Averages/Mean time of day

A particular activity of bats occurs at these times of the day:

23:00:17, 23:40:20, 00:12:45, 00:17:19

Using the idea that their are twenty four hours in a day which is analogous to their being 360 degrees in a circle, map times of day to and from angles and using the ideas of Averages/Mean angle compute and show here the average time of the nocturnal activity to an accuracy of a second of time.

C

<lang c> /*29th August, 2012 Abhishek Ghosh*/

include<stdlib.h>
include<math.h>
include<stdio.h>

typedef struct {

 int hour, minute, second;

} digitime;

double timeToDegrees (digitime time) {

 return (360 * time.hour / 24.0 + 360 * time.minute / (24 * 60.0) +
         360 * time.second / (24 * 3600.0));

}

digitime timeFromDegrees (double angle) {

 digitime d;
 double totalSeconds = 24 * 60 * 60 * angle / 360;

 d.second = (int) totalSeconds % 60;
 d.minute = ((int) totalSeconds % 3600 - d.second) / 60;
 d.hour = (int) totalSeconds / 3600;

 return d;

}

double meanAngle (double *angles, int size) {

 double y_part = 0, x_part = 0;
 int i;

 for (i = 0; i < size; i++)
   {
     x_part += cos (angles[i] * M_PI / 180);
     y_part += sin (angles[i] * M_PI / 180);
   }

 return atan2 (y_part / size, x_part / size) * 180 / M_PI;

}

int main () {

 digitime *set, meanTime;
 int inputs, i;
 double *angleSet, angleMean;

 printf ("Enter number of inputs : ");
 scanf ("%d", &inputs);
 set = malloc (inputs * sizeof (digitime));
 angleSet = malloc (inputs * sizeof (double));
 printf ("\n\nEnter the data separated by a space between each unit : ");

 for (i = 0; i < inputs; i++)
   {
     scanf ("%d:%d:%d", &set[i].hour, &set[i].minute, &set[i].second);
     angleSet[i] = timeToDegrees (set[i]);
   }

 meanTime = timeFromDegrees (360 + meanAngle (angleSet, inputs));

 printf ("\n\nThe mean time is : %d:%d:%d", meanTime.hour, meanTime.minute,
         meanTime.second);
 return 0;

}

</lang>

Output:

Enter number of inputs : 4


Enter the data separated by a space between each unit : 23:00:17 23:40:20 00:12:45 00:17:19


The mean time is : 23:47:43

Go

<lang go>package main

import (

   "errors"
   "fmt"
   "log"
   "math"
   "time"

)

var inputs = []string{"23:00:17", "23:40:20", "00:12:45", "00:17:19"}

func main() {

   tList := make([]time.Time, len(inputs))
   const clockFmt = "15:04:05"
   var err error
   for i, s := range inputs {
       tList[i], err = time.Parse(clockFmt, s)
       if err != nil {
           log.Fatal(err)
       }
   }
   mean, err := meanTime(tList)
   if err != nil {
       log.Fatal(err)
   }
   fmt.Println(mean.Format(clockFmt))

}

func meanTime(times []time.Time) (mean time.Time, err error) {

   if len(times) == 0 {
       err = errors.New("meanTime: no times specified")
       return
   }
   var ssum, csum float64
   for _, t := range times {
       h, m, s := t.Clock()
       n := t.Nanosecond()
       fSec := (float64((h*60+m)*60+s) + float64(n)*1e-9)
       sin, cos := math.Sincos(fSec * math.Pi / (12 * 60 * 60))
       ssum += sin
       csum += cos
   }
   if ssum == 0 && csum == 0 {
       err = errors.New("meanTime: mean undefined")
       return
   }
   _, dayFrac := math.Modf(1 + math.Atan2(ssum, csum)/(2*math.Pi))
   return mean.Add(time.Duration(dayFrac * 24 * float64(time.Hour))), nil

}</lang>

Output:

23:47:43

J

use avgAngleR from Averages/Mean angle#J <lang J>require 'types/datetime' parseTimes=: ([: _&".;._2 ,&':');._2 secsFromTime=: 24 60 60 #. ] NB. convert from time to seconds rft=: 2r86400p1 * secsFromTime NB. convert from time to radians meanTime=: 'hh:mm:ss' fmtTime [: secsFromTime [: avgAngleR&.rft parseTimes</lang>

Example Use <lang J> meanTime '23:00:17 23:40:20 00:12:45 00:17:19 ' 23:47:43</lang>

Mathematica

<lang mathematica>meanTime[list_] :=

 StringJoin@
  Riffle[ToString /@ 
      Floor@{Mod[24 #, 24], Mod[24*60 #, 60], Mod[24*60*60 #, 60]} &[
    Arg[Mean[
       Exp[FromDigits[ToExpression@StringSplit[#, ":"], 60] & /@ 
           list/(24*60*60) 2 Pi I]]]/(2 Pi)], ":"];

meanTime[{"23:00:17", "23:40:20", "00:12:45", "00:17:19"}]</lang>

Output:

23:47:43

OCaml

<lang ocaml>let pi_twice = 2.0 *. 3.14159_26535_89793_23846_2643 let day = float (24 * 60 * 60)

let rad_of_time t =

 t *. pi_twice /. day

let time_of_rad r =

 r *. day /. pi_twice

let mean_angle angles =

 let sum_sin = List.fold_left (fun sum a -> sum +. sin a) 0.0 angles
 and sum_cos = List.fold_left (fun sum a -> sum +. cos a) 0.0 angles in
 atan2 sum_sin sum_cos

let mean_time times =

 let angles = List.map rad_of_time times in
 let t = time_of_rad (mean_angle angles) in
 if t < 0.0 then t +. day else t

let parse_time t =

 Scanf.sscanf t "%d:%d:%d" (fun h m s -> float (s + m * 60 + h * 3600))

let round x = int_of_float (floor (x +. 0.5))

let string_of_time t =

 let t = round t in
 let h = t / 3600 in
 let rem = t mod 3600 in
 let m = rem / 60 in
 let s = rem mod 60 in
 Printf.sprintf "%d:%d:%d" h m s

let () =

 let times = ["23:00:17"; "23:40:20"; "00:12:45"; "00:17:19"] in
 Printf.printf "The mean time of [%s] is: %s\n"
   (String.concat "; " times)
   (string_of_time (mean_time (List.map parse_time times)))</lang>

Output:

The mean time of [23:00:17; 23:40:20; 00:12:45; 00:17:19] is: 23:47:43

PARI/GP

<lang parigp>meanAngle(v)=atan(sum(i=1,#v,sin(v[i]))/sum(i=1,#v,cos(v[i])))%(2*Pi) meanTime(v)=my(x=meanAngle(2*Pi*apply(u->u[1]/24+u[2]/1440+u[3]/86400, v))*12/Pi); [x\1, 60*(x-=x\1)\1, 60*(60*x-60*x\1)] meanTime([[23,0,17], [23,40,20], [0,12,45], [0,17,19]])</lang> Output:

[23, 47, 43.361528520325019522213261334501251061]

Perl 6

<lang perl6>sub tod2rad($_) { [+](.comb(/\d+/) Z* 3600,60,1) * pi / 43200 }

sub rad2tod ($r) {

   my $x = $r * 43200 / pi;
   (($x xx 3 Z/ 3600,60,1) Z% 24,60,60).fmt('%02d',':');

}

sub phase ($c) { $c.polar[1] }

sub mean-time (@t) { rad2tod phase [+] map { cis tod2rad $_ }, @t }

say mean-time($_).fmt("%s is the mean time of "), $_ for

   ["23:00:17", "23:40:20", "00:12:45", "00:17:19"];</lang>

Output:

23:47:43 is the mean time of 23:00:17 23:40:20 00:12:45 00:17:19

PicoLisp

<lang PicoLisp>(load "@lib/math.l")

(de meanTime (Lst)

  (let Tim
     (*/
        (atan2
           (sum '((S) (sin (*/ ($tim S) pi 43200))) Lst)
           (sum '((S) (cos (*/ ($tim S) pi 43200))) Lst) )
        43200 pi )
     (tim$ (% (+ Tim 86400) 86400) T) ) )</lang>

Test: <lang PicoLisp>: (meanTime '("23:00:17" "23:40:20" "00:12:45" "00:17:19")) -> "23:47:43"</lang>

Python

<lang python>from cmath import rect, phase from math import radians, degrees

def mean_angle(deg):

   return degrees(phase(sum(rect(1, radians(d)) for d in deg)/len(deg)))

def mean_time(times):

   t = (time.split(':') for time in times)
   seconds = ((float(s) + int(m) * 60 + int(h) * 3600) 
              for h, m, s in t)
   day = 24 * 60 * 60
   to_angles = [s * 360. / day for s in seconds]
   mean_as_angle = mean_angle(to_angles)
   mean_seconds = mean_as_angle * day / 360.
   if mean_seconds < 0:
       mean_seconds += day
   h, m = divmod(mean_seconds, 3600)
   m, s = divmod(m, 60)
   return '%02i:%02i:%02i' % (h, m, s)

if __name__ == '__main__':

   print( mean_time(["23:00:17", "23:40:20", "00:12:45", "00:17:19"]) )</lang>

Output

23:47:43