How do I perform cumulative adding of data by month and then plot it by year?

I have data in a 8500x3 matrix - columns being year, month, day of each earthquake (all are in numerical representation - e.g. 1985 01 23). The data is in chronological order, with oldest first. As the number of earthquakes varies per day, the number of rows dedicated to each day/month/year changes.

I need to make a plot of cumulative number of earthquakes per month. I know I have to assign a one to every earthquake, but my problem comes in the cumulative adding. How do I add the data from one month in a given year to the next month? The problem arises due to the changing year as well.

Example of data:

[1985 01 01; 1985 01 12; 1985 01 14; 1985 01 25; 1985 03 02; 1985 06 16; 1985 06 18; 1985 11 09; 1986 01 01; 1986 01 30] ...

I hope I explained this easily.

Thanks, Gareth

Answer 1

[Star Strider]

I don’t understand your Question and your ‘desired output’. This accumulates the total number in each month, and then the cumulative sum:

Seism = [1985 01 01; 1985 01 12; 1985 01 14; 1985 01 25; 1985 03 02; 1985 06 16; 1985 06 18; 1985 11 09; 1986 01 01; 1986 01 30];
SeismDN = datenum([Seism(:, 1:2) ones(size(Seism,1),1) zeros(size(Seism,1),3)]);
[SeismU,~,Idx] = unique(SeismDN,'stable');
SeisHist = accumarray(Idx,1);
Result = [str2num(datestr(SeismU, 'yyyy mm')) cumsum(SeisHist)]

Result =
        1985           1           4
        1985           3           5
        1985           6           7
        1985          11           8
        1986           1          10

[Gareth Maver]

Sorry I didn't phrase my question very well.

This is pretty much the result I want - except is there a way of continuing the sum over months that experience no earthquakes?

For example, a new second line of the result would read: 1985 2 4

This is because I want to eventually plot the cumulative sum against year and so will need it to be continuous.

Sorry if I havent been clear again

[Star Strider]

You may not need the intervening months to be continuous if you just want to plot them.

Add this code to the end of my previous code:

PlotMtx = [SeismU  cumsum(SeisHist)];

figure(1)
stairs(PlotMtx(:,1), PlotMtx(:,2), 'LineWidth',2)
datetick('x', 'yyyy mm')
grid
axis tight
xlabel('Time')
ylabel('Cumulative Earthquakes')

to get this plot:

You can change the tick numbers and labels (and rotate the labels to make them more readable in recent MATLAB versions), change the axis ranges and several other customisations to create the plot appearance you want.

[Gareth Maver]

Is there anyway of plotting one continuous line instead of steps?

Basically I am wanting to recreate this figure but with the cumulative sum plotted at monthly intervals - i.e. more line detail is wanted in between the year ticks.

I have this code which creates the above figure:

    long = data(:,1) ;
    lati = data(:,2) ;
    year = data(:,3) ;
    month = data(:,4) ; 
    mag = data(:,6) ;

 for i = 1:length(mag)
    if mag(i) < 3 
        mag(i) = NaN ;
        lati(i) = NaN ;
        long(i) = NaN ;
        year(i) = NaN ;
        month(i) = NaN ;
    end
 end

    cum_year = [1985:1:2015] ;
    n = zeros(length(cum_year),1) ;
    cum_year = cum_year' ;

    for j = 1:length(n)
     for i = 1:length(mag) ;
         if year(i) == cum_year(j)
             n(j) = n(j)+1 ;

         end
     end
    end

    year_sum = zeros(length(n),1) ;    
    for i = 1:length(n) ;
       year_sum(i) = sum(n(1:i)) ;
    end

figure ; 

plot(cum_year(1:24),year_sum(1:24),'b','LineWidth',1.5) ;
hold on
plot(cum_year(24:29),year_sum(24:29),'Color',[0.0 0.8 0.3],'LineWidth',1.5) ;
plot(cum_year(29:31),year_sum(29:31),'r','LineWidth',1.5) ;

So is there anyway of a cumulative sum on a monthly basis, where the year is changing?

[Stephen23]

Question continues here:

http://www.mathworks.com/matlabcentral/answers/267831-cumulative-sum-by-month

[Star Strider]

Use plot instead of stairs, although if you want different coloured lines for each section, you would use the hold function and a loop.

[Gareth Maver]

Thanks that works. I still need to only plot earthquakes that have a value of 3.0 or above in the mag column. How do I go about doing this now? Also, the xlim function does not seem to work now after applying your code.

Sorry about all the questions, I am a beginner at MATLAB

[Star Strider]

My pleasure.

I don’t have your data, so I don’t have the ‘mag column’.

I did nothing with the xlim function in my code. If you want to use it to define the axis limits, remove or restate the axis call in my code.

No worries about the questions. I’ll answer as well as I can.

[Gareth Maver]

Basically there is another column with earthquake magnitude values in it - ranging from 2.0 up to about 5.0. How would I code to only count the earthquakes above value 3.0 for the cumulative sum?

[Star Strider]

This is how I would edit the original date and magnitude matrix:

datenms = datenum(bsxfun(@plus, [1985 01 01], [zeros(20,1) [1:20]' zeros(20,1)]));  % Create Dates
Data = [datenms rand(20,1)*3.3+2];                                                  % All Dates & Magnitudes
Data3 = Data(Data(:,2) > 3,:);                                                      % Select Magnitude > 3

If you wanted only the dates, in this example you would select ‘Data3(:,1)’.