gnuplot, calculating and plotting monthly averages

Question

I have a datafile with several months of minute data with lines like "2016-02-02 13:21(\t)value(\n)".

I need to plot the data (no problem with that) and calculate + plot an average for each month.

Is it possible in gnuplot?

I am able to get an overall average using

    fit a "datafile" using 1:3 via a

I am also able to specify some time range for the fit using

    fit [now_secs-3600*24*31:now_secs] b "datafile" using 1:3 via b

... and then plot them with

    plot a t "Total average",b t "Last 31 days"

But no idea how to calculate and plot an average for each month (= one stepped line showing each month average)

Answer 1

You can also do averages with the option smooth unique which is available at least since gnuplot 4.0 (2004). The following is an example which runs for gnuplot>=5.0.0 (Jan. 2015).

Some explanations (intentionally kept outside the script to keep it readable):

• some random test data is created

• the option smooth unique returns the average of the y-values for identical x-values

• so, if the format fmtYm = "%Y-%m" only contains the year and month, all x-values, e.g. in 2024-03 will return 2024-03-01 00:00 and hence all y-values for this month will be averaged. Check help smooth option unique.

• I want this average value plotted with boxes. However, gnuplot would center the box, e.g. at t0=2024-03-01 00:00 and not at the middle of the month

• so, you have to calculate the middle of the month by calculating the next month, e.g. t1=2024-04-01 00:00 using the functions tm_year() and tm_mon() (check help tm_year, help tm_mon, help sprintf, help strptime).

• note that the months returned by tm_mon() are zero based, so you have to add +2 to get the following month via sprintf() and strptime(). Fortunately, gnuplot interprets, e.g. 2024-13 as 2025-01.

Script: (works for gnuplot>=5.0.0, Jan. 2015)

### plot time data and monthly average
reset session

fmt   = "%Y-%m-%d %H:%M"
fmtYm = "%Y-%m"           # format only year and month

# create some random test data
set print $Data
    t0 = time(0)  # now
    y0 = 100
    do for [i=0:1000] {
        print sprintf("%s %g", strftime(fmt,t0+i*3600*8), y0=y0+rand(0)*2-1)
    }
set print

set format x "%Y\n%m-%d" timedate
set style fill transparent solid 0.4
set key noautotitle invert

tmc(col) = (t0=timecolumn(col,fmtYm), t1=strptime(fmtYm,sprintf("%4d-%02d",tm_year(t0),tm_mon(t0)+2)), (t0+t1)/2.)

plot $Data u (tmc(1)):3 smooth unique w boxes lc rgb 0xccccff ti "monthly average", \
        '' u (timecolumn(1,fmt)):3 w l lc "red" ti "data"
### end of script

Result:

Answer 2

Here is a way to do it purely in gnuplot. This method can be adapted (with a not small amount of effort) to work with files that cross a year boundary or span more than one year. It works just fine if the data starts with January or not. It computes the ordinary average for each month (the arithmetic mean) treating each data point as one value for the month. With somewhat significant modification, it can be used to work with weighted averages as well.

This makes a significant use of the stats function to compute values. It is a little long, partly because I commented it heavily. It uses 5.0 features (NaN for undefined values and in-memory datablocks instead of temporary files), but comments note how to change these for earlier versions.

Note: This script must be run before setting time mode. The stats function will not work in time mode. Time conversions are handled by the script functions.

data_time_format = "%Y-%m-%d %H:%M" #date format in file
date_cols = 2 # Number of columns consumed by date format

# get numeric month value of time - 1=January, 12=December
get_month(x) = 0+strftime("%m",strptime(data_time_format,x))

# get numeric year value of time
get_year(x) = 0+strftime("%Y",strptime(data_time_format,x))

# get internal time representation of day 1 of month x in year y
get_month_first(x,y) = strptime("%Y-%m-%d",sprintf("%d-%d-01",y,x))

# get internal time representation of date
get_date(x) = strptime(data_time_format,x)

# get date string in file format corresponding to day y in month x of year z
get_date_string(x,y,z) = strftime(data_time_format,strptime("%Y-%m-%d",sprintf("%04d-%02d-%02d",z,x,y)))

# determine if date represented by z is in month x of year y
check_valid(x,y,z) = (get_date(z)>=get_month_first(x,y))&(get_date(z)<get_month_first(x+1,y))

# Determine year and month range represented by file
year = 0 
stats datafile u (year=get_year(strcol(1)),get_month(strcol(1))) nooutput
month_min = STATS_min
month_max = STATS_max

# list of average values for each month
aves = ""

# fill missing months at beginning of year with 0
do for[i=1:(month_min-1)] {
    aves = sprintf("%s %d",aves,0)
}

# compute average of each month and store it at the end of aves
do for[i=month_min:month_max] {
    # In versions prior to 5.0, replace NaN with 1/0
    stats datafile u (check_valid(i,year,strcol(1))?column(date_cols+1):NaN) nooutput
    aves = sprintf("%s %f",aves,STATS_mean)
}

# day on which to plot average
baseday = 15

# In version prior to 5.0, replace $k with a temporary file name
set print $k
# Change this to start at 1 if we want to fill in prior months
do for [i=month_min:month_max] {
    print sprintf("%s %s",get_date_string(i,baseday,year),word(aves,i))
}
set print

This script will create either a in-memory datablock or a temporary file for earlier versions (with the noted changes) that contains a similar file to the original, but containing one entry per month with the value of the monthly average.

At the beginning we need to define our date format and the number of columns that the date format consumes. From then on it is assumed that the data file is structured as datetime value. Several functions are defined which make extensive use of the strptime function (to compute a date string to an internal integer) and the strftime function (to compute an internal representation to a string). Some of these functions compute both ways in order to extract the necessary values. Note the addition of 0 in the get_month and get_year function to convert a string value to an integer.

We do several steps with the data in order to build our resulting datablock/file.

1. Use the stats function to compute the first and last month and the year. We are assuming only one year is present. This step needs to be modified heavily if we need to work with more than one year. In particular months in a second year would need to be numbered 13 - 24 and in a third year 25 - 36 and so on. We would need to modify this line to capture multiple years as well. Probably two passes would be needed.
2. Build up a string which contains space separated values for the average value for each month. This is done by applying the stats function once for each month. The check_valid function checks if a value is in the month of interest, and a value that isn't is assigned NaN which causes the stats function to ignore it.
3. Loop over the months of interest and build a datablock/temporary file with one entry for each month with the average value for that month. In this case, the average value is assigned to the start of the 15th day of the month. This can be easily changed to any other desired time. The get_date_string function is used for assigning the value to a time.

Now to demonstrate this, suppose that we have the following data

2016-02-03 15:22 95
2016-02-20 18:03 23
2016-03-10 16:03 200
2016-03-15 03:02 100
2016-03-18 02:02 200

We wish to plot this data along with the average value for each month. We can run the above script, and we will get a datablock $k (make the commented change near the bottom to use a temporary file instead) containing the following

2016-02-15 00:00 59.000000
2016-03-15 00:00 166.666667

This is exactly the average values for each month. Now we can plot with

set xdata time
set timefmt data_time_format
set key outside top right
plot $k u 1:3 w points pt 7 t "Monthly Average",\
     datafile u 1:3 with lines t "Original Data"

Here, just for illustration, I used points with the averages. Feel free to use any style that you want. If you choose to use steps, you will very likely want to adjust the day that is assigned^† in the datablock/temporary file (probably the first or last day in the month depending on how you want to do it).

It is usually easier with a task like this to do some outside preprocessing, but this demonstrates that it is possible in pure gnuplot.

---

^† Regarding changing the day that is assigned, using any specific day in the month is easy, as long as it is a day that occurs in every month (dates from the 1st to the 28th) - just change baseday. For other values modifications to the get_date_string function need to be made.

For example, to use the last day, the function can be defined as

get_date_string(x,y,z) = strftime(data_time_format,strptime("%Y-%m-%d",sprintf("%04d-%02d-01",z,x+1))-24*60*60)

This version actually computes the first day of the next month, and then subtracts one whole day from that. The second argument is ignored in this version, but preserved to allow it to be used without having to make any additional changes to the script.

Answer 3

With a recent version of gnuplot, you have the stats command and you can do something something like this:

stats "datafile" using 1:3 name m0

month_sec=3600*24*30.5
do for [month=1:12] {
   stats [now_secs-(i+1)*month_sec:(i+0)*now_secs-month_sec]  "datafile" using 1:3 name sprintf("m%d")
}

you get m0_mean value for the total mean and you get all m1_mean m2_mean variables for the previuos months etc... defined in gnuplot

Finally to plot the you should do something like:

plot 'datafile', for [month=0:12] value(sprintf("m%d_mean"))

see help stats help for help value help sprintf for more information on the above commands