accumarray

Create a vector of data and a corresponding vector ind that defines groups.

data = (1:6)'

data = 6×1

     1
     2
     3
     4
     5
     6

ind = [1 3 4 2 4 1]'

ind = 6×1

     1
     3
     4
     2
     4
     1

Sum the values in data by the groups specified in ind.

B = accumarray(ind,data)

B = 4×1

     7
     4
     2
     8

Alternatively, use the groupsummary function, specifying 'sum' as the group computation.

B = groupsummary(data,ind,'sum')

B = 4×1

     7
     4
     2
     8

Create a vector of groups.

ind = [1 1 4 2 4 3]';

Apply scalar expansion to the number 1 to count the number of elements in each group defined in ind.

B = accumarray(ind,1)

B = 4×1

     2
     1
     1
     2

Alternatively, use the groupcounts function.

B = groupcounts(ind)

B = 4×1

     2
     1
     1
     2

Create a vector of data and a matrix of output indices ind that defines groups of data.

data = 1:6

data = 1×6

     1     2     3     4     5     6

ind = [1 1; 2 2; 3 2; 1 1; 2 2; 4 1]

ind = 6×2

     1     1
     2     2
     3     2
     1     1
     2     2
     4     1

Sum the values in data for each group in ind. The indices in ind define a 4-by-2 matrix of locations for the output.

B1 = accumarray(ind,data)

B1 = 4×2

     5     0
     0     7
     0     3
     6     0

Pad the output to a 4-by-4 matrix by specifying the output size as [4 4].

B2 = accumarray(ind,data,[4 4])

B2 = 4×4

     5     0     0     0
     0     7     0     0
     0     3     0     0
     6     0     0     0

Calculate group variances rather than sums.

Create a vector of data and a matrix ind that defines groups of the data.

data = [100.1 101.2 103.4 102.8 100.9 101.5]'

data = 6×1

  100.1000
  101.2000
  103.4000
  102.8000
  100.9000
  101.5000

ind = [1 1; 1 1; 2 2; 3 2; 2 2; 3 2]

ind = 6×2

     1     1
     1     1
     2     2
     3     2
     2     2
     3     2

Compute the variance of each group by specifying the function handle @var as the method input. This syntax applies the var function to the groups instead of sum.

B1 = accumarray(ind,data,[],@var)

B1 = 3×2

    0.6050         0
         0    3.1250
         0    0.8450

You can specify the group computation as an anonymous function that accepts vector inputs and returns a scalar. This is useful when you want to pass additional arguments to a function. For example, use the var function with the normalization argument value 1.

A2 = accumarray(ind,data,[],@(x) var(x,1))

A2 = 3×2

    0.3025         0
         0    1.5625
         0    0.4225

Specify an additional argument to the sum function by using an anonymous function for the method input.

Create a vector of data and a matrix ind that defines groups of the data and 3-D indices into the output.

data = int8(10:15)

data = 1x6 int8 row vector

   10   11   12   13   14   15

ind = [1 1 1; 1 1 1; 1 1 2; 1 1 2; 2 3 1; 2 3 2]

ind = 6×3

     1     1     1
     1     1     1
     1     1     2
     1     1     2
     2     3     1
     2     3     2

Sum the data by group in their native integer class int8 by using the 'native' option for the sum function. To do this, specify an anonymous function using @(x) sum(x,'native') for the method input. The result is a 2-by-3-by-2 multidimensional array of type int8.

B = accumarray(ind,data,[],@(x) sum(x,'native'))

B = 2x3x2 int8 array
B(:,:,1) =

   21    0    0
    0    0   14


B(:,:,2) =

   25    0    0
    0    0   15

Create a vector of data and a matrix ind that defines groups of the data.

data = 1:10

data = 1×10

     1     2     3     4     5     6     7     8     9    10

ind = [1 1; 1 1; 1 1; 1 1; 2 1; 2 1; 2 1; 2 1; 2 1; 2 2]

ind = 10×2

     1     1
     1     1
     1     1
     1     1
     2     1
     2     1
     2     1
     2     1
     2     1
     2     2

Group the elements of data into a cell array.

B = accumarray(ind,data,[],@(x) {x})

B=2×2 cell array
    {4x1 double}    {0x0 double}
    {5x1 double}    {[      10]}

Verify that the vector elements are in the same order as they appear in data.

B{2,1}

ans = 5×1

     5
     6
     7
     8
     9

Create a vector of data and a matrix ind that defines groups of the data.

data = (101:106)'

data = 6×1

   101
   102
   103
   104
   105
   106

ind = [1 1; 2 2; 3 3; 1 1; 2 2; 4 4]

ind = 6×2

     1     1
     2     2
     3     3
     1     1
     2     2
     4     4

The elements of ind define a 4-by-4 matrix for the output, but only reference 4 out of the 16 elements. By default, the other 12 elements are 0 in the output. Fill in the extra output elements with NaN values instead of 0.

B = accumarray(ind,data,[],[],NaN)

B = 4×4

   205   NaN   NaN   NaN
   NaN   207   NaN   NaN
   NaN   NaN   103   NaN
   NaN   NaN   NaN   106

Create a vector of data and a matrix ind that defines groups of the data.

data = [34 22 19 85 53 77 99 6];
ind = [1 1; 400 400; 80 80; 1 1; 400 400; 400 400; 80 80; 1 1]

ind = 8×2

     1     1
   400   400
    80    80
     1     1
   400   400
   400   400
    80    80
     1     1

The elements of ind define a 400-by-400 matrix for the output, but only reference 3 out of the 160,000 elements. When the output of accumarray results in a large array with a low density of nonzero elements, you can save memory by specifying the issparse option as true, creating a sparse matrix instead of a full one.

B = accumarray(ind,data,[],[],[],true)

B = 400x400 sparse double matrix (3 nonzeros)
   (1,1)      125
  (80,80)     118
 (400,400)    152