How to convert from day of year and year to a date YYYYMMDD?

This Bash function works for me on a GNU-based system:

jul () { date -d "$1-01-01 +$2 days -1 day" "+%Y%m%d"; }

Some examples:

$ y=2011; od=0; for d in {-4..4} 59 60 {364..366} 425 426; do (( d > od + 1)) && echo; printf "%3s " $d; jul $y $d; od=$d; done
 -4 20101227
 -3 20101228
 -2 20101229
 -1 20101230
  0 20101231
  1 20110101
  2 20110102
  3 20110103
  4 20110104

 59 20110228
 60 20110301

364 20111230
365 20111231
366 20120101

425 20120229
426 20120301

This function considers Julian day zero to be the last day of the previous year.

And here is a bash function for UNIX-based systems, such as macOS:

jul () { (( $2 >=0 )) && local pre=+; date -v$pre$2d -v-1d -j -f "%Y-%m-%d" $1-01-01 +%Y%m%d; }

Can't be done in just Bash, but if you have Perl:

use POSIX;

my ($jday, $year) = (100, 2011);

# Unix time in seconds since Jan 1st 1970
my $time = mktime(0,0,0, $jday, 0, $year-1900);

# same thing as a list that we can use for date/time formatting
my @tm = localtime $time;

my $yyyymmdd = strftime "%Y%m%d", @tm;

Run info 'Date input formats' to see what formats are allowed.

The YYYY-DDD date format does not seem to be there, and trying

$ date -d '2011-011'
date: invalid date `2011-011'

shows it doesn't work, so I think njd is correct, the best way is to use an external tool other than bash and date.

If you really want to use only bash and basic command line tools, you could do something like this:

julian_date_to_yyyymmdd()
{
    date=$1    # assume all dates are in YYYYMMM format
    year=${date%???}
    jday=${date#$year}
    for m in `seq 1 12`; do
        for d in `seq 1 31`; do
            yyyymmdd=$(printf "%d%02d%02d" $year $m $d)
            j=$(date +"%j" -d "$yyyymmdd" 2>/dev/null)
            if test "$jday" = "$j"; then
                echo "$yyyymmdd"
                return 0
            fi
        done
    done
    echo "Invalid date" >&2
    return 1
}

But that's a pretty slow way to do it.

A faster but more complex way tries to loop over each month, finds the last day in that month, then sees if the Julian day is in that range.

# year_month_day_to_jday <year> <month> <day> => <jday>
# returns 0 if date is valid, non-zero otherwise
# year_month_day_to_jday 2011 2 1 => 32
# year_month_day_to_jday 2011 1 32 => error
year_month_day_to_jday()
{
    # XXX use local or typeset if your shell supports it
    _s=$(printf "%d%02d%02d" "$1" "$2" "$3")
    date +"%j" -d "$_s"
}

# last_day_of_month_jday <year> <month>
# last_day_of_month_jday 2011 2 => 59
last_day_of_month_jday()
{
    # XXX use local or typeset if you have it
    _year=$1
    _month=$2
    _day=31

    # GNU date exits with 0 if day is valid, non-0 if invalid
    # try counting down from 31 until we find the first valid date
    while test $_day -gt 0; do
        if _jday=$(year_month_day_to_jday $_year $_month $_day 2>/dev/null); then
            echo "$_jday"
            return 0
        fi
        _day=$((_day - 1))
    done
    echo "Invalid date" >&2
    return 1
}

# first_day_of_month_jday <year> <month>
# first_day_of_month_jday 2011 2 => 32
first_day_of_month_jday()
{
    # XXX use local or typeset if you have it
    _year=$1
    _month=$2
    _day=1

    if _jday=$(year_month_day_to_jday $_year $_month 1); then
        echo "$_jday"
        return 0
    else
        echo "Invalid date" >&2
        return 1
    fi
}

# julian_date_to_yyyymmdd <julian day> <4-digit year>
# e.g. julian_date_to_yyyymmdd 32 2011 => 20110201
julian_date_to_yyyymmdd()
{
    jday=$1
    year=$2

    for m in $(seq 1 12); do
        endjday=$(last_day_of_month_jday $year $m)
        if test $jday -le $endjday; then
            startjday=$(first_day_of_month_jday $year $m)
            d=$((jday - startjday + 1))
            printf "%d%02d%02d\n" $year $m $d
            return 0
        fi
    done
    echo "Invalid date" >&2
    return 1
}