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plot #

Plotting functions.

Functions:

plot_timeseries #

plot_timeseries(
    ax: Axes,
    data: NDArray[float64],
    times: NDArray[Union[int64, float64]],
    n_blocks: int = 100,
    time_units: str = "ns",
    y_label: str = "$\\Delta G$ / kcal mol$^{-1}$",
) -> None

Plot the (multi-run) time series data.

Parameters:

  • ax (Axes) –

    The axes to plot on.

  • data (ndarray) –

    The time series data. This should have shape (n_runs, n_samples), or (n_samples,) if there is only one run.

  • times (ndarray) –

    The times at which the data was sampled. This should have shape (n_samples,).

  • n_blocks (int, default: 100 ) –

    The number of blocks to use for block averaging. This makes trends clearer. If 0, no block averaging is performed.

  • time_units (str, default: 'ns' ) –

    The units of time. The default is "ns".

  • y_label (str, default: '$\\Delta G$ / kcal mol$^{-1}$' ) –

    The y-axis label. The default is "ΔG / kcal mol−1".

Source code in red/plot.py 
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def plot_timeseries(
    ax: _Axes,
    data: _npt.NDArray[_np.float64],
    times: _npt.NDArray[_Union[_np.int64, _np.float64]],
    n_blocks: int = 100,
    time_units: str = "ns",
    y_label: str = r"$\Delta G$ / kcal mol$^{-1}$",
) -> None:
    r"""
    Plot the (multi-run) time series data.

    Parameters
    ----------
    ax : Axes
        The axes to plot on.

    data : np.ndarray
        The time series data. This should have shape
        (n_runs, n_samples), or (n_samples,) if there
        is only one run.

    times : np.ndarray
        The times at which the data was sampled. This
        should have shape (n_samples,).

    n_blocks : int, optional
        The number of blocks to use for block averaging. This
        makes trends clearer. If 0, no block averaging is
        performed.

    time_units : str, optional
        The units of time. The default is "ns".

    y_label : str, optional
        The y-axis label. The default is "$\Delta G$ / kcal mol$^{-1}$".
    """
    # Check that data is valid.
    data = check_data(data, one_dim_allowed=True)
    n_runs, n_samples = data.shape

    # Check that times is valid.
    if not isinstance(times, _np.ndarray):
        raise InvalidInputError("Times must be a numpy array.")

    if times.ndim != 1:
        raise InvalidInputError("Times must be one dimensional.")

    if times.shape[0] != n_samples:
        raise InvalidInputError("Times must have the same length as the number of samples.")

    if n_blocks < 0 or n_blocks > n_samples:
        raise InvalidInputError(
            "n_blocks must be greater than or equal to 0 and less than or equal to"
            " the number of samples."
        )

    if n_blocks == 0:
        n_blocks = n_samples

    # Get the block size based on the number of blocks requested.
    block_size = n_samples // n_blocks
    # Pick the final sample based on the block size, rather than the number of blocks.
    # We might end up with more blocks than requested, but this is better than failing
    # to show too much of the data.
    n_samples_end = n_samples - (n_samples % block_size)
    # Update the number of blocks according to the block size.
    n_blocks = n_samples_end // block_size
    # Trim the data and times so that they are divisible by the block size.
    times = times[:n_samples_end]
    data = data[:, :n_samples_end]
    data = data.reshape(n_runs, n_blocks, block_size).mean(axis=2)  # type: ignore
    times = times.reshape(n_blocks, block_size).mean(axis=1)

    # Decide the transparency of the individual run lines.
    alpha_runs = 1.0 if n_runs == 1 else 0.5

    # Plot the data.
    for i in range(n_runs):
        label = None if n_runs == 1 else f"Run {i + 1}"
        ax.plot(times, data[i, :], alpha=alpha_runs, label=label)

    # If we have more than one run, plot the mean.
    if n_runs > 1:
        ax.plot(times, data.mean(axis=0), color="black", label="Mean")

    # Only show the legend if there is more than one run.
    if n_runs > 1:
        ax.legend()

    # Set the axis labels.
    ax.set_xlabel(f"Time / {time_units}")
    ax.set_ylabel(y_label)

plot_p_values #

plot_p_values(
    ax: Axes,
    p_values: NDArray[float64],
    times: NDArray[float64],
    p_threshold: float = 0.05,
    time_units: str = "ns",
    threshold_times: Optional[NDArray[float64]] = None,
) -> None

Plot the p-values of the paired t-test.

Parameters:

  • ax (Axes) –

    The axes to plot on.

  • p_values (ndarray) –

    The p-values of the paired t-test.

  • times (ndarray) –

    The times at which the data was sampled.

  • p_threshold (float, default: 0.05 ) –

    The p-value threshold to use. The default is 0.05.

  • time_units (str, default: 'ns' ) –

    The units of time. The default is "ns".

  • threshold_times (ndarray, default: None ) –

    The times to plot the p-value threshold at. If None, this is set to the times at which the data was sampled. Useful when using this plot underneath a time series plot.

Source code in red/plot.py 
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def plot_p_values(
    ax: _Axes,
    p_values: _npt.NDArray[_np.float64],
    times: _npt.NDArray[_np.float64],
    p_threshold: float = 0.05,
    time_units: str = "ns",
    threshold_times: _Optional[_npt.NDArray[_np.float64]] = None,
) -> None:
    """
    Plot the p-values of the paired t-test.

    Parameters
    ----------
    ax : Axes
        The axes to plot on.

    p_values : np.ndarray
        The p-values of the paired t-test.

    times : np.ndarray
        The times at which the data was sampled.

    p_threshold : float, optional
        The p-value threshold to use. The default is 0.05.

    time_units : str, optional
        The units of time. The default is "ns".

    threshold_times : np.ndarray, optional
        The times to plot the p-value threshold at. If None, this is
        set to the times at which the data was sampled. Useful when
        using this plot underneath a time series plot.
    """
    # Check that p_values is valid.
    if not isinstance(p_values, _np.ndarray) or not isinstance(times, _np.ndarray):
        raise InvalidInputError("p_values and times must be numpy arrays.")

    if p_values.ndim != 1:
        raise InvalidInputError("p_values must be one dimensional.")

    if p_values.shape[0] != times.shape[0]:
        raise InvalidInputError("p_values must have the same length as the number of samples.")

    if threshold_times is None:
        threshold_times = times

    # Plot the p-values.
    ax.scatter(times, p_values, color="black", label="p-value")

    # Plot the p-value threshold.
    ax.plot(
        threshold_times,
        _np.full(threshold_times.shape, p_threshold),
        color="black",
        linestyle="-",
        linewidth=0.5,
        label="p-value threshold",
    )

    # Shade the region where the p-value is less than the threshold.
    ax.fill_between(
        threshold_times,
        0,
        p_threshold,
        alpha=0.3,
        # Black
        color="black",
    )

    # Plot a vertical dashed line at the first time point where the p-value is
    # greater than the threshold.
    ax.axvline(
        x=times[p_values > p_threshold][0],
        color="black",
        linestyle="--",
        label=f"Equilibration Time = {times[p_values > p_threshold][0]:.3g} {time_units}",
    )

    ax.legend()

    # Set the axis labels.
    ax.set_xlabel(f"Time / {time_units}")
    ax.set_ylabel("$p$-value")

plot_sse #

plot_sse(
    ax: Axes,
    sse: NDArray[float64],
    max_lags: Optional[NDArray[float64]],
    window_sizes: Optional[NDArray[float64]],
    times: NDArray[Union[int64, float64]],
    time_units: str = "ns",
    variance_y_label: str = "$\\frac{1}{\\sigma^2(\\Delta G)}$ / kcal$^{-2}$ mol$^2$",
    reciprocal: bool = True,
) -> Tuple[List[Artist], List[Any]]

Plot the squared standard error (SSE) estimate against time.

Parameters:

  • ax (Axes) –

    The axes to plot on.

  • sse (ndarray) –

    The SSE estimate.

  • max_lags (ndarray, default: None ) –

    The maximum lag times.

  • window_sizes (ndarray, default: None ) –

    The window sizes.

  • times (ndarray) –

    The times at which the data was sampled.

  • time_units (str, default: 'ns' ) –

    The units of time. The default is "ns".

  • variance_y_label (str, default: '$\\frac{1}{\\sigma^2(\\Delta G)}$ / kcal$^{-2}$ mol$^2$' ) –

    The y-axis label for the variance. The default is "1σ2(ΔG) / kcal−2 mol2".

  • reciprocal (bool, default: True ) –

    Whether to plot the reciprocal of the SSE.

Returns:

  • handles ( List[Line2D] ) –

    The handles for the legend.

  • labels ( List[str] ) –

    The labels for the legend.

Source code in red/plot.py 
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def plot_sse(
    ax: _Axes,
    sse: _npt.NDArray[_np.float64],
    max_lags: _Optional[_npt.NDArray[_np.float64]],
    window_sizes: _Optional[_npt.NDArray[_np.float64]],
    times: _npt.NDArray[_Union[_np.int64, _np.float64]],
    time_units: str = "ns",
    variance_y_label: str = r"$\frac{1}{\sigma^2(\Delta G)}$ / kcal$^{-2}$ mol$^2$",
    reciprocal: bool = True,
) -> _Tuple[_List[_Artist], _List[_Any]]:
    r"""
    Plot the squared standard error (SSE) estimate against time.

    Parameters
    ----------
    ax : Axes
        The axes to plot on.

    sse : np.ndarray
        The SSE estimate.

    max_lags : np.ndarray, optional, default=None
        The maximum lag times.

    window_sizes : np.ndarray, optional, default=None
        The window sizes.

    times : np.ndarray
        The times at which the data was sampled.

    time_units : str, optional
        The units of time. The default is "ns".

    variance_y_label : str, optional
        The y-axis label for the variance. The default is
        "$\frac{1}{\sigma^2(\Delta G)}$ / kcal$^{-2}$ mol$^2$".

    reciprocal : bool, optional, default=True
        Whether to plot the reciprocal of the SSE.

    Returns
    -------
    handles : List[Line2D]
        The handles for the legend.

    labels : List[str]
        The labels for the legend.
    """
    # Check that sse is valid.
    if not isinstance(sse, _np.ndarray) or not isinstance(times, _np.ndarray):
        raise InvalidInputError("sse and times must be numpy arrays.")

    if sse.ndim != 1:
        raise InvalidInputError("sse must be one dimensional.")

    if sse.shape[0] != times.shape[0]:
        raise InvalidInputError("sse must have the same length as the number of samples.")

    if max_lags is not None and window_sizes is not None:
        raise InvalidInputError("Only one of max_lags and window_sizes can be supplied.")

    with _plt.style.context(PLT_STYLE):
        # Plot the SSE.
        to_plot = 1 / sse if reciprocal else sse
        label = "1/SSE" if reciprocal else "SSE"
        if "ess" in variance_y_label.lower():
            label = "ESS" if reciprocal else "1/ESS"
        ax.plot(times, to_plot, color="black", label=label)

        # If lags is not None, plot the lag times on a different y axis.
        if max_lags is not None or window_sizes is not None:
            label = "Max Lag Index" if window_sizes is None else "Window Size"
            to_plot = max_lags if window_sizes is None else window_sizes  # type: ignore
            ax2 = ax.twinx()
            # Get the second colour from the colour cycle.
            ax2.set_prop_cycle(color=[_plt.rcParams["axes.prop_cycle"].by_key()["color"][1]])
            ax2.plot(times, to_plot, alpha=0.8, label=label)
            # Remove the horizontal lines.
            ax2.yaxis.grid(False)

            # Set the grid ticks and label colour to match the line colour.
            lag_colour = ax2.get_lines()[0].get_color()
            ax2.tick_params(axis="y", labelcolor=lag_colour)
            ax2.set_ylabel(label, color=lag_colour)

        # Plot a vertical dashed line at the minimum SSE.
        ax.axvline(
            x=times[sse.argmin()],
            color="black",
            linestyle="--",
            label=f"Equilibration Time = {times[sse.argmin()]:.3g} {time_units}",
        )

        # Combine the legends from both axes.
        handles, labels = ax.get_legend_handles_labels()
        if max_lags is not None or window_sizes is not None:
            handles2, labels2 = ax2.get_legend_handles_labels()
            handles += handles2
            labels += labels2

        ax.legend(handles, labels)

        # Set the axis labels.
        ax.set_xlabel(f"Time / {time_units}")
        ax.set_ylabel(variance_y_label)

        return handles, labels

plot_equilibration_paired_t_test #

plot_equilibration_paired_t_test(
    fig: Figure,
    subplot_spec: SubplotSpec,
    data: NDArray[float64],
    p_values: NDArray[float64],
    data_times: NDArray[float64],
    p_times: NDArray[float64],
    p_threshold: float = 0.05,
    time_units: str = "ns",
    data_y_label: str = "$\\Delta G$ / kcal mol$^{-1}$",
) -> Tuple[Axes, Axes]

Plot the p-values of the paired t-test against time, underneath the time series data.

Parameters:

  • fig (Figure) –

    The figure to plot on.

  • gridspec_obj (GridSpec) –

    The gridspec to use for the plot.

  • data (ndarray) –

    The time series data. This should have shape (n_runs, n_samples), or (n_samples,) if there is only one run.

  • p_values (ndarray) –

    The p-values of the paired t-test.

  • data_times (ndarray) –

    The times at which the data was sampled.

  • p_times (ndarray) –

    The times at which the paired t-test was performed.

  • p_threshold (float, default: 0.05 ) –

    The p-value threshold to use. The default is 0.05.

  • time_units (str, default: 'ns' ) –

    The units of time. The default is "ns".

  • data_y_label (str, default: '$\\Delta G$ / kcal mol$^{-1}$' ) –

    The y-axis label for the time series data. The default is "ΔG / kcal mol−1".

Returns:

  • ax_top ( Axes ) –

    The axes for the time series data.

  • ax_bottom ( Axes ) –

    The axes for the p-values.

Source code in red/plot.py 
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def plot_equilibration_paired_t_test(
    fig: _figure.Figure,
    subplot_spec: _gridspec.SubplotSpec,
    data: _npt.NDArray[_np.float64],
    p_values: _npt.NDArray[_np.float64],
    data_times: _npt.NDArray[_np.float64],
    p_times: _npt.NDArray[_np.float64],
    p_threshold: float = 0.05,
    time_units: str = "ns",
    data_y_label: str = r"$\Delta G$ / kcal mol$^{-1}$",
) -> _Tuple[_Axes, _Axes]:
    r"""
    Plot the p-values of the paired t-test against time, underneath the
    time series data.

    Parameters
    ----------
    fig : plt.Figure
        The figure to plot on.

    gridspec_obj : plt.GridSpec
        The gridspec to use for the plot.

    data : np.ndarray
        The time series data. This should have shape
        (n_runs, n_samples), or (n_samples,) if there
        is only one run.

    p_values : np.ndarray
        The p-values of the paired t-test.

    data_times : np.ndarray
        The times at which the data was sampled.

    p_times : np.ndarray
        The times at which the paired t-test was performed.

    p_threshold : float, optional
        The p-value threshold to use. The default is 0.05.

    time_units : str, optional
        The units of time. The default is "ns".

    data_y_label : str, optional
        The y-axis label for the time series data. The default is
        "$\Delta G$ / kcal mol$^{-1}$".

    Returns
    -------
    ax_top : Axes
        The axes for the time series data.

    ax_bottom : Axes
        The axes for the p-values.
    """
    with _plt.style.context(PLT_STYLE):
        # We need to split the gridspec into two subplots, one for the time series data (above)
        # and one for the p-values (below). Share x-axis but not y-axis.
        gs0 = _gridspec.GridSpecFromSubplotSpec(2, 1, subplot_spec=subplot_spec, hspace=0.05)
        ax_top = fig.add_subplot(gs0[0])
        ax_bottom = fig.add_subplot(gs0[1], sharex=ax_top)

        # Plot the time series data on the top axis.
        plot_timeseries(ax_top, data, data_times)
        # Add dashed vertical line at the equilibration time.
        ax_top.axvline(
            x=p_times[p_values > p_threshold][0],
            color="black",
            linestyle="--",
        )

        # Plot the p-values on the bottom axis.
        plot_p_values(
            ax_bottom,
            p_values,
            p_times,
            p_threshold=p_threshold,
            threshold_times=data_times,
        )

        # Set the axis labels.
        ax_top.set_xlabel(f"Time / {time_units}")
        ax_top.set_ylabel(data_y_label)

        # Move the legends to the side of the plot.
        ax_top.legend(bbox_to_anchor=(1.05, 0.5), loc="center left")
        ax_bottom.legend(bbox_to_anchor=(1.05, 0.5), loc="center left")

        # Hide the x tick labels for the top axis.
        _plt.setp(ax_top.get_xticklabels(), visible=False)
        ax_top.spines["bottom"].set_visible(False)
        ax_top.tick_params(axis="x", which="both", length=0)
        ax_top.set_xlabel("")

        return ax_top, ax_bottom

plot_equilibration_min_sse #

plot_equilibration_min_sse(
    fig: Figure,
    subplot_spec: SubplotSpec,
    data: NDArray[float64],
    sse_series: NDArray[float64],
    data_times: NDArray[Union[int64, float64]],
    sse_times: NDArray[Union[int64, float64]],
    max_lag_series: Optional[NDArray[float64]] = None,
    window_size_series: Optional[NDArray[float64]] = None,
    time_units: str = "ns",
    data_y_label: str = "$\\Delta G$ / kcal mol$^{-1}$",
    variance_y_label: str = "$\\frac{1}{\\sigma^2(\\Delta G)}$ / kcal$^{-2}$ mol$^2$",
    reciprocal: bool = True,
) -> Tuple[Axes, Axes]

Plot the (reciprocal of the) squared standard error (SSE) estimates against time, underneath the time series data.

Parameters:

  • fig (Figure) –

    The figure to plot on.

  • subplot_spec (GridSpec) –

    The gridspec to use for the plot.

  • data (ndarray) –

    The time series data. This should have shape (n_runs, n_samples), or (n_samples,) if there is only one run.

  • sse_series (ndarray) –

    The SSE series.

  • data_times (ndarray) –

    The times at which the data was sampled.

  • sse_times (ndarray) –

    The times at which the ESS was computed.

  • max_lag_series (ndarray, default: None ) –

    The lag series. If None, the lag times are not plotted. If supplied, they are plotted on the bottom axis.

  • window_size_series (ndarray, default: None ) –

    The window size series. If None, the window sizes are not plotted. If supplied, they are plotted on the bottom axis.

  • time_units (str, default: 'ns' ) –

    The units of time. The default is "ns".

  • data_y_label (str, default: '$\\Delta G$ / kcal mol$^{-1}$' ) –

    The y-axis label for the time series data. The default is "ΔG / kcal mol−1".

  • variance_y_label (str, default: '$\\frac{1}{\\sigma^2(\\Delta G)}$ / kcal$^{-2}$ mol$^2$' ) –

    The y-axis label for the variance. The default is "1σ2(ΔG) / kcal−2 mol2".

  • reciprocal (bool, default: True ) –

    Whether to plot the reciprocal of the SSE.

Returns:

  • ax_top ( Axes ) –

    The axes for the time series data.

  • ax_bottom ( Axes ) –

    The axes for the p-values.

Source code in red/plot.py 
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def plot_equilibration_min_sse(
    fig: _figure.Figure,
    subplot_spec: _gridspec.SubplotSpec,
    data: _npt.NDArray[_np.float64],
    sse_series: _npt.NDArray[_np.float64],
    data_times: _npt.NDArray[_Union[_np.int64, _np.float64]],
    sse_times: _npt.NDArray[_Union[_np.int64, _np.float64]],
    max_lag_series: _Optional[_npt.NDArray[_np.float64]] = None,
    window_size_series: _Optional[_npt.NDArray[_np.float64]] = None,
    time_units: str = "ns",
    data_y_label: str = r"$\Delta G$ / kcal mol$^{-1}$",
    variance_y_label: str = r"$\frac{1}{\sigma^2(\Delta G)}$ / kcal$^{-2}$ mol$^2$",
    reciprocal: bool = True,
) -> _Tuple[_Axes, _Axes]:
    r"""
    Plot the (reciprocal of the) squared standard error (SSE)
    estimates against time, underneath the time series data.

    Parameters
    ----------
    fig : plt.Figure
        The figure to plot on.

    subplot_spec : plt.GridSpec
        The gridspec to use for the plot.

    data : np.ndarray
        The time series data. This should have shape
        (n_runs, n_samples), or (n_samples,) if there
        is only one run.

    sse_series : np.ndarray
        The SSE series.

    data_times : np.ndarray
        The times at which the data was sampled.

    sse_times : np.ndarray
        The times at which the ESS was computed.

    max_lag_series : np.ndarray, optional
        The lag series. If None, the lag times are not
        plotted. If supplied, they are plotted on the
        bottom axis.

    window_size_series : np.ndarray, optional
        The window size series. If None, the window sizes
        are not plotted. If supplied, they are plotted on
        the bottom axis.

    time_units : str, optional
        The units of time. The default is "ns".

    data_y_label : str, optional
        The y-axis label for the time series data. The default is
        "$\Delta G$ / kcal mol$^{-1}$".

    variance_y_label : str, optional
        The y-axis label for the variance. The default is
        "$\frac{1}{\sigma^2(\Delta G)}$ / kcal$^{-2}$ mol$^2$".

    reciprocal : bool, optional, default=True
        Whether to plot the reciprocal of the SSE.

    Returns
    -------
    ax_top : Axes
        The axes for the time series data.

    ax_bottom : Axes
        The axes for the p-values.
    """
    with _plt.style.context(PLT_STYLE):
        data = check_data(data, one_dim_allowed=True)
        n_runs, _ = data.shape

        # We need to split the gridspec into two subplots, one for the time series data (above)
        # and one for the p-values (below). Share x-axis but not y-axis.
        gs0 = _gridspec.GridSpecFromSubplotSpec(2, 1, subplot_spec=subplot_spec, hspace=0.05)
        ax_top = fig.add_subplot(gs0[0])
        ax_bottom = fig.add_subplot(gs0[1], sharex=ax_top)

        # Plot the time series data on the top axis.
        plot_timeseries(ax_top, data, data_times)
        # Add dashed vertical line at the equilibration time.
        ax_top.axvline(
            x=sse_times[sse_series.argmin()],
            color="black",
            linestyle="--",
        )

        # Plot the sse on the bottom axis.
        sse_handles, sse_labels = plot_sse(
            ax_bottom,
            sse_series,
            max_lag_series,
            window_size_series,
            sse_times,
            time_units=time_units,
            variance_y_label=variance_y_label,
            reciprocal=reciprocal,
        )

        # Set the axis labels.
        ax_top.set_xlabel(f"Time / {time_units}")
        ax_top.set_ylabel(data_y_label)

        # Move the legends to the side of the plot.
        if n_runs > 1:
            ax_top.legend(bbox_to_anchor=(1.05, 0.5), loc="center left")
        is_second_axis = max_lag_series is not None or window_size_series is not None
        side_shift_bottom = 1.15 if is_second_axis else 1.05
        # Remove the 1/SSE label if there isn't a second axis.
        if not is_second_axis:
            sse_labels.pop(0)
            sse_handles.pop(0)
        ax_bottom.legend(
            sse_handles,
            sse_labels,
            bbox_to_anchor=(side_shift_bottom, 0.5),
            loc="center left",
        )

        # Hide the x tick labels for the top axis.
        _plt.setp(ax_top.get_xticklabels(), visible=False)
        ax_top.spines["bottom"].set_visible(False)
        ax_top.tick_params(axis="x", which="both", length=0)
        ax_top.set_xlabel("")

        return ax_top, ax_bottom