Loren on the Art of MATLAB

Contents

By Default, Column-wise Operations

By default, MATLAB performs many operations by treating the columns as individual vectors and acting on them. However, if the array has only a single element per column, then MATLAB performs the operation along the first non-singleton dimension.

User Issue and Solution

So, that's the default behavior. However, for this user's application, he always wanted the sum to be along the first dimension (down the columns), even if there was only a single entry per column.

To accomplish this, the altered code used the optional second input argument, dimension. This works similarly with other functions that typically reduce the dimensionality from the input to the output, such as

Here's the relevant portion of the help for sum. I happen to know that I only need to go up through the second instance of DIM.

h = help('sum');
f = strfind(h,'DIM');
disp(h(1:f(2)+5))

 SUM Sum of elements.
    S = SUM(X) is the sum of the elements of the vector X. If
    X is a matrix, S is a row vector with the sum over each
    column. For N-D arrays, SUM(X) operates along the first
    non-singleton dimension.
    If X is floating point, that is double or single, S is
    accumulated natively, that is in the same class as X,
    and S has the same class as X. If X is not floating point,
    S is accumulated in double and S has class double.
 
    S = SUM(X,DIM) sums along the dimension DIM. 

Examples

Let's see this behavior in action.

n = 4;
A = cat(3, pascal(4), magic(4), invhilb(4), hadamard(4), hilb(4))

A(:,:,1) =
     1     1     1     1
     1     2     3     4
     1     3     6    10
     1     4    10    20
A(:,:,2) =
    16     2     3    13
     5    11    10     8
     9     7     6    12
     4    14    15     1
A(:,:,3) =
          16        -120         240        -140
        -120        1200       -2700        1680
         240       -2700        6480       -4200
        -140        1680       -4200        2800
A(:,:,4) =
     1     1     1     1
     1    -1     1    -1
     1     1    -1    -1
     1    -1    -1     1
A(:,:,5) =
    1.0000    0.5000    0.3333    0.2500
    0.5000    0.3333    0.2500    0.2000
    0.3333    0.2500    0.2000    0.1667
    0.2500    0.2000    0.1667    0.1429

Sum A down the columns.

sumA = sum(A)

sumA(:,:,1) =
     4    10    20    35
sumA(:,:,2) =
    34    34    34    34
sumA(:,:,3) =
    -4    60  -180   140
sumA(:,:,4) =
     4     0     0     0
sumA(:,:,5) =
    2.0833    1.2833    0.9500    0.7595

Sum A along the rows.

sumA2 = sum(A,2)

sumA2(:,:,1) =
     4
    10
    20
    35
sumA2(:,:,2) =
    34
    34
    34
    34
sumA2(:,:,3) =
    -4
    60
  -180
   140
sumA2(:,:,4) =
     4
     0
     0
     0
sumA2(:,:,5) =
    2.0833
    1.2833
    0.9500
    0.7595

Sum A across the third dimension.

sumA3 = sum(A,3)

sumA3 =
  1.0e+003 *
    0.0350   -0.1155    0.2453   -0.1248
   -0.1125    1.2123   -2.6858    1.6912
    0.2513   -2.6888    6.4912   -4.1788
   -0.1338    1.6972   -4.1758    2.8221

Try summing A along the 7th dimension.

sumA7 = sum(A,7)

sumA7(:,:,1) =
     1     1     1     1
     1     2     3     4
     1     3     6    10
     1     4    10    20
sumA7(:,:,2) =
    16     2     3    13
     5    11    10     8
     9     7     6    12
     4    14    15     1
sumA7(:,:,3) =
          16        -120         240        -140
        -120        1200       -2700        1680
         240       -2700        6480       -4200
        -140        1680       -4200        2800
sumA7(:,:,4) =
     1     1     1     1
     1    -1     1    -1
     1     1    -1    -1
     1    -1    -1     1
sumA7(:,:,5) =
    1.0000    0.5000    0.3333    0.2500
    0.5000    0.3333    0.2500    0.2000
    0.3333    0.2500    0.2000    0.1667
    0.2500    0.2000    0.1667    0.1429

How Can That Be?

Why did I get no error for summing along dimension 7 when I only have a 3 dimensional array? The reason is that MATLAB treats all arrays as having an infinite number of dimensions, most of them trailing singletons. So if I sum along the 7th dimension here, I am only summing single elements, or effectively in this case just returning the original array.

Ever Used Dimension to Your Advantage?

Have you ever used the dimension argument to your advantage? Or tripped over the issue of having an unexpected singleton dimension? Any thoughts, please post them here.

Get the MATLAB code

Published with MATLAB® 7.4