Using the diff comand with a 3D array to get Partial derivatives

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Bernd Ab
Bernd Ab 2016-1-11
评论： Star Strider 2016-1-11
Dear all
I have a 3D Matrix with the Size of 167x176x2000 Datapoints. Now i want to compute the Partial derivatives in X and Y direction of this matrix. The derivatives would have to be computed parallel to the XY-plane.
But i am not quite sure how to use the diff command. In the matlab help it is stated: "Y = diff(X,n,dim) is the nth difference calculated along the dimension specified by dim. The dim input is a positive integer scalar."
Lets asume the Matrix has the name 3D_Matrix the new matrix should be named delta_x_Matrix. Would i have to type:
delta_x_Matrix = diff(3D_Matrix,1,1);
Would
delta_x_Matrix = diff(3D_Matrix,1,2);
compute the derivative in Y-Direction?
All the best
And thank you in advance!

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回答（1 个）

Star Strider
Star Strider 2016-1-11
I would use the gradient function, not diff, since gradient is specifically designed to do what you want.
  2 个评论
Bernd Ab
Bernd Ab 2016-1-11
编辑：Bernd Ab 2016-1-11
Hello Star Strider;
Thank you for you answer!
So if i use
[FX,FY] = gradient(3D_Matrix);
I would actually get what i desire?
But it still resdueces the dimension of the resulting matrix. I was actually hoping that i could use : diffxy
for my endeavor later on. But at the moment i do not understand what i have no idea what i need to type for "X" into this function. The info for this function is as follows:
DY = DIFFXY(X,Y) returns the derivative of Y with respect to X using a % pseudo second-order accurate method. DY has the same size as Y.
% DY = DIFFXY(X,Y,DIM) returns the derivative along the DIM-th dimension % of Y. The default is differentiation along the first % non-singleton dimension of Y.
% DY = DIFFXY(X,Y,DIM,N) returns the N-th derivative of Y w.r.t. X. % The default is 1. %
% Y may be an array of any dimension. % X can be any of the following: % - array X with size(X) equal to size(Y) % - vector X with length(X) equal to size(Y,DIM) % - scalar X denotes the spacing increment % DIM and N are both integers, with 1<=DIM<=ndims(Y)
% % DIFFXY has been developed especially to handle unequally spaced data, % and features accurate treatment for end-points.
Thank you
Star Strider
Star Strider 2016-1-11
My pleasure.
The gradient function should not reduce the dimensions of the matrix. I checked it with this code snippet to be sure:
M = randi(9, 5, 6, 7);
[GMx, GMy] = gradient(M);
The ‘GMx’ and ‘GMy’ matrices are the same size as ‘M’ here. If you have unequally-spaced data (the gradient function assumes equally-spaced data), then ‘diffxy’ might be more suitable. I’ve not used it, so I can’t comment on it.

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