# timeplot.py - time plotting functions # RMM, 20 Jun 2023 """Time plotting functions. This module contains routines for plotting out time responses. These functions can be called either as standalone functions or access from the TimeResponseData class. """ import itertools from warnings import warn import matplotlib.pyplot as plt import numpy as np from . import config from .ctrlplot import ControlPlot, _make_legend_labels, \ _process_legend_keywords, _update_plot_title __all__ = ['time_response_plot', 'combine_time_responses'] # Default values for module parameter variables _timeplot_defaults = { 'timeplot.trace_props': [ {'linestyle': s} for s in ['-', '--', ':', '-.']], 'timeplot.output_props': [ {'color': c} for c in [ 'tab:blue', 'tab:orange', 'tab:green', 'tab:pink', 'tab:gray']], 'timeplot.input_props': [ {'color': c} for c in [ 'tab:red', 'tab:purple', 'tab:brown', 'tab:olive', 'tab:cyan']], 'timeplot.time_label': "Time [s]", 'timeplot.sharex': 'col', 'timeplot.sharey': False, } # Plot the input/output response of a system def time_response_plot( data, *fmt, ax=None, plot_inputs=None, plot_outputs=True, transpose=False, overlay_traces=False, overlay_signals=False, add_initial_zero=True, label=None, trace_labels=None, title=None, relabel=True, **kwargs): """Plot the time response of an input/output system. This function creates a standard set of plots for the input/output response of a system, with the data provided via a `TimeResponseData` object, which is the standard output for python-control simulation functions. Parameters ---------- data : `TimeResponseData` Data to be plotted. plot_inputs : bool or str, optional Sets how and where to plot the inputs: * False: don't plot the inputs * None: use value from time response data (default) * 'overlay': plot inputs overlaid with outputs * True: plot the inputs on their own axes plot_outputs : bool, optional If False, suppress plotting of the outputs. overlay_traces : bool, optional If set to True, combine all traces onto a single row instead of plotting a separate row for each trace. overlay_signals : bool, optional If set to True, combine all input and output signals onto a single plot (for each). sharex, sharey : str or bool, optional Determine whether and how x- and y-axis limits are shared between subplots. Can be set set to 'row' to share across all subplots in a row, 'col' to set across all subplots in a column, 'all' to share across all subplots, or False to allow independent limits. Default values are False for `sharex' and 'col' for `sharey`, and can be set using `config.defaults['timeplot.sharex']` and `config.defaults['timeplot.sharey']`. transpose : bool, optional If transpose is False (default), signals are plotted from top to bottom, starting with outputs (if plotted) and then inputs. Multi-trace plots are stacked horizontally. If transpose is True, signals are plotted from left to right, starting with the inputs (if plotted) and then the outputs. Multi-trace responses are stacked vertically. *fmt : `matplotlib.pyplot.plot` format string, optional Passed to `matplotlib` as the format string for all lines in the plot. **kwargs : `matplotlib.pyplot.plot` keyword properties, optional Additional keywords passed to `matplotlib` to specify line properties. Returns ------- cplt : `ControlPlot` object Object containing the data that were plotted. See `ControlPlot` for more detailed information. cplt.lines : 2D array of `matplotlib.lines.Line2D` Array containing information on each line in the plot. The shape of the array matches the subplots shape and the value of the array is a list of Line2D objects in that subplot. cplt.axes : 2D array of `matplotlib.axes.Axes` Axes for each subplot. cplt.figure : `matplotlib.figure.Figure` Figure containing the plot. cplt.legend : 2D array of `matplotlib.legend.Legend` Legend object(s) contained in the plot. Other Parameters ---------------- add_initial_zero : bool Add an initial point of zero at the first time point for all inputs with type 'step'. Default is True. ax : array of `matplotlib.axes.Axes`, optional The matplotlib axes to draw the figure on. If not specified, the axes for the current figure are used or, if there is no current figure with the correct number and shape of axes, a new figure is created. The shape of the array must match the shape of the plotted data. input_props : array of dict List of line properties to use when plotting combined inputs. The default values are set by `config.defaults['timeplot.input_props']`. label : str or array_like of str, optional If present, replace automatically generated label(s) with the given label(s). If more than one line is being generated, an array of labels should be provided with label[trace, :, 0] representing the output labels and label[trace, :, 1] representing the input labels. legend_map : array of str, optional Location of the legend for multi-axes plots. Specifies an array of legend location strings matching the shape of the subplots, with each entry being either None (for no legend) or a legend location string (see `~matplotlib.pyplot.legend`). legend_loc : int or str, optional Include a legend in the given location. Default is 'center right', with no legend for a single response. Use False to suppress legend. output_props : array of dict, optional List of line properties to use when plotting combined outputs. The default values are set by `config.defaults['timeplot.output_props']`. rcParams : dict Override the default parameters used for generating plots. Default is set by `config.defaults['ctrlplot.rcParams']`. relabel : bool, optional (deprecated) By default, existing figures and axes are relabeled when new data are added. If set to False, just plot new data on existing axes. show_legend : bool, optional Force legend to be shown if True or hidden if False. If None, then show legend when there is more than one line on an axis or `legend_loc` or `legend_map` has been specified. time_label : str, optional Label to use for the time axis. title : str, optional Set the title of the plot. Defaults to plot type and system name(s). trace_labels : list of str, optional Replace the default trace labels with the given labels. trace_props : array of dict List of line properties to use when plotting multiple traces. The default values are set by `config.defaults['timeplot.trace_props']`. Notes ----- A new figure will be generated if there is no current figure or the current figure has an incompatible number of axes. To force the creation of a new figures, use `plt.figure`. To reuse a portion of an existing figure, use the `ax` keyword. The line properties (color, linestyle, etc) can be set for the entire plot using the `fmt` and/or `kwargs` parameter, which are passed on to `matplotlib`. When combining signals or traces, the `input_props`, `output_props`, and `trace_props` parameters can be used to pass a list of dictionaries containing the line properties to use. These input/output properties are combined with the trace properties and finally the kwarg properties to determine the final line properties. The default plot properties, such as font sizes, can be set using `config.defaults[''timeplot.rcParams']`. """ from .ctrlplot import _process_ax_keyword, _process_line_labels # # Process keywords and set defaults # # Set up defaults ax_user = ax sharex = config._get_param('timeplot', 'sharex', kwargs, pop=True) sharey = config._get_param('timeplot', 'sharey', kwargs, pop=True) time_label = config._get_param( 'timeplot', 'time_label', kwargs, _timeplot_defaults, pop=True) rcParams = config._get_param('ctrlplot', 'rcParams', kwargs, pop=True) if kwargs.get('input_props', None) and len(fmt) > 0: warn("input_props ignored since fmt string was present") input_props = config._get_param( 'timeplot', 'input_props', kwargs, _timeplot_defaults, pop=True) iprop_len = len(input_props) if kwargs.get('output_props', None) and len(fmt) > 0: warn("output_props ignored since fmt string was present") output_props = config._get_param( 'timeplot', 'output_props', kwargs, _timeplot_defaults, pop=True) oprop_len = len(output_props) if kwargs.get('trace_props', None) and len(fmt) > 0: warn("trace_props ignored since fmt string was present") trace_props = config._get_param( 'timeplot', 'trace_props', kwargs, _timeplot_defaults, pop=True) tprop_len = len(trace_props) # Determine whether or not to plot the input data (and how) if plot_inputs is None: plot_inputs = data.plot_inputs if plot_inputs not in [True, False, 'overlay']: raise ValueError(f"unrecognized value: {plot_inputs=}") # # Find/create axes # # Data are plotted in a standard subplots array, whose size depends on # which signals are being plotted and how they are combined. The # baseline layout for data is to plot everything separately, with # outputs and inputs making up the rows and traces making up the # columns: # # Trace 0 Trace q # +------+ +------+ # | y[0] | ... | y[0] | # +------+ +------+ # : # +------+ +------+ # | y[p] | ... | y[p] | # +------+ +------+ # # +------+ +------+ # | u[0] | ... | u[0] | # +------+ +------+ # : # +------+ +------+ # | u[m] | ... | u[m] | # +------+ +------+ # # A variety of options are available to modify this format: # # * Omitting: either the inputs or the outputs can be omitted. # # * Overlay: inputs, outputs, and traces can be combined onto a # single set of axes using various keyword combinations # (overlay_signals, overlay_traces, plot_inputs='overlay'). This # basically collapses data along either the rows or columns, and a # legend is generated. # # * Transpose: if the `transpose` keyword is True, then instead of # plotting the data vertically (outputs over inputs), we plot left to # right (inputs, outputs): # # +------+ +------+ +------+ +------+ # Trace 0 | u[0] | ... | u[m] | | y[0] | ... | y[p] | # +------+ +------+ +------+ +------+ # : # : # +------+ +------+ +------+ +------+ # Trace q | u[0] | ... | u[m] | | y[0] | ... | y[p] | # +------+ +------+ +------+ +------+ # # This also affects the way in which legends and labels are generated. # Decide on the number of inputs and outputs ninputs = data.ninputs if plot_inputs else 0 noutputs = data.noutputs if plot_outputs else 0 ntraces = max(1, data.ntraces) # treat data.ntraces == 0 as 1 trace if ninputs == 0 and noutputs == 0: raise ValueError( "plot_inputs and plot_outputs both False; no data to plot") elif plot_inputs == 'overlay' and noutputs == 0: raise ValueError( "can't overlay inputs with no outputs") elif plot_inputs in [True, 'overlay'] and data.ninputs == 0: raise ValueError( "input plotting requested but no inputs in time response data") # Figure how how many rows and columns to use + offsets for inputs/outputs if plot_inputs == 'overlay' and not overlay_signals: nrows = max(ninputs, noutputs) # Plot inputs on top of outputs noutput_axes = 0 # No offset required ninput_axes = 0 # No offset required elif overlay_signals: nrows = int(plot_outputs) # Start with outputs nrows += int(plot_inputs == True) # Add plot for inputs if needed noutput_axes = 1 if plot_outputs and plot_inputs is True else 0 ninput_axes = 1 if plot_inputs is True else 0 else: nrows = noutputs + ninputs # Plot inputs separately noutput_axes = noutputs if plot_outputs else 0 ninput_axes = ninputs if plot_inputs else 0 ncols = ntraces if not overlay_traces else 1 if transpose: nrows, ncols = ncols, nrows # See if we can use the current figure axes fig, ax_array = _process_ax_keyword( ax, (nrows, ncols), rcParams=rcParams, sharex=sharex, sharey=sharey) legend_loc, legend_map, show_legend = _process_legend_keywords( kwargs, (nrows, ncols), 'center right') # # Map inputs/outputs and traces to axes # # This set of code takes care of all of the various options for how to # plot the data. The arrays output_map and input_map are used to map # the different signals that are plotted onto the axes created above. # This code is complicated because it has to handle lots of different # variations. # # Create the map from trace, signal to axes, accounting for overlay_* output_map = np.empty((noutputs, ntraces), dtype=tuple) input_map = np.empty((ninputs, ntraces), dtype=tuple) for i in range(noutputs): for j in range(ntraces): signal_index = i if not overlay_signals else 0 trace_index = j if not overlay_traces else 0 if transpose: output_map[i, j] = (trace_index, signal_index + ninput_axes) else: output_map[i, j] = (signal_index, trace_index) for i in range(ninputs): for j in range(ntraces): signal_index = noutput_axes + (i if not overlay_signals else 0) trace_index = j if not overlay_traces else 0 if transpose: input_map[i, j] = (trace_index, signal_index - noutput_axes) else: input_map[i, j] = (signal_index, trace_index) # # Plot the data # # The ax_output and ax_input arrays have the axes needed for making the # plots. Labels are used on each axes for later creation of legends. # The generic labels if of the form: # # signal name, trace label, system name # # The signal name or trace label can be omitted if they will appear on # the axes title or ylabel. The system name is always included, since # multiple calls to plot() will require a legend that distinguishes # which system signals are plotted. The system name is stripped off # later (in the legend-handling code) if it is not needed, but must be # included here since a plot may be built up by multiple calls to plot(). # # Reshape the inputs and outputs for uniform indexing outputs = data.y.reshape(data.noutputs, ntraces, -1) if data.u is None or not plot_inputs: inputs = None else: inputs = data.u.reshape(data.ninputs, ntraces, -1) # Create a list of lines for the output out = np.empty((nrows, ncols), dtype=object) for i in range(nrows): for j in range(ncols): out[i, j] = [] # unique list in each element # Utility function for creating line label # TODO: combine with freqplot version? def _make_line_label(signal_index, signal_labels, trace_index): label = "" # start with an empty label # Add the signal name if it won't appear as an axes label if overlay_signals or plot_inputs == 'overlay': label += signal_labels[signal_index] # Add the trace label if this is a multi-trace figure if overlay_traces and ntraces > 1 or trace_labels: label += ", " if label != "" else "" if trace_labels: label += trace_labels[trace_index] elif data.trace_labels: label += data.trace_labels[trace_index] else: label += f"trace {trace_index}" # Add the system name (will strip off later if redundant) label += ", " if label != "" else "" label += f"{data.sysname}" return label # # Store the color offsets with the figure to allow color/style cycling # # To allow repeated calls to time_response_plot() to cycle through # colors, we store an offset in the figure object that we can # retrieve in a later call, if needed. # output_offset = fig._output_offset = getattr(fig, '_output_offset', 0) input_offset = fig._input_offset = getattr(fig, '_input_offset', 0) # # Plot the lines for the response # # Process labels line_labels = _process_line_labels( label, ntraces, max(ninputs, noutputs), 2) # Go through each trace and each input/output for trace in range(ntraces): # Plot the output for i in range(noutputs): if line_labels is None: label = _make_line_label(i, data.output_labels, trace) else: label = line_labels[trace, i, 0] # Set up line properties for this output, trace if len(fmt) == 0: line_props = output_props[ (i + output_offset) % oprop_len if overlay_signals else output_offset].copy() line_props.update( trace_props[trace % tprop_len if overlay_traces else 0]) line_props.update(kwargs) else: line_props = kwargs out[output_map[i, trace]] += ax_array[output_map[i, trace]].plot( data.time, outputs[i][trace], *fmt, label=label, **line_props) # Plot the input for i in range(ninputs): if line_labels is None: label = _make_line_label(i, data.input_labels, trace) else: label = line_labels[trace, i, 1] if add_initial_zero and data.ntraces > i \ and data.trace_types[i] == 'step': x = np.hstack([np.array([data.time[0]]), data.time]) y = np.hstack([np.array([0]), inputs[i][trace]]) else: x, y = data.time, inputs[i][trace] # Set up line properties for this output, trace if len(fmt) == 0: line_props = input_props[ (i + input_offset) % iprop_len if overlay_signals else input_offset].copy() line_props.update( trace_props[trace % tprop_len if overlay_traces else 0]) line_props.update(kwargs) else: line_props = kwargs out[input_map[i, trace]] += ax_array[input_map[i, trace]].plot( x, y, *fmt, label=label, **line_props) # Update the offsets so that we start at a new color/style the next time fig._output_offset = ( output_offset + (noutputs if overlay_signals else 1)) % oprop_len fig._input_offset = ( input_offset + (ninputs if overlay_signals else 1)) % iprop_len # Stop here if the user wants to control everything if not relabel: warn("relabel keyword is deprecated", FutureWarning) return ControlPlot(out, ax_array, fig) # # Label the axes (including trace labels) # # Once the data are plotted, we label the axes. The horizontal axes is # always time and this is labeled only on the bottom most row. The # vertical axes can consist either of a single signal or a combination # of signals (when overlay_signal is True or plot+inputs = 'overlay'. # # Traces are labeled at the top of the first row of plots (regular) or # the left edge of rows (tranpose). # # Time units on the bottom for col in range(ncols): ax_array[-1, col].set_xlabel(time_label) # Keep track of whether inputs are overlaid on outputs overlaid = plot_inputs == 'overlay' overlaid_title = "Inputs, Outputs" if transpose: # inputs on left, outputs on right # Label the inputs if overlay_signals and plot_inputs: label = overlaid_title if overlaid else "Inputs" for trace in range(ntraces): ax_array[input_map[0, trace]].set_ylabel(label) else: for i in range(ninputs): label = overlaid_title if overlaid else data.input_labels[i] for trace in range(ntraces): ax_array[input_map[i, trace]].set_ylabel(label) # Label the outputs if overlay_signals and plot_outputs: label = overlaid_title if overlaid else "Outputs" for trace in range(ntraces): ax_array[output_map[0, trace]].set_ylabel(label) else: for i in range(noutputs): label = overlaid_title if overlaid else data.output_labels[i] for trace in range(ntraces): ax_array[output_map[i, trace]].set_ylabel(label) # Set the trace titles, if needed if ntraces > 1 and not overlay_traces: for trace in range(ntraces): # Get the existing ylabel for left column label = ax_array[trace, 0].get_ylabel() # Add on the trace title if trace_labels: label = trace_labels[trace] + "\n" + label elif data.trace_labels: label = data.trace_labels[trace] + "\n" + label else: label = f"Trace {trace}" + "\n" + label ax_array[trace, 0].set_ylabel(label) else: # regular plot (outputs over inputs) # Set the trace titles, if needed if ntraces > 1 and not overlay_traces: for trace in range(ntraces): if trace_labels: label = trace_labels[trace] elif data.trace_labels: label = data.trace_labels[trace] else: label = f"Trace {trace}" with plt.rc_context(rcParams): ax_array[0, trace].set_title(label) # Label the outputs if overlay_signals and plot_outputs: ax_array[output_map[0, 0]].set_ylabel("Outputs") else: for i in range(noutputs): ax_array[output_map[i, 0]].set_ylabel( overlaid_title if overlaid else data.output_labels[i]) # Label the inputs if overlay_signals and plot_inputs: label = overlaid_title if overlaid else "Inputs" ax_array[input_map[0, 0]].set_ylabel(label) else: for i in range(ninputs): label = overlaid_title if overlaid else data.input_labels[i] ax_array[input_map[i, 0]].set_ylabel(label) # # Create legends # # Legends can be placed manually by passing a legend_map array that # matches the shape of the subplots, with each item being a string # indicating the location of the legend for that axes (or None for no # legend). # # If no legend spec is passed, a minimal number of legends are used so # that each line in each axis can be uniquely identified. The details # depends on the various plotting parameters, but the general rule is # to place legends in the top row and right column. # # Because plots can be built up by multiple calls to plot(), the legend # strings are created from the line labels manually. Thus an initial # call to plot() may not generate any legends (e.g., if no signals are # combined nor overlaid), but subsequent calls to plot() will need a # legend for each different line (system). # # Figure out where to put legends if show_legend != False and legend_map is None: legend_map = np.full(ax_array.shape, None, dtype=object) if transpose: if (overlay_signals or plot_inputs == 'overlay') and overlay_traces: # Put a legend in each plot for inputs and outputs if plot_outputs is True: legend_map[0, ninput_axes] = legend_loc if plot_inputs is True: legend_map[0, 0] = legend_loc elif overlay_signals: # Put a legend in rightmost input/output plot if plot_inputs is True: legend_map[0, 0] = legend_loc if plot_outputs is True: legend_map[0, ninput_axes] = legend_loc elif plot_inputs == 'overlay': # Put a legend on the top of each column for i in range(ntraces): legend_map[0, i] = legend_loc elif overlay_traces: # Put a legend topmost input/output plot legend_map[0, -1] = legend_loc else: # Put legend in the upper right legend_map[0, -1] = legend_loc else: # regular layout if (overlay_signals or plot_inputs == 'overlay') and overlay_traces: # Put a legend in each plot for inputs and outputs if plot_outputs is True: legend_map[0, -1] = legend_loc if plot_inputs is True: legend_map[noutput_axes, -1] = legend_loc elif overlay_signals: # Put a legend in rightmost input/output plot if plot_outputs is True: legend_map[0, -1] = legend_loc if plot_inputs is True: legend_map[noutput_axes, -1] = legend_loc elif plot_inputs == 'overlay': # Put a legend on the right of each row for i in range(max(ninputs, noutputs)): legend_map[i, -1] = legend_loc elif overlay_traces: # Put a legend topmost input/output plot legend_map[0, -1] = legend_loc else: # Put legend in the upper right legend_map[0, -1] = legend_loc if show_legend != False: # Create axis legends legend_array = np.full(ax_array.shape, None, dtype=object) for i, j in itertools.product(range(nrows), range(ncols)): if legend_map[i, j] is None: continue ax = ax_array[i, j] labels = [line.get_label() for line in ax.get_lines()] if line_labels is None: labels = _make_legend_labels(labels, plot_inputs == 'overlay') # Update the labels to remove common strings if show_legend == True or len(labels) > 1: with plt.rc_context(rcParams): legend_array[i, j] = ax.legend( labels, loc=legend_map[i, j]) else: legend_array = None # # Update the plot title (= figure suptitle) # # If plots are built up by multiple calls to plot() and the title is # not given, then the title is updated to provide a list of unique text # items in each successive title. For data generated by the I/O # response functions this will generate a common prefix followed by a # list of systems (e.g., "Step response for sys[1], sys[2]"). # if ax_user is None and title is None: title = data.title if title == None else title _update_plot_title(title, fig, rcParams=rcParams) elif ax_user is None: _update_plot_title(title, fig, rcParams=rcParams, use_existing=False) return ControlPlot(out, ax_array, fig, legend=legend_map) def combine_time_responses(response_list, trace_labels=None, title=None): """Combine individual time responses into multi-trace response. This function combines multiple instances of `TimeResponseData` into a multi-trace `TimeResponseData` object. Parameters ---------- response_list : list of `TimeResponseData` objects Responses to be combined. trace_labels : list of str, optional List of labels for each trace. If not specified, trace names are taken from the input data or set to None. title : str, optional Set the title to use when plotting. Defaults to plot type and system name(s). Returns ------- data : `TimeResponseData` Multi-trace input/output data. """ from .timeresp import TimeResponseData # Save the first trace as the base case base = response_list[0] # Process keywords title = base.title if title is None else title # Figure out the size of the data (and check for consistency) ntraces = max(1, base.ntraces) # Initial pass through trace list to count things up and do error checks nstates = base.nstates for response in response_list[1:]: # Make sure the time vector is the same if not np.allclose(base.t, response.t): raise ValueError("all responses must have the same time vector") # Make sure the dimensions are all the same if base.ninputs != response.ninputs or \ base.noutputs != response.noutputs: raise ValueError("all responses must have the same number of " "inputs, outputs, and states") if nstates != response.nstates: warn("responses have different state dimensions; dropping states") nstates = 0 ntraces += max(1, response.ntraces) # Create data structures for the new time response data object inputs = np.empty((base.ninputs, ntraces, base.t.size)) outputs = np.empty((base.noutputs, ntraces, base.t.size)) states = np.empty((nstates, ntraces, base.t.size)) # See whether we should create labels or not if trace_labels is None: generate_trace_labels = True trace_labels = [] elif len(trace_labels) != ntraces: raise ValueError( "number of trace labels does not match number of traces") else: generate_trace_labels = False offset = 0 trace_types = [] for response in response_list: if response.ntraces == 0: # Single trace inputs[:, offset, :] = response.u outputs[:, offset, :] = response.y if nstates: states[:, offset, :] = response.x offset += 1 # Add on trace label and trace type if generate_trace_labels: trace_labels.append( response.title if response.title is not None else response.sysname if response.sysname is not None else "unknown") trace_types.append( None if response.trace_types is None else response.trace_types[0]) else: # Save the data for i in range(response.ntraces): inputs[:, offset, :] = response.u[:, i, :] outputs[:, offset, :] = response.y[:, i, :] if nstates: states[:, offset, :] = response.x[:, i, :] # Save the trace labels if generate_trace_labels: if response.trace_labels is not None: trace_labels.append(response.trace_labels[i]) else: trace_labels.append(response.title + f", trace {i}") offset += 1 # Save the trace types if response.trace_types is not None: trace_types += response.trace_types else: trace_types += [None] * response.ntraces return TimeResponseData( base.t, outputs, states if nstates else None, inputs, output_labels=base.output_labels, input_labels=base.input_labels, state_labels=base.state_labels if nstates else None, title=title, transpose=base.transpose, return_x=base.return_x, issiso=base.issiso, squeeze=base.squeeze, sysname=base.sysname, trace_labels=trace_labels, trace_types=trace_types, plot_inputs=base.plot_inputs)