4
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This question was posed to me by someone in my university's athletics department who had a USB sound level meter and a simple Python script which printed the current sound level (he was provided with that script when he bought the meter):

Can you write a Python script to read the decibel level of the arena during basketball games? We're interested in adding that data as a 'live stat' in our official app.

This script represents my attempt at meeting his requirements. I'm self-taught in Python, and most of what I do in the language uses the NLTK and BeautifulSoup, so building a GUI and handling data from a USB device are outside my 'comfort zone'. So far it does what we need it to do, but I'm sure it can be improved.

Usage

For FTP uploading, the script assumes a ftpconfig.py file structured like this:

#!/usr/bin/env python
# -*- coding: utf-8 -*-

FTP_HOST = 'ftp.example.com'
FTP_USERNAME = 'username'
FTP_PASSWORD = 'password'
FTP_DIR = 'subdirectory'

To send output via FTP, call the script with python decibelviz.py --ftp. Calling the script without that --ftp flag won't try to send anything via FTP.

Note also that the DecibelVisualizer.live_dbs() method, which gets the reading from the USB meter, will return random values in the same interval if the meter's not connected. This makes for a useful demo mode.

The visualization itself looks like this:

dB reader screenshot

Output

The script saves two sorts of JSON output files.

The file kudbs.json is the file that's sent via FTP every fifteen seconds. It's saved with no indentation (it's assumed that this will be for machine reading, not human reading) and is overwritten on successful upload.

kudbs.json

[[1449674472,52.0],[1449674473,67.0],[1449674473,31.0],[1449674474,91.0],[1449674475,87.0],[1449674475,129.0],[1449674476,108.0],[1449674477,35.0]]

The file totalresults_XX.json is saved when the Stop button is pressed, and contains all data gathered since the Start button was pressed. This file is indented (since it might be human-read) and is not overwritten. The script checks existing files in the current working directory and auto-increments the number in the filename as needed.

totalresults_01.json

[
   [
      1449674472,
      52.0
   ],
   [
      1449674473,
      67.0
   ],
   [
      1449674473,
      31.0
   ],
   [
      1449674474,
      91.0
   ],
   [
      1449674475,
      87.0
   ],
   [
      1449674475,
      129.0
   ],
   [
      1449674476,
      108.0
   ],
   [
      1449674477,
      35.0
   ]
]

Constraints

During games this script runs on an old Windows XP netbook. To that end, this script does not use any code not available in the standard library of Python 2.7.9.

The JSON format of the output (a list of 2-tuples in which the first item is a Unix timestamp and the second item is the decibel reading) was requested by the app developers. They also requested the 15-second standard interval between FTP upload attempts (as well as the Fibonacci-series backoff intervals, if the upload doesn't go through).

Questions

  1. Is it okay having all the grid configuration commands inside the DecibelVisualizer.__init__() method, or would it be better to separate them into something like a ._configure_grid() method (which would be called by .__init__())?

  2. The visualization pauses/lags while the FTP upload attempt is in progress. Is this unavoidable, or can I do something about it? (Would multithreading help here?)

  3. The refresh rate of the USB meter we're using is 0.5 seconds, and I wanted a way to smooth the transitions between those points for a more fluid-looking visualization. What I've tried to do in this script is add a one-second delay between reading a decibel value and displaying it, and then every 0.1 second, display one tenth of the interval between readings. I think this works, but the resulting animation seems 'jumpy' and I worry that I've made an error. Maybe it's just lagging while it reads a new data point, or maybe I've got the bars incrementing in the wrong direction (left-to-right instead of right-to-left?). I would appreciate some thoughts on this too.

I would also be very grateful for any general feedback on how well my code conforms to best practices: function/method naming, docstrings, organization, etc.

The Script

This is the main decibelviz.py script:

#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""Display current decibel readings with a graphical gauge."""

import ftplib
import json
import math
import os
import random
import sys
import time
import Tkinter
import usb.core

try:
    from ftpconfig import FTP_HOST, FTP_USERNAME, FTP_PASSWORD, FTP_DIR
except ImportError:
    print "FTP configuration import failed. Saving output locally only."
    pass

def fibonacci_number(n):
    """Return the Nth Fibonacci number."""
    a, b = 1, 1
    for _ in range(n - 1):
        a, b = b, a + b
    return a

class FTPConnection(object):
    """FTP connection for uploading files."""

    def __init__(self, host, user, password, directory):
        """Initialize the FTP connection object.

           Parameters
           ----------
             host (str) : FTP hostname
             user (str) : FTP username
             password (str) : FTP password
             directory (str) : desired FTP subdirectory
        """
        self.host = host
        self.user = user
        self.password = password
        self.directory = directory

    def __enter__(self):
        # called at the beginning of a 'with' block
        self.ftp = ftplib.FTP(self.host)
        self.ftp.login(self.user, self.password)
        # self.ftp.set_pasv(False)
        return self

    def __exit__(self, *args, **kwargs):
        # called at the end of a 'with' block
        try:
            self.ftp.quit()
        # if there's no connection to close, don't do anything
        except AttributeError:
            pass

    def send_file(self, filename, ext='.json', directory=None):
        """Upload a plain text file to the specified FTP directory.

           Parameters
           ----------
             filename (str) : file name, minus extension
             ext (str) : file extension
             directory (str) : destination subdirectory
        """
        if directory is None:
            directory = self.directory
        self.ftp.cwd(directory)
        fname = filename + ext
        return self.ftp.storlines('STOR {}'.format(fname), open(fname, 'r'))

class ReadoutHeading(object):
    """Display a description of some measurement."""

    def __init__(self, parent, text):
        """Initialize the ReadoutHeading object.

           Parameters
           ----------
             parent (Tkinter widget) : the parent widget
             text (str) : text for the label
        """
        self.Label = Tkinter.Label(parent, text=text)

class ReadoutValue(object):
    """Display a measurement in units."""

    def __init__(self, parent, value, fontsize=60, units='dB'):
        """Initialize the ReadoutValue object.

           Parameters
           ----------
             parent (Tkinter widget) : the parent widget
             value (str) : starting text for the label
             fontsize (int) : font size for the label
             units (str) : units of measurement for the value displayed
        """
        self.text = Tkinter.StringVar()
        self.Label = Tkinter.Label(parent, textvariable=self.text,
            font=('Helvetica', '{}'.format(fontsize)))
        self.units = units
        self.update(value)

    def update(self, db):
        """Update the label with new content.

           Parameters
           ----------
             db (float, int) : decibel value
        """
        self.text.set('{} {}'.format(db, self.units))

class DecibelVisualizer(object):
    """Cool-looking way to visualize decibel levels."""

    def __init__(self, parent, width=320, height=150, min_db=30, max_db=130,
                 delay=500, subintervals=10, title="Live Decibel Reading",
                 units='dB', use_ftp=False, ftp_host='', ftp_username='',
                 ftp_password='', ftp_dir='', fname_send='kudbs',
                 fname_save='totalresults', seconds_between_uploads=15):
        """Initialize the DecibelVizualizer widget.

           Parameters
           ----------
             parent (Tkinter widget) : the parent widget
             width (int) : width of the visualization in pixels
             height (int) : height of the visualization in pixels
             min_db (int) : minimum decibel level of the USB sound meter
             max_db (int) : maximum decibel level of the USB sound meter
             delay (int) : refresh rate of the USB sound level meter in
               milliseconds (i.e, delay=500 means a refreshed rate of 2x
               per second)
             subintervals (int) : number of times per second that the
               visualization will be refreshed
             title (str) : title displayed at the top of the main window
             units (str) : units of measurement for the meter readings
             use_ftp (boolean) : should readings be sent to FTP server?
             ftp_host (str) : hostname for FTP server
             ftp_username (str) : username for FTP server
             ftp_password (str) : password for FTP server
             ftp_dir (str) : path to desired directory on FTP server
             fname_send (str) : filename for sending live readings via FTP
               while the script is running
             fname_save (str) : filename for saving all results locally
               when script is stopped
             seconds_between_uploads (int) : seconds between each attempt
               to send data to the FTP server
        """
        self.parent = parent
        self.parent.wm_title(title)
        self.Canvas = Tkinter.Canvas(parent, width=width, height=height)
        self.w = width
        self.h = height
        self.min_db = float(min_db)
        self.max_db = float(max_db)
        self.min_scale = 0
        self.max_scale = max_db + 10
        self.db_current = min_db
        self.db_maximum = min_db
        self.all_dbs = []
        self.temp_dbs = []
        # live decibel tracking won't happen while self.event is None
        self.event = None
        # delay between readings of the USB device, in milliseconds
        self.delay = delay
        # number of times per second that the visualization will refresh
        self.subintervals = subintervals
        self.seconds_between_uploads = seconds_between_uploads

        # filename for the JSON to be sent via FTP
        self.fname_send = fname_send
        # filename for the JSON to be saved locally with all results
        self.fname_save = fname_save

        # ftp login credentials
        self.use_ftp = use_ftp
        self.ftp_host = ftp_host
        self.ftp_username = ftp_username
        self.ftp_password = ftp_password
        self.ftp_dir = ftp_dir

        # if self.use_ftp == True:
        #    self.ftp_connection = FTPConnection(
        #             self.ftp_host, self.ftp_username, self.ftp_password,
        #             self.ftp_dir)

        self.colors = {
            13: '#E50000',
            12: '#E14400',
            11: '#DD8700',
            10: '#D9C701',
            9:  '#A7D501',
            8:  '#65D201',
            7:  '#25CE02',
            6:  '#02CA1C',
            5:  '#02C658',
            4:  '#03C391',
            3:  '#03B6BF',
            2:  '#037ABB',
            1:  '#0341B7',
            0:  '#040AB4',
        }

        # counters
        self.counter = 0
        self.subcounter = 0
        self.ftpcounter = 0
        self.fibcounter = 1

        # set up the labels and headings
        self.cur_heading = ReadoutHeading(parent,
                                          text="Current Decibel Reading:")
        self.cur_value = ReadoutValue(parent, value=min_db)

        self.avg_heading = ReadoutHeading(parent, text="Today's Average:")
        self.avg_value = ReadoutValue(parent, value=min_db, fontsize=44)

        self.max_heading = ReadoutHeading(parent, text="Today's Maximum:")
        self.max_value = ReadoutValue(parent, value=min_db, fontsize=44)

        # buttons
        self.close_button = Tkinter.Button(
                parent, text='Stop', font=('Helvetica', '30'),
                command=self.stop_reading)
        """Stop reading and displaying dB values and save all readings."""

        self.demo_button = Tkinter.Button(
                parent, text='Demo', font=('Helvetica', '30'),
                command=self.live_display)
        """Display one new data point."""

        self.start_button = Tkinter.Button(
                parent, text='Start', font=('Helvetica', '30'),
                command=self.start_live_db_reading)
        """Start reading and displaying dB values."""

        # configure the parent widget's grid
        parent.grid_columnconfigure(0, weight=1)
        parent.grid_columnconfigure(1, weight=1)
        # add widgets to the parent widget's grid
        self.Canvas.grid(row=2, column=1, columnspan=3, rowspan=3)
        self.cur_heading.Label.grid(row=0, column=0, columnspan=2, padx=10,
                                    pady=10)
        self.cur_value.Label.grid(row=1, column=0, pady=5)

        self.avg_heading.Label.grid(row=0, column=2, padx=10, pady=5)
        self.avg_value.Label.grid(row=0, column=3, pady=5)

        self.max_heading.Label.grid(row=1, column=2, padx=10, pady=5)
        self.max_value.Label.grid(row=1, column=3, pady=5)
        self.close_button.grid(row=4, column=0, padx=10, pady=5)
        self.demo_button.grid(row=3, column=0, padx=10, pady=5)
        self.start_button.grid(row=2, column=0, padx=10, pady=5)

    def _send_file_via_ftp(self, fname, ext='.json'):
        """Try to send a file to the FTP server.

           Parameters
           ----------
             fname (str) : file name, minus extension
             ext (str) : file extension
        """
        ftp_conn = FTPConnection(self.ftp_host, self.ftp_username,
                                 self.ftp_password, self.ftp_dir)
        # ideally data is sent every 15 seconds
        standard_wait = self.seconds_between_uploads
        try:
            with ftp_conn as ftp:
                cmd = ftp.send_file(filename=fname)
            # confirm successful upload and delete temp file
            if cmd == '226 Transfer complete.':
                print 'Successful upload! {}'.format(cmd)
                self.temp_dbs = []
                self.fibcounter = 1
                self.ftpcounter = 0
        # if we get an error, keep trying
        except AttributeError as e:
            print "AttributeError: {}".format(e)
        except:
            print 'Unexpected error: {}'.format(sys.exc_info()[0])
            wait = (standard_wait + fibonacci_number(self.fibcounter)) * 1000
            self.Canvas.after(wait, self._send_file_via_ftp, fname)
            self.fibcounter += 1

    def save_json(self, obj, filename='results', overwrite=False):
        """Save an object to file in JSON format."""
        # convert a single reading to a list
        if isinstance(obj, tuple):
            obj = [obj]
        if overwrite == False:
            file_number_in_use = True
            idx = 1
            while file_number_in_use:
                str_idx = str(idx).rjust(2, '0')
                fname = '{}_{}'.format(filename, str_idx)
                if os.path.isfile(fname + '.json'):
                    idx += 1
                else:
                    filename = fname
                    break
        # the overwritten file should be as small as possible for FTP
        indent = 3 if overwrite == False else None
        json_output = json.dumps(obj, indent=indent, separators=(',', ':'))
        with open(filename + '.json', 'w+') as stream:
            stream.write(json_output)

    def live_dbs(self, lower_bound=None, upper_bound=None):
        """Return the live decibel reading from the USB device.

           Parameters
           ----------
             lower_bound (int) : minimum decibel reading
             upper_bound (int) : maximum decibel reading

           Returns
           -------
             (float) : current decibel reading, either the actual
               reading from the connected USB device, or a random
               reading which may approximate it for testing purposes.
               The returned reading is rounded to two decimal places.
        """
        if lower_bound is None:
            lower_bound = self.min_db
        if upper_bound is None:
            upper_bound = self.max_db
        try:
            # identify the usb device
            dev = usb.core.find(idVendor=0x16c0, idProduct=0x5dc)
            # decipher its signal
            ret = dev.ctrl_transfer(0xC0, 4, 0, 0, 200)
            db = (ret[0] + ((ret[1] & 3) * 256)) * 0.1 + 30
            db_as_string = '{0:.2f}'.format(float(db))
            return float(db_as_string)
        # allow a demo mode in case the demo mode isn't connected.
        except ValueError:
            return float('{0:.2f}'.format(
                    float(random.randrange(lower_bound, upper_bound))))
        except Exception as e:
            print "Unknown exception: {}".format(e)
            return float('{0:.2f}'.format(
                    float(random.randrange(lower_bound, upper_bound))))

    def draw_frame(self):
        """Draw the frame and labels."""
        x1, y1 = 10, 10
        x2, y2 = 10, self.max_scale
        x3, y3 = self.w, self.max_scale
        self.Canvas.create_line(x1, y1, x2, y2, x3, y3, fill='black')

    def draw_one_bar(self, bar_height=130, bar_width=20, left_edge=20):
        """Draw a single bar composed of colored bins.

           Parameters
           ----------
             bar_height (float, int) : height of the bar in pixels
             bar_width (int) : width of the bar in pixels
             left_edge (int) : horizontal position of the bar's left edge,
               in pixels
        """
        # incremental height -- a bar is built up bin by bin
        inc_height = 0
        for i in range(0, int(bar_height) / 10 + 1):
            # the topmost bin will often be shorter than the usual bin height
            dif = bar_height - (i * 10)
            bin_height = min([dif, 10])
            col = self.colors[i]
            # define the top-left and bottom right corners of the bin
            x1, y1 = left_edge, self.max_scale - ((i * 10) + bin_height)
            x2, y2 = left_edge + bar_width, self.max_scale - (i * 10)

            inc_height += bin_height
            if inc_height > bar_height:
                break

            # draw a single bin
            self.Canvas.create_rectangle(x1, y1, x2, y2, fill=col)

    def draw_multiple_bars(self, list_of_height_edge_tuples):
        """Draw multiple, potentially different, bars at once.

           Parameters
           ----------
             list_of_height_edge_tuples (list) : list of 2-tuples, e.g.:
                 [(105, 20), (115, 50), (125, 80)]
               Each tuple represents one bar. The first entry in the tuple
               (int) is the bar's height, while the second (int) is the
               horizontal position of the bar's left edge.
        """
        for h, e in list_of_height_edge_tuples:
                self.draw_one_bar(bar_height=h, left_edge=e)

    def draw_identical_bars(self, bar_height):
        """Draw ten bars with identical heights.

           Parameters
           ----------
             bar_height (float, int) : height of the bars
        """
        self.draw_multiple_bars(
            [(bar_height, e) for e in [20+i*30 for i in range(0,10)]])

    def draw_interpolated_individual_bars(self, subcounter=None):
        """Draw ten bars which show smooth transitions between values.

           Parameters
           ----------
             subcounter (int) : number of transitional points to be
               generated between pairs of measurements
        """
        if subcounter is None:
            subcounter = self.subcounter
        # create a list of tuples representing all measurement pairs
        # e.g. [0, 1, 2, 3] --> [(0, 1), (1, 2), (2, 3)]
        tup_list = [(self.all_dbs[i][1], self.all_dbs[i+1][1])
                    for i in range(len(self.all_dbs) - 1)]
        # create a new list with finer-grained intervals by interpolating
        # between each measurement pair in tup_list
        int_list = []
        for a, b in tup_list:
            vals = self.interpolate_two_values(a, b)
            int_list += vals
        # number of bars to be drawn (ten is default)
        num = 10
        # the zip here joins a list of ten heights to a list of ten edges
        self.draw_multiple_bars(
            [(v, e) for (v, e) in zip(
                int_list[-(num + subcounter):],
                [20+i*30 for i in range(0, 10)])])

    def interpolate_two_values(self, val_a, val_b, subintervals=None):
        """Return a list of values evenly spaced between two values.

           Parameters
           ----------
             val_a (float, int) : older measurement
             val_b (float, int) : more recent measurement
             subintervals (int) : number of transitional points to be
               generated between the pair of measurements
        """
        if subintervals is None:
            subintervals = self.subintervals
        interval = val_b - val_a
        increment = interval / float(subintervals)
        return [val_a + (increment * s) for s in range(0, subintervals)]

    def fetch_new_reading(self):
        """Get a new reading from the decibel meter."""
        new = (int(time.time()), self.live_dbs())
        self.all_dbs.append(new)
        self.temp_dbs.append(new)
        self.ftpcounter += 1
        self.save_json(self.temp_dbs, filename=self.fname_send,
                       overwrite=True)
        if self.use_ftp == True:
            if self.ftpcounter % self.seconds_between_uploads == 0:
                self._send_file_via_ftp(fname=self.fname_send)
        self.update_stats()

    def live_display(self, subintervals=None):
        """Monitor live decibel readings and plot with smoothness.

           Parameters
           ----------
             subintervals (int) : number of transitional points to be
               generated between each pair of measurements
        """
        if subintervals is None:
            subintervals = self.subintervals
        delay = self.delay / subintervals
        if len(self.all_dbs) >= 2:
            # the USB meter's refresh rate and the subcounter are in sync
            self.subcounter = self.counter % subintervals
            # clear the canvas before drawing any new bars
            self.clear()
            self.draw_interpolated_individual_bars()

            # if subcounter is zero, it's time to read the meter
            if self.subcounter == 0:
                self.fetch_new_reading()
                self.counter += 1
            else:
                self.counter += 1
        else:
            self.fetch_new_reading()
            self.counter += 1
        # call this function recursively, if desired
        if self.event:
            self.Canvas.after(delay, self.live_display)

    def update_stats(self):
        """Update labels with new information."""
        self.db_current = self.all_dbs[-1][1]
        temp_average = sum(
            [e[1] for e in self.all_dbs]) / float(len(self.all_dbs))
        self.db_average = float('{0:.2f}'.format(temp_average))
        self.db_maximum = max(self.db_current, self.db_maximum)
        self.cur_value.update(self.db_current)
        self.avg_value.update(self.db_average)
        self.max_value.update(self.db_maximum)

    def start_live_db_reading(self, ms_between_readings=None):
        """Start live tracking and outputting of decibel readings."""
        if ms_between_readings is None:
            ms_between_readings = self.delay
        self.event = 'something'
        self.live_display()

    def clear(self):
        """Remove existing bars from the visualizer and redraw the frame."""
        self.Canvas.delete('all')
        self.draw_frame()

    def stop_reading(self, filename=None):
        """Stop tracking decibel input and save all results."""
        if filename is None:
            filename = self.fname_save
        self.use_ftp = False
        self.event = None
        self.save_json(obj=self.all_dbs, filename=filename, overwrite=False)

def main():
    root = Tkinter.Tk()
    root.geometry('570x330+30+30')
    if len(sys.argv) == 2:
        if sys.argv[1] == '--ftp':
            g = DecibelVisualizer(
                    root, use_ftp=True, ftp_host=FTP_HOST,
                    ftp_username=FTP_USERNAME, ftp_password=FTP_PASSWORD,
                    ftp_dir=FTP_DIR)
    else:
        g = DecibelVisualizer(root, use_ftp=False)
    g.draw_frame()
    # have the app open with some nice-looking bars on the screen
    g.draw_multiple_bars(
        [(105, 20), (115, 50), (125, 80), (121, 110), (120, 140),
         (119, 170), (118, 200), (115, 230), (112, 260), (108, 290)]
        )

    root.mainloop()

if __name__ == '__main__':
    main()
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1 Answer 1

3
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I can answer question 1, and I have some general feedback besides that. First, your question.

Your DecibelVisualizer's init is very long. I think at the very least you should split some of them up into separate functions to make it easier to see what's happening at each point. Your configure_grid certainly seems like a good candidate.

I'd also question whether or not you actually need all of those optional parameters. For settings that are almost never supplied, perhaps they could be set up separate to __init__ with a different function? Normally I would advise that it's helpful to let the user provide them on __init__ but there are really a lot of parameters there and it harms readability.

In particular, I don't think self.colors should be defined in the __init__ since it's a constant. You should instead have it at class level.

class DecibelVisualizer(object):

    self.COLORS = {
        13: '#E50000',
        12: '#E14400',
        11: '#DD8700',
        10: '#D9C701',
        9:  '#A7D501',
        8:  '#65D201',
        7:  '#25CE02',
        6:  '#02CA1C',
        5:  '#02C658',
        4:  '#03C391',
        3:  '#03B6BF',
        2:  '#037ABB',
        1:  '#0341B7',
        0:  '#040AB4',
    }

When defined here it can either be accessed with DecibelVisualizer.COLORS or still with self.COLORS. Each instance of the class can refer back to it. And since it's always the same there's no need to make a new one with each visualiser.


You don't need pass in your except block here, you may have misunderstood its use. It's merely a keyword that does nothing, used as a placeholder where Python expects a block of code but you don't need to write any. For example, here's what would happen if you tried to remove both print and pass:

try:
    from ftpconfig import FTP_HOST, FTP_USERNAME, FTP_PASSWORD, FTP_DIR
except ImportError:
    # Nothing here

This will raise a syntax error, because there must be indented code after except ImportError. However you can just put pass in there to tell Python to do nothing while still satisfying the syntax requirement. But if you have actual code in there, like your print, then there's no longer a need for pass.

In your fibonacci_number function you call range, but since you're using Python 2.7 you should use xrange, which doesn't create a full list in one go and so is more efficient.

It's good that you've documented well, your classes and functions are quite clear. Avoid over commenting though. People will know what __init__ does especially when your initialisations are simple so you could leave out notes like Initialize the ReadoutHeading object..

It's not Pythonic to use if boolean == False, instead use the boolean value directly. Either with if boolean or if not boolean. Also it's not necessary to set a boolean for your while loop since you're just going to break out of it anyway. You can just do while True:

    if not overwrite:
        idx = 1
        while True:
            str_idx = str(idx).rjust(2, '0')
            fname = '{}_{}'.format(filename, str_idx)
            if os.path.isfile(fname + '.json'):
                idx += 1
            else:
                filename = fname
                break

Likewise in the ternary, use if not:

    indent = 3 if not overwrite else None
\$\endgroup\$
2
  • \$\begingroup\$ Thanks very much for your answer! I've taken into account all of the minor changes you've suggested (class-level .COLORS, extraneous pass, xrange(), and if not overwrite). I'll have to think about how best to shrink the DecibelVisualizer.__init__() method. I think I'd like to have it call ._configure_geometry(), ._configure_grid(), ._configure_labels(), and .configure_buttons(). Does that sound reasonable? \$\endgroup\$ Dec 10, 2015 at 13:25
  • \$\begingroup\$ @menzenski Yeah that sounds like a good way to organise the functions. They have clear separate purposes that way so similar attributes are set together. \$\endgroup\$ Dec 11, 2015 at 9:22

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