How to expand dimension of a 2D array

I have a 2D array M with dimension 60, 60. However, I want to expand the array dimension to 60, 60, 1.

I tried by reshape which simply doesn't work for dimension 1 at the end/3rd.

M=reshape(M,[60, 1, 60]);

This changes to 60, 1, 60 but if I do:

M=reshape(M,[60, 60, 1]);

or

M=reshape(M,[size(M), 1]);

It still gives M with 60, 60.

[Stephen23]

"I have a 2D array M with dimension 60, 60. However, I want to expand the array dimension to 60, 60, 1. "

There is no difference. All arrays implictly have infinite trailing singleton dimensions, so your 6x6(x1x1x1x1...) array already has size 6x6x1(x1x1x1x1...). This has been explicitly stated by TMW several times, e.g. "Arrays in MATLAB are N-dimensional, with an infinite number of trailing singleton dimensions."

source: http://blogs.mathworks.com/loren/2006/08/09/essence-of-indexing/

https://www.mathworks.com/matlabcentral/answers/143734-what-is-the-difference-between-matrix-and-array-in-the-meaning-and-functions#answer_268939

https://www.mathworks.com/matlabcentral/answers/21992-singleton-dimention-as-last-dimension-in-matrix

https://www.mathworks.com/matlabcentral/answers/229956-how-can-i-reshape-a-20370x1-matrix-into-2037x10x1

Clearly there is no way for MATLAB to explicitly store the sizes of infinite singleton dimensions, nor is there any need for it to do so: you can still get the size of any dimension that you want:

M = rand(60,60);
size(M,1) % rows

ans = 60

size(M,2) % columns

ans = 60

size(M,3) % pages

ans = 1

size(M,4) % books

ans = 1

size(M,5) % shelves

ans = 1

... etc
size(M,9999) % whatever this dimension is called

ans = 1

And you can access them using indexing, if you really want to:

M(2:3,7:9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)

ans = 2×3

0.4572 0.0337 0.0507 0.2278 0.3131 0.3043

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Or using multiple outputs from SIZE:

[s1,s2,s3,s4,s5,s6,s7,s8,s9] = size(M)

s1 = 60

s2 = 60

s3 = 1

s4 = 1

s5 = 1

s6 = 1

s7 = 1

s8 = 1

s9 = 1

So far you have not stated what the actual problem is.

[Steven Lord]

All arrays implictly have infinite trailing singleton dimensions

If you wanted to be technical it's not infinite but it's effectively infinite. If you tried to create an array with anywhere near the theoretical upper limit of the number of dimensions you'd run into memory problems creating the array to store the size information! But you can ask for the size of an array in a surprisingly large dimension.

s = size(1:10, 2^48)

s = 1

But if you try to use too large a dimension you receive an error.

s = size(1:10, 2^48+1)

Error using size
Dimension argument must be a positive integer scalar or a vector of positive integers. When an empty dimension argument is specified, it must be a 0-by-0, 1-by-0, or 0-by-1 array.

Hmm. That error message should be updated. I thought that in the past it had mentioned something about the upper limit. Maybe it's been reworded. I'll note that to the development staff.

Answer 1

[James Tursa]

All MATLAB trailing singleton (1) dimensions beyond the 2nd dimension are not physically stored, and will not show up in a size( ) call, but you can still treat the variable as if they are there.

A = reshape(1:9,3,3)

A = 3×3

1 4 7 2 5 8 3 6 9

size(A)

ans = 1×2

3 3

A(:,:,1)  % this works, even though size( ) did not indicate the 3rd dimension existed.

ans = 3×3

1 4 7 2 5 8 3 6 9

A(:,:,1,1,1,1,1,1,1,1,1,1,1,1,1)  % this also works!

ans = 3×3

1 4 7 2 5 8 3 6 9

If you do an operation (e.g., reshape) that results in singleton (1) trailing dimensions beyond the 2nd dimension, MATLAB will simply delete them from the resulting variable. There is nothing you can do to get MATLAB to physically store trailing singleton (1) dimensions beyond the 2nd dimension. But this does not affect your ability to index into these trailing dimensions using a 1 index.

And you can physically expand an array dynamically by assigning into currently non-existing indexes. E.g.,

A(4,4,2) = 10

A = 
A(:,:,1) =

     1     4     7     0
     2     5     8     0
     3     6     9     0
     0     0     0     0


A(:,:,2) =

     0     0     0     0
     0     0     0     0
     0     0     0     0
     0     0     0    10

[Steven Lord]

Also FYI, if you explicitly ask what size your matrix is in the third dimension, MATLAB will include the size in the trailing singleton dimension.

A = magic(3)

A = 3×3

8 1 6 3 5 7 4 9 2

sz = size(A)

sz = 1×2

3 3

sz3 = size(A, 3) % or

sz3 = 1

sz123 = size(A, 1:3)

sz123 = 1×3

3 3 1

Answer 2

[Sulaymon Eshkabilov]

Yes, it is correct. It is 2D array (or matrix) but not 3D. You can create and test it with this:

M = randi(15, 60);
MM(:,:,1)=M

MM = 60×60

9 5 5 14 1 12 5 3 15 5 2 12 11 11 2 12 5 3 5 11 5 14 3 8 14 13 9 14 4 13 1 2 13 15 4 11 3 11 1 11 11 13 9 3 4 11 13 14 2 13 8 1 13 5 7 10 3 2 4 5 6 9 2 5 14 13 2 13 7 9 5 4 12 7 9 3 3 9 4 13 6 14 4 7 3 12 5 11 11 15 11 8 8 5 6 5 10 4 10 14 9 7 7 15 11 8 9 1 11 11 12 7 10 4 11 9 9 2 11 12 2 12 3 6 9 15 11 12 11 15 13 12 3 11 10 5 10 14 10 2 4 9 9 8 3 7 14 4 7 10 1 3 7 1 14 9 3 2 13 9 15 3 13 4 2 2 9 11 6 6 9 14 2 12 6 6 14 14 13 8 7 13 5 9 11 10 15 15 15 3 1 10 1 11 5 9 13 4 10 2 2 5 8 9 15 2 15 6 14 13 3 14 3 15 1 10 14 9 8 13 5 7 9 8 15 13 8 9 7 15 1 2 10 2 14 2 15 9 4 4 15 8 12 4 9 7 8 9 13 4 3 1 6 1 5 8 12 3 4 4 6 9 3 12 1 2 6 10 1 2 4 11 10 15 1 11 7 12 2 8 3 7 6 12 1 1 6 4 7 13 4 5 9 11 13 14 6 6 14 13

% MM is 60-by-60 -by-1   

Now let's see how to establish a larger (3D) array

%% Mnew is 6-by-6 - 2 % To be able to view/display here
M1 = randi(5, 6);
Mnew(:,:,1)=M1

Mnew = 6×6

2 2 2 4 3 3 5 5 3 1 4 5 3 5 2 4 3 5 5 2 1 2 1 5 5 2 5 2 1 4 3 2 2 4 4 4

M2 = randi(10, 6);
Mnew(:,:,2)=M2

Mnew = 
Mnew(:,:,1) =

     2     2     2     4     3     3
     5     5     3     1     4     5
     3     5     2     4     3     5
     5     2     1     2     1     5
     5     2     5     2     1     4
     3     2     2     4     4     4


Mnew(:,:,2) =

     5     4     8     6    10     4
     5     9     1     2     9     1
     7     6     6     4     8     8
    10     8     3     9     3     7
     5     2     1     5     3    10
     6     3     3     4     5     7

[banikr]

I don't understand,

Mnew(:,:,1)=M;
size(Mnew)

still give 60 60 not 60 60 1.

I need to save the matrix with an additional 3rd dimension as 1.

Could you also post the results of `size(Mnew)` etc?

[Stephen23]

"MM is 60-by-60 -by-1 "

So is M:

M = randi(15, 60);
[s1,s2,s3] = size(M)

s1 = 60

s2 = 60

s3 = 1

"still give 60 60 not 60 60 1. "

Which are exactly the same: both have size 60x60(x1x1x1x1x1....)

"I need to save the matrix with an additional 3rd dimension as 1."

You already made that clear in your question. Some people explained how MATLAB actually works. As the code I give in this very comment shows, your matrix does have 3rd dimension with size 1.

Repeating your request does not change how MATLAB actually works.

Rather than repreating it again, tells us what you are trying to do that does not work. As I showed, SIZE is gives you the size of any trailing dimension that you desire. I also showed that you can index into any dimension. Yet so far you have not give any explanation of what you are trying to do and why it does not work.

[John D'Errico]

Think of it this way. ALL arrays, already and always have infinitely many trailing singleton dimensions.

So even though MATLAB tells you an array has size 60x60, the size is also really 60x60x1x1x1x1x1x1...

You don't really want MATLAB to display infinitely many ones when you ask for the size of a 2-d arrray? Of course not. So MATLAB just shows the leading dimensions, before the trailing singletons appear.

Answer 3

[Sulaymon Eshkabilov]

M1 = randi(5, 6);
Mnew(:,:,1)=M1;
[row,col,Layer]=size(Mnew)

row = 6

col = 6

Layer = 1

%% Mnew is 6-by-6 - 2 % To be able to view/display here
M1 = randi(5, 6);
Mnew(:,:,1)=M1;
M2 = randi(10, 6);
Mnew(:,:,2)=M2;
[row,col,Layer]=size(Mnew)

row = 6

col = 6

Layer = 2

[Stephen23]

The indexing here does nothing whatsoever:

Mnew(:,:,1)=M1;

because both M1 and MNEW have exactly the same size:

M1 = randi(5, 6);
[row,col,Layer] = size(M1)

row = 6

col = 6

Layer = 1