Using python to create an average out of a list of times

Question

I have a huge list of times (HH:MM:SS) and I know that if I wanted to create an average I could separate the Hours, Seconds, and Minutes and average each one and then concatenate them back together. However I feel that there must be a better way to do that. Does anyone know of a better way to do this?

Thanks!

Answer 1

There's a problem with converting to seconds since midnight and averaging. If you do that with 23:50 and 00:10 you get 12:00 when what you want it 00:00.

A better approach is to average the angles.

import datetime
import math
import numpy

def datetime_to_radians(x):
    # radians are calculated using a 24-hour circle, not 12-hour, starting at north and moving clockwise
    time_of_day = x.time()
    seconds_from_midnight = 3600 * time_of_day.hour + 60 * time_of_day.minute + time_of_day.second
    radians = float(seconds_from_midnight) / float(12 * 60 * 60) * 2.0 * math.pi
    return radians

def average_angle(angles):
    # angles measured in radians
    x_sum = numpy.sum([math.sin(x) for x in angles])
    y_sum = numpy.sum([math.cos(x) for x in angles])
    x_mean = x_sum / float(len(angles))
    y_mean = y_sum / float(len(angles))
    return numpy.arctan2(x_mean, y_mean)

def radians_to_time_of_day(x):
    # radians are measured clockwise from north and represent time in a 24-hour circle
    seconds_from_midnight = int(float(x) / (2.0 * math.pi) * 12.0 * 60.0 * 60.0)
    hour = seconds_from_midnight / 3600
    minute = (seconds_from_midnight % 3600) / 60
    second = seconds_from_midnight % 60
    return datetime.time(hour, minute, second)

def average_times_of_day(x):
    # input datetime.datetime array and output datetime.time value
    angles = [datetime_to_radians(y) for y in x]
    avg_angle = average_angle(angles)
    return radians_to_time_of_day(avg_angle)

average_times_of_day([datetime.datetime(2017, 6, 9, 0, 10), datetime.datetime(2017, 6, 9, 0, 20)])
# datetime.time(0, 15)

average_times_of_day([datetime.datetime(2017, 6, 9, 23, 50), datetime.datetime(2017, 6, 9, 0, 10)])
# datetime.time(0, 0)

Answer 2

You don't want to "average" times on hours, minutes and seconds this way:

00:59:00
01:01:00

average clearly to 01:00:00, but not with the logic you presented.

Instead convert all your time intervals into seconds, calculate the average and convert back to HH:MM:SS.

00:59:00 -> 3540 seconds
01:01:00 -> 3660 seconds
            ============
average:    3600 seconds converted to HH:MM:SS -> 01:00:00