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Merge pull request #1094 from murrayrm/userguide-22Dec2024

Updated user documentation (User Guide, Reference Manual)

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control/timeplot.py

# 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)

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