Averages/Mean time of day: Difference between revisions
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{{task|Date and time}} |
{{task|Date and time}} |
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{{task heading}} |
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A particular activity of bats occurs at these times of the day: |
A particular activity of bats occurs at these times of the day: |
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:<tt>23:00:17</tt>, <tt>23:40:20</tt>, <tt>00:12:45</tt>, <tt>00:17:19</tt> |
:<tt>23:00:17</tt>, <tt>23:40:20</tt>, <tt>00:12:45</tt>, <tt>00:17:19</tt> |
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compute and show the average time of the nocturnal activity |
compute and show the average time of the nocturnal activity |
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to an accuracy of one second of time. |
to an accuracy of one second of time. |
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{{task heading|See also}} |
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{{Related tasks/Statistical measures}} |
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<hr> |
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=={{header|AutoHotkey}}== |
=={{header|AutoHotkey}}== |
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Revision as of 14:48, 21 August 2016
You are encouraged to solve this task according to the task description, using any language you may know.
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 there are twenty-four hours in a day, which is analogous to there 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 the average time of the nocturnal activity to an accuracy of one second of time.
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AutoHotkey
<lang AutoHotkey>MsgBox, % "The mean time is: " MeanTime(["23:00:17", "23:40:20", "00:12:45", "00:17:19"])
MeanTime(t, x=0, y=0) { static c := ATan(1) / 45 for k, v in t { n := StrSplit(v, ":") r := c * (n[1] * 3600 + n[2] * 60 + n[3]) / 240 x += Cos(r) y += Sin(r) } r := atan2(x, y) / c r := (r < 0 ? r + 360 : r) / 15 h := SubStr("00" Round(r // 1, 0), -1) s := SubStr("00" Round(Mod(m := Mod(r, 1) * 60, 1) * 60, 0), -1) m := SubStr("00" Round(m // 1, 0), -1) return, h ":" m ":" s }
atan2(x, y) {
return dllcall("msvcrt\atan2", "Double",y, "Double",x, "CDECL Double")
}</lang>
- Output:
The mean time is: 23:47:43
AWK
<lang AWK>#!/usr/bin/awk -f {
c = atan2(0,-1)/(12*60*60);
x=0.0; y=0.0;
for (i=1; i<=NF; i++) {
split($i,a,":");
p = (a[1]*3600+a[2]*60+a[3])*c; x += sin(p); y += cos(p);
}
p = atan2(x,y)/c;
if (p<0) p += 24*60*60;
print strftime("%T",p,1);
}</lang>
$ echo 23:00:17, 23:40:20, 00:12:45, 00:17:19 | awk -f mean_time_of_day.awk 23:47:43
BBC BASIC
<lang bbcbasic> nTimes% = 4
DATA 23:00:17, 23:40:20, 00:12:45, 00:17:19
DIM angles(nTimes%-1)
FOR N% = 0 TO nTimes%-1
READ tim$
angles(N%) = FNtimetoangle(tim$)
NEXT
PRINT "Mean time is " FNangletotime(FNmeanangle(angles(), nTimes%))
END
DEF FNtimetoangle(t$)
LOCAL A%, I%
REPEAT
A% = A% * 60 + VAL(t$)
I% = INSTR(t$, ":")
t$ = MID$(t$, I%+1)
UNTIL I% = 0
= A% / 240 - 180
DEF FNangletotime(a)
LOCAL A%, I%, t$
A% = INT((a + 180) * 240 + 0.5)
FOR I% = 1 TO 3
t$ = RIGHT$("0" + STR$(A% MOD 60), 2) + ":" + t$
A% DIV= 60
NEXT
= LEFT$(t$)
DEF FNmeanangle(angles(), N%)
LOCAL I%, addsin, addcos
FOR I% = 0 TO N%-1
addsin += SINRADangles(I%)
addcos += COSRADangles(I%)
NEXT
= DEGFNatan2(addsin, addcos)
DEF FNatan2(y,x) : ON ERROR LOCAL = SGN(y)*PI/2
IF x>0 THEN = ATN(y/x) ELSE IF y>0 THEN = ATN(y/x)+PI ELSE = ATN(y/x)-PI</lang>
- Output:
Mean time is 23:47:43
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
C#
<lang csharp>using System; using System.Collections.Generic; using System.Linq; using System.Text;
namespace RosettaCode {
class Program
{
static void Main(string[] args)
{
Func<TimeSpan, double> TimeToDegrees = (time) =>
360 * time.Hours / 24.0 +
360 * time.Minutes / (24 * 60.0) +
360 * time.Seconds / (24 * 3600.0);
Func<List<double>, double> MeanAngle = (angles) =>
{
double y_part = 0.0d, x_part = 0.0d;
int numItems = angles.Count;
for (int i = 0; i < numItems; i++)
{
x_part += Math.Cos(angles[i] * Math.PI / 180);
y_part += Math.Sin(angles[i] * Math.PI / 180);
}
return Math.Atan2(y_part / numItems, x_part / numItems) * 180 / Math.PI;
};
Func<double, TimeSpan> TimeFromDegrees = (angle) =>
new TimeSpan(
(int)(24 * 60 * 60 * angle / 360) / 3600,
((int)(24 * 60 * 60 * angle / 360) % 3600 - (int)(24 * 60 * 60 * angle / 360) % 60) / 60,
(int)(24 * 60 * 60 * angle / 360) % 60);
List<double> digitimes = new List<double>();
TimeSpan digitime;
string input;
Console.WriteLine("Enter times, end with no input: ");
do
{
input = Console.ReadLine();
if (!(string.IsNullOrWhiteSpace(input)))
{
if (TimeSpan.TryParse(input, out digitime))
digitimes.Add(TimeToDegrees(digitime));
else
Console.WriteLine("Seems this is wrong input: ignoring time");
}
} while (!string.IsNullOrWhiteSpace(input));
if(digitimes.Count() > 0)
Console.WriteLine("The mean time is : {0}", TimeFromDegrees(360 + MeanAngle(digitimes)));
}
}
} </lang>
- Output:
Enter times, end with no input: 23:00:17 23:40:20 00:12:45 00:17:19 The mean time is : 23:47:43
D
<lang d>import std.stdio, std.range, std.algorithm, std.complex, std.math,
std.format, std.conv;
double radians(in double d) pure nothrow @safe @nogc {
return d * PI / 180;
}
double degrees(in double r) pure nothrow @safe @nogc {
return r * 180 / PI;
}
double meanAngle(in double[] deg) pure nothrow @safe @nogc {
return (deg.map!(d => fromPolar(1, d.radians)).sum / deg.length).arg.degrees;
}
string meanTime(in string[] times) pure @safe {
auto t = times.map!(times => times.split(':').to!(int[3]));
assert(t.all!(hms => 24.iota.canFind(hms[0]) &&
60.iota.canFind(hms[1]) &&
60.iota.canFind(hms[2])),
"Invalid time");
auto seconds = t.map!(hms => hms[2] + hms[1] * 60 + hms[0] * 3600); enum day = 24 * 60 * 60; const to_angles = seconds.map!(s => s * 360.0 / day).array;
immutable mean_as_angle = to_angles.meanAngle;
auto mean_seconds_fp = mean_as_angle * day / 360.0;
if (mean_seconds_fp < 0)
mean_seconds_fp += day;
immutable mean_seconds = mean_seconds_fp.to!uint;
immutable h = mean_seconds / 3600;
immutable m = mean_seconds % 3600;
return "%02d:%02d:%02d".format(h, m / 60, m % 60);
}
void main() @safe {
["23:00:17", "23:40:20", "00:12:45", "00:17:19"].meanTime.writeln;
}</lang>
- Output:
23:47:43
EchoLisp
<lang scheme>
- string hh
- mm
- ss to radians
(define (time->radian time)
(define-values (h m s) (map string->number (string-split time ":"))) (+ (* h (/ PI 12)) (* m (/ PI 12 60)) (* s (/ PI 12 3600))))
- radians to string hh
- mm;ss
(define (radian->time rad) (when (< rad 0) (+= rad (* 2 PI))) (define t (round (/ (* 12 3600 rad) PI))) (define h (quotient t 3600)) (define m (quotient (- t (* h 3600)) 60)) (define s (- t (* 3600 h) (* 60 m))) (string-join (map number->string (list h m s)) ":"))
(define (mean-time times) (radian->time (angle (for/sum ((t times)) (make-polar 1 (time->radian t))))))
(mean-time '{"23:00:17" "23:40:20" "00:12:45" "00:17:19"})
→ "23:47:43"
</lang>
Erlang
<lang Erlang> -module( mean_time_of_day ). -export( [from_times/1, task/0] ).
from_times( Times ) -> Seconds = [seconds_from_time(X) || X <- Times], Degrees = [degrees_from_seconds(X) || X <- Seconds], Average = mean_angle:from_degrees( Degrees ), time_from_seconds( seconds_from_degrees(Average) ).
task() -> Times = ["23:00:17", "23:40:20", "00:12:45", "00:17:19"], io:fwrite( "The mean time of ~p is: ~p~n", [Times, from_times(Times)] ).
degrees_from_seconds( Seconds ) when Seconds < (24 * 3600) -> (Seconds * 360) / (24 * 3600).
seconds_from_degrees( Degrees ) when Degrees < 0 -> seconds_from_degrees( Degrees + 360 ); seconds_from_degrees( Degrees ) when Degrees < 360 -> (Degrees * 24 * 3600) / 360.
seconds_from_time( Time ) -> {ok, [Hours, Minutes, Seconds], _Rest} = io_lib:fread( "~d:~d:~d", Time ), Hours * 3600 + Minutes * 60 + Seconds.
time_from_seconds( Seconds_float ) -> Seconds = erlang:round( Seconds_float ), Hours = Seconds div 3600, Minutes = (Seconds - (Hours * 3600)) div 60, Secs = Seconds - (Hours * 3600) - (Minutes * 60), lists:flatten( io_lib:format("~2.10.0B:~2.10.0B:~2.10.0B", [Hours, Minutes, Secs]) ). </lang>
- Output:
17> mean_time_of_day:task(). The mean time of ["23:00:17","23:40:20","00:12:45","00:17:19"] is: "23:47:43"
Euphoria
<lang Euphoria> include std/console.e include std/math.e include std/mathcons.e include std/sequence.e include std/get.e
function T2D(sequence TimeSeq) return (360 * TimeSeq[1] / 24 + 360 * TimeSeq[2] / (24 * 60) + 360 * TimeSeq[3] / (24 * 3600)) end function
function D2T(atom angle) sequence TimeSeq = {0,0,0} atom seconds = 24 * 60 * 60 * angle / 360
TimeSeq[3] = mod(seconds,60) TimeSeq[2] = (mod(seconds,3600) - TimeSeq[3]) / 60 TimeSeq[1] = seconds / 3600
return TimeSeq end function
function MeanAngle(sequence angles) atom x = 0, y = 0 integer l = length(angles)
for i = 1 to length(angles) do x += cos(angles[i] * PI / 180) y += sin(angles[i] * PI / 180) end for
return atan2(y / l, x / l) * 180 / PI end function
sequence TimeEntry, TimeList = {}, TimeSeq
puts(1,"Enter times. Enter with no input to end\n") while 1 do
TimeEntry = prompt_string("")
if equal(TimeEntry,"") then -- no more entries
for i = 1 to length(TimeList) do
TimeList[i] = split(TimeList[i],":") -- split the times into sequences
for j = 1 to 3 do
TimeList[i][j] = defaulted_value(TimeList[i][j],0) -- convert to numerical values
end for
end for
exit
end if
TimeList = append(TimeList,TimeEntry)
end while
sequence AngleList = repeat({},length(TimeList))
for i = 1 to length(AngleList) do AngleList[i] = T2D(TimeList[i]) end for
sequence MeanTime = D2T(360+MeanAngle(AngleList))
printf(1,"\nMean Time: %d:%d:%d\n",MeanTime)
if getc(0) then end if
</lang>
- Output:
Enter Times. Enter with no input to end. 23:00:17 23:40:20 00:12:45 00:17:19 Mean Time: 23:47:43
F#
<lang fsharp>open System open System.Numerics
let deg2rad d = d * Math.PI / 180. let rad2deg r = r * 180. / Math.PI let makeComplex = fun r -> Complex.FromPolarCoordinates(1., r) // 1 msec = 10000 ticks let time2deg = TimeSpan.Parse >> (fun ts -> ts.Ticks) >> (float) >> (*) (10e-9/24.) let deg2time = (*) (24. * 10e7) >> (int64) >> TimeSpan
[<EntryPoint>] let main argv =
let msg = "Average time for [" + (String.Join("; ",argv)) + "] is"
argv
|> Seq.map (time2deg >> deg2rad >> makeComplex)
|> Seq.fold (fun x y -> Complex.Add(x,y)) Complex.Zero
|> fun c -> c.Phase |> rad2deg
|> fun d -> if d < 0. then d + 360. else d
|> deg2time |> fun t -> t.ToString(@"hh\:mm\:ss")
|> printfn "%s: %s" msg
0</lang>
- Output:
>RosettaCode 23:00:17 23:40:20 00:12:45 00:17:19 Average time for [23:00:17; 23:40:20; 00:12:45; 00:17:19] is: 23:47:43
Fortran
<lang fortran> program mean_time_of_day
implicit none integer(kind=4), parameter :: dp = kind(0.0d0)
type time_t integer(kind=4) :: hours, minutes, seconds end type
character(len=8), dimension(4), parameter :: times = & (/ '23:00:17', '23:40:20', '00:12:45', '00:17:19' /) real(kind=dp), dimension(size(times)) :: angles real(kind=dp) :: mean
angles = time_to_angle(str_to_time(times)) mean = mean_angle(angles) if (mean < 0) mean = 360 + mean
write(*, fmt='(I2.2, :, I2.2, :, I2.2)') angle_to_time(mean)
contains
real(kind=dp) function mean_angle(angles) real(kind=dp), dimension(:), intent (in) :: angles real(kind=dp) :: x, y
x = sum(sin(radians(angles)))/size(angles) y = sum(cos(radians(angles)))/size(angles)
mean_angle = degrees(atan2(x, y)) end function
elemental real(kind=dp) function radians(angle) real(kind=dp), intent (in) :: angle real(kind=dp), parameter :: pi = 4d0*atan(1d0) radians = angle/180*pi end function
elemental real(kind=dp) function degrees(angle) real(kind=dp), intent (in) :: angle real(kind=dp), parameter :: pi = 4d0*atan(1d0) degrees = 180*angle/pi end function
elemental type(time_t) function str_to_time(str) character(len=*), intent (in) :: str ! Assuming time in format hh:mm:ss read(str, fmt='(I2, 1X, I2, 1X, I2)') str_to_time end function
elemental real(kind=dp) function time_to_angle(time) result (res) type(time_t), intent (in) :: time
real(kind=dp) :: seconds real(kind=dp), parameter :: seconds_in_day = 24*60*60
seconds = time%seconds + 60*time%minutes + 60*60*time%hours res = 360*seconds/seconds_in_day end function
elemental type(time_t) function angle_to_time(angle) real(kind=dp), intent (in) :: angle
real(kind=dp) :: seconds real(kind=dp), parameter :: seconds_in_day = 24*60*60
seconds = seconds_in_day*angle/360d0 angle_to_time%hours = int(seconds/60d0/60d0) seconds = mod(seconds, 60d0*60d0) angle_to_time%minutes = int(seconds/60d0) angle_to_time%seconds = mod(seconds, 60d0) end function
end program </lang>
- Output:
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
Groovy
Solution: <lang groovy>import static java.lang.Math.*
final format = 'HH:mm:ss', clock = PI / 12, millisPerHr = 3600*1000 final tzOffset = new Date(0).timezoneOffset / 60 def parseTime = { time -> (Date.parse(format, time).time / millisPerHr) - tzOffset } def formatTime = { time -> new Date((time + tzOffset) * millisPerHr as int).format(format) } def mean = { list, closure -> list.sum(closure)/list.size() } def meanTime = { ... timeStrings ->
def times = timeStrings.collect(parseTime)
formatTime(atan2( mean(times) { sin(it * clock) }, mean(times) { cos(it * clock) }) / clock)
}</lang>
Test: <lang groovy>println (meanTime("23:00:17", "23:40:20", "00:12:45", "00:17:19"))</lang>
- Output:
23:47:43
Haskell
<lang haskell>import Data.Complex (cis, phase) import Data.List.Split (splitOn) import Text.Printf (printf)
timeToRadians :: String -> Float timeToRadians time =
let hours:minutes:seconds:_ = splitOn ":" time
s = fromIntegral (read seconds :: Int)
m = fromIntegral (read minutes :: Int)
h = fromIntegral (read hours :: Int)
in (2*pi)*(h+ (m + s/60.0 )/60.0 )/24.0
radiansToTime :: Float -> String radiansToTime r =
let tau = pi*2
(_,fDay) = properFraction (r / tau) :: (Int, Float)
fDayPositive = if fDay < 0 then 1.0+fDay else fDay
(hours, fHours) = properFraction $ 24.0 * fDayPositive
(minutes, fMinutes) = properFraction $ 60.0 * fHours
seconds = 60.0 * fMinutes
in printf "%0d" (hours::Int) ++ ":" ++ printf "%0d" (minutes::Int) ++ ":" ++ printf "%0.0f" (seconds::Float)
meanAngle :: [Float] -> Float meanAngle = phase . sum . map cis
main :: IO () main = putStrLn $ radiansToTime $ meanAngle $ map timeToRadians ["23:00:17", "23:40:20", "00:12:45", "00:17:19"] </lang>
- Output:
23:47:43
Icon and Unicon
<lang>procedure main(A)
every put(B := [], ct2a(!A)) write(ca2t(meanAngle(B)))
end
procedure ct2a(t)
t ? {s := ((1(move(2),move(1))*60 + 1(move(2),move(1)))*60 + move(2))}
return (360.0/86400.0) * s
end
procedure ca2t(a)
while a < 0 do a +:= 360.0 t := integer((86400.0/360.0)*a + 0.5) s := left(1(.t % 60, t /:= 60),2,"0") s := left(1(.t % 60, t /:= 60),2,"0")||":"||s s := left(t,2,"0")||":"||s return s
end
procedure meanAngle(A)
every (sumSines := 0.0) +:= sin(dtor(!A)) every (sumCosines := 0.0) +:= cos(dtor(!A)) return rtod(atan(sumSines/*A,sumCosines/*A))
end</lang>
Sample run:
->amtod 23:00:17 23:40:20 00:12:45 00:17:19 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>
jq
The "mean time" of two times that differ by 12 hours (e.g. ["00:00:00", "12:00:00"]) is not very well-defined, and is accordingly computed as null here. <lang jq># input: array of "h:m:s" def mean_time_of_day:
def pi: 4 * (1|atan); def to_radians: pi * . /(12*60*60); def from_radians: (. * 12*60*60) / pi;
def secs2time: # produce "hh:mm:ss" string def pad: tostring | (2 - length) * "0" + .; "\(./60/60 % 24 | pad):\(./60 % 60 | pad):\(. % 60 | pad)";
def round: if . < 0 then -1 * ((- .) | round) | if . == -0 then 0 else . end else floor as $x | if (. - $x) < 0.5 then $x else $x+1 end end;
map( split(":")
| map(tonumber)
| (.[0]*3600 + .[1]*60 + .[2])
| to_radians )
| (map(sin) | add) as $y
| (map(cos) | add) as $x
| if $x == 0 then (if $y > 3e-14 then pi/2 elif $y < -3e-14 then -(pi/2) else null end)
else ($y / $x) | atan
end
| if . == null then null
else from_radians
| if (.<0) then . + (24*60*60) else . end
| round
| secs2time
end ;</lang>
Examples <lang jq>["0:0:0", "12:0:0" ], ["0:0:0", "24:0:0" ], ["1:0:0", "1:0:0" ], ["20:0:0", "4:0:0" ], ["20:0:0", "4:0:2" ], ["23:0:0", "23:0:0" ], ["23:00:17", "23:40:20", "00:12:45", "00:17:19"] | mean_time_of_day</lang>
- Output:
<lang sh>$ jq -r -n -f Mean_time_of_day.jq null 00:00:00 01:00:00 00:00:00 00:00:01 23:00:00 23:47:43</lang>
Liberty BASIC
<lang lb> global pi pi = acs(-1)
Print "Average of:" for i = 1 to 4
read t$ print t$ a=time2angle(t$) ss=ss+sin(a) sc=sc+cos(a)
next a=atan2(ss,sc) if a<0 then a=a+2*pi print "is ";angle2time$(a)
end data "23:00:17", "23:40:20", "00:12:45", "00:17:19"
function nn$(n)
nn$=right$("0";n, 2)
end function
function angle2time$(a)
a=int(a/2/pi*24*60*60) ss=a mod 60 a=int(a/60) mm=a mod 60 hh=int(a/60) angle2time$=nn$(hh);":";nn$(mm);":";nn$(ss)
end function
function time2angle(time$)
hh=val(word$(time$,1,":")) mm=val(word$(time$,2,":")) ss=val(word$(time$,3,":")) time2angle=2*pi*(60*(60*hh+mm)+ss)/24/60/60
end function
function atan2(y, x)
On Error GoTo [DivZero] 'If y is 0 catch division by zero error
atan2 = (2 * (atn((sqr((x * x) + (y * y)) - x)/ y)))
exit function
[DivZero]
atan2 = (y=0)*(x<0)*pi
End Function </lang>
- Output:
Average of: 23:00:17 23:40:20 00:12:45 00:17:19 is 23:47:43
Mathematica / Wolfram Language
<lang mathematica>meanTime[list_] :=
StringJoin@
Riffle[ToString /@
Floor@{Mod[24 #, 24], Mod[24*60 #, 60], Mod[24*60*60 #, 60]} &[
Arg[Mean[
Exp[FromDigits[ToExpression@StringSplit[#, ":"], 60] & /@
list/(24*60*60) 2 Pi I]]]/(2 Pi)], ":"];
meanTime[{"23:00:17", "23:40:20", "00:12:45", "00:17:19"}]</lang>
- Output:
23:47:43
MATLAB / Octave
<lang MATLAB>function t = mean_time_of_day(t)
c = pi/(12*60*60); for k=1:length(t)
a = sscanf(t{k},'%d:%d:%d'); phi(k) = (a(1)*3600+a(2)*60+a(3));
end; d = angle(mean(exp(i*phi*c)))/(2*pi); % days if (d<0) d += 1; t = datestr(d,"HH:MM:SS");
end; </lang>
mean_time_of_day({'23:00:17', '23:40:20', '00:12:45', '00:17:19'})
ans = 23:47:43
Nim
<lang nim>import math, complex, strutils
proc rect(r, phi): Complex = (r * cos(phi), sin(phi)) proc phase(c): float = arctan2(c.im, c.re)
proc radians(x): float = (x * Pi) / 180.0 proc degrees(x): float = (x * 180.0) / Pi
proc meanAngle(deg): float =
var c: Complex for d in deg: c += rect(1.0, radians(d)) degrees(phase(c / float(deg.len)))
proc meanTime(times): string =
const day = 24 * 60 * 60
let
angles = times.map(proc(time: string): float =
let t = time.split(":")
(t[2].parseInt + t[1].parseInt * 60 + t[0].parseInt * 3600) * 360 / day)
ms = (angles.meanAngle * day / 360 + day) mod day
(h,m,s) = (ms.int div 3600, (ms.int mod 3600) div 60, ms.int mod 60)
align($h, 2, '0') &":"& align($m, 2, '0') &":"& align($s, 2, '0')
echo meanTime(["23:00:17", "23:40:20", "00:12:45", "00:17:19"])</lang>
- Output:
23:47:43
Oberon-2
<lang oberon2> MODULE AvgTimeOfDay; IMPORT
M := LRealMath, T := NPCT:Tools, Out := NPCT:Console;
CONST
secsDay = 86400; secsHour = 3600; secsMin = 60;
toRads = M.pi / 180;
VAR
h,m,s: LONGINT; data: ARRAY 4 OF LONGREAL;
PROCEDURE TimeToDeg(time: STRING): LONGREAL; VAR
parts: ARRAY 3 OF STRING; h,m,s: LONGREAL;
BEGIN
T.Split(time,':',parts); h := T.StrToInt(parts[0]); m := T.StrToInt(parts[1]); s := T.StrToInt(parts[2]); RETURN (h * secsHour + m * secsMin + s) * 360 / secsDay;
END TimeToDeg;
PROCEDURE DegToTime(d: LONGREAL; VAR h,m,s: LONGINT); VAR
ds: LONGREAL; PROCEDURE Mod(x,y: LONGREAL): LONGREAL; VAR c: LONGREAL; BEGIN c := ENTIER(x / y); RETURN x - c * y END Mod;
BEGIN
ds := Mod(d,360.0) * secsDay / 360.0; h := ENTIER(ds / secsHour); m := ENTIER(Mod(ds,secsHour) / secsMin); s := ENTIER(Mod(ds,secsMin));
END DegToTime;
PROCEDURE Mean(g: ARRAY OF LONGREAL): LONGREAL; VAR
i,l: LONGINT; sumSin, sumCos: LONGREAL;
BEGIN
i := 0;l := LEN(g);sumSin := 0.0;sumCos := 0.0; WHILE i < l DO sumSin := sumSin + M.sin(g[i] * toRads); sumCos := sumCos + M.cos(g[i] * toRads); INC(i) END; RETURN M.arctan2(sumSin / l,sumCos / l) * 180 / M.pi;
END Mean;
BEGIN
data[0] := TimeToDeg("23:00:17");
data[1] := TimeToDeg("23:40:20");
data[2] := TimeToDeg("00:12:45");
data[3] := TimeToDeg("00:17:19");
DegToTime(Mean(data),h,m,s);
Out.String(":> ");Out.Int(h,0);Out.Char(':');Out.Int(m,0);Out.Char(':');Out.Int(s,0);Out.Ln
END AvgTimeOfDay. </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
ooRexx
<lang oorexx>/* REXX ---------------------------------------------------------------
- 25.06.2014 Walter Pachl
- --------------------------------------------------------------------*/
times='23:00:17 23:40:20 00:12:45 00:17:19' sum=0 day=86400 x=0 y=0 Do i=1 To words(times) /* loop over times */
time.i=word(times,i) /* pick a time */ alpha.i=t2a(time.i) /* convert to angle (degrees) */ /* Say time.i format(alpha.i,6,9) */ x=x+rxcalcsin(alpha.i) /* accumulate sines */ y=y+rxcalccos(alpha.i) /* accumulate cosines */ End
ww=rxcalcarctan(x/y) /* compute average angle */ ss=ww*86400/360 /* convert to seconds */ If ss<0 Then ss=ss+day /* avoid negative value */ m=ss%60 /* split into hh mm ss */ s=ss-m*60 h=m%60 m=m-h*60 Say f2(h)':'f2(m)':'f2(s) /* show the mean time */ Exit
t2a: Procedure Expose day /* convert time to angle */
Parse Arg hh ':' mm ':' ss sec=(hh*60+mm)*60+ss If sec>(day/2) Then sec=sec-day a=360*sec/day Return a
f2: return right(format(arg(1),2,0),2,0)
- requires rxmath library</lang>
- Output:
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, round(60*(60*x-60*x\1))] meanTime([[23,0,17], [23,40,20], [0,12,45], [0,17,19]])</lang>
- Output:
[23, 47, 43]
Perl 6
<lang perl6>sub tod2rad($_) { [+](.comb(/\d+/) Z* 3600,60,1) * tau / 86400 }
sub rad2tod ($r) {
my $x = $r * 86400 / tau;
(($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 $_ }, @t }
my @times = ["23:00:17", "23:40:20", "00:12:45", "00:17:19"];
say "{ mean-time(@times) } is the mean time of @times[]";</lang>
- Output:
23:47:43 is the mean time of 23:00:17 23:40:20 00:12:45 00:17:19
Phix
<lang Phix>function atan2(atom y, atom x)
return 2*arctan((sqrt(power(x,2)+power(y,2))-x)/y)
end function
function MeanAngle(sequence angles) atom x=0, y=0, ai_rad integer l=length(angles)
for i=1 to l do
ai_rad = angles[i]*PI/180
x += cos(ai_rad)
y += sin(ai_rad)
end for
if abs(x)<1e-16 then return "not meaningful" end if
return atan2(y,x)*180/PI
end function
function toSecAngle(integer hours, integer minutes, integer seconds)
return ((hours*60+minutes)*60+seconds)/(24*60*60)*360
end function
constant Times = {toSecAngle(23,00,17),
toSecAngle(23,40,20),
toSecAngle(00,12,45),
toSecAngle(00,17,19)}
function toHMS(object s)
if not string(s) then
if s<0 then s+=360 end if
s = 24*60*60*s/360
s = sprintf("%02d:%02d:%02d",{floor(s/3600),floor(remainder(s,3600)/60),remainder(s,60)})
end if
return s
end function
printf(1,"Mean Time is %s\n",{toHMS(MeanAngle(Times))}) {} = wait_key()</lang>
- Output:
Mean Time is 23:47:43
PHP
<lang PHP> <?php function time2ang($tim) {
if (!is_string($tim)) return $tim;
$parts = explode(':',$tim);
if (count($parts)!=3) return $tim;
$sec = ($parts[0]*3600)+($parts[1]*60)+$parts[2];
$ang = 360.0 * ($sec/86400.0);
return $ang;
} function ang2time($ang) {
if (!is_numeric($ang)) return $ang;
$sec = 86400.0 * $ang / 360.0;
$parts = array(floor($sec/3600),floor(($sec % 3600)/60),$sec % 60);
$tim = sprintf('%02d:%02d:%02d',$parts[0],$parts[1],$parts[2]);
return $tim;
} function meanang($ang) {
if (!is_array($ang)) return $ang;
$sins = 0.0;
$coss = 0.0;
foreach($ang as $a) {
$sins += sin(deg2rad($a));
$coss += cos(deg2rad($a));
}
$avgsin = $sins / (0.0+count($ang));
$avgcos = $coss / (0.0+count($ang));
$avgang = rad2deg(atan2($avgsin,$avgcos));
while ($avgang < 0.0) $avgang += 360.0;
return $avgang;
} $bats = array('23:00:17','23:40:20','00:12:45','00:17:19'); $angs = array(); foreach ($bats as $t) $angs[] = time2ang($t); $ma = meanang($angs); $result = ang2time($ma); print "The mean time of day is $result (angle $ma).\n"; ?> </lang>
- Output:
The mean time of day is 23:47:43 (angle 356.9306730355).
PicoLisp
<lang PicoLisp>(load "@lib/math.l")
(de meanTime (Lst)
(let Tim
(*/
(atan2
(sum '((S) (sin (*/ ($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>
PL/I
<lang pli>*process source attributes xref;
avt: Proc options(main);
/*--------------------------------------------------------------------
* 25.06.2014 Walter Pachl taken from REXX
*-------------------------------------------------------------------*/
Dcl (addr,hbound,sin,cos,atan) Builtin;
Dcl sysprint Print;
Dcl times(4) Char(8) Init('23:00:17','23:40:20','00:12:45','00:17:19');
Dcl time Char(8);
Dcl (alpha,x,y,ss,ww) Dec Float(18) Init(0);
Dcl day Bin Fixed(31) Init(86400);
Dcl pi Dec Float(18) Init(3.14159265358979323846);
Dcl (i,h,m,s) bin Fixed(31) Init(0);
Do i=1 To hbound(times); /* loop over times */
time=times(i); /* pick a time */
alpha=t2a(time); /* convert to angle (radians) */
x=x+sin(alpha); /* accumulate sines */
y=y+cos(alpha); /* accumulate cosines */
End;
ww=atan(x/y); /* compute average angle */
ss=ww*day/(2*pi); /* convert to seconds */
If ss<0 Then ss=ss+day; /* avoid negative value */
m=ss/60; /* split into hh mm ss */
s=ss-m*60;
h=m/60;
m=m-h*60;
Put Edit(h,':',m,':',s)(Skip,3(p'99',a));
t2a: Procedure(t) Returns(Bin Float(18)); /* convert time to angle */
Dcl t Char(8);
Dcl 1 tt Based(addr(t)),
2 hh Pic'99',
2 * Char(1),
2 mm Pic'99',
2 * Char(1),
2 ss Pic'99';
Dcl sec Bin Fixed(31);
Dcl a Bin Float(18);
sec=(hh*60+mm)*60+ss;
If sec>(day/2) Then
sec=sec-day;
a=2*pi*sec/day;
Return (a);
End;
End;</lang>
- Output:
23:47:43
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
Racket
<lang racket>
- lang racket
(define (mean-angle/radians as)
(define n (length as))
(atan (* (/ 1 n) (for/sum ([αj as]) (sin αj)))
(* (/ 1 n) (for/sum ([αj as]) (cos αj)))))
(define (mean-time times)
(define secs/day (* 60 60 24))
(define (time->deg time)
(/ (for/fold ([sum 0]) ([t (map string->number (string-split time ":"))])
(+ (* 60 sum) t))
secs/day 1/360 (/ 180 pi)))
(define secs
(modulo (inexact->exact (round (* (mean-angle/radians (map time->deg times))
(/ 180 pi) 1/360 secs/day)))
secs/day))
(let loop ([s secs] [ts '()])
(if (zero? s) (string-join ts ":")
(let-values ([(q r) (quotient/remainder s 60)])
(loop q (cons (~r r #:min-width 2 #:pad-string "0") ts))))))
(mean-time '("23:00:17" "23:40:20" "00:12:45" "00:17:19")) </lang>
- Output:
"23:47:43"
REXX
<lang rexx>/* REXX ---------------------------------------------------------------
- 25.06.2014 Walter Pachl
- taken from ooRexx using my very aged sin/cos/artan functions
- --------------------------------------------------------------------*/
times='23:00:17 23:40:20 00:12:45 00:17:19' sum=0 day=86400 pi=3.14159265358979323846264 x=0 y=0 Do i=1 To words(times) /* loop over times */
time.i=word(times,i) /* pick a time */ alpha.i=t2a(time.i) /* convert to angle (radians) */ /* Say time.i format(alpha.i,6,9) */ x=x+sin(alpha.i) /* accumulate sines */ y=y+cos(alpha.i) /* accumulate cosines */ End
ww=arctan(x/y) /* compute average angle */ ss=ww*86400/(2*pi) /* convert to seconds */ If ss<0 Then ss=ss+day /* avoid negative value */ m=ss%60 /* split into hh mm ss */ s=ss-m*60 h=m%60 m=m-h*60 Say f2(h)':'f2(m)':'f2(s) /* show the mean time */ Exit
t2a: Procedure Expose day pi /* convert time to angle */
Parse Arg hh ':' mm ':' ss sec=(hh*60+mm)*60+ss If sec>(day/2) Then sec=sec-day a=2*pi*sec/day Return a
f2: return right(format(arg(1),2,0),2,0)
sin: Procedure Expose pi
Parse Arg x prec=digits() Numeric Digits (2*prec) Do While x>pi x=x-pi End Do While x<-pi x=x+pi End o=x u=1 r=x Do i=3 By 2 ra=r o=-o*x*x u=u*i*(i-1) r=r+(o/u) If r=ra Then Leave End Numeric Digits prec Return r+0
cos: Procedure Expose pi
Parse Arg x prec=digits() Numeric Digits (2*prec) Numeric Fuzz 3 o=1 u=1 r=1 Do i=1 By 2 ra=r o=-o*x*x u=u*i*(i+1) r=r+(o/u) If r=ra Then Leave End Numeric Digits prec Return r+0
arctan: Procedure
Parse Arg x
prec=digits()
Numeric Digits (2*prec)
Numeric Fuzz 3
o=x
u=1
r=x
k=0
Do i=3 By 2
ra=r
o=-o*x*x
r=r+(o/i)
If r=ra Then
Leave
k=k+1
If k//1000=0 Then
Say i left(r,40) format(abs(o/i),15,5)
End
Numeric Digits (prec)
Return r+0</lang>
- Output:
23:47:43
Ruby
Using the methods at [angle]
<lang ruby>def time2deg(t)
raise "invalid time" unless m = t.match(/^(\d\d):(\d\d):(\d\d)$/)
hh,mm,ss = m[1..3].map {|e| e.to_i}
raise "invalid time" unless (0..23).include? hh and
(0..59).include? mm and
(0..59).include? ss
(hh*3600 + mm*60 + ss) * 360 / 86400.0
end
def deg2time(d)
sec = (d % 360) * 86400 / 360.0 "%02d:%02d:%02d" % [sec/3600, (sec%3600)/60, sec%60]
end
def mean_time(times)
deg2time(mean_angle(times.map {|t| time2deg t}))
end
puts mean_time ["23:00:17", "23:40:20", "00:12:45", "00:17:19"]</lang>
- Output:
23:47:43
Run BASIC
<lang runbasic>global pi pi = acs(-1)
Print "Average of:" for i = 1 to 4
read t$ print t$ a = time2angle(t$) ss = ss+sin(a) sc = sc+cos(a)
next a = atan2(ss,sc) if a < 0 then a = a + 2 * pi print "is ";angle2time$(a) end data "23:00:17", "23:40:20", "00:12:45", "00:17:19"
function nn$(n)
nn$ = right$("0";n, 2)
end function
function angle2time$(a)
a = int(a / 2 / pi * 24 * 60 * 60) ss = a mod 60 a = int(a / 60) mm=a mod 60 hh=int(a/60) angle2time$=nn$(hh);":";nn$(mm);":";nn$(ss)
end function
function time2angle(time$)
hh=val(word$(time$,1,":")) mm=val(word$(time$,2,":")) ss=val(word$(time$,3,":")) time2angle=2*pi*(60*(60*hh+mm)+ss)/24/60/60
end function
function atan2(y, x)
if y <> 0 then
atan2 = (2 * (atn((sqr((x * x) + (y * y)) - x)/ y)))
else
atan2 = (y=0)*(x<0)*pi
end if
End Function</lang>
Scala
<lang Scala>import java.time.LocalTime
import scala.compat.Platform
trait MeanAnglesComputation {
import scala.math.{Pi, atan2, cos, sin}
def meanAngle(angles: List[Double], convFactor: Double = 180.0 / Pi) = {
val sums = angles.foldLeft((.0, .0))((r, c) => {
val rads = c / convFactor
(r._1 + sin(rads), r._2 + cos(rads))
})
val result = atan2(sums._1, sums._2)
(result + (if (result.signum == -1) 2 * Pi else 0.0)) * convFactor
}
}
object MeanBatTime extends App with MeanAnglesComputation {
val dayInSeconds = 60 * 60 * 24
def times = batTimes.map(t => afterMidnight(t).toDouble)
def afterMidnight(twentyFourHourTime: String) = {
val t = LocalTime.parse(twentyFourHourTime)
(if (t.isBefore(LocalTime.NOON)) dayInSeconds else 0) + LocalTime.parse(twentyFourHourTime).toSecondOfDay
}
def batTimes = List("23:00:17", "23:40:20", "00:12:45", "00:17:19")
assert(LocalTime.MIN.plusSeconds(meanAngle(times, dayInSeconds).round).toString == "23:47:40")
println(s"Successfully completed without errors. [total ${Platform.currentTime - executionStart} ms]")
}</lang>
Sidef
Using the mean_angle() function from: "Averages/Mean angle" <lang ruby>func time2deg(t) {
(var m = t.match(/^(\d\d):(\d\d):(\d\d)$/)) || die "invalid time"
var (hh,mm,ss) = m.cap.map{.to_i}...
((hh ~~ 24.range) && (mm ~~ 60.range) && (ss ~~ 60.range)) || die "invalid time"
(hh*3600 + mm*60 + ss) * 360 / 86400
} func deg2time(d) {
var sec = ((d % 360) * 86400 / 360) "%02d:%02d:%02d" % (sec/3600, (sec%3600)/60, sec%60)
} func mean_time(times) {
deg2time(mean_angle(times.map {|t| time2deg(t)}))
} say mean_time(["23:00:17", "23:40:20", "00:12:45", "00:17:19"])</lang>
- Output:
23:47:43
Tcl
<lang tcl>proc meanTime {times} {
set secsPerRad [expr {60 * 60 * 12 / atan2(0,-1)}]
set sumSin [set sumCos 0.0]
foreach t $times {
# Convert time to count of seconds from midnight scan $t "%02d:%02d:%02d" h m s incr s [expr {[incr m [expr {$h * 60}]] * 60}] # Feed into averaging set sumSin [expr {$sumSin + sin($s / $secsPerRad)}] set sumCos [expr {$sumCos + cos($s / $secsPerRad)}]
}
# Don't need to divide by counts; atan2() cancels that out
set a [expr {round(atan2($sumSin, $sumCos) * $secsPerRad)}]
# Convert back to human-readable
format "%02d:%02d:%02d" [expr {$a / 60 / 60 % 24}] [expr {$a / 60 % 60}] [expr {$a % 60}]
}
puts [meanTime {23:00:17 23:40:20 00:12:45 00:17:19}]</lang>
- Output:
23:47:43
XPL0
<lang XPL0>include c:\cxpl\codes;
proc NumOut(N); \Display 2-digit N with leading zero int N; [if N<10 then ChOut(0, ^0); IntOut(0, N); ];
proc TimeOut(Sec); \Display real seconds as HH:MM:SS real Sec; [NumOut(fix(Sec)/3600); ChOut(0, ^:);
NumOut(rem(0)/60); ChOut(0, ^:); NumOut(rem(0));
];
func real HMS2Sec(H, M, S); \Convert hours, minutes, seconds to real seconds int H, M, S; return float(((H*60 + M)*60) + S);
func real MeanTime(A); \Return the mean of the given list of times int A; real X, Y, Sec; int I; def Pi = 3.14159265358979323846; def S2R = Pi/(12.*60.*60.); \coefficient to convert seconds to radians [X:= 0.0; Y:= 0.0; for I:= 1 to A(0) do
[Sec:= HMS2Sec(A(I,0), A(I,1), A(I,2)); X:= X + Cos(Sec*S2R); Y:= Y + Sin(Sec*S2R); ];
Sec:= ATan2(Y,X)/S2R; if Sec < 0.0 then Sec:= Sec + 24.*60.*60.; return Sec; ];
TimeOut(MeanTime([4, [23,00,17], [23,40,20], [00,12,45], [00,17,19]]))</lang>
- Output:
23:47:43
zkl
This solution is a bit greasy, combining the solution to task "Averages/Mean angle" and some on-the-fly time-to-angle and back conversions. <lang zkl>var D=Time.Date; fcn meanT(t1,t2,etc){
ts:=vm.arglist.apply(fcn(hms){
(D.toFloat(hms.split(":").xplode())*15).toRad()
});
n:=ts.len();
mt:=(ts.apply("sin").sum(0.0)/n)
.atan2(ts.apply("cos").sum(0.0)/n)
.toDeg() /15;
if(mt<0) mt+=24; //-0.204622-->23.7954
D.toHour(mt).concat(":")
}</lang> Time.Date.toFloat/toHour convert 24hr HMS to fractional time and back. Multiplying fractional time by 360/24=15 yields angle.
- Output:
meanT("23:00:17", "23:40:20", "00:12:45", "00:17:19")
23:47:43