How to remove rows in a multidimensional matrix?

I have a three dimensional matrix (A) and I want to remove rows that contain 0. I tried to do this in a 'for loop', but it gives an error "A null assignment can have only one non-colon index.". When I replace [] with NaN, it seems the code and index are right. Does it possible to do this outside of 'for loop'? Thank you in advance for your help.

 clear all
clc
A1 =  [50, 1, 130; 50, 1, 140; 0, 0, 0; 0, 0, 0];
A2 =  [0, 0, 0; 51, 2, 131; 51, 2, 141; 0, 0, 0];
A3 =  [0, 0, 0; 0, 0, 0; 52, 3, 132; 52, 3, 142];
A (:,:,1)= A1;
A (:,:,2) = A2;
A (:,:,3) = A3;
disp (A)
[r,c] = size(A);
for i = 1:3
    for h = 1:r
        if A (h,:,i) == 0
           A (h,:,i) = [] ;  % = NaN          
        end
    end
end
disp(A)

Answer 1

[Thorsten]

 for k=1:size(A,3)
   Ak = A(:,:,k);
   B(:,:,k)= Ak(sum(Ak')~=0,:);
 end

[Ali Y.]

Thank you for your reply and help. A problem arises when the number of rows in each dimension is different. For example, in the following code TA have various non-zero rows.

For me it is not crucial to store output matrices in one parent one. Actually, by the code I want to divide a main matrix to minor ones. I even tried 'removerows'; but ND arrays, again, is the problem.

 clc
clear all
A1 = [1;1;1;2;2;3;3;3;3;4;4;4;5;5];
A2= [1;1;1;1;2;2;2;2;2;2;2;2;3;3];
A3 = (10:10:140); A3 = A3';
A = [A1,A2,A3];
[r,c,n] = size(A);
b = min(A2): max(A2);
for k = 1:r
    for i = b      
        if A2(k) == i;
           TA(k,:,i) = A(k,:);
        end        
    end
end
for k1 = 1:size(TA,3)
   Ak = TA(:,:,k1);
   B(:,:,k1)= Ak(sum(Ak')~=0,:);
end

[Image Analyst]

Then you will have to store your data in a cell array like John said. A cell array must be rectangular like any other array, but the contents of the cells can be of different sizes which, in effect, will allow you to do this complicated thing you want to do. See the FAQ: http://matlab.wikia.com/wiki/FAQ#What_is_a_cell_array.3F

Answer 2

[Image Analyst]

A "row" is really a plane. For example row 2 will occur for every value of column and slice, so it's really a plane. That is A(2, :, :) is a plane along the x-z plane. To get rid of "row" 2, use []:

A(2, :, :) = [];

Any element which would have appeared with 2 as the first index (the "row" index) will now be gone.

[Ali Y.]

Thank you for your reply. Your notation is right; but my question was how to delete rows in different dimensions. The effect of the code seems correct, since when I replace [] with NaN. I just do not know why deletion does not work. I will be grateful if you modify the code to see the effect of your suggestion.

[John D'Errico]

Deletion DOES work. I think the problem is that when you delete one "row" of a multidimensional matrix, you are also deleting that same row from other parts of the matrix, since a row is really a plane. matrices MUST be rectangular. you cannot delete one row from one plane, but not the corresponding row from another plane.

A = rand(4,3,2)
A(:,:,1) =
      0.81472      0.63236      0.95751
      0.90579      0.09754      0.96489
      0.12699       0.2785      0.15761
      0.91338      0.54688      0.97059
A(:,:,2) =
      0.95717      0.42176      0.65574
      0.48538      0.91574     0.035712
      0.80028      0.79221      0.84913
      0.14189      0.95949      0.93399

A(1,:,:) = []
A(:,:,1) =
      0.90579      0.09754      0.96489
      0.12699       0.2785      0.15761
      0.91338      0.54688      0.97059
A(:,:,2) =
      0.48538      0.91574     0.035712
      0.80028      0.79221      0.84913
      0.14189      0.95949      0.93399

So deletion worked just fine. I deleted the first row of each plane. I cannot delete the first row of A(:,:,1) but NOT from A(:,:,2).

[Image Analyst]

I'm not sure what you want. I did delete a "row". What started as a 4 row by 3 column by 3 slice array turned into a 3 row by 3 column by 3 slice array. There is now one row fewer than before so it did indeed get deleted. Why do you say the deletion does not work? By the way, it wasn't just a suggestion, I actually did try it before I posted, to prove it.

[Ali Y.]

In your example deletion works, because in A(1,:,:) you say delete row one in all columns and dimensions, as (1,:,:). My point is to delete separately in different dimensions. I think this is the point of introducing n-dimensional matrix. Besides that as would you noticed I am try that within loop. Please note that, the possibility of deletion deserves a notice since the code justify the EFFECT of multidimensional manipulation of matrix SEPARATELY by NaN.

[John D'Errico]

And my comment is you CANNOT delete one row from the first plane, and NOT from the second plane!!!!!!! Trying to do so would have the effect of creating a non-rectangular matrix.

If you absolutely need to do this, then you need to consider a different structure for your data storage. Perhaps use a cell array of rectangular matrices, which can then be different sizes. Any sizes at all in fact.