How to obtain average in a matrix without loop?

In matrix A, I want to create a new column that contains the yearly average of the 5th column for each stations. The columns from left to right are: station, year, month, day, value. I want to avoid loops if possible.

   A= [10  2000  1  1  1.5;
       10  2000  1  3  1.1;
...
       20  2000  1  1  1.2;
       20  2000  1  2  1.4;
... 
       10  2001  1  1  1.1;
       10  2001  1  4  1.3;
...
       ]

   B= [10  2000  1  1  1.5  1.2;
       10  2000  1  3  1.1  1.2;
...
       20  2000  1  1  1.2  1.4;
       20  2000  1  2  1.4  1.4;
... 
       10  2001  1  1  1.1  1.1;
       10  2001  1  4  1.3  1.1; 
...
       ]

so I want to make B in which the 6th column is yearly average of 5th column for each station.

thanks!

Why do you want to avoid loops? At least a loop over the stattions would decrease the complexity of the code substantially. Some Matlab programmers use the avoidance of loops as a mantra without any real benefit since the JIT has been introduced in Matlab 6.5. As long as I do not see a good reason to avoid FOR loops, I'm not going to struggle with ACCUMARRAY. It is not worth to spend 5 minutes programming time only to save some microseconds of runtime.

The 4th column is the "day". Do you want the average of the 5th column? But even then: (1.5 + 1.1) / 2 ~= 1.2. Thefore please explain, what you want to calculate.

sorry.yes, I want the average of the 5th. I,m not that familiar with the details. I just wanted to avoid loops to save time, but If there is no other way or the codes get complicated, I can use loops.

@Jan - that's why I love accumarray!! It's usually slower than a for-loop but it saves me a few minutes writing the same generic for-loops over and over again :)

@Sean: I've read the docs 8 times, and I'm still missing the "click". At least when I reach the 2nd section, I give up:

 A = accumarray(subs,val,sz) creates an array A with size sz, where sz is a vector of positive integers. If subs is nonempty with N>1 columns, then sz must have N elements, where all(sz >= max(subs,[],1)). If subs is a nonempty column vector, then sz must be [M 1], where M >= MAX(subs). Specify sz as [] for the default behavior.

I'm convinced, that this is meaningful and most likely even clear and trivial. But I do not understand anything of it - in opposite to all other help and doc textes of Matlab. When I read http://blogs.mathworks.com/loren/2008/02/20/under-appreciated-accumarray, I see that I'm not alone:

 Eris S wrote: I think that ACCUMARRAY has one of the worst documentation pages in MATLAB. I also find ACCUMARRY to be probably the number one most confusing function in MATLAB – there might be causation behind this correlation ;)

It means that you can fix the end result size if you want it to be bigger in the event that subs does not cover data at that size.

Let's say I have:

x = accumarray([1;2;1],ones(3,1))

But I always want the result to be 5x1 even if I don't have any 5s in my subs vector:

x = accumarray([1;2;1],ones(3,1),[5 1])

How could this be useful?

f() expects x to be a 5x1. I pull unique values from another vector but it turns out that there are only four unique values. The first implementation will return a 4x1 and would break f().

I concur, Jan! Every time I know intuitively that ACCUMARRAY would work in a given situation, I have to re-read the doc. Then I have to work through a few of the doc examples to remember how to interpret what the doc says. Then I can proceed to use the function, if I am lucky and don't have to re-read the doc. And English is my native tongue (I can't imagine trying to figure this function out otherwise)!

It is a useful function, but I usually spend more time trying to figure out how to apply it to the problem at hand as I would just writing the FOR loops. I cannot tell you how many times I have seen this error message:

Error using accumarray
Second input VAL must be a vector with one element for each row in SUBS, or a scalar.

It is one of the few MATLAB error messages I have memorized and that I expect to see the first time I try that function on a given day.

Answer 1

    A= [10  2000  1  1  1.5;
       10  2000  1  3  1.1;
       20  2000  1  1  1.2;
       20  2000  1  2  1.4;
       10  2001  1  1  1.1;
       10  2001  1  4  1.3];

   [~,~,idxA] = unique(A(:,1:2),'rows');
   means = accumarray(idxA,A(:,4),[],@mean);
   B = [A means(idxA)]

But your example does not actually make it look like B contains the means of column four for the unique combinations of columns 1/2.

Perhaps "A(:,4)" -> "A(:,5)", but this will not create B also.

thanks to both of you. Fatemeh