How Gradient is calcuted
显示 更早的评论
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.
采纳的回答
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.
4 个评论
Jan
2013-2-17
No, gradient does not replicate the last element and it is not almost the same as diff. While the values equal the output of diff at the edges, the two-sided difference quotient is used inside.
Sven
2013-2-17
Thanks Jan, you're right... I should have just pointed to help gradient :)
Shashank Prasanna
2013-2-17
Quick note, doc gradient is generally more updated than help gradient or even better is the web documentation search. just an fyi.
Jan
2013-2-17
The web documentation concerns the newest release only. For the locally installed version, the local help is more accurate, when there have been changes.
更多回答（1 个）
Jan
2013-2-17
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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