Vectorising a Meshgrid Coordinate Construction
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I have three coordinate arrays (file attached) of size [M x 2], where M is the number of elements and the 2 represents different points in a 1D system. To find the 3D meshed coordinates upon which I perform calculations I use code of the form:
for ele = 1:size(X_co,1) %Loop Over Each Element
[X_cube,Y_cube,Z_cube] = meshgrid(X_co(ele,:),Y_co(ele,:),Z_co(ele,:)); %Construct Meshgrid of size [2x2x2] for an Element
X_save(:,:,:,element) = X_cube; %Save Coordinates
Y_save(:,:,:,element) = Y_cube;
Z_save(:,:,:,element) = Z_cube;
end
The solution then is of size [2x2x2xM]. My best attempt to vectorise this was:
[X_cube,Y_cube,Z_cube] = meshgrid(X_co,Y_co,Z_co);
X_save = reshape(X_cube,2,2,2,[]); Y_save = reshape(Y_cube,2,2,2,[]); Z_save = reshape(Z_cube,2,2,2,[]);
However this solution is of size [2x2x2x(M^3)] which, when plotting both solutions has many many many repeated points so doesn't actually work for my application.
Can this problem be vectorised, or is a for loop the best way to construct this coordinate array?
3 个评论
KSSV
2020-9-2
Are you looking for ndgrid?
jessupj
2020-9-2
ndgrid is the way to go here i think. i think it can be done using meshgrid along with some resize + repmat statements.
ADSW121365
2020-9-2
编辑：ADSW121365
2020-9-2
采纳的回答
Bruno Luong
2020-9-2
编辑：Bruno Luong
2020-9-2
One way
[~,nx] = size(X_co);
[~,ny] = size(Y_co);
[m,nz] = size(Z_co);
[NX,NY,NZ] = meshgrid(1:nx,1:ny,1:nz);
sz = [size(NX),m];
% if you know nx, ny, nz are 2 you can replace the 5 above commands by
% [NX,NY,NZ] = meshgrid(1:2);
% sz = [2,2,2,m];
X_save = X_co.';
Y_save = Y_co.';
Z_save = Z_co.';
X_save = reshape(X_save(NX,:),sz);
Y_save = reshape(Y_save(NY,:),sz);
Z_save = reshape(Z_save(NZ,:),sz);
Note: I honestly prefer your for-loop if you add a preallocation
6 个评论
ADSW121365
2020-9-3
ADSW121365
2020-9-3
Bruno Luong
2020-9-3
编辑：Bruno Luong
2020-9-3
The for-loop code is more readable and I would guess is not slow at all if you properly allocate the output array.
In two ways of indexing (resp for-loop and vectorization)
A(:,:,:,elem) % and
A(NX,:),
MATLAB prefers the first since it's access contiguous memory in the first case and scattered in the second case, which is not good for speed on modern CPU.
However the for-loop needs to call MESHGRID many time, which in turns is a penalty compared to the vectorization code.
But really up to you.
ADSW121365
2020-9-3
Bruno Luong
2020-9-3
"So by properly allocate you mean initialise the arrays as zeros before the for loop starts?"
Yes intiialize the 3 zeros arrays with SZ from with my code.
ADSW121365
2020-9-3
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