matrix - MATLAB find and apply function to values of repeated indices

Question

I have a 352x11 matrix, indexed by column 1 with 10 data points. Some of the index values are repeated. I'd like to find the repeated indices and calculate the mean data points for the repeated trials (avoiding loops, if possible).

For example,

x =

   26   77.5700   17.9735   32.7200
   27   40.5887   16.6100   31.5800
   28   60.4734   18.5397   33.6200
   28   35.6484   27.2000   54.8000
   29   95.3448   19.0000   37.7300
   30   82.7273   30.4394   39.1400

to end up with:

ans =

   26   77.5700   17.9735   32.7200
   27   40.5887   16.6100   31.5800
   28   48.0609   22.8699   44.2150
   29   95.3448   19.0000   37.7300
   30   82.7273   30.4394   39.1400

I was thinking if I used

J = find(diff(x(:,1))==0);

to find the position of the repeated values, I could then apply the function to the corresponding positions of x, but where do I begin?

Answer 1

A more general approach would employ unique to find the unique index values:

[U, ix, iu] = unique(x(:, 1));

and then accumarray:

[c, r] = meshgrid(1:size(x, 2), iu);
y = accumarray([r(:), c(:)], x(:), [], @mean);

Explanation

The input values to process are actually the second parameter of accumarray.

The first parameter of accumarray is a matrix, each row being a set of indices in the (accumulated) output matrix, and it corresponds to a value from the matching row in the vector given as the second parameter.

Think of the output as a cell array. The second parameters are the input values, and each row in the first parameter tells in which cell of the output matrix accumarray should store the corresponding input value. When output "cell array" is finished, a function (mean in our case) is applied to each cell.

Example

Here's a short example with a smaller matrix:

x = [27, 10, 8;
     28, 20, 10;
     28, 30, 50];

We find the unique values by:

[U, ix, iu] = unique(x(:, 1));

Vector U stores the unique values, and iu indicates which index of the value associated with each row (note that in this solution we have no use for ix ). In our case we get that:

U = 
    27
    28

iu =
    1
    2
    2

Now we apply accumarray:

[c, r] = meshgrid(1:size(x, 2), iu);
y = accumarray([r(:), c(:)], x(:), [], @mean);

The fancy trick with meshgrid and [r(:), c(:)] produces a set of indices:

[r(:), c(:)] =
     1     1
     2     1
     2     1
     1     2
     2     2
     2     2
     1     3
     2     3
     2     3

and these are the indices for the input values x(:), which is a column-vector equivalent of x:

x(:) =
    27
    28
    28
    10
    20
    30
     8
    10
    50

The process of accumulation:

• The first value 27 goes to cell <1,1> in the output matrix.
• The second value 28 goes to cell <2,1> in the output matrix.
• The third value 28 goes to cell <2,1> in the output matrix.

See what just happened? Both values 28 get accumulated in the same cell (and eventually they will be averaged). The process continues:

• The fourth value 10 goes to cell <1,2> in the output matrix.

and so on...

Once all values are stored in cells, the function mean is applied on each cell and we get the final output matrix:

y =
    27    10     8
    28    25    30