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Parameters ---------- projs : list of Projection The projections. %(info_not_none)s Must be associated with the channels in the projectors. .. versionchanged:: 0.20 The positional argument ``layout`` was deprecated and replaced by ``info``. %(proj_topomap_kwargs)s %(sphere_topomap_auto)s %(extrapolate_topomap)s .. versionadded:: 0.20 %(border_topomap)s Returns ------- fig : instance of matplotlib.figure.Figure Figure with a topomap subplot for each projector. 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Parameters ---------- data : array, shape (n_chan,) The data values to plot. pos : array, shape (n_chan, 2) | instance of Info Location information for the data points(/channels). If an array, for each data point, the x and y coordinates. If an `~mne.Info` object, it must contain only one data type and exactly ``len(data)`` data channels, and the x/y coordinates will be inferred from the montage applied to the `~mne.Info` object. %(vmin_vmax_topomap)s %(cmap_topomap_simple)s sensors : bool | str Add markers for sensor locations to the plot. Accepts matplotlib plot format string (e.g., ``'r+'`` for red plusses). If True (default), circles will be used. res : int The resolution of the topomap image (number of pixels along each side). axes : instance of Axes | None The axes to plot to. If None, the current axes will be used. names : list | None List of channel names. If None, channel names are not plotted. %(show_names_topomap)s If ``True``, a list of names must be provided (see ``names`` keyword). %(mask_topomap)s %(mask_params_topomap)s %(outlines_topomap)s contours : int | array of float The number of contour lines to draw. If ``0``, no contours will be drawn. If an array, the values represent the levels for the contours. The values are in µV for EEG, fT for magnetometers and fT/m for gradiometers. Defaults to ``6``. %(image_interp_topomap)s show : bool Show figure if True. onselect : callable | None Handle for a function that is called when the user selects a set of channels by rectangle selection (matplotlib ``RectangleSelector``). If None interactive selection is disabled. Defaults to None. %(extrapolate_topomap)s .. versionadded:: 0.18 %(sphere_topomap)s %(border_topomap)s %(ch_type_topomap)s %(cnorm)s .. versionadded:: 0.24 Returns ------- im : matplotlib.image.AxesImage The interpolated data. cn : matplotlib.contour.ContourSet The fieldlines. Notes ----- The ``cnorm`` parameter can be used to implement custom colormap normalization. By default, a linear mapping from vmin to vmax is used, which correspond to the first and last colors in the colormap. This might be undesired when vmin and vmax are not symmetrical around zero (or a value that can be interpreted as some midpoint). For example, assume we want to use the RdBu colormap (red to white to blue) for values ranging from -1 to 3, and 0 should be white. However, white corresponds to the midpoint in the data by default, i.e. 1. Therefore, we use the following colormap normalization ``cnorm`` and pass it as the the ``cnorm`` argument: .. code-block:: python from matplotlib.colors import TwoSlopeNorm cnorm = TwoSlopeNorm(vmin=-1, vcenter=0, vmax=3) Note that because we define ``vmin`` and ``vmax`` in the normalization, arguments ``vmin`` and ``vmax`` to ``plot_topomap`` will be ignored if a normalization is provided. See the :doc:`matplotlib docs ` for more details on colormap normalization. r NormalizeNcnormzvmin=z/ is implicitly defined by cnorm, ignoring vmin=.zvmax=z/ is implicitly defined by cnorm, ignoring vmax=)r@rrBrr)rmatplotlib.colorsrrrrr _plot_topomap)rLrvrrrrrrr show_namesr- mask_paramsrrrronselectrr@rrBrrrDrDrEr s4Y r c Cs|dkrtd|dtd|d|d|tjtj f}tjtj f}tj|d}|d} |d d } ttj|d |ddd f| d | d ft tj|d |ddd f| d | d f} } ttj|d |ddd f| d | d ft tj|d |ddd f| d | d f} }t | | |}t | ||}t ||\}}t |||| | |}| | | |f}||||fS) N)rgrirhz;`image_interp` must be `cubic`, `linear` or `nearest`, got a . 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Each row in this matrix contains the (x, y) position of an electrode.zL{ndim}D array supplied as electrode positions, where a 2D array was expected)rj r;zThe supplied electrode positions matrix contains 3 columns. Are you trying to specify XYZ coordinates? Perhaps the mne.channels.create_eeg_layout function is useful for you.r;zOData and pos need to be of same length. Got data of length %s, pos of length %sRedsRdBu_rr=r)rrrh)rvrrrrrrrrbilinear)rrWrr interpolationrmarkeredgewidthrrrrrY@rr?)rrzFTo show names, a list of names must be provided (see `names` keyword).cSs|SrrDr_rDrDrE _show_names sz"_plot_topomap.._show_namescenterx-small)horizontalalignmentverticalalignmentrffffff?top)r)rr)Lrrrrmatplotlib.widgetsrrnZasarrayrrrrcr3rrrrirjpoprr rr rQrrk_check_extrapolaterjrkrrr"Zget_cmaprr$r>Zgca_prepare_topomapr0rrrwrrrrisnanr rrrrrrrrTrqrrr3r6rJrdrtextfigureget_constrained_layoutsubplots_adjustZdataLimx0y0widthheightZRSryr')7rLrvrrrrrrrrr-rrrrrrrr@rrBrrrrrtZ info_helpruZpos_helperrorrrrrrrrrrr/rcolrrrzrZshow_idxrqpch_idZlimrrrrrDrrErs                            &           &     rrc!Csddlm}|jdkrtdt||j}t| |sDtdt| t|||j d}|dkrjt ddS| dd|f}t |||d \}}}}}}}||}t ||| |} |rt|||\}}|j|}tt|d kr|d |d 7}| j|d dt|||\}}t|||||| || | || | ||||dd}|rzt| ||dddd\}} |jjd d|||ft| dS)zPlot single ica map to axes.r)rN_The ICA's measurement info is missing. Please fit the ICA or add the corresponding info object.z>axis has to be an instance of matplotlib Axes, got %s instead.) allow_ref_megrQz7Cannot produce topographies for MEG reference channels.rNr  ()rr)rrrrrrrrrrrr@rrBrAU%3.2f)rrrZ labelsize)Zmatplotlib.axesrrArrrcrjtyperrrZget_componentsr|rr _ica_namesriryget_channel_typesrr"r rrr tick_params set_ticks _hide_frame)!icarzrBrrrrrrrrrrrrrrr@rrrLrrvrwrrurCZ topo_titlevmin_vmax_rrrrDrDrE_plot_ica_topomap8sf         rrrc2sjddlm}ddlm}|jdkr*tddkr8tntdkrV|d<|dkrt||}|j j d}d}g}t d ||D]R}t |t |||}t ||||||||| | | | | ||d |q|St|j|}t||}t|t|d }t|j dd|fj|jd|j}t|||d \}}}} }}}!t||| |!} t|}|dd|f}tt|d d\}"}#}#| dkrd} | t}$t|||"D]*\}%}&}'|%|jkrtddnt}(|j|%})tt |!dkr |)d|d7})|$|'j"|)fddi|(|rBt#|&|| \}&}*t$|&||\}+},t%|&&|f|+|,||'|d | | | d||d d }-|-j'(|j|%|rt)|'|-|ddddd\}.}/|.j*j+dd|.,|+|,ft-|'q~t.dj/dd d!j01||$ffd"d# }0j02d$|0t3|||fr^||ffd%d& }1j02d$|1t4| S)'uProject mixing matrix on interpolated sensor topography. Parameters ---------- ica : instance of mne.preprocessing.ICA The ICA solution. %(picks_ica)s If ``None``, all components are plotted in batches of 20. ch_type : 'mag' | 'grad' | 'planar1' | 'planar2' | 'eeg' | None The channel type to plot. For 'grad', the gradiometers are collected in pairs and the RMS for each pair is plotted. If None, then channels are chosen in the order given above. res : int The resolution of the topomap image (n pixels along each side). %(vmin_vmax_topomap)s cmap : matplotlib colormap | (colormap, bool) | 'interactive' | None Colormap to use. If tuple, the first value indicates the colormap to use and the second value is a boolean defining interactivity. In interactive mode the colors are adjustable by clicking and dragging the colorbar with left and right mouse button. Left mouse button moves the scale up and down and right mouse button adjusts the range. Hitting space bar resets the range. Up and down arrows can be used to change the colormap. If None, 'Reds' is used for all positive data, otherwise defaults to 'RdBu_r'. If 'interactive', translates to (None, True). Defaults to 'RdBu_r'. .. warning:: Interactive mode works smoothly only for a small amount of topomaps. sensors : bool | str Add markers for sensor locations to the plot. Accepts matplotlib plot format string (e.g., 'r+' for red plusses). If True (default), circles will be used. colorbar : bool Plot a colorbar. title : str | None Title to use. show : bool Show figure if True. %(outlines_topomap)s contours : int | array of float The number of contour lines to draw. If 0, no contours will be drawn. When an integer, matplotlib ticker locator is used to find suitable values for the contour thresholds (may sometimes be inaccurate, use array for accuracy). If an array, the values represent the levels for the contours. Defaults to 6. %(image_interp_topomap)s inst : Raw | Epochs | None To be able to see component properties after clicking on component topomap you need to pass relevant data - instances of Raw or Epochs (for example the data that ICA was trained on). This takes effect only when running matplotlib in interactive mode. plot_std : bool | float Whether to plot standard deviation in ERP/ERF and spectrum plots. Defaults to True, which plots one standard deviation above/below. If set to float allows to control how many standard deviations are plotted. For example 2.5 will plot 2.5 standard deviation above/below. topomap_args : dict | None Dictionary of arguments to ``plot_topomap``. If None, doesn't pass any additional arguments. Defaults to None. image_args : dict | None Dictionary of arguments to ``plot_epochs_image``. If None, doesn't pass any additional arguments. Defaults to None. psd_args : dict | None Dictionary of arguments to ``psd_multitaper``. If None, doesn't pass any additional arguments. Defaults to None. reject : 'auto' | dict | None Allows to specify rejection parameters used to drop epochs (or segments if continuous signal is passed as inst). If None, no rejection is applied. The default is 'auto', which applies the rejection parameters used when fitting the ICA object. %(sphere_topomap_auto)s %(verbose)s Returns ------- fig : instance of matplotlib.figure.Figure | list of matplotlib.figure.Figure The figure object(s). Components are plotted on a grid with maximum dimensions of 5⨉4. If more than 20 components are plotted, a new figure will be created for each batch of 20, and a list of those figures will be returned. Notes ----- When run in interactive mode, ``plot_ica_components`` allows to reject components by clicking on their title label. The state of each component is indicated by its label color (gray: rejected; black: retained). It is also possible to open component properties by clicking on the component topomap (this option is only available when the ``inst`` argument is supplied). r)BaseRaw) BaseEpochsNrr@r r)rtrBrrrrrrrrrrrpplot_std topomap_args image_argspsd_argsrejectr@)n_axesrNrzICA componentsgrayrrrrrF) rrrrrrrrrrrBrrrr)rrrrrrg)\(?r<)rbottomcsd}|D]}||dr|}q$q|dk r|}t|dddd}||jkrp|j||dn|j||dj dS)NrrrYr) containsZget_textrEsplitrRr set_colorrrr)eventrtitlesZ title_pressedrlabelicrrDrE onclick_titles     z*plot_ica_components..onclick_titlebutton_press_eventc sV|jdk rR|j}|drRt|dddd}|j||dddS)NZICArrrT)rtrrrrrr)inaxesZ get_labelrfrErZplot_properties)rrrprr)rrrrrrDrE onclick_topo1s    z)plot_ica_components..onclick_topo)5iorepochsrrArr$r?rZmixing_matrix_rrkrplot_ica_componentsrrr+rirndotrZpca_components_Z n_components_r|rrr#suptitlerrrRrryrrr r"r flattenr set_labelrrrrrr!rrr mpl_connectrcr')2rrtrBrrrrrrrrrrrrprrrrrr@rrr n_componentsrfigsrYrLrrvrwrrCrrurrqdata_rkwargsZ comp_titleZnames_rrrrrrrrD)rrrrrrrEr ise                    r rP%1.1ec.Csddlm}t||}t|||d\}}}}}}}t||||}|sHd}|j|ddddf}|rxt|||dd\}}t||j||dd}t |rt || j }d\} }!t t|j||d}"|dk r|"d} |dk r|"d d }!d\}#}$t t|j||d}"|dk r |"d}#|dk r6|"d d }$|dd|#|$| |!f}t jt j|d d d d ddt jf}t |dkrd nd}%t||| |%\}} t| |%d} |dkr|j||fdd n|}|j}&t|d}'t|tt jfst|| |\}'}|dk r||t}(tt|||| |!|#|$| d|(d })t|tt jfs^t|| |\}}t |dddf||| || dt!|||d |)| ||||d\}*}| rddl"m#}+t$d| d} t%||*| | |d\},}-|'dkr|+j&dd}'|'|,_'|,(|,j)j*ddt+||&S)aPlot topographic maps of specific time-frequency intervals of TFR data. Parameters ---------- tfr : AverageTFR The AverageTFR object. tmin : None | float The first time instant to display. If None the first time point available is used. tmax : None | float The last time instant to display. If None the last time point available is used. fmin : None | float The first frequency to display. If None the first frequency available is used. fmax : None | float The last frequency to display. If None the last frequency available is used. ch_type : 'mag' | 'grad' | 'planar1' | 'planar2' | 'eeg' | None The channel type to plot. For 'grad', the gradiometers are collected in pairs and the mean for each pair is plotted. If None, then channels are chosen in the order given above. baseline : tuple or list of length 2 The time interval to apply rescaling / baseline correction. If None do not apply it. If baseline is (a, b) the interval is between "a (s)" and "b (s)". If a is None the beginning of the data is used and if b is None then b is set to the end of the interval. If baseline is equal to (None, None) the whole time interval is used. mode : 'mean' | 'ratio' | 'logratio' | 'percent' | 'zscore' | 'zlogratio' | None Perform baseline correction by - subtracting the mean baseline power ('mean') - dividing by the mean baseline power ('ratio') - dividing by the mean baseline power and taking the log ('logratio') - subtracting the mean baseline power followed by dividing by the mean baseline power ('percent') - subtracting the mean baseline power and dividing by the standard deviation of the baseline power ('zscore') - dividing by the mean baseline power, taking the log, and dividing by the standard deviation of the baseline power ('zlogratio') If None no baseline correction is applied. %(vmin_vmax_topomap)s cmap : matplotlib colormap | (colormap, bool) | 'interactive' | None Colormap to use. If tuple, the first value indicates the colormap to use and the second value is a boolean defining interactivity. In interactive mode the colors are adjustable by clicking and dragging the colorbar with left and right mouse button. Left mouse button moves the scale up and down and right mouse button adjusts the range. Hitting space bar resets the range. Up and down arrows can be used to change the colormap. If None (default), 'Reds' is used for all positive data, otherwise defaults to 'RdBu_r'. If 'interactive', translates to (None, True). sensors : bool | str Add markers for sensor locations to the plot. Accepts matplotlib plot format string (e.g., 'r+'). If True (default), circles will be used. colorbar : bool Plot a colorbar. unit : str | None The unit of the channel type used for colorbar labels. res : int The resolution of the topomap image (n pixels along each side). size : float Side length per topomap in inches (only applies when plotting multiple topomaps at a time). cbar_fmt : str String format for colorbar values. %(show_names_topomap)s title : str | None Plot title. If None (default), no title is displayed. axes : instance of Axes | None The axes to plot to. If None the axes is defined automatically. show : bool Show figure if True. %(outlines_topomap)s contours : int | array of float The number of contour lines to draw. If 0, no contours will be drawn. When an integer, matplotlib ticker locator is used to find suitable values for the contour thresholds (may sometimes be inaccurate, use array for accuracy). If an array, the values represent the levels for the contours. If colorbar=True, the ticks in colorbar correspond to the contour levels. Defaults to 6. %(sphere_topomap_auto)s Returns ------- fig : matplotlib.figure.Figure The figure containing the topography. rNrNrPmethodTrrr^r rrFrZfigsize) tfrrvrBitminitmaxifminifmaxrr)rrrrrrrrrrrrrBrr@tickerunitsmisc)rrrZnbinsrr),rrrr|rrLr rtimesrnZ iscomplexobjsqrtZconjr"rrfreqsrPrKrr"r+subplotsrrrcrr_set_contour_locatorrr _onselectr r r1rr0r MaxNLocatorlocatorZ update_ticksrrr').rtmintmaxfminfmaxrBbaselinemoderrrrrunitrrcbar_fmtrrrrrrr@rrtrvrwrrurCrLrrrzrrrrr*Z fig_wrapperZselection_callbackrrrrrDrDrEplot_tfr_topomapBsa        & "       r3z%3.1fr`c^s ddlm}ddlm} ddlm}!ddlm}"t|"dt|t d t |}t | j \} }#| d krvd nd }$t|dtfd |dkr| d krd nd}~ td|}|d| d9<|d| d9<t||d\}%}&}'}}}(t||&||(}|dk })t|to|dk}*|*r0|)r0td|dr@dn|}+td||+},td| |+}-|'}.|snd}'td|d|dkrjsn|dkrjjgjd<W5QRXj|%dd t||jr|g}|)rt|t|nd}/t ||/}t|}0d!djd"}1t!|t!j |1ks`t"|t"j |1krtd#j dd$d%j d&d$d'|0t|}2|*r:d(d!g}3d}|2}| |}4| t!dd)d*| t |d+}5t#|4d,|5d,fd-}6d.d/d0d1d2}7| ||fd3|3i|7}8g}t$|0D]}9|%|&|8d|9fqnx|dkrbt'|0||||| d4\}6}}}nPd5\}}|d(}6t||2kr|rd6nd7}:t)d8|2d9|:d:t|d'|6*s|j+d;d|2};t!|dkrd0nd|D}=d?}>g}?|dkrLt-.dg|0}t-/|%|=nt0|rht-.|g|0}n6t-.|j1dkrt2|>d@t3|d'n t-.|}t||0krtdA|0dBt|dCt-4t|%t|=f}@t5t6|j |=|=D] \}A\}B}C}Dt0|Br|Bdks*t0|Bsd|Bdk rdt|d!krH|>dD|B}En|>dD|BdE|}Et|E|Bdkr|%dd|Df|@dd|Af<|?%|Cgnb|C|Bd}F|C|Bd}G|Fj kj |Gk@}H|%dd|Hf7d&|@dd|Af<|?%j |Hq|@|,9r2t8||.\}.|t9kr2d|dk r|j:t ddF}|dkr|t-/|%ddd|=|t-/|%d!dd|=B}In|t-/|%|=}IfdGd>t$|0D}Jt-"|Jt-!|Jt;||0dkdH}t|t|\}#}t?|| |'||d||||d||||dI}Kgg}L}Mt5t6||D]&\}A\}N}B|oj|dk oj|A|d!k}O|Orz|Ad!n|A}9t@dd|Af|&f||9|dk r|Idd|AfnddJ|K\}P}Q}R|L%|P|Qdk r|M%|Q|d7krB|Bdkr||N|$}SnT|?|Ad}F|?|Ad&}G||F|$}T|TAdKd}T||G|$}U|TdL|U}S~T~U~F~G||9B|SqB|* r>|%|&|8d!dd&f|!|d&dMj dj d&|ddNdO}V|VjCDrt8ndPdQ}WtEtF|djj |&|,|W||$|KdR }X|VG|Xt-Hj tjIjjJ}Y|d&jK|YjdSdT|V|d&_L|dk rX|jM|dUdVdW| r&|* r|&|8dX}ZtN|Z|| n6|dk s|dk r|d&}Zn||d!}ZtN|Z|| |-dk r|ZB|-|6jO|Ld&|Z|Z| dY}[|Qdk r|[P||[jQjRdZd[|d! r&|LD]}\tS|[|\|\jT_U q|dk rptVt?|6jd\|%|L|M|&|=| tW|,|||R|d]}]tXd|]tY|dd^|) r|6jZ[|6S)_a Plot topographic maps of specific time points of evoked data. Parameters ---------- evoked : Evoked The Evoked object. times : float | array of float | "auto" | "peaks" | "interactive" The time point(s) to plot. If "auto", the number of ``axes`` determines the amount of time point(s). If ``axes`` is also None, at most 10 topographies will be shown with a regular time spacing between the first and last time instant. If "peaks", finds time points automatically by checking for local maxima in global field power. If "interactive", the time can be set interactively at run-time by using a slider. %(ch_type_evoked_topomap)s %(vmin_vmax_topomap)s %(cmap_topomap)s %(sensors_topomap)s %(colorbar_topomap)s %(scalings_topomap)s %(units_topomap)s %(res_topomap)s %(size_topomap)s %(cbar_fmt_topomap)s time_unit : str The units for the time axis, can be "ms" or "s" (default). .. versionadded:: 0.16 time_format : str | None String format for topomap values. Defaults (None) to "%%01d ms" if ``time_unit='ms'``, "%%0.3f s" if ``time_unit='s'``, and "%%g" otherwise. Can be an empty string to omit the time label. %(proj_plot)s %(show)s %(show_names_topomap)s %(title_none)s %(mask_evoked_topomap)s %(mask_params_topomap)s %(outlines_topomap)s %(contours_topomap)s %(image_interp_topomap)s average : float | array-like of float, shape (n_times,) | None The time window (in seconds) around a given time point to be used for averaging. For example, 0.2 would translate into a time window that starts 0.1 s before and ends 0.1 s after the given time point. If the time window exceeds the duration of the data, it will be clipped. Different time windows (one per time point) can be provided by passing an ``array-like`` object (e.g., ``[0.1, 0.2, 0.3]``). If ``None`` (default), no averaging will take place. .. versionchanged:: 1.1 Support for ``array-like`` input. %(axes_topomap)s %(extrapolate_topomap)s .. versionadded:: 0.18 %(sphere_topomap_auto)s %(border_topomap)s nrows : int | 'auto' The number of rows of topographies to plot. Defaults to 1. If 'auto', obtains the number of rows depending on the amount of times to plot and the number of cols. Not valid when times == 'interactive'. .. versionadded:: 0.20 ncols : int | 'auto' The number of columns of topographies to plot. If 'auto' (default), obtains the number of columns depending on the amount of times to plot and the number of rows. Not valid when times == 'interactive'. .. versionadded:: 0.20 Returns ------- fig : instance of matplotlib.figure.Figure The figure. Notes ----- When existing ``axes`` are provided and ``colorbar=True``, note that the colorbar scale will only accurately reflect topomaps that are generated in the same call as the colorbar. Note also that the colorbar will not be resized automatically when ``axes`` are provided; use Matplotlib's :meth:`axes.set_position() ` method or :doc:`gridspec ` interface to adjust the colorbar size yourself. rN)GridSpec)Sliderr)Evokedrrr`r@@ time_formatz%0.3f sz%01d msrZ markersizerrrN interactivez8User-provided axes not allowed when times='interactive'.rr:scalingsr r)TFr9 reconstructTr;rKFrr sfreqzTimes should be between z0.3z and r^rr皙?r;rArr皙?皙?rg?)leftrrr height_ratios)rrrrrrz plus one for the colorbarzYou must provide z axes (one for each timez), got zfigure.subplot.wspacerDc s2g|]*}ttj|djddddqS)Nr<)r+r,r<r)rnrrr#rArrrDrEr[sz'plot_evoked_topomap..z_"average" must be `None`, a positive number of seconds, or an array-like object of the previousz ; got type: z+You requested to plot topographic maps for z time points, but provided zV periods for averaging. The number of time points and averaging periods must be equal.z; got z in rcs(g|] }tdd|fdqS)Nr)r"r)rLrwrrrDrEr[s)rr)rrrrrrrrrrrrrr@rrB)rr-ru – ZTimez%1.2fs)ZvalfmtcSs|SrrDrrDrDrE.z%plot_evoked_topomap..) rrLr#rvscalingfuncr8 scaling_timerrYrrzx-large)rr)rr^)rrrrr)rrrrtrrrvrrZplot_update_proj_callbackrwrrrrrblock)\rrZmatplotlib.gridspecr4rr5rr6rrqr?rr,r#rkr0r|rrcrjrfrrrZ_reconstruct_projrLrArZ_pick_drop_channelsrrirEr(r%rr&rkrZsubplotr#r rrr)rrnroZix_rrj TypeErrorrrprdrrPr rgrTr+rrr'r$rrrZvlinerr_slider_changedZ on_changedrIrQrr3sliderr  _resize_cbarrrrrr)rrr$rr%r'rr)^rr#rBrrrrrr:r rrr2 time_unitr8rrrrr-rrrrZaveragerrr@rrrrr4r5r6rurHrtrvrrCZ axes_givenr9r5rFr1rGZn_peaksZn_timesspaceZ want_axesrArrrZg_kwargsgsZax_idxZcbar_errZ side_marginZ top_marginrZavg_errZaveraged_timesrZ average_idxZ this_averageZ this_timeZ this_time_idxmsgZtmin_Ztmax_Z time_maskrrrrrtimeZadjust_for_cbarrcnrZ axes_titleZ from_timeZto_timerNrGZchanged_callbacktsrrrrrD)rLrrwrrrEplot_evoked_topomapsb               & "             &                                   rWcCsP|}|dkr&ddd|||_|jd||_d|_d|_||dS)zResize colorbar.r ffffff?r=r>N)Z get_positionrx1ry1Z set_position)rZ n_fig_axesrcposrDrDrErO`srOc Cstt||} ||dd| f|}|t||fd|i| \} } t|drt| |j_t |jj j d|dk r| |||dS)z(Handle selection in interactive topomap.Nrrr) rnargminabsrclearr hasattrrmappablerOrrr) valrrLr#rvrFrGr8rHrrzrrurDrDrErMks rM%3.3fc Cst||dkrt|n|}|dkr0t|n|}t||g} tt| dkp^t| dk}t||d}|dk r|j |ddt ||||||dt d|d| | d \}}| rt |||d dd | d \}}| ||f|dk r|jj|d d|jjd d dS)zPlot topomap multi cbar.Nr rrrrF) rrrrrrrrr@rBrDz10%)rrrrr)rrnrr%signriryrr+rr r rrr set_ylabelr)rLrvrrr1rrrrrr2r@rBZsignsrrrurrrDrDrE_plot_topomap_multi_cbarys4     rflengthc!Cst|| } tdd}tdd}|| }|| }t|| |d\}}}}} }}t||||}t|||||||||| d \}} tj|dd}||d9}|rt|| |d d \}}t|| || || | ||||||||| d S) aPlot the topomap of the power spectral density across epochs. Parameters ---------- epochs : instance of Epochs The epochs object. %(bands_psd_topo)s tmin : float | None Start time to consider. tmax : float | None End time to consider. proj : bool Apply projection. bandwidth : float The bandwidth of the multi taper windowing function in Hz. The default value is a window half-bandwidth of 4 Hz. adaptive : bool Use adaptive weights to combine the tapered spectra into PSD (slow, use n_jobs >> 1 to speed up computation). low_bias : bool Only use tapers with more than 90%% spectral concentration within bandwidth. %(normalization)s ch_type : 'mag' | 'grad' | 'planar1' | 'planar2' | 'eeg' | None The channel type to plot. For 'grad', the gradiometers are collected in pairs and the mean for each pair is plotted. If None, then first available channel type from order given above is used. Defaults to None. %(cmap_psd_topo)s %(agg_fun_psd_topo)s %(dB_psd_topo)s %(n_jobs)s %(normalize_psd_topo)s %(cbar_fmt_psd_topo)s %(outlines_topomap)s %(axes_psd_topo)s show : bool Show figure if True. %(sphere_topomap_auto)s %(vlim_psd_topo_joint)s %(verbose)s Returns ------- fig : instance of Figure Figure distributing one image per channel across sensor topography. r Nr:rN) r+r, bandwidthadaptivelow_bias normalizationrtrn_jobsrrrrPr)psdsr%rvagg_funbandsrdB normalizer2rrrr@rr1rB) rr0r|rr/rnrPr plot_psds_topomap)!r ror+r,rrhrirjrkrBrrnrprlrqr2rrrr@rrr r:r1rFrtrvrwrrCrmr%rDrDrEplot_epochs_psd_topomapsN8      rs%0.3fcsddlm}t| } |dkr(r$dnd}|dkr@dddd d g}n8td}td|g|d fd d |D}dkrrtjntjrjdddtjdddst t |}| dk rt | || dj }n,|j d|d |dfd\}} |dkr| g} | dkrrfdd |D}fdd |D}fdd |D}t|}t|}n| \}}|dkrrsdnd}n.d|krd|}|d7}rȈs|d7}t| |D]\}\}}}|k|k@}|dkrtd |||fdd|fdd}rBsBd!t|}t|||||||| d||| |d" qt|d#|jt| |S)$aPlot spatial maps of PSDs. Parameters ---------- psds : np.ndarray of float, shape (n_channels, n_freqs) Power spectral densities freqs : np.ndarray of float, shape (n_freqs) Frequencies used to compute psds. pos : numpy.ndarray of float, shape (n_sensors, 2) The positions of the sensors. %(agg_fun_psd_topo)s %(bands_psd_topo)s %(cmap_psd_topo)s %(dB_psd_topo)s %(normalize_psd_topo)s %(cbar_fmt_psd_topo)s %(outlines_topomap)s %(axes_psd_topo)s show : bool Show figure if True. %(sphere_topomap)s %(vlim_psd_topo_joint)s unit : str | None Measurement unit to be displayed with the colorbar. If ``None``, no unit is displayed (only "power" or "dB" as appropriate). %(ch_type_topomap)s Returns ------- fig : instance of matplotlib.figure.Figure Figure with a topomap subplot for each band. rNrz%0.1frt)rr;zDelta (0-4 Hz))r;rczTheta (4-8 Hz))rcrzAlpha (8-12 Hz))rzBeta (12-30 Hz))ru-zGamma (30-45 Hz)rc sJg|]B}t|dkrBttt|d|dfn|qS)rrr )rituplernr\r])rXZband) bin_edgesr%rDrEr[s  $z%plot_psds_topomap..r^TrBrrr rrrcs"g|]\}}}|k|k@qSrDrD)rXr-r.ru)r%rDrEr[3scs$g|]}dd|fddqSr=rD)rXZ _freq_mask)rnrmrDrEr[5scs&g|]}rsdt|n|qS)r)rnlog10)rXZ_d)rprqrDrEr[7srppower/z(%s)u²/Hzz (dB)z$No frequencies in band "%s" (%s, %s)r) rrrrrrr1r2r@rBr)rrrrnrLrorNrPZallcloser>rir*rr&rr%rrryrfr!rrr')rmr%rvrnrorrprqr2rrrr@rr1rBrZ bin_spacingrrZ _freq_masksZ_datasrrrr-r.rZ freq_maskrLrD)rnrxrpr%rqrmrErrs&                  rrcCsddlm}|jt|jdfdd}|d}|jddddddd|jggd d tdddddgdddddgfd }t ||t t |j |}|j |}t|j |} tt|| D]\} \} } t| d| dd | d| d d f} |j| | dddd|r| d| d| d| d| d| d f\}}}}|j|||||g|||||gddq|dt|ddddt||S)aPlot the sensor positions. Parameters ---------- layout : None | Layout Layout instance specifying sensor positions. %(picks_nostr)s show_axes : bool Show layout axes if True. Defaults to False. show : bool Show figure if True. Defaults to True. Returns ------- fig : instance of Figure Figure containing the sensor topography. Notes ----- .. versionadded:: 0.12.0 rNzfigure.figsizerror )r@rrrZwspaceZhspacer)Zxticksyticksr)rrr;rr)ZxyrrrrYroff)rrZw_padZh_pad)rrrr%r) add_subplotrryr$r6rrirrvrnrordrZannotater3rr!r')rsrtZ show_axesrrrrrrvrrqrrZ center_posrYZx2rZy2rDrDrE plot_layoutZs2  "  . 4& rc sddlm} ddlm} |j}t|j|j}t|j|j}t|j|j}t|j|j}|dddf|k|dddf|k@|dddf|k@|dddf|k@}dd|D}t |d}|j D]}t || r| |q|jjt|dkrdSj}|dkrTtj|dd t j||||||fdd }fd d|D}n|d krtj| dd }t}|D].}|||d|||ddqxt j||||||fdd }fdd|D}nP|dkr,tjddddt j||||||fdd }fdd|D}tdt|t| dkrX| t| | djstt| d<| dd}|dkrtjdnt|tjd}|dkrtj dnt|tj d}|dkrd}|dkrd}j|dj|dj |j |f}dt||f}|!||"d|#d|j$||dd| d}t| d%dkr| dj&|d| d%d_'n| d%dj'j(|d| dj| | djt)ddS)z=Handle drawing average tfr over channels called from topomap.rN)PathCollectionr cSsg|]}|rdndqS)rrYrDrrDrDrEr[sz_onselect..r9F)rPrQrcsg|]}j|qSrDrVrXr_rtrrDrEr[sr:)rsrrcsg|]}j|qSrDrVr)rrDrEr[srOT)rPrOrQcsg|]}j|qSrDrVrrrDrEr[szAveraging TFR over channels r|r7zAverage over %d %s channels.z Time (ms)zFrequency (Hz)rr)rrrWr)r`)*rrZmatplotlib.collectionsrrrZxdatar%ZydatarnrrrcrrrrrirLrrArPr rrrrkr&Z fignum_existsnumberrr#r%rZ set_xlabelrerZget_axesrrZon_mappable_changedr')ZeclickZereleaserrvrBrrrrrrrsrrrrrrrrtrZ collectionrLrHZgradsZidxsrzrrZimgrDrrEr(s  &                       r(cCs t||r|stddS)zxPrepare the topomap axis and check positions. Hides axis frame and check that position information is present. zENo position information found, cannot compute geometries for topomap.N)rrr)rvrZ check_nonzerorDrDrErs rcCs.||jg|jg|ddS)zHide axis frame for topomaps.FN)Z get_yticksZxaxisrZyaxisZ set_frame_on)rrDrDrErs  rcCs(td|d|dkr$|tkr dnd}|S)Nr)r8r9rrrr9r)rr)rrBrDrDrErs rc $ Cstd|d} t} |dr|d} tt| D]} |j| | | dddq4t| dd\}}|jt t ||d d | d d gd |j | d d d|d<| |d|rd dl m}|| dg\} }t| d krdnd}|rdnd}t| dd|\}}t||dd|d}t|t|dd|||d d\}}}}t||||}t|d<|dD],}|d || dd|f||q^|dd }t|d}t|d}tj ||ddddd}|||||||||d|j||||d d!|d"d#}|jddd$|jj||d%|j||||ddd&} |||jd'd(d)|jd*d+d,}!|!|d-<| || |!| j D]}"|"|q|t!||}#|||#d.t"|jd/t#| t#| j S)0zInitialize animated topomap.zInitializing animation...rL butterfly all_timesrYr rrNrr^r)r}rrrline)r r:TFrrrvrrCr)rvrrrrrZisframesrIrF)rrrrrrr cont_limsrrrrrrrWrrr)enableZtight)rZlevelsrr皙?rrBrr)rvaZhar)r*rr)$rrArrkrir3r"ryrnaroundraxvlinerZmne.channels.layoutr rrrrrrnanminZnanmaxupdaterZ autoscalerrrrrrrr6r!rw)$rax_lineax_cbarrrwr@rBrrrrLr2rrzrrr rurrrrrrrrframerZzi_minZzi_maxrrrrrr4rDrDrE _init_anims       *       rc Cs|dr|d}|d|}|ddkr@d|d|df}nd |d|f}|d rd|d }nT||jd d d|jd}|dD]*\}\}} d|krq|j|| ddddqt||||d} |d} |d} |d} |d|}|d}|d}|d}|j||| | dd|d d!}|d"}tj d#d$&t d%|j | | ||ddd&}W5QRX| ||j D]}| |qx||g}|d'r|d(}|d)}||}|j||d*d+|d)<||||d)||d<t|t|j S),zUpdate animated topomap.pauserrrPmsz%6.0f msr#r7z%6.3f sblitrg?rrB)rrr-rYr Fr.rrrrrrrr*rrrrrTrrrrrrrr)Zclarrr2r3rZset_textrrrrrrrrZget_ylimrZset_ylimrrw)rrrrrrrrYr_rrrrrrrrr*rrrrr2rrrrDrDrE_animate, sl          rcCs|d |d<dS)z/Pause or continue the animation on mouse click.rNrDrrrDrDrE _pause_animf srcCsb|jdkr*d|d<t|ddd|d<n4|jdkr^d|d<t|ddt|dd|d<d S) z%Handle key presses for the animation.r@Trrr rrrN)r5r%rrirrDrDrE _key_pressk s   rc # sddlm} m} |dkr*tjdd}|dkr:tdt|j\}}|dkrlt jdjdd}t |}|j dkrtd |j t |jdkst |jdkrtd fd d |D}t||d \}}}}}}}j|ddf}|td|9}| jdd}d}|dd}|dt|}| j|d||d}|rd| j||df|d}nd}t|trt dtjd|t}| j|d|f|d}|jtd|ddt| |} t||jd|||d|||d }tt|||||||| | | d }tt|||d}tt|d}|j !d|tt"|d} |j !d| |dkr`jdd }d!|}!| j#|||t||!|d"}"|"|_$t%|dd#d$|kr|d$&||"fS)%zeMake animation of evoked data as topomap timeseries. See mne.evoked.Evoked.animate_topomap. r)r animationN)r9r:rOr5r6r8r7zChannel type not supported. Supported channel types include 'mag', 'grad', 'eeg'. 'hbo', 'hbr', 'fnirs_cw_amplitude', and 'fnirs_od'.r^rr z#times must be 1D, got %d dimensionsz0All times must be inside the evoked time series.cs g|]}tj|qSrD)rnr]r#r\)rXrTrCrDrEr[ sz&_topomap_animation..rNr:)rrr)rcrr)rowspancolspan)r)rr rF) rLrvrrrrrrr#rPrC) rrrrrwr@rBrrr)rrr)rrZkey_press_eventr<g$@i) init_funcrintervalrrJr)'r1rrrrArjr,r#rnrrorjr%rr|rLr0rrqZ subplot2gridrcrrirTrErrr$rrrrrrrZ FuncAnimationZ mne_animationr'r)#rrBr#Z frame_raterrrrPr@rrrrrrurrtrvrwrCrLrrrrrrrrrZ animate_funcZ pause_funcZkey_press_funcrZanimrDrCrE_topomap_animationu s  $              rcCsFd}t|tr>|dkr>ddlm}|j|dd}|||}||fS)zSet correct contour levels.Nrrr r")rcrr1rr)Z tick_values)rrrr*rrDrDrEr' s   r'c s| sd} dk r"| d7} nd} ttt} dt| kr|t| } f ddtd|D}|St| r| g} t| d \}}}}}} }t| ||tdd|ftt| d d \}}}}| | t | | D]\}}}}}| r8d |j |}|j |d dn| d ||r^t|g\}}t|dd\}}t||||d|dtd dt|qt|d|jdd|jt |S)z*Customize ica.plot_components for corrmap.zDetected componentsNz of type zSupplied templatercsLg|]D}t|| |||| d qS))rrr) _plot_corrmaprW rBrrrLrrtrrrrsubjsrDrEr[ sz!_plot_corrmap..rrNrrz Subj. {}, {}rrzSubj. {}rF) rrrrrrrrrrr?r)rrkrirnZisscalarr|rrr#r rrrrr r"r r r rr!rrrr') rLrrtrBrrrrrrtemplater@rrtrrrrvrwrrurCrrrqrrsubjectrzttlrrrDrrEr s^          rc Csbddlm}m}t<tjdtd|||}|||}||j|j \}}W5QRX||fS)zTake gradients of z on a mesh.r)CubicTriInterpolator Triangulationr)category) Zmatplotlib.trirrrrfilterwarningsDeprecationWarningZgradientr_r) r_rzrrr[Ztcir'r(rDrDrE _trigradient s   rgLa㧝=c#Csddlm}ddlm}t||}t|}t|dkr@tdn |dd}|dkr`td||d krv|d krv|}n>t|}t|dkrtd n |dd}|d krtd |||k rt|t |d d}t|t |d d}|||ddd}t ||}t |d |d\}}}}}}}t ||||}| d kr>|\}} n| j}t||| |||||| | | | |||d||||dt|j\}}t|||\}} | j}!|j }"| j|||!|"|dddd| jjtjd dtdt|dW5QRXt||S)uy Plot arrow map. Compute arrowmaps, based upon the Hosaka-Cohen transformation :footcite:`CohenHosaka1976`, these arrows represents an estimation of the current flow underneath the MEG sensors. They are a poor man's MNE. Since planar gradiometers takes gradients along latitude and longitude, they need to be projected to the flattened manifold span by magnetometer or radial gradiometers before taking the gradients in the 2D Cartesian coordinate system for visualization on the 2D topoplot. You can use the ``info_from`` and ``info_to`` parameters to interpolate from gradiometer data to magnetometer data. Parameters ---------- data : array, shape (n_channels,) The data values to plot. info_from : instance of Info The measurement info from data to interpolate from. info_to : instance of Info | None The measurement info to interpolate to. If None, it is assumed to be the same as info_from. scale : float, default 3e-10 To scale the arrows. %(vmin_vmax_topomap)s %(cmap_topomap_simple)s sensors : bool | str Add markers for sensor locations to the plot. Accepts matplotlib plot format string (e.g., 'r+' for red plusses). If True (default), circles will be used. res : int The resolution of the topomap image (n pixels along each side). axes : instance of Axes | None The axes to plot to. If None, a new figure will be created. names : list | None List of channel names. If None, channel names are not plotted. %(show_names_topomap)s If ``True``, a list of names must be provided (see ``names`` keyword). %(mask_topomap)s %(mask_params_topomap)s %(outlines_topomap)s contours : int | array of float The number of contour lines to draw. If 0, no contours will be drawn. If an array, the values represent the levels for the contours. The values are in µV for EEG, fT for magnetometers and fT/m for gradiometers. Defaults to 6. %(image_interp_topomap)s show : bool Show figure if True. onselect : callable | None Handle for a function that is called when the user selects a set of channels by rectangle selection (matplotlib ``RectangleSelector``). If None interactive selection is disabled. Defaults to None. %(extrapolate_topomap)s .. versionadded:: 0.18 %(sphere_topomap_auto)s Returns ------- fig : matplotlib.figure.Figure The Figure of the plot. Notes ----- .. versionadded:: 0.17 References ---------- .. footbibliography:: r)rr)_map_meg_or_eeg_channelsr z]Multiple channel types are not supported.All channels must either be of type 'grad' or 'mag'.)r9r:zNChannel type '%s' not supported. Supported channel types are 'mag' and 'grad'.Nr9z)Multiple channel types are not supported.z,only 'mag' channel type is supported. Got %sT)rP)r<r<g{Gz?Zaccurate)rWr0rNF)rrrrrrrrr-rrrrrrrr@rBrY)rrrr0rrr)r1rforwardrrrrirjrrrnr r|rr&rr rwrrrLZquiverrZ draw_idlerrrr!r')#rLZ info_fromZinfo_torrrrrrrrrr-rrrrrrrr@rrrBmappingrurvrCrr_rr'r(ZdxxZdyyrDrDrE plot_arrowmap sO              rcCs ddlm}|dkrt}n|}t|dd}|dd|dd|d t||j|d d|d d d |kr|d ntd}d|kr| \}} | |d<nd}d|kr| dnd} |j dd|j |j fkrt d|j d|j |j fd|j |}t|j } t|j dD]} || j| || | <q(tjtj|dddd} t| t||f|\}}|dkr|jn|}|D]F\}}t|||g|d}|jj|d|dg|d|dgddq|dk r|j|| r||}|d|S)aTopoplot electrode distance matrix with bridged electrodes connected. Parameters ---------- %(info_not_none)s bridged_idx : list of tuple The indices of channels marked as bridged with each bridged pair stored as a tuple. Can be generated via :func:`mne.preprocessing.compute_bridged_electrodes`. ed_matrix : array of float, shape (n_channels, n_channels) The electrical distance matrix for each pair of EEG electrodes. Can be generated via :func:`mne.preprocessing.compute_bridged_electrodes`. title : str A title to add to the plot. topomap_args : dict | None Arguments to pass to :func:`mne.viz.plot_topomap`. Returns ------- fig : instance of matplotlib.figure.Figure The topoplot figure handle. See Also -------- mne.preprocessing.compute_bridged_electrodes rNT)rOrrhrZsummer_rrrrFr@rrr z Expected z shaped `ed_matrix`, got rrNr)r r)rr )r r rrz Electrical Distance ($\mu$$V^2$))rrr$r?r setdefaultrrGrr&rrrrrnZ tril_indicesrkrrOrr rrrr3rrr)rAZ bridged_idxZ ed_matrixrrrrtr@rrrZtril_idxZepo_idxZ elec_distsrrUZidx0r\rvrrDrDrEplot_bridged_electrodes sX                 r2dc sddlm}ddl}ddlm}ddlm}t|tdtt j |j fdt |j } |rl|dkrlt d t|j|d d } t|| }t|j} jd| krt d jdd | d|dkr|ddi|||dd} W5QRXt| jdnB|dkr<|ddi||ddd} W5QRX| jdd| jd|jj} | dd|dkr| dd| d}| ddfddtjdD}dd|D}| d|n.| dj }t j!|dj"|dj"|dgdd}| jd}t#}jd} t| D]}||ddf}| rF|$d}nt %|d}t|dkrfq||d7}|D]B}|||gddf}t&||g}|j'|j(ddd d||<qvq|rt#}t)t*|||||| d!}| j+,d"|| S)#aPlot channel adjacency. Parameters ---------- info : instance of Info Info object with channel locations. adjacency : array Array of channels x channels shape. Defines which channels are adjacent to each other. Note that if you edit adjacencies (via ``edit=True``), this array will be modified in place. ch_names : list of str Names of successive channels in the ``adjacency`` matrix. kind : str How to plot the adjacency. Can be either ``'3d'`` or ``'2d'``. edit : bool Whether to allow interactive editing of the adjacency matrix via clicking respective channel pairs. Once clicked, the channel is "activated" and turns green. Clicking on another channel adds or removes adjacency relation between the activated and newly clicked channel (depending on whether the channels are already adjacent or not); the newly clicked channel now becomes activated. Clicking on an activated channel deactivates it. Editing is currently only supported for ``kind='2d'``. Returns ------- fig : Figure The :class:`~matplotlib.figure.Figure` instance where the channel adjacency is plotted. See Also -------- mne.channels.get_builtin_ch_adjacencies mne.channels.read_ch_adjacency mne.channels.find_ch_adjacency Notes ----- .. versionadded:: 1.1 r)sparseNr ) plot_sensorsrA adjacencyZ3dz-Editing a 3d adjacency plot is not supported.T)orderedz]``adjacency`` must have the same number of rows as the number of channels in ``info``. Found z channels for ``adjacency`` and z for ``inst``.ZtoolbarNoneF)rerrZtopomaprr<rXrcsg|]}t|dqSr rnrNrrrDrEr[B sz%plot_ch_adjacency..cSsg|]}t|ddqS)r;@)r%rrDrDrEr[D srr)rrrg?r)r positions highlighted line_dictr node_sizepath_collectionZ pick_event)-Zscipyrr1rrrBrrr3rnrZ csr_matrixrcrjrrGrrirZ rc_contextr-rrZfindobjrrZset_linewidthsZ set_alphaZ get_offsetsZ set_zorderrk set_sizesZ _offsets3drUrLr$Znonzerorrwr3rr_onpick_ch_adjacencyrr)rArrGreZeditrZmplrrZ has_sparseselZ n_channelsrrrv n_connectionsrrlinesZch_idxrowZ ch_neighboursZngb_idxZthis_posZch_pairrZ this_onpickrDrrEplot_ch_adjacency s)              $      rcs|jd}||kr4||||=|jjnt|dkrt||dd} |j||ddfjd| dd} | ||<|jjn:t | d} | |g} | t | } | | krd|| || =t | d n>d || ddf} |j| jd did}||| <t | d || || =fd d| D}t| |D]\}}t|dd||<qR|d|t||dd} |j||ddfjd| dd} | ||<|jjdS)z*Handle interactivity in plot_ch_adjacency.rrrNz tab:green)rr`Zzorderr^Fr rTcs"g|]}t|dqSrr)rXrzrZ n_conn_changerDrEr[ sz(_onpick_ch_adjacency..r;r)indrrrrrir%rrrkeyssortrw_set_adjacencyr3rr)rrrrrrrrZnode_indrdotsr5 both_nodesZ selected_posrrrzZn_connrDrrErp s\        rc Cs:ddl}|jdd||||dddf<W5QRXdS)zDSet adjacency for given node pair, caching errors for sparse arrays.rNTrr^)rr)rrvaluerrDrDrEr sr)N)rrNNr)T)NNNNNNrPNNNTTNrrrFNNTrrN)r ) NNNNNrFrbNrO)NNNFNFTrgNNNFNFrrNTNrN) NNNTFrtrNTNrNrO)NFT)N)T)FN)NN)rF)NNNNNNN)sr}r?r functoolsrnumbersrrnumpyrnr/rZchannels.channelsrZchannels.layoutrrr r defaultsr r r Zio.pickrrrrrrrrutilsrrrrrrrrrrr!r"r#r$r%r&r'r(r)r*r+r,r-r.Ztime_frequencyr/r0Z transformsr1r2Z io.meas_infor3r4rgrFr|rhrrrrrrr6r`r rarrr rrrrrrr r3rWrOrMrfrsrrrr(rrrrrrrrr'rrrrrrrrDrDrDrEsZ     (0@   K3+  . b1 {N  i&  , 1Y 6 i   S n / F  B:  K 7   L  E