gnuplot：如何获得正确的周数？
gnuplot: How to get correct week numbers?
源自这个问题，
发现 gnuplot 中使用时间说明符 %W 和 %U 的周数在某些情况下是错误的。
显然，周数有不同的定义。
此外，一周开始的时间也有不同的定义，例如在周日或周一。
根据 ISO 8601，一种常用的周数定义（但不在美国和其他一些国家/地区使用）。
代码：（说明错误的周数）
### wrong week numbering in gnuplot with %W and %U
reset session
StartDate = "24.12.2020"
myTimeFmt = "%d.%m.%Y"
SecondsPerDay = 3600*24
print " date %a %w %d %j %W %U"
print "===================================="
do for [i=0:20] {
t = strptime(myTimeFmt,StartDate) + i*SecondsPerDay
myDate = strftime(myTimeFmt." %a %w %d %j %W %U", t)
print sprintf("%s", myDate)
}
### end of code
gnuplot 时间说明符：
%a abbreviated name of day of the week
%w day of the week, 0–6 (Sunday = 0)
%d day of the month, 01–31
%j day of the year, 1–366
%W week of the year (week starts on Monday)
%U week of the year (week starts on Sunday)
结果：
date %a %w %d %j %W %U
====================================
24.12.2020 Thu 04 24 359 52 52
25.12.2020 Fri 05 25 360 52 52
26.12.2020 Sat 06 26 361 52 52
27.12.2020 Sun 00 27 362 52 53
28.12.2020 Mon 01 28 363 53 53
29.12.2020 Tue 02 29 364 53 53
30.12.2020 Wed 03 30 365 53 53
31.12.2020 Thu 04 31 366 53 53
01.01.2021 Fri 05 01 001 01 01 ???
02.01.2021 Sat 06 02 002 01 01 ???
03.01.2021 Sun 00 03 003 00 01 ???
04.01.2021 Mon 01 04 004 01 01
05.01.2021 Tue 02 05 005 01 01
06.01.2021 Wed 03 06 006 01 01
07.01.2021 Thu 04 07 007 01 01
08.01.2021 Fri 05 08 008 01 01
09.01.2021 Sat 06 09 009 01 01
10.01.2021 Sun 00 10 010 01 02
11.01.2021 Mon 01 11 011 02 02
12.01.2021 Tue 02 12 012 02 02
13.01.2021 Wed 03 13 013 02 02
问题：是否有解决此问题的解决方法？
根据此处的描述：https://en.wikipedia.org/wiki/ISO_week_date，
我猜ISO 8601定义的本质是：
- 一周从星期一开始
- 第 01 周是一年中第一个星期四的那一周
- 一周属于一年中大部分天数在
- 从星期四开始或结束的年份有 53 周，其他年份有 52 周
代码：
### correct week number according to ISO 8601
reset session
dow(t) = int(tm_wday(t)) ? tm_wday(t) : 7 # day of week 1=Mon, ..., 7=Sun
week(t) = int((11 + tm_yday(t) - dow(t))/7) # "raw"week of year
wday(d,m,y) = tm_wday(strptime("%d.%m.%Y",sprintf("%02d.%02d.%04d",d,m,y))) # week day of certain date
wpy(y) = wday(1,1,y)==4 || wday(31,12,y)==4 ? 53 : 52 # weeks per year
woy(t) = week(t) < 1 ? wpy(tm_year(t)-1) : \
week(t) > wpy(tm_year(t)) ? 1 : week(t) # week of year
yow(t) = int(week(t) < 1 ? tm_year(t)-1 : week(t) > wpy(tm_year(t)) ? \
tm_year(t)+1 : tm_year(t)) # year of week (could be previous, current or next)
StartDate = "24.12.2020"
myTimeFmt = "%d.%m.%Y"
SecondsPerDay = 3600*24
print " date %a DoW %d %j YoW WoY"
print "======================================"
do for [i=0:20] {
t = strptime(myTimeFmt,StartDate) + i*SecondsPerDay
myDate = strftime(myTimeFmt." %a", t)
myDate2 = strftime("%d %j", t)
print sprintf("%s %02d %s %04d-W%02d", myDate, dow(t), myDate2, yow(t), woy(t))
}
### end of code
结果：
date %a DoW %d %j YoW WoY
======================================
24.12.2020 Thu 04 24 359 2020-W52
25.12.2020 Fri 05 25 360 2020-W52
26.12.2020 Sat 06 26 361 2020-W52
27.12.2020 Sun 07 27 362 2020-W52
28.12.2020 Mon 01 28 363 2020-W53
29.12.2020 Tue 02 29 364 2020-W53
30.12.2020 Wed 03 30 365 2020-W53
31.12.2020 Thu 04 31 366 2020-W53
01.01.2021 Fri 05 01 001 2020-W53
02.01.2021 Sat 06 02 002 2020-W53
03.01.2021 Sun 07 03 003 2020-W53
04.01.2021 Mon 01 04 004 2021-W01
05.01.2021 Tue 02 05 005 2021-W01
06.01.2021 Wed 03 06 006 2021-W01
07.01.2021 Thu 04 07 007 2021-W01
08.01.2021 Fri 05 08 008 2021-W01
09.01.2021 Sat 06 09 009 2021-W01
10.01.2021 Sun 07 10 010 2021-W01
11.01.2021 Mon 01 11 011 2021-W02
12.01.2021 Tue 02 12 012 2021-W02
13.01.2021 Wed 03 13 013 2021-W02
为了使用周数，例如作为时间轴标签，最好为 %W 实现此功能。一不小心，最近在SourceForge上有一个bug report。
所以，我认为它会很快在下一个版本中得到修复。
鉴于持续的大流行以及随之而来的对绘制来自所有来源的流行病学数据的兴趣，清理和扩展 gnuplot 对周日期格式的支持似乎是权宜之计。 gnuplot 文档的“新功能”部分现在列出：
• Time specifier format %W has been brought into accord with the ISO 8601 week date standard.
• Time specifier format %U has been brought into accord with the CDC/MMWR week date standard.
• New function tm week(time, std) returns ISO or CDC standard week of year.
• New function weekdate iso(year, week, day) converts ISO standard week date to calendar time.
• New function weekdate cdc(year, week, day) converts CDC standard week date to calendar time.
这里是一个示例（来自 the online demo set），它将以 ISO 8601 周日期格式给出的数据转换为标准日历日期，以便沿 gnuplot 时间轴绘制。
# Epidemiological data
#
# Plot from data file that encodes date as an ISO 8601 "week date".
# Example: week date 2004-W01-1 is calendar date 29 December 2003
# The data is from the European Centre for Disease Prevention and Control
# https://www.ecdc.europa.eu/
# The ECDC data file uses fields containing week date as "YYYY-WW".
# First we define a function that extracts the integer year and week
# from this string and converts it to standard time representation.
calendar(date) = weekdate_iso( int(date[1:4]), int(date[6:7]) )
set datafile separator comma
set style data lines
set key Left left reverse box samplen 2 width 2
set grid x lt 1 lw .75 lc "gray"
set tics nomirror
set border 3
set xtics time format "%b\n%Y"
set ytics format " %4.0f"
data1 = '< grep "Denmark.*cases" ECDC-weekly-national-COVID.csv'
data2 = '< grep "Sweden.*cases" ECDC-weekly-national-COVID.csv'
data3 = '< grep "Norway.*cases" ECDC-weekly-national-COVID.csv'
data4 = '< grep "Finland.*cases" ECDC-weekly-national-COVID.csv'
data5 = '< grep "Iceland.*cases" ECDC-weekly-national-COVID.csv'
set title "weekly COVID-19 cases per 100,000 people" font "/Bold,15"
plot data1 using (calendar(strcol(7))) : (1.e5*/) lw 2 title "Denmark", \
data2 using (calendar(strcol(7))) : (1.e5*/) lw 2 title "Sweden", \
data3 using (calendar(strcol(7))) : (1.e5*/) lw 2 title "Norway", \
data4 using (calendar(strcol(7))) : (1.e5*/) lw 2 title "Finland", \
data5 using (calendar(strcol(7))) : (1.e5*/) lw 2 lt 6 title "Iceland"
源自这个问题%W 和 %U 的周数在某些情况下是错误的。
显然，周数有不同的定义。 此外，一周开始的时间也有不同的定义，例如在周日或周一。 根据 ISO 8601，一种常用的周数定义（但不在美国和其他一些国家/地区使用）。
代码：（说明错误的周数）
### wrong week numbering in gnuplot with %W and %U
reset session
StartDate = "24.12.2020"
myTimeFmt = "%d.%m.%Y"
SecondsPerDay = 3600*24
print " date %a %w %d %j %W %U"
print "===================================="
do for [i=0:20] {
t = strptime(myTimeFmt,StartDate) + i*SecondsPerDay
myDate = strftime(myTimeFmt." %a %w %d %j %W %U", t)
print sprintf("%s", myDate)
}
### end of code
gnuplot 时间说明符：
%a abbreviated name of day of the week
%w day of the week, 0–6 (Sunday = 0)
%d day of the month, 01–31
%j day of the year, 1–366
%W week of the year (week starts on Monday)
%U week of the year (week starts on Sunday)
结果：
date %a %w %d %j %W %U
====================================
24.12.2020 Thu 04 24 359 52 52
25.12.2020 Fri 05 25 360 52 52
26.12.2020 Sat 06 26 361 52 52
27.12.2020 Sun 00 27 362 52 53
28.12.2020 Mon 01 28 363 53 53
29.12.2020 Tue 02 29 364 53 53
30.12.2020 Wed 03 30 365 53 53
31.12.2020 Thu 04 31 366 53 53
01.01.2021 Fri 05 01 001 01 01 ???
02.01.2021 Sat 06 02 002 01 01 ???
03.01.2021 Sun 00 03 003 00 01 ???
04.01.2021 Mon 01 04 004 01 01
05.01.2021 Tue 02 05 005 01 01
06.01.2021 Wed 03 06 006 01 01
07.01.2021 Thu 04 07 007 01 01
08.01.2021 Fri 05 08 008 01 01
09.01.2021 Sat 06 09 009 01 01
10.01.2021 Sun 00 10 010 01 02
11.01.2021 Mon 01 11 011 02 02
12.01.2021 Tue 02 12 012 02 02
13.01.2021 Wed 03 13 013 02 02
问题：是否有解决此问题的解决方法？
根据此处的描述：https://en.wikipedia.org/wiki/ISO_week_date， 我猜ISO 8601定义的本质是：
- 一周从星期一开始
- 第 01 周是一年中第一个星期四的那一周
- 一周属于一年中大部分天数在
- 从星期四开始或结束的年份有 53 周，其他年份有 52 周
代码：
### correct week number according to ISO 8601
reset session
dow(t) = int(tm_wday(t)) ? tm_wday(t) : 7 # day of week 1=Mon, ..., 7=Sun
week(t) = int((11 + tm_yday(t) - dow(t))/7) # "raw"week of year
wday(d,m,y) = tm_wday(strptime("%d.%m.%Y",sprintf("%02d.%02d.%04d",d,m,y))) # week day of certain date
wpy(y) = wday(1,1,y)==4 || wday(31,12,y)==4 ? 53 : 52 # weeks per year
woy(t) = week(t) < 1 ? wpy(tm_year(t)-1) : \
week(t) > wpy(tm_year(t)) ? 1 : week(t) # week of year
yow(t) = int(week(t) < 1 ? tm_year(t)-1 : week(t) > wpy(tm_year(t)) ? \
tm_year(t)+1 : tm_year(t)) # year of week (could be previous, current or next)
StartDate = "24.12.2020"
myTimeFmt = "%d.%m.%Y"
SecondsPerDay = 3600*24
print " date %a DoW %d %j YoW WoY"
print "======================================"
do for [i=0:20] {
t = strptime(myTimeFmt,StartDate) + i*SecondsPerDay
myDate = strftime(myTimeFmt." %a", t)
myDate2 = strftime("%d %j", t)
print sprintf("%s %02d %s %04d-W%02d", myDate, dow(t), myDate2, yow(t), woy(t))
}
### end of code
结果：
date %a DoW %d %j YoW WoY
======================================
24.12.2020 Thu 04 24 359 2020-W52
25.12.2020 Fri 05 25 360 2020-W52
26.12.2020 Sat 06 26 361 2020-W52
27.12.2020 Sun 07 27 362 2020-W52
28.12.2020 Mon 01 28 363 2020-W53
29.12.2020 Tue 02 29 364 2020-W53
30.12.2020 Wed 03 30 365 2020-W53
31.12.2020 Thu 04 31 366 2020-W53
01.01.2021 Fri 05 01 001 2020-W53
02.01.2021 Sat 06 02 002 2020-W53
03.01.2021 Sun 07 03 003 2020-W53
04.01.2021 Mon 01 04 004 2021-W01
05.01.2021 Tue 02 05 005 2021-W01
06.01.2021 Wed 03 06 006 2021-W01
07.01.2021 Thu 04 07 007 2021-W01
08.01.2021 Fri 05 08 008 2021-W01
09.01.2021 Sat 06 09 009 2021-W01
10.01.2021 Sun 07 10 010 2021-W01
11.01.2021 Mon 01 11 011 2021-W02
12.01.2021 Tue 02 12 012 2021-W02
13.01.2021 Wed 03 13 013 2021-W02
为了使用周数，例如作为时间轴标签，最好为 %W 实现此功能。一不小心，最近在SourceForge上有一个bug report。
所以，我认为它会很快在下一个版本中得到修复。
鉴于持续的大流行以及随之而来的对绘制来自所有来源的流行病学数据的兴趣，清理和扩展 gnuplot 对周日期格式的支持似乎是权宜之计。 gnuplot 文档的“新功能”部分现在列出：
• Time specifier format %W has been brought into accord with the ISO 8601 week date standard.
• Time specifier format %U has been brought into accord with the CDC/MMWR week date standard.
• New function tm week(time, std) returns ISO or CDC standard week of year.
• New function weekdate iso(year, week, day) converts ISO standard week date to calendar time.
• New function weekdate cdc(year, week, day) converts CDC standard week date to calendar time.
这里是一个示例（来自 the online demo set），它将以 ISO 8601 周日期格式给出的数据转换为标准日历日期，以便沿 gnuplot 时间轴绘制。
# Epidemiological data
#
# Plot from data file that encodes date as an ISO 8601 "week date".
# Example: week date 2004-W01-1 is calendar date 29 December 2003
# The data is from the European Centre for Disease Prevention and Control
# https://www.ecdc.europa.eu/
# The ECDC data file uses fields containing week date as "YYYY-WW".
# First we define a function that extracts the integer year and week
# from this string and converts it to standard time representation.
calendar(date) = weekdate_iso( int(date[1:4]), int(date[6:7]) )
set datafile separator comma
set style data lines
set key Left left reverse box samplen 2 width 2
set grid x lt 1 lw .75 lc "gray"
set tics nomirror
set border 3
set xtics time format "%b\n%Y"
set ytics format " %4.0f"
data1 = '< grep "Denmark.*cases" ECDC-weekly-national-COVID.csv'
data2 = '< grep "Sweden.*cases" ECDC-weekly-national-COVID.csv'
data3 = '< grep "Norway.*cases" ECDC-weekly-national-COVID.csv'
data4 = '< grep "Finland.*cases" ECDC-weekly-national-COVID.csv'
data5 = '< grep "Iceland.*cases" ECDC-weekly-national-COVID.csv'
set title "weekly COVID-19 cases per 100,000 people" font "/Bold,15"
plot data1 using (calendar(strcol(7))) : (1.e5*/) lw 2 title "Denmark", \
data2 using (calendar(strcol(7))) : (1.e5*/) lw 2 title "Sweden", \
data3 using (calendar(strcol(7))) : (1.e5*/) lw 2 title "Norway", \
data4 using (calendar(strcol(7))) : (1.e5*/) lw 2 title "Finland", \
data5 using (calendar(strcol(7))) : (1.e5*/) lw 2 lt 6 title "Iceland"