How to add columns equally in each page of a multidimensional array within a for loop?

I have a problem inside a for loop where I am defining a multidimensional array by adding more columns at every loop. The multidimensional array I have problems with is array R. The starting dimension for k =1 of R is 4425x2x11. At the end of the for loop I should get R of dimension 4425x23x11. Hence, for each k within the loop the array R gets more columns but equally for every page. The for loop for R calculation is following: Omega_rs has size 4425x11.

kmax = 21;
A = 11;

for k = 1:kmax

    for i = 1:A

        Vkm1 = 2*sum(Omega_rs(:,i).*R(:,k+1,i).*R(:,k,i).*q(:,i));

        Sk = Omega_rs(:,i).*R(:,k+1,i)-Vkm1*R(:,k,i);

        Dk = sqrt(2*sum((Sk.^2).*q(:,i)));

        R(:,:,i) = [R(:,:,i),Sk/Dk,i];

        coeff(:,k+2,i) = -Vkm1*coeff(:,k,i);

        coeff(2:k+1,k+2,i) = coeff(2:k+1,k+2,i)+coeff(1:k,k+1,i);

        coeff(:,k+2,i) = coeff(:,k+2,i)/Dk;

    end

end

I have checked the for loop line by line, and it is ok for all variables inside except the R array.. After executing this for loop I get a note Dimensions of matrices being concatenated are not consistent. Any advice how to solve this problem would be greatly appreciated.

Thank you in advance!

[Rik]

Sk = Omega_rs(:,i).*R(:,k+1)-Vkm1(:,i)*R(:,k,i); is that correct? Or should it be R(:,k+1 ,i)

Also, pre-allocating your matrices (especially large ones) is generally a good idea.

If that doesn't solve your issue, check all your * and / if they should indeed be non-element-wise operation.

[EB]

Thank you Rik Wisselink for your answer. YOu were right, the expression for Sk had an error, so R should be R(:,k+1 ,i). I did pre-allocation and it didn't help. * and / are definitely correct because the expressions were checked for 2d arrays. Still I have the problem in the row where I have to calculate R. The same message appears Error using horzcat Dimensions of matrices being concatenated are not consistent.

I think the problem is in the way how I concatenate the matrix R and the product Sk/Dk. It shoul go like this: So for k=1 and for all 11 pages the starting matrix R that was 4425x1x11 will change to 4425x2x11, for k=2 and all 11 pages it will change from 4425x2x11 to 4425x3x11 and it will continue to 4425x23x11. The error is in

R(:,:,i) = [R(:,:,i),Sk/Dk,i];

I don't know is there another (correct) way of doing this?

Many thanks!

Answer 1

[Rik]

You need to think about what your syntax does.

R(:,:,i) = [R(:,:,i),Sk/Dk,i];

What that line does is evaluating the right hand side and saving to de left hand side. When it evaluates the right hand, this goes wrong. You are trying to concatenate R(:,:,i) (a 2D matrix) with something that is either a matrix or a scalar (you can easily check with the debugging tools) and with a scalar. I don't think there is any implicit expanding for this syntax. What do you want to achieve? Because you can use a syntax like R(:,k,:)=Some_2D_matrix;. You can also look into the permute and cat functions.

Also, I expect you will get an error for i=2, because it looks like Vkm1 is a scalar, so Vkm1(:,i) will result in an error.

[EB]

For k=1 With the right hand side

[R(:,:,i),Sk/Dk,i]

I want to concatenate R(:,:,i) that is (4425x2x11) and Sk/Dk that is (4425x1) for every dimension of R (:,:,i) (in total I have 11 dimensions). I should get on the left hand side R (4425x3x11). Sk/Dk is changing for every k but its always (4425x1).

Again in for k=2 I concatenate R(:,:,i) that is (4425x3x11) for each dimension and Sk/Dk that is (4425x1) and as a result I should get on the left hand side R(:,:,i) that is (4425x4x11).

Lastly for k=21 I concatenate R(:,:,i) that is (4425x22x11) and Sk/Dk that is (4425x1) and as a result I should get on the left hand side R(:,:,i) that is (4425x23x11).

Vkm1(:,i) was a mistake, it's only Vkm1.

Now I get the error Error using horzcat Dimensions of matrices being concatenated are not consistent.

[Rik]

What you want to do is saving a 4425x1x1 to R. Just do that.

R(:,k+1,i)=Sk/Dk;
%for this syntax it is best to pre-allocate R:
%R=zeros(4425,22,11);

At the end of your loop R will be 4425x22x11

I'm getting the idea you don't understand how concatenation works. The syntax you are using tells Matlab to replace R(:,:,1) with the matrix that is the result of [R(:,:,i),Sk/Dk,i]. That last is the concatenation, but it doesn't affect R, until you save it with the R(:,:,i)=

[EB]

You are right Rik Wisselink, the solution is really simple and the pre-allocation of R did what I needed. Thank you for your replies.