How Gradient is calcuted
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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.
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Sven
2013년 2월 17일
편집: Sven
2013년 2월 17일
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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Shashank Prasanna
2013년 2월 17일
Quick note, doc gradient is generally more updated than help gradient or even better is the web documentation search. just an fyi.
Jan
2013년 2월 17일
The web documentation concerns the newest release only. For the locally installed version, the local help is more accurate, when there have been changes.
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Jan
2013년 2월 17일
Beside help gradient you can read the source code also: edit gradient. There you find, that at the edges the single sided difference quotient is calculated - demonstrated on a vector at first:
dx(1) = (x(2) - x(1)) / h;
dx(3) = (x(3) - x(2)) / h;
while h==1 as default. In the inner points the 2nd order two sided difference quotient is created:
dx(2) = (x(3) - x(1)) / (2*h);
For a matrix input the two out puts are calculated a long the rows and the columns respectively.
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