How to transpose many matrices X_1 ... X_N at once?

My question is very simple. I have the objects X_1 X_2 ... X_N. I want to get all of their transposes:

Y_1 = X_1';

...

Y_N = X_N';

But when I try to use for loop like

for t = 1:10

Y_t = X_t';

end

It doesn't work. How do I most easily achieve what I am trying to do? Thanks

[Stephen23]

https://www.mathworks.com/matlabcentral/answers/304528-tutorial-why-variables-should-not-be-named-dynamically-eval

"How do I most easily achieve what I am trying to do?"

By using one container array.

Answer 1

[Star Strider]

Try something like this —

X1 = randi(9,3)

X1 = 3×3

9 1 6 9 8 7 3 6 8

X2 = randi(9,3)

X2 = 3×3

5 1 2 6 9 3 5 8 2

X3 = randi(9,3)

X3 = 3×3

6 3 6 6 7 8 3 6 2

Xcat = cat(3,X1,X2,X3);
Ycat = permute(Xcat,[2 1 3]);
Y1 = Ycat(:,:,1)

Y1 = 3×3

9 9 3 1 8 6 6 7 8

Y2 = Ycat(:,:,2)

Y2 = 3×3

5 6 5 1 9 8 2 3 2

Y3 = Ycat(:,:,3)

Y3 = 3×3

6 6 3 3 7 6 6 8 2

See the documentation on cat and permute to usnerstand how it works.

.

[JJJ]

Thanks for the quick reply.

Yes but instead I could have written

Y_1 = X_1';

Y_2 = X_2';

Y_3 = X_3';

My question here does not really concern the transpose, but a function f in general. So my question is: What is the way of executing the function f on objects X_1 ... X_N to get Y_1 ... Y_N. I dont want to write out everything by hand. Sorry if this is a bit off my original question, but this is what I want to know.

Edit: X_1 ... X_3 may not even have the size compatible to be catted.

[Image Analyst]

Like the others say, that's the burden you have to suffer if you have N separately named variables. How did you ever land in such an unfortunate situation? Try to avoid that situation. How were all those created? Maybe you can just transpose them during the creation process.

[Star Strider]

You have to create the individual matrices somehow.

Another way of doing this is to put the matrices in a multi-dimensional array or alternatively a cell array first, when they are created (they all have to be the same sizes for cat and permute to work, so I assume that condition already) —

X(:,:,1) = randi(9,3);                      % Multi-Dimensional Array
X(:,:,2) = randi(9,3);
X(:,:,3) = randi(9,3);

X

X = 
X(:,:,1) =

     1     7     2
     8     5     2
     5     8     2


X(:,:,2) =

     6     1     9
     3     9     1
     1     9     8


X(:,:,3) =

     8     4     2
     2     2     7
     3     7     5

Ycat = permute(X,[2 1 3]);
Y1 = Ycat(:,:,1)

Y1 = 3×3

1 8 5 7 5 8 2 2 2

Y2 = Ycat(:,:,2)

Y2 = 3×3

6 3 1 1 9 9 9 1 8

Y3 = Ycat(:,:,3)

Y3 = 3×3

8 2 3 4 2 7 2 7 5

Xc{1} = randi(9,3);                           % Cell Array (New Matrices)
Xc{1}

ans = 3×3

5 1 6 1 1 9 2 9 8

Xc{2} = randi(9,3);
Xc{2}

ans = 3×3

9 8 1 8 8 7 3 8 1

Xc{3} = randi(9,3);
Xc{3}

ans = 3×3

9 6 5 2 2 9 1 1 3

Xcat = cat(3,Xc);
Ycat = cellfun(@(x)permute(x,[2 1 3]), Xc, 'Unif',0);
Y1 = Ycat{1}

Y1 = 3×3

5 1 2 1 1 9 6 9 8

Y2 = Ycat{2}

Y2 = 3×3

9 8 3 8 8 8 1 7 1

Y3 = Ycat{3}

Y3 = 3×3

9 2 1 6 2 1 5 9 3

They have to be assigned to some sort of array for this (or likely any other approach) to work.

.

[JJJ]

I am sorry that my original problem quite deviates from the problem I wrote down here, but I just thought they are the same thing basically and so I should post something simpler.

My concern is that I have many X's that are 3D objects, with basically random dimensions. So nothing can be assumed about their compatibility. And I have a function decode which takes a 3D object and outputs a struct. It is just a compression function. Now, I want to compress these many 3D datas I have at hand all at once. I just thought this is such a simple question that there must be an easy solution, but maybe this isnt the case

[Star Strider]

If you put the matrices in cell arrays, the matrices do not all have to be the same sizes, although the approach to transposing them changes if they are not.

To use any MATLAB functions efficiently, the matrices must be assigned to some sort of array so that they can be referenced easily. (I assumed here that they are all the same sizes, since I had no reason to assume otherwise.) Using eval to deal with them is considered to be poor programming practise, so please do not.

.

[JJJ]

So then my code must contain the line:

cel = {X_1, X_2, ... , X_20}

And that I would have the fill the ... myself. Right?

I guess this is as minimal as it gets.

and then I would have smth like

for ii = 1:20

Y_ii = Decode(cel.ii);

end

Would this work?

[Star Strider]

‘And that I would have the fill the ... myself. Right?’

Right.

It might be easier to write or import them as ‘X{1}’, ‘X{2}’ and so forth first, however that depds on what you want to do with them and what they are.

This:

Y_ii = Decode(cel.ii);

would likely not produce the resutl you want, although something like:

Y.ii = Decode(cel.ii);

or something similar would likely work better.

Using your ‘Decode’ function depends on what ‘Decode’ is. Consider using cell2struct and structfun if those functions are appropriate to your data, the structure itself, and the function.

.

[Stephen23]

"And that I would have the fill the ... myself. Right?"

In fact the best approach by far is to avoid getting into this situation entirely. The point where you created those variables is the point where you should fix your code, not later by making a cell array by laboriously listing all of those variable names. No one here would do that.

"I guess this is as minimal as it gets."

No, better data design easily allows you to write simpler, more efficient code. For example, if you are LOADing data from MAT files always LOAD into an output variable rather than durectly into the workspace:

S = load(..)

Your data design (forcing meta-data into variables names) makes your code complex, slow, and inefficient.

Solution: better data design using one container array.

[JJJ]

@Stephen23 please check my latest comment.

@Star Strider I think this is the best approach.

Answer 2

[Matt J]

The matrices must be put into some kind of container if you want to operate on them as a group. If you can't cat() them, then they must go in a cell array or struct, e.g.

X={randi(9,2), randi(9,3)}; X{:}

ans = 2×2

3 9 2 3

ans = 3×3

1 1 5 1 3 9 8 5 1

Y=cellfun(@transpose, X, 'uni',0); Y{:}

ans = 2×2

3 2 9 3

ans = 3×3

1 1 8 1 3 5 5 9 1

[Rik]

I was going to post this as an answer, but then I saw this answer, so I'll post it as a comment instead.

The solution is to use Matlab as it is intended. Clearly the number has a meaning apart from you being able to distinguish Y_1 from Y_5. That means the number is data. You should use indices instead of numbering variables. That will allow you to use a simple loop:

for n=1:numel(X),Y{n}=X{n}.';end

Answer 3

[Matt J]

In R2020b or higher, you can use pagetranspose or pagectranspose

X=randi(9,3,3,2)

X = 
X(:,:,1) =

     1     7     2
     4     7     3
     6     9     9


X(:,:,2) =

     5     8     8
     8     6     7
     9     4     7

Y=pagetranspose(X)

Y = 
Y(:,:,1) =

     1     4     6
     7     7     9
     2     3     9


Y(:,:,2) =

     5     8     9
     8     6     4
     8     7     7

[JJJ]

Please check my comment on the other answer.

Answer 4

[Bruno Luong]

This is the solution for the endless issues you are and will be enountered due of your naming variable with counter

X_1 = rand(3),
X_2 = rand(4),

for t = 1:2
    eval(sprintf('Y_%d = X_%d''', t, t));
end

Y_1 = 3×3

0.6087 0.0830 0.2248 0.0339 0.9532 0.8557 0.7319 0.8093 0.8381

Y_2 = 4×4

0.7585 0.5014 0.3957 0.9816 0.9527 0.4223 0.5779 0.1252 0.3383 0.6818 0.6281 0.3371 0.7860 0.7223 0.8108 0.6294

[Matt J]

This is the solution for the endless issues you are and will be enountered due of your naming variable with counter

Yes, so please don't pursue this line of solution.

[JJJ]

Sure, how should I go about executing a function on many objects that I have that aren't dimension compatible in general. Counter was just my approach in naming the variables. Any help is appriciated. Could you please write the above code for, say, function 'encode'

[Bruno Luong]

"Could you please write the above code for, say, function 'encode'"

Yes, but you should be the person who are strugling with your naming strategy, not me.

[JJJ]

Sure. I would be glad to hear how you would go about the same problem.

[Image Analyst]

But @JJJ you never answered my question here. https://www.mathworks.com/matlabcentral/answers/1784125-how-to-transpose-many-matrices-x_1-x_n-at-once#comment_2328410

It would be good to know how and why you made over 20 separately-named variable of different sizes. If we know that it might help devise a better approach.

[JJJ]

Sorry I just got back. The reason is that I have no control over that. The sizes of these 3D tomograms depend on the sample at hand. We use the dimensions for the biological sample at hand.

I have created a function Encode() which takes a 3D array and turns it into a struct, for the purpose of compression.

Now I have many Tomograms at hand. I am willing to name them any way you advise. My goal is just to run this function on all of them and get a compressed representation for each of the tomogram seperately.

Thank you

[Stephen23]

"The reason is that I have no control over that."

You do have control over that: you import that data into the MATLAB workspace, which means you make the choice about what variable/variables the data are imported into. The sizes are not the problem.

If you show us how you import this data into MATLAB we can show you how to fix it.

[Rik]

Why do you insist on using numbered variables? Just use a cell array. If you don't know how to implement that, just show us how you import the data initially and we will try to help you.

[JJJ]

Thanks. I get it now. Its as @Star Strider mentioned. Now I import the tomograms as:

load(Tomogram_1,...)

X{1} = Tomogram_1;

and so on.

Then I just use

for t = 1:20

Y{t} = Encode(X{t});

end

If you have further suggestions, I would be glad to know.

[Stephen23]

"If you have further suggestions, I would be glad to know."

You are still using numbered variable names here:

load(Tomogram_1,..) % LOADing directly into the workspace is the rootcause...
X{1} = Tomogram_1; % because you still have numbered variable names!

So you have not really fixed the problem, because you still need to write out all of those names by hand. Do you really want to spend your time writing out variable names? Yesterday I showed you how to avoid this: by LOADing into an output variable. Assuming exactly one variable per file, you could do this:

F = {.. filenames in a cell array ..}
N = numel(F);
X = cell(1,N);
for k = 1:N
    X(k) = struct2cell(load(F{k}));
end

https://www.mathworks.com/help/matlab/import_export/process-a-sequence-of-files.html