters:

• xname – Axis label of the x-axis (str), e.g. r”$log_10 lambda$”
• yname – Axis label of the x-axis (str), e.g. r”$1 / epsilon$”