MATLAB: How Gradient is calcuted

matlab basics

In matlab i have found following answers. let X =
     1     2     3
     3     4     5
     3     2     1
 z=gradient(X)
z =
     1     1     1
     1     1     1
    -1    -1    -1
[z,c]=gradient(X)
z =
     1     1     1
     1     1     1
    -1    -1    -1
c =
     2     2     2
     1     0    -1
     0    -2    -4
But how z and c is calculated,what z and c indicates.

Best Answer

Hi Tinkul,
It is probably clearer if you call your variables z and c different names such as dx and dy. This is because the first and second outputs from gradient is the gradient in each of those directions.
So if you have:
M =
   1     2     3
   3     4     5
   3     2     1
 [dx,dy]=gradient(M)
 dx =
     1     1     1
     1     1     1
    -1    -1    -1
 dy =
     2     2     2
     1     0    -1
     0    -2    -4
You'll notice that dx(1,:) is almost the same as diff(M(1,:)), and dy(:,1) is almost the same as diff(M(:,1)). The main difference is that gradient replicates the last result so that the output has the same size as the input.
Update: this is not quite correct. The two-sided gradient is used in gradient... the one-sided gradient is used in diff.
Does that help? You can also check out the help for gradient which says even more.
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