pynamical package

pynamical module

pynamical core.

pynamical.pynamical.bifurcation_plot(pops, xmin=0, xmax=4, ymin=0, ymax=1, figsize=(10, 6), title='Bifurcation Diagram', xlabel='Growth Rate', ylabel='Population', color='#003399', filename='image', save=True, show=True, title_font=None, label_font=None, folder='images', dpi=300, bbox_inches='tight', pad=0.1)

Plot the results of the model as a bifurcation diagram.

Parameters:
  • pops (DataFrame) – population data output from the model
  • xmin (float) – minimum value on the x axis
  • xmax (float) – maximum value on the x axis
  • ymin (float) – minimum value on the y axis
  • ymax (float) – maximum value on the y axis
  • figsize (tuple) – (width, height) of figure
  • title (string) – title of the plot
  • xlabel (string) – label of the x axis
  • ylabel (string) – label of the y axis
  • color (string) – color of the points in the scatter plot
  • filename (string) – name of image file to be saved, if applicable
  • save (bool) – whether to save the image to disk or not
  • show (bool) – whether to display the image on screen or not
  • title_font (matplotlib.font_manager.FontProperties) – font properties for figure title
  • label_font (matplotlib.font_manager.FontProperties) – font properties for axis labels
  • folder (string) – folder in which to save the image file
  • dpi (int) – resolution at which to save the image
  • bbox_inches (string) – tell matplotlib to figure out the tight bbox of the figure
  • pad (float) – inches to pad around the figure
Returns:

(fig, ax) if show=False, otherwise returns None
Return type:

tuple
pynamical.pynamical.cobweb_plot(model=<function logistic_map>, r=0, function_n=1000, cobweb_n=100, cobweb_x=0.5, num_discard=0, title='', filename='', show=True, save=True, start=0, end=1, figsize=(6, 6), diagonal_linewidth=1.35, cobweb_linewidth=1, function_linewidth=1.5, title_font=None, label_font=None, folder='images', dpi=300, bbox_inches='tight', pad=0.1)

Draw a cobweb plot.

Run the map once each for 1000 population values evenly spaced between 0 and 1. This gives us the results of the equation (y values) across the entire range of possible population values (x values). The gray diagonal line is just a plot of y=x.

Parameters:
  • model (function) – defining an iterated map to simulate
  • r (float) – growth rate parameter value to pass to the map
  • function_n (int) – number of iterations of the function to run
  • cobweb_n (int) – number of iterations of the cobweb line to run
  • num_discard (int) – how many initial iterations of the cobweb line to throw away
  • title (string) – title of the plot
  • filename (string) – name of image file to be saved, if applicable
  • save (bool) – whether to save the image to disk or not
  • show (bool) – whether to display the image on screen or not
  • start (float) – lower limit of the function range
  • end (float) – upper limit of the function range
  • figsize (tuple) – (width, height) of figure
  • diagonal_linewidth (float) – width of y=x line
  • cobweb_linewidth (float) – width of cobweb line
  • function_linewidth (float) – width of function line
  • title_font (matplotlib.font_manager.FontProperties) – font properties for figure title
  • label_font (matplotlib.font_manager.FontProperties) – font properties for axis labels
  • folder (string) – folder in which to save the image file
  • dpi (int) – resolution at which to save the image
  • bbox_inches (string) – tell matplotlib to figure out the tight bbox of the figure
  • pad (float) – inches to pad around the figure
Returns:

(fig, ax) if show=False, otherwise returns None
Return type:

tuple
pynamical.pynamical.cubic_map(pop, rate)

Define the equation for the cubic map.

Parameters:
  • pop (float) – current population value at time t
  • rate (float) – growth rate parameter values
Returns:

scalar result of cubic map at time t+1
Return type:

float
pynamical.pynamical.get_bifurcation_plot_points(pops)

Convert a DataFrame of values from the model into a set of xy points.

You can plot these points as a bifurcation diagram.

Parameters:pops (DataFrame) – population data output from the model
Returns:
Return type:DataFrame
pynamical.pynamical.get_cobweb_points(model, r, x, n)

Calculate the vertices of cobweb lines for a cobweb plot.

Steps in the calculation: 1) Let x = 0.5 2) Start on the x-axis at the point (x, 0). 3) Draw a vertical line to the red function curve: this point has the coordinates (x, f(x)). 4) Draw a horizontal line from this point to the gray diagonal line: this point has the coordinates (f(x), f(x)). 5) Draw a vertical line from this point to the red function curve: this point has the coordinates (f(x), f(f(x))). 6) Repeat steps 4 and 5 recursively n times.

Parameters:
  • model (function) – defining an iterated map to simulate
  • r (float) – growth rate parameter value to pass to the map
  • x (float) – starting population value
  • n (int) – number of iterations to run
Returns:

cobweb_x_vals, cobweb_y_vals
Return type:

tuple
pynamical.pynamical.get_function_points(model, r, n, start, end)

Calculate model results for n population values.

Values are evenly spaced between start and end values.

Parameters:
  • model (function) – defining an iterated map to simulate
  • r (float) – growth rate parameter value to pass to the map
  • n (int) – number of iterations to run
  • start (float) – lower limit of the function range
  • end (float) – upper limit of the function range
Returns:

x_vals, y_vals
Return type:

tuple
pynamical.pynamical.get_label_font(family='Helvetica', style='normal', size=16, weight='normal', stretch='normal')

Define fonts to use for image axis labels.

Parameters:
  • family (string) –
  • style (string) –
  • size (numeric) –
  • weight (string) –
  • stretch (string) –
Returns:
Return type:

matplotlib.font_manager.FontProperties
pynamical.pynamical.get_phase_colors(color_request, length=1, color_reverse=False, default_color='#003399')

Return a list of colors based on a request.

Request could be a list, string color name, or string colormap name.

Parameters:
  • color_request (string or list) – what color the caller wants, could be a list, string color name, or string colormap name
  • length (int) – how many total colors to return in the list
  • color_reverse (bool) – reverse the returned list of colors if True
  • default_color (string) – if the list is shorter than the specified length, pad it out with default_color
Returns:
Return type:

list
pynamical.pynamical.get_phase_diagram_points(pops, discard_gens=1, dimensions=2)

Convert a DataFrame of values from the model into a set of xy(z) points.

Parameters:
  • pops (DataFrame) – population data output from the model
  • discard_gens (int) – number of rows to discard before keeping points to plot
  • dimensions (int) – {2, 3}, number of dimensions specifying if we want points for a 2-D or 3-D plot: (t, t+1) vs (t, t+1, t+2)
Returns:
Return type:

DataFrame
pynamical.pynamical.get_title_font(family='Helvetica', style='normal', size=20, weight='normal', stretch='normal')

Define fonts to use for image titles.

Parameters:
  • family (string) –
  • style (string) –
  • size (numeric) –
  • weight (string) –
  • stretch (string) –
Returns:
Return type:

matplotlib.font_manager.FontProperties
pynamical.pynamical.logistic_map(pop, rate)

Define the equation for the logistic map.

Parameters:
  • pop (float) – current population value at time t
  • rate (float) – growth rate parameter values
Returns:

scalar result of logistic map at time t+1
Return type:

float
pynamical.pynamical.make_jit_simulator(model, num_gens, rate_min, rate_max, num_rates, num_discard, initial_pop)

Create a jitted simulator function.

It receives the jitted model function, without it being an argument passed to the simulator function, because of the closure local scope.

Parameters:
  • model (function) – the function defining an iterated map to simulate
  • num_gens (int) – number of iterations to run the model
  • rate_min (float) – the first growth rate for the model, between 0 and 4
  • rate_max (float) – the last growth rate for the model, between 0 and 4
  • num_rates (int) – how many growth rates between min and max to run the model on
  • num_discard (int) – number of generations to discard before keeping population values
  • initial_pop (float) – starting population when you run the model, between 0 and 1
Returns:
Return type:

function
pynamical.pynamical.phase_diagram(pops, discard_gens=0, figsize=(6, 6), xmin=0, xmax=1, ymin=0, ymax=1, title='', xlabel='Population (t)', ylabel='Population (t + 1)', marker='.', size=5, alpha=0.7, color='#003399', color_reverse=False, legend=False, filename='image', save=True, show=True, title_font=None, label_font=None, folder='images', dpi=300, bbox_inches='tight', pad=0.1)

Draw a 2D phase diagram for one or more time series.

Plot the value at time t on the x-axis and the value at t+1 on the y-axis.

Parameters:
  • pops (DataFrame) – population data output from the model
  • discard_gens (int) – number of rows to discard before keeping points to plot
  • figsize (tuple) – (width, height) of figure
  • xmin (float) – minimum value on the x axis
  • xmax (float) – maximum value on the x axis
  • ymin (float) – minimum value on the y axis
  • ymax (float) – maximum value on the y axis
  • title (string) – title of the plot
  • xlabel (string) – label of the x axis
  • ylabel (string) – label of the y axis
  • marker (string) – the type of point to use in the plot
  • size (float) – the size of the marker
  • alpha (float) – the opacity of the marker
  • color (string) – color of the points in the scatter plot
  • color_reverse (bool) – reverse the returned list of colors if True
  • legend (bool) – if we should display a legend or not
  • filename (string) – name of image file to be saved, if applicable
  • save (bool) – whether to save the image to disk or not
  • show (bool) – whether to display the image on screen or not
  • title_font (matplotlib.font_manager.FontProperties) – font properties for figure title
  • label_font (matplotlib.font_manager.FontProperties) – font properties for axis labels
  • folder (string) – folder in which to save the image file
  • dpi (int) – resolution at which to save the image
  • bbox_inches (string) – tell matplotlib to figure out the tight bbox of the figure
  • pad (float) – inches to pad around the figure
Returns:

(fig, ax) if show=False, otherwise returns None
Return type:

tuple
pynamical.pynamical.phase_diagram_3d(pops, discard_gens=0, figsize=(10, 8), xmin=0, xmax=1, ymin=0, ymax=1, zmin=0, zmax=1, remove_ticks=True, title='', elev=25, azim=240, dist=10, xlabel='Population (t)', ylabel='Population (t + 1)', zlabel='Population (t + 2)', marker='.', size=5, alpha=0.7, color='#003399', color_reverse=False, legend=False, legend_bbox_to_anchor=None, filename='image', save=True, show=True, title_font=None, label_font=None, folder='images', dpi=300, bbox_inches='tight', pad=0.1)

Draw a 3D phase diagram for one or more time series.

Plot the value at time t on the x-axis, the value at t+1 on the y-axis, and the value of t+2 on the z-axis.

Parameters:
  • pops (DataFram) – population data output from the model
  • discard_gens (int) – number of rows to discard before keeping points to plot
  • figsize (tuple) – (width, height) of figure
  • xmin (float) – minimum value on the x axis
  • xmax (float) – maximum value on the x axis
  • ymin (float) – minimum value on the y axis
  • ymax (float) – maximum value on the y axis
  • zmin (float) – minimum value on the z axis
  • zmax (float) – maximum value on the z axis
  • remove_ticks (bool) – remove axis ticks or not
  • title (string) – title of the plot
  • elev (float) – the elevation of the viewing perspective
  • azim (float) – the azimuth of the viewing perspective
  • dist (float) – the distance of the viewing perspective
  • xlabel (string) – label of the x axis
  • ylabel (string) – label of the y axis
  • zlabel (string) – label of the z axis
  • marker (string) – the type of point to use in the plot
  • size (float) – the size of the marker
  • alpha (float) – the opacity of the marker
  • color (string) – color of the points in the scatter plot
  • color_reverse (bool) – reverse the returned list of colors if True
  • legend (bool) – if we should display a legend or not
  • legend_bbox_to_anchor (float) – amount to offset the legend from its natural position
  • filename (string) – name of image file to be saved, if applicable
  • save (bool) – whether to save the image to disk or not
  • show (bool) – whether to display the image on screen or not
  • title_font (matplotlib.font_manager.FontProperties) – font properties for figure title
  • label_font (matplotlib.font_manager.FontProperties) – font properties for axis labels
  • folder (string) – folder in which to save the image file
  • dpi (int) – resolution at which to save the image
  • bbox_inches (string) – tell matplotlib to figure out the tight bbox of the figure
  • pad (float) – inches to pad around the figure
Returns:

  • tuple
  • (fig, ax) if show=False, otherwise returns None
pynamical.pynamical.save_and_show(fig, ax, save, show, filename='image', folder='images', dpi=300, bbox_inches='tight', pad=0.1)

Consistently handle plot completion.

Save then either display or return the figure.

Parameters:
  • fig (matplotlib figure) –
  • ax (matplotlib axis) –
  • save (bool) – whether to save the image to disk, or not
  • show (bool) – whether to display the image or instead just return figure and axis
  • filename (string) – filename of image file to be saved
  • folder (string) – folder in which to save the image file
  • dpi (int) – resolution at which to save the image
  • bbox_inches (string) – tell matplotlib to figure out the tight bbox of the figure
  • pad (float) – inches to pad around the figure
Returns:

(fig, ax) if show=False, otherwise returns None
Return type:

tuple
pynamical.pynamical.save_fig(filename='image', folder='images', dpi=300, bbox_inches='tight', pad=0.1)

Save the current figure as a file to disk.

Parameters:
  • filename (string) – filename of image file to be saved
  • folder (string) – folder in which to save the image file
  • dpi (int) – resolution at which to save the image
  • bbox_inches (string) – tell matplotlib to figure out the tight bbox of the figure
  • pad (float) – inches to pad around the figure
Returns:
Return type:

None
pynamical.pynamical.simulate(model=<function logistic_map>, num_gens=50, rate_min=0.5, rate_max=4, num_rates=8, num_discard=0, initial_pop=0.5, jit=True)

Simulate a module.

Call simulator (either JIT compiled or not) to create a DataFrame with columns for each growth rate, row labels for each time step, and values computed by the model.

Parameters:
  • model (function) – the function defining an iterated map to simulate; default is the logistic map
  • num_gens (int) – number of iterations to run the model
  • rate_min (float) – the first growth rate for the model, between 0 and 4
  • rate_max (float) – the last growth rate for the model, between 0 and 4
  • num_rates (int) – how many growth rates between min and max to run the model on
  • num_discard (int) – number of generations to discard before keeping population values
  • initial_pop (float) – starting population when you run the model, between 0 and 1
  • jit (bool) – if True, use jit compiled simulator function to speed up simulation, if False, use uncompiled simulator function
Returns:
Return type:

DataFrame
pynamical.pynamical.simulate_jit(model, num_gens, rate_min, rate_max, num_rates, num_discard, initial_pop)

Create a DataFrame with columns for each growth rate.

Row labels for each time step, and values computed by the model (with JIT compilation). You can’t pass a jitted function to a jitted function unless you turn off ‘nopython’ mode (which makes it slow). In other words, you can’t pass different model functions directly to the simulate function. Instead, use a closure: The make_jit_simulator function returns a jitted simulator function that receives the jitted model function, without it being an argument passed to the simulator function, because of the closure local scope

Parameters:
  • model (function) – the function defining an iterated map to simulate
  • num_gens (int) – number of iterations to run the model
  • rate_min (float) – the first growth rate for the model, between 0 and 4
  • rate_max (float) – the last growth rate for the model, between 0 and 4
  • num_rates (int) – how many growth rates between min and max to run the model on
  • num_discard (int) – number of generations to discard before keeping population values
  • initial_pop (float) – starting population when you run the model, between 0 and 1
Returns:
Return type:

DataFrame
pynamical.pynamical.simulate_no_compile(model, num_gens, rate_min, rate_max, num_rates, num_discard, initial_pop)

Create a DataFrame with columns for each growth rate.

Row labels for each time step and values computed by the model (without JIT compilation).

Parameters:
  • model (function) – the function defining an iterated map to simulate
  • num_gens (int) – number of iterations to run the model
  • rate_min (float) – the first growth rate for the model, between 0 and 4
  • rate_max (float) – the last growth rate for the model, between 0 and 4
  • num_rates (int) – how many growth rates between min and max to run the model on
  • num_discard (int) – number of generations to discard before keeping population values
  • initial_pop (float) – starting population when you run the model, between 0 and 1
Returns:
Return type:

DataFrame
pynamical.pynamical.singer_map(pop, rate)

Define the equation for the singer map.

Parameters:
  • pop (float) – current population value at time t
  • rate (float) – growth rate parameter values
Returns:

scalar result of singer map at time t+1
Return type:

float